{ "cells": [ { "cell_type": "markdown", "id": "5b8f3d82-22c4-4725-b770-3e7ddfcf7deb", "metadata": {}, "source": [ "# Stuying the harmonic expansions of functions" ] }, { "cell_type": "markdown", "id": "815b7cfe-f12f-44b5-bccd-ec06ba713146", "metadata": {}, "source": [ "The module `biosspheres.miscella.harmonicex` give us an approximation of the spherical harmonic expansion on the surface of a sphere for some functions. Additionally, the package SHTOOLS has a function to approximate the expansion given the values of the function in some points in the surface of the sphere, see [SHTOOLS - spherical harmonic transforms](https://shtools.github.io/SHTOOLS/python-spherical-harmonic-transforms.html)." ] }, { "cell_type": "code", "execution_count": 1, "id": "26685f74", "metadata": {}, "outputs": [], "source": [ "import biosspheres.miscella.harmonicex as harmonicex\n", "import pyshtools" ] }, { "cell_type": "markdown", "id": "6e2a900f-bb87-4a4c-b740-018f68100048", "metadata": {}, "source": [ "Import of other libraries used." ] }, { "cell_type": "code", "execution_count": 2, "id": "04161259-c584-4df3-87c3-979ce8463ea7", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import biosspheres.utils.auxindexes as auxindexes\n", "import biosspheres.quadratures.sphere as quadratures\n", "import biosspheres.miscella.mathfunctions as mathfunctions" ] }, { "cell_type": "markdown", "id": "bc956f1b-6941-458e-8a98-40b042c67d1c", "metadata": {}, "source": [ "## Preliminaries" ] }, { "cell_type": "markdown", "id": "4c437ce0-d21a-4043-a301-cec275f7630d", "metadata": {}, "source": [ "### Spherical coordinate system" ] }, { "cell_type": "markdown", "id": "167790fd-803d-4604-9e36-ee762fcefc93", "metadata": {}, "source": [ "A vector is written as $\\mathbf{r}=\\left(r,\\varphi,\\theta\\right)^t$, with $r \\in [0,\\infty)$, $\\varphi \\in [0,2\\pi)$ and $\\theta \\in [0,\\pi]$, which in Cartesian coordinates is equivalent to $\\mathbf{r}=r\\left(\\sin \\theta \\cos \\varphi,\\sin \\theta \\sin \\varphi,\\cos \\theta\\right)^t$. The unitary vectors of the spherical coordinate system can be written in Cartesian coordinates as\n", "$$\\begin{aligned}\n", " &\\widehat{\\mathbf{e}}_r= (\\sin \\theta \\cos \\varphi , \\sin \\theta \\sin \\varphi , \\cos \\theta )^t, \\\\\n", " &\\widehat{\\mathbf{e}}_\\theta=(\\cos \\theta \\cos \\varphi , \\cos \\theta \\sin \\varphi , -\\sin \\theta )^t, \\\\\n", " &\\widehat{\\mathbf{e}}_{\\varphi}=(-\\sin \\varphi , \\cos \\varphi , 0 )^t.\n", "\\end{aligned}$$\n", "\n", "Also, the gradient operator in spherical coordinates:\n", "$$\\begin{aligned}\n", " \\nabla f&=\\frac{\\partial f}{\\partial r} \\widehat{\\mathbf{e}}_r+\\frac{1}{r} \\frac{\\partial f}{\\partial \\theta} \\widehat{\\mathbf{e}}_\\theta+\\frac{1}{r \\sin \\theta} \\frac{\\partial f}{\\partial \\varphi} \\widehat{\\mathbf{e}}_{\\varphi}\n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "id": "6d2f1365", "metadata": {}, "source": [ "### Associated Legendre functions" ] }, { "cell_type": "markdown", "id": "5fb58bee", "metadata": {}, "source": [ "$P_l^m$ are the associated Legendre functions of degree $l$ and order $m$ defined as:\n", "$$P_{l}^m\\left(x\\right) := (-1)^m \\left( 1- x^2\\right)^{\\frac{m}{2}} \\frac{d^m}{dx^m}P_l(x), \\quad P_{l}\\left(x\\right) := \\frac{1}{2^ll!}\\frac{d^l}{dx^l}(x^2-1)^l.$$\n", "\n", "Here, the term $(-1)^m$ is the Condon-Shortley phase factor." ] }, { "cell_type": "markdown", "id": "5d541c13-eee4-4db9-b5e3-3874e2a5aa4f", "metadata": {}, "source": [ "### Real spherical harmonics" ] }, { "cell_type": "markdown", "id": "fea7703e-394c-4f0f-b12e-42e1000e2f69", "metadata": {}, "source": [ "Real spherical harmonics of degree $l$ and order $m$ are defined using spherical coordinates:\n", "$$\\begin{aligned}\n", "\t\t Y_{l,m}\\left(\\theta,\\varphi\\right) &:= \\sqrt{ (2-\\delta_{m,0}) \\frac{\\left(2l+1\\right)\\left(l-m\\right)!}{4 \\pi \\left(l+m\\right)!}} P_l^{m} \\left(\\cos\\theta\\right) \\cos m \\varphi ,\\\\\n", "\t\tY_{l,-m}\\left(\\theta,\\varphi\\right) &:= \\sqrt{ (2-\\delta_{m,0})\\frac{\\left(2l+1\\right)\\left(l-m\\right)!}{4 \\pi \\left(l+m\\right)!}} P_l^{m} \\left(\\cos\\theta\\right) \\sin m \\varphi ,\n", "\\end{aligned}$$\n", "with $l\\in \\mathbb{N}_0$, $m\\in \\mathbb{Z}$ such that $0\\leq m\\leq l$. If $m=0$, then $\\delta_{m,0}=1$, and it is zero otherwise." ] }, { "cell_type": "markdown", "id": "8f7d9b10", "metadata": {}, "source": [ "### Complex spherical harmonics" ] }, { "cell_type": "markdown", "id": "d56ca943", "metadata": {}, "source": [ "Complex spherical harmonics of degree $l$ and order $m$ are defined using spherical coordinates:\n", "$$Y_{l,m}\\left(\\theta,\\varphi\\right) := \\sqrt{ \\frac{\\left(2l+1\\right)\\left(l-m\\right)!}{4 \\pi \\left(l+m\\right)!}} P_l^{m} \\left(\\cos\\left(\\theta\\right)\\right) e^{i m \\varphi},$$\n", "$$Y_{l,-m}\\left(\\theta,\\varphi\\right) := (-1)^m\\overline{Y}_{l,m}\\left(\\theta,\\varphi\\right),$$\n", "with $l\\in \\mathbb{N}_0$, $m\\in \\mathbb{Z}$ such that $0\\leq m\\leq l$. If $m=0$, then $\\delta_{m,0}=1$, and it is zero otherwise." ] }, { "cell_type": "markdown", "id": "44fe00a3-dabd-4541-a444-b19fe15d3009", "metadata": {}, "source": [ "### Orthonormal basis" ] }, { "cell_type": "markdown", "id": "622b4712-269e-4c5a-ba32-a0b883a9c196", "metadata": {}, "source": [ "Spherical harmonics are dense in $C(\\mathbb{S}^2)$, with $\\mathbb{S}^2$ the surface of the unit sphere, and form a complete orthonormal system in $L^2(\\mathbb{S}^2)$ with respect to the internal product defined by:\n", "$$\\left( \\psi , \\xi \\right)_{L^2(\\mathbb{S}^2)} = \\int_{0}^{2\\pi}\\int_{0}^{\\pi} \\psi\\left(\\theta,\\varphi\\right) \\overline{\\xi\\left(\\theta,\\varphi\\right) }\\sin\\left(\\theta\\right) d\\theta d\\varphi,$$\n", "with $\\overline{\\xi\\left(\\theta,\\varphi\\right)}$ the conjugate of $\\xi\\left(\\theta,\\varphi\\right)$.\n", "\n", "They also are orthogonal in $H^1(\\mathbb{S}^2)$." ] }, { "cell_type": "markdown", "id": "f27cb73e-bcb1-4ab9-b1d8-85e32cd4aaac", "metadata": {}, "source": [ "This means that any function in $L^2(\\mathbb{S}^2)$ can be written as:" ] }, { "cell_type": "markdown", "id": "56a4cd4e-b6c8-47c7-a916-f76f7410aa99", "metadata": {}, "source": [ "$$f(\\theta,\\varphi) = \\sum_{l=0}^\\infty \\sum_{m=-l}^{m=l} f_{l,m} Y_{l,m}(\\theta, \\varphi)$$\n", "with $f_{l,m}\\in \\mathbb{R}$." ] }, { "cell_type": "markdown", "id": "6d1e365f-ee2b-4431-89af-f69a048319d6", "metadata": {}, "source": [ "## Constant function" ] }, { "cell_type": "markdown", "id": "b2976054-3549-488f-a3ae-35d392394d6e", "metadata": {}, "source": [ "A function of the form $f(\\mathbf{x}) = c$ has only the first $f_{l,m}$ different from zero." ] }, { "cell_type": "markdown", "id": "0de385ee-29f8-453e-9d68-f7c71ddda275", "metadata": {}, "source": [ "The following is the known dirichlet expansion for $f(\\mathbf{x}) =$ `cte`:" ] }, { "cell_type": "code", "execution_count": 3, "id": "98b14ae8-224f-4a7b-baf9-61b11ee4732e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([17.72453851, 0. , 0. , 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0. , 0. , 0. , 0. , 0. ,\n", " 0. ])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cte = 5.\n", "big_l = 3\n", "dirichlet_expansion = harmonicex.function_cte(big_l, cte, azimuthal=False)\n", "dirichlet_expansion" ] }, { "cell_type": "markdown", "id": "edd186dc-0476-43ae-98df-f8c7dbd3e58c", "metadata": {}, "source": [ "The following is the approximated dirichlet expansion with the package SHTOOLS, from the values in the sphere." ] }, { "cell_type": "code", "execution_count": 4, "id": "e832afef-758f-4b9b-ada1-2151a9e5f8e9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1.77245385e+01, -0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " -0.00000000e+00, -0.00000000e+00, 1.06581410e-14, 0.00000000e+00,\n", " 5.80672801e-16, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, -2.76647309e-16])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max_l = big_l\n", "quantity_theta_points, quantity_phi_points, w, pre_vector = (\n", " quadratures.gauss_legendre_trapezoidal_2d(max_l))\n", "grid_analytic = np.ones((quantity_theta_points, quantity_phi_points)) * cte\n", "coefficients = pyshtools.expand.SHExpandGLQ(\n", " grid_analytic, w, pre_vector[2, :, 0], norm=4, csphase=-1, lmax_calc=max_l\n", ")\n", "dirichlet_expansion_2 = np.empty_like(dirichlet_expansion)\n", "\n", "pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q = auxindexes.pes_y_kus(max_l)\n", "eles = np.arange(0, max_l + 1)\n", "l_square_plus_l = eles * (eles + 1)\n", "\n", "dirichlet_expansion_2[p2_plus_p_plus_q] = coefficients[0, pesykus[:, 0], pesykus[:, 1]]\n", "dirichlet_expansion_2[p2_plus_p_minus_q] = coefficients[1, pesykus[:, 0], pesykus[:, 1]]\n", "dirichlet_expansion_2[l_square_plus_l] = coefficients[0, eles, 0]\n", "\n", "dirichlet_expansion_2" ] }, { "cell_type": "markdown", "id": "bf639a6c-c6bd-4a6d-8ead-9da468295b7e", "metadata": {}, "source": [ "The difference between the results is" ] }, { "cell_type": "code", "execution_count": 5, "id": "ccee7485-151f-4fd2-817e-579ca423a5bb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.2825629922959107e-14" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.norm(dirichlet_expansion - dirichlet_expansion_2)" ] }, { "cell_type": "markdown", "id": "39a7751a-1b1d-4a13-b949-fe6c0868e2d8", "metadata": {}, "source": [ "## Linear function" ] }, { "cell_type": "markdown", "id": "65681b1f-1eae-4974-9a2b-166bb066c2ff", "metadata": {}, "source": [ "A function of the form $f(\\mathbf{x}) = \\mathbf{c} \\cdot \\mathbf{x} + c_3$ has only the two first degrees of coefficients $f_{l,m}$ different from zero." ] }, { "cell_type": "markdown", "id": "0cb69226-54b1-461f-91fc-33ff00c4cd50", "metadata": {}, "source": [ "Example with\n", "$$f(\\mathbf{x}) = \\begin{pmatrix}0 \\\\ 0 \\\\ cte \\end{pmatrix} \\cdot \\mathbf{x}$$\n", "where the only coefficient different from zero is $f_{1,0}$" ] }, { "cell_type": "markdown", "id": "0f0f46f7-91f1-4e79-8b1e-6c0ae2b6ce3d", "metadata": {}, "source": [ "The following is the approximated dirichlet expansion with the package SHTOOLS, from the values in a sphere of radius `r`." ] }, { "cell_type": "code", "execution_count": 6, "id": "7c285e50-174b-4b51-8921-bd1023ddc2a2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.00000000e+00, -0.00000000e+00, 1.33032472e+01, 0.00000000e+00,\n", " -0.00000000e+00, -0.00000000e+00, 0.00000000e+00, -1.81613969e-16,\n", " 0.00000000e+00, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00,\n", " 5.87474805e-15, 0.00000000e+00, 4.04347043e-16, 0.00000000e+00])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cte = 5.\n", "r = 1.3\n", "big_l = 3\n", "max_l = big_l\n", "quantity_theta_points, quantity_phi_points, w, pre_vector = quadratures.gauss_legendre_trapezoidal_2d(max_l)\n", "grid_analytic = pre_vector[2, :, :] * (cte * r)\n", "coefficients = pyshtools.expand.SHExpandGLQ(\n", " grid_analytic, w, pre_vector[2, :, 0], norm=4, csphase=-1, lmax_calc=max_l\n", ")\n", "dirichlet_expansion_2 = np.empty((big_l+1)**2)\n", "\n", "pesykus, p2_plus_p_plus_q, p2_plus_p_minus_q = auxindexes.pes_y_kus(max_l)\n", "eles = np.arange(0, max_l + 1)\n", "l_square_plus_l = eles * (eles + 1)\n", "\n", "dirichlet_expansion_2[p2_plus_p_plus_q] = coefficients[0, pesykus[:, 0], pesykus[:, 1]]\n", "dirichlet_expansion_2[p2_plus_p_minus_q] = coefficients[1, pesykus[:, 0], pesykus[:, 1]]\n", "dirichlet_expansion_2[l_square_plus_l] = coefficients[0, eles, 0]\n", "\n", "dirichlet_expansion_2" ] }, { "cell_type": "markdown", "id": "879a90fe-f0be-43e3-977f-8935a8a3531d", "metadata": {}, "source": [ "## Point source" ] }, { "cell_type": "markdown", "id": "c8921768", "metadata": {}, "source": [ "We define the point source function as:\n", "$$f(\\mathbf{r}) = \\frac{1}{4 \\pi \\sigma_e ||\\mathbf{p} - \\mathbf{r}||_2},$$\n", "with $\\sigma_e \\in \\mathbb{R}$ a parameter, $\\mathbf{p} \\in \\mathbb{R}^3$ the point source vector, and $||\\cdot||_2$ the Euclidean norm." ] }, { "cell_type": "markdown", "id": "70f27097", "metadata": {}, "source": [ "In this case, $f_{l,m}$ decays to zero when $l\\rightarrow \\infty$, but there is not $L$ from which every $f_{l,m}=0$, with $l>L$. Thus, the series has to be truncated, and its accuracy will depend on the distance between $\\mathbf{p}$ and $\\mathbf{r}$." ] }, { "cell_type": "markdown", "id": "fc0d1d6e", "metadata": {}, "source": [ "Let us see an example where $\\mathbf{p}$ is on the $z$-axis, and the distance of $\\mathbf{p}$ to the center of the sphere is $d$:" ] }, { "cell_type": "code", "execution_count": 7, "id": "8c89a6bb-7658-469c-b1fe-fca7017bf707", "metadata": {}, "outputs": [ { "data": { "image/png": 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pU1jk8Q4uarnJ+Vl5BSQH9yLlciZxm+JQUU2CKahKVD8950UtqNLp0Pn4UHoyjeMjR6FeuaL9JSFFQIUQ4upKL8MCC9t7Xc6B9/5U//f9vyxw96nz8KlTpzJq1CjeeOMNALp27crnn39OYmIiPj7G14mLi2PcuHFXvV5ISEi9p6yqKjNmzGDQoEGEh4cDkJOTQ3l5OUFBQUZjg4KCOFNLKkpD3mMrElA5oc6BPryiH0RIx2ieTZtkOmDiZt4K6Mgta25BRcVFcTEJpiq1HDsWn0GDKElLx71TR1AUMiY+TvGRI1WDKnKrfAYNkpUqIYRwYmlpaWzZsoXERON8LTc3N7PbfQEBAYYVJGt68skn2bt3Lzt37jQ5p9RYbVNV1eSYNd5jbRJQOaGwisT0rLwrFUd0gPG23eeHPjd8X66WsyRpCU/2edLs9dzatTMKlNrOmknGEzUCsIoioBJQCSGEGW7e2kpRfZzZa35F6q//g3aRpsevdu86Sk5OxtXVlYiICKPjiYmJPPDAAybjbbHlN23aNL7++mu2b99OaGjVtmZgYCAuLi4mK0vZ2dkmK1CWvMdWJKByQpUBVepFd9QWbVH8QsC/Ixz8CnRuxGf8wNI/PuKJyCf4+tjXnC48zTt738FV51rrSlV1Hj16mM2tcmlt/X+lCCFEk6Ao9dp2A8DVq+Kbyn8UV3x19ar/tepIp9Oh1+spKSnB1VULATZu3Mj+/fvNPuFnzS0/VVWZNm0a69evZ9u2bYSFhRmdd3d3JyYmhk2bNjFmzBjD8U2bNjFq1Ciz12zIe2xFAion1DHAG0WBo8X+nH8mgUD/FlqC48GviPfzYukfHxlypjr7d2b2jtm46dxYmrwU4JpBlUluVYVT056i3UsvgV4viepCCGEpnzbg2xb8QqDvw5D4IeSf0o7bSExMDG5ubsyaNYtZs2aRmprK5MmTAWy+5Td16lQ++eQTvvrqK1q0aGFYVfL398fLSwsuZ8yYwUMPPUS/fv0YOHAgK1asID09nbg47XNryZIlrF+/ns2bNxuue633NBYJqJyQp5sLwf5enMq9wsncMgJbKtCyA4T0Q194hKmBNxqCpjvC7uA/B/7D/vP76d26N3pVf42ra6rnVumLizjz4lxKTpwg/eGHtQGSqC6EEJbxD4HpqeDirq1wxTwK5SXg6mGzWwYHB/Puu+8ye/ZsPvvsM/r06cOECRNYuXJlg5LL66OyjMHQoUONjr///vs88sgjAIwfP57z588zb948Tp8+TXh4OBs3bqRTp06AloR+7Ngxo/df6z2NRVErCxUJq8rPz8ff35+8vDz8/Pysfv0H3/2VnUdzeG1sJOP6ddAO7nobfngBOg2CR/9rGPvCzhf46thXuCgurBu5jq4tuxrOxafEo1f1TImectX7XTlwgJP33Gt8UKej25bNslIlhBCiyWjo57cU9nRSlXlUJ3OqKszSq2K/OO1nuHTWcDi0hZb0V66WsyhhkeG4uWKftdHnXzJzUE/x4cMNmL0QQgjRtEhA5aQqW9CcqB5QtewIITGACge/NhyOi4rjL9f/BYDtmdvZfXq3IZgyV5/KHEMR0BrOvvIql5OSpLmyEEKIZk0CKicVFqg9JmsUUAH0Gq19PWBcRv25Ac8REag9Jjvph0n1CqagKlHdEFTpdCg+PpQcP07a/Q9Ic2UhhBDNmgRUTios0BeAtPOX0eurpcFV3/YryDZ6z9LbtKf8rlXsszYtx46l25bNdPzgA7pt2Uyn9983HiDNlYUQQjRTElDVIiMjg6FDh9KrVy8iIyP54osv7D0lI6GtvHDRKVwpLefspaKqE606QXBfUPVw8Buj96w5VNV4s1wt563Et+p9X7d27fAZ0B+3du3QXzbTt0qvp+iPQ/W+rhBCCOHMJKCqhaurK4sXL+bAgQP8+OOPPPPMMxQWFl77jY3EzUVHx4Batv16j9a+Jn0Eq++CU4mGnKnJkZPp7NcZgJX7VhKfEt/gOdSeV7WQ4hMnKD1zRnKrhBBCNAsSUNWiffv2hqqxbdu2JSAggAsXLth3UjV0bl1bHlXFtl9WEpzcQfwv8w05U1P6TOHZG54FQKfoWJq8tMFBlbm8Kp2vL6Un0zgxegxHh90quVVCCCGaBacNqLZv387dd99NcHAwiqKwYcMGkzHLli0jLCwMT09PYmJi2LFjR4PutWfPHvR6PR06dLBw1tZVmUdlVDohNx2uXITAHoZD+uwDTO16L3FtBkBuOoNDBzM4ZDB6VU9nv851LvZpTs28qq7fbcQzIgK1uBgqS5xJbpUQQogmzmkrpRcWFhIVFcWjjz7Kvffea3J+zZo1TJ8+nWXLlnHzzTfzzjvvMGLECA4cOEDHjh0BrQR/cXGxyXt/+OEHgoODATh//jwPP/ww77777lXnU1xcbHSt/Px8S369Oql60q9aLtPiCJNxU7LPwI9vAm9qB+bmEeIbgg4dJ/NPEtXGuN1AXYt9VqrZXLnN9KfJeGyi8SBpriyEEKIJc9oVqhEjRjB//nzuueces+cXLVrEY489xsSJE+nZsyeLFy+mQ4cOhtL3AAkJCaSmppq8KoOp4uJixowZw+zZs7npppuuOp+FCxfi7+9veDXGalZVLaqCqoP3rARdzTi5YqVI56qdB1p7tUaPtjL12u+vUaovBepX7LM2Hl27ms2t0l+5LHlVQgghmiSnDaiupqSkhISEBGJjY42Ox8bGsmvXrjpdQ1VVHnnkEW699VYeeuiha46fPXs2eXl5hldGRkaD5l4fldXS0y9cpryydELkOJi42fwbJm7WzqMV+5wYoa0iHc87zueHPq93sc/amORWVcic+qTkVQkhhIN65ZVXGDhwoL2n4bSaZECVk5NDeXk5QUFBRseDgoIM3a2v5eeff2bNmjVs2LCB6OhooqOj2bdvX63jPTw88PPzM3rZWrC/F+6uOkrLVU5dvGJmhHLV9z/d92mGdhgKwCu/vWKVYKpS9dyqsG+/wXvQzVBeLnlVQgjhoFJSUoiKirr2wAaqS+7z3LlzURTF6NWuDqki1sqZtkSTDKgqKYpxQKGqqsmx2gwaNAi9Xk9ycrLhFRFhmp9kTzqdUvWk3/lqiek+bcC3LQSFYwiqvFtrx2tYPHQxSsUYnaKzSjBVqbJmlWe3brSeONF0QEVelRBCNDfLkpfV+oR1fEo8y5KXNfKMtICq8ul2W6jMfV6yZMlVx/Xu3ZvTp08bXldbzICqnOnnn3+epKQkBg8ezIgRI0hPb9zPlyYZUAUGBuLi4mKyGpWdnW2yauXsOrc20yTZPwSmp0LcDggbrB27cbJ2vIaV+1aiVuRY6VU9L//ysk3m6dG5s9m8qpL0NMmrEkI0O7WVrbFGHmtdHDx4kKFDh+Ll5UWfPn3Ys2cPhw8ftukK1bVynyu5urrSrl07w6tNG9PFgOrqkjPdGKzyJ1ZaWkpGRgaHDh1yiFpN7u7uxMTEsGnTJqPjmzZtumZyubMJM9ckGcDVAxQFwiuegNz/FTVVz5kaETYCgM8Pf25Rsc/a1JZXdeYfcySvSgjh9FRV5XLp5Tq/Hu71MJMitL6qbye+zeXSy7yd+DZLk5cyKWISD/d6uM7XUlX12hOs5o8//mDAgAH069eP1NRU5syZw6hRo1BVlcjISKOxCxYswNfX96ova2+vHTlyhODgYMLCwvjzn//M8ePHax1rjZxpa2lw2YSCggI+/vhjPv30U3777TejkgGhoaHExsYyadIkbrjhBqtM1Nz9jx49avj5xIkTJCcnExAQQMeOHZkxYwYPPfQQ/fr1Y+DAgaxYsYL09HTi4qy3peUIag2oKvUcCf+dBWf3wblD0EarT1UzAf1s4Vm2ZWzjStkVliZrPf+suf0HWl6Vz6BBWvmE4PacX7GS3C++MMmr8hk0SMorCCGcypWyKwz4ZECD3rti3wpW7FtR68/X8usDv+Lt5l3n8VOnTmXUqFG88cYbAHTt2pXPP/+cxMREfHx8jMbGxcUxbty4q14vJMR096OhBgwYwIcffsh1113H2bNnmT9/PjfddBP79++ndevWJuOtkTNtLQ0KqN58803++c9/0rlzZ0aOHMlzzz1HSEgIXl5eXLhwgdTUVHbs2MHtt9/OjTfeyNtvv0337t2tOvE9e/YwbNgww88zZswAYMKECaxevZrx48dz/vx55s2bx+nTpwkPD2fjxo106tTJqvOwt8rSCYfOXDI/wDsAut0Gh/8Hqetg2P8DtO296gnoQT5BTIqcxL8T/423qzdFZUXmr2eh6jWr/O68UwuoqpN6VUIIYTNpaWls2bKFxMREo+Nubm5mt/sCAgIICAhorOkxYsQIw/cREREMHDiQrl278sEHHxg+582xJGfaWhoUUO3atYutW7cSERFBdnY2rVu3xsXFxXC+f//+/PWvfyU+Pp5Vq1bx008/WT2gGjp06DWXOadMmcKUKXUrTums2vt5AnAmv4gZa5L555gIvNxdjAeF36sFVPvWwtDZoChmi3Y+3OthVqeuJq8kj3K13OR8fQt+XouhF6DeuFJ7wfafcOsQSml6Bu6dO0lwJYRweF6uXvz6wK/1ft+qfatYsW8Fbjo3SvWlTIqYxGMRj9X73nWVnJyMq6uryUNWiYmJPPDAAybjFyxYwIIFC656ze+++47BgwfXeQ714ePjQ0REBEeOHDF73pFyphsUUH1Rsapw4sQJXnjhBd577z2jgKqSh4dHkw9o7OnI2UtM+ijB8POG5FMkZ+byzoMxdA9qUTWwxx3g6gUXjsHpZAjuY/Z67i7uDA4dzLfHv+XD/R8yptsYurTsAhhvEVpLZV7V6TkvakGVooCqcmHVe1xY9Z42SKej/byXaDl2rNXuK4QQ1qYoSr223UD7e3XFvhWG3YLKv2fdXNysnnJRSafTodfrKSkpwdVVCwE2btzI/v37zT7h19hbfjUVFxdz8ODBWgO26jnTY8aMMRzftGkTo0aNstm8zLGo9cw//vEP3nrrLTw8PAAoKioiLi6O4OBgbr/9dqMtOWFdaxMyeX79Psr0Vat0ehXSzl/mrrd3smBMBPfGhGonPHzhuuFwYIO27VdLQAWwcPBCUnNSOZl/kic3P8l/7/kv7+x9x6o1qqqrnlfl3qkj+Rs3kv3a61UDJK9KCNEEmSukXPnVVnmsoLVcc3NzY9asWcyaNYvU1FQmT54MYPMtv2vlPgPMmjWLu+++m44dO5Kdnc38+fPJz89nwoQJACxZsoT169ezeXNVAWtHyZm2KKAqLi42ShJ76qmnGDNmDB06dGD79u306dOHli1bWjpHUcO+zDxmfZFi9ly5XqVcrzLzixSuC2pBRKi/diJirBZQpXwGWclw+zwI6Wv2GktvW8rdG+4moyCDPh/1oVwtt0kwVal6XpVnr96mA/R6itPSJKASQjQZNfNYK1X+bEnT+qsJDg7m3XffZfbs2Xz22Wf06dOHCRMmsHLlSpuuNMG1c58BMjMzuf/++8nJyaFNmzbceOON7N6925D/nJOTw7Fjx4yu6yg504pa3+ctqxkzZgzr168HtIJgb731FkuXLuXy5cts2rSJd99916R0QXORn5+Pv78/eXl5Vq+arqoqo5b+TOqpPPRm/vR0CkSE+LNh6s1VSXmlRfBGdyiuaNo8IA5GvFrrPd5KfIuV+7S+f246NxIfSqx1rDWVnjnD0VtvM8mr8hk8mJBF/0JfWEjJyTTJrRJCCGETDf38tqgO1fnz59m4cSOZmZnMnj2bhQsXotfrCQgIYPz48Xh6elpyeVELRVGYGdvDbDAF2tbfzNgeVcFUbjqcOwgdq9XgSl2nrVRlJWnna96jWtuaUn2pTWpTmWNSr0pRwMWFwh07OBY7XGpWCSGEcEgWbfmNHz+eb7/9ltTUVJYtW8alS5do27at4bwEVLYzpHsgkaH+JqtUlatTg7sHVh1cbKZlTmEOrLil6ue5eYZvKxMl/9T5T/zv5P8MFX3BNnv6NdXMqyrLziZz2lOUnT1bNUhyq4QQQjgQi1aopk6dSps2bcjMzGT79u106NDB6HxZWZlFkxO1q22VymR1CuCelaCrGTtXvFHnqp2vUD1R8rUhrzGw/UD0qp6OLTqabZNgK5V9AN3atcMrMpJ2c/5hOkh6AQohhHAQFq1QAbz00ktmj7/yyis8/PDDll5eXMWQ7oF8O20QABPe+43zhSX8675I49UpgMhxEHid8YpUpYmbITja8GPNRMnZA2Zzz9f3kH4pnTvC7rBZouS1ePbubbZmlVpaQumZM5JXJYQQwq4sDqjMKSwspGvXrkY1IYT1KYpCeIj2FF+Pdi3Ydew8Kso1qsMqGFanzKhZtDPMP4yI1hEknUsi5VwKL91kHEBbu9hnbUxqVlXIeCJO+1lVpWaVEEIIu7FJO2sfHx/uu+8+W1xa1KJrG18Ajp0rMD/Apw34ttVWo7wqaop4+GnHr+GGdlo/xlMFp1iVuspwvLG6oldqOXYs3bZspuMHH9D5qw143TgAystNegGWNnL/JiGEEKJBn4Tp6fXLWzl16lRDbiPqoUsbraff8doCKv8QmJ4Kj2+Ffn/VjnW4UTt+DdP6TuNPnf8EwMq9K8nIzzBblK4xVOZWefXoQeATT5gOkLwqIYQQdtCggOqGG27g8ccf57fffqt1TF5eHitXriQ8PJwvv/yywRMUdVO1QlVY+yBXD60MQWRFG4HjW6DwfJ2u/9qQ1+jg24FytZw7199pl2CqJo+wsKryCtVcSUmh5PRpCnf/KqtVQgghGkWDCnteuHCBBQsW8N577+Hm5ka/fv0IDg7G09OTixcvcuDAAfbv30+/fv144YUXjLpHNxe2LOxpTubFywx6dStuLgoH5/0JV5drxMrxg+HMXrhzEdxQt0acJ/JOMHLDSABcFBeSH062cNaWy1271iSvyojkVQkhhKiHRi3sGRAQwBtvvEFWVhbLly/nuuuuIycnx9AN+i9/+QsJCQn8/PPPzTKYsodgfy883XSUlqtkXLxy7TdEVOS47fuizvf4/uT3hu/L1XKWJC2p7zStrnpeVdctm2lds3eT5FUJIYRoBBY95efp6ck999zDPffcY635iAbS6RTCAn05eDqf4+cKCAv0ufobIsbCpjmQ/otWKb1lx6sOr8yZmhQxiW+Of8PpwtO8s/cdXHWudt32A+NegD433sj5+Bq1sqQXoBBCXNMrr7zCV199xS+//GLvqTileq9QXblyxWyS+f79+60yIdFwXSsS02t90q86v2DorNWwutYqVfUE9Gl9p/H3/n8HMFRQb6xin3Xh3rmT2byqC6veozw/n9IzZyS3SgghzEhJSSEqKspm19++fTt33303wcHBKIrChg0bTMYsXLiQG264gRYtWtC2bVtGjx7NoUOHrnntZcuWERYWhqenJzExMezYscMGv8HV1SugWrt2Lddddx133HEHkZGR/Prrr4ZzDz30kNUnJ+qnMjH9+NUS06szbPtdvSdezWKft3a4lcEhg9GrekJ9QynXlzd4ztZWay/A7dulF6AQQlxFSkoK0dHRNrt+YWEhUVFRLFlSe7rITz/9xNSpU9m9ezebNm2irKyM2NhYCgtr/1xbs2YN06dP5/nnnycpKYnBgwczYsSIelcksJhaD1FRUWp2draqqqr6+++/q7169VI//vhjVVVVNTo6uj6XavLy8vJUQM3Ly2u0e25IylQ7/f1bdezyn+v2hssXVXVeoKq+6Keq7wxV1cyEOt9rwe4FatQHUWr46nD1u+PfGZ1bnrxcXZq0tB4zt76S06fVgt2/qiWnT6uX9+5VD98yVD3Q43rjV89easnp03adpxBClJw+rRb8srtR/z46cOCAesstt6ienp5qdHS0+vvvv6suLi7qrl27GuX+gLp+/fprjsvOzlYB9aeffqp1TP/+/dW4uDijY9dff7363HPPNWhuDf38rtcKVWlpKW3aaIUg+/Xrx/bt23nnnXeYN2/eNapzi8ZQ7xUqr5bQPVb7PisR9q6p871aebaiXNVWpl7//XUKS7V7Nnaxz9oY9QKMiJBegEIIm1JVFf3ly/V+XfjkE47eepth5fzCJ5/U+xpqPR/W/+OPPxgwYAD9+vUjNTWVOXPmMGrUKFRVJTIy0mjsggUL8PX1verLlttreXl5gPYwnDklJSUkJCQQGxtrdDw2NpZdu3bZbF7m1CspvW3btuzdu9fwP3jr1q3ZtGkTEyZMYO/evTaZoKi7yuKe5wtLuFhYQisf99oH56bD5fMQegP88a12LHUtRN0PqODd+qqJ6nFRcZTry4nfG0/2lWyWJS+jhXsLh6hPZY5nr15mewGW5+ZKL0AhhMXUK1c41DfGsovo9Zyd9zJn571cr7f1SExA8fau8/ipU6cyatQo3njjDQC6du3K559/TmJiIj4+xg80xcXFMW7cuKteLyTk2gWiG0JVVWbMmMGgQYMIDw83OyYnJ4fy8nKCgoKMjgcFBXGmkXNl6xVQffTRR7i6Gr/F3d2dTz/9lCeffNKqExP15+3uSrC/J1l5RRzPKSDGx3xED8DiCNNjhTnGDZTn5l31flP7TOVUwSm+Of4NHx74UDvmgMEU1N4L8NT06do30gtQCNEMpKWlsWXLFhITE42Ou7m5mU1IDwgIqHV1yNaefPJJ9u7dy86dO685tuYumaqqjb5zVq+AKjQ0tNZzN998s8WTEZbr0saXrLwijp0rJKbTVf4juGclbJgM+jLTczpXGL28TvdbMHgB3x7/FlVry8ykyEkNnLnttRw7Fp9BgyhJS8e1TSDnFi/m0g+bqgZU1KzyGTRIVqqEEPWieHnRIzGhXu8pPXuW43feZbxyrtPR5b/f4lZjxeVa966r5ORkXF1diYgw/kd1YmIiDzzwgMn4BQsWsGDBgqte87vvvmPw4MF1nkNdTJs2ja+//prt27dfNfYIDAzExcXFZDUqOzvbZNXK1iyqQyUcT9c2Puw8mnPt0gmR4yDwOuMVqUoTN2tNlOsgPiUeFW3/XkXlma3P8O9b/13PWTee6jWrWj3wF+OACgx5VRJQCSHqQ1GUem27gdY+y2jlvGKV3CMszEazBJ1Oh16vp6SkxLDjtHHjRvbv32/2Cb/G3vJTVZVp06axfv16tm3bRtg1/rdwd3cnJiaGTZs2MWbMGMPxTZs2MWrUKKvNqy5sFlAdPnyYRx99lJ9//tlWtxBmdKlvYjoAClDvDkRG9am8XL14Y88bbMnYwuKExUyPmV7v6zU2Q82qGnlV+f/7H27B7Sk9lSV5VUIIm6q+cu7eqaPN/76JiYnBzc2NWbNmMWvWLFJTU5k8eTKAzbf8CgoKOHr0qOHnEydOkJycTEBAAB07ajm7U6dO5ZNPPuGrr76iRYsWhpUnf39/vLy8WLJkCevXr2fz5s2G68yYMYOHHnqIfv36MXDgQFasWEF6ejpxNTtn2JjNAqrS0lJ2795tq8uLWlQ1Sa5DcU+fNuDbFvxCwLMlHN8KLh7a8WuoHkzFRcVRqi9lw9ENHM09yqrUVXi6ejpkLlV1JnlVigKqSu6nn5L76afaIMmrEkLYWPWVc1sLDg7m3XffZfbs2Xz22Wf06dOHCRMmsHLlSpsll1fas2cPw4YNM/w8Y8YMACZMmMDq1asBWL5cSzcZOnSo0Xvff/99HnnkEXJycjh27JjRufHjx3P+/HnmzZvH6dOnCQ8PZ+PGjXTq1Ml2v4wZDWqOXBf79+8nMjKS8nLHKfrYmBq7OXKlrNwr3PTKFlx1Cgdf/hNu12qSXFYMLu5wdj/E3ww6N/jbEfBqddW3LUtehk7RGQVNSdlJPPzdwwCM6TaGeTfPs/j3aQylZ84Y/nVYsO0nzsydazxAp6Pbls2yUiWEEM1AozZHBm1fdeXKlezZs4eSkpKGXkZYWTs/T7zdXSjTq6RfuHztN7h6aCsz7cKhbW/Ql8KBr675tinRU0xWoPq07cP1ra4HYP/5/ZTVSHiPT4lnWfKyuv8yjaR6zSr3zp1NB+j1FB85anpcCCGEqNDggGrv3r3MmDGD/v3706JFC/r06cNjjz3GsmXL2L1791XLxAvb0Zoka3VE6pdHhZaoDrD38wbf/+YQ7WnPwxcP88nBTwzHHaXg57XU1gvw7MKFFB87Jr0AhRBCmGXRlp+qqvzxxx8kJiYaXsnJyYbKpoqiyJZfI2/5ATz1aRJfp2Tx3Ijribula93fmJcJb4YDKkzfd9XCnle9/5an2JqxFTedGxvv2ciGoxsctuCnOblr1xo9daN4eaEWFoKbG5SVSc0qIYRowhr6+W1RUrqiKPTs2ZOePXvyl7/8xXD82LFjJCQkkJycbMnlRQNVVkw/XpfE9Or8Q6HzIDi5A/Z9AYNnNuj+i4ctZvja4Zy5fIbYtbGoqE4TTIHpUzeKiwuZ06dzJaFaITypWSWEEKIam+y/dO3alXHjxl2zGJiwjaon/Rqw7Ro5XvuaskZbiWkAnaJjyW1aN3EVFVfF1WmCqUrV86pc27Qh0FwnAOkFKIQQooJjJ7SIBmnwChVAr5Hg6gk5h+BMw/szbs3Yavi+TC1jSdKSBl/LEXiEhZnNrSrcvZuSrCzJqxJCiGZOAqqruHz5Mp06dWLWrFn2nkq9dAnUVqguXi5l97Hz9Xuzpz/0GKF9v+ttWH0XnEq8+ntqqExAnxQxiSBvrfT/O3vfIT4lvn5zcSCVNatqBlXnly/nWLVO8blr19pphkIIIexJAqqr+Oc//8mAAQPsPY1683J3ob2/JwB/XrmbWV+kcKWkHg8HVG77/fGtlk+1d02d31q94Oe0vtOY3X82oG0DLk1e6tRBVcuxY+m2ZTMdP/iArlu30KaiKJ1BRV6VrFQJIUTzIwFVLY4cOcIff/zBHXfcYe+p1NuRs5fIvVxq+PnLxEzufHsHR85euvabc9PBOxA8/KD0inYsdR1kJUNWknb+KvSq3igB/daOt9KpRSf0qp4Q3xDK9caBnaPWpqpNZW6Ve/v2eEVGmg7Q6yk+frzxJyaEEMKurBJQbd68mf/3//4fEydO5K9//avRyxa2b9/O3XffTXBwMIqisGHDBpMxy5YtIywsDE9PT2JiYtixY0e97jFr1iwWLlxopRk3nrUJmdz19k6KSqsCF70Kaecvc9fbO1mXkHn1CyyOgFX/B8X5VccKc7QmyiuGauevombBT0VRGNJhCACnCk7R0a+qFIOz1KaqTW01q869/gaXk5Ikr0oIIZoRiz/JXnrpJWJjY9m8eTM5OTlcvHjR6GULhYWFREVFsWSJ+UTnNWvWMH36dJ5//nmSkpIYPHgwI0aMID29anUlJiaG8PBwk1dWVhZfffUV1113Hdddd12d51RcXEx+fr7Rq7Hty8xj1hcpFJfpTVodl+tVisv0zPwihX2ZebVf5J6VoKtZTaPiajpX7Xw9PXvDs9zY/kYAXt79MnnFeSa9AJ2RSV6VoqB4elJ08CBp9z8geVVCCNGMWNzLr3379rz22ms89NBD1ppTvSiKwvr16xk9erTh2IABA+jbt6+hySJAz549GT16dJ1WnWbPns1//vMfXFxcKCgooLS0lJkzZzJnzpxa3zN37lxeeuklk+ONWdhTVVVGLf2Z1FN56M38qeoUiAjxZ8PUm1EUpfYLZSVrK1I1TfoJgqMbNLfS8lJu++I2LhZfRKfoTLYGnVn1XoBlZ85w8s/3Gw+QXoBCCOE0Gr2XX6WSkhJuuukmSy9jNSUlJSQkJBAbG2t0PDY2ll27dtXpGgsXLiQjI4OTJ0/yxhtv8Pjjj181mAItCMvLyzO8MjIyGvw7NJSiKMyM7WE2mAJt629mbI+rB1M24ubixqKhiyrmoXfK2lS1qV6zSl9UbDpAr6dgx87Gn5gQQohGY3FANXHiRD755JNrD2wkOTk5lJeXExQUZHQ8KCiIMzbMZ/Hw8MDPz8/oZQ9DugcSGeqPrkbMpFMgKtSfwd0Dr30Rnzbg2xba9qo65h2oHbfAnrN7DN+XqWVOlYxeV7XlVZ2ZN48L//mYktOnJbdKCCGaIItazwAUFRWxYsUKfvzxRyIjI3FzczM6v2jRIktv0SA1V2FUVW3QyswjjzxipRk1jspVqgnv/WZ0vF6rU/4hMD0VXNxhVSxk/gY3TdOON1BlztRj4Y+x7sg6cotzWZ6yHJ2iazIrVVCVV1W9F6BH9+4UHzrE2fnzOTt/vjZQegEKIUSTYnFAtXfvXqKjowFITU01OmePraXAwEBcXFxMVqOys7NNVq2aqiHdA/l22iD+tekQW/84x4MDOvLn/h3pHVyPVTNXD+1r1HgtoEpdC4OmN2g+NRPQO/l1Ys6uObjqXFmavBSgSQVVNXsBugYFkbN0GTnVH6KQXoBCCNGkWBxQbd269dqDGpG7uzsxMTFs2rSJMWPGGI5v2rSJUaNG2XFmjUdRFMJD/LmhcwBb/zhHQXEZ4SH+DbtY73vgu+fgzD44ewCCel37PTXUTEAf3W00Xx37ioSzCXT264xe1Tdsbg7MrV07o0DJu18/00HValaVnEzDvXMnCa6EEMJJWRxQ2UNBQQFHjx41/HzixAmSk5MJCAigY8eOzJgxg4ceeoh+/foxcOBAVqxYQXp6OnFxTWcVpC4sapJcyTsArhuuVU3f+xncPq/el5gSPcXoZ0VR6NayG0nZSZzMP0mPgB5G5+NT4tGrepP3OTNDbpXeOHg8/fwLlJ09a9gelG1AIYRwTg0KqGbMmMHLL7+Mj48PM2q236jBFjlUe/bsYdiwYUbzAZgwYQKrV69m/PjxnD9/nnnz5nH69GnCw8PZuHEjnTp1svpcHFlVQFWAXq+iq5mpXleR4ysCqi/gthdB52Lx3AK9Ag0rUwt/XcjA9gPxdvM22h5sSkxyqxQF3NwoO326apBsAwohhNNqUECVlJREaWmp4fva2CqHaujQoVyrfNaUKVOYMqXprHA0RKfW3rjqFC6XlHMmv4jgll4Nu9B1w8GzJVzK0nr7dRlq8dziouIo05fxzt53OHv5LEuTl9LCvYXTF/u8mpq5VZf3JJBVs/G2Xk9JWroEVEII4WQaFFBVz5tytBwqUcXNRUen1t4cO1fIsXMFDQ+oXD2g9xhIeB9+WQbb39C2/kL6WjS/J/s8SVZBFt8c/4YPD3wI0GSDqUrVc6u8+8WY3QZUi4u1YqGSVyWEEE7DOZuoiTqr3PY7ml1g2YWi/qx9PbZFW6Xau8bCmWkWDF6AgraSqaDweMTjVrmuMzBpXVMhY/Jkjg67VVrXCCGEE5GAqonr1rYqj6rBctPBxQNatAe9ttVL6jqtRU1Wkna+geJT4lEregWqqDy19amGz9MJtRw7lm5bNtPxgw/o/NUGvG++GcrLoXJLuyKvSgqBCiGEY3PKp/xE3RkS07MteNJvcYTpscIc435/c6/ScLkW1RPQ/T38WfDrArZnbudfe/7FzH4zGz5fJ1N9G7D14xO5/PPPxgMkr0oIIRyerFA1cV0rVqiOWrJCdc9K0NWMvStWUHSu2vl6qlnsc9x144gI1AK31ftXE58S3/D5OjGPzp3Ntq7J/+9/KUnPkLY1QgjhoCwKqEpLSxk2bBiHDx+21nyElXVt4wPAuUvF5F0pbdhFIsfBxM3mz03crJ2vp5rFPl10LlwfcL0hn+pE3gmj8fEp8U2y919NJnlVFU/K5n7+OcdiYyWvSgghHJRFAZWbmxupqal2aTEj6qaFpxtBflobGYvyqAys82c9JXqKydN8bb3bGvKpUs6lcKXsClC1mqVTmseCavW8qm5bt9Bu/svGAySvSgghHI7Fn1APP/wwq1atssZchI1U5VFZEFD5tAHfttAuAioDG68A7biVxEXFMSliEgCnCk4RnxJvsjXYXLi1a4fPgP64tWuHe2gH0wF6PUUHDzb+xIQQQphlcVJ6SUkJ7777Lps2baJfv374+PgYnbdFpXRRP93a+rLr2HnLWtD4h8D0VHBxhzUPapXTo/6sHbeiaX2nkVmQycYTG3kv9T2g6demupba2tacmfsSLv7+uAUHS80qIYSwM4sDqtTUVPr21Qo81sylkq1Ax2C1WlSu2tYhUfdrAVXqlxA73yqtaKp7dcirfHfiO1RUFBQmRU6y6vWdjUnbGp0OF39/ys6eJe0vD2qDVFV6AQohhB1ZHFBJpXTHV1mL6rhVcqiA7rHg1QoKzsDxbdDtNutct4JJbaotT7HktiVWvYezqdm2RufrS9bs2RRs+rFqkPQCFEIIu2keWb7NXOUKVdqFy5SU6a8xug5c3SH8Xu17K1VMr1Q9Z+rvN/wdgJ8yf2LRHtk6rp5X5eLrS0Dl6lR1FTWrhBBCNC6rFPbMzc1l1apVHDx4EEVR6NmzJ4899hj+/v7WuLywUJCfB74erhQUl5F2vpDuQS0sv2jU/fD7u3DwGyi+BB6WX7NmAnq5vpxvjn/DgfMHeH//+3i7eTfrXKqaasutuvjZp7i2bUPZ2WzJqxJCiEZi8QrVnj176Nq1K2+++SYXLlwgJyeHN998k65du5KYmGiNOQoLKYpiqEdlndIJQEgMBHSF0staUGUF5mpTvTjwRUO5hJN5J61yn6aitppVl777H8dH3CE1q4QQohFZHFA988wzjBw5kpMnT/Lll1+yfv16Tpw4wV133cX06dOtMEVhDYbSCZY86VedomirVAApn1nlkuZqU/Vq3Yvw1uEAJJ9LNtSmqtRcCn7WpmbNquA33zQeIDWrhBCiUVhlhervf/87rq5Vu4eurq48++yz7Nmzx9LLCysxtKCx9Em/6iorpJ/4Cd69HU7ZZkXyxvY3AlW1qSo1t4KftameW+XaqpXpAL2eyykpjT8xIYRoRiz+JPLz8yM93TQJNiMjgxYtrJCrI6yiaoXKigFVq07Q6Wbt+8zfrJ6gXmla32ncEXYHAKtTV3P44uFmW/DzWgx5VTWcmfMiF7/8UnoBCiGEjVgcUI0fP57HHnuMNWvWkJGRQWZmJp999hkTJ07k/vvvt8YchRV0a1uRQ5VdgKqqll8wNx2ykqoCKoDUdZCVrB3Pte6TZq8OeZUu/l3Qo2fs12MlmKqFSV6VTodru3bo8/I48/+el7wqIYSwEUW18NO1pKSEv/3tb8THx1NWVgZoPf4mT57MK6+8goeHh1Um6mzy8/Px9/cnLy8PPz8/e0+HkjI9Pef8j3K9yi+zb6W9v5dlF5xbhyc45+ZZdo8azhae5f/W/h8ALooLyQ8nW/X6TUnpmTOGmlX6klKODx+uFf+spNPRbctmeQJQCCFqaOjnt0UrVKWlpQwfPpypU6dy8eJFkpOTSUpK4sKFC7z55pvNNphyRO6uOjq19gbgWLYVEtPvWQm6Wqpu6Fy181a2/uh6w/flarnUprqK6nlVZVlZxsEUgF7P+XdXoaoqpWfOyFagEEJYyKI6VG5ubqSmpqIoCt7e3kRERFhrXsIGurbx5fi5QnYeOceg7oGWXSxyHAReBytuMT03cTMER1t2/Roqc6amRE1he+Z2Us+nSm2qOqq1XtV//sPl336j+OhRQ0sbaV0jhBANY3EO1cMPP8yqVausMRdhYx0DtBWq+O3HmfVFCldKyq10Zdv2bKyegD45ejIv3vQiLorWP3Bp8lKjJ/+EKXN5VX533AGurhQfPlwVaEmJBSGEaDCLK6WXlJTw7rvvsmnTJvr164ePj4/R+UWLZFvGERw5e4mvk7MMP3+ZmEli+kXeeTCm4ZXTfdqAb1vwCwFPf62vn4uHdtyKahb8vD7gesIDw0k5l0ILtxYUlxUbjY9PiUev6pkSPcWq83BmNXsBurVrh/cXaznzj38YD6xoXSO5VUIIUT8WB1Spqan07dsXgMOHDxudUxTbrlyIulmbkMnz6/dRWl615aNXIe38Ze56eycLxkRwb0xo/S/sHwLTU8HFHc6mQvwgUPXg7m3F2WM2MBrQbgAp51K4VHqJMrXMcLz6apYw5taunVGg5Dt4kNmtQNDyqkpOpknrGiGEqCOLn/IT5jnKU377MvO4e8nOa4775slBRIRa2Htx+c1aYHXnIrjhMcuuVQezd8zm2+PfoqDw+d2fsy1jm5RTqKfctWs5PedF46DK1RXKy7VEdsmrEkI0M3Z7ym/YsGEmK1PCcYSH+BEZ6o+ulsVCnQJRof6Eh1gh6Iv6s/bVSq1ormXh4IV0a9kNFZVx34yTYKoBqreu6fzFF3jF9IWysqqnAiWvSggh6sSigKr6U37CMSmKwszYHuhrWYfUqzAztod1/gwj7gNFp1VNP3/M8uvVwYrbVwCgouKiuEgw1QCVJRa8IsIJfPJJ0wEVeVVCCCFqJ0/5NQNDugeaXaWqXJ0abGkJhUot2kHXW7XvG2mVat2RdYbvy9Vy3vj9jUa5b1PlERZmtnVN/ncbKUnPkHpVQghRC3nKrxmoXKWa8N5vRsetujpVKep+OPoj7P0Mhs42++FsLYbaVNFT2HVqF8nnkvngwAf4uvvKSlUDVZZYMORVKQqoKrmfrSH3s4pejZJXJYQQJixOSh82bFjtF1cUtmzZYsnlnZajJKVXUlWV/Vn5JGfk8sKGVIJberLioX70DvazbkBVegXeuA6K8+GuxVp/v9vnQUhf690DTJojH7l4hHHfjDM88Se5VJap3rqmYPt2zsx50XiAtK4RQjRRDf38tniFauvWrZZeQjQCRVEID/GnTQsPXtiQypm8IroH+Vo//83NC3qNgqSP4NflcO4Q7F1j9YCqZm2q7q2682j4o6zctxIfNx+Kyoqser/mpnqJBfeOnUwH6PUU7T8gAZUQQlSw3X6Mkztx4gTDhg2jV69eREREUFhohf53DqBtCw9aeLiiV+FkzmXr3yA3HUL6ad+fq3j6M3UdZCVDVpJ23gqmRE8xuwLl7+5PYWkhl8uMf7f4lHiWJS+zyr2bG0PrmhpOv/iiIadKcquEEM2dVQKqHTt28OCDDzJw4EBOnToFwEcffcTOndeuf+SoHnnkEebNm8eBAwf46aefmkyjZ0VR6NLWF4Cj2QXWv8HiCPj26YofKnaTC3O0nn8rhmrnbcTdxZ28kjwAPvvjM/ae2wtUbQ/qFPn3Q0OYa13j0ro15Tk5pD/yCEeH3ap9vfU2cteute9khRDCTiz+hFm3bh3Dhw/Hy8uLpKQkiou1NiCXLl1iwYIFFk/QHvbv34+bmxuDBw8GICAgAFdXi3dHHUa3NlpAdeycDQKqe1aCrub/VhWBlc5VO28jcVFxhgrpKiov/fISy5KXSX0qK6her6rbls102/QDfnfeqZ2UmlVCCGF5QDV//nzi4+NZuXIlbm5uhuM33XQTiYmJll7erO3bt3P33XcTHByMoihs2LDBZMyyZcsICwvD09OTmJgYduzYUefrHzlyBF9fX0aOHEnfvn2dNjCsTTdbrlBFjoOJm82fm7hZO29DcVFx/DX8rwAcvniY5SnLJZiyksp6VW7t2qHz9qblffeZDtLrKU5La/zJCSGEnVkcUB06dIghQ4aYHPfz8yM3N9fSy5tVWFhIVFQUS5YsMXt+zZo1TJ8+neeff56kpCQGDx7MiBEjSE+vyt+JiYkhPDzc5JWVlUVpaSk7duxg6dKl/PLLL2zatIlNmzbZ5HexB5sGVGY1buHXZ2KewUVxMfx8Z5c7G/X+zUVtuVUXVr1H0eHDklclhGhWLN7Hat++PUePHqVz585Gx3fu3EmXLl0svbxZI0aMYMSIEbWeX7RoEY899hgTJ04EYPHixXz//fcsX76chQsXApCQkFDr+0NDQ7nhhhvo0KEDAHfccQfJycncfvvttb6nuLjYsN0J2mOXjqoyoDqeU4Ber6KrrS9NQ/m0Ad+24OIBeRng6gGeftrxRhCfEk+5Wo6CgorKE5ue4L9j/isV/a3MbM0qRaFw+3ZObN+uDZKaVUKIZsLiFaonnniCp59+ml9//RVFUcjKyuLjjz9m1qxZTJkyxRpzrJeSkhISEhKIjY01Oh4bG8uuXbvqdI0bbriBs2fPcvHiRfR6Pdu3b6dnz55Xfc/ChQvx9/c3vCqDMUfUoZUX7i46ikr1nMq9Yv0b+IfA9FR4YocWVJUVwfiPteM2Vr0+1TdjvsFFcSHjUgYzf5pp83s3R0a5VVu3ELp8ufEAyasSQjQTFgdUzz77LKNHj2bYsGEUFBQwZMgQJk6cyBNPPMGT5vqC2VhOTg7l5eUEBQUZHQ8KCuJMHf9Sd3V1ZcGCBQwZMoTIyEi6d+/OXXfdddX3zJ49m7y8PMMrIyOjwb+Drbm66Ogc6A3AUVskpoO2KuXdCq6/Q/s59Uvb3KeamsU+O/l1Ykq0FtRvStvEvxP+bfM5NEdGuVXmnobV66W8ghCiybPKc+T//Oc/ycnJ4bfffmP37t2cO3eOl19+2RqXbrCa2zuqqtZry2fEiBHs27eP1NTUOrXP8fDwwM/Pz+jlyCq3/Y7ZOo8q6n7t674voLzUpreqWewT4NHej9LKoxUAO0+ZlvGQ+lTWVWvNqhdekPIKQogmzWqFeby9venXrx/9+/fH19fXWpett8DAQFxcXExWo7Kzs01WrZqzytIJNk9M73qbljt1OUfr8WdD5op9urm4cWtHrWHzHxf/4PczvxvOSX0q6zNXs8qtY0coK5PyCkKIJq3JfZK4u7sTExNj8lTepk2buOmmm+w0K8fTtbGe9HNxhYiKUgnJn9j2XrWYe9NcerfuDcCMbTMoLi822R4U1lOzZlW7l+aaDtLrKUmzTtV8IYRwBE5ZrbKgoICjR48afj5x4gTJyckEBATQsWNHZsyYwUMPPUS/fv0YOHAgK1asID09nbg4+eCs1LVyhepcQb23Q+st+n7YvRQO/w8uXwDvANvdqxYrYldw+xe3k1ucS/+P+5vdHhTWU70XIKCtWOn1RmPyN27EtX17yrKycO/cSfoCCiGcmlOuUO3Zs4c+ffrQp08fAGbMmEGfPn2YM2cOAOPHj2fx4sXMmzeP6Ohotm/fzsaNG+nUyUyT12aqaxtfFAVyL5dyobDEtjdrFwFB4VBeAvttn5xujp+7Hy/frOX16VU9rjpXCaYaick2YEXwnrtmDcdjYyWvSgjRJCiqWpnYIKwpPz8ff39/8vLyHDZBfdCrW8i8eIU1k25kQJfWtr3ZriXww/PQpif4BMLt8yCkr23vWUPlNl+lKdFTmBw1uVHn0JyVnjlDSVo67p06UrBzJ2de+IfxAJ2Obls2y0qVEMKuGvr5Lc2RmzFDxXRblU6oLuI+UFzg3EE4uQP2rrH9PaupDKYm9JqAt6tWMmJZ8jLiU+IbdR7NWfXyCu6hZuq06fVcSU1t/IkJIYQVSHPkZqzRnvTLTYdLWRB6Q9Wx1HWQlQxZSdp5G6qegD7rhlk81fcpANx17ixNXipBlR3UWl5hzhwKduyUmlVCCKfjlM2RhXU02pN+iyNgxVDI2F11rDAHVtyiHV8cYdPb10xA/3OPPxPeOpwSfQld/buiV/XXuIKwNnPlFVzatkF/4SIZjz8uNauEEE7HKZsjC+sw9PQ7V2jbG92zEnQ1HyitSN3TuWrnbahmfSoXnQs9W/dEQeFY3jF6Bhi3FZJin42jZnmFbj/8gP+YMdpJqVklhHAyFgdUlc2Ra7Jlc2RhHZVbfqdyr1BYXGa7G0WOg4mbzZ+buFk738jaerdFrQjq/vnrPyks1YJKKfbZuIza1nh64j9qlOkgvZ7itLTGn5wQQtSDxXWoKpsjv/fee4bmyL/88guzZs0ylDEQjqmVjzutfdw5X1jC8XOFRIT6N8JdFQyrU3YUFxVHmb6Md/a+w9nLZ1mStAR/D38p9mlnhtyqGjWrcpYuw8XXF/2lAqlZJYRwSBYHVM8++yx5eXkMGzaMoqIihgwZgoeHB7NmzbJLc2RRP13b+nL+xAWOnrtk24DKpw34tgW/EMjN0FrRePhpx+3kyT5PcrrgNF8f/5r/HPwPgARTdlaZW3V6zotaUKUo4OLCld9+4+S9Y7VBOh3t571Ey7Fj7TtZIYSoxmp1qC5fvsyBAwfQ6/X06tXLrv38HIEz1KECmP3lPj79LZ2pw7ryt+HX2/ZmZcXg4g7b34Ct86HTzfDoRtvesw6iPohCjx4FhYSHEnDTuV37TcKmqtesKjlxgvRH/2o8QGpWCSFsxG51qB599FE2b96Ml5eXQzRHFvVTmZielJ5r+5u5emgrDlHjtZ/TfrZ5yYRriU+JR4+2vaSiMvXHqXadj9BUz63CXD6bXk/Bjh1SXkEI4TAsDqjOnz/PnXfeSWhoKDNnziQ5OdkK0xKNpUMrLwB2HTvPrC9SuFJSbvubtuwInQdr36c0boHP6qrXp5p/83wAfjn9C6/+9qrd5iRM1Vaz6syLc6W8ghDCYVgcUH399decOXOGF198kYSEBGJiYujVqxcLFizg5MmTVpiisJUjZy/x8n8PGH7+MjGTO9/ewZGzl2x/8+gHtK8pn1Y9It+IqgdTcVFxjOw6kgHtBwDwn4P/kWKfDsRczSr3bt20HCspryCEcBBWeTa8ZcuWTJo0iW3btpGWlsajjz7KRx99RLdu3axxeWEDaxMyuevtnWTlFhmO6VVIO3+Zu97eybqETNtOoOdIcPOBC8cg4zfb3suMmsU+FUWhq39XXBQXAA6eP2g0XmpT2VfNmlVBLzxvOkivpyTNvlvIQojmy6rFdkpLS9mzZw+//vorJ0+eJCgoyJqXF1ayLzOPWV+kUFymp1xvvDpUrlcpLtMz84sU9mXm2W4SHr7Qa6T2fcontrtPLWoW+wRo5dmKclXb8kzMTuRC0QVAalM5iup5VR6dO5vdBrz42afoCwslt0oI0eis8gmxdetWHn/8cYKCgpgwYQItWrTgm2++ISMjwxqXF1YWHuJHZKg/OsX8eZ0CUaH+hIfY+OnEqPu1r3u/gPfvgFP2bVUUFxXH5KjJAOQW5/LG72+YbA0Kx2CyDaho/2e+9N3/OHp7rORWCSEancVlE0JDQzl//jzDhw/nL3/5C3fffTeenp7Wmp/TcvSyCT8dPseE92rfavvwr/0Zcp2Na0Tp9fDvSMirCLwHxMEI+yeEv7TrJdYeqfoQlmDKcRmVV0hP59Ssv1GenW08SEosCCHqwW5lE+bMmUNWVhYbNmzgvvvuk2DKSQzpHmh2lapydWpw90DbTiA3Hc6kQJehVcdS10FWMmQl2bWcwos3vWi0vTeh9wS7zUVcXfVtQJ/+/Wn/4oumgyS3SgjRCCwOqCZNmkSrVq2sMRfRiBRFYWZsD2qkUKFXYWZsDxSllv1Aa1kcASuGQtJHVccKz8GKW7TjiyNse/+riE+JR69WtT554ocn7DYXUT+evXuZza0qPnxI8qqEEDbVoC2/GTNm8PLLL+Pj48OMGTOuOnbRokUNnpwzc/QtPwBVVdmflU9ZuZ57l++iXIX3H7mBoT3a2D6g2vs5bJgMejNNmXWuMHq5XZomV8+Zuj7geqZtmQbAuOvG8Y+B/2j0+Yj6y127tqp1jTnSukYIcRUN/fxuUC+/pKQkSktLDd/XxuYfysIiiqIQHqL17wtr48vR7AJ0OqVx/twix0HgddqKVE0TN0NwtO3nUIO5BPTYTrH8kPYDnx/+nNZerZkSPaXR5yXqp+XYsfgMGkRJWjpuIcFc+PhjLr6/umpARc0qn0GDJK9KCGE1DQqotm7davj+gw8+IDQ0FF2NZXZVVeUpPyfSrSKgOppdwC22TkY3oQCNX9yzppq1qQBmD5jNtoxtlOhLSMlOMXlP5fagBFqOxa1dO0Ow1OKWocYBFYBeT/GxYxJQCSGsxuIcqrCwMHJyckyOX7hwgbCwMEsvLxpJZU+/o9kFjXdTnzbg21ZbjWofrR1z89KO24G52lSBXoHcHHIzAL+d/Y1TBacM56Q+lXOorXVN9quvUfjb75JXJYSwCos/CWpLwSooKJAn/pxIZUB1rDEDKv8QmJ4Kj2+FYRWVr13tF1DVZvGwxQT7BFOmL2PSD5NQVVXqUzkRczWrFC8vig8fJv3hh6VelRDCKhq05QcYktEVRWHOnDl4e3sbzpWXl/Prr78SHR1t8QRF4zCsUJ1rxIAKwNVD+9r1VvANgoKzcHQTXH9n487jKnSKjvjb4xn91WjSL6XT56M+lKvlEkw5kep5Ve6dOlKWfY6T46o99CB5VUIICzV4hSopKYmkpCRUVWXfvn2Gn5OSkvjjjz+Iiopi9erVVpyqsKUubXwAuFBYwvmC4safgItr1VN9yY3fiuZawvzDDFXUy9Vy3HRuEkw5meo1q/SXL5sO0OvJ+/a/jT8xIUST0OAVqsrE9EcffZR///vfDlsaQNSNt7srIS29OJV7haPZBbT29Wj8SUQ9ALvehsPfQ+F58Gnd+HO4Cn21x/BL9aXEp8RLUOWkDHlVNUornHvjDcrOnqXVg3+h7PQZ3Dt3khUrIUSdWJxD9f7770sw1UTYbduvUlAvaB8F+lJIdax8lviUeJbvXc693e9FQSsrsTR5KfEp8XaemWgIk7wqnQ7vAQMAuPjRRxwf/ifJrRJC1EuDV6hqOnDgAOnp6ZSUlBgdHzlypLVuIWysW1tffjp8rnGf9Ksp6gE4naJt+w1wjArlNRPQXXWurDm0Bj93P5YmLwWQlSonVDOvyq1dO3K/+orTf3+uapDkVgkh6sjigOr48eOMGTOGffv2oSiK4am/yuKQ5eXllt5CNBK7lE6oKWIs/PA8nE6GFbfCnW9ASF/7zQfT+lTT+05na8ZWsi9n07dtX6M2NcK5VK9XBeAWZCZo0uu5nJyCdzSUnEyTbUAhhFkWb/k9/fTThIWFcfbsWby9vdm/fz/bt2+nX79+bNu2zQpTFI3FLqUTavIJhOv+pH2flQB719hvLhVq1qfydfelb1styEs5l8JtHW8zGh+fEs+y5GWNOkdhHbXVrDr9979zdNitsg0ohKiVxQHVL7/8wrx582jTpg06nQ6dTsegQYNYuHAhTz31lDXmKBpJtzZaQJWVV0RhsZkee7aWmw5ZSdDhxqpj+9ZCVrJ2PDe98edUi64tuwLaE39zd82lXK+txEqxT+dmLrfKJSgItbgYKmvuVWwDSjFQIUR1Fm/5lZeX4+urfRAHBgaSlZVFjx496NSpE4cOHbJ4gqLxtPJxJ9DXnZyCEo6dKyAytGXjTmBxhOmxyznG/f7m5jXefK4iLiqOwtJCVu9fTer5VD7941MKSguk2GcTUDO3qvjoUTImPm48SK/XegXK1p8QooLFAVV4eDh79+6lS5cuDBgwgNdeew13d3dWrFhBly5drDFH0Yi6tvElp+ACR7PtEFDdsxI2TAa9mdUxnSuMXt6487mGmf1mciLvBD9l/sSrv78KIMFUE1Ezt8pciYVL27biFhJMaeYpyasSQli+5ffCCy8Y6vPMnz+ftLQ0Bg8ezMaNG3nrrbcsnqC9vPnmm/Tu3ZtevXrx1FNP1dpip6mxa2J65DiYuNn8uYmbqwp/OpC3bn3LUEZBQeGJSMd4MlFYj7nWNQAX31/Nsf+7XfKqhBCAFVaohg8fbvi+S5cuHDhwgAsXLtCqVSvDk37O5ty5cyxZsoT9+/fj5ubGkCFD2L17NwMHDrT31GzOIZ70A0ABHD+IXbF3BWrFPFVUZv00i38N/ZedZyWsreY24KVNmzj7zwVVA6S8ghDNnk0yZwMCApw2mKpUVlZGUVERpaWllJaW0rZtW3tPqVHYvbinTxvwbQvB0dCzooaZzs3hGiaDcX2qKdFTAPgh7Qf+nfBvO89M2EL11jUe3a8zHaDXU7T/QONPTAjhEBq0QlXZGLkuFi1a1JBbXNX27dt5/fXXSUhI4PTp06xfv57Ro0cbjVm2bBmvv/46p0+fpnfv3ixevJjBgwfX6fpt2rRh1qxZdOzYEVdXV+Li4ujatavVfw9HVBlQpZ2/TEmZHnfXRn5azT8EpqeCi7vWKPngt1rl9FIzvdfsqGaxz9LyUr4/8T3H8o7xbuq7eLh6SC5VE1Zb65rTL76IztsL97AwqVklRDPToIAqKSmpTuNstUpVWFhIVFQUjz76KPfee6/J+TVr1jB9+nSWLVvGzTffzDvvvMOIESM4cOAAHTt2BCAmJobiYtMmwD/88ANeXl58++23nDx5Ei8vL0aMGMH27dsZMmSITX4fR9LOzxNfD1cKistIO19I96AWjT8J14o+gi3aQff/gyM/QMqncNucxp9LLWoW+3RzcSOyTSTH8o4BkJ5vXOIhPiUevao3rGQJ51aZV3V6zotaUKXT4dKqFeU5OaQ/+lctz0pVQaej/byXaDl2rL2nLISwsQYFVJWNke1lxIgRjBgxotbzixYt4rHHHmPixIkALF68mO+//57ly5ezcOFCABISEmp9/xdffEG3bt0ICAgA4M4772T37t1XDaiKi4uNArT8/Px6/U6OQlEUurbxISUzjyPZBfYJqKqLfqAioPoMhj0POhf7zqeCucAo2DfY8H3yuWSKyorwdPU0Ws0STUfNvCoXPz9Oz3mR/G+/NalZJblVQjR9VtnP2bFjBw8++CA33XQTp06dAuCjjz5i586d1rh8vZSUlJCQkEBsbKzR8djYWHbt2lWna3To0IFdu3ZRVFREeXk527Zto0ePHld9z8KFC/H39ze8OnTo0ODfwd66OkxiOnDdCPD0h/xTcGK7vWdzVXFRcTweodUryriUQXxKvMnWoGhaqudV6by9za9E6fUUp6U1/uSEEI3K4oBq3bp1DB8+HC8vLxITEw2rNJcuXWLBggXXeLf15eTkUF5eTlBQkNHxoKAgztSxsvGNN97IHXfcQZ8+fYiMjKRr167XbPI8e/Zs8vLyDK+MjIwG/w725jhP+gFunhBe8SGV/Il951IHT/V9ijvC7gBgVeoqCaaamdpa1+QsWcqV1FQKd/8qFdaFaKIsDqjmz59PfHw8K1euxM3NzXD8pptuIjEx0dLLN1jN/C1VVeuV0/XPf/6TgwcPsn//ft56661rvtfDwwM/Pz+jl7OqbEHjEAEVaNt+AAe/gSLH30p9dcirRrWpKletRNNntmaVqytXfv+dk2Pvk5pVQjRhFgdUhw4dMptb5OfnR25urqWXr7fAwEBcXFxMVqOys7NNVq2EeZUrVMdzCth/ygFavYTEQOvuUHYFDnxl79lcU3xKvFFtqie3PGnnGYnG1HLsWLpt2UzHDz6g29YtdHx3pfEA6QUoRJNkcUDVvn17jh49anJ8586ddmk94+7uTkxMDJs2bTI6vmnTJm666aZGn48z6hjgjZtOoahUz51v72TWFylcKSm334QUpWqV6tcVsPouOGW/1c+rqZ4zNWeg9lTizlM7ef331+08M9GYqudWgZnVbb2eS1u3UnrmjGwDCtFEWBxQPfHEEzz99NP8+uuvKIpCVlYWH3/8MbNmzWLKFNs8Il5QUEBycjLJyckAnDhxguTkZNLTtUfVZ8yYwbvvvst7773HwYMHeeaZZ0hPTycuTvJY6uJETqHRZ8CXiZnc+fYOjpy9ZL9JRY4HFDi7F07ugL1r7DeXWtRMQL+3+730bdsXgA8PfEh8SrydZyjsoba8qrPzXubosFtlG1CIJkJRrdCk7vnnn+fNN9+kqKgI0PKJZs2axcsvv2zxBM3Ztm0bw4YNMzk+YcIEVq9eDWiFPV977TVOnz5NeHg4b775ZqPWkcrPz8ff35+8vDynyqdam5DJ8+v3UVKmN2r84qJTcNUpLBgTwb0xoY07qdx0uHweNv4NMn/Xjvm0gb+sBVTwbg0tOzbunMxYlrwMnaIzSkA/kXeC0RtGo0fPbR1vY/GwxUbvkfpUzUPu2rVGNas8rutO8R+HjAfpdHTbslnKKwhhZw39/LZKQAVw+fJlDhw4gF6vp1evXvj6+lrjsk7LGQOqfZl53L3k2qUuvnlyEBGh/o0wowpzzd2rRq+/uQ6Q61WLid9P5Nczv+Ll6sUP9/5AS8+WgOmKlmjaSs+cMdSsKj55koxHHjUZ0+GD1fgOGGCH2QkhKjX089uiLb/S0lKGDRvG4cOH8fb2pl+/fvTv37/ZB1POKjzEj8hQf3S1PNCoUyAq1J/wkEYOEO9ZCbqaNWgrgimdq3begS3/v+UEeAZwpewKE3/Qis1KMNX8GPUC7NzZ7DbghfdXU3T4sORVCeGELF6hatOmDbt27aJ79+7WmlOT4IwrVAA/HT7HhPd+q/X8h3/tz5Dr7NCoOCsZVtxienzST1ojZQeXci6FBzc+CICr4kqZWibBVDNntA2oKNqrem9AaVsjhF3YZYUK4OGHH2bVqlWWXkY4iCHdA82uUlWuTg3uHmifiRnYpj+krUW1ieL+6+8HoEwtw03nJsFUM1ezvELosmXGA6S8ghBOpUG9/KorKSnh3XffZdOmTfTr1w8fHx+j84sWLbL0FqIRKYrCzNgeJqtUehVmxvawWcPra/JpA75twS8EcjPgcg54+GnHnUQLt6q+iKX6UuJT4iWoaubc2rUzJKGXnDTTnkavp+Dnn2llpgm8EMKxWBxQpaam0rev9mj44cOHjc7Z7cNXWGRI90C+nTaIl77Zz+8nLzL5li7cGRlM72A7bl36h8D0VHBxh+1vwNb50C5CO+4E4lPiWbFvBXeG3cl/T/wXBYWlyUsBJKgSQLXyCtW3/YAzc19CLSjA9/bbKU3PwL1zJ3kSUAgHZHFAtXXrVmvMQzgQRVEID/Gnb8dW/H7yIoUl5YSHNOJTfbVx9dC+Rv0Ztv4T0n7WSio4QMmEq6mZgF6mlvH9ye8J9AqUoEoYVLatMSqv0K0bxYcPc3bhK5xd+Io2UHKrhHBIFudQiabLoZokV9eyA4RV1BRL+cy+c6kDvao3SkB/rv9z+Ln7kXMlh5uCb0Kv6q9xBdFcGOVVbdlM2FcbaPPMdONBklslhEOSgErUymEDKqhqRZP8CVinlJrNTImeYrQCFegVaKignng2kbu73m00Pj4lnmXJNRKURbNRvbyCoih4RUWbDtLrKfrjkLSuEcKBSEAlatW1IqDKvlRM3pVSO8+mhp53g7svXDwB6bvtPZt66x3YG4Ci8iLm/TKPyuollduDOkX+0xSa2lrXZP3979K6RggHIn9ri1r5eboR5KflLTncKpW7D/QarX2f/LFdp9IQcVFxPNhTq0u1+/Ruvj72tRT7FGZV5lYZgiqdDl2LFujz8qpWZ2UbUAi7k4BKXFX3ttqj/sccLaCCqm2/fevg/TvgVKJ951NPf+//d25sfyMAL/z8ggRTolY1c6uCX3vVdJBeT0laeuNPTggBNPApvxkzZtR5rNShcm7d2vqy82gOR885YEDVcSC06gwXT2pP/O1dAyF97T2reln2f8uI+SgGFRUFRYIpUavqNasAsyUWruzbi1vHDpSmpUt5BSEaWYMCqqSkJKOfExISKC8vp0ePHoBWj8rFxYWYmBjLZyjsqqujJqbnpsPl89BlGCS8rx1LXQdR9wMqeLd2+HIKAKv2rUKt6EuoojJ7x2wWDl5o51kJR2dSYqHCuTf+xbk3/qX9IOUVhGhUDQqoqteeWrRoES1atOCDDz6gVatWAFy8eJFHH32UwYMHW2eWwm66tdECqiPZl+w8kxoWR5geKzxn3O9vbl7jzacBqudMXSq5xIcHPuTb498S7BPMtL7T7D094eBajh2Lz6BBlKSl49YhlNzPv+B8fHzVgIq8Kp9Bg2SlSohGYHEO1b/+9S8WLlxoCKYAWrVqxfz58/nXv/5l6eWFnXUP0gKqzItXKCott/NsqrlnJehq+feAzlU778BqJqBPjZ5KiK9W9X3FvhXEp8Rf4wpCVJVYcA8OxufGG00H6PUUHzna+BMTohmyOKDKz8/n7NmzJsezs7O5dMnBVjVEvbX2caeltxuqCsccKY8qchxM3Gz+3MTN2nkHVrPYp7ebN33a9DGcP11w2mi81KYS11JbeYUz8+dTdOCA1KwSwsYsDqjGjBnDo48+ytq1a8nMzCQzM5O1a9fy2GOPcc8991hjjsKOFEUxbPs5XB6VgfP1jKxZ7BOgk38nw/d7c/ZSWq7V/pLaVKIuzJVXUHx9KU1L48R946RmlRA2ZnEvv/j4eGbNmsWDDz5Iaan2AeDq6spjjz3G66+/bvEEhf11a+vLnrSLjhdQ+bQB37bgF6Jt82X+Dq6e2nEnFBcVR1FZEatSV3E09yjv738fvaqXcgqizqrnVbl36oji4UHWs89SuGNn1SDJrRLCJiwOqLy9vVm2bBmvv/46x44dQ1VVunXrho+PjzXmJxyAw7ag8Q+B6ang4g4nd8IHd4HODbwD7D2zBpseM520S2n8mPYjbye9DSDBlKiXmuUVAh57zDigAkPNKgmohLAeq+0h+Pj4EBkZSVRUlARTTYzDBlQArh6gKNDpZq1MQskl+OO/9p6VRRbdsgilYhtTQWFS5CQ7z0g4M4/Onc3mVl344AOKDh+RvCohrMQqAdWOHTt48MEHGThwIKdOnQLgo48+YufOndd4p3AGlQHViZxCSsv11xhtJzpdRQ0qnLIVTXXv7H3HqDbV01uftvOMhDMzya1SFFAUCrZs4cTIkZJXJYSVWBxQrVu3juHDh+Pl5UVSUhLFxcUAXLp0iQULFlg8QWF/wf5eeLu7UKZXSTt/2d7TqV3Un7Wvx7dBfpZdp9JQ1cspPHvDswBsy9jGv/ZICRLRcEata7ZuIXTpEuMB0gtQCItZHFDNnz+f+Ph4Vq5ciZubm+H4TTfdRGKic/VWE+bpdApdHf5JPyCgi7b1p+oh5TN7z6beatameuD6BwhvHQ7A6v2rpTaVsEhlzSq3du3QeZtJy9DrKfj5ZymvIEQDWRxQHTp0iCFDhpgc9/PzIzc319LLCwdRue3nULWozKlsmJz8CaiqfedSTzVrU7noXOjZuie6iv9Mj140LtAotalEQ9Vas2rOi1JeQYgGsjigat++PUePmlbi3blzJ126dLH08sJBVAZUR846eLHWXqPAzRvOH4EVQ+GU86ySmqtN1da7LXq0vLWE7ATyS/IBqU0lLGOuZpVbWGcoL6/6h4hsAwpRLxaXTXjiiSd4+umnee+991AUhaysLH755RdmzZrFnDlzrDFH4QAMT/o5+gqVRwvoORL2fgank2HvGgjpa+9ZNVhcVBzl+nLi98aTcyWHRXsW0c6nndSmEharWbOq+ORJMh551HiQlFcQos4sDqieffZZ8vLyGDZsGEVFRQwZMgQPDw9mzZrFk08+aY05Cgdg2PLLLkSvV9HpHLA6eW46XD4PHQZoARXAvrUVT/+p4N1aK63gZKb2mcqZy2fYcHQD646s045JMCWsoGbNKnQ60Bs/yXvx00/x7N0LfUEBJSfTcO/cSQIsIcxQVNWyRJP09HRCQ0MpKiriwIED6PV6evXqhY+PDxkZGXTs6HwfYNaQn5+Pv78/eXl5+Pn52Xs6Fisr19Nzzv8oLVfZ8ewwOgR423tKpub612FMnu3nYSNRH0ahV7UPuz0P7sHDxcPOMxJNTe7atZye86IWVCkV/2hSVVxataI8N1fbDtTpaD/vJVqOHWvXuQphKw39/LY4ASMsLIycnBy8vb3p168f/fv3x9fXlwsXLhAWFmbp5YWDcHXR0bm19mTQlkPZdp5NLe5ZqbWgMUfnqp13UvEp8YZgCuCJH56w42xEU1WzvEKn/3yEa7t2lF+8KLlVQlyDxQFVbQtcBQUFeHp6Wnp54UDC2mirUi9+tZ9ZX6RwpaTczjOqIXIcTNxs/tzEzdp5J1S9nMLioYsBLUF9/u759p2YaJKql1fwjomh3dwXTQdV5FYJIao0OIdqxowZACiKwpw5c/D2rtoCKi8v59dffyU6OtriCQrHcOTsJX47ftHw85eJmSSmX+SdB2PoHtTCjjOrjQ5w0Kru9VCzNhXA/3X8P35M/5E1h9bQ2rM1k6Mn23mWoinzvP56s7lVV5KTcOvYgdK0dMmrEgILVqiSkpJISkpCVVX27dtn+DkpKYk//viDqKgoVq9ebcWpCntZm5DJXW/vJL+o1HBMr0La+cvc9fZO1iVk2nF2Nfi0Ad+2EBwFkRWV0xUX8Am077waqGZtKoDZA2bjrnMHIDk72eQ9Up9KWJNJiYUK595czDGpWSWEgcVJ6Y8++ij//ve/nTbxesyYMWzbto3bbruNtTX+Qvj222+ZOXMmer2ev//970ycOLHO120qSen7MvO4e8m1ezJ+8+QgIkLrkBTeGMqKwcUdSgrg9e5QdkXb8gvtZ++ZWc20LdPYlrENV50r34z+htAWoYD5FS0hrKH0zBmthEKHUPLWrSNnaY2gXaej25bNslIlnJ7dktLff/99pw4YnnrqKT788EOT42VlZcyYMYMtW7aQmJjIq6++yoULF+wwQ/sKD/EjMtSf2qok6BSICvUnPMSB/j/g6qE9oeTRQiv0CU7fMLmmfw/7N8E+wZTpy5i0aRKqqkowJWyqMrfKPTgY7xv6mw7Q6yk+fLjxJyaEg7BameUDBw7wv//9j6+//tro5eiGDRtGixamOUC//fYbvXv3JiQkhBYtWnDHHXfw/fff22GG9qUoCjNje6CvZR1Tr8LM2B4oigPWpYKqVjT71kFpkX3nYkU6Rcc7t7+Di+JCxqUM+nzUR4Ip0WhqbV3z0jwubd0qvQBFs2RxQHX8+HGioqIIDw/nzjvvZPTo0YwePZoxY8YwZswYi669fft27r77boKDg1EUhQ0bNpiMWbZsGWFhYXh6ehITE8OOHTssumelrKwsQkJCDD+HhoZy6tQpq1zb2QzpHmh2lapydWpwdwfOT+o8GPw7QHEeHPqvvWdjVZ39O/NkH614brlajpvOTYIp0SjMta7R+flReuoUmZOnSF6VaJYsDqiefvppwsLCOHv2LN7e3uzfv5/t27fTr18/tm3bZtG1CwsLiYqKYsmSJWbPr1mzhunTp/P888+TlJTE4MGDGTFiBOnpVY/zxsTEEB4ebvLKysq66r3NpZY57CqMjdW2SuXwq1Og/YUfVZGcnvyJfediAyXlJYbvS/WlxKfE23E2ojkxqlm1ZTOd/vMf4wFSr0o0Mxa3nvnll1/YsmULbdq0QafTodPpGDRoEAsXLuSpp54iKSmpwdceMWIEI0aMqPX8okWLeOyxxwzJ4osXL+b7779n+fLlLFy4EICEhIQG3TskJMRoRSozM5MBAwbUOr64uJji4mLDz/n5+Q26r6Ma0j2Qb6cN4ocDZ3hr81EiQ/1ZMCaC3sEOlDtVm6j7YfvrcGwL5GeBX7C9Z2QV8SnxLE9Zzn3X3ce6I+vQq3qWJi8FkJUq0Siqt64pOZlmOkCv58KHH9H2b7MoO3tWWteIJs3iFary8nJ8fbU+b4GBgYaVn06dOnHo0CFLL1+rkpISEhISiI2NNToeGxvLrl27LL5+//79SU1N5dSpU1y6dImNGzcyfPjwWscvXLgQf39/w6tDhw4Wz8GRKIpCeIg/w3q0BeBMXhHhIf6OvTpVqXVX6DgQVD3sXASr74JTifaelUWqJ6DPGTiHB3s+CICvmy9Lk5fKSpVodLXlVV147z1O3HMvR2+9TbYCRZNmcUAVHh7O3r17ARgwYACvvfYaP//8M/PmzaNLly4WT7A2OTk5lJeXExQUZHQ8KCiIM/VYYh4+fDj33XcfGzduJDQ0lN9//x0AV1dX/vWvfzFs2DD69OnD3/72N1q3bl3rdWbPnk1eXp7hlZGR0bBfzMF1rWiSnH2pmLwrpdcY7UAqk9P3fgEnd8DeNfadj4Vq1qeaGj2VEN8QCkoLiAyMNGpTI0RjMJdX1WL4cHB1pfjgwarCoLIVKJooi7f8XnjhBQoLCwGYP38+d911F4MHD6Z169asWWP7D62aKySqqtZr1eRqT+6NHDmSkSNH1uk6Hh4eeHg0/Wa1fp5utPPz5Ex+EUezC4jp1MreU7q23HQI6AIuHlCUqx1LXadtBaKCd2to6VxNvKdETzH62dvNmz5t+3Cq4BT7cvbxbP9njc5X9gKs+T4hrKnl2LH4DBpESVo67p064tauHRc//5wzc2q0r6loXSNbf6IpsTigqr4N1qVLFw4cOMCFCxdo1aqVTbeDAgMDcXFxMVmNys7ONlm1EtbVra0vZ/KLOOYsAdXiCNNjhTmw4paqn+fmNd58bKSTXycAVFTm7prL53d9jpuLm9H2oBC2Vj2vCsB3yBCzrWv0xUVasVDJqxJNhMUBFUBRURF79+4lOzsbfY3/aOq6wlNf7u7uxMTEsGnTJqPyDJs2bWLUqFE2uafQdGvry86jORzJvmTvqdTNPSthw2TQl1U7WPHIos4VRi+3y7SsLS4qjqKyIlalruJo7lFWpa4CkPpUwq4qtwJPz3nRKKjKjJsMqqq9dDraz3uJlmPH2nGmQljG4oDqf//7Hw899BDnz583OacoCuXl5Q2+dkFBAUePHjX8fOLECZKTkwkICKBjx47MmDGDhx56iH79+jFw4EBWrFhBeno6cXHywWFL3SryqI5mF9h5JnUUOQ4CrzNekao0cTMERzf6lGxlesx0Mi5l8EPaD4Yn/iSYEvZWfStQ19Kfc4vepPCnn6oGVORV+QwaJCtVwmlZnJT+5JNPMm7cOE6fPo1erzd6WRJMAezZs4c+ffrQp08fAGbMmEGfPn2YM2cOAOPHj2fx4sXMmzeP6Ohotm/fzsaNG+nUqZOlv5a4isqA6oizBFTNzBu3vIGCtt2uoDApcpKdZyREVesarx49CHj0EdMBej3FaWZKLwjhJCxeocrOzmbGjBk2yVsaOnSo2QKb1U2ZMoUpUyTRtjF1rwioTuVe4UpJOV7uLnaeUR34tAHftuAdCNkHtGPegdrxJuadve+gVmxpqqhM2zKNpbcttfOshKji0bmz2byqC++9j0vLlugv5kpelXA6Fq9QjR071uKK6MK5tPb1oJW3G6oKx845ySqVfwhMT4XJu6DjTdqxG+O0401I9QT02f1nA7A9cztv/P6GnWcmRBWTEguKAjodhT/9xMlRo6VelXBKinqtJaBruHz5Mvfddx9t2rQhIiICNzc3o/NPPfWURRN0Vvn5+fj7+5OXl4efnxNUE6+ncfG/8NvJCyweH83oPk4WlCR+BF8/qeVVTf1N+8u8CageTMVFxaFX9Tz83cOknEsBJJdKOJ7SM2cMJRaKDh0m84knjAfodHTbsllWqkSjaujnt8Vbfp988gnff/89Xl5ebNu2zahUgqIozTagauq6tvXlt5MXnCcxvbreo+G7ZyHnMJxKgNB+9p6RVdQs9qlTdFwfcD37cvahV/UcvnjYaLzUphL2VpfWNQU7duA7eLCUVxAOzyqFPefNm8dzzz2HzkzbAdE0VSWmO0nphOo8WkDPkbD3M0j+uMkEVOYCo0CvQEPV9ISzCeQW5dLSs6XUphIOx9C6pkZe1ZkX50p5BeEULI6ASkpKGD9+vARTzUx3ZyudUFNlK5p966C0yL5zsaG4qDjiIrUVqwtFF3hjzxsmW4NCOAJzrWvcu3XTAqzKzBRpWyMcmMVR0IQJExqlxYxwLJUrVGnnL1NS5oR94zoPBv8OUJwHh/5r79nY1NQ+U7m3+70AfHXsKwmmhMNqOXYs3bZspuMHH9Bty2aCXnjedJCUVxAOyuItv/Lycl577TW+//57IiMjTZLSFy1aZOkthANq7++Jj7sLhSXlpJ0vpHtQC3tPqX50Oq2X3/bXYHc87Hkfbp8HIX3tPTObmHvTXNYfXW/Y/pvQe4KdZySEeTVb15jbBry4ejVe11+P/soVya0SDsPiFap9+/bRp08fdDodqampJCUlGV7JyclWmKJwRIqiOF/F9Jqi79e+Zv4GJ3fA3qa70lqZgF5p0g9S7FM4PrPlFRSFgq3bOHp7LEeH3SolFoTDsHiFauvWrdaYh3BCXdv6kpKZx5HsAkbYezL1lZsORXnQLhLO7NWOpa7TVq1Qwbs1tOxo1ylaS/WcqV6tezF181SSzyUz75d5zBk4x97TE+Kqqretce/UkbJz5zj1zAxKMzOrBknrGuEArNIcWTRP3dtq23xOuUK1OML0WGGOcb+/uXmNNx8bMZeAPiJsBN+d+I4vDn9BoFeglE0QDq/6NqBbu3a0+8cLZDxRIwdQr6ckLV0CKmE3DQqoZsyYwcsvv4yPjw8zZsy46ljJoWq6nLqn3z0rYcNk0JdVO1jxJJHOFUYvt8u0rK1mbSqA5/o/x5b0LRSXF5N4NtHkPVKfSjg6jx49zOZWFf7yC24dQilNz5C8KtHoGhRQJSUlUVpaavheNE+VpROOnyugXK/ionOiiuOR47RK6dVXpCpN3AzB0Y0+JVswFxQFeAYwOGQwP6b/yJ6zeziZd5LO/p0BpD6VcAqVuVWn57xoFFSdj4/nfHy89oPUrBKNzOLWM8K8pt56BqBcr9Jzzv8oKdOz/W/D6Nja295Tqp+s5IqASsGwOgUw6acmE1DVRlVV7lx/JxmXMgj2Cea7e79jxd4VUlJBOJXK1jVuHTuQ/9//cu6NfxkPkNY1ogEa+vlt8VN+P/74Y63n3nnnHUsvLxyYi06hS6AP4KQV033agG9bLXjybKUd8/DTjjdxiqKwMnYlrjpXsgqz6PtRXwmmhNNxa9cOnwH9cW/fHq9wM3mRej1FBw40/sREs2RxQHXnnXcyc+ZMSkpKDMfOnTvH3XffzezZsy29vHBwTl06wT8EpqfC41thQEUZgZC+2vFmIMQ3hBkxWg5kuVqOm85NginhtAyta2o4/eJc8jZupHD3r1JhXdiUxQHV9u3b+eabb7jhhhvYv38///3vfwkPD6egoICUlBRrzFE4sMqA6veTF+w8kwZy9dBq20RV1KQ6/hPknbLvnBpRQUlVIFyqLyU+Jd6OsxGi4cy1rnEJCKD83DmyZsyUelXC5iwOqAYMGEBSUhKRkZHExMQwZswYZs6cyZYtW+jQoYM15igcWMcALW/qx4PZzPoihSsl5XaeUQMFhEGnQYCqNU1uBuJT4lmWsow/9/gzror2fMrS5KUSVAmnVbN1TaeP/2M8QHoBChuySkfjQ4cO8fvvvxMaGoqrqyt//PEHly9ftsalhQM7cvYS//rhsOHnLxMzufPtHRw564T5VFDVMDn5k6pmrE1U9af5nr/xef4a8VcAvF29JagSTq0yr8qtXTvKzmabDtDryVkej6rXU3rmjGwFCquxOKB65ZVXGDhwILfffjupqan8/vvvhhWrX375xRpzFA5obUImd729kzP5RYZjelVrlnzX2ztZl5B5lXc7qF6jwM0Hzh+FjN/sPRubqlmf6onIJwjzD+Ny2WV6BvQ0alMjhLOqLa8qd80ajt95F0dvvU22AoXVWBxQ/fvf/2bDhg28/fbbeHp60rt3b3777Tfuuecehg4daoUpCkezLzOPWV+kUFymp1xvvJJTrlcpLtMz84sU9mU6WaVxD18tqAJI/ti+c7GxKdFTjBLQ3V3ciQqMAuDghYPEBMUYjY9PiWdZ8rJGnaMQljKXV+U3aiR4elJy4kRVDSvZChRWYJXmyCNGGHdyc3Nz4/XXX+eHH36w9PLCAYWH+BEZ6k9tdTx1CkSF+hMe4oT1tyq3/fathffvgFOmlcSbqpAWVU83vvTLS1wpuwJUbQ/qFKtkCAjRqGrmVYW8+irBL71kOrCidY0QDWXx35CBgYG1nrvlFjNVqIXTUxSFmbE90NeSZqRXYWZsDxTFiSqnV+p0M7TsBKWFkPYz7F1j7xk1mrioOB6PeByAjEsZLE9ebrYXoBDOpnpeFYD3gP5mtwLLzudIXpVoMKtUSs/NzWXVqlUcPHgQRVHo2bMnjz32GP7+/taYo1Nq6pXSVVVl1NKfST2VZxRY6RSICPFnw9SbnS+gyk2Hy+ch4QNIeF875tMG/rIWUMG7NbTsaNcpNobntj/Hf0/81/CzBFOiKcpdu9akdQ2glVFRVWld04w19PPb4oBqz549DB8+HC8vL/r374+qquzZs4crV67www8/0LdvX0su77SaekAF8NPhc0x4zzR5+8O/9mfIdU5YbXxuHf4BMNfJ8sIaKPKDSFRUFBQSHkrATedm7ykJYXWVrWtc27YhZ9ly8r/5xniAtK5pluzWeuaZZ55h5MiRnDx5ki+//JL169dz4sQJ7rrrLqZPn27p5YUDG9I9kG+nDWJt3EDDsU8mDmBw99q3gR3aPStBV0u/cJ2rdr4ZiE+JR63obaiiMuVH0wbLQjQFlVuBHmFhtLz3XtMBej3FJ082+ryEc7I4oNqzZw9///vfcXWt+iBydXXl2WefZc+ePZZeXjgwRVEID/GnX+cAQlp6AeDqonO+rb5KkeNg4mbz5yZu1s43cdVzpubfPB+A3ad388pvr9h5ZkLYVm0lFs4t/jdXUlIkr0pck8UBlZ+fH+nppk9GZGRk0KJFC0svL5xEZQsap2ySbJaTBoUWqJmAPrLrSAa211YfPz74MctTltt5hkLYjkmJBUUBd3eKkpM5Of7PUq9KXJPFAdX48eN57LHHWLNmDRkZGWRmZvLZZ58xceJE7r//fmvMUTiB7s7cJLk6nzbg2xaCoyG0v3bM1VM73sTVLPapKApd/LvgWrENuj9nv9F4qU0lmhqjEgtbt9DpvVXGA6RelbiKWhJG6u6NN95AURQefvhhysrKAK0O1eTJk3nlFdkmaC66NZWAyj8EpqeCizuk7YLVd4DiCl4t7T0zm5sSbZor1dKzJWV67b/rxLOJZF/Opq13W6PVLCGaErd27QxJ6CUn00wH6PXkf/cdrR99VEtqP5mGe+dOkrguLAuoSktLGT58OO+88w4LFy7k2LFjqKpKt27d8Pb2ttYchRPoHtREAioAVw/ta6eboFVnuHgSDn4DUX+256zsIi4qDlVVWZayjEull/jn7n/Ss3VPqU0lmgVDXlWN0grZr75G4Y4dFO7+VTsnJRYEFm75ubm5kZqaiqIoeHt7ExERQWRkpARTzVC3Nlq+3Om8Ii4Vldp5NlaiKBD9F+37Jt6K5momR09mfI/xAGzJ2CLBlGg2zLWu8ep/AwCFu36R1jXCiMU5VA8//DCrVq269kDRpPl7u9Gmhbayc+xcoZ1nY0WVq1IntmuFP5upF258waj1zP3XS36kaB5qtq7p/OGHtJnxjOlAaV3T7FkcUJWUlLB8+XJiYmJ44oknmDFjhtHL0Y0ZM4ZWrVoxtsZSbUZGBkOHDqVXr15ERkbyxRdf2GmGzqNbm4on/c42lSf90Cqjhw3Rvk/5zL5zsaP4lHj0atW2x+M/PG7H2QjRuGq2rvEfOdJsiQWdh7u0rmnGLA6oUlNT6du3L35+fhw+fJikpCTDKzk52QpTtK2nnnqKDz/80OS4q6srixcv5sCBA/z4448888wzFBY2oZUXGzDkUZ1rAnlU1UU/qH1N/ti0TUUzUD0B/YM/fQDAwQsHeWHnC3aemRD2YbIVWCFtwiMcHXarlFhopix+ym/r1q3WmIfdDBs2jG3btpkcb9++Pe3btwegbdu2BAQEcOHCBXx8fBp5hs7D8KTf2SYWUPW8C/7bQktOT/wAUtfB7fMgpOm3VTLXHHl8j/GsObSGr459RTufdjzZ50k7z1KIxtdy7Fh8Bg2iJC0dxdWFs/9cQNGBA1UDKvKqfAYNkicAmwmLV6iqU1UVK/RaNti+fTt33303wcHBKIrChg0bTMYsW7aMsLAwPD09iYmJYceOHVa7f6U9e/ag1+vp0KGD1a/dlBgCqqa2QuXuA71Ha9/vXg4nd8DeNXadUmOpWZsKYHrf6fi4av+w+PX0rybvkfpUormo3Ar0jomhzayZpgMkr6pZsUpAtWrVKsLDw/H09MTT05Pw8HDeffddi69bWFhIVFQUS5YsMXt+zZo1TJ8+neeff56kpCQGDx7MiBEjjCq3x8TEEB4ebvLKysqq0xzOnz/Pww8/zIoVKyz+fZq6yoAq/cJlikrL7TwbK8pNhw4DtO9zDmlfU9dBVjJkJTXpZPUp0VNMnubzdfdlaIehAKScS2H/+aqCn5UrWtUT2IVoDjy6dDGbV5X39VcUp6VJXlUzoKgWLin94x//4M0332TatGkMHKi1qfjll19YsmQJTz/9NPPnz7fORBWF9evXM3r0aMOxAQMG0LdvX5Yvr2qJ0bNnT0aPHs3ChQvrfO1t27axZMkS1tbY7y4uLub222/n8ccf56GHHrrqNYqLiykuLjb8nJ+fT4cOHerdrdqZqapK9LxN5F0pZeNTg+kV3ER+77n+Zg4qQLX/dObmNdZsHMaYr8ZwNPcogV6B/DD2B1btWyUlFUSzlrt2LafnvKjlWioK1Px4lXpVTiE/Px9/f/96f35b/M/I5cuXs3LlShYuXMjIkSMZOXIkCxcuZMWKFcTHx1t6+VqVlJSQkJBAbGys0fHY2Fh27dpl8fVVVeWRRx7h1ltvvWYwBbBw4UL8/f0Nr+a4PagoiqEFTdPp6QfcsxJ0NdMNK/6i1Llq55uhd2PfxcPFg5wrOdzwnxskmBLNXs3WNe1frdEtROpVNWkWB1Tl5eX069fP5HhMTIyhFY0t5OTkUF5eTlBQkNHxoKAgztTj/6zDhw/nvvvuY+PGjYSGhvL7778D8PPPP7NmzRo2bNhAdHQ00dHR7Nu3r9brzJ49m7y8PMMrIyOjYb+Yk6vc9jvWFCqmV4ocBxM3mz83cbN2vhlq7dWaOQPnAFCuluOqc5VgSjR71UssuAWZSUbX67m8J6HxJyZszuKn/B588EGWL1/OokWLjI6vWLGCv/zlL5Ze/poURTH6WVVVk2NX8/3335s9PmjQIPT1eETew8MDDw+POo9vqroZVqiaUEAlapVVUJWLWKYvY3nKciZHTbbjjIRwHLW1rjn9j39QlpODx/U98OjcWZ4CbCIsDqhAS0r/4YcfuPHGGwHYvXs3GRkZPPzww0bFPWsGXZYIDAzExcXFZDUqOzvbZNVKNJ4m0yS5Jp824NsWXL0h96TWPNmzpXa8mapMQH+o10OsPbyWK2VXWJa8DAVFVqqEoKpelSGvSqfDLTSU0vR0sl+p2A6UvKomw+KAqrKwJ8CxY8cAaNOmDW3atCE1NdUwrj6rRnXh7u5OTEwMmzZtYsyYMYbjmzZtYtSoUVa9l6i77kFaT78TOYWUlutxc2kiT3v5h8D0VNCXw796QHE+jInXjjdDNetTtfdpz2u/v4a7zp2lyUsBJKgSAuN6Ve6dOqKWl3Ps/26vSliXelVNhkMX9iwoKODo0aOGn0+cOEFycjIBAQF07NiRGTNm8NBDD9GvXz8GDhzIihUrSE9PJy5O/iK3l2B/T7zdXbhcUk7a+cuGFasmwbViSzf8HkhYDXs/h2632XVK9lKzPtUD1z/A6tTVZF/JJswvjHK9cdmMytY1U6Kn2GO6QtiVW7t2hmCpcPevpk//6fWcmf9PQl5/jfK8PEpOpuHeuZMEWE7GoQt77tmzhz59+tCnTx8AZsyYQZ8+fZgzR0uEHT9+PIsXL2bevHlER0ezfft2Nm7cSKdOnaw2B1E/iqJU2/ZrQk/6VVfZiubAV1CUb9+52EnN+lQuOhdu7XgrACfyT9CtVTfDOalNJUQVQ15VDQU//sjR22OldY0Tc+jCnkOHDjUEadVfq1evNoyZMmUKJ0+epLi4mISEBIYMGWLxfYVlKpskN7k8qkqh/aB1dyi7ogVVAoDnb3yefkHaE7//+Pkf5BXnmW1dI0RzZtIHUKej1YQJuAQEUJ6TY7IVKCUWnIfFW361FfZ85plnOHnypNUKewrn0S2oiT/ppyjQ5y/w41ytYXLfa9cpay7euf0d/u+L/+Ni8UWGfDYEPaata4Ro7mrmVbm1a4f3Df049eQ044EVrWtk6885WBxQVRb2vP/++w3HRo4cSWRkJNOmTZOAqhmqXKE60tSaJFcXOR42z4P0X+D8MWjd1d4zcgjuLu68detbPPTdQ+jR46pIbSohzKmeVwXgFR5utsRC0f5U3Dp2oDQtXfKqHJzTFvYUjqvySb9j5wpIPdVEW7L4BUNXLWeI5E/sOxcHs/v0bsP3ZWoZbye+bcfZCOEcTLYCK2S/9jrHJK/KKVgcUFUW9qypsQp7CsfToZUXbjqF4jI9d729k1lfpHClpAk1S64UXfH/78QPYPVdcCrRvvNxAJU5U5MiJtHOR/uX9Ip9K4hPsV0bKiGaiuqta7pu/pHWT0wyHiB5VQ7NaQt7Csd1IqeQ6mXHvkzMJDH9Iu88GGNYvWoSetwBnv5QeE577V0DIX3tPSu7qZmAHtU2iqmbp6KgSG0qIeqo+lagz8CbOP/OCuMBej3Fhw/L1p8DctrCnsIxrU3I5Pn1+ygtryqfoVch7fxl7np7JwvGRHBvTKgdZ2gluelw+Tx0GQYHNmjHUtdB1P2ACt6toWVHe86w0dWsTTUkdAh3hN3BxhMbCfAMoLS81M4zFMK51Na65sxL8wh64Xl0Xt6SV+VAbFrYMzk5mejoaEtvIZzEvsw8Zn2RYvZcuV6lXK8y84sUrgtqQUSofyPPzsoWR5geK8yBFbdU/Ty3ieaP1cJc0c623m3xdPHkQtEF3F3cjc5JsU8hrs5c6xqdry+lp06RObnivxtpXeMwrF5pLy8vj2XLlhETE0NMTIy1Ly8cWHiIH5Gh/uhqWYzUKRAV6k94iF/jTswW7lkJupr/HqlYldO5aucFPm4+FJUXAfDO3nc4nnsckGKfQtRV9byqbls20+k//zEeIHlVDsNqf5tt2bKFBx98kPbt2/P2228zYsQI9uzZY63LCyegKAozY3ugr6VYvl6FmbE9msb2b+Q4mLjZ/LmJm7XzgrioOKZGTwWgVF/K3F/msjxluRT7FKIe3Nq1w2dAf9zataP8wgXTAXo9599fjaqqlJ45Q+HuXyXAsgOLtvwyMzNZvXo17733HoWFhYwbN47S0lLWrVtHr169rDVH4USGdA8kMtSf1FN5RoGVToGIEH8Gdw+03+RsRsGwOiVMxEXFcankEh8e+JCk7CSSspMkmBKigWrLq7r4wQdc/uUXio8eNWwPylZg42rwCtUdd9xBr169OHDgAG+//TZZWVm8/bbUm2nualulalKrU5V82oBvWwiOhrYV/4Bw89aOCyN/u+FvuCguhp9HdR1lx9kI4bzMta5pMeJP4OZG8eHDVYGWbAU2ugavUP3www889dRTTJ48me7du1tzTsLJDekeyLfTBjH/2wPsPnGBSYPDGBkdQu/gJpA7VZ1/CExPBRd3OPgNfP4QePhBC3nipqb4lHjK1XIUFFRUHv/hcb4Z803TCrCFaCTmWtdcXLuWMy/8w3igtK5pVA1eodqxYweXLl2iX79+DBgwgCVLlnDu3Dlrzk04KUVRCA/xp2+nVgAUlJQTHuLfND88XT203n7X/Qm8AqDgDByr/cnX5qh6faoNozagU3SkXUpj5k8z7T01IZxW9bwqAN9Bg0yqrAOU5+dLXlUjaXBANXDgQFauXMnp06d54okn+OyzzwgJCUGv17Np0yYuXbpkzXkKJ9S9okny0abaJLk6V3eIuE/7Pvk/Vx/bjNQs9tmlZRcmR00GYFPaJhYnLLbvBIVoImprXXPqqac4Kq1rGoXFT/l5e3vz17/+lZ07d7Jv3z5mzpzJK6+8Qtu2bRk5cqQ15iicVLc2WlX0ZhFQAfSpaEXzx3/hykX7zsVB1Cz2CVBaXkqAZwAA2zO3G42PT4lnWfKyRp2jEE1F9RILYd9+Q4vYWFBV7QWSV2VjVi0C06NHD1577TUyMzP59NNPrXlp4YS6tvUB4EJhCecLiu08m0bQLhKCwqG8BPbJvwJBK/ZZ82k+Nxc3LhRpj34fyT3CjswdgNSmEsIaKrcCPbt1o9UDD5gO0OspPnmy0efVHNjkby4XFxdGjx7N119/bYvLCyfh7e5KSEsvoJmsUilKVcPk5E/sOxcHVr02FcC83fN4O/FtqU0lhJUZSizUkLNkKVf27ZO8KiuTfwoKmzLkUZ1rBgEVaAU9da6QlQgrb4VTifaekUOKi4pjUsQkAM4UnmHFvhUSTAlhZSZ5VYoCrq5c2bOHk/eNk7wqK5OASthU97ZaQHXkbDMJqHwCtSf+AE4lwN419p2PA5vWdxquSlXllhvb32jH2QjRNBm1rtm6hY7vrTIeIHlVViMBlbCpbm2b0ZN+uemQlQQdB1Yd27cWspK147npdpuaI4pPiadMLUNX8dfQU1ueoqS8xM6zEqLpMSqxYK43mF5P/nf/A5ASCxawqPWMENfSrW0zetJvcYTpscs5sOKWqp/n5jXefBxY9XIKf+7xZ2LXxXKx+CJxP8bx3vD37D09IZqs2lrXZL/6KoU7d1L4yy/SuqaBZIVK2FTlCtWZ/CLyi0rtPBsbu2ellj9ljs5VOy9MalO19GzJvJvmAfD7md9ZsHuBnWcoRNNlrnWNV79+ABT+/LO0rrGABFTCpvy93GjbwgOAY019lSpyHEzcbP7cxM3aeWG2NtXwzsPp1KITAJvTN1OuLzd6j9SnEsJ6jPKqtmym838+IvDpp00HVrSuEXUjAZWwucon/Y409YDKiPynVRtztakURWFoh6EAZF/J5rNDnxnOSX0qIayvZuualmNGmy2xoLi7S15VHcnfUMLmurXRAqomv0IF4NMGfNtCcBSE36sd07lqx8VVzbphFreEavlmb+x5g6yCLJPtQSGEbdTWuiZ9wgRpXVNHkpQubK5bkJaY3ixWqPxDYHoquLhr7WcOfA36Urh8XjsnruqtW9/iT+v+xOnC0/xp3Z9QUSWYEqKRtBw7Fp9BgyhJS0dxc+XsgoUUpaZWDajIq/IZNMiwsiWqyAqVsLnKFaoj2c2kYbarh1ZAzzsArr9TO5b8sX3n5CR0io53bn8HABUVF8VFgikhGlHlVqB33760mTHDdIDkVdVKAiphc5U5VJkXr3ClpPwao5uYPg9qX/d+DmVSY6kuvj/5veH7crWcN/e8acfZCNF8eXQJM5tXlbf+S4pPnpS8qhokoBI219rHnZbebqgqHGsuLWgqdb0VWrSHKxfg8Hf2no3Dq8yZmhw1metaXQfAe/vfIz4l3s4zE6L5Mdu6Bsjb8BXH/zRC8qpqkIBK2JyiKIYWNM0uoNK5QNSfte+TZNvvaqonoE+JnsK8m+YZnuxbmrxUgioh7KBm65r2r79mPEDqVRlIQCUaRWXF9GbT06+66L9oX4/+CJfkL53a1KxP1TuwNxGtterzPm4+FJUVGY2X2lRCNI7qJRbc2rQ1HaDXU7j718afmIORgEo0imbV06+mwO4Q2h/UctixCFbfBacS7T0rh2OuPtWNwVrD5MLSQgpKq/6/I7WphLAPQ+uaGk7PmcOFDz+iJCur2eZWNfu/jcaMGUOrVq0YW0u/osuXL9OpUydmzZrVyDNrWiq3/JrNk3419alYpdq7Bk7u0L6Ka3qyz5OM6joKgDWH1pB4NlFqUwlhR+Za17h36wYlJZxdsIBjt97WbHOrmn1A9dRTT/Hhhx/Wev6f//wnAwYMaMQZNU2VK1Qnz1+mpEx/jdFNTG46tO4GLh5QlKsdS10HWcmQlaSdF7WaP2g+PQN6AjDhfxMkmBLCzmq2runyzdcETq/RuqYZ5lY1+4Bq2LBhtGjRwuy5I0eO8Mcff3DHHXc08qyanvb+nvi4u1CuV9nyx1l7T6dxLY6A1XdCeXHVscIcWHELrBiqnRdXtTK2qrG0TtFJMCWEnVXPq1IUBe/oPqaD9HqKDhxoNq1rHDqg2r59O3fffTfBwcEoisKGDRtMxixbtoywsDA8PT2JiYlhx44dVrv/rFmzWLhwodWu15wpikJYoA8Acf9JZNYXKc2nJtU9K7X2M0ZU7YvOVTsvrurTPz41fK9X9czfPd+OsxFC1FRbbtWpZ//ebFrXOHRAVVhYSFRUFEuWLDF7fs2aNUyfPp3nn3+epKQkBg8ezIgRI0hPr9pCiYmJITw83OSVlZV11Xt/9dVXXHfddVx33XVW/Z2aqyNnL3Hy/GXDz18mZnLn2zs4crYZ5FRFjoOJm82fm7hZOy9qVT1n6raOtwFaPpU84SeE4zCXW6Vr2RK1oADUin9ANvFtQIfu5TdixAhGjBhR6/lFixbx2GOPMXHiRAAWL17M999/z/Llyw0rSwkJCQ269+7du/nss8/44ov/3969B0Vd/nsAf+/CgshPMCIuK4Ic8zIJUmCljKF5TiiTacdSKcewCw3ldbSfl2kM63SOHmts5hyvTXjp1IxN/dSTaXkwgXSIZFhQJDNUBEyQtFgQ4rqf88fCwrJcVhf2u7u8XzOM8Hwf8LMPny98+D7f7/N8iTt37qC5uRk+Pj545513uu3f2NiIxsaOKZ2ampp7+n9d0Vd51/H24UI0tXbcO2UQoPR2PWb/9xn8x79G4rmYEAUjJEfV9Qb0qvoqnK04i9rmWuw6t4vTf0QOpPNegB5hoWj85RLKU7qcn21b17jiXoAOfYWqN01NTcjLy0N8fLxZe3x8PLKzs23++ps3b0Z5eTmuXbuGDz/8EMnJyT0WU+39fX19TW8jR460OQZXUHhdj7e+PIfGFoPpj5R2rQZBY4sBa748h8LremUCtBfvB4C/BQCBEQCMqw1j6P3GdupR17WpAoYGIDowGgDgrnLHnw1/mvXn2lREyup8b5Xn+HHdTgPW5eS45PIKTltQ3bp1C62trQgMDDRrDwwMROVdfINmzpyJ+fPn4/jx4wgJCUFubu49xbNhwwbo9XrTW3l5+T19HVcTMcIHE0N8oVZ1f1ytAqJCfBExwse+gdmb7whg1QUg5Qwwpu2PgKhEYzv1qLu1qSL8IwAALdKCK9VXIG2VOtemInIsFtOAbW7v2uWSyys49JSfNVQq89/UImLR1psTJ0702WfJkiV99vH09ISnp6fV/+9goVKpsCZ+HJL2nu32uEGANfHj7up75rTc2/IjejFQfAI4/yXwL+8Cbhpl43IyKVEp0Dfq8dnFz/BT5U84cvkIbtbf5HIKRA6o8zSgJnQkao5+g9+3bevo0HZflffUqU4/Dei0BZW/vz/c3NwsrkZVVVVZXLUiZcWN8cfEEF9c+E0PQ6dpP7UKiBzhiyfG+CsXnBLGzjJO9dVVAcX/B4x/WumInM66x9bhqv4qsm9k451s41Q8iykix6QJCjIVS14TJ1p2MBjQUPSz0xdUTntt3MPDAzExMUhPTzdrT09PR2xsrEJRUXfar1IZutxDNaiuTnXmpgGiXjC+r/sfZWNxYjv+eQdUbfejqaBiMUXkBHrbuqb666NOfV+VQ1+hunPnDi5fvmz6uKSkBAUFBfDz80NoaChWr16NxYsXY9KkSZgyZQo+/vhjlJWVIaXrUwWkuLgx/vhm+VSL9glaF793qiePLAay/8s49VdTAfgEKx2R0/mk8BNI23peAsHaH9Zia9xWhaMiot6031dV8U4qYDAAajXc7rsPrbdvo2LtWmMntRrB772L4T1sCeeoVCJdn71yHJmZmXjyySct2pOSkrB//34AxoU9t27dioqKCkREROCjjz5CXFycnSO1VFNTA19fX+j1evj4DNKigXqXNhMozwEefQ34/RLw1HvAiGilo3IKnZdTaGxtxCeFnwAAkiOTsSJ6hcLREVFfmisrTcsrGBoacHVWlyWS1Go8eOp7RaYB7/X3t0MXVM6MBRX1Kf9z4H/fBDx9gMYa4PEUIOE/lY7K4XVdm6qhpQHPH30epTWlAHgvFZGzqcv5CWXdPPzl88wz0P77+2j54w80XSuFx6gwuxRY9/r722nvoSJyatVlgN8/Ae5DjcUUwA2TrdR1baoh7kOQOiXVdLy8lkuWEDmTnu6rqjl6FJfjZzrN1jW8QjVAeIWKerXJt5tGFUx7/AHAJhdf7LSfLTi6ABf/uIgwnzD8Y84/4OnWsYzJ7nO7YRAD3nz4TQUjJKKeVH/1ldl9VcMXLEDN8eMwdN11xA5TgbxCReRMuGFyv5s6wvjQQ2lNKXaf221q54KfRI5v+PPP48FT3yP0wAE8eOp7BG9KRfC/vWfZsW3rGkfk0E/5EbmsiQsA/7HAx9Msj732PaB92O4hObsV0Stw/c51fFvyLdIK0zBr1CxklGdwwU8iJ9F5vSoA8IqKMk4FGgxm/f44cABq76Ew3Kmz231V1uCU3wDhlB/16UZBW0GlBmDo+Pf1LBZUNnj2yLO4or8CFVQQCIspIidmNhXYvmZh57JlAJZY4JQfkbNp3zBZGwXM/sj4798CuGGyjT6ZaVxCQSBQq9QspoicmNlUYMYphOzebd6hbesaR1gMlFN+REpp3zDZzcP4l1fMy0BrU8eef3RPvvq14ykggxiwNmsttk7jgp9EzqrzVGDTtVLLDm33VSk99ccrVERKcvfsuIytUrGYslHnNapejngZAPDttW/xQe4HCkdGRP2h2yUW1Gp4hIUqE1DnMJQOgIioP3Rd8HP5I8sR4BUAAPj050+xs2CnRf+ubUTk2Nq3rjEVVW33UCl9dQpgQUVELqLrgp8atQYzR800Hc+pyDG9z6UUiJxX1yUWHGXPPz7lN0D4lB+RY/h71t/x3bXvAAB7ntqD87+f51IKRNQj7uXnYFhQETmOxG8SUXS7yPQxiyki6gmXTSAi6sH+WfuhgvHmf3e1O4spIup3LKiIyOXtL9oPgUCj1qDF0GK2NQ0RUX9gQUVELq3z03+6xTosfXgpdhTsYFFFRP2KC3sSkcvqupQCANO/Owp2mH1MRGQLFlRE5LK6LqXQrv1jgxi6+zQiorvGp/wGCJ/yIyIicj58yo+IiIhIISyoiIiIiGzEgoqIiIjIRiyoiIiIiGzEgoqIiIjIRiyoiIiIiGzEgoqIiIjIRiyoiIiIiGzEgoqIiIjIRiyoiIiIiGzEvfwGSPuOPjU1NQpHQkRERNZq/719tzvzsaAaILW1tQCAkSNHKhwJERER3a3a2lr4+vpa3Z+bIw8Qg8GAGzduYNiwYVCpVP32dWtqajBy5EiUl5cP6k2XOQ4dOBZGHAcjjkMHjoURx8HI2nEQEdTW1kKr1UKttv7OKF6hGiBqtRohISED9vV9fHwG9YnRjuPQgWNhxHEw4jh04FgYcRyMrBmHu7ky1Y43pRMRERHZiAUVERERkY1YUDkZT09PpKamwtPTU+lQFMVx6MCxMOI4GHEcOnAsjDgORgM9DrwpnYiIiMhGvEJFREREZCMWVEREREQ2YkFFREREZCMWVEREREQ2YkHlZHbu3Inw8HAMGTIEMTExOH36tNIhDajNmzfj0UcfxbBhwxAQEIBnn30Wly5dMuuzZMkSqFQqs7fJkycrFPHA2LRpk8VrDAoKMh0XEWzatAlarRZeXl6YPn06ioqKFIx4YIwaNcpiHFQqFZYuXQrAtXPhhx9+wDPPPAOtVguVSoUjR46YHbcmBxobG7F8+XL4+/vD29sbc+bMwfXr1+34KmzX2zg0Nzdj3bp1iIyMhLe3N7RaLV566SXcuHHD7GtMnz7dIk8SExPt/Eps01c+WHMuuEI+AH2PRXc/M1QqFT744ANTn/7ICRZUTuSLL77AqlWr8PbbbyM/Px9PPPEEEhISUFZWpnRoAyYrKwtLly5FTk4O0tPT0dLSgvj4eNTV1Zn1mzVrFioqKkxvx48fVyjigTNhwgSz11hYWGg6tnXrVmzbtg3bt29Hbm4ugoKC8NRTT5n2lHQVubm5ZmOQnp4OAJg/f76pj6vmQl1dHaKiorB9+/Zuj1uTA6tWrcLhw4dx8OBBnDlzBnfu3MHs2bPR2tpqr5dhs97Gob6+HjqdDhs3boROp8OhQ4fw66+/Ys6cORZ9k5OTzfJkz5499gi/3/SVD0Df54Ir5APQ91h0HoOKigrs3bsXKpUKzz33nFk/m3NCyGk89thjkpKSYtY2fvx4Wb9+vUIR2V9VVZUAkKysLFNbUlKSzJ07V7mg7CA1NVWioqK6PWYwGCQoKEi2bNliamtoaBBfX1/ZvXu3nSJUxsqVK2X06NFiMBhEZHDkgogIADl8+LDpY2tyoLq6WjQajRw8eNDU57fffhO1Wi3fffed3WLvT13HoTtnz54VAFJaWmpqmzZtmqxcuXJgg7Oj7sahr3PBFfNBxLqcmDt3rsyYMcOsrT9ygleonERTUxPy8vIQHx9v1h4fH4/s7GyForI/vV4PAPDz8zNrz8zMREBAAMaOHYvk5GRUVVUpEd6AKi4uhlarRXh4OBITE3H16lUAQElJCSorK81yw9PTE9OmTXPp3GhqasJnn32GV155xWwD8sGQC11ZkwN5eXlobm4266PVahEREeHSeaLX66FSqTB8+HCz9s8//xz+/v6YMGEC3nrrLZe7mgv0fi4M1ny4efMmjh07hldffdXimK05wc2RncStW7fQ2tqKwMBAs/bAwEBUVlYqFJV9iQhWr16NqVOnIiIiwtSekJCA+fPnIywsDCUlJdi4cSNmzJiBvLw8l1kZ+PHHH8enn36KsWPH4ubNm3j//fcRGxuLoqIi0/e/u9woLS1VIly7OHLkCKqrq7FkyRJT22DIhe5YkwOVlZXw8PDAfffdZ9HHVX+GNDQ0YP369XjxxRfNNsNdtGgRwsPDERQUhAsXLmDDhg04d+6caQrZFfR1LgzGfACAAwcOYNiwYZg3b55Ze3/kBAsqJ9P5L3HAWGR0bXNVy5Ytw/nz53HmzBmz9oULF5rej4iIwKRJkxAWFoZjx45ZnDTOKiEhwfR+ZGQkpkyZgtGjR+PAgQOmG00HW26kpaUhISEBWq3W1DYYcqE395IDrponzc3NSExMhMFgwM6dO82OJScnm96PiIjAmDFjMGnSJOh0OkRHR9s71AFxr+eCq+ZDu71792LRokUYMmSIWXt/5ASn/JyEv78/3NzcLP5yqKqqsvir1BUtX74cX3/9NTIyMhASEtJr3+DgYISFhaG4uNhO0dmft7c3IiMjUVxcbHrabzDlRmlpKU6ePInXXnut136DIRcAWJUDQUFBaGpqwp9//tljH1fR3NyMBQsWoKSkBOnp6WZXp7oTHR0NjUbj0nnS9VwYTPnQ7vTp07h06VKfPzeAe8sJFlROwsPDAzExMRaXH9PT0xEbG6tQVANPRLBs2TIcOnQIp06dQnh4eJ+fc/v2bZSXlyM4ONgOESqjsbERFy9eRHBwsOkydefcaGpqQlZWlsvmxr59+xAQEICnn366136DIRcAWJUDMTEx0Gg0Zn0qKipw4cIFl8qT9mKquLgYJ0+exP3339/n5xQVFaG5udml86TruTBY8qGztLQ0xMTEICoqqs++95QTNt3STnZ18OBB0Wg0kpaWJj///LOsWrVKvL295dq1a0qHNmDeeOMN8fX1lczMTKmoqDC91dfXi4hIbW2trFmzRrKzs6WkpEQyMjJkypQpMmLECKmpqVE4+v6zZs0ayczMlKtXr0pOTo7Mnj1bhg0bZvreb9myRXx9feXQoUNSWFgoL7zwggQHB7vUGLRrbW2V0NBQWbdunVm7q+dCbW2t5OfnS35+vgCQbdu2SX5+vunpNWtyICUlRUJCQuTkyZOi0+lkxowZEhUVJS0tLUq9rLvW2zg0NzfLnDlzJCQkRAoKCsx+ZjQ2NoqIyOXLl+Xdd9+V3NxcKSkpkWPHjsn48ePlkUcecZlxsPZccIV8EOn73BAR0ev1MnToUNm1a5fF5/dXTrCgcjI7duyQsLAw8fDwkOjoaLPlA1wRgG7f9u3bJyIi9fX1Eh8fLw888IBoNBoJDQ2VpKQkKSsrUzbwfrZw4UIJDg4WjUYjWq1W5s2bJ0VFRabjBoNBUlNTJSgoSDw9PSUuLk4KCwsVjHjgnDhxQgDIpUuXