{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Systems of non-linear equations\n", "\n", "Sometimes we need to solve a system of non-linear equations, e.g.\n", "\n", "$$\n", "f_1(x_1,\\ldots,x_N) = 0,\\\\\n", "f_2(x_1,\\ldots,x_N) = 0,\\\\\n", "\\ldots \\\\\n", "f_N(x_1,\\ldots,x_N) = 0\n", "$$\n", "\n", "Denoting ${\\bf f} = (f_1,\\ldots,f_N)$ and ${\\bf x} = (x_1,\\ldots,x_N)$ this can be written in compact form as\n", "$$\n", "{\\bf f}({\\bf x}) = 0~.\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example of a system of non-linear equations consider the intersection point (x,y) of functions $y = x + \\exp(-x) - 2$ and $y = x^3 - x - 3$. This can be cast as a solution to a system of two non-linear equations\n", "$$\n", "x + \\exp(-x) - 2 - y = 0,\\\\\n", "x^3 - x - 3 - y = 0.\n", "$$\n", "\n", "This implies $(x,y) = (x_1,x_2)$, \n", "$$f_1(x_1,x_2) = x_1 + \\exp(-x_1) - 2 - x_2$$ \n", "and $$f_2(x_1,x_2) = x_1^3 - x_1 - 3 - x_2$$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "import matplotlib.pyplot as plt\n", "# Default style parameters (feel free to modify as you see fit)\n", "params = {'legend.fontsize': 'large',\n", " 'axes.labelsize': 'x-large',\n", " 'axes.titlesize':'x-large',\n", " 'xtick.labelsize':'x-large',\n", " 'ytick.labelsize':'x-large',\n", " 'xtick.direction':'in',\n", " 'ytick.direction':'in',\n", " }\n", "plt.rcParams.update(params)\n", "\n", "\n", "def y1f(x):\n", " return x + np.exp(-x) - 2.\n", "\n", "def y2f(x):\n", " return x**3 - x - 3.\n", "\n", "xref = np.linspace(-1,2,100)\n", "y1ref = y1f(xref)\n", "y2ref = y2f(xref)\n", "\n", "plt.xlabel(\"${x_1}$\")\n", "plt.ylabel(\"${x_2}$\")\n", "plt.plot(xref,y1ref,label = '${f_1(x_1,x_2)}$')\n", "plt.plot(xref,y2ref,label = '${f_2(x_1,x_2)}$')\n", "plt.plot([1.64998819 ], [-0.15795963], 'ro')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def f(x):\n", " return np.array([x[0] + np.exp(-x[0]) - 2. - x[1], x[0]**3 - x[0] - 3 - x[1]])\n", "\n", "def jacobian(x):\n", " return np.array([[1. - np.exp(-x[0]), -1.], [3*x[0]**2 - 1., -1]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also introduce a scalar-valued *objective function*\n", "$$\n", "\\tilde{f}(\\mathbf{x}) = \\frac{\\mathbf{f}(\\mathbf{x}) \\cdot \\mathbf{f}(\\mathbf{x})}{2}\n", "$$\n", "which is equal to zero at the root.\n", "Finding roots is thus similar to minimizing this function" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from matplotlib import colors, cm, pyplot as plt\n", "\n", "def ftil(f):\n", " return np.dot(f,f) / 2.\n", "\n", "xplot = np.linspace(-1,3,200)\n", "yplot = np.linspace(-2,2,200)\n", "\n", "X, Y = np.meshgrid(xplot, yplot)\n", "\n", "\n", "fdat = []\n", "for yin in yplot:\n", " ftmp = []\n", " for xin in xplot:\n", " ftmp.append(ftil(f([xin,yin])))\n", " fdat.append(ftmp)\n", "\n", "funclabel = \"${\\\\tilde f(x,y)}$\"\n", "\n", "#plt.contourf(X, Y, Vdip, 10)\n", "plt.title(funclabel)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "norm = colors.LogNorm(0.01, 100., clip='True') # log scale\n", "CS = plt.imshow(fdat, origin=\"lower\",extent=[-1,3,-2,2], aspect=1, norm = norm)\n", "#CS = plt.imshow(fdat, vmax=5, vmin=0.,origin=\"lower\",extent=[-1,3,-2,2], aspect=1)\n", "#plt.plot([0],[0],'r.')\n", "plt.colorbar(CS)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Newton-Raphson method can be readily generalized to multi-dimensional systems of equations.\n", "There is also a multi-dimensional version of the secant method called Broyden's method.\n", "\n", "Let us explore these methods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Newton method\n", "\n", "Recall the Taylor expansion of function $f$ around the root $x^*$ in one-dimensional case:\n", "$$\n", "f(x^*) \\approx f(x) + f'(x) (x^* - x)\n", "$$\n", "\n", "The multi-dimensional version of this expansion reads\n", "$$\n", "{\\bf f} ({\\bf x^*}) \\approx {\\bf f}({\\bf x}) + J(\\bf{x}) ({\\bf x^*} - {\\bf x})\n", "$$\n", "\n", "Here $J(\\mathbf{x})$ is the Jacobian, i.e. a $N \\times N$ matrix of derivatives evaluated at $\\bf{x}$\n", "$$\n", "J_{ij}(\\mathbf{x}) = \\frac{\\partial f_i}{\\partial x_j}~.\n", "$$\n", "\n", "Given that $\\mathbf{f}(\\mathbf{x^*}) = 0$, we have\n", "$$\n", "J(\\mathbf{x}) (\\mathbf{x^*} - \\mathbf{x}) \\approx -\\mathbf{f}(\\mathbf{x}),\n", "$$\n", "which is a system of linear equations for $\\mathbf{x^*} - \\mathbf{x}$.\n", "Solving this system yields\n", "$$\n", "\\mathbf{x^*} \\approx \\mathbf{x} - J^{-1}(\\mathbf{x}) \\, \\mathbf{f}(\\mathbf{x})~.\n", "$$\n", "Here $J^{-1}(\\mathbf{x})$ is the inverse Jacobian matrix.\n", "\n", "The multi-dimensional Newton's method is an iterative procedure\n", "$$\n", "\\mathbf{x_{n+1}} = \\mathbf{x_n} - J^{-1}(\\mathbf{x_n}) \\, \\mathbf{f}(\\mathbf{x_n})~.\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "last_newton_iterations = 0\n", "newton_verbose = True\n", "\n", "\n", "def newton_method_multi(\n", " f, \n", " jacobian, \n", " x0, \n", " accuracy=1e-8, \n", " max_iterations=100):\n", " x = x0\n", " global last_newton_iterations\n", " last_newton_iterations = 0\n", " \n", " if newton_verbose:\n", " print(\"Iteration: \", last_newton_iterations)\n", " print(\"x = \", x0)\n", " print(\"f = \", f(x0))\n", " print(\"|f| = \", ftil(f(x0)))\n", " \n", " for i in range(max_iterations):\n", " last_newton_iterations += 1\n", " f_val = f(x)\n", " jac = jacobian(x)\n", " jinv = np.linalg.inv(jac)\n", " delta = np.dot(jinv, -f_val)\n", " x = x + delta\n", " \n", " if newton_verbose:\n", " print(\"Iteration: \", last_newton_iterations)\n", " print(\"x = \", x)\n", " print(\"f = \", f(x))\n", " print(\"|f| = \", ftil(f(x)))\n", " \n", " if np.linalg.norm(delta, ord=2) < accuracy:\n", " return x\n", " return x\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 0\n", "x = [0. 0.]\n", "f = [-1. -3.]\n", "|f| = 5.0\n", "Iteration: 1\n", "x = [-2. -1.]\n", "f = [ 4.3890561 -8. ]\n", "|f| = 41.63190671978017\n", "Iteration: 2\n", "x = [-1.28753717 -1.16290888]\n", "f = [ 1.49922234 -2.68397122]\n", "|f| = 4.725684585141539\n", "Iteration: 3\n", "x = [-0.65344197 -1.32745762]\n", "f = [ 0.59616108 -1.29811125]\n", "|f| = 1.0202504224353612\n", "Iteration: 4\n", "x = [ 0.92104475 -2.18320228]\n", "f = [ 1.50234993 -0.95649863]\n", "|f| = 1.5859724775723376\n", "Iteration: 5\n", "x = [3.52831703 0.88845726]\n", "f = [ 0.66921404 36.50731858]\n", "|f| = 666.6160786805304\n", "Iteration: 6\n", "x = [2.51526632 0.57435797]\n", "f = [0.02174973 9.82337075]\n", "|f| = 48.249542955733645\n", "Iteration: 7\n", "x = [1.94074619 0.06803257]\n", "f = [0.01631038 2.30103357]\n", "|f| = 2.647510761586109\n", "Iteration: 8\n", "x = [ 1.69879947 -0.122861 ]\n", "f = [0.00456345 0.32666032]\n", "|f| = 0.053363893975197814\n", "Iteration: 9\n", "x = [ 1.65171385 -0.15677108]\n", "f = [0.00020597 0.01119461]\n", "|f| = 6.268087547408287e-05\n", "Iteration: 10\n", "x = [ 1.64999046 -0.15795808]\n", "f = [2.84874536e-07 1.47119183e-05]\n", "|f| = 1.0826084693606538e-10\n", "Iteration: 11\n", "x = [ 1.64998819 -0.15795963]\n", "f = [4.94243535e-13 2.54747057e-11]\n", "|f| = 3.2460245303301063e-22\n", "Iteration: 12\n", "x = [ 1.64998819 -0.15795963]\n", "f = [ 0.00000000e+00 -6.66133815e-16]\n", "|f| = 2.2186712959340957e-31\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 556 ms, sys: 16.9 ms, total: 572 ms\n", "Wall time: 223 ms\n" ] } ], "source": [ "%%time\n", "\n", "x0 = np.array([0., 0.])\n", "root = newton_method_multi(f, jacobian, x0)\n", "#print(root)\n", "\n", "xplot = np.linspace(-1,3,200)\n", "yplot = np.linspace(-2,2,200)\n", "fdat = []\n", "for yin in yplot:\n", " ftmp = []\n", " for xin in xplot:\n", " ftmp.append(ftil(f([xin,yin])))\n", " fdat.append(ftmp)\n", "\n", "funclabel = \"${\\\\tilde f(x,y)}$\"\n", "\n", "#plt.contourf(X, Y, Vdip, 10)\n", "plt.title(funclabel)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "norm = colors.LogNorm(0.01, 100., clip='True') # log scale\n", "CS = plt.imshow(fdat, origin=\"lower\",extent=[-1,3,-2,2], aspect=1, norm = norm)\n", "#CS = plt.imshow(fdat, vmax=5, vmin=0.,origin=\"lower\",extent=[-1,3,-2,2], aspect=1)\n", "plt.plot([root[0]],[root[1]],'r.')\n", "plt.colorbar(CS)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 0\n", "x = [0. 0.]\n", "f = [-1. -3.]\n", "|f| = 5.0\n", "Iteration: 1\n", "x = [-2. -1.]\n", "f = [ 4.3890561 -8. ]\n", "|f| = 41.63190671978017\n", "Iteration: 2\n", "x = [-1.28753717 -1.16290888]\n", "f = [ 1.49922234 -2.68397122]\n", "|f| = 4.725684585141539\n", "Iteration: 3\n", "x = [-0.65344197 -1.32745762]\n", "f = [ 0.59616108 -1.29811125]\n", "|f| = 1.0202504224353612\n", "Iteration: 4\n", "x = [ 0.92104475 -2.18320228]\n", "f = [ 1.50234993 -0.95649863]\n", "|f| = 1.5859724775723376\n", "Iteration: 5\n", "x = [3.52831703 0.88845726]\n", "f = [ 0.66921404 36.50731858]\n", "|f| = 666.6160786805304\n", "Iteration: 6\n", "x = [2.51526632 0.57435797]\n", "f = [0.02174973 9.82337075]\n", "|f| = 48.249542955733645\n", "Iteration: 7\n", "x = [1.94074619 0.06803257]\n", "f = [0.01631038 2.30103357]\n", "|f| = 2.647510761586109\n", "Iteration: 8\n", "x = [ 1.69879947 -0.122861 ]\n", "f = [0.00456345 0.32666032]\n", "|f| = 0.053363893975197814\n", "Iteration: 9\n", "x = [ 1.65171385 -0.15677108]\n", "f = [0.00020597 0.01119461]\n", "|f| = 6.268087547408287e-05\n", "Iteration: 10\n", "x = [ 1.64999046 -0.15795808]\n", "f = [2.84874536e-07 1.47119183e-05]\n", "|f| = 1.0826084693606538e-10\n", "Iteration: 11\n", "x = [ 1.64998819 -0.15795963]\n", "f = [4.94243535e-13 2.54747057e-11]\n", "|f| = 3.2460245303301063e-22\n", "Iteration: 12\n", "x = [ 1.64998819 -0.15795963]\n", "f = [ 0.00000000e+00 -6.66133815e-16]\n", "|f| = 2.2186712959340957e-31\n", "CPU times: user 7.36 ms, sys: 898 μs, total: 8.26 ms\n", "Wall time: 4.9 ms\n" ] } ], "source": [ "%%time\n", "\n", "x0 = np.array([0., 0.])\n", "root = newton_method_multi(f, jacobian, x0)\n", "#print(root)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Broyden method\n", "\n", "Generalization of the secant method to multiple dimensions\n", "\n", "Approximates the Jacobian by finite differences (see lecture notes)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "last_broyden_iterations = 0\n", "broyden_verbose = True\n", "\n", "# Direct implementation of Broyden's method \n", "# (using matrix inversion at each step)\n", "def broyden_method_direct(\n", " f, \n", " x0, \n", " accuracy=1e-8, \n", " max_iterations=100):\n", " global last_broyden_iterations\n", " last_broyden_iterations = 0\n", " x = x0\n", " n = x0.shape[0]\n", " J = np.eye(n)\n", " \n", " \n", " for i in range(max_iterations):\n", " last_broyden_iterations += 1\n", " f_val = f(x)\n", " Jinv = np.linalg.inv(J)\n", " delta = np.dot(Jinv, -f_val)\n", " x = x + delta\n", " if np.linalg.norm(delta, ord=2) < accuracy:\n", " return x\n", " f_new = f(x)\n", " u = f_new - f_val\n", " v = delta\n", " J = J + np.outer(u - J.dot(v), v) / np.dot(v, v)\n", " \n", " return x" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "55\n", "[ 1.64998819 -0.15795963]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 550 ms, sys: 18.8 ms, total: 569 ms\n", "Wall time: 220 ms\n" ] } ], "source": [ "%%time\n", "\n", "x0 = np.array([0., 0.])\n", "root = broyden_method_direct(f, x0)\n", "print(last_broyden_iterations)\n", "print(root)\n", "\n", "xplot = np.linspace(-1,3,200)\n", "yplot = np.linspace(-2,2,200)\n", "fdat = []\n", "for yin in yplot:\n", " ftmp = []\n", " for xin in xplot:\n", " ftmp.append(ftil(f([xin,yin])))\n", " fdat.append(ftmp)\n", "\n", "funclabel = \"${\\\\tilde f(x,y)}$\"\n", "\n", "#plt.contourf(X, Y, Vdip, 10)\n", "plt.title(funclabel)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "norm = colors.LogNorm(0.01, 100., clip='True') # log scale\n", "CS = plt.imshow(fdat, origin=\"lower\",extent=[-1,3,-2,2], aspect=1, norm = norm)\n", "plt.plot([root[0]],[root[1]],'r.')\n", "plt.colorbar(CS)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "55\n", "[ 1.64998819 -0.15795963]\n", "CPU times: user 10.4 ms, sys: 5.56 ms, total: 16 ms\n", "Wall time: 6.68 ms\n" ] } ], "source": [ "%%time\n", "\n", "x0 = np.array([0., 0.])\n", "root = broyden_method_direct(f, x0)\n", "print(last_broyden_iterations)\n", "print(root)\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "last_broyden_iterations = 0\n", "broyden_verbose = True\n", "\n", "\n", "# Implementation of Broyden's method using Sherman-Morrison formula\n", "def broyden_method(\n", " f, \n", " x0, \n", " accuracy=1e-8, \n", " max_iterations=100):\n", " global last_broyden_iterations\n", " last_broyden_iterations = 0\n", " x = x0\n", " n = x0.shape[0]\n", " Jinv = np.eye(n)\n", " #Jinv = np.linalg.inv(jacobian(x))\n", " \n", " if broyden_verbose:\n", " print(\"Iteration: \", last_broyden_iterations)\n", " print(\"x = \", x0)\n", " print(\"f = \", f(x0))\n", " print(\"|f| = \", ftil(f(x0)))\n", " \n", " for i in range(max_iterations):\n", " last_broyden_iterations += 1\n", " f_val = f(x)\n", " delta = -Jinv.dot(f_val)\n", " x = x + delta\n", " if np.linalg.norm(delta, ord=2) < accuracy:\n", " return x\n", " f_new = f(x)\n", " df = f_new - f_val\n", " dx = delta\n", " Jinv = Jinv + np.outer(dx - Jinv.dot(df), dx.T.dot(Jinv)) / np.dot(dx.T, Jinv.dot(df))\n", " \n", " if broyden_verbose:\n", " print(\"Iteration: \", last_broyden_iterations)\n", " print(\"x = \", x)\n", " print(\"f = \", f(x))\n", " print(\"|f| = \", ftil(f(x)))\n", " \n", " return x" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1.64998819 -0.15795963]\n" ] }, { "data": { "image/png": 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8qgH5gC7ytdQHBd2o/Lbl+MjkUZXdEp8MgUhPlFB2dilaZ0hI8jg5NhTSlhKZIUnjCIn/u3BERhEiUxEFTdI7AuP850RmWisMKOnRCoM6rSEh5vh0TVKUHkBpVXEIXT0Fw2F9PuZvTVKgFfSwKlfV9lRNWoZDsw/eflUTwfok7LnTKxoQGfOXEJnBwP2ViMyCKYnI1ASGEZmFg2ksUEMsGExjoTJEZoApNSRkR9VEZromL6oiTPX3Ki0wBY0FaqomMsCU0lhY/7YXwOSpCMqU0vbvQihMKWAKAwzgE5kpVRGYiq4ACyZAZNy96N4mxZ57DBoTGTButfnJYXcOFUBqzOsZmNFlzhOZj3zkI3jve9+Lo48+GjfffDP222+/4rxHHnkkAGDjxo3i8e9+97sAgCOOOCJjqXoBZ2+vkKDLR0LrRHWX+Y1SLUZBe5VTGS3juTLlaQVAI/Xu8FquKVv1S097e8pRWo6P3AXVgKquSYmtZloYK6o4TfxONtW1RH8198UQEY7cE6Ui32VHuC25TFiS06QMm4eRsPT1Un7CiD9JaGPGf7Jj4A2RihTxNJqll+0Etsx+5W83hXTl0+nHSywmjWk9xPSIL/xp3S2RGbUxPynMaSJjFsR78YtfjC984QvFSozBihUrAABr167FcDj0gp2efPJJ3Hbbbdh1113xspe9LGlnWFjVl3dItEPKvtJp0hCzQ8T+dB7T+ixQRoz9HP3jllJpqQJQvXTLr7RfzmjdTg51F8QEXsYlHjdRYmKg19goKb592a64v2FXmQSNUBGqDsjnmle9QvtGUaHETRumpCHa4/ts+sCniuZGf5e6+j2VeqsIeYn9tgbZt1DdiadgnK7tmf0jqL5KF6ufA6ji99WOgiE0hi1rgE9etRmfuvpJTI/KhBi6a8yPF3N2+PUHP/hBvO9978MxxxyDm2++OUlinnnmGdx9993YtGmTt/+www7Dqaeeivvuuw9XXHGFd2zVqlXYsmUL3vSmN7Vfn6Z+0dlPOysdQfm+RF7CHO6dbV9l+XJIvqx9FpuQ96PM7rCuaEtJpiunmf8zgSbXQmeugURizP3g5ZX5xrqarM1Y2U71yBEN9wwaRMgK/a4BaH5+8jU0ZM+pMIIP2mkW1gfz7NJyhHITJ1al9crbgWpxJas49rCiSk+PNvidt+yJb3z5OfjKPx7QqV3emKdo0pgfN+akInPNNdfgggsuwNTUFE488URcfvnlQZqlS5firLPOAgA89NBDWLZsGQ4++GDcd999Xrorr7wSy5cvx8qVK3HzzTdj2bJlWL9+PdatW4cjjjgCF198cWs/m8r140Ss66KkmvcVmnQniFVmTPpEC463DQcayRZoqXISVEKqUdTSmBSa7tCoC0jH08eeT76/iXoiEpGIDzwYmD87YVqXbigQDRtwGzmPoFxD2EhDw/kjq0lhefQcUcIsK8y2h2pEpALgCzve5zyGGGLUjqHRLfgwjfm1a9fiiiuuwLnnnmuPmcb829/+9rEtNluKOUlkvve97wEApqen8bGPfUxM8/KXv9wSmRQOO+ww3HnnnXadiRtvvBFLlizBypUrsWrVqsaredIXeZsqsGl0x6jvQxOrYpCXc/24h7LuoVQbmqat/CkJ3DV2i85fk4BqZWTyMnD/DSZZD7WpAvLqRkSJKfDFy0fUjRKfqnIKyjBBvSV+WaJkdAGjxER8bgJLeJzfzh7TIXT415GbMJ4ISgFaVz1IZrdWMCOXSpwr6X6xwfANLoGyZzjTOrKaM90K01pjesRA2ZL8a9aswZo1awDADo2+4447bH2477774iMf+YhNP87GfFeYk4tGzhZs3rwZe+21F8796mux8+4L/QqzJZr046uGSkPWHprFllR5yvu9gbKRVQMMi1+6TUiJ82H0cWLtRjq1Q5uK2IzmSR0P9kViS6QRSHabqS1iWu1iWYIRT0SRKRmtxBUZOmrJ5B2CDKcG3NBp+KOWhnpQp6uHbkPZUUvm7/SQdH3WpGbI99lh2Aj/AqBDrwMoVHFl9V+oWt0YmL8ag8FQHLVkRyvVw6inBhoL6qHYCwf1MOn62E4DN8Ta7Lff6yHVC8W/1RDqBd6wa42dlBt2PVBme2iHXS9AZXuAYTU6CmR4N+rzgI6OWlqAAQYK3iilsQ2/fnKInzriXjzxxBPYc889O7Nr7df1xAN3P6f5qCVu68khDjrqoaSvq1evxoUXXhi1IfVMPPDAA9FFI5s25seBOanIzEY0kt9T9KNB/ag1oDM/6CatKt7PX9oyHEIVl1OipHAylyI/vNur5C54LXzVjpTkqFDT1uyo3ZCmsqfbcjoh+DaieFCbOf+C2BQA8W6i0bVE7REcapcpJySmxQ3Npt1HjkjxGBlPXSXKjLEdXshYrMxIp9oIhO6NyX6zaRHywcXzB6ME+/7Z1U/h01c/VRTsu3r16sbzuRx00EG46qqrWvk2CfREZhLQzd5VnWpkOZleFarUEXNlXTz+t2R6jXpOglx3lCm/HtlRYhuqAZmq7dfSviuvG5T6LPnUpqxSGpciOMG+gJyng4b9gz7BkHwIj7fpiqXdPOE10N53F4fjTWAX+Jjyoy7DdhtRohcYCm1peXeXGG+3p3S14r+5LnyZK+FEQ2hMtyQybz1rEd561iI8+eQQhxz1w449m/3oicwEkGudNx322Ski3V0lXTw8aDbX7UTLSSkSvDsiFRNDK40Sn4c1mWkUA0PNdthd19VEhylwVSKervysuLoTS1RiM6f20G6j1PVy3U9KqEphZweWfWhOFGkwMFdmaOHRayU5qdn3CdTQpZMytoIqGc7dDaoOpblCaXo0RU9kZgFmo7Barl44qMTLl78ujZKCeJZiGF8Z38imb2LfbYTdabPt9Rm2h0dRYqRjkr1Q6ZAJShgIXOxbRNHx5m+JGhAUJeqr5vtdYLB3MmIZSjhUxcWU5IseN7+nsZOa5IXLNsOS+QXFV6aao8F1EO64GKVridqYj+iJzAxgRhWYQnit1MI4ETrkNRcY7FcWafumZZ6LheEmUuX76lAzhaY0PmemUKLA2LSIqxE0qDaFIa3ImcLnXy8XGxPr0in1l/oWV3WUXeagaL92vpiq1pZhy5F/u1U3VISYmHMjpMZTbuxf2oep3TGloHVFv8snwKvNmE+LWr6Kd6mCc1PKzaDB2mKj5JnrmNSopbmInsjMWozvZ97YskarWJpShaZSU0qCfPNKi5faVgy5oaXpmBw5vfOpVLMYFwIloIEHcRITPy5PXld6xrHYGKpqhKRU9JF8ogn48YBguLKBJoQq0c0lKU2ErMj+juuJ6eItEpeV2ni9oysn48Kw/rTB1VdvwdXX/LjzmX13FPREZoKI9pfH0o6BzJBXdqN8tNVbOqx7iHrBvUwrkpOaEh+AJqOVeCk8rX+0ySglaWp/BT3SVO3NodjyAHmklRinQgR5Olg6AODLGfg+DRsoSiK0fF9MnA0dWWSGVzeNEbJlkGHXbsI95VQXr/tIEQPke0fXtCsoJY8myikzPWYOZ521CGfVwb5HLfvPmXZn4uiJzAQgVQqxdO57173I8bIMGg3DLiQfJINJHE0SajKjKTTUitJGpc+fI0/R5sXd5HWfJG8FHpSqybw7R7Yl0z7Jj8CGDsvQsbSZ/ajLo11R4rUwpIQE+cpDyH27JKtYppvV1xAUQ+QEH8Rz8ON2JkFrVSZQhF8VZf+jNsbnaa67uZsydtyQ32m0H7VEbcxH9ERmAihbt2icszsQXxAnMcUvAC6dq3jwLC8vtTglP/+BtRBJXxA7Y9BktJKksDRBkxgoMxdPVC1KLObYFDk7lAgE+xMKikE8NiZmVyUVHqOU0InxQh+UnajPEhDx3EIlhncRulFS9Fq4hog/j4wjNuF8Mrxw4RyllgonWyrYmUH8DlcqIVFklUwqMlxoZIx3FFO3E+FNGtMaHax+3Y0vOxp6IjOD4ArMzEJ+vaTargbNFJoqcNFuJd47zm5emXHW0+narILdhUKTtj1eAlum6siBvUVKTBNfBEUjp9oEaQuDkC0JoRMBctJRWG7orED2ArWI/HqscgSI3U2xshT5C/a9I1TkpUGUkzAdglJuKLexN8C4n+wePSr0RGYG0fglOkZIvuRiS2hmj0wUkRNTRqpbpVZcSE4xHRvtES+el9ZcoRlH1NK4BxqUEgQ5sDevxDRDXDEpQsFoJd+uT5RCPYDGrRQUD6L6aH7A3ww2gr8FZY+BuARQcYVGTCuqKv4+Q2Z6lGOUYF9qYz6iJzITRPQlWpa5deXRtl+at5RLX05mSQJbfpaEpEcV8YozN1TbvGxL4Cs0udFNsXswW+hoBUoWsxV9ZAI5qTsp1inAVQa/G0d5/khpqB3XjdNOpXREwx+B5Csx5Jw1LZfmpR+I/shdWVVcjSX3hLQYNQne/gYn5k4nCaXSjYkdBQOYRsz8wBAK0y3fJJ+9egv+8tofYzhP+5Z6IjNhtK3yRulZTg2DLinX3zJadzKTS5GI/4C1lJ6gLhyqnbGp8+Vyu0Bp1S+laDbB3rjR5BlrosTEbPtdpOnYGFt/i11MNEaFdr+EPsdA41wCcuUlDGk5JSv+37rDJFaw0F3l0gvnoenxxAkpvlH2jE3qWWzySmnz+lFtM85DnHHWIpxx1iI89eQQP/v8ftRSjzHABCyW/ipjcn5bmGHQMZQrNqqeObKBQqOBocovGumfc0oZca3pkkn0ABQPF+cqRGppBA5p+vzuwnSblZsCVxBGea5K51wx5Qb7kCZdtgupvnuxla5jQ7ZFUiQea0D8KFGyyxM45SZMD6fClJCXMUMpXT/XlQOjBN+qBpPaKQyz0xoYBaYa5m3y0f1zm9cMdfUZ1cZ8RE9kJobCn3xLSb3ArIgmL4awi8AoNJlSChQhmjOl+lAFp1RoqhaiLEjHlB9oVwe17NTDOGusppZdHdpWFeRIPdMpMs6VmFh5rouG5vWVGz9/SGYIwUg8np5f2t8fZPPUHEpglHNIKot0M8mOKDSdubcNeOlt1ZLo3Re4Ya4Mo4bGbFYm5zKNAaZH6FqiNuYjeiIzAeTaLU2mlO8aXIUAyEsq+5tQXnBZ6uXWbCFI36eB6Isf25FTfLxYmAKFxnpHKrWmyxHkFIdJonRhRDF2pZCE02scO3f3rPtdLt0OynVxLsF+Sbkh5WtthnsLMTLB6Ce+7fbZZ1jz47xw344lv5pte+2FauRfmpxXysukH78B5Mn0cnlK1ctKoZnj0kyPxuiJTI8AlByUpDOoXrlM1YiiXK2QlBdJHeLWo/ZaKjS0MtoRgim1/Q8o7egKSYz5m87rjjuCGRclytWaNkiVzcuPnW+YVyZA0cwpmYg7ydOq0ZU80pnVMthfe8pK6nnv4qdQaqNZR+COhV6RaY+eyMwASlvHaRtxmlAaE5K0L7TMcy/FJoHB/BpklxvQMWXGeRcSq1KFJn83eJtxoPWElyFojpLJ9CRFzh2LjDhi905SYmwd3WgBSxUoHaWo4mSMjTA/jaHx42rKq0ar0Hj73LWwBE6YY0Yeaq1iP49OUf1um6TXdjmCnMKioDFoHKnVQ8JQN19qRLIxH9ETmUmjwYs6FwgZs6MLJAf36m0ImkWlDoVRLLmRSfnuHhJCIJbNFJQCm85Y824jMDI002hDAnKjk8JJ3vJlxKu8TBpi26hJVriIrDxN42gAuQunhMxVeUOyYZ8r0sUoKzECUdGV377ywrcjDk2gPpKKiE1B0IzyhXnj5bf73Sjy/1xBr8i0R09kJgndZJSJ3LIsz5tzRWPQ0LxpbdtSdLwCD9JmqhOtAa1UeiQSeSXmFqM0SxJUZadhWtVNRil5vtQ16Ux3N5VHGuSUGJkoj6IkhspFmqTbWBU4ZcmoIXb0EtknPTYmrdsR/03xEVHD2BwyNRnxF4k0TsfOSdl8WRIzIZjRS9wRaZ89llBmYkirOZUS244cqXrm4B4A8P+ueRL/79qnMJynw5Z6IjMpJCqBmQoIlcpt+qIqjxthFb/sELRSQg4xaUUeqoTRMm3aAptGx/Fz58EDg8UUHd5irga1yp99FsMulIDYeHb84GuXh6ZlZVmVo8uB6o6Q8LLdXzpsWlZxSsuiZdhyqRITKDQILwbfVmS/8pONcpVmbkiBj0rZiROm+YppDDDdcgrA1715L7zuzXvhqSeHOOXoBzr2bPajJzITQkqJaRsXMBoiqk2D+JqgO0fr6GmYFnRuLgnPp8RilICrdKMjpUgaky6nCnnn06C7KNVWdS/ujtBI2QuyJpU+SS2JzsWSjI0pI+hD087vqG+fqip0pxfHo52v5QRKOWWGqTTS8G7z24hqETllhg/FHpHFNI2TGS+0XZeph4PuIEamq9/RjoaeyEwATWZJnWlUs+K2U2pMvEI6IJgSkLRt40uJMuP8RPKFb5ZPKD6fFgqNWO4seMHklJhSqtXkuQ1IERJ1dwv7vl2JgLn9sXO0E+t5swJTMuLPFRPaUL5CRtUY/uFOg+03jxw9lQnML1PabWTS8d+42Tdp1UdBQc0ehtZjhtATmQkg9dOefQxaUmrKukZc11EqjX80G+BbRGZUdEtOV1ZVUoWmOv92L+nZQlibKjFpW7kUVAGhyk26jJyP8WOxOWJ8ZSZePo/Hget2IiTG/+uOywTJTyuehLStEttjQpP4MCmdQm5U4XigYKbJmx2/sVHQB/u2R09kJgop7iCNcfQkN++FrYa2UjKTJBaFyw3wFnhMKeEqUZbUZFQhwO+aKVFoRlGqZgq0Io09a7k2dJ5ou0kRXVdLjqykCY3tpjLBvfU99YiG/S6XJw6LtvbLY2MCUUWT61oTXWvGWyySBbcE28ShCcItUVBhoJp1oRaXU3cf8X1dRkPNNUzrAab1aMtkztM1I3siM0nEXrp5dPvT161eJk6pyb34fKVcIfXGDhUabqFOR7uPMs5rILlQZlNVSPKBZJ61L+aSZy2pxCSVBsBdOVqZl9XPOXXF8007YmP3a5/MZG0LK3mnoeynCuAtixuKOzA7YM7KYTzEIvY7rmJ1ZvEF6rFDoicyE0JJjETVsh1/tZgOTC2YHI69xFMT8PHWqcrIzyUxLEOtspP+8YUyS+N2jI+ld6HN4pTjQhOiXKLEhATBjxUxz6sW8vA5X2TCpOyzZFSXUUEXlAyOwQyrpj76Q6mp6kK7ldy1JX568ipJYxUXxf6y73U+uoaQVpQJNouNUcooLhj7a8QoLrMjPKXqYBrM2iZFGYaoltYczcb8JIk9kZkASqaSot0Asx/cz3KFpnrpJEiPUIbUuitZZsBXhlLpeFlheSUoXfpgfGgQ44LmSoxUHqvLo/5Y4sQSxfY3RbKbKNfVBXItGFkJyJzm6U0iSsRSM6dk9iWUxCRUuMmVl3FgtnSt7ihvzhT6GJn26InMBBCPTxiXsNsevKXeRqFJLzdQtVqbLTcg+9BkIcghU4VK43YAZIeMx8rhaBJQ2cZ+CUZXYkZDSWxMM3uwSw2II6Si59NklBZ8HiANO4+oNKmP4ipUy1urIt2bCtVSA31XztzHmmsfx9985vF+Qrwe44Qkc5e9tLtorUruNHlnSsVLkS0mtfbF8ojNUmXGlRHrdzd7y8+pPG7HnyJvx2z5SRV5LGHJoybPKUO30lqAUR9jCg5/5r35aQKDfhBtjFSIPgjnS7kGB5/hVweJmzwdE3iSVPOSlPeptWRFDhbZSGlzPWIYJdj3NWcuxmvOXIwtT07jV1/03Y49m/3oicwMoFHLU7ef/EyCApIT14XFSwlT3ivvhR9TSmw8QY3copHZcuvrVBKnYspOKTN+2T7xaSunN1EBuoR/1eQTjgXNiiOCajsmvb9opD+5XexZH5rumIgvxq5RWrR2o5eGZJ/c9eMrLoFqwnw1MTJDGyvjHzNpQ0T0Sg148TH+xYCi6y/xfHzl69QDk1hOIAdxVFE9D0wV+0I+RtkpsDuwdunvpYqoSv3Ge5gYmdHe9fN1+c7RIotmKa6//nqce+65OPHEE7HnnntCKYUzzjijsZ2lS5dCKSV+nv3sZzeyxZXlZDoN74XaJezLXYefcqiic7HllChPGYOuUsoP4iz1zcY1ZBLbitCetwo+swncR8D3X8oQU038fbaNXlx90udNyhSz07TKi6ooALxYneizHsaqOPWFkpHI0O32nMLLp9h2LF1TFM+DRIJrnCojSFwZ2/wX0V4Vmj8Y1ksUjPIZNVh4R8WcVGQuuugifPOb38Tuu++OAw88EHfffXdrW3vttRfOO++8YP/uu+9ebKOpApOLYxgVEmtvVj3x88krNMgoJfScYwtChnO/VDk9O7yln2hJ8vsyKFCqpHujgupyZtGEXJUsP+DstiPWjlgJ+zuZENIoMH7Vx5UYj3yWDE23i1O6cvwyWXrAEh1flWHfg0z131qMUUpB27kOeHpVPdMtLtuoVdzAKDP054WyOLpy+5Wf5vts+U31mN2Yk0Tm0ksvxYEHHojnPe95+PKXv4wVK1a0trX33ntj9erVI/mTU2BAKt9RGnajQny5F0jKYcUu2YY3pCfb/WM4RaJwQx/StsLg5aQ9Wn8Uv0VDSjXJTqSmNCodzyIRmEiQBCNB/veEfUY2aV3uyEOWUVqSElViSBeOpMJQouL7S6pm2t1kP7y7SHllhdcpvG7eX7p/hmrucRRrr2TGeJUm/nuZLxpDNxPizVTtMbOYk0RmFOIyExi3AlPmg1whDIperiWjjFgLNqHQ0Io5lcYEDKfc47/r1EuVV8Slo5V4xTv5zqYGfesRBcYejpyyZN9/bkOVIx4UHLGlq7lpgkUfJT/h1CR5Zl82p42goNh0wjwyPtKdHPS343WRegeETLMI43pmBwVvN4U4WbFdTPNAmhl20DXUzyPTQ8S2bdvw2c9+Fvfffz8WLVqEF77whTjppJMwNTXV2ma72JfRh8C2GYZJK4BKpShXaLIEo0ChoZWU7L+bIt+UmevCSpUX+EjsNrllOWLRpitv1FdUapX1Rs+j9v3hBJAS0WjXVVkxAFxgsL8kQew8/GfGL4cG82Z80N6fIC5G10qMOAFewqY35JoRe6/sMVXcRv0w5geZLt+ojQ4qTKV0cbXt7vg8YDQ9GqMnMhk8/PDDOPPMM719hxxyCK666iq8/OUvL7Lx9JZn7HcNYLBwAQY7NSNCXQT+SjEl2XIFG7H3L92rkXtBUmImy89B2cILnnerlHRZobDvnV/v0pd32X1q1iFU1N2SMZALkC59NHg1FhIkFU3r8pSci3LPvXbXIEVCeFeTHyNjfMvHyMhllOgWrkuKG4uSGLOtyN8xwQbm2jJ0dB6aqA3waKQR/IFG2ezFqrMyZyumtcL0iDFjo+bfUdETmQTe8pa34MQTT8RP//RPY4899sC9996Lj3/84/jUpz6FV73qVbjjjjvwohe9KGvnL3/pBm/7Z3/7hfjZ/y+eLz7kdTSkWuSprh7Ph4bLDdC08aRuUcqsmqLTypKp6JKKhwaGqtQ3m6XRueeRrpC7QPJ+mzTmKkndLvYKjv5ydM80V29Gs218HFqVxtF1T5mJdSuBdFHZfT4J8fKabR7UGwUjNNJfk4yTGFZu9QMZZit+X3UZ5xNGylThsOuxlANUI0fHWsrMwIw8Gs3GZO73bENPZBJYtWqVt3300Ufjk5/8JHbffXdccsklWL16NW644YZIboff/IdfxU6LFlYVKBSmkmrM+MbAJKlE4dwyXKqX9sTy5TpbtE4HBpqS0gtCVrZUslZgm3zujkz5Nls2R87WeF/HTUbKhTDVYDsfRRUmowg1fwUbpSassgPVKEkcXTeYM+TbTD3lgU2aiX6CxJnns+GlV+xLSaBtt5hMbNhcJDE9RkNPZFrgd37nd3DJJZfg1ltvLUq/024LsXDRzgAiL/hgMrLJ/1R5C9Z4kVtssVyl4LEsckAwnWE7ptCULAjpV2RVWHA8Dsd/BZdM3OVG37AzmMFJv0oUGJvW69oTjgl2jH1N05F9gZIhXHFJhaEjlezEdzH/tFNNhpB7aKLLOJigXvmoPUc7GorG4tD5YyQbVKEBggTJbqWuEFmOwExq121ZwEANo3YVdPR3pGCCgHtQDPUAw5ajlv7ps49g7Wcf6Zco6FGO/fbbDwCwZcuW4jzxxyuU3GcGUneWrnumM2SGWAhHJsUhNzoTrVThSEoBcharc+Aji+K2c0O6497N7F3sICCYdf2k7OeCh11aP2ZGctIJF0wdEXyxfKGwC9avMhU/WJN4wb6Yp+Aaa0d+4oqM3z2i5R9DOcpCjjJ5ogPt81lFxJ+gZNdvMWb6ndktRula+vkzno2fP+PZ+PGT0/jtn/16x57NfvREpgXWr18PADj00EOL0vMRLGFruPwHKSknRVDNFj80mYbkDZtTaMIJ69JkgX8L0tQt9VTsjLkeKd/Cbpz8kG2bouF1k9SAsUn8uvmU5CklhupkXpIW5disWgnXv8yeH7dC42DktEMznwsthw2tpj654d5OhXLzx4AMywZRaMCO191bGvBGLVHFUCu2ryYxnqqo3CR41Y66EJWPiVExDc03x0kEV0Xofu/TkaKjgA5tKQxyLaUe8wbznsg888wz2LRpExYuXIjDDjvM7v/2t7+NJUuWYPHixV76Bx54AO985zsBoNWyB6ZfPx+EGdvf8perxQYs9Sp7hC8HmdXImQSfW3Fa9sMoQgXlJgxxhcYpOgXnMEvfl12KyFElRsvPXCy9Fh2Lx5u4rh5ZqRHtCwmCLqZIF5ImX8LuIfrXaRONrzO1w09aIyAx9jiJ1fJ00An2Fnh3VdH9XTjR3YnMxt/jqBhi9FFHw3ySOYk5SWTWrFmDNWvWAKiGTwPAHXfcgbPOOgsAsO++++IjH/kIAOChhx7CsmXLcPDBB+O+++6zNq677jp8+MMfxooVK3DIIYfYUUt///d/j61bt+LVr3413vOe9zT0TMX77wlK0rRBUskpWhSuLIYF8LsJqpxy2pIhzn4MUTV1ea681HIDJm3pJGC0/JJFKcPyRp8DaBSUPE/8+pmd0Ynw2EKR+Tzh80eVkLbPfBUrE5Ig6ZpbhSVhi88xY5UWti3OH0PT8uHX9d+ieWRmAINIfE2PyaGbCfHmyzzIPuYkkbnrrrtwzTXXePvuvfde3HvvvQCAgw8+2BKZGFasWIENGzbgX//1X3HHHXdgy5Yt2HvvvXHCCSfgzDPPxJlnngnVoL8gFhtQHZt5cB+KzkwDuuGyA0BcmaF+pBSiEjVFQxWNxGo6VwzvJuk8iLJDSF06YZpIVISoxLjhys4++a59e5KSUnK1vKUDzOrTZFi0NwIpIDChX1KMjOtCqrurBMdi3b/yOcjExQ+Gj5AYYmHcT9MoYyKlxgjrkKv2CY2icY2einc27njoZomCnsjMGaxevbp4faSlS5f6fdM1Xv7ylxdPeJdHegKu6oU8wz9HPnKqaAZfvwJIrbBrKpQB4mmszYxSUl3L/FBtDZVRZvxzLoqF4S36WdrtBGQUOJMG8tUuUVVSSoykwAR5IvZjsTFeLIsO75/oY2L5Aqu+iKSN5yHqjKfE0G0ERMVajXQzNempHRWm0m+rvMRGP9FlCOzd8y6ni0DqGqr+12N+Y04SmdmG+DBXgybKTrP0bXL4OX2kCQZJEemC4RWNHAiroIOWn+RfQbeUR7ZK5qnxu8PytYv8ep60UtM0diqmxMgjkXwlplk5zoa3L5hyoC04qTEKjjtH2l2UKtMG9Jqh1IlziPlSZaj+qlSBnMxwUpOFrklJkzwhYl2+PSaPIRqsmZawMR/RE5kJINkKbajENA/2LRtKHJQjroSd784hBsqWHSiwFaUKnhoUV4JcjrR4T9uMrAMinifC9ib5OmkbgxOLfwn3NX9OvfyRYdJdVJ9GUUqqRfWx/DWi1NWRIGiiyER8kJmSIgl4BrbNL9GkuEVRbFyPSaDvWmqPnshMGH7/faa7qaO2UomoWxT4qhH0gGW7gArIDyck4Tu9UmhS/eF0EcpUAHKTZQZot0ujlquGFzvEMcpdjU9Ul8+X0riaTabnCwo+UZEDauUuLFlNKYVYDldihG4jrwvL/mU2jDrDfhlUndHhTlIAwgtF/iq22250wCoqlVPb316X3ToKZSta9+gxSfREZoJo2rKd7KuiLNQwvxq1s6eBbMCtr5i4fWGWnH9VZZTr/+eVeZL0eF7kJwf08qddbV1fjTL6KTPTSPHzxmNjyJ9oObGyHelocEUs+aHdhqFPwX5zjHU1hXyDd4ORfRoQJ7qzGWQZkgb6+rNSd/s7N91Nin7vWnJRwKTfTvMB3ay11CsyPcaIanx/+o0yk+0c3mIuUWi0Vt57WwqWDVSQxEuQpi1ZdkD6yTZZbsCUl1Nmas8xJBRrlNgCft3KM7bJklY7+LIDPvzh9rKqEisXjGhUSA2zNn4OtfmrrB23dIAi5MI/D6o98OfA2BnCKTG+rKSEodYyywiITzDhHapJ8OqE4mglmtZsdkE4IjYqUuOec1UPtx53t9LALiY5PlQq0TgY22Qx1O2nIaA25iN6IjMB8Mo8lqa8RdwMY320aUUnKg2skixYGFIBwZTtsl3pRRx2I6S7tqo87YZdSydSeHfG+m4XunASaWPHUgTIHU/s42QjkY+X6Sk8lmwRYiPlFZQYS2oYIfPTkOHe7JiXKRilRAlKTBFCeOLJe1+u+nEXk2sqCb+lUd4LUt605pazpekda+FQP3ZpPqMnMhNATDZvo8CEC0wW5WrcWIn5lmpdUaUhpuhouOthpG/+4rIVqJHiI4qJiZ1JiammZZ5TZnyf8ldYvj66ahnOsOzO1b9YpZ+qYnItO3rNfCWFp5OuU3cTBHoqDagy42/LeTn5IXnsfn+SvIDcRZYl8MhOvR086lSVUVWZSrd4ejoSIxRqBcV8YJYnkGGOV3nTabPlAjZ/9b36O5/IybCDrqV+QrweE0VJuyPW4m3yojPVMx/OHE9b7pOYvk6gVUzl4BVsnPB4eepYm5gyE/epIha6QHUx5aqY2BL1z5RkfFFsfyzHqIh3CY1yt6Wwaq87RVA3itQbppiE9X+Li54o2w9gNl1HYE5nCJtJQ/NyNYb6plkMDDvmg5DegmfOZz786yjPl8TAIPz1IT5lmYZMzgf+5HWhHu0oGGX1a2pjPqInMjMAI48n02RazE3Kqr6kbSkAucXpKnsqusULHkJl++FNazqrmCA+uV3eJ38kTW6ZATrlfalCY/yMdTeN40Uce46S3ur0XBPSwoy0HPNdR/JQpcazEXn+jPKTm//CcQgXRzAUlRjlbfNzcBPqkYn1dP0c8vljMoTHkrNgWQJGfMD+No1jUAhr+JZQ3lVy9lNLFBilpknxlbKSCy8vGwE1EBswPXo49ERmQvDbPBGpW3hhdtGOL7ZhX7Ax9YPb9btR4lV4vs1txgTRPaItb6x2aE+7QwJMJac9LT4XQ+O939uJBvmMLVF0bz0FJeZHJO6ktIyCvJToSWKG2aBkiapDNHi4lKADaNiNVZWXyqKDL+Q7OWn7RKeEjSIlJoFE3lICnlc90sqMbK/kl1BGjsx1nOtkZhoK0yOe5aj5d1T0RGYCKFJghDRdkJgmoHSjZJ2iKk9GDeHKktiyY4oJ4pPp5ed1MXtTV5zFaJQoNM79xlO8z/SsGyWzfZqRQhQlz20MUbUooTS6pQPoaCVVxfxE48xg1RUJ0nlFfdZOoQFTaIKOD3tDDbkSupooqbFcQHnEWJvx1y2WDaDhz/LxPCUbZGxQuJiZ0Z7mNvE0lXqjGq1vt6NhlK6l2//P93HH/70fQylQbR6gJzITQZcKzKg/ZLkELjpIQ2eBXCWei1eRy5KPm3ZYwt96zaWUMpPzxaUvU2gAJgrN5vdqgjS4JAmCwPcFzysbXSTZSRCJ7LNeJIvkyzRkB4SoaDhSxQPo/XN3w71pjA1Vlzx/dGDAIzEcvl7ZHVRwBuOr4EqHcfvEan5WuClMo72i8nO/uRQ/95tLsfWpZ/AHP/fFbh3bAdATmQkg9pNtN2qpfSs5FYfilcH+GuS66fnLXRzXw17mMjEyLeH8UO2K8KSUGZc6SqwCn5z1WJk2baFyNRMofb74+UfVFE5c2LMYWyRS8mH0+S6UFyMT88n54c6Lx8hUCSgp4eqKT4oCw+S76yAlcTL2GPx97lTs8VGqdzP5nT9fjIkJGw8UzDwxZZ4PkG8o9OjRFD2RmQGUkZHuf+50Gv+wNKDkZUQroFgXkC3PaTuJNLR84XjBTMK0RZ3qlqIoIWRlo5wk5ar5cPeRkKi8Q0hztPh5cuTAnLNEeM21C8tWUQWSqiLeUGq4fdQPaWkCfi4un6wsipDUI0p0LBtSAtnxTsiqMIofK/BBKXmU4cjUjygnzUcV+X6kxsuNYruk7MFsbTmMiH7UUnv0RGZG0K6lPCpi3UUAIrErPD/LkmlDlhACO39LZCZfv7zQC/l1H4nDiW5JPpWREVkLGleHQcyHctJLiUHMFk8fXK2MEhMjGVGVRzu/ODeg8S/0b5xsUdITV5ckaDAy5NkAolQiRlQ8RYbH1jgo7QtCyZuZk0ULsqn6v6axXs5W/LehxLvTnSLU8vR3CPSLRrZHT2QmiJwSkyQa40bEt1w3C1dMpLPzgmUjV2AIHn0hlFe3mLPrKRUQkWFNsOJJqgneqI1SuqABlIymaVORjLQKNe1KCY4JJKZIOYzYi0zcWCZKlEVcOBIkxMNI/ggxMiBqUGhDkvbYfDSExNilCIwqY43VAb6c8HRYI8/qWC3QLqgePbpHT2QmilQHjpHrZ+aNJGsY1ZF4HpZWK7QZfYE6r32/x7qQrNoSVzxoHRH4J6RNX21X8StbM5Wh5Cq0udNtqwLTfZM6LpUxStUT7XwIDsjEI2vcs+MrMaJNu981GGz6aDdRQeOCqS3BsGvmhPFM04d1BDQiMQ0lja46uMcRFzPLuVtjaKiiEYY5G/MRPZGZADRcbIn/c2YTcBU8hEmJO4OmLxP3gs/HqZiktAKSgou58CypImapA1kxURhqf9aZaLcU6w8JX/j10N6ELy63XLkOEopVDl13HQb2EwqMSyM8d4luIGh3tjRvvAsnVE2sb4grN1F/tZyH3x9rW+evgTlfq9iISgx8O4zkKEpmvA9RYxgX9sh2g0aA5SKtupjCGBYFF4Q7gFuawAy1no1V41wcit13LbVHT2QmgjiJafOaaLtOTZvffTgsWe7M5y7Rl3Sr101SLvGDe2PZA390u2vgLEjltH/Rj1toTw19dj4wJUaT72Fill5WK7z6PkqKjD25nMAHLX51diJKjCFYvFcnSGMPKGYPSHcTkmuQuaEB5+U/Eh2mL9NDI2UVwTnvYmecDTWLg1JmsWs9JoyeyEwA4SunjMTEJhRri6FWiYq8JNhXeQ5ULaLEqzYRyEttasiLUXot74hCY1QHVVAO/xbzxaCkT5/fx9Ih7uNAqMCkupISqkvUboFimIiNSS6eqtlfa4sek8NIqRzvlBjBLxojo6k93i1F8xHfjSrDV8EG+6thVRiqxjSTnlCziAxhES6p+S2UzO8yUPlYrUqlGXr73KR22voxEDpG6MKSPdIYajXytASjT2uwY6InMhMCqf4LScxopCVqN2KzVKnw/NaaybuhQmOUEJpNKoo3VMUECYUmTOCfqD3KKqv8PDUZv1iZfqdXzuIokLs/cuQl5om0EKQtR7CbslXtG/GF6nUThYqm5QaU6Xoo7LLyXvzse2KkkW/D/VXcRiyt9MjG0jaCPO4sbqywkMztTKsjPZEpwXQHq1+Pmn9HRU9kJoo04y6JaRgXpNZubnFF6q+VoSVlhcjvlXwdSWO/pxWaaOwN2S35zlWI6uVbouKEWzLic5zEfGoH1WjqfSCuwNBjotoRITFaIBoc0rPeZKh40lcdPjMuxiWtAAU2qS2rujAbXImhBfO/ghrjjVoy6VSu+6gc5lmWfoO5+Z569NjR0ROZiSH/Ap9t7RZNXrbZtPVfxSp/8ZxoBRORv2nDNXYsdtwmKpDmOXGMv/DDScra1A3dhU42j4IQj2UfOjnmhNvVAOjIM4kUcUM2lLTgwfdm4PXUI5+8SOX4X91MJ/HengKyRTIrdtKhNiT4o/zv4pPa9FGJpFf2bxDh1Mh0UyI+mRl801rQjoS+a6k9eiIzEcgPaKNWI7qrBJvM5+DNmptTaApm2AXKiIjropGVGftdRdSbuoJLjSri1zR3XcLA52YY9yglsUykn5tRJtMr6cSIPeMmmqJEgUzHyPiKn+RjGB9Tp/GWJaD7pULY/DH0BOvy/Xlk6Hc4VYaWF+8JrU2W3Znqt5ZOSxVThXZLBcQmu5MwsD6Nl8woqGoE01hLmQyGGGA4YtfQqPl3VPREZgKQXtZi61FMY9DdTzX1asmVUqSG2LQhGeH50zP7lvmWVG+sMmPSJIiYqYiKZjn229Cz6UVaUnU0nZyxlEjTLhrJr5QCwglLKsjYpXc2vOMFw7qzDQmqAjF/A7JC0+cKDd0lOwuMkLWUdmRU5EpbTYV/Sm3MFUxrhekRGzuj5t9R0ROZCUBquZa0zsc1g0PabmJUD69UEhW+qwjLlBlmOeKNUF5d+SUn0dNkK1NvaQADHXGmqW8zhFLCEa8yfQLRRDkEmsfGpEhM/Fz8bqlQiUH4gMXKJ+s8uZ11daqZGcbGgsnvqPpC/opKTsklNaSl/pjn3CksOy5MV1c1KsqpRONc5LLH3ERPZCaMlBJTotKMH7TCyVWJftxInAARRSTS1eN3S8UUGhV46B/ryBdbkdd2CtehkojZJO5mEwG/XIlJpXHHK8IQH3ItKSVtYQkOZJXT2KdPAY+f0fSueMTCJ0FeGdJf1nWk6m2lfVvOE5K/PqwMSSolNaVQ5tkLiTtfHdtHNRmemRgvYrpO47YVucKF7mU7QFz31/xBHyPTHj2RmTDSL/LJhMelwLuz0jExVRqbumjhx3wXkm9VThtTZpwBqbpmpWtZoZEIiWbbISQVYpIqTY54xLe9YxkSU+UXFEahDHHNI2+r2dXJqzQ+AfGUnfoD85344vGZgLRQ0qNEkuIX7kiL/Zup5ws7lIpgxRuVUzbCEk16N/tvhMwo/1iz2X99SpnCpBoCswW6g9WvdT+zb49xQmydsn2jVjBNUbJoYWxMUXxvWhUJyQ8gnflQq6Qy46k3CYUm3YkGwE4SKF8Lk8b6a2uoEig2jVgqJe+oyuthJSidPdqRDomkqOA7wFt/8tQBrtoKy3NEg06A5+wOa+IwBAQC4U+iFx7z427k83UBvJrlNc5bxYkzH+njn7TMlMx2Jz9l7akrsjKSCLpVqCeyo5Pb+b/fpgs9monyZKKkSRBwoT01/whNj+aYn/RtBiCv+ZIbBhpPO+qn2G8xb6RrTJvzjL96XFsv3iZr4nP0XIwvseMAXNszDd+P+H0YBbERQKPZdH9L/IzGctlMssLiypHuabrbyakjjthYX8z9s395uS6WR+xq8kgzJWP1YUaq/bWUePeT0B3F4HUrlTxUHaMi/pFjsf1IxY3FaGjGh4I0TaBa5drxMA3VyWemceutt+JXfuVX8JznPAdKKVx99dVjL7MnMhOALMUngh/rvlL66fq9Z1q+QTkFBTn/E2RE+2ni54o08bFDZ+O+DZOkqJrCfpjxwZ1/+lVslQP26eIGDYmvo764rZ8ZO9o+X346ek213S4tm6garJwuIP8eqsn7RPKq3fNYdQ+FeQ3pEVWliOrix8VYS9U+m6b+O6y+m4+x0QVSBKYr+4Pkr7hHFxhq+Z3c7DPTZwE89dRTOProo3HZZZdh1113nUiZc5LIXH/99Tj33HNx4oknYs8994RSCmeccUYrWw8++CDe+ta34oADDsDOO++MpUuX4rzzzsOPfvSjYhtxyV1KPJbGWgOUvRGL1BLtPnE7fvcEbdOF9jMjXzKOpkbA0OiAHGJqTMn5jgOalU27QcpcEdSgxI0ND3HSkvPX3d8S+MpSqHg4f0I1iBuyKgy5PkH3U0KBkkF88p11ZIbn4OlGRomR8NdWhEhXUMn8NY3L6rHD49WvfjX+8A//EKeffjoGg8lQjDlJZC666CJ8/OMfx1133YXnPOc5re1s2rQJxxxzDK666iq89KUvxfnnn49DDz0Ul112GY477jg89thjjW0m1QOthGXXJgtJqcmNNPFVj8S5JSY04xOWSX45laHED/nkStQt2jIqHWUzZNdgolxGK6/8tALFlT5Bicndb++6mPsWkiHJB3OfS9U/a6v2NVgMUvKXKDOUpPjk0x++zR01ef1J8+r0bMQSJyvB0Ou6m8z7mLS0wBKMINYN6oIobR8Fg+DpkWHKahpvw20MlMLcmPpOxrAO9h31k0Obhn4XDfpxYk4G+1566aU48MAD8bznPQ9f/vKXsWLFilZ2zj77bDzyyCO4/PLLce6559r97373u3HppZfi/e9/Pz75yU8W24sqBqnjswCmhW5fIYl3ic4nSeQzveGaWNBemkqyJ8O+VaysKo10LB+UTOImoMGXXShCibIW9T1qUjRa/ty4mJJS+/S+0OO+AuKqxLJn3I9b8dIIxKNNzc3VsliiQOWhRIUbJFCxc2AFmy6mztHwkiiWpzWJScXTCMfsVepXwM7CdSuPZiOHiy66CN/85jex++6748ADD8Tdd9+dTL9p0yYsX74cjzzyCF772tfiqKOOwte+9jVcdtlluOmmm3Dbbbdhn332GcnvUTEnFZkVK1bg8MMPZyszN8OmTZuwdu1aHHLIITjnnHO8YxdeeCEWLVqEa6+9Fk899VSRPUmt0KwlLUEj1yc62qd8iQTS0i9QaHLKTGrOBHPOsnrjt6hjvrg08kEvxiV5Ns2vl1EjUh9/or5CaP8+5GJ/wvPgnQsO0n0NriFTcKyyYmwI18c84zEfh+b6kr9OsUldb/8YXTCSwyl5gi1qIzhflkZQY7wJ7wghUoCXLmRWDe8/Ca6xNG/C4sQgoapUcTRD8AbCQI2mxMwnmJl9R/3kcOmll2Ljxo3YvHkzPvGJT2TT0wb9mjVr8OEPfxi33HILzj//fGzYsAHvf//7uzj9kTAniUwXWLduHQDg1FNPDfr59thjDxx//PH4yU9+gvXr12dtiS/XxG/bC6Qd8zvAIwW03Fw+7T5xu/lWca7F7MfNyLEzqUBg0/Ys8SPbgrdpy69Tujy/Oy33ad6OJvc0p8SI+yRik79GMRVl1OHkdn4YTe+9JJ4YQlE/MyZNTUSC59ZseySFxeIUVBDeqGNLZozKyHqFOvhdBx7VO9zsv9pNgNda2xrRp7GUMXe7lyaBJg39rhv040JPZCLYsGEDAODwww8Xj5v9GzduzNp6esszeGbL0/azfdswrhaAVWCtvG8GseJMvCwC8hMlMwVDrWMtZThlJq3eoG4H5pSZjA9ZBYCck5d2NDKTU278TzPYUTzJa4xg1FVSzSo6r3hszCgwahQPWXVz0sB9ZzEyNI3XVUbteGUBwbDvmMJCiI93lTXcPq7ilMCyn3gG5Sk1mqxdpO0ir55PCjt0N48i/+Ya2sTDPLNNY+uT2+1n21PbO/Wpywb9ODEnY2S6wBNPPAEA2GuvvcTjZv/jjz+etfUPp/0fb3vZW4/B83/rWLvdRnlp07ptVDVJZEbFbPiVVHzdI8+U26/9HbEz0xqkFRGW4ZGQyLICJj4mdfW45WRaSemIXqdxo1kAbfU3VF0kJcZXJIRKXyhAusrePDGA6G8wV49gi8/Oa/wqAV39mo/yks4jBz4CyXU3KclJL18XI9ya0mkprQncrRQc2JmBW/s0Y7+BHReme7UJ/u3qf8O3Pv2vY/KorEG/du1abNy4Ea94xSsAVMOv77nnHgDAcDjE/fffj7vuuguLFy/Gc5/73LH42ROZltD1G6hEnvulNb+JhYt2si/kwcIpZqyF8tIiT+VrWS6RrjDCEUsrEwj/CH/JFZMQLRMlXl8MtBJbssaP1EvW9yX9QpY8VVo3q1k6Quksvi59YfeP9tUgXk7MjnTVvC6ylFJERinJqp8QIyNaisOlT+UVyAhXY8BiZbSXmxdm9/PLphCS+mKM9Ly5LqjRO02NO/28M5PA0W9+EZb95tF2+5ktT+OGX/l8Z/bbNOjvvPNOb4DNqlWrsGrVKrz5zW8e2+R4PZGJwNwgcyM5Nm/e7KVLYeGinbBgt50B8Pch6b+PIh702hRSaztfEstfUMnziq3pApDV3hiZMf/V+a1uH6bTWlmpnYMGVydf3FqucFIIFQwkfW2D/DpGQh7vuxT/IuzjSoz2j/vpI8SogHRTwpJMq+Gl4emNz+6v8znoOtQItt0QabgPK1/ZZ1eRfF48bnzV68g5NYJVS8ozum4mrmHFZ/VRMEsX+M6aLiw/zWRJS3U+c6t7yXSdNoHaaQEW7OSq8dEpaDNIDfqTTz7Z7p8UeiITwZFHHgkgHgPz3e9+FwBwxBFH5I3FXs4lL3h0Iz8jY6dURqYmShSaaDdR4rjtrkl2D7nEsYUflfelPfwVs0tuRuy13tVrpnmbOSQl/LisxJi81oaXLk1szM5mJKbkvHwffCZDyAX5y6vvqC9hVkJsfOJiyItohHtp/Mj9IDIuKpVPI+YTSUy6C0hBPsb3N+3a6gJzMU5mNq5+3WWDfpzoiUwERhpbu3YthsOhF+j05JNP4rbbbsOuu+6Kl73sZVlbUpsm9YKnMTOT4rVtYj248hDr8rGBkA1Xx9Zaedp8urvJlhYcp5XtILMIpfEhWt9o5VVGTYaWdrXwZ9NnQlJbUsdypCdXmBjsS7uJADS5DhLRCZSYSLlRe163FACj1liSInQpAdWyBKjVAEtmlKfAKJafT5bX5jFQAlswRCRMm49vqdKUPUlGdZljvKFHATpt0I8R837U0jPPPIO7774bmzZt8vYfdthhOPXUU3Hffffhiiuu8I6tWrUKW7ZswZve9CYsWrQoW0bwuki2Up28nmondfMJ/fQ+BW9cP0+8sizJLx7XYcUT2qDDi9258fPJ+VIMYrSZvXCYe5tP0xoltRaUGOxLSLTX7i442dS9tDRVZ7qbgntt7idViMKRSB6xEfKHvuauI1V3lP8QxQurcnqkpiBPRySh1EyT4mJdT3GU64WKfZnPXGmU2Xw3XP8fuPE3rsPat67p1CfeoKdo2qAfJ+akIrNmzRqsWbMGAPDwww8DAO644w6cddZZAIB9990XH/nIRwAADz30EJYtW4aDDz4Y9913n2fnyiuvxPLly7Fy5UrcfPPNWLZsGdavX49169bhiCOOwMUXX9zQM3lRr9QQ5jBtN5VxVR2qrLUhITO5kQiGTESDcUkFNUDYwjNkKKaIDLWK+lApM6TajQQ2m8pPUmaoLY0ytWUUhWZcSJHKVJq4EqM8Uqu9fWkFJld+OFxakWOh7WBaApbGECWneipLhIMh4JqqMcYpJasxEhOWlBeyT3EbdR5VJ6nSac9ccNuadB8RAdN0/3BlZtxBuKpgAjyFKo2ZLG8AN9neTHRTzRaM0rV02K+9AIf92gvwzJan8Ten/kVnPpkG/dq1a3HFFVd4M9ybBv3b3/72ogb9ODEnicxdd92Fa665xtt377334t577wUAHHzwwZbIpHDYYYfhzjvvxAUXXICbbroJN954I5YsWYKVK1di1apVWLx4cSO/ogqLeCDxQHfQD6pt/IncYSPm0YA/SksmLEB6VFCVLpUmTrAqH+I2eQnUjvkmWc9dheQVJwm93rAZQmw4f0ql4EoMTReSnlRsTIoIhT5ywcLW/TpFxki3kMCGaf7wMkiRIuG5iE+foMgU8Y7iB6nEmJBMVYX4yolm+53JNsOq4zpuczv0b7Whg+M9xocmDX1gHA367qH0pMOL5xE2b96MvfbaC7+y9i2YqkctUaRbrbEJ0Mok/izsGyN8rZe22ErmiqhenPE0kjIT2khUaZGAYJuvfplzn5r46Pk6AlK+tkFcQYmkTZROW4K0WqHDmnl5HlHQ/kgwPnTaG9Rr0mq3sCRXZMxCmMY3txyC88kuY0C+D4nyolG3cOu8w6HylBm6DQ3oehvD+nc5XaszQwDDWmWZrrbVdBUXY7fNp95v9tnH25BEBWAAaPvR0FOoPgNAL6gy6IUaeqCBBZW0oxZoYKAxmNJQgyEGA42pqervgqlpDAYaCwdDDNQQC6aGmFJDLKz/LhhUf6fUEDsNpjE10FigpjFQGgsH05jCEAsH9baarvKoof1O/w5QHau2t2MKurKNquyFqrK3QA1t2gGq8qagnY1akTH5B0C1D8CCujEwADBQwBQUBlCYUgpTGGAAhQVqAFXvV1AYjDLpTQabnxzip464F0888QT23HPP7u3X9cRr1v4WFi7aaSRbz2x5Gn936qeTvq5evRoXXnhh1IbUO/HAAw/YBv1jjz2GJUuW4LTTTmvVoB8H5qQiM9sQHZYaQGgtjotmWrtcew4HPktVnNujSLqUQiPb0FDVvCsRd9zOFupNfYwv+ii3tpU9Hld8Mm4WYCZaDakyDWkI09H4k6bgz60jMLScuG1CngQ7AYFLxABRhUb0MwYpPX9MqTJDL5bQnVRkPyPzmLNv8+xJSoxttFj7ua6ddNn5Y82eprhiTNPMHQ1nlK6le//qW/jeDf8OLcUuMKxevRqrV69uZP+ggw7CVVdd1cq3SaAnMhOAJKtLE3wN678zCZl0aTEqnJ9DPC7F7VXK71KiSkFMDTJpJEXEtLxjagdVFKSYAVqGSRV7YYddV83QeiTQiEh5Go+JaRdJkYuNMc946oXtqSlA4Avv1jJkWfLDqTzKyy/NJ2OVGV3bo8OudV1palQjlyipqZ3wRi4NyT4CZfxPcijhAnqT1JQpiDw/JS2mpEr5cPEqZlK8pjCxMXJeT48rswd4MT/xdGqkGYhnE0YhMkt/7YVY+msvxDNbnsY//uKfdezZ7EdPZCaMrDqTeIeMozUfeCMVovzKIta64hWK+FLTgFZyfIxRB8IXrjnuiFJ4WHkVQPx14JQXBN9MRVOfZyYgWLoGs+GdGqh6sTQNlBh+1T0BQvvHqJ3cQ0v9yMV+USXGftf0mE+avbzaVKeFKFFRBCWInoG3dAE/2BbERmzKgZJiFPnIx2dCOwxR+TiXdJce40BPZCaImBID5FvrVLno3qtckvq1ZhPG1A9/OzZRHXR1MN0VlSZKGn7MCq9MY3PWVKsHlHUf+RaltDKdmmkUPSdaisHy52px9vznMxhJJJLz8HkQ3ajtDklsTCybOIsvuF9GRZEMwCNLyfljaB4IpEQTIsDyekOuefmAfajsJHmSq0WKiw5Vi1qtKZ9HRiBCCjMyW28MA8ytLqQYZuOEeDsKeiIzIQSjPrxjsTzjRyNlwbx4lZ8irtD4VryzZhUmJR5eK93kSyg0cjcQ9S2WN+O/1y1VJueXdEp1hZg2lctTMsQ6VoavxLC0gl07lsZey4b+auqzuVOKTWgnjYoyik2omvDzCcF8NNdFk24l9hEXjoTftUQvj50YryOo2mj8LdPOaGCjIcmphlr3KEFPZNqjJzITQThctSReYjzVX2k5idJpq1klLJBz5i3EnPLBuztiCk1sLpxU9xAfnhydkTjjowQ5n+xjF2hsNaJ4xJYH8JUYWa3J+ULnhmnkqukOSqk00XJJFxT3WTs1xj8BiaSYbi9eoEtrrNswFk5uyHFtbJReigaxMEr4zv82gZlzJhyC0GTCu+bxMT16NEVPZCYA9xpIjwRpUimNMmi+zbpKNm80XVrhqAIca3LRmHgAsdiZsGxWLiMRccJF1aHQf8Bv7aS6pwL71o/JI0+ay5SYZBnar0KrMmNpXZnapjXDquH9bXIutEvJDr/2Pm6f8dMHf7DItvb/0rhbj/CY49zpWJEtUOlS7NmLPK/GWeU9/827jNyCkxLcRHa+n/L+tlAK9VDruQsNNF400uD7N3wT99/wb0WjluYieiIzAdiXN0I1wEuHKl2x3ZYPfcmLrDj+Q7Mj4kR71dH0ZHamjObHU+oOraRT6zH5+fMKzThVlnEgrpbklRiHWFXmf08vbeGrM5orHonycuSd6gfutxTqFD6hMU6zbb6f/62/K5pO+iBMX/zUxC8h20xPHUh/c4YINUPGvnCyTYh+KeYyiQFG61o66LQX46DTXoztW7bhll/6ZMeezX70RGYiSI0E8dMFSLRO2yLdQk8FwoavYYnuDJnHnFhYqqNC9WaoSauL9dGXdQmlVJ+60AwFdEst+L755cjXsetJ79qg7GXYTImh7Xg6csizB0cQzDE7hHqEqyJda6vk0GDdElvBxH+kaqcEhz5nZFQVJS522DWcSkP3AfDml9ElwSKce0HYNruV/Bvo0WO+oScyE0JMicm94CUCNLovceSqm9wEeFyhqV60ih50SetDvEybl2YVLEjHvfyS/xrR+W5cfhqTE/FdyCennExLMk+SKeLdN47g+LZK7HNipAUSk32WiV+OOEnl5BH3mahAgXqi4A0HJ8TG47WSgsOPd/njlQgOPx44IBzOFjO60zNN5HdU9MG+7dETmRkAldbF4y0nI+sCdIh4JUunK3yql4iT5qGa3yX2Hi5ZaDK2FMIQ9TTxsaHWIOdBPbXKjDkeUXa8GlP2MTwf+b6Os+Xc7HkpG2JtMGTExKuzhXJdNRh2C/lxMLLqM/TSCHZg7g3fT+Ni/MntUqoNrbY13eCJvL/KKS9DwAsSBoKgX8+Oqo4Vx7glVMEgqdIYqHpUUXB5tbhQapXHLeI4amBuZadtpMf8Rk9k2qMnMhNAkyosNqHXTMDI7WV93Y6whEZURD7R5H8eyKf9r+neMOqGeDgomeURSVagPsW0I2mrPRrFUaCk4e8rIjElRrIrb/Bd4biWuEOhOmP9j5YRDt32CEikpKgLGghWuZYqAF6IIS9COo+4pNSY1I0q6hGMGwh6pBL2YoPh8y4wXWsG6s35WVX3SKEnMhMAlcrlwMq0QtM2bQlyQXnSJH6xPEYFEZcSYJUdb/n5yxiwuBr4agFtWfJrGlNohjVRio2Yonulliu/DlKaFJosT6CURmpiuGZIdSOVKjHpZ04aKBEnTDydP4Ip5SP3lS4AmbtW3sgluI8PFRwMliWghKYmQEY08ZQYY5EpMtHHoODxsHE3NjZGu23xbNJBurFFUOURR065sdvJuzYeVEsSzE0qM4oi89Cau/DQ39zVj1rqMUYkpOT0CA8JXf+Im7b/K5TOERN03ZOd2qowTNnQlVHpWCofzR+dVRj5K5gTgFwZso6T3xOHAqm0G+QLrdDyi4IrSPqSNGFbPkpEUkRF3BnG1mTz2DJoHqlDk8TH5OyKN0H5x3k+o9gYUtMWCqIB+tznwmaMQ7ThoUymjl8jsUZCLC1sN1a82zleztyE7QJtgQNe+zM44LU/g+1btuG21368Y89mP3oiMyG0UWIm0d8Za5GnFIfAZ+0rNExrEaV4nZhTpjYZ7/KpW9WDKFlRgU/UG0poonPaRFq5nh1RqWpHDH3bo6FEtStRYuL2I5PqCSQhNzdMzLehna1XCj7m+8iIKau8+HPJeMbZvDd+UK/y/9o8cuxLsGAkhO0Rf8aVAiMdMLbjTwxXN53a0m3LXcHE2JSkrZYd8D8zP9pvpjGEaj2PDLUxH9ETmQlAfOkLSoyObjS3L6HJI85X6C1TKIT9MR9q+9rf679gCeEJjsERDmfBl31cBZYaUh4nS03O33no9KKwpDzaVS+ku6W4jBIlJiQ73jBs6Tx13gfHBdycMn6AbySfR6B4l1K86yzajickR/ztMdJCjytynJKZIFaGuxeQMoaGksM4qy2j5HRVRm4yPoUIYevRI4OeyEwAQW9zrHXaIi6idMSKkXOL7TqWkc1r527RWnjrBfTDIzPedVCGBGhzmFUG/lIF/LivCvk+xCe5U4jcDb8SL2htVv6EJY17bpmYuhJNHxkxFFwhRkrCUUsRXxJnS5crCEcypckMvd/m3knrLPmZQmUmRuTcyamarChvWyIuQX6y35AdTY/HlJXQCeHYZFEpJ90qNyk1qEvStCOiH7XUHj2RmTCiSkyiJdvFqyRnI/X4B4TC5OE9TCxdUxXEZZeJR3U8QUp0fBK71BIIPtmKVcOV2uK2GiBGXKn1aBdBpqIuK96zFx4ThlELC0LKSkw89iVKGIqhAv9iQ7ctwbFBwQl7ltgop8oIXUmUmEirX0Orevg1gGGYhzYETLZkx2PyUhlH5Gx2GQEae0Ke9ZwakkLVbRTfLrVRmqVElFJQGMwx2jNKjAy1MR/RE5kJIq7E5Fux3ZSfsJNRDWS/47ExYVcPTyPFztSDnO1QbablmIohEodiKqmmgb5F6g0noA1UlqKUsZieAhKUN53KX6DEiETHS45wXpeQ8AQJMjBKE1ecCEcQ01JSExpNX4ukX3SEEs2lXeUrdi3xx1Xmq9FDXLExo5YUOa5IOhNTU/nk6GTbbhtnh9LKZqSIE6t0WeYTd9gen5/1dg+GnshMCGklRm4lk43xQyvhHZ/VEaCjQbUIfI93/fhXRtI9PM1E+8bC7iZyjL08/cotHhAc26Iea+HmtH+vxpSX5hZTCoyfJq/ENC1XIhggZGRYl2v+unKN2uL+BvZp15ZVVeQ7ZKc8YARCVInYhHZckQlUFg1gqNg2SQdny0x+pwxHKv09F8kSIV1sChP8aybDa54/3XVqgoDb+Ta/eMooXUsP/+038J9/9w3o4bBjr3YM9ERmEmiqxMzAzL4i8YASAgFYnrq5KSsdMtmQ9vhBvuwYU2ior7Ql6vtFz0KLx2ILPxalEYhpam2mHMQKtjXKuqOkJE3b2X7e2DNOSYgKrp3tDKn3J6+FddAnNb49Vy5M2VRlSqouxrry/lIoltbu0/5+PodMPT1QpygyF2cZZGXrtoQoPQNQTJnNwipK8wejdC3t/5pjsP9rjsH2Ldvw9ddd2rFnsx89kZkAhlCYItu0lYqC/UGaTn/e8RcYVzcseAtMJB5CKXUNI6kgQ8RfXKbROxBIhakkY5OCFS2BEPHJpEmRtaAswdAkaCn1rmyVaLYv8twNvS4dSpD8zgaSKFm1+WWmryrtVnL2lOirJSoCwTT5iItEaRFkQlGJUcI+QA1h42SUJt9pw9jw8BIEPwLK2NthYGUiv5ggkFehtTLDYZSeHj0mgZ7IzARo69DbX/IKyfTjN0V2AUXJAz9PqLXEbaV6vcUlDoCqElFAOLQ5VbLvX0xZcfnS1yCdn6SVL9hYW5Y6Vm4srbRTTEu9Dr9Toss5gJwvUg4V44gxc15cYRH9qH3xyBZTRHznIjIeJ+6GsJhc4gX0bXDOHFNiGv+MM5dSaghwRURBuji++fhMwQ34WGcP/PzRZHQHo5b6YN8eE4HfwoX3hgsVmi7efhloeHO1GKQoFe8a4GoHPUeudvD4B7//3MROkLyeqy4upXqpku4mVtEpNlR7SHw2/frOrv8CkFqwGvL9KGl1lgyRzw3R5j42QVL8b6zEUD6gyDbvZiK2i7tKFVFh5GO0ALvsQJCPxtoIZKzOa4Zm87rdW47A7B/CH3Y9JGqM+S4pMqr+iUcIrnNJJ7qd3Oy3pvsyHKrsRiqlRigpq7rEYX8f7Hft7E8OCsBAKbGLb66hSYMkZWM+oicyE4T4ck5mKLDZwo/glRB7yTYoN6W0JNUOyhlyNTlJpJWpStsrLfGiVDUnToFfaZWpCXK+tiUxCauNlRiaKE5iuG1PGNH+37g7ITGi3z3uIZ6H39VGVRuxYF1TBe+2q7DgWEnEKR4bk31IxJ4w7YiOLLP431k6u6nMdjMC4sz5T5BXnEhqRoiL6dGjJXoiMyFwJSbVutb8BRpNF6lECnLmcon+RSTn1Bwt/Fz5y4+2HZUwnLuqAyR/TT5/Ej3nU7VnIHSdGZ+4MuMdp+pNiohR/zNpU+hyMdCSKIc2SkxYju+zySvJ43REEkg+kzb+e/BjYtzEdgXXiqW1C0am5o9xJwYrzLH4GGgVDrM26el8MoI/2RsjEJIcREKhYNUZt6vEAWoiveyANLmdUt1PojdfUC1sO9o7oF+ioMf40PR3nW2tjo6u2/60Ms8lJCsLsEMK0flUuH+mZc/kHN4adLqNfMbpkVVhi5+2clM+Ukzi1dLk+UhOFpeEXBXmZtYtKz88nhqOzkkUleXFfKluOW+tJX5MKh2E5NTfta/EmFmuLSHWze5R11Ds745ezlxEPyFee/REZgKgL7BYa7VMgemuxR5DsjpjqoE0R4unTiRGL8Umx5LIDPc3MXA7SJ2aRC/ollCRyfCS5afTpvZ2hSbKXHTelYKKNlaOvG+Ul6oK/dRMRdJsnzb5nPrixcRIxXBWJigyACEpGjYexn6nxyypcQWqmrlrWsNL3UUtEAvK7bFjYqhVFZ81oo35iJ7ITAix103p/kmF2Gmhm8aAe6ATSgeYlSAvOxhQBa2j6oen/vDilfHLP6hdDlOCaFhHyIzve5zMyZAnz/NTJMorsJ9CSTdm+nljE9GJaQRiSPZztcSbM0YcZs3yC/7kfjv+vDRgygthEx4JgVNb2PlQzY8TGHFGX40iwmI5F5d7fInHxs1QTYoixo8khdObP8azmQfvsqrK1pm7Mhqqc5uflXQJHv37O/HoP9zZT4jXY8xIzBsTzTJDP9xURApLGFVognMTYmPIIe+l7UhHWt+Ixuuo8Cy82N1U15COH3e+EVsFlRUnUTHE1KBRq4ZkflGtEEYpBUsQSKqOrMyYYdE0n83PSExAZjTA41jciKOC306MGUXh/BIVGkZUOJkxakyjye9S6ZT/1U4XKObRIrGWCIYZgWTiXMpHI2nPD+pc+0n1yjDXxy7RhU2bYp9fOhb7/NKxmP7xNnz79X/crWM7AHoiM0PglZtmf2Nvt1GH56WQq8CpEhInGPG5YHTkZUlb8r4PlTIT808QYwJ/pJamNHEdfTHzCjKluvBuwTKFRrJTeSHvb2iroAZtosTwZ9OSkYhzOYJe4FztX1h+fJg3nT/G3RNNtj1CFpASFexT9Dw8suI7FVNnrLaZEiokxZHvy1xKQ0RMOkkx4elj+wcS6bFDuruBQnoV7PmKPkamPXoiMyEEP9lYrEyRre4f1oKZTkj5MbICxCbYsxVKlMzku4NSsTOe/6YitMqMrwXVplzehgSpbdocunytZ22JSgy9LoZE+EQt2uXk2RC6nBqAdlJ4JCahrtD5Y+QkfrdSoPqAdV1wsgL/3kqjlpTW3lwzRhyMnr9EeqVuoFh+koD659+h0FaqwRJTZjolHWqU38n8rKh7pDGYaQfGiQcffBBvfetbccABB2DnnXfG0qVLcd555+FHP/pRsY2lS5dWk6sJn2c/+9lFNvyVe8O2jdjS1G4RMfoZl3irIZSlVeQtrDAkH14puCm5hNdfbVcL52Jb1/Z4WG5cBYiMqGEfUfUwxCeqgsV9Tqa1n2SWkWEnhoteN8E3fgy0Ndgs2sGUH+xH4TUDufcR+/7EkSpxP9319n53vqxDPipQY2zApYad6M4eqyfAo0qMqMjQskoQf/yqw/Vxs/K1zRLJY7t/TFpVT4RXtAJ1uQJToq4oVGUPoL20/v4yVPE8mYu1g0J+dzT/zEfMWUVm06ZNWL58OR555BG89rWvxVFHHYWvfe1ruOyyy3DTTTfhtttuwz777FNka6+99sJ5550X7N99992L8kutP/p1pmJhcjD+lXhHz9GfrNdvkwbpEmoIP25ef2Zoa+gDC9Q1rXRiUNU2eA2j67KiXV8Jn2NpbZ50u7wD5NvLWSGfKTSlI+mS5bOdUbXEELG0e156cxMk4urt95SVlFYhGIr08Shq17Ewfwh25jnh/paBpbaKoww6+2/TN0yT9Cla4ZEuZjv2N1/e3IyV6UcttcecJTJnn302HnnkEVx++eU499xz7f53v/vduPTSS/H+978fn/zkJ4ts7b333li9evVI/sReN8F+XTapUfGkYCmPil60roWrInnCcyN7NLwlELxYFMBWFk2Gag9JJct9qirsmL6iMExoL3TIb3QRSvgt/UFBC5fnmTSSKk1C5XJp/HscH8IdP0e3ZID8N5XHkRaZXOl6BJJMlJy6EiVbwseGnAhKTEqN4YqMIV7FoVOKf+TMM/E0GfWkFEYVKsnDT7tHjyaYk11LmzZtwtq1a3HIIYfgnHPO8Y5deOGFWLRoEa699lo89dRTk3OKtAzdO4+8ZM2n2KCKvYOLPm1eF7bi0XLr2k/LNupPrAWdspMuS+7Rjxuj7b/4q9OvRBMV9Cx/7eZF/3BfU+1IC9+DZ7ywHc7nheEF2W4lcy/Nb4qQBlDCIyor5lhelbFkhnoTIz5ckSFkO4q2NXeOGbUMOg/MgLqn2d+y/E3La5NvLoC+W0f5zEfMSUVm3bp1AIBTTz0Vg4HP1fbYYw8cf/zxWLt2LdavX49XvOIVWXvbtm3DZz/7Wdx///1YtGgRXvjCF+Kkk07C1NRUkT+x+AH3vaRV2i10xC+DmNLgT1KWU2gEz+vJwWLKDADSBeSsOFXIV2jMecjKjNuiT4E75ihdXKGpy41NlifcH+7jpFGySKWsxJhFO935UHWQn2t83pe00pL2yz2Xttrk5Xok3h+t5FQbEivjGa/3S3VyyPYJmanVwSECNcZOgKcBlEzjoWBDc2zRCnb9sCYwqgddLJIvKzBILtmdsh1XUxSAAYaR57z2o+hihBgo0x07vxCLNWtqYz5iThKZDRs2AAAOP/xw8fjhhx+OtWvXYuPGjUVE5uGHH8aZZ57p7TvkkENw1VVX4eUvf3k2//YfPw2AVIoLpzDYaSF50UpEZ2ZhYkaAdOsoNz8LPQ+/u8m366WrRzeJ5XFb2cKqDW+klWaJlDsatj6pz/JwbtkN6VU8zrvqPIuVkiYWhJRwAhBsSLZJ2SQtJRO0vhd5hA6vfmqkUnKXQNKC74KdYORS7C/7kPnqvOzNlyaIpFaStqWDH0Iq+Nd9J8G8ym3H88TPIKaHzj8a0mMmMSeJzBNPPAGgCtKVYPY//vjjWVtvectbcOKJJ+Knf/qnsccee+Dee+/Fxz/+cXzqU5/Cq171Ktxxxx140YtelLTx1dd/2tte+qaX4dCzjgMgVy5tArZKmHwTlaBkfpQwvqdweDQAbwisoNBoraJDQaVFKvmrWFqAMlaV+619eQSFraBV2Uta6iaMqTqjoiTOJRZDYo/Bvw5pJUZWZmLPoB8T49IachPrfOHHys7TpIUneXgzCntMqlZayMglPk+Mp8QM/TR0yDVXZNQAjeKLbRqFkBXVxxTbr+x/ZbAkRmkb82Jn+e1ARXSkaKabYjse+nlk2mNOEpkczCRrqiDaddWqVd720UcfjU9+8pPYfffdcckll2D16tW44YYbkjaO//xvYcFuO7mW+oIpUXpvKwsWv9x1vMWWzGf/q5CcOC+SzhAJCk8hERlGS2WG+JLyIVRoKqd17VBMfZHoUBFBqVWdzpFVS/JKjLnHTR9Bnp6SjjbwJqyzf1TwDJouIivHk9gaX0lyBCWIiUmerCE44SOo6rzhrL7umbL+BmyW7cq5FJE3yjgRm/UnSlTMVTbdogXGJ4ASZWeWuNoJuqB/85U+zkkiYxQXo8xwbN682UvXBr/zO7+DSy65BLfeems27YLddsLUol3sdjx+IDUHSHV8NORbtMnFHIkzJaOX+NmkFBqztICkzBjwuB1JmeFl8aHaYfRNkLHaG1WDhJ0wpDh9cYPKeCJI33OrxFjiUP6MpWJk2sCSIGaXXzf3wo+wABJjE/hniQ3rQhJUGc+6znzIQpJGtdM0L4VCWEs3ICx2HpbEZXZFuLSDgjszW9SUyve4twoKg9nCuDrCKIrM4/+4Hk/809f6tZbmEo488kgAwMaNG8Xj3/3udwEARxxxROsy9ttvPwDAli1bsmndC9psy0pM0LqdgfeJWGbQnaKQWjqA24qTnrA68sSRIE9kf0ItMpVgKn5Hdt8pM3RPDPxMxtGFVIriWBjklRj+PMQIdezZDYdaw/6lvkqTL1qCRX4fuRd9sEyBpMQwqEAmISdV55eGWNvPkP6t463yvNYVI7MVayCnkoxbSVHwGxFVWcEdLyJKPcaDvV/1c9j7VT+H6R9vxb1v+sOZdmfimJNEZsWKFQCAtWvXYjgceiOXnnzySdx2223Ydddd8bKXvax1GevXrwcAHHrooQWp3c+7eD4Zlm9yiNT44qKOZkdcoYl1z7jjrKlNrxUfvaRrew18cUG8MkPTXirPOV9BysQPeGSKuTQTiM+A7Csw/rGQBRbNH5OwJ80bA/K3shvG6HCfSHhq9LwqKI8o+cfYTkp2Yvs1SDwM6WripIbOMYPoIh55KLjnm5nILy2QHmzfFvTKK8jKjiM33ZY/r4hRF5dv5sW0GcGcnEfmsMMOw6mnnor77rsPV1xxhXds1apV2LJlC970pjdh0aJFAIBnnnkGd999NzZt2uSl/fa3v43//u//Duw/8MADeOc73wkAOOOMM/IOabkS0Jn9EVMYjuGTe/7T8xTE55fRLG94PLLUgbHLrw1oxSf5HZkYLekDEvZoGjreI12p0rQledohLCMeECtXc+68hWeQbVviIaWHeY5GP0fzzDglxidKmsXHmLQ66C6i2xmFhpEV/p1/KvKi2ZIFLvDX3nHtzNO/FiaR8HhY0k4np/HSuWHXXj66FIFq3l1UKTBDIEPeJwOFAebqXL4MXSxP0Af7zi1ceeWVWL58OVauXImbb74Zy5Ytw/r167Fu3TocccQRuPjii23ahx56CMuWLcPBBx+M++67z+6/7rrr8OEPfxgrVqzAIYccYkct/f3f/z22bt2KV7/61XjPe96T9SXW2kR0f1hJeN/H8bAqHdEswm86UD14St9ScvRSkE4YJi12Fyl3SFRo4tEwoQ9sxJMoL7C9SrOXKzvnyMXs8s7ZCj8KqgSGhMAdiyshXl5iN0aWGkMglZItHaRVke9R0/52hr2KigMnN94+7WyZbiV+boLRplTBPoWJZ4lfGdXwuWtOu8dIeJTI8Xr08DBnicxhhx2GO++8ExdccAFuuukm3HjjjViyZAlWrlyJVatWYfHixVkbK1aswIYNG/Cv//qvuOOOO7BlyxbsvffeOOGEE3DmmWfizDPPLBr5xBEMK42+oKXKajw/6ao1K7/RwxLTMTJ+HEPY1eN3w+SHSWeDiOvRTV4qj3gIZehwv0Edr0nKCxFSocj18/zsRrEogxALI2zL8VqUtPqEBnw7UEuczeKJ+UhausimpC7FAiKpSuMPu2ZKTMyhiPISdD9ZRUaHyxaQBSajbQ2FfM2cSVMd0tlXQayrp+oeSjcqymEm4JsN6s2OjS5m5u0nxJuDOOigg3DVVVdl0y1dutSrmA1e/vKXF0141wby6yV/bLyQq2wtplBeipg20WbBxCAQOGQNQVnccya2CypR6qoyEiQ6SdIok66E8owTkoqR6gJLKzHWRnS7quSlMwzn0VH2ryZ/DXnhxgP1xKQl9ltrBpzhOZFDzOgtOyDkEZcmaHvbo6ckX02+ocjfNF/SQlrxTiZda/pm6pWVOPp5ZNpjThOZ2QIXsMhauMLLuFSBCdO1Q0529pQaFfEoqX4A0hICJDW0FoZWC+SDHqv8IKWa6xoZNj2MLWNAihiIrVzlTbQeCzmV6q5JS+KhDxJRiRCYBmoRVWJi9qhdS1qCyfBiz7YfsBtL68XIBMcEJYaqNWYiPPMskWHZNs6FKCz+yCSybxouVkZX36GY8sMeBBPKoOkxaQI8clyRj2FNCrDLEZhnOxaUXh2v1RPyGzFqCl/WwOSp0vvbbeHKmaeyQY+xoScyk0Tm95tu+zRPVwY+yFiCeflr3pMg5GuuwBjTAITYG8GTiMNl5xH3LZ8/kVHKqVIWR3mZJ7xs0yKL+B/3UFZikvPVFDz7PA4HllwR8pFErr+GFOYXHOxX0jUh6aQg4MZ1fPJ0Mr9yT6rUwmrtoTNUgZFUnOp77CRoc4xupyHpzNZOphEl25rDikMXwbq9ItNjnODLDvAWplNYxqvABHaJbE8hKzUsviU2eV6t4iRjY4SFIesS/PJiW6aSYy9wfl2lBSapvZiPKnJ+vD0ZW1RPSmv2djFUkC/uWJanXIkJJqUTJqmLDc1uu8SGff7tM+mzZvMbcEqMCr57i0JKM/l6ZMQ8c66c2PIEdmTSkH3qkUpqqG3+YBkECuuSZtt+Gqq8SCZSqgZVUZpAMbUmhxJ1RaFaPHLAfg0DVL+d1O/Ht6PqJT7mLvoYmfboicwEIE8qRrbtt5Dc+BjHzzjWUZJ5D2ePZ5QZ2qInpIlfG3GCO6SvREDKoinjPur6P956TZUVJBMvkCrSwPJQycubcsEeixzkdXCsTpbshDZZTAzvVhIMB2V7aUrVylQips5wRUZQWSyvkNLQkcqpixX23di/7regxSSjoLnqwREfc5myo4Tv0TIL1Jm5TGJ6jIaeyEwAfstVbhVLJKYkoHEUAp6q4KVKLlAoWCudH8+NXiIbNm9qmLSo2jBFIeaDrK5Ux6OLU4oqkZym+l6gtmiMZ70lASnVplSJoepKRe5CZikHDcM+H1JsjCZ5RfKjQ1tFIEqMzRcjF5wx1YwiNvGdPTbU3qy+qNUZ673WUX+1qdV5T1estq8Laj3ZnAqVx6ZwI5xK1ZNaiSmMh6mWT+jR4BKnbcxD9ERmBsGfuabPYBfPfJP3m2YZ4lqOnCalXsgxMsoeiCkzYRlykHBOOdGR89L2v9C/EEZtiZQjOdMxStrzUSWGqGRyEpU4Frebh6/aRO1ps5+MeIpeZUbAgFCJMX/NsyepMyQ9X+Wadi8FY/a52x1w1+rZ02w7/kxKk+WVFeSmcIzbjRzLHE8Wi/mtuvSjltqjJzIzjCBWJjqSY0zlR/bLXrDWs7CEALXsv2BZV4g4Sin0SCImyXll6lY+j43hTCUYYO2RlUR5keUYZN8mN2tMVVq+xFIlhqtt/nwyzTogcvDVGyTLldZS4vPHGDug+wXi4t3zQJ2BqM6YEUpmEjy6xpJtGfDfcG6hpGCfjtbq3JQhDfw3UhGREQhFQgEytpseKyq3Vc45hHmqqIyKnshMCIFUTvbxbZ6uvIyy10DJZFopZSWWjtMLIDYHTUyBcQZjygw/BrjGcEghIupIrcBEz0nwgZ5FyYKZkg+hpeZIPRNtlBJzzdu8P9PKTk0qEt1LQOSZ5WSLkJykP3XadIIKdKVrTlxQkx/7fegf87uUtFVm7AwAIJzGnUJ0ZQTz8OqC3yVQkxfh+bXDs1N5LcGph2NDi92uTSGRqXFA2X89ejj0RGZiSCsvxZJgycu8wBeVqhVKXWEKDNjL1RshFLwszbG8AmP2E8OB2hMs00f1fCbJ2wovERsT60TRnu91S7xYofHR5sXfpo2dzBNRaEazK5MYTpjkNr9yB+ldsKQ/0X+jSVqqxBC1hs/uq7zyBOeMOEJIDIwaw2f2NcXwEwsYB92n4+mSCK9eiRpi56Mh6bsgBdXopDyR6gKK/D+X0HcttUdPZCYAqryklBm+X7SV+AGXVou8MuZoHGNi96YUmJpsBGSHWVGhAhMQpPo4JzNDQH4xa9QBtpzsKNbjJJAdKxHJ5x34Ss4jh3G3X8uUGCXsd1fCD2aWnz+jwDSdbVe2A1sdh7MD1z6bdHTIdkm5Eouy5ET5iou57USRoUOwvRiZoYYaaugBPNlF+5tEeSHHcq6b545w8tyZ8t/vwMa8yNQRQDA8eqaggHqRyHmI+O3J4skv3oEnb/5n6OEwn3gOoicyEwF9RTRUYoQHu4vXTcyGyh6Elc0Dm0kFxhjgZIdb0vX/adVDJjPUgudy7bTf1aNZYjmgWEV94GlcmWV3aPwRNAlPYkpMECvj/Qn2V1+NnZiOFclrbNsMKswslu+n8whbQKaY4kJICs2j6DE6NFz7aYKZfk2cjGbpUyggL95Xo6Aoyfm0eUWe0OTTlpizpqS8LlHC73r42OPnj8MeP38chj/Zigd+58KZdmfi6InMBDCKEjPpdpLU6jYyNE9Hjwd2CNvhygyX06Xj0iKPYhBusBJ3SIwomRGVGa9smYTlAoJTafn5dI2YEhLU13woNU9bqMSkljPQ7Hg8jibsduL2TRVslzkQSb9QToyM0DwaYZwM+wQKjR2lRJSYadPFVD/wSioP7vYIHMt+9xhInuZWw5a1jZnpGm624IrFDVQ4gZ2Z8G5CMwrMcXRB3+bnjeiJzMRQqMQkKomZgm3TabeHB+mGHlcVUFyZcbljCk/gg5ZUE79rJ6bQpJQZr4yEL1ypSAf6OkzibubIblYsEJQYkVgXPZ+GXLBn3io2ITkP/PM23Ggl8Rxo/EvURn08Rmz4Hld/W1uqvigisbEEyEVYcfdEElOozKTSSA2NLtDM7niaW7PrTThmlCp6ORvzED2RmSC4MkP3u+9lr45xBXVVUna8kq/ShEQgVnHzOIcwRqa25e2vKy5hGQNpCYFUILA7JikztjT/XBJDtXO+SJAnfZMRLJvQAbENhlbDKTDeNkI1KaXElMTGWLtcgYkk9q69lFbX5dKlCNg5aZLOU2e4Y0x58bZpOjNzryEu09rGxbhRS7ouhvULMY7F+JmfLnBTw87pQp1SwEA4JbtopAKgdOOlChRmT6wMoDCY40sS9OgOPZGZOFooMRN8r9T8wSHmUnLOGIqwqydUYJTd7+VKSDUxhabyLa7MWPu0AuTkiqfLvE1zSk5jdHi/U428UYqxKl39l9f9pQVp+18oV8jZ/HSa7Xf2hILoh1vT7P4RgsP/UnKj6KglStoF9cUF9/oOeE++4o64/PLV9p3OCT2pKxtDTJnpoiOkB0GvyLRGT2QmgNJJ7sRnMNWCHRPygbY+uEITHid5Sa0fKjO20PqYr2Q0ipHJxM74k+hVW6llDKgP0t2kSsMoU8J30R7OqTjSoo5hXE9z+051aWCnJjE8rsaa0CDKD1F1iNoikRc3EZ45L/NEEVZBVZjaRoy8UOVFDYHBUENtr2JkqnThqCUoyN1K3F0V7JEZgiojDslZeWHiXMqfMpOHU8hAKeoxGmKTDTW1MQ/RE5kJIfpzTyoxqbZXymgLRF6SGkroaRLIDa3sheNeQbWNqPCj3e+Rk6CQIFQT1MWUGZsqUpFwJSb7Gqjnn0lDsbOjR7pF01JKHpmAYGuzXyJA+fLdcGpDOuK6QZbcR9QW+3swBCaVjz6eOjwudjWR77abqWZtsRFLgau1hEGHXSfvR+Zh8UKzWY8WT2dWtrb7zO9dhWqLU1rST0sZqXJlGWWn2W+gn/6uRx49kZkQaBxB5F0c7EiRmK5jZKouFLlESVQO5lwpOB5VYAIFIxYoHO7XxnJu9JJwPKCJlDgKL3hTHvV9EIsnSqhwUp62aPIcyEoMRF/D+WUkBQaIVWe2ik3M6Cs+8ySYpHxeGl91iYKTGUZiqtFHTqnxliYwH282Xw01DTu5pAqWJiCfjDt+Op9wuL+hamPUv1gxlsTUd9Dag7ajkPjvTFJg2sKVbcqTf1fR/Jg/VMYplKPZmI/oicwEoGPfydowdDtqg9ayHSOq8MSUmowCIx2PKjCkaK7AQMn7Y8qM3YooNCHZCVujxqHUMgbc7yB/Ks8EXzapoiwJjKXVQhpGGDTZ3+60XLcS5RXa0wWUQOzD6d3oekvRvhyunnAyw/NQRYZMjEfJjJOstMumfDOSGkPjYUqeo4qIaEtqONX08zUjIqUEo5TkpBasVAAhNeN4m+2gEFS9VjbmIXoiMwFoHf+5Fj93uumrqTkk+yUvN65upAiLjHIFJrafv8ZjCk04Hw4jXN7BAoXGI2yIqlqxMseJ1AihEiVG8+3gGXTqijnetFqyNj1GEpIQbf+SuCm23ADPQ07C2+cLH7TrVPlKDMnvzx8DMoeMtgw5WGeREhfEXQ0uWU1yBK7uqJ1wmfmEebw7KYUmcV2GUGXTJN4d7bqZ5jj6GJnW6InMhNBUieEVTfR93REDj77ExMowfOnFZvW1BEMkHnEFBuR4cn/Ufzl2RloSwfnkFBpRhWLlS2hO4rpFyeMgnWGOtARKjI43IDnpoEO0zXOtIT27wu/AkpgIuYn4Rk6UWFdOLjGkhqsuJh8hNGqoWbeSIzFqupoSXg/IKQjtlmz9UqssoQI6cwG1LramWZ6mwcQ9eoyKnshMElr8WpI8gW6qy2jArFiiH8waZGPEw25m9fPYKKVwv679iPlvKutGCgxCdck3SAooiY0pmJ21S1TkoKDEYKK6PInJzR/Dr4YN8KXdQ3XZjsQwPxg5smlitwPERurHkph80vvO61+6b1g5pMgaSxjqekZfyBO7NEWgzNBnWj7BGMno6rlrqiPbWJyOyp9PKFyBImtjPqInMhME7zVOKTFiS7egBdsefoyJ3RsjN4kK23QVcAXGJxFgdMjtt3kIIcrvjykwlcoin0fdRQVOgthQ6jBrsFcmPwlxfUSS0yTIN1VSnsSEZENSc9qCE6JYuSZtQCipDxpk2DX5axKQjyIkSQ7oJdt8/7SG2j7EYPsQavsQGJjh4OR5J91KflxM5GNQcFtN146ZCoBnt5PiNYbGQA2jWZ3aIvs0QLsFC6u8PToRsnoi02OmEVHEq32RF3gsfVMo8n9j6xpFgbFBNvO+jWaMx8iYzL74E5KZmDJT7CPpbiKlF6hL6SunioZxp/waLYN71hIkhmXzuoeE/bmyRJc0tREWau5fSVoZsqIDRC5/TJGxhEfb7iaYVa8BO3LJFBklKjG3AzbCDtPfl+JJhAaIqJimL5azHyMrKYJk7lRzRC5TNG2PHhw9kZkAwhd/mRJT0upuP1qEIUJESmbwtS1lrsww/2PBufmh2m4HJy3y/rDMofY6okIFxquH4kO5Y4RI0KSSCFStMcB152SOIyQxWdsRZYYuAinGyGiXLvTHV8O80Urav2ZenJklG3HGIC4QSdIEs/bSoN6auKghMJgmiswzQ2B6WNFkPVUXxLiQIg8o+1RKDScHAilR7lg4IWM9/Dpy64xCMzBLFoAMu+5AAlBAbXd0VItgypaUUvWxOUxl+mDf1uiJzCSg06REUmIC8pPJOzK0/BtQwVaiRGYjMKelnf61kVt9sUnvfGUmWi4pvjqeOQ8gMsQ7UY53IG+fZxkbtPdHLDtKYqIECDBnH2uHO3sh2aF5dXjQ5eE/jOCHYm68oAZFfm+KpfWEEB1RBijRIWssWUWGPCjWHVonKcF1aZs3JrgzmTpKvuKyCX+SOgnlT+fkRh/N8Up6dF45oZfK7ENPZCaA+IwKJkGZEjPO+Udsy5aDvVxTCk0wjLYwdoYUldhfkRlLRhTdT9LyZQxqf4N4Ha0C5cXzEzH1RdV8LEPohJfuOEefFKl3EuGI+Monz4sqKCMtoaF81YUpRKXQnA1IbIF8lFFvavUFdDumzEwDg2mNwXQ9YumZOj5meljzeyP9qNoFJhVaBUb4AK47p1Zp/PgXnSULdskAcvL5BSBNOX4ap7LM01qxxw6HnshMGjr8WqTEiO+UrlooGXWibYkxhSZi0FZmAtlRLLHpVuL+NPU1lT41VJvnLSkzIkiNjHRVFT9Q1dcyuZG23bMoDJ+mhKhAyYke175d9xuhtgnpID6xDNkWrschWD7b42O+e8RGA8Nh9dFD+SEnJMXngC3JQcSG3KXUTCGpXM0Qnsj+cUkAc1x7kdErMq3RB4tPEpq1q7TyWro60keaioMx01q3/uRcJmnDxJX/mp2HzUuO+3PiuPYjtxkjbqGfSvY/5ouwXzP/gwqc+imdm/hJQPPyhE8sa+CrfG2jeYUuHpnE+Gn5ZI7+wpD8nob5Q1/M82RG+oS+0rT2N1OXxzmH73vsQPjx11NSwXIEVpGxBKbuUto+hHpGQz0zDfXM9mp72h+t43UpcWJDlRmbvrz2MfEwdNSSdxzueBPQZQw45GUMuouNCcubH0sSBBCe01afWYArr7wShxxyCHbZZRccc8wx+MpXvjLW8noiMyHQSsq+zL3j5Dv5SOQh1bPd3DFuM6Z9538zuUnSJOKhvbc9LUciHhwqWmbUR8E3fg7iflMWJXYxG5GyyzD6fU2V73wXrnnkmdTkOPczTrz85yFHbvgsvYagyb+BunzN8hFiQv+aifCk6pELHYrYUfUJuBWwDaGpyct0rciY7PZRVv7pCKcuHuNBOnXByfWWkFNTuge985MmHNXlEaTYHrMGn//85/Gud70L73vf+/Cv//qvOP744/GqV70K999//9jK7InMJCDUpnzECH09pBQTfrwT93T8k0obQtm3eXoeEL6/bJ+8Xy4r5oOvioT+pSvcuEIjpWl1ezQiqksTEyrpq+hbgRIjkZ/kecCoLsqeF89kSIxPvEhVmXkQtLcduS8B0cl/AvIyDTej7/Yh8Mx2qO3T1YR4NDI80g7QbNuxJr6//kqP+VckgB21NIHKvVJ84vPJjL98hYGao4qNYcKjfmYYH/3oR3HWWWfht3/7t7Fs2TJcfvnlWLJkCT7xiU+Mrcw5TWQefPBBvPWtb8UBBxyAnXfeGUuXLsV5552HH/3oRzNipyIhvMIA0i9u9waMEYEqW6yrI//J+RxVgbwWt0C6BNLjd5GQOkboKtFsPx1yK5Yn7JfqKYeQzHC/SxSaOJRYfldVQCPblhgzMsIIsyHKnv3ItrNLu5VK/DbXJewYyRFoS4pI+cmJBzX7W5cT2/LiYTT9aDcZ3vQQ2D5dfYYadhoAE+jL6xNDZowbMdIxUh1UX03e3aNgf+kDpEmIe8vUv3qFGSMs8xHBBIwtPzlcf/31OPfcc3HiiSdizz33hFIKZ5xxRjJPaR349NNP4+tf/zpOPfVUb/+pp56K22+/vfE1KUXrYN9HHnkE++23X5e+dIpNmzZh+fLleOSRR/Da174WRx11FL72ta/hsssuw0033YTbbrsN++yzz8TsAPBfwPBJjNsWspXVDu2Qe3kynxUZWsyJlzg82pghw6c1OS5VQZrk9MrmB8lmoL6YF7pXyclDuDWrUulWqiWsI/7zNFKJXaE0SkEmDoKNzGglqbtPJuAxP5QjVMV5gFxXVgx2faX6rxgLw/bb7SGqUU00yHd6CDWtgelpYcQSqqHYhPdrUnxAYERC0/7ZkJolpoiBgouDSTwyNBamrKnTozN00copyH/RRRfhm9/8JnbffXcceOCBuPvuu5Ppm9SBjz76KKanp7H//vt7Nvbff3988YtfbH1aObRWZA466CC8/vWvxy233NKlP53h7LPPxiOPPILLL78ca9aswYc//GHccsstOP/887Fhwwa8//3vn5id+MgQqjzwFMq+9LmtpqpKxrmoTblbAuSYoNCwFr53PmJLWw5ylYJYbdnBNYmemuhDsN+oQ4IaYO5N/HgYO5MjnhoKww4+WTXNux8xJSb1DJJrwI6nrrlRHY19+jf0kag52t9v1B4e8+IdC5xU7G91mLdUvauh2cdeINiJ8JQZdl13K+HpZ6CffsautaQHys4nY7qRbHfSwBToCE9wDRX5a4ZeG05EnFXKEZaKlMQfNmlotStO+7MFZ1CRofzbRsEsc1ApP/ZDJuErWYSyumxztAtphnHppZdi48aN2Lx5c1F3T5s6ULGbXDVkx3c3WxOZI444Atdddx1+4Rd+AUcccQQuueQSPPbYY1361hqbNm3C2rVrccghh+Ccc87xjl144YVYtGgRrr32Wjz11FMTsQP4L60g2NJWrqzZlqwtEL5820KyF7MbHKNdX36lV0xmIqZjxZvWtWTDbusIaSFkxj/FSPcZfKInoVNi2RV0md80vaeg8bQkRkZH8rhyyTNu/Uj7Km1q5k/6MU9cc+kBqz9ciQEgDr22ay1N14G+27dXqgxlrvSnS5mI3SZucmUmOB3KwKqPNWHUlZSykr4i5BdbCvPLK8ujkp8SG9KF6tEFVqxYgcMPP7yIWDStA/fdd19MTU3h4Ycf9tI+8sgjgUrTJVoTmW9961v4yle+gje+8Y148MEH8d73vhcHHnggzjjjjLEPtcph3bp1AKp+ucHAP8U99tgDxx9/PH7yk59g/fr1E7Hjt1L9CsFVtsptk3ejeYXZCilCBEaJkUlVNKkKOlQhShQaP0bG2QpjZML9/vnmyEy8O4KpKPychUBgV0YYsyNhqJX9dBWUnYPWpFyJkNF4o0CJYaSBPIOeDfLFxrpkhlzLzkbs22BxSDeOQFBeUmRcC1WiyQ9SyZo8Q/e9UmIqNUY9vR3Y9gyGW7diuG2bFx9jH936VUHFIVuIt02cyiz0GAvmNcRgwLbLCUda1SlFpcSUlzuYHXR/VsE8fyN9OvapaR2400474ZhjjsEXvvAFL+0XvvAFLF++vGPvHEYK9j3++ONx7bXX4gc/+AE++tGP4pBDDsH/+T//ByeffDKe//zn4/LLL8fjjz/ekavl2LBhAwDg8MMPF4+b/Rs3bpyInekfb/M+w2e2Vz93QmJQb4fwX9SJ97TYxVH6gWBX851FkBUad648rQypyLCFToJDyTl4eRLKDG23huXlfXMkoACpSrYpWtiSVSizISkxYc0pkRjxuLSt/b/0uW91GbT4NZ2WER/b28M+dhS0JmRGazcR3rQJ9DVDr5XXneRdUvJXIjW+97krKkMBTsFBnPTE8vq0tmllSJ+Ycn97vaUb6O3bK1JNPl2iTR347ne/G1dffTX+/M//HN/5zndw3nnn4Qc/+AF+53d+p1PfKDqZ2XfvvffGeeedh/POOw+33norPvWpT+Gv/uqvcP755+N//a//hV//9V/HOeecg2OPPbaL4rJ44oknAAB77bWXeNzsz5Gsruz825uu9Laf/Zsn4Nm/eZLdtoSBIbpUgfTzb1spJmwqAF4grGbplP/y8ip1BdA1jew5Kv/lFVtCALoOpOUij1Y2LX/tKloWOQfjm9nPYwMqH0KpvnTBTK9nQWjdptqpSst5YuBLB5RAjEECIMYgkVpYJGoJEmNHldm4l8oWDe6l6eDlkZ/3YLRSZNSS9NcsFOkCflmrlX03JAYaLsDXG3atgW1PA9uehh5OA2oADAbAQEFPKeiBqqJqB47YANJfzfmjhSEhtchj/9ZXMjoRHlDHsHjTFJejUlTcxWiimOSXQoiVWQchN845R9Fi+PTja2/B4/+0dkwOtasDX//61+Oxxx7DRRddhB/+8Ic4+uijceONN+Lggw8em5+dL1GwZMkSPPvZz8aiRYuwbds2bNu2Dddccw2uvfZanHbaafj0pz+Nvffeu+tiG0HXb+dRg49K7bzg2nMwtdvOrpJYOEWOpslK+HpQbd5TeUhEShky45Vebk/xHHGiIUPBrK7kpauJh0RyZMLBd2jnnpdGB5ehyRNiiVLTPOO4n8a+jpjXsU3J+8gZGaIi2JOK8e4k8SsdvN3Anxw8ZYZ9QEgMJTRa18OxNdTQDLveXjltRT1lv1tzjLwESgz9W0Jkg1OOvyHkvPTqh2SHKzIlV72B8BN3K7FNy5gXZKcFB93751+BvU5+ud0ebt2KBy78YLd+JRCrA88++2ycffbZE/Ojk3lknnnmGXz+85/HK17xChx11FH46Ec/imc961m49NJL8eijj+KLX/wifuEXfgE33HBDEDA0DhiWaNgkx+bNm71047YztdvOGOy6C6Z226X6vjDNH/nEYV6cSqLCGOUTM5oMGK1byNElCjT5SPu8/fJopNgkakG8jj2P2H7Br2C/HL+D2m5JbIxuERvTJJapyJ52sTLiyDPtVw11fe2dl5nnLdX9U42+QqsYmWi8F1FeYpfPdiXm5o8hxEWR74A5q/p/XakvjsRUD4cbsQQMtg+hnpkGtm6D/snW6gIpAGpgRyzpauKVMvJS/7X+Z2prebSPznYjKcAbPdRmMjszAonfsEHR2LkS++mKSCmFfvySDLVgAQa77OJ9ukRXdeC4MZIic8899+BTn/oUrrnmGjz66KOYmprCr/7qr+Lss8/GKaecYtOdcsopOOWUU3DaaafhxhtvHNnpHI488kgA8diV7373uwCqkVeTsGOggy+KbUfaWWNssdMixFeFJ584hcTu8pI6/UZ45zqNnNlwZXP9x5VimL8xrFBVdrHuJ4gvfu61fzYxhUYyozWSo0YCv+neMbyT/WJSRItt8+Pelv8s0gkJU/a1TaQsGTaZkkHU3LYt2Kg+5RdOrPgomZGYvCE87K/SGqiHX+vt01WMjC1I+YqM8JfwwaSsUQmY2hMyzXDrNEIyUZmlDI4dVx2pHD2/6A7JVmUDGx2i6zpwXGhNZH7+538e69atg9YaBxxwAC644AL89m//Ng444IBonmOOOQZ/93d/17bIYqxYsQIAsHbtWgyHQy/a+sknn8Rtt92GXXfdFS972csmYocimIuDk5jEtpdvDJApBDmu/T1BbAdtwQsvYKnyt9dDOXJCDSp7CRzp8+Np/EnpnDmfFJFiSNl+WVDS8XC/sUTvpRwbw0u0OYN9o0CaJ0ZOJ6fxYlYAjzCkiU5ox6g75vrw2Bhq3ypB5jm38S+u1qfEKPi9kDzi/DFBxRBSVXpiHomxMTLam81XP/008PTTzgKNi6nVGG+oNSEqgrjoO2NPu3LExrtkbq0lLXAKjI2nieZpF9fSY3wonZlXwhNf/So233479HCYT9wA46gDx4HWXUu33HILTj75ZFx33XX4/ve/j1WrViVJDACcdtpp+Iu/+Iu2RRbjsMMOw6mnnor77rsPV1xxhXds1apV2LJlC970pjdh0aJFAKqusbvvvhubNm0ayU4MOngJm+ZafRzshW8zCrbEAoCZWaNDxesMbVrZvvjsXrfsLR85N7EFz0YixdYkig3djp2LfJxUuon8mt+7BEYZXRYbcRYty3wEzkn3W9+lZ84O2XaZOSnJgzNYsk8jeHa8v9L+wnK9QN86rzSjr6fA8OUJ6NIEHnsFCe6tlBlKYuwpeiRFvhyeTWl37bw1p8JGQewJbgKqBhkyFa58PR4S1HcgtcdeJ5yAg/7n/8SB553Xqd2u6sBxo7Ui853vfMfKTqV4wQtegBe84AVti2yEK6+8EsuXL8fKlStx8803Y9myZVi/fj3WrVuHI444AhdffLFN+9BDD2HZsmU4+OCDcd9997W2E4MU2xJ0BWg/fTMlppvXivQS4XabKzT1V1UrJ6zSsssWaP4SdRvhEgLVMemsjUIjEZLUqKbKh0qBSY1eio8womQpPVnZpGbQSMXySMeTsT/edzd/TGvfAmLj301H/jM+cibN2aT200lkJkhPiY0dsVQNuVaaPVtTA+jBAHoA1p2kvJ+1x9sKyExIUjSZCE9+gnKT5OVA1Ry6HaYbrZxU+fOayJS2hHI2MlizZg3WrFkDAHbiujvuuANnnXUWgGpSu4985CM2fRd14LjRmsg0JTGTxmGHHYY777wTF1xwAW666SbceOONWLJkCVauXIlVq1Zh8eLFE7VTwR/hYV8XWbWAHEsFOI4IqWKSYlCSNry8/FhIPjRMN1BFAOodvg3tUxMXaqNE0pCKneH7WXHBOfDz0EIG8appwd8JoEShoen4Nk/n75SfPduVBENAjLroCLy1T2wEQ65NXtHp2P4EJGWH+MHJjKpPwI1S0lUX07SuRis9s50pMsoNvzYfttaS19VET4MOwSbsip9lKpalytqeFltiNLY3SreY83rNhIjMXXfdhWuuucbbd++99+Lee+8FABx88MEekem2DhwPOh9+PZtw0EEH4aqrrsqmW7p0qRiU2dROESJKjCE1QQxNKvtEoLxSpfItr/CUC6akmPNUjMwY7qJIMu1shKW4BK7dGL7MY7EzQF1hRclMLvYlHxvD/aULZo4TXCGLpytUYkrIDaoyDYkxz7Qf4OsIfPaZjhQi/zyJxKHpX2KHEBeJ2Fi+wZUY8zGEZnoItX174Eg1Ukm50UpGkUndBuMKn8TOPyvbnRQPnBj9uYoTodlFbky301ymMqPEyFAbOaxevRqrV69uZLfTOnAMmNNEZtZArBAEEhPPklViRpH5bemxRi+zXXUBhSSBUw3eyWMJj08bqn01m1E2N6kzWKuUdwHFJq6TlZmqRKX9/R7R8cpyO6QrzCfak9PJo5fs0Ra3Llmx03TwySHdL9nxn0EV7DN5UlMBZKFZuWzbESK/C8veZ4mwENiWuyHElMCY267Dj+tOAouN0dUikduehh4yFjQ1gJ4aVMOvB7ABv54SY5gSvT1EmfFqnxYT2sW6lAaAXbAx3SXlKzMKEJcbcMOwe8w2PHH7V/HEGIJ9dxT0RGYCcK8Hg46VmA7eLUykGD2t9s9b1VK6IHAIhomaEW0xykqRIU8qkc7s8XyJnpCqR1uVKy+y2dQVa3MD4/YkEiymK1BiAhLjlZ1+CsKzYkoQs8NHK3lG2N/s74Gl924f57aczIBt14oMAkWm6k6iw689xJSZ3OUjtkp/kx7pqF2iq18qm0a+ciXdS7wBk0xn0fzZnsuqSxKtB10Aex13IvY67kQMt27F91a9r2PHZj96IjMRyK3XpBKTiUfoHukWNq/IvW4kALbPn+6j6WEGRLPA3Wqctq/M2DLh78soM1U5qF4Gisxqw4J1+XVX8O+CqDAJ7C2nvJQqLaOqabLNyP7Ica7EeIfJsGppIkIwhcZ9d6PLAlXF5Au28+cW1MeR70orp76AiR+aqC7aiCbaKTJ86PW2pzH8yVbsO/0UnqM34yHsjkfVLrUiY9QYp8pQZcYQGg2kA30V/aqtYwqGK7kxgDEVxjzLsS4jp7aMBwPlJt8bqGH9vXwZg+rc5nw0jIzmYpxsYx6iJzIzBKlCoSQmjhn6iedkGOqzEiaSqys0UbGI2K52m9Y6nW6P5A32kvKkVm2srEiAMC2tTWxMzF6XdzFQTTJkN6XEpNXAiLLDvxtCU/hSjSUr2s+7m3gi6a/Nw9IbolOzNi/od3oav/jMRrxr+C+YAjAN4GPbj8NNg0PdzL6Ap6bwou3DniExdFewmygsMtIkJdOBnciXAidVrhvLkC5jo+S5J/yvR48idLJEQY80vLk67Bwo0vwqcK1fwUZ6avzuPqJ9uDlZonOSGL/phGfsXMJp943/QhuS+eP56O2XfFLi9ZL2Oz9j++X7Maw/8eqAXjP52nUFf/kE6bzpsgP+fq+Op1Vd5JnLPYt5Z1l+tq29i06kDC5pBEwB4kKRHnHhN5QQGLNMQbXSNeqh19XSBPts24x3TVckBgCmAJy37Z+xz/STVpFBPQRbnBDPc1t725acKDPEuuwympgVk7yJ0jJA+cKQVbphhH8ZBWZYZG+catCODm/uohE+8xG9IjNR8D4Q9lWaI0PKyzCuyjEO5RcquVZ379hN2Pd1kE8jdXbmuCJboploZk8sokYFA36XWaT1zDJx5SX9oq4UpEndsrAcWfoSSaRVw3K2ad6QDHIFROAfQn5BNUkhZMziX4/mmX06/O5m963Y6oHTj4Mu9QoAU9B4ztM/wn+qZ9nuo8q4Yu6TwqW//DvbtpPhSQoj/1GVsoRApqTfhaemQDHqCcqIkC99ER6/46t44p9v64N9e4wX0enhI9/FygWTIS1SGcFcLcS32Agg7n1AWOpztEO1+TmrmkzUqoe0vIGpN2JdP8HkgjZ2xnfYxc6w82b+S+dVle1XJkliNoaYGLEc8HspKIAsvfnCr09sfhd/rhgpDR95RPxgCpFTYiLRFMEwaxWeCFdbABID446b2JhApTHHrCJTTYb3kNoT04BHZqah8ODu+4aKDJkcT1JkPMgCWkAHTYzMQCDX1Qjwdi8GE9NS2dHFiokyClKLmlehHq3eM5/OsPdxJ2Dv407AcOtW3PsH8y/Yt+9amiCihJtHq+tIRSPsDLtqRvvEquBU15MlC0GrWPmfCFIt9LD7za8dpGKNv7HCovcgQN1VU/Suln2K+TcueGVa0pC6r34XX2CLEg+L+PgXt7+sOqzyCLW8duXYzRxERYYrO/795PPGODWm6l7CcAhMD/Go2g0fwzGYrn2chsJl+74C/7XL3mGMjCmGE+/gMmbOSqXSxPPShSbpr7qpWJNbWLILHpL2S2FeLVtAnsPW3UqTetHMMvSKzIQhx23w7QZKTMcPrqR8SL4kFRoYNcSHiuyjyoyXwrT0Wy5vIA2b1qhndA32o4qvyMyPw89LvFQxRWHM8QFU+Ygdb7K/OkaIpCEXMTJo0xmCkiA7BaOVjEITkEmJMPMC4JQYjw3x71TgsCSmzjutobYPq+UJtMZN6hDcqffHAYMf4z+ftRT/tee+0AucGoOB6/uxyxXQuBlamNL+3zof6vlezJWXKnqFOMmwTRIFMnqIzCPT4AEMI9m6hVFmYkfNwK95gy6ISE9keowLpXNnBoGYKfWjUfk+ci8HcamCYPg1Pcbzy/vdMCL5BKS9yh5LLW8Q7xYyw6aDLqLofiWSH68VL5Ad6msKqVvX5KXd9H0VPmsquT/IHygzlKyUeU6XL3Bl806UHLGK7ND1sxC2CoKMUYJjW7bazehbj1hCPRHeo2o3PDrYA1M77wUsmAKUqhUZhOIj/WuITXjKxCGyi5N6CUR5qTZLngrTldSuxqvIRx+w22N2oScyk4BISCQUvB7avH/427Pj0PZQoXH0g7sRUzeoMmOtGD+tMsPya6Mg1WRGJFfKyC2sXFmZkRwtJSvS+XnHE2pJfDh3zFbOG5K24X45XUIlLDAUS8tn+HVxL/yvU2iYY8HfgNBQsuMRHyfHKzPcWpsupXrfdNW1FAS3T00BC6aqCfHM3DFUQqGkJeR/bec98+C6jdwdypmt1JzRfv8uNmaeNv/HhV6RaY2eyEwArsHHWsHeGjRcwuc2ZCWmLPiXtXoL8qRWgKZm0xPZse4mcwqRyfQEHQiavKR5m5N2YRllxjnsKhKrzHh+h754gcApBYYv2RBRaLxzzECacG8URMlLgRJjzlEUN7Rs2/GD2j5RX8Su0sCJjJ7AZQ7t/1WJuXEMYfGCe+G+8yBgQ2zsjL7T08GPRi8YQC+YqgN9lSMvwqJJhp+BnYLJ460zSbPXx6Bcd5G00GMJgeFQ8AOEfZVFixPYjaubqfKlc7M7HEYZPv34+q/i8a/1o5Z6jBnupU73kWN5AxG0eQPk88SXBvASFRcvdQ3lzBnVgSszFkT4qdQaR2Y0S+JLLNqrZGyKwvMJFJqMZFNmtrs5ZkQzOnO8xEYmr/+MK7fPgpAo6k9pSzSiwEjpVC6dQGrCodeVc5orMlDAYODP5MvUmKBbiWT1/tr9sVpMhwSHbaMmN01eBTyM2gsQVvQ4yTOmGK/qEs2joN4xYO+fOwF7/9wJmN66FZv+cP6NWuqJzETApe7IKJECJUZSBCQUV4oq8v4TfQyDBfkSA1LZqUUczfl4io1zzZQafKNb/hBtX5mRlzdQdu6XwJ6GVWa8c4QsyWvPDwRD0b3zZOjyxZ273bE5YXJKTHTUUkRpiUORUW+SNEF8IOVqK2fQBJELrIkyE1FfDFGxH8AF99qPtnEy2D4NTG8HdN3SHQyAqSnohfWnVmQ4qbHBvu705dgZ+VLZgN8UTABvGQvcMaEwz0Yu9WiFnshMADwOoNFrJ6h5mmfJJi5+S/gkoY2NeNKI7TpTRVLyCkq1S7F9UpWrPGWG+9fospC81q7JP4E3cEqB0bl07JjQDnf7DblgGTX5Huwzu2iNTpLTWa+D2XsDZxhJ4eUG2/5aS2J+7YiwR3aGcFMhD4c2vRoMgKlBRWjqBSMtaZFUGEGR8Wb2TSCkj/7Jynwofid3VMwbGtMFJ507t70ReiIzITRt7cbyB/s7eHBTNpKxMkS58OJhWH+LP4opNnEdwEcMETGl3vZfad4kespVSB7ZsWqQdD6RIdpkdJWkzFifIgoN036CNPz8xoVUREMQ8xQ8mxLhkJencAoNsVPfl9SSF9y5VBUsdz+FNnyCQlIS1cVLo0EUGV0vFol6Hpkh1PQQeruLkVG77ALssjOGO01BLxxAT8EG+0IRRQZmn3ZkxpAYdgr0OQriXxRcXIzSdSyJfFGrodZk4UY7wZ38JCibR3vbUmzMIPok9egKXSwx0C9R0GMG0KClMUMPaFKZiBwMVZGE89yGZvnYJm1clysnpi0rv8yleXGoe74V4nbsIE1XvOTB6ODEODjbGEGWDwX7Y/ZE4pHYp70EptYn2/Vxmy7mBHc+95c5Y2NivHIqFcYQHG8mSAVgagpqwQI3CZ6CDfCNKTIS/wpOgis3XjpGLJSQRLLH3Cl59AIX7Nwz8d+w8vyUOxzLH/t5or706BQ9kZkBBBVOpp5HEMeQK6FF4KhRNAQHJIVDKocG5aZUEbrftMw9ZcZar6gKV2ZsGYoEEHNlxiRjSkxsiLaoEmUUGG+oeKSbip1xUqEZHQnrOlLFFCkx3JSy97h0XiOr1iTIVLAjobb4yosK85DuKWW2DXHh5MU8I2ZpAo16Hpl66PVwCDOuTu20ENhlp2rotY2PcYoM/5ifuhcMbGBIgjKHmBITXioLOuLIKCkpGFWlCU0oUWKqNEOnAIF9lC6ePl5B9VPNz1NFZVT0RGZSKArw9V/0ImkprTRmACLhQFXZ8f79aGYDZVQP180j5lF8iHYKRsNx+a15bjbjXphHVWRGOkjTFQRqR+f5iJGRHIR8TZSYeLufkRjSreQrQzLZSSozZHh1lLxHlBdxwjtug3335pcxDI6SHEMzpupgXxPgmyIv3mVgzwa/x2TUka+4xBcOsb+p4hFLccVkVKjI3yblznsthj7/o9iYh+iJzASgC0cpBa3VAiWmswUII5VkakZf05J0ByOkQ1vOEdiySgkr258jxpphaWDVLV8NIkqJVVfMtiMz5ppKMxBrSOee7iaSlmnwj+eRuptt33OyEuPvpyqhpMSUqIbmetLYmNKZgn2uoaxNt9MRm8rBalt5youkzLi/ldLCjhniQtQYDHXVrTRkV1wp6IULgJ0WVvExC5RdMNJ0MXmjlewyBPU+TjiES8O7cXiMjJ9YZ5Ubyb6Sn4hGMGpNaexMtUjkPK1lJ4Af/ctX8fi/9PPI9JgQpKBJeYh1fJtWOOMGD7AlHnmKhvMKweRubj8lGJWB2HIGdP0kjYwyU5ciKTPeEO3AI3MSkJUZch4CxROHcLu8adITg1eBt0WElDr7jMQAyLT5SVpCUho5RWcu4QTdJyetISkxmuyHv98qHTSfITx0hVSlgAULqn1TU8DUwCoyQbeR9OGI7bfOmWcmvMKdzeXChm3TmXoVkCRIbct3lyT95LjLQ39DZhD23NVtRgn2XXzsCVh87AmY3rYV3/2jfh6ZHuOEQGLcfrodV2JyMQmjjmIK1QmhOBab4vaTL3a/XIkzriN5AjpsWkqvbUpBmZESAaKiFFVmyHlo+HPomFd+ScxLyWSAksttkazqEkqMmDzy7DVVAi2Bii6aWnCFUmVKCgzImfH9tQqDofvuCEydblg/gYNBNexaKWDhgmpGX7O+0gDyWktceUmwAvPMKr4/TNpZE6Za59JdeeU933ybQls1pl25JV1M8swxgyYrXu6IYAJgaxvzED2RmQBiz1ZTJabNgpFNkScYqBUMpjggpsTUyoXZR5iJhgqUGT9dlZcqM7ZLAYg0X5wyQ/0QlRkdOCQqTNauFl7uXrdhmUITeNy2GZZQXkgSS6DtV+uT2x+m53ZSJKJuzzOibpdDEE/PqDChw95Qa03Shk7Zv9EFI2krlys1cM+Dqh311Zj6fpO5Y/TCBdXyBFN1t1JEffGIjSssJDjSlcn8AGPdQ0atqYgGJShyY6IpqN1RMYj8Tnr0aIOeyMwkEkoMPz7aWkvNfBLpQUwOAfw3UkyhsYebSuNKzKMBOyEe5U+8cvaWN5CUIaLEBJV48LINyQynTOMdlcRRdiXFtY4iJKbROl8AaGxMnMQk8qcdD+8Jt8f/xozHiBD5KOl7rchgwYIqyHfBAFgwqEYpmbljFFxfjKS+mDQFKBUdpGSVG9rORaNsDI17AtqSB3dqoz/fKYFqPqOfR6Y9eiIzIaRap4Hyovnx0oqg69eDpzVErZtlCpwXvkLj5dM1MTHkIUI8pEn0wuUN3ArWxtPQRxI7Q5SkYIi2EkZW1QqNRGacv6y4wqUdvKNdBWx7JcZ8KVFi5JFCljNE7GZ9or8Byy9VqMKImcPvigyp9o7xJQ1sYLBMVvgoJWVm9NW6JjFTUAsXQC+oupWGU5UiMzRxMmRZguyaS8o4Qh2CHYYNmpwSErNNJsxTMBPemTuWvoDScgYmf49ZgNwtLLUxD9ETmUnAtlJjx1OvkpDEJFWYxDF+KPkCEyQQSxbEvpNIXpEBySpLG1BlRjxuSUpamXH7mXoUITN+xtiWSe13d42j4ogJDvI+SZpixyLPUVsSY+zmYnKSoC/6EidImmDAD91PWsKU6JiEql5fCQum6uHXIYGhRCVwzWfyoZ+Knxxx2OaNn3DJKKSYChKqLC1fLj1GR09kWqMnMjMAb5VgGtgbEJZ0q7lZmfK+tBW5xo+NSrIp2EKS4pDtzBBnSZnhypSbRC9UZjzfajIjKTMunRb8VI7McP+ZvzCeyBzBJ6sdt4JLF3BMKTGujQ/vGrtRSiGBcQqLrzbS/b79unz67DMFRZN9wXWLnpj/oRI9X5KAKjHe8CsNu9o1NLlKdbcSHXY9XEAmwSPdS5bQ8Any4L470qPd0GqQdFY5GQ/ckgRhGVTh4Xm6GLIdlmeGZceOqeKuth7zGz2RmQk0aVVK+YRWc7EpNow5mo83CO2GAquZMgpHxp1oMpXyLshc8RgVNr1NUg07h4xVcWhRUdtMTdGMkzT1ubbdbW9SqbE0iXE7zVdHHEtjsWKrbKee1ahWFfudJCUPFaRT5HuQS7RNnm+lqsjUqQF0PezaMBC3RAF8omJMmctXIpeYv8rfJZ0hT5vYJZygREljx93fcfCJrE1VlGrOoI+RaY+eyEwAXqtWeNCySox3PNSuy0kM+96UaHAiVdcE8ogjdh5GodFWIKkT+aN+eOwMVWaCuWbqa0GXN+BkxtZHxqYSAnKNosFaoy7GxxEUrli0U2jCezgOpLpxqCARU2IkH0dxO9clauNktPu9uLqU1vbEGWIziIEx+Ui9TCe/s0TH5tN+ZaJU1aW0ENVopYVVsO9wgcJwClaVsR/z7CpjFJU6Y9zmHwJptw3UZRPfpUctaW+5gFFoQOV+H0MzMchCWRH++xtfxX9/o58Qr8cEMHrdRSR4sYAmr5yCylRc/yjuU5MzlHmUFDtDSIRAZrgxS2a8/gGeVh6iLSoqRJnxd+bOZTZAUGCCjbgSE72bPJgWEIiHVCjd36TriPhoSAolMFI5fB8lM2QfDfQNWrMK1bMyUHYItpkEL0pKpNMJWwKho5zYKPeX/upDpUb7Sg7zRVZpaFptXYxT3hL0hGcmsfhnT8Din60mxNvwsX5CvB4TQOwFXqrEBK+WxLum9DUkvoR06qBg3HTdaLarTkvnjeEVpa/QMGWGqCiSbVGZYaREUmasHXJhNcJJ9eSFJtkxJV0mxfKOV4YpV2D8/SklRlJmLCdgQ6zNwB++XIG710o4jsB+9AQ8KJ/YAP42JVKmrhf2AfBVGNIq1moANYWKzCwc2PljhmZpgim40Up1vIxdokAgOeFEeX7BVnmJ/N7sUgXkahp1Jj5BnT/SycDEvdhtNcx2OaUwinrTLxZZYwRFxrMxDzFnn5/bb78dr371q7F48WLstttueOELX4iPfexjmJ6eLrZx3333QSkV/bzhDW8osmODMWMVSRYRJSYYMtHGdioteSubSot9Ur4CYeWZaJN6Nrh6YMINw1lpZSOWLBLfg7S00iLZzSs+3siPX+/Uu6jzOX8Kkb63NJ0jHdrt9O20De5J3CtwuzqRJnaRKWEk+zwxhOeTtj3mg0qBmVLQA7osgYmNMZKH+23QR8N/phI3P9KKKCMWheRBJNqp5Pla1ZtMsPbFECf3i+1RCsNrR/3MR8xJReZv/uZv8LrXvQ677LILXv/612Px4sX4u7/7O5x//vm47bbbcN111zWy96IXvQinnXZasP/oo48uN5JoDTeNiWlPiNKQbKhUAv6WMsfJwowA/C4h7b96/cUe48qMVzZd+JHYripioubQLHXsjHWRus1GSrkaCfXQa7829/wk52jL4gWQI3Eyk55rJkhdSCg0+PNEbXili6TGtzNKtSQtzcEIugaCLifBd0WYgp1LxrNL8kkvd7OP/DXpXVpVBfmaKn0BUWRofIwlPPAIjOt20uS72db+fgGGHxn6Pioqe2XPmFIF6oqCH4tDllkwMwDP2VZyj1mHOUdkNm/ejLe97W2YmprCl770JRx77LEAgA9+8IM45ZRTcP311+Nzn/tcsZoCAC9+8YuxevXqTvwzL2n74k4iosTk2jmjvvei5kPmEuc2KkgnmdXwJ6Lz08nzr0jdTe4FLU9Yp+HITAoB0dF1y5u92Cs/ZSaXKiF+53y/R0GuHQ3ESYx2O+P2NOEJ2uUPn22JZLAxMWWiQ/kzTQmlZvsZqbFkRkrvmER1frUaowduPxUsXR44klIIK+qoylE+8SMUIdlmV4sh/FJ6Q3Ca2smTK0NsyGR+jUqhZUm/tTmIJs95ysY8xJwjzddddx0effRR/MZv/IYlMQCwyy674KKLLgIAXHnllTPiW47E0AV3bSXgvYzdW1OzTwjV8hP6LH08f3irWHLMO7fE/mDblaFZPm/T26a1jJxFdFFHxHDbxA791JHz0jr85NH+PjX1zSX1SUw1wi5GoEkeq7CQa8xiY9y8Mp5rIrkZCfZmKn8fPQZGWNjDEEyEh4rA2q4l8xkotlCkIzW0pzc6w2/tiK+MmEqfEhofdLf9PuJlM4SkkZmGKpFCrdygvbvzgsQAjbuQ+q4lhzmnyKxbtw4A8Iu/+IvBsZNOOgm77bYb7rjjDmzbtg0777xzkc0f/OAH+NM//VM89thj2GeffXDcccfhhS98YSf+yq+RXEWSONgFYnaFeoLtDhUaDdD+IQ35hZZWZpxxak6aPE8eoq29PMo65nxWbCM4Pw1xoUyazVih5xH4H6mk2kC8TZrvZ95o+kdQTCT7VEVp+cylphiw5IbHwEjkJMHgiahh/bbHeJ76uyM19GA1R4yaqv5iwEiMCfIlAb7iXDLmmUs1NQTi4ohCwPhCtaY2pOxwazOpnenykWyHZRrwIGDRrzHxCoV5sMJ1j7FgzhGZDRs2AAAOP/zw4NiCBQtwyCGH4Nvf/jbuvfdeLFu2rMjmF77wBXzhC1/w9p188sm45ppr8NznPjebf/rH27wRHVi4AIMFC+BL8ia1ULkQRSD+SuwKMs0oyufV/qwZ7riMn4zt97YV94YcjEAeoq28PBJJ8lykFaCqKiKvgkRFanjsjGeLxQnZJILro7y7S4hFcvXpWJ6onVGcDVUtudzSMtg5UPWF/hV/T8I+x2NqQqLscgS+EqOslh29JIoci36qQimxoEQhIDm1ksOJhuu+IaYVXYPJP+lYN09SaYmU3SXmi/IShfSstrExDzHniMwTTzwBANhrr73E42b/448/nrW122674X//7/+N0047DYceeigA4N/+7d+wevVqrFu3Dq94xStw1113YdGiRUk79/5/l3rbi//HyVj8P04RUhYqMYkEXT3HYqtNMi7Uh1yhsSRAWEKbkwpveYMI6dH1PDEpZaYkT1KZ8fZJ89vA29NKobHnHD00AhJdmMJNEwlEZF2l6ArXzL4l7mFBxJZRYYRKzFNoVK2guH0+WWHKDflrnz+P6Ogw4NdAVYRFGRJTLxJph1yTSfDskGsS+GsvhUqOVfJgJr4L9/vExMCpLnmMPjGexgDdTLQmCFA9DHoi0xqzksgsXboU3//+94vTv/nNb8bVV19dlNYEVKqCZvB+++2HP/iDP/D2nXTSSVi7di1OOOEErF+/Hn/+53+Od73rXUk7h37qfKhddrEVi1q4kDkFEB3aPYtSc897UFX80IjwK/XYtdI8ITlkmpWanQ8jSVyJCQtP+JQ/Yx4I3ESZ4f55dV2KvRlD3rG40jX6fYvcn4Ykpj2hYiSCiwCBIlLubxYCWTH00SMwxNMgCJgcM7tUrch4Skw9GR4dreRlpJeWHqMKTO61w2waEiMcsgQ5ZTKmysjbQn6q8oz4pNpL1jMZEV2QvPl6aWclkTnssMOwyy67FKdfsmSJ/W4UF6PMcGzevNlL1wYLFizA2972Nqxfvx633nprlsgMdt0Zg10dkQnXsBFIDEHq9VFU+eTSxOoVIV9uZl1aXPJH5bEXHXQJ+d072uah2XLKDD2PXB7rL2tFOw994ZsrNHyhTF6+BKn7qS2KuphSJMbbDjIWtemjw7yBUN0RSLpVkHjLVBpizTNyAsXSe8sXkDSG7PgjlmrCsgB2fSWjxgztyCWiyihCbMx2cHqUMXFmxXy1n+BCVPtaRHS6WZi0t22+x+Jp6NDqHrMXj931VTz2zdugdb9EwazBzTff3DrvkUceiTvvvBMbN27EMccc4x3bvn07vve972HBggW2q6gt9ttvPwDAli1bsmmLXgOcxEhSuUXmxT5O8Be+2SnV/kDY+qZzuXACxMiMK1JYH8krLCWPSPkSBEJYq8lUdvzUJfWmeZNo9DZUGZf1nxmvehTZs/NLtq8ix1Tku0us2XY8fwtIokNKiIg8OlUMFCw5MaqMWa6ZBvT6M/bqUK2haWh/mCJXMThtKjUF7glIUlGxtR/+1vy842rd5xWkeQrpWS3EPi86Afu8qFqi4D8+Mf+WKJhzw69POaWKPbnpppuCY7feeit+/OMfY/ny5cUjlmJYv349AJQRIrMInoaLCeBJhA2NdCs3OKQjn6x/5Xm9wzHbOkybLJu8usRhw+a6sTRuW7FtmkYV5aH+cvIl1vNem5bbVfGh3F7abj5RTgbni3wv3VBrz4yOjJmxZSpSdnitTBqQa26rWSlmhvw+3EcFD48fH6NgxQlyfoZ0GtuEX3j2UkNVDWGpJr+rPq6LCS42ph6CbYhKMIl05PbbdZRYUhuga7pzVFnFrpTGoFYDB8rEz8xupIZjq/rffEM//Lo95hyROf3007Hvvvvic5/7HO688067f+vWrfjABz4AAHjHO97h5XniiSdw991344c//KG3f/369Xj66aeDMr785S/jox/9KADgjDPOaO2rOAokWJClTtNkzhaar/GHOyl8guNBszRITyvJgOjY65DwA8gQg0gegSh5eaLnlSEz7NyyhG3C0PY/tx34KTI0SUWJVzmBqQY2w6QNKq/cxU4djzBwbXxQqOJjzMJHhsSQx1x8ZLkKI6WBn8ZnW3Hnw6xVreVUFfPrMGcRfyJtfiASYDze7qQsMStI06MHxazsWhoFe+65J/7sz/4Mp59+Ok4++WS84Q1vwOLFi/G3f/u32LBhA04//XS8/vWv9/LccMMNeMtb3hIEDf/e7/0evv3tb+Pkk0/GgQceCAD41re+Zbu+PvjBD2L58uWt/AwmE6PHpPStCmmeT0Hlab2Gk+BpXg3w5QnkbMqvTOpNRbYBlyRceFKLx73WPmmVVl1Wzq9gWQObRXu3hM8ETE7b7YsN1Sb+coyrkoit55U7TkmIZgfoxHZRu4bQpSa2SxLKRB5xbhnueAUeeiKdq423lcpXClrpSnEx52RGKdWjlmAmwiNLFAST3xEndCArwXs2ve6lxIXgywuYEeAp3W+gQkJiRjvZbcgLTvaxMTOALlpD8/SWzTkiAwCnnXYavvzlL+Piiy/GX/3VX2Hr1q143vOeh49+9KNYuXJl0YglADjzzDNxww034F/+5V/wj//4j3jmmWew//7749d//dfxzne+EyeeeGIn/npqRbCTvfRjD6pQibR5pjXqCpyDv9Q8BkN21RWWsvtJ7agYmWHGfKKgvGN+0X7MjEQwoOHNQ5Ne1oDY4cYYORLLYn4IlybwP4bSkSGlnQecmESPC6qJ3FaPmpJtp+vnlhB+J4m/4mR4YPs8IqKcqmJm9zXkxRIX5eejp6PI5aREJ4C2aeyzqNy+6o/2u6LaLE0QlJ9QalT8+Q7t0qVc2y1F0KsvDPOUiIyKOUlkAOD444/HjTfeWJT2rLPOwllnnRXs/63f+i381m/9VseeRRCds6PkZ97tNFViYzWXQSIFXk6feHh265FElujQygV5ZcZUuj4x4cZCP0Myo+osvjLj+Sr5T+yLC2JypFQTPtFeNGE+iUuaV/4kJSZIr+nfzHOpBTuWONB9RnGhyosKnUucL1dZFPtr05E0bl+YSA/I9yl4o5VcfIxPbHSttNih2ew0RYdgiIMm390+Q2KIjlWg3oTn12xJgbK0Ck7NMbMK00/ZW6ufybdHN5izRGY2wbz4eUUQW3vIQVZo/PSR186ozIYTEy2E39GaQVJoBALC8/uEZ3RlJshVG3Pbqt52yozNY1vWCtA6UGzo3DhlqCbS8/fkMWqoZrFaAgTPTyymSCLUVHHhk+PVVTNJKA2/zvkrsGNGWgIjEdVFnOGXm6jlAaPYajtCSbnoVKqwcDnB+67DfXRbCc9XAl3PqKta2PTISyavUWdGwQDzK+i3i2Dd+dob2BOZCSFozdoXbeyHOoISM6aHOeAhghITR8AKvG9OmYH7NbZQZqxNS17yyozd7Sk0jlhxj5WwD9IxRgqKXuyd3Lt0XEtUianz2mMJEkMzBzP8SuqPVKgwciywb/lASOr5iKXgNyXY9mbzFVHFyVjSQpQXTmK0y0IICv1IZEaH2wUwccddwJCMpuZs91EB1W672rVf3nyiMcgqj8U25iF6IjNLQFu3Zof2DprvI5AXMfYlkjlmj9cnWtUvWKGJzQiI3cVFFk+ZEU14mcK0NJUjNRpEZWEkKDaBXTh5HilF2F+dT3uFxj/aDFGRriRPoRIT5DXqSiknC5QT4fmNqSt8W7OPgKA7KZVHYqGV7GBXtfaHXSuf2JDJ8OjQa7+7iThCyYgif5Sp+DX5GycututJuQUiLTkhx4JTiz2nKgwCDi9L8xrSTqiXTVepL/OLtfToEj2RmSEEDVSveRdJGG5248ioL5AGNlxSWfHgyownpnhKDMQuq3iMiZS43G/JXwk0RaBBaWlvnVZVFK0xmSmIoZK8TikxaUNtljIgBCll2ygsLKGKqDyBuJEtnWxHHLGBvEaNodtWlXGVbtDNlDJuyqcO0fpbCfsSNvzYmjDwNsiDuN2UytIkxkYsM3MyRnmZ7zym71pqj57ITAKmFVpSEejIa1Cc4l1O18a/LITum2q/U2bsLvMyl1q8gBtqbYZEJ5QZU2SozACajNlWJHF+iHZEXan9DrqwIOc1vkGHC1DaYwSpq1ydY9eREMJjElP0zGHvYK6LyhGMIO5LnDvG98Ptj1S7RSqj+0ufgagSk1BzTHekW4JAkUUilafEmCHYPoEhpyMSHO/simodRYZQVxPelZOK2bNYpLZDxXskkHg2G9mYh+iJzKRg3nCxF31J9jkEUZmpd8aUGZNM0f803UmRUlDkYyOLU1w5aph3/CRmxPyRBGHcV+QvNxwjMZqnoYikF9I2uQ2GSBpyQYdZe4tEEtXEL0SnJQ/BoZhq4r63fyLcb2Q0dKeSzP7ZhmcavSLTHj2RmWHQCtrrJrAPpJIDJQND8mui7YrG0RE7NoGg0BDFxdNQEsG7njJj0rDGuDgxnWUdVd5QeamOJZUZHpBo1Rx4Nt15VDb9mB9N/HXNcikeIUWrRkWedMSG90sesCUfaP7C58lyCz5nv+iE+bDjmh+HH6xrvoM8HkYdE5QYaeQS+ZlVSovxlw6xNkOujUozsEUFH2ur/mg7d7xxgjijnOKi6Hf4E+BVptoRAa7imG1z9tKEeGY4dU88euwo6InMhBHnJJHXxigMe9LsPCppKJJAyGIq0wQ54iOaJDIjI3Es4q9tnRdcwOgps0DhGakVcqpfTBER0zVJFsgVjeyU5yn/zSTP0igvdDZoBTeLr1VnSBFcnYmcsugEVXEEpxn1c38567a7Es9Xwh9nM8Uuu0X+aQtTzJvRS11c8l6R6TEx5B622HvF2+5WgSmx471M2Yy3LiPPQJUXlkaxLFollQz7ziX5XCBwG2WGqV2mItO1bbbcghw7o+qRTr7f/mVIk6JxvXtEu7XqFOwWEhslJtyv7DUyZIjGxojKjRDj5aXjE+JlTyQiowsqjvcB+06KV0RVscsQTAF8wcggNsZTYJg6A3OsvurKLQxZAhsjQ39uqhowZZYgsBPRKXm5gdmEepJkEQoqWPxPQc2fSfN6ItMaPZGZGMiL2mvaVdvy5HgNe8nH/BAn1YdM52xFOhj5SSovdS5Geux1pMpMaETwoEBh0fCXNSA2FdkjZuWNYnaLi5Z9GBUFCoz4mHk7EwG+uvBvLD3xk5OaaFm0uy743WTKQarS9LMrwE4w7RQakpipMl6XEjWaWsyJO6P8ryrYH9pwz2H82QmmQ7B5Xb74UOuZqwnnCV0ZC/7r21/Fo9++DVp3EZy946EnMhOA1iqot8XWrId4y9a3nSt8xNcDVxrIptdQkhSamPICBHEv1oyXhSki9BjZ8JUZ38+kMhO0Dpkx4p4ObAnKTHQrQq0KCGATJC0VKjGp+WNyi1LG8nm+NXkeOTms62HvkjES0+ppD9QT5Y9cIiRGHK3ECQ3C41LXk1FmrOJSq0I8RsalNzE06XOh6zPZ3XbOGWdrwGy5eV/mabN+hjFKsO9+zz8B+z3/BEw/vRXfvOZ93Tq2A6AnMrMJRGaPtZda2RsXYhINr6AF5cWqFKWBwJIyQzK2UmY0418ml0hyakJKWFSU1PFjnt/caME9VbosXQwFSgwnKY68IPEccZ2KkG/J3wwpF5F5himpJTGsfgXN70VgwWemQQCvnfiOPBQeOdH+voSi4tKnT6wLdaI0QFiZtEWFskUiWxIfwwV7EOQfizIb8xA9kZl1iM3cy2tK9syOWik0qmi1FS+ozUChkZoXhHFUX33VRU6aUmZqY4XLGnBlxqu8FSnPk3lIGh2SFhkuUWyiu5J3ToqSlaIoJiZGMiIF+0tuwJHv+voG2WLl1entSzzoqwE5hjCdZKfeVvy4hnDiJBtTXfRAiXPGeItF0qHZ3Ka0n51aKZqOWqrUlejbJGK/PK0ZCWXicpr5liH3PXo0RE9kJoRYqzXZ4iWVBN+vpXSjOjjqi4XbSAUEe8pLO2UmKM7PCk6AfFdpKl+haarM2LQEYUCwjhxLo3o+mitx9HkLDhcoMaFJ1fw5M6QmR5oieds+jgH/LCHwhMRwwhLblmzJpMZJRqYCdxW5rrMSpUNZc1b14C4bcWgAN3Q7Bko03CzA5aCEJRas6y2vMNILqRqjpOZLgC+B0hpqxNEao+bfUdETmQlAm9YhMq3WImMSiRF+9G2MFys2rFIjgbeIKRaJeJC2yox3LKrMVHmSK3EL89jAlDeyMkNseZmb5G2GVDVVrMR4aEFiEuWZqjvqQ24/EpevkMRoEG5cP5peHAxZlsBu84IJCaIjlbRhYQrwup0ARmbcmkq214qdmBQr4/JSEiRD2eMkbcNAjJJuJHO8nnJnpMdbqXky3JqDKoij2JiH6InMLILOyPlZEjPOh1iyzUmBSBKojZzyUqLMhGWOoswY2yBrNHElRrPzcftJCQ0UmpS6YSbYK4JOk5aYL5IPXIlJLk1Qn3e0Wyn2Qi4cVi3BVG3WAskrDhTK2eZKDN1nJsAbuO9UkaELR+oBIS2UwPAyEvdVVFwY4TBDrVNkQprcLofs2ky54OKk3Vyafo2lHt2gJzKTRmN53pGbkUhM03JbqQ1EmTFHApaRU2aalWUy+cqMDsUUqsxI8rjEhqgyY/ePX02ZyKiRIiUmTJqOjUkQIEN+uFFK3iUir6WP8o9J5xPbR6EYabXPkvLM0iIlRSZ1jP6VFBeeT3rk6K6kCiiIRjmII5zosZbPoiFjKX96EuOjX6KgPXoiM0G4l3jhdO8lJKZQSm+MlALD00hKTL3fkomcMmNN+DqKTWBazVyZYe5ILgbKjPYvIVdYYssamNS6PinvlGqDMdk+NcIpTDva6710ocdqGx6JCYdjk7vQ8NnSwZhkcyDy7BLQeXd4R0NK4IgNCFJC+lqIA1T9ezQPKlNk9FTNQoRFIrmy4xQeUitx4lw7abqUUPvhlitwJ9CGTEgqSuV+uR0+NLstjJ2esBQgpmQ2tTEP0ROZiYFUFpnjHEklZpLISiZc0iDZGigzfnEK4hWjMTGcUDHW45dP7AX5uoB8DSiax9d0BYFYJG9BA8WPp49BUlBS36WXe1cva/5oseHXUO4x8yYepvnpX247kcbdf1lSKn08JDXFqSFt1ZRu11nqSUwZekWmPXoiMwmwGILgMG+hxlrkbZSYUSfEs0UKCkpCiYHV7eHxCptEMd9ysTOUGDFCRFuwMW5iyQw9Wp+XuKAkQmXG5FF1uX4dKKQtVGicDTFpFmUDFeSFIGM2ZFVIeeqg/9yy2Bghf9rPPGlSsWO6Ks+bL0aTv6lyiVxgyQtfLNIoMSRmhg+7To5mgnOGHraLRUpuCUsTAGQpApWZvE65uBoJseUMBmrYE48eOxx6IjPb4TXYZqsSE0OM6bS1RciOpO5otosqEEqLHCxslmcQuRbxS5RXaMaHOFFp7go7u4B8l5rndiIZpO2SfQ3hcVvePaQQjF6yaU1+SmYA2BFLMUhdNmQkk7eb7FKQiS5VYJR/RnEXnPeJY92jme15SKf6rqXW6InMLAYNqPQPRL5LaQOjmUJj2VPqCc8blBHmDYdDK+84lVZcL5Hyj9O6lCkz0NxlkpekcU7klRmbrS7bbyyrOuZCSGudSAfydj0FRJOFIF0exbYBsUuqyAFSVvDMxm0qCHm8vO5voNKUyPNcPRnAPS+UtJDtYOSSAkzgDf3uM4/qY0e0CUSI+uSWJvBPID1PjCbKjgYfPTdbkBqSrYBgYcjqks+bda8BoO9aGgE9kZkUeMuTk5TYdszOKD6MjIYqBvdhlHdTYgi3I0P1wehxHRxqo8x4xbndnsUwT3jy3Y1SSlvS9j9hfwE0/0KeWc22i/PyfSnVJabeZB2OH1bKEdPwo/wJ7uhpKXaase8e43L7ms7lkgOd6yVwh5CbVFfU2EfLzR9O0mPC6InMJBEMVZVJTHb1Yf6d5I0eL/YxccxTXBoqNIrs1C5PY2UGpsUeOuqTEz+NdywgOGY7rcyYPHQmYHt63P/KUtgdIF3fjl7w6dFKkAlGJE9qGDUnLcltlld2LL6vuEXOSZAuuKw1ibH3mSkyXJXx4mA8NYYdM4VHCJAbqeQWgaQkwmzTTxOY5QNA7RDSHcbW9ItFzgpIRL6NjXmInshMAKYeb/WMNW2FjhOjqCk8b3abKC/s+CiT5/lfWigzlrXoYLdvp9qikTmxSzfqcOsYdHRD3hWfFq1LR1D2TMfyEJpqXvxtliSwjxdXUtgnSmh4Hmabl2cITOpqeseFhP4yAIA4629DlI9QImXXZL7p5HtVeb0wk8J87RoaFT2RmQRaqyNMsZHslSoxbX1IKQqCClHtlwlGUpkxX1NkhrmReiFWxzmT4cpMTP2RlRlrQ6NeC4YRLWuYnYP92u2w1ixyk9xR9xOjlEZ2g5XVLKP1pPobIUHW+0w5uibA9lnT5DJ5aoxKKjI8yLe6VEQGMqpN7bTKOaeIEpN4TjwSQ7bbwNkpuzmBUtQgr8vfE5ke3aMnMjOE6JDr3HthR2fskhJjvkqt5ERMjNY1VZkFyxr4+92299LWTKHp+I2eIwwxhSZXFdqkuYkck7EyKi6de5O0CMS89Jlv8ttQ8LqVrLvSBwhrX8PxPMJC0+own0mr4HX1xIiLW4fJ7x4KT0UmSpTk2BWrGzT5lSLDvSM3wl4mVa2zNAoU1Mg2dmhojZEj/vtFI3tMHOyFn30GveOstdxEXpdsxF5w0u5Q6GD7I0qHSeNt05pE58mM4F6eD8gO27y6dkogPLVborvRwiXVStzR8UvH1qyp43yX/xzllhhwCMvxiVIhMWd2/HpfIDUxtLmU5Fn042OU+w4Eio1IbqL7tLdpVA1YYpKmkU6BSZ9HbIVsv/xmF8lXYOJP1gBEpRnhmVbk//mIftRSe/REZkLwFJiiIdKkggkeTtVNHciJUedyj1BpS1KIIukpmfFca6fMGIUgRkDSykxIgMIFJX35RVRozGFeL+v8NZe6tRKpxb3xgF4/fVAV6gx3iD6fzGZAshPqjEkvEvP6rhixo0StofzUKCHK3XevLUBUGPudDbv2jgkfb+Vr0GP0QQjvq10kUvnZmsDErhSlRUoJiiswJXYHBbXpQDU/vx49YpjXSt7EUfxeKCE65HtyW8U/3GY0nZS2pGxhH/c/2HYVaJNXaTadrQgpoeTlKj95qqJt4YR8OFEritVSKn05eBXmny8hMYR4J68Jva7SsTbXzBAWv4R8vjbgSgp9HARSYkkNdycgKGE5ZXcqfPoVvyCB6fgCkGLaROmtY2+U+DVIMp/mhykGf6+2/exguPXWW/Erv/IreM5zngOlFK6++urGNnoiMxF09KPlBCT70HZVbkNbkl+S71ES5Fd8dur7jA2dOK6NnYi7mm7Qrx4BcoQh1p2tdaIK0C5fcVe2VpXN+lOUBely+GKOml/7iM1yVumuUeiYYL8uXzG/XMFl5YlCgBKKpV1HdLmBAaAHyi1PoPxjnNzoulBtFBd7zFdllH10QmJiJ7vzlBiJvupa7ai6clLDpQfwY2EGcMsOVLEyQzGfgjQ0ux0G6BeLbAo17Oazo+Gpp57C0Ucfjcsuuwy77rprKxtzjsg888wzuOyyy/CWt7wFL37xi7HTTjtBKYU///M/b23z9ttvx6tf/WosXrwYu+22G174whfiYx/7GKanp8sMsJZ/J6Q5p3xIlcKo5cUUHalFMHLrgFW2DdxMvj7bKjMFlX1jZ8eFRPm5drg5z7iJiBTRUqUqAn+miE3F0ohnJwiK3n57ShE5g5EhzfIFao5wAuyJSqdV8JQVBUOG5B9V6o1i8/JfBrdPbHRFPnoS0xDzVJF59atfjT/8wz/E6aefjsGgHSWZc0Rmy5YtOO+883D11Vfj4YcfxrOf/eyR7P3N3/wNTjrpJNx666341V/9VZxzzjl4+umncf755+MNb3hDY3vae+gMKQBTHZB+MEWyEKoG40ekzKjSgjgJkvIKyoym1y1iw6YRbBq1QoJnJkaibCJfmdGs8vdVlIjKoYWP7FoUko0wDfFFup6oz0cL5xsrkyTUydFMLVQWfv9ieaTfR+q3Qx5V7Q8bqrbJYpH2p8kWh+RqS0Bq7HcdqDSWoNCJ8JQhGGZUkTNhFoeMjTRSyk1+VxKXkoKzsQPWhD0a4frrr8e5556LE088EXvuuSeUUjjjjDOSeR588EG89a1vxQEHHICdd94ZS5cuxXnnnYcf/ehHE/I6jTlHZHbbbTfceOON+MEPfoCHH34Yb33rW1vb2rx5M972trdhamoKX/rSl/DpT38af/zHf4y77roLxx13HK6//np87nOf69D7FArISY6Vd83yx9US4GSmNTKEiU8GEpAovx0dnmZBZRvfPXLibi65T7R80kba6tHC+DUg19PbH9kWSXkkT+mx0mxUXCJ/Qf+SdPaRyKXlXyNCT3qISfkJRmhydedUKg1NOz5kNEDweJn5quRY7jviJ4eLLroIH//4x3HXXXfhOc95Tjb9pk2bcMwxx+Cqq67CS1/6Upx//vk49NBDcdlll+G4447DY4891sHZj4Y5R2R22mknvOpVr8KSJUtGtnXdddfh0UcfxW/8xm/g2GOPtft32WUXXHTRRQCAK6+8MmvHVgSFMQ6hARWrSWHfriWt3FFQkl8iBtGPYh9WhmZ2KakwSkLChoZRG2Kv+Tw/E88jSOTbF1UVjUZxLqJSI3xy9yRWXqDc1LaCczZ/7IGy59cpNhGSw7c1qcw0K6nguWskRlBSYiJPzD6jxAzcNlVeOInhQ7E1n0+m0DnalUSo40io3CdLFSiII5GqeWJGLi7qRHUJ5fOpfFRCN9f8WizSovSHn30xpHHppZdi48aN2Lx5Mz7xiU9k05999tl45JFHcPnll2PNmjX48Ic/jFtuuQXnn38+NmzYgPe///1e+g984ANQSiU/X/rSl9peJRH98OsE1q1bBwD4xV/8xeDYSSedhN122w133HEHtm3bhp133rl1Oe7R6/jH25bcxNzQBWm6hG5ZDs1nap3kpHnmZaqD46EDsWUNSOEZvzXSq2B3g9yFy7WThX2c7NBuoxQrFLeTFyjc7vpyMRWFu0XnkEmNXgptaT+NB/JL95SS+Mk53uWCZ90aTVpI2+ZCjftZbI55SGMmhhUrVhSn3bRpE9auXYtDDjkE55xzjnfswgsvxKc+9Slce+21+MhHPoLdd98dAHDeeedlu6qe+9znNnc8gZ7IJLBhwwYAwOGHHx4cW7BgAQ455BB8+9vfxr333otly5ZF7Qx/vM2++DUANbUAamF16V3LWqgUYq33Lt4743p3cZUitVyBt00OMF4QpCELTirJhnJkwhWjEDtpV4SfJiQsifNgCVPzx1SEILy3bVdE5pPaRdNFSYVkM7HP3NJGz6ti2xkEaRpWbTw5uV92SiJCWkCVGKLQeNuRcoK5Y9hxsyaSIt+tS1SJEWJU+MKSdK2loKhJL4HRo1O0mRBvOL0dw+F2uz39zNZOfTKN+VNPPTUIxN1jjz1w/PHHY+3atVi/fj1e8YpXAAD23Xdf7Lvvvp36kUNPZBJ44oknAAB77bWXeNzsf/zxx5N2HnzXH/n5TjsFe//qLzRzpqTFW9oqblsWIFfgdL+YoaEDXNFIbGv4lVK1U3lkBqDKS0qZQXh+wXm5BEESDcJafEJUUsG0roYaXV65DNEE2dl45vMcaaIkiH2i3QpeGmOj/JrZ26MZ52IcK+BjRIEJJsXjLhilJqHGcHijipT/SSGmwHBCo+yF8/fl1Ru3QKT5DOyn1IbxqVdZsmihPD644RY8cPcXxuIOkG7Mm/1r167Fxo0bLZFpiqeeegr33HMPAGA4HOL+++/HXXfdhcWLFxcrN7OSyCxduhTf//73i9O/+c1vbjWJzqjQ2rx80j/RAy/7nxjsurNtOauphbWB0oLYX7t/B3g1mMqmiTJjSAjIMY8NKMI8ImQm4koqSXVcJiLUFesnV49ihfDTiTnRsUoWX24gshl5ntqtzi2oRJHtJvEQHmmUbJYaoSSNEhJCVLyQL7Jt540BPS48C8JsvuKMvsSOVV5KSIKowPhzzEjLC7jTTNuvRCm6QCSIIqRpCFGBnZ7IjAMHHnEKDnjeSXZ7+zNb8fV/urgz+1015lO48847ve6uVatWYdWqVY3q9VlJZA477DDssssuxem7COyVYG6SuZkcmzdv9tLFMNh1Zwx23bV6bYhNvjZgzUiKbEOrrOqoOEis1mNuZBWaBsqM1f6J7aZkRjPHrPLSfqFJYVPe5ykzPFW5QtMtypUY7R0QnjM+3JoE7fp5hQKaqCi6odQupA26kRAhvZS4iIRG+8dq296K18SWcVyR9NRR02XkZWlwql5xxatQuy6q9G8xvQK3V7Ytvz0qotPTnDZdS1ODBZgauGp80mstlTbmUzj55JOtnbaYlUTm5ptvnmkXAABHHnkk7rzzTmzcuBHHHHOMd2z79u343ve+hwULFuDQQw/N2ur0+RqRCJXmVkCwmnNrlCgzHjvogMwkXMmfEmMyEoMxqoOJ2aFJRBnHmSxSaFog+T4oUGKiJCZuRtjP8pXMCTMG2Psc4dBSEC9XYqIMQ8grpwkLlmJkqv05giFDofwZcvE2GXvF/RzxmJ2Y7XCfGonIzRnMwtWvu2rMjxtzbvh1lzjllFMAADfddFNw7NZbb8WPf/xjLF++vN2IJa/1qkKpPDYfh2DH+y42sRUU+TSBgp83mEZes0+BL1EErXf2ehO7E3x/AkUg4k/b5Qy8NBG/g6xWhWBNelb0yJ/osxJe86gSw3a0fi/mG/214iLcg+BZUiO3NKnawkciSRPf8X3J2Bj716k2NiZEUaJhmtzayyqOQLI2XNfOQGk79b8Ebyi1aqaUVLaHdoK9pjDxMyXdVcU+YTBSS38+4Qf33o6v3/wR3PXlyzu1e+SRRwIANm7cKB7/7ne/CwA44ogjOi23KXoig4pt3n333fjhD3/o7T/99NOx77774nOf+xzuvPNOu3/r1q34wAc+AAB4xzveUVBCSEoakZgoKSgoGuUvjlIkO6ZihIZVTMn03J60nSMzBcimixGQ4H6Q2rE+tyCJdB2kY6N8RKiQpNlyfX/9Lwl7XYNfyxYllaS1xUSJCIJbHbiXsyGm0Xbbmi5iZmS0E7PJY2ucp84uu7PRi0TTjXJ33aWIn1voc8KeGs2fHQ2jTIL3nEOW49hT3oOfOWllpz6tWLECALB27VoMh/5CTk8++SRuu+027LrrrnjZy17WablNMSu7lkbFhz/8Ydx9990AgLvuugsAcNVVV+GrX/0qAOCEE07A2972Npv+hhtuwFve8pYguGjPPffEn/3Zn+H000/HySefjDe84Q1YvHgx/vZv/xYbNmzA6aefjte//vXNnBupW0jJb1WhshfJxiitWmaOtqTFOAEd5vGP07eU9tMbPxVJWxXq2/bKUPC6mWzdIeQltsWYGcojdVq2565yG9FMntER5YYAuVo4dCdMKylhmfY2J+b8WE6hyeQxPS+WF+SIPnFH8RvF7w/lqJzQDGCXL6gmzdOO4/K/XvcQiTVhxIUrMabSHhAlJgY7nLtWQUrgFJPxor5E84qAdIbcb6TURoc47LDDcOqpp2Lt2rW44oorcO6559pjq1atwpYtW/D2t78dixYt6rbghpiTROamm27Cl7/8ZW/f7bffjttvv91uUyKTwmmnnYYvf/nLuPjii/FXf/VX2Lp1K573vOfhox/9KFauXDlZ6TOlXHj7OyYxJn/0VBX8iVNYmdntmpXkCIDkT4LMlKIyYYxxm9xv4rzIYowfAJQOLjvlbqFN7lUJIierxa9kR0qJUd7pFXkUe+74vhZEPpmjyXPNHlNvPyMvHqHhhVDFxhzPnJYn8ih2wKJcFXFxKfIFsO4RUiTfna5JdNf25g/aBPtKNnJYs2YN1qxZAwB4+OGHAQB33HEHzjrrLADVPDAf+chHbPorr7wSy5cvx8qVK3HzzTdj2bJlWL9+PdatW4cjjjgCF1/c3SiptpiTRKbp9MdnnXWWvYkSjj/+eNx4442jOZV7wHhrVrP9MVvsu6fElPwoEi3ZorRWWGEKTRNYhaIrZcalKVdm6jQxZQbpCkYkLCXELHr9VeIgKSWTpCsSIxo13VI5pUViRKnWZxctU+kZku4HITFSkK/XYyilgbkM2uZxK1WHJyZ1l7SdCFFCJSD5sSqxUU12gr6efMwr3HXXXbjmmmu8fffeey/uvfdeAMDBBx/sEZnDDjsMd955Jy644ALcdNNNuPHGG7FkyRKsXLkSq1atwuLFiyfqv4Q5SWRmG4qFBpHEIP3C9743JDE5X0qcpuU0VmJ4eV0pMyOAjpaK+W12mgosp8yYzALvSLs82gl5ZTElpJjEMNLSrnBhO7JfLKWrepZzQxX+9ZQZ0Q3t0uaUGGafTnxn99mPJsclBYUsURAUw8iI4sdjyI9gGgUlgb+5PfMKQ119WuAH992OH9x/B7QeZtOuXr0aq1evbmT/oIMOwlVXXdXKt0mgJzIzCkXfW2WQG3plSkzT30hEgUmmV86XVsqMUUWaKDOsfCmN63GKKzPuq6yGyCQknVbR1FL3WwwjVt4yUUmZFjoqCIkpdoc+z7lFI6nkpevjoz67kWfGinT8Z+KpKu67IzQ6XKqAEh9OZkgaZe2HhMcnLi69v5QBmUk3sr4STB40i38xs/OOCwMV7/pSUHXZiu0HBmqeLhgJjKREHnDwchxw8HJsf2Yrbv/iqk7d2hHQE5lJokSKL7ZVuD8n++fA3yk5cpMkIJltyb+m7zSeh2x7h2Lz1Fi/EsqMSaZpZQX/2oh+c8eac0UJTdq9KRJTZJSTlCaqYSpdad4Rfjv8lhvCEXQbEXIjCVEV59IBqaHRyNVz4Q+zBhB0O/mLR5Yhupq0RJZYWjOU2xKsovJMmc0vfkrxmad0pccY0BOZCUPziqBT45ntcSFCONorM0Q1ySkzCggCfD1/FPhoJks+gpqNFyOrLSEEtlf7EOU2sfvfNl6i4Hka+XEQSIy2+xuoKY3ITEe/k/pWBmsssY+/XIG2+6RZfwOWQr+ToVUhwWBZmt5zVSke1IghGwMzo7BRccKsUSIULU6VL0fAy+pHMJWDcdzWNuYjeiIz68Favhy6rnBLKos2P5JSyUAiHFKG2DpKMbvcduxYQonhZMbPH1deogtNUrP1fnHwmtCVUfKiGQf/DGyyHbJKqBxZaYzMmWZEgcaqlBLsmdtOnw96E8z9Y0SFz8NoHZLIi2LH4x76hEXJBMats1SbTAxlCbqnEnCjl+JpKRmy3VlwXUQmUFnxc+nRDWbhzL47CnoiM1tApfoGqk3n88WUoGGXj8cvkoSDl9NEmdGhrTZkhh9KuBdPGGV0+d6nDpW6guotnbE1iUG2G8gj3x12IVm+Ym6pRGYAj8TQvPaYoMJo6CBPlb7AWfMokxMT+ZKCN5ooxY8sqciX7khREm5BSHfa1F9KcKr0PWYHHrr/juJg37mInshMAhpyBTWKQmLUgpTN/HurOaQ6OlZvC8TDVGBekCRtLdN8kr8p0lNIZvhCgl5+5i+AcNI8atuYrbeja0VmblVX9CV6SyMHggZcQvmr/jrC7VXJMVJi8xcoNCMQmCQEMkMJidht5Nzy7AQKjN2uUtJFIm38C+vi8YN2yarSCaKhFBiJYG6RvAOE3Vk5NM9TdTcNWnY7GSg1b0N7A4wyj8yBBx2HAw86Dtu3b8VXb1ndqV87AnoiM9MQm3h5iKOUGv8ImpYbqw1bmErZkEgGICszEhlpS2YK3StPSBzNsJauLmH+QItSkiQG4fMXIy3J53NM1RklLzWZ8X5yXHWJ7PeZSPXHxn4pf7+i320+lpbYyi3kaJWRiKpjyJCDxAhTF5+uil0GWm5pILBIwIpTzwN0QeTnqUjWE5mZQJctz1wLuiRtMRSiQ4hTCk1TZSZVvqlFc3kSZUfJjDThHrGRVGYUyUIvUcy3jELTGSIkJq3EKBKUnrOdV1qS2yXgv5fU74dyR3p/CZmx92rg8vBJ7+iopGAb7jtdR4kufuOeE0I6FONDDRZ1DE+zlDyULDQ55tpPNQv6VZjHQ7B7tEJPZGYEDVusTRWXwpZvOz2GKkG6uZGSQkzFw4qrjjUgM0mMoswIDC5FqKR1lTIKzUgQ77+g4IlQ5c9ZKYL5ZDq2z4uDe0wsCJmx2/XfwB0z95CkxiC+7e1mgb0VeXe/oHQ3TkS98c1FDpe/JIyqMrugMkrN3IXSGmrEYN1R8++o6InMJFHSiBJkfL5f/JFnW85AQGIaPvMKvE6KKDRJNcTftspMbE4XjhSZoYWkZueV6lVNKpesMuPyKlpjltj2WFrcp27hkxivdO5KlEw3cLBEDdTkE7Wj8jEDwf0Pi1E8Ld2mn4GvzHhm+X5xHhl4+/ghKASxMDaw1kyApzQGCnYivFTsjJs4r9o28SqmTJM/yIdwGYNRoQAxfqdHAwzrz6g25iF6IjNxCD/1sElYlruRUtONWMtt+K+uEV6MMcKRU2baltXVG5f7klJmDHIKDUfO15wCQ9Klr1hEOYktbyCWUar8+AbHVgGWCEwqOEW7n8sD4rIEUpSyUWFMi0HxbGnVJeImIx8ScUiTCd4O6QrK+x6/4nG1pe9O6hWZ9uiJzGxB0+cvRmI0/96iYikpl5mujtUVehNlxrZejdBdqMxwf1opM3UtxxeYLFRm7C5dqMyY7IFM0PXLpw2JCdNHbZjnSlALwzyFlRNRaFqNXlKRx0WyY1UVeEpLMHqJmhD2U1up55SuQE2zlcbIOLUjrdCUoJrcbjg2ypAaDl6ds3QJFQYh0+vRAA8+eAcefOif++HXPcaP4PXTdf0VsTe294PXZWKKV8jGzkhdQjmyU9BF1Bpd2DK1nTR5nkBq/KnyMxerUHGTfQrdkXeWSBcjgpPMcSNQ8dgx0Y2a1Hqkhs0fkyEvbjcf0qylRMQdMo+LCl2ktkIyw4mS3KU0bsQVl0l6sYOiDYGvceBzjsOBz6mGX9/61T/o1K0dAT2RmQS06ib2IFlGwm607BHKCxQQJ3D4laJQiCEmwqk3UmZSK1XTNICfLrDVkTITcTOr0Eh5Co+mkLy97GDnz6eW86pxLM0RKR6IXD3zeFJCQlQZPYD/CPO0McNGLVGOjHgdcQo2piWs8LWbDA9AavZcPlFeNfLIlSXPNZMevdRjFqCf2bc1eiIzE8g9a4Fkn/kbsZ18aY3jeRcVGoQVOVdZKGLKDDdKSUZTqZ2Wn2q1B9usLIkUlazMzbPwe/b/t3fmQVZU99t/zmXAEVGjEBYTBaEUpQiMwWhABcQEg1VGSIgbRplIlQY3SKRwDRh9X7VCjGiisTQFLrE0omB8YwQdtgD+RvnpxC0IQUUNoAUawG2Y4Z73j9un+/Tpc7pPL3f/fqjLnXv6bN23b/fTz9mS3m2izBvt+RKisCySW6EzD4p5vTW5dkyqjvhbCBgAYm0lOb5vuYLAO3c/67Sx+ydT3BTlAMgddoP4lwmIC4vMX6oDPBEkJu3LSeXrFqEMLTd2bQkiGSRkykVsMeN4FWEiBoDWJrAtUxfPdDUyxQmEiztGRHOTAnMvmRaV1jkzat1MzozvZqc4M+LPMDGjVkUpNrAx4hikaeWKLWKi0sjxpPMwUUXK9KCobc2SRYyII4sW39+eWPF19NWIGfmlui0+hPPiODhhR1RdriAJuQjlyCCNknLe5VFTYq6ZOCOdhPAh7Ekzs6+cRz1CQqYSiBQnFmklmC48iYgRn6OuoIa7t7vWjS4vC8eFAeDybL1y/EB6g8VjW3+DExMpZgzCKXJZA1/dlShZX4wMTgwPi2OxpID/nfk/29aLF0RrJvh1aPj3LgsSWbDIecmiRkrDZfEivasaRwgWJ1XAmUlCTvrb75CIJQPs8/IcmHgnXBpRJchl963XDtS0lJhcdBQiM8IejHyPhUUoN6w+8itNvNCyZQ/fHq0oM5Wj9gvSCUTt0sZqGf56cl0dLL6nmrukBMSLeA8RMZEHoQy3s4Di8NBWV9u8JIsZ71E62ISk5p78rHBHLSlhafJP4px4zUzJ8A4nSRkiG8iRqRVCBZJlXAf5idYYVecsGNwJK2fGlBdznti58ySsc2aYmkHEDnIU7jhcvhlBydvZbuvMyHlLeXJJ8KidP437nhU2Toxmu5qHVshlWqeY+Qer6BO8XG7a0ThywSYkbmxW8lwZrm9ekl0W91zgvjJlJ8YVAYwrf8sjljjkTsGRh0O7cCMPdVvi9HcJKzcqj8Jil5b5wRmGXaewfOGVhA+2/Q8+3NZKw6+Jasf28TJGLjbNMra4eZkUTJw8QsKFsxXV2dZq3yzETByyPJ4lwjuKMStegtFJhcOZ/KAGmozg/6zF5ObIysknWIPnuX9kkvM3k8NlpyT6CYVpyhGi2bQrurlt4mIlsjLOr6ZJ0bR0eN8TcXjfE9HZ+RVWvvR/Mq5Y5UNCplSIG6wvLKKpRe5DYLL1JSKbYZRtNh3DdHEC9ygLV8XNS+yKzlmxyMNXZuiVz3FmVJFjEkLGMoNiBlx6Cg8bpaTUmzvxA86Mmka3K2FYXfsMUwDEvW4Ws72M252ThqTSdyJ9LSLI3x4jCRJpjhitK6O8fHGdCivfj0+YMPgdlph3ayE4ctLII+YsY6DLiyF8+QGRV1ZfpFtevfYyJSoCEjKVSIVfExhH8gduRwTwgGpIlpdRpLh3tjAxwyzL94sZbXmx661mVkwiBHPWmE6OMp3X2gmHAY0wkcO4FFeqeJRbw/RxtMmMefndFn00WYyoB1bjAjnhWXTUVcvyDmOFX7gqnSz0ZZ1+BSRkygFHtBKwPSF1To8uvXwtzuBk902nYnJoQkSGO3meaVkDtyA5DXN0CTfnbSLQ/CQVELaMgfuZSW1LWTgzUg0ycVxMWDox6npKUWWK887CKRTh7jiVqAu28/uwvuGqnbAkfao2H7nRHFdMHpmkjlLSujKiPMeJYY4zo53kzrCcgDzsWu4j4y0SabnbgOOu2MTl1nGTUHBmiDTQWkvJISFTSaQ4B0OvfZVwboeJmSR56P6OElBZUJQ8mZJn2i9MVU0piXrwtxAx2R80fTHukle684EpVZF0VSAnU3UtXBQ1qt+x8MdTRUvQ1DF/gWr+QpyFUexvQZe/TwMqG8yOUx1Cw68TQ0Km0khwHoZev2ycmLhlqhdf1YTQOhoIETOuPRO8qmkcjfjLGDgRNHn5KpzEmXG2BZwZt7JKnpryYzs0EYRey+I6MUnmh9GUV5KbFSvU3ydm5G2iIsKNkT9rnRe4zkvBqZF2Rr0Di7go5O1zYmL3kXEmolN+WKHLDDBpqQL5t8I4cqx4i0TaEhxVJVyccteMqAVIyJSCqCfSrEV0sUV5GlfC1pnRxHOfsk1CCRHhUWXEoZhpizXiJ6vzwjYfi3ip91R2XkzhqhNjUleSQDHqt6jmGZvlAMRLzD2DiDSBbbq1lCySaeP4lx8Qf0P5HKf/i+2q3oQCB5B29HR9GjIkZEqB1T2vWItHirJt+kkkLcdkQoQ4MVbOTEQ6rTNjrCvTOy4+YWThzMg+fpgz45at5GnYl0B1y02xOuxy5e80+QkHJmS7W6Trsjjfl891MQgXn7CRCnLDOfx9ZaQoDNq5YFxh4OsjY95F3QgkBvhGHgmnJhDHQoD45rFh/mUJ5HfrpQnc/a2Is7iqoD4yySEhU/FIdoX2vYROTxqsxYxFOoEsQLKaLC8Ki/3QfiVhk+fJ1cuSqF2NsWCkPSYrI2PUr1IMpdOdQ3IcQD/5nchTakoylmsIYm4e8jY75eaudq1xMzyXxFwHuYxAfG15CIifKNxh4LFSxYeBli+Iy/sfv4QPPn6JJsQjSkCCJ1DVDc9ExJi22bpCljfkJM6MXgQYwuXiOPP6MJjSqs6MWv8wZ8ZYT8WZEX9W+pXYNINv3PTq+VgC8RxYhFx8DpsXIETEqFV336W4gOZd/O07nzz3QggbuX8MYzCeG0xKE9jGosWJIBfm8ohTW3KFbAnTd1lRKINZ9iWqMTiQtLPuEV//Do74+nfQua8dy9tuy7ZeVQAJmXIS94lZA1Ovvup2m3LiEvNG7Xt4jnBNCjckBm4zb4uaV1R4MZHqZxQzpmYmOQ+VOPtg+z1HiRg1n6zOn2KIHHFyue+GE0XWWJJ4cfNQ3RhJoARXvS48kfhLcdwUNx43fndu9ob+NP7lCuDN0itEkRBKLEK0KHnm5Hyjk0TmFR5HMxyblUYMVS00aikxNTf0v6OjA/Pnz0dzczOamprQrVs3MMbwwAMPxM7rvffeA2PM+Dr33HPTVzjkvIsSIVYXBBtn251EwxbmpTHNNqaUG+GGaz5n+HRvdKAQfnxiHRd/fXlYuXHI/LpkI2KY8jkiDxsy3g9dNb2viisvv4jRvpvwOTLcH8b0DordGkkRQsC96ftPSr8ZZD/nDJhfIKVBXnE7pLiAaPE+k5QhsqXmHJnPP/8cM2bMAAD06dMHffv2xQcffJAqz+HDh2PixImB8KFDh6bK10ia60zctDGEkjGqTZOQI2ZCh2abCrV0XBhn/qdnY12UtgkbrOrLYLU2k2mIdlTZaUnToTxgZ9jDoqbWNQlsbWaauFJYYEoepSi3SUn8LbYxaZvpLlzYGd9Ht6lGK16CI3/UOCI8x+w71XoCx0+OJe/0Gxf9QpUJ8wJDri7bkhTySH9A67OLTO0Jme7du+PZZ59FU1MT+vXrh7lz5+Kmm25KlWdTUxPmzp2bTQVtKYVDGHJj07lB5gnsmHTXzobCvUnc6Lh3s4r8oevudA4mMWMrqqywFDPVSpyvOEKgxD4kIV+tWqxNXqqW8uehuC9SXC883HZ03Rrh3hgs1qj+LGrRarXc8rXWZvE652a13EFwX+oTGrWUnJoTMt26dcOECRPKXY0g5T6/Ate44KXDF6JtgvJfdANRuHSnMYgCbQdgNT7zynLLkMIDeUs7wJzMjevj+ESFKSPNfsUSPUEx46tOWofGlggHxnfNU9teoqpgXcUi3aJMwlbn1kjvgVFKgDu0WrckgTcJnuF8ghhtJP0tmnwS7LroByO7KLKjo00D3fIDpRlhRGQI9ZFJTM0JmWKwdetW3Hfffdi5cyd69uyJkSNHYtiwYeWuViTGi1iaOULkONpsFBclCQExYyk4ovLThUPaFurEWNoBcvw0x6DYaHclYWXVLhPFvpbG/SocfElkMaOIjsC8RGpckZuSzlud2istYOY4QiWsH43OAJLLVYd0mwwjuU6VSAVXjagySMhY8Pzzz+P555/3hY0dOxYPPvggjjjiiMj0+S/bgbz3pMu6dAVr0Bz6DG8AcR7qkxoAxqUJClv9zU1xnRl44YEmrZC42nCxzXjlNAilgPuTxJlB4EAZJ89zI2g22HxJln1ggk5MSDpbZ0Y7HDsjTF+P9HVEqYLABHjS31pRo9vmley6f8ZiWcEpAfPcFK+/jPNiwjUxOyde35lCmpw0Goq5fWK8AyPilGolam9uGX15xqUJklpWtQw5MokhIRNC9+7dceONN2LixIkYOHAgAOC1117D3LlzsWLFCpx22mloa2vDAQccEJrP1l/4x/UfdOb38LUffl8fuRiWfbWf20LMqGJE19zkxg8Zwq3LB9Af0lABZF//9HnId+2UdUlMlIeQYR0YB1dWwDa1JEWVHmx08RKpOsxUF/ddvf/KM/sG0jlRmS9IFw1gntiJIvpox7FWdR2SubSbds1TIn2cE4xkjAIJmcRUpJAZMGAAtmzZYh3/oosuwsKFCzOvR+/evfHrX//aFzZ69GgsW7YMJ598MlpbW/HAAw/gqquuCs3nsDuuQW6/xsIHx5FJBWf297TAVdy7fETmYdpuuAIFXBb5g60zI5edUpxo49tgEkwW+5PEmXGjR96R0136ra5xpjhFXEIjgPg+NeGBw6iGKdX0OTHiXXZptEsPOPmq25wdcP9k8pvTlJTQaGBOWnfkUpHv8mKEk/rO3M955JC3nv1XNbAIopRUpJAZNGgQGhsbreP369eviLUJ0tDQgGnTpqG1tRWrV6+OFDK5/ffzCZnC/CQJCq43sa193Gbmvidx4kc1SWThosTIsxjFBQqoJRSxY3JrVNwwpoS5Do0mlSx4fHdsydVwRIjXh4W7AkeIVObkw9Sh1ponCtmdcbWUFI+ZnkIM4a5QMqY1nyBuXSKefNKev0wc2HpVQymGX7//yXq8/8n/0hIFlURLS0u5qxBJ7969ARTmrSkpWp+8yGVEbVd+fGK4sS9alJOh5i07HCnEDHP+j1xYUtRRvkH5nBi1XhbOjLbeMN4Q3F3KyvyI/B7VuznMn6PCS4nswEnHXVs1ptnuhvFAnKBYMWYXDASUDr9w+8oE+seIbYwHipK3C3KSE2Sa2C4HbpzhVJ6vRs7LBgZ9X5esYWDI1a2KQarh1/0PGYH+h4xA5752vLDxjoxrVvnU3My+paK1tRUA3L4zqYiy7ZM2I8UtJ0ti/h6tasb9LQGRZZkePMPqluWNOoEY4OI/9RWnTJs0WexnCURN5ClreUqrIkbX5CSLXW8eGaX9z3VnJIfGVDV3VWkhSsJPvLAJ85TqK+UgIGp8+WYynD/OYpSacCYcF4LIHhIyAHbt2oUNGzZg27ZtvvDW1lbs3bs3EH/VqlW4446C6r3ggguyqUTaG08MESOuw9o8kjZ56Rz5OE39ap3i1iNKNMQSAyla+9VjYbIJQu7QiXUMt0yTZv+ksopO2A1Y3gWdk6JzVmzeTY6MQYjojmTwyIY12zjvrtjxp/MP09Yv9Bg26om529N/YTb5eOUFw4kIRGfftK86pCKbltJy2223YcOGDQCAtrY2AMCCBQuwZs0aAMDJJ5+MadOmufEXL16M5ubmQKfh2bNn480338TYsWPxzW9+EwDw+uuvu01fN998M0aNGlWCPbIn8sGv1KhNLNomFw/tAsbaZijm/Wh18dXmLjBn1BMPxtXlYcorkLfcvhGSh6meMGwz5ZEmiq1DFPicVVuXIVxtvjPFcY696WsPLVJSHBxwzwN31LivlU3jwrifPSeGSc6Mb2VrFqybrykpZDkCtUkpDAZoJsKTtmUkYHRlZpUvuTQSedMTZsw86pCaFDLPPfccVq1a5Qtbt24d1q1b536WhYyJn/70p1i8eDFefvll/P3vf0dHRwf69OmDs88+G5dffjlOOeWUzOuemqSOSlZla65LfnHC/P1ENDd5C2kQHVMrZkLyDRNYYWKGOzknugDJd89w+yqr20ZkxnFFTMR2d2uaHZBEjO9dLkCXv+q4uOF+EeNmEObIhOL5YHLHWG0zkPw301XP3ocz7Z6Xf3Fuahn4eVI+jMQMkZqaFDIrV66MFX/q1KmYOnVqIPziiy/GxRdfnE2l6oUQMSM0jDaeLl3IzYpB3IiYJwLCnA9x0+DiWVLzWK8KlLD6BT4rYsZmf3xI+5E1tk5M0nyyLseSUO2pNhc5f/scGhFmbAMV4ob789EgHBnhyhScFS6FG5wTw7acz9XhkGcDFhPp6Q+sN4yaqDJoHpnE1KSQITIi6jdh62BowxVnRt4e0fwkF8/dvCJEgCxmIO1a1N0wTJxEiZnYFEvMZJBhHBFj+jtLnC/R/QpM9oevyUgK16WJcGR02ggINgWpDossSIKIM5hLfzvphFhh2upoArz0Nt94Vs5KaAFEDDIQMhXVr6B0kJCpWJitw6zHkK5kD2qWYsSErzkqxGnxnBlN2TauT1Rdw4Zkaz9LYibMIdKFi8DATHkxyeKcSdovhnvvsZsMNNpWF0fdP210nRMjZRxwbJjIS8nNdWPkpien6Ug4MJa4C0Jq+pgwOEOclfxysBuRwZg3yZ1VXcDdCe8YyztDt+1PnEJ9zc4PY8F6F9IwGmFighyZxNA5VUdoH+DSnPdRzfkpf1OpHui48m7argtXt8X+nPZR1GAJFDOPCr7+FUSIZoPOQVF3WyNiAo6MTtQozU0mE8fksvj7v8hOixMubWe+P3T5R53MUdtEWbLrI/aPK4cr/hwzpk7LpvgEkTXkyBDFRXEfgotFOo/Ysvsi/W10XKQ83Q9cSqTGD9j/hlFMWRHHmYFhu8gna9KK12LjOxcK1lwsg88kYlzXRfpb2mae1Ve8OORRSp4rw5WXIwgYQvvIMHhpZIFhdDmgH4nELNyUgkPCQ50Xb3kC+0nzXCepkpVwtZBP+2QJGrVEEC5JfguhzSVRaNoLYqaWqxBKouYeorwoMibsC4+yAhS3Rrst0Lk32Axkh5dOODO64r2iubaagNn1EIJJV7bfoIr3+/LyzuDmalEYjV0CwPOFV9o86hBqWiJKg3I9DEzKZ+M8mK6pYeFZwRmUyUaCnVqjyouKU+yHqSTHqQT3sVLhW+JMODDmNiO47p4qbqQ+MnHwuTcacSSvraQuHqlPEzZ6SWzPx16SQK5v0rSxyiEZQ6SEHJmKxXkKTWdWlJ4snA31AZzHbGHRtUNo6sUg9Y0rhkOTZBRTrDaUclOiijp9OcQt1bTStQjzHXHTekry37KoUV9xqqnk61vNWptAMwOuhQMS6rC4ZWaHzaEQ4itJWsKBOvsmhoRMJVNqEVNJvwEbMWPqK+PbGA6D5YKSbpniEdnQ/0UVIjoxEyWS5OhZ3AXifK+2irGU63bFwCRi5H4xgKb6CXfHmyuGe5/hXzdJ10fGv/SAmmdUdcx9WLwmquzETFi/HX+5wXqLPjSEBdRHJjEkZIjKwdbBMLgW+lW3xUZNHjbh5XJm5PqkdbfSbC81zHmolG/mqg60OR46J0a8K01Fcodf33Brp/DACCP33YsDRDshpjWI5CakYBq/0yOEk45iLEkg1yOz/FlhlWtqTiKygoQMEQuf2RAW0VIoaEcxpRAzFds0k8SZUePZxFXjZxGv6vDvmLrStXF0kg6fAOI+AcSUV2RWLFg3Tyjp6yQv1BjapAQbJycdWbk81NxkgJqWEkNChrDCZGMDRbwf2ooSyz4xpnDm2Dg85Mk4SEi7n1FkiTuNRtDYlpvFwTbmUcLbCwM452CMeftvqpeNNaOKRKZECTgyuhdX3p1kwmlxnRkeLrZdcSMvEOlsksRJjvndHrEsgRAs8jDpMDekkLZ0N7BiOj91DUdiIbLls9fw/uevgZOQIcpK2IW8mknbNJNYzGQsswJ9X5wy5L4y6vY4jlHZnSSlTS5oHBSnSO44FVFiJmU5bnmJ08rNT0LgmOJ7fR08AcN9UXRNTL7aWTg83nb79kNfU1UiCvsWNwtqRiou/XsMQ/8ew9CZ34sXtt1X7uqUHBIylUDUBTzJPbnodkm2RfkOgTpJnoijNkPFIW1fmSQkcWYExbjuV4JQjnGyqP2qA2l1s/UqaWXHRTcyiat5yPko/WzUphvh1rhNQCy8k623MrY/LCcLn4g8fPlZLEkg3Joc8o4DxMGcv+XJ73Isn4nLUtgfQz1S517jUNNSYkjIVARlfxwvPZqbk2hl8DYk+1FWlLlVsQ6MQsUcMBTlC9RlZzVazSdmNP1bAJ84CftKWUAFaf5W4jFNnPDTJkxIwRVJupFNno7zhFUYcU7fYsWtKfJ5ACkntMvX54R4JGSIzCiaCZTATfGLIjuS95VxCo1dT4MzE5YmCZEtDyW4dcQ9OcLETEh1tX1i5HTGl6Z/jOvEyK6N069FfqnVY05/F6V/jFcN+z4mYRPhmfvMOE5LApfFdWgi6xhehyTkwAp9puoVcmQSQ25fHSG6dRgxXJirmrS/a7XfSNZ9R+rzuhOPpOekT8zEPdBRTTY88HPx95sxzPNicFZEs5XWqInpxogOxclQRVMybC8ltXjJIUoPOTLVhMVTbaBfgbod1X/hMPaV0e4cc3qUauJCFz8DiummxMmzEkRSBk6MKsDlc9s4sR2Ttxv6xkS5MdIK2EKk+MNFvxZH2Ljv/rle5GUJZIEhx2OA0iE46ObI/XB05BA9cV0cbBaj1KcrvHKIem6qcwdGhRyZxJCQKQdhF3er/gFS24mIb5UuRj2yppjCwVCeuEZyJVxbB1+4QfzUIhU6Qy8A8zltqrK2WSn4PUb3jdFsl4dQ6+IaXB9tCxdDQKB4o5wKf+v0mXrPF+IndBmEDAjLvyBa4qjUqJA6hmb2TQw1LZUFw8lm+6tmSj8O/RW2OlCabgILSaZdTDKqTE144eIc42ByOPWMSGOsZwyDncd4RealKVNNG/hs+Z3EwD18OkKqyHXxpPfAbyTqBSWueHPzUA6q49CYZvQVIiO4S154wKUBAi6ICAuKG+5uS+Kc2BLVp0d1k8Li5RjN6EtkDzkypSKJY5Jp+TzVDai6m6RCHBabHSuFm1TdBzgFmoOrOoUxBH5UePAnaHZRCh+4EsjdjybXRHUpWOAP8dEfh8nlwcsnICJYHBeEqBY4z4PzdKOO0qavVkjI1BPVLmZSCYqUYsYG0ZnDtKCkL54unCF0xthaJKvmTZvmJgZA2zdG95L6x6huDeB+T74hzE7zkruQJLy42nWWpDhG90azX7pmJqIG4Dx901Cd9pGhpqVKhS5UyUjbzGzVJJOyjNC8S/TFl6Cc0L4o2rYYJdzU9KPbroTrml6N9XEEiPsuBwtxIhepFRxhfUjktPoq6PILui42w6I9/BPeORPhSXm4SyVY5lcY1m3+KqI69xJEsSBHphIpdjNUVP5ZPSUTySi2M1PCeWNC+0wr52EmLXgGEWN0XkTJvnjce5fCtCJEEj+B+V5YsMOR9fwxbno13P68kJum5OHi7t9uE5VlnSKatKi5KyU8gyekOnVkSMiUkwjBwCEtqpemDCW92gISR7jIUUwtJqXCqqVM3KPUw2hx12TcuTTHFhUZKNGwyfISk/JcyqgK2jowLp2YTpgaL6r5CAYRI8Ij0sojk4xFMu9NdPL1NxF5YkFOIosgeSI5xgouhz+u/4YWNexazrfguORjdf4tuCnF6TDMWGGiu/DymROnzv2cfB5gKfu41GkfGWpaqmSy+l0X6fpQ7nsiUFzjAlAOXdDp16MOwzE9aEXVPet9K3V5JkLPRx6v5Y7Jo5j0Isb9HNZEZfrb7QtTqBvTxZPCRDxX8ChNU25U5cTyqq3G1fTFkfLQzfprrJ+JmM5MHGyqUfha6lzEEKkgR6aUJGiycV0Z23RS1Mwf6DVUgphxSdNp1zatGi9Ombq4Uc5Q1AyH1YLRiUHwGHDnQFkcVy7/pTYjOX8HimVKfCeMSWkC2sbdLk98J8URHXrVSe6k8nJK81ROETA6RyQHfROTSMN8fWDSnSO2zoxuKHj8cki6BKCmpcSQkKkUErRGcPDQy4H+HhvjzptAeGVBBg0zyRCHJo0gsi2jHon1xXKL26WUmcmJASCPQHLTMWmbDmV9Jbcs39MBhzpcWlc/ncMS+GzcVcMcNXLeRTif1En7NBWIE5wqZr3A83nwlE1LNPyaKBqRP1kG7yk0ZkaBVFE3irKphBg49xm3dSYzV0I8nqs3Nn0dKupaKzdVxRPbqTAAABOFSURBVLXaSjl7r634DTsPVWdGi+Y71DgynIWIHd3K1rKjorg0btbKV6E6JsLZ8JqV/C6Nv49M4bOK6O+iQ7g3xepcy5x+NkkuFIX9q6yfTtVAjkxiqI9MKdDdeEy/9NhXAMsTVyeCmBKufo4Kr2Sy/D0Xp/tAciqpLpGEVDbMRfGl17zCRIyuZK14MdWB+36zahMRYHAs3AC1j0zwJyRmBA5UzyACXAFVQpFQKMfki+nnxgnPiyCKAwmZcmB6oi7Dr72q7olxsdk5C5HCkHBa9TjT+ccVS1ZLN8Qov1gwxRUJiacNM710aaX3wqKQPFyES+KGOe8IiAVZbMj74RdTot9MTlloUs5HnfSOBfIE5OULfOFMmvOlRF+puz/abWLemOjvtrCf1CcmkjzP5lVl3HrrrfjOd76Dgw46CF//+tdx5pln4o033oiVBwmZSiWrX732BuFv29emydqZiZO2Au6/oaiio1yOTUUfpAQk2Z1QZ0WNKwkbkzMj56sKJ9HUxDznhLl/6/rKeO6NP2t9s5BpZt+g2DHsnvuSOh67nZMR+GxLHOeFSAHnAM+nfFWfkFm5ciWmT5+OdevWYfny5WhoaMD3vvc9fPLJJ9Z5UB+ZSoQhsxsjh3MhraLzO7KqIkK1Xl2zrH+1iRlRXfkYcM12wHwimByZqDK14Rz60UreBHKum+JG464wkPvA+PvOyM6MMpJJboJS8gxW0TARnzGuN5svU145SdzEuSAU3BcSM0RxWLp0qe/zww8/jIMPPhhr167FmWeeaZVHzTkymzZtwu23345x48bh8MMPR7du3dCnTx/88Ic/xIoVKxLluW7dOpxxxhk49NBD0b17dwwbNgx33nkn9u3bZ59JlL0dki50qnc4lySbJ1ODKxJn8eWwfCoaW0e+igRfppRzv+P8NixEjPt78bkpihsT+L1w/7uUf2CYtdKkpKuBW7zlqtDBMH0Tk5pOCJS4k9kJcZJFp+GcYSLBartElBue55m8oli0aBGuuOIKnHLKKTjooIPAGMMFF1wQmubDDz/Ez372Mxx22GHYb7/9MGDAAMyYMQOffvppVrvvsmfPHuTzeRxyyCHWaWpOyNx444245pprsH37dpxxxhn45S9/iZNOOgnPPvssxo0bh/nz58fK7+mnn8bo0aOxevVqTJo0CZdddhn27t2LmTNn4txzzw1N297eDgDgHZ1OiHqRjOyc4b1HXBWsxUxY+rio1rtpW4muaLyzE5/+fSl4Z6chQmnqESw3RltZOZqpUpTHOzrx32eWFY65vItJxLEp3HQeaT5znWI1/s784kUereTbHkLQbfF/jk4fFEduuCZ+5959WHvvm+jcuw+ib4+N6AmUK897k+IEiPr51wLt7dx5by9uQamblZxXBLfccgt+//vfo62tDd/4xjci42/evBkjRozAggULcMIJJ2DmzJkYOHAg5s+fj5EjR2Lnzp1Z7L3LVVddhaamJowcOdI6Tc0JmdNPPx3r16/HW2+9hfvuuw+33nornnrqKbS0tKBr166YNWsWtm3bZpXX7t27MW3aNHTp0gUrV67En/70J/zmN79BW1sbRo4ciUWLFuGxxx4zpneFTKeFc+PY3Hbx1Pdox0Z7H1X6yliPYsqSDPPnnZ3YtfR5s5CJnSHq16ExoZ4znZ3Y/f9eiDzm3PkXnnecegQ/283sG2bNeaOVmHvuS6OU1LllFKfG11Sk+V36m6c0ebpx9HVk4OB792Hdff9CvmNfZj8dt+ko0gHKdhkDxkQX4MqWPO0dJRIyJeJ3v/sdNm7ciN27d+Pee++NjD99+nR8/PHHuOuuu7BkyRLcdtttWL58OWbOnIm3334b119/vS/+DTfcUPhuQ14rV67UlnX11VdjzZo1ePLJJ9GlSxfrfao5IdPc3IwRI0YEwseMGYOxY8eio6MDa9eutcrriSeewI4dO3Deeefh+OOPd8MbGxtxyy23AADuueee9JW2+B2HOi5ZioGkCcvgwFQ99SSSdCI5LF7US4lrXCgyok5hUaK2BZwM2ZkJVEWIGK/ZSztiCQi4M6YyssRbIyqy6PBtMSpWKI9GMwlK1bR06qmn4qijjvJmjA9h8+bNWLZsGY488khcdtllvm033XQTDjjgADz00EP47LPP3PAZM2bgX//6V+jrhBNOCJT1i1/8An/+85+xfPlyDBw40OKIedRVZ99u3boBALp27WoVX/Sp+cEPfhDYNnr0aHTv3h0vvvgi2tvbsd9++0VnKM6bsHPNaiXEGDBNeRH1CKxXaFPvYqLpt1DzcNTkfgpXhskqIsl5xeSkISJGN1LJ2c508aWaggVdk7DPAa3mbJOdGCFg9MOuzbubi9ieDYWJ8OI2U3lpo8QOc5YmqMETOwt4HkBlLRop7oHjx49HLuf3PQ488ECcdNJJWLZsGVpbW3HaaacBAHr16oVevXrFKufKK6/E448/jpUrV+KYY46JXc+6ETJbtmzBCy+8gO7du2P06NFWad5++20AwFFHHRXY1tDQgCOPPBJvvvkm3nnnHRx77LGBONwZCtf5393eqDgOsC4NYA3Ooee+K7LXDiR/duIxNZ5uO5Rw6e/A9UlKq6JtsSqGkNFc0wLViRAyIn7+q69879q44n9d04OpTuIrihJUkQ6A5gBauAZFJ+x7NXYvKVQscMwtzxmmE+u255eUNNSJkYdYs+Bn5ooc7jkkQnzkpHWTGHdFCc8572JOGCceZ07jWS6PPAorWvNcHjnG0YXlkWcAZ3knv4JYyLPC9hzj4CyPHCukZU6aHDi6sMKLs33IsTw6v+gAALR/3uHG6WT7CuWgkFcD2+esv5RHDvlCHsijC8t7+TorZIu4DU5cIWTcOAxogKhL3m1eyjGOBufvLk7ZDN6svg3OYc6xwrpKXVBoUmgAc/91YQw5wBU3DKwEYi0+ez4riANe5KHNneiIfY3NYx/ykvjpREbN6g5h90ARvmzZMmzcuNEVMnGZPn06HnnkESxZsgSHHHIItm/fDgDo0aMHevToYZVHXQiZ9vZ2TJkyBe3t7bj99tute0Pv2rULAHDwwQdrt4vw//73v9rtHR2Fi85HN2XQ/ERY8+HcW8pdhbpj6zX/t9xVqCv+MH5pdCQiU8T1PGu6deuGvn37Ys32ZzPJr0ePHm7rQ1rS3gNtEP10VCE0Z84czJ071yqPihQyAwYMwJYtW6zjX3TRRVi4cKF2W2dnJ6ZMmYK1a9di8uTJmDVrVka19BS6qa1xwIAB2Lx5M7p27eqLs99++9k1RREEQRBlhXOOPXv24LDDDitK/o2NjXj33Xexd+/e2Gnb29sDnZAPPPBANDY2ZlW9UKLugXHySENFCplBgwbF+iL69eunDe/s7MT555+PJ598Ej/5yU/w6KOPxjrgQm0KVaqye/duXzyVXC4Xu9MSQRAEUVmYrvFZ0djYWDLxEYe098BSUZFCpqWlJXUeHR0dOOecc7B48WKcf/75eOihh2IN5wKAwYMHY/369di4cWNgJFRnZyfeffddNDQ0kFghCIIgao7BgwcDADZu3KjdvmnTJgDA0UcfXbI66ai54dcAsHfvXvz4xz/G4sWLceGFF+Lhhx+OLWIAYNy4cQCA5557LrBt9erV+OKLLzBq1ChqJiIIgiBqjlNPPRUAsGzZMuTz/hFRe/bswdq1a7H//vvju9/9bjmq51JzQqa9vR2TJk3CM888g4svvhgLFiwIDBtT2bVrFzZs2BCYKG/y5Mno1asXHnvsMaxfv94N/+qrr3DDDTcAAH7+859nvxMEQRAEUWYGDRqE8ePH47333sMf/vAH37Y5c+bg888/x4UXXogDDjigTDUswHixx5SVmObmZixcuBC9evXC9OnTtX1ixo4di7Fjx7qfFy5ciObmZm2n4SVLlmDy5MlobGzEueeei0MPPRR//etf8fbbb2Py5Mn4y1/+YtXvpqOjA/fccw/a2trw6quv4q233kJHRwfuv/9+TJs2Le1u1zUffvghfvWrX+G5557Dzp070a9fP0ycOBFz5syJtV4HYceiRYuwatUqtLW14Z///Cf27NmDKVOm4JFHHil31WqOnTt3YvHixfjb3/6G119/Hf/5z3/QrVs3fOtb30JzczOam5sjH9SI+MyePdvtVrBjxw7sv//+6N+/PyZOnIjLL78cPXv2LHcVE7NkyRIsWbIEALB9+3YsXboUAwcOxCmnnAKgMA/MvHnz3PibN2/GqFGj8PHHH+Oss87Csccei9bWVqxYsQJHH3001q1bV/7jwWuMMWPGiLnCja85c+b40ixYsIAD4BdddJE2zzVr1vAJEybwr33ta7yxsZEPHTqU33HHHbyzs9O6Xp9++qlbfp8+ffjhhx/OAfD7778/xd4S//73v3nv3r05AH7WWWfx2bNn81NPPZUD4IMHD+Y7duwodxVrjuHDh3MAvEePHvyYY47hAPiUKVPKXa2a5N577+UAeN++ffn555/Pr7nmGt7c3MwPPvhgDoD/6Ec/4vl8vtzVrDm6du3KTzzxRN7c3Mxnz57NL7/8cn788cdzAPywww7jW7ZsKXcVEzNnzpzQ+2P//v0Dad5//30+depU3rdvX961a1d+xBFH8CuvvJLv3Lmz9DugoeaETKXS3t7On332Wb5161bOuXcykZBJx/jx4zkAftddd/nCZ86cyQHwSy65pEw1q12WL1/ON27cyPP5PF+xYgUJmSLS0tLClyxZEnho2rZtm/sw9MQTT5SpdrXLl19+qQ2/7rrrOAB+6aWXlrhGRBjkSZaIbt26YcKECcah4kR8kqwDQqQnzlotRDrGjRuHs846KzBYoW/fvrj00ksBwLgAH5Ec01Dos88+G0Dh2kNUDiRkiKrFZh2QL7/8Eq2treWoHkEUlbhrxxHpeeaZZwAAw4YNK3NNCJmKnEeGIGwoxTogBFGJdHZ24sEHHwSgX9SWyIZ58+bhs88+w65du7B+/XqsWbMGxx13HK699tpyV42QICFDVC2lWAeEICqRa665Bm+88QYmTJiA008/vdzVqVnmzZuHjz76yP08YcIELFy4sPyjdAgf1LQUgwEDBoAxZv2aOnVquatc1/AM1gEhiErjzjvvxG9/+1sMHjwYDz30ULmrU9Ns374dnHNs374dTz31FDZv3oympia88sor5a4aIUGOTAyyWgOKyIZqWQeEILJi/vz5mDlzJo499lgsX74cvXr1KneV6oI+ffpg0qRJGDFiBI466ihceOGFeOONN8pdLcKBhEwMslgDisiOalkHhCCyYN68eZg1axaGDh2KlpYW9O7du9xVqjuOOOIIDBkyBG1tbdixYwcJyQqBmpaIqqVa1gEhiLTceuutmDVrFpqamrBixQoSMWVk69atAJBo/T6iOJCQIaqWalkHhCDScPPNN+O6667DiBEj0NLSQi5AkdmwYQO2b98eCM/n87j++uvx8ccfY9SoUbT8SQVRc2stVTK33XYbNmzYAADuOjWjRo1yhw+ffPLJtO5STKpiHZAaI+5aLURyHnzwQUydOhVdunTBFVdcoe3vNWDAABpYkCF33nknZs2ahdGjR2PQoEHo2bMnPvroI6xatQrvvPMO+vbti5aWFgwZMqTcVSUE5Z1YuL6IWgfKtNYTEU6lrwNSayRZq4VIRtSxBsDHjBlT7mrWFK+//jqfPn06Hz58OO/Zsyfv0qULP+igg/jxxx/P58yZQ9eVCoQcGYIgCIIgqhbqI0MQBEEQRNVCQoYgCIIgiKqFhAxBEARBEFULCRmCIAiCIKoWEjIEQRAEQVQtJGQIgiAIgqhaSMgQBEEQBFG1kJAhCIIgCKJqISFDEARBEETVQkKGIAiCIIiqhYQMQRAEQRBVCwkZgiAIgiCqFhIyBEEQBEFULSRkCIKwZuLEiWCM4e677w5su/HGG8EYwyWXXFKGmhEEUa8wzjkvdyUIgqgOPvnkExx33HH46KOP8OKLL+K4444DALS0tGD8+PEYMmQIXnrpJey///5lrilBEPUCCRmCIGKxbt06jBkzBkceeSReeeUVfPHFFxg+fDh2796Nl19+GUOGDCl3FQmCqCOoaYkgiFiMGjUKN998MzZt2oRLLrkEF1xwAbZv3467776bRAxBECWHHBmCIGLDOceECROwdOlSAMB5552HRx99tMy1IgiiHiFHhiCI2DDGMGnSJPfzjBkzylcZgiDqGnJkCIKIzaZNm/Dtb38bXbt2xa5duzB06FC0traisbGx3FUjCKLOIEeGIIhYtLe345xzzsHnn3+Oxx9/HNdeey1ee+01zJw5s9xVIwiiDiEhQxBELK6++mq8+uqrmD17Nr7//e/jpptuwkknnYQ//vGPWLRoUbmrRxBEnUFNSwRBWLNkyRJMmjQJI0eOxOrVq9HQ0AAA+OCDD9DU1IR9+/ahra0NAwYMKG9FCYKoG0jIEARhxfvvv4+mpiZwztHW1ob+/fv7tj/99NOYOHEiTjzxRPzjH/9A165dy1RTgiDqCRIyBEEQBEFULdRHhiAIgiCIqoWEDEEQBEEQVQsJGYIgCIIgqhYSMgRBEARBVC0kZAiCIAiCqFpIyBAEQRAEUbWQkCEIgiAIomohIUMQBEEQRNVCQoYgCIIgiKqFhAxBEARBEFULCRmCIAiCIKoWEjIEQRAEQVQt/x8FEZ0yKi+gAgAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 558 ms, sys: 12.6 ms, total: 571 ms\n", "Wall time: 255 ms\n" ] } ], "source": [ "%%time\n", "\n", "x0 = np.array([0., 0.])\n", "broyden_verbose = False\n", "root = broyden_method(f, x0, 1.e-8, 5000)\n", "print(root)\n", "\n", "xplot = np.linspace(-1,3,200)\n", "yplot = np.linspace(-2,2,200)\n", "fdat = []\n", "for yin in yplot:\n", " ftmp = []\n", " for xin in xplot:\n", " ftmp.append(ftil(f([xin,yin])))\n", " fdat.append(ftmp)\n", "\n", "funclabel = \"${\\\\tilde f(x,y)}$\"\n", "\n", "#plt.contourf(X, Y, Vdip, 10)\n", "plt.title(funclabel)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "norm = colors.LogNorm(0.01, 100., clip='True') # log scale\n", "CS = plt.imshow(fdat, origin=\"lower\",extent=[-1,3,-2,2], aspect=1, norm = norm)\n", "plt.plot([root[0]],[root[1]],'r.')\n", "plt.colorbar(CS)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1.64998819 -0.15795963]\n", "CPU times: user 1.84 ms, sys: 2.16 ms, total: 4 ms\n", "Wall time: 2.95 ms\n" ] } ], "source": [ "%%time\n", "\n", "x0 = np.array([0., 0.])\n", "broyden_verbose = False\n", "root = broyden_method(f, x0, 1.e-8, 5000)\n", "print(root)" ] } ], "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": "3.10.16" } }, "nbformat": 4, "nbformat_minor": 4 }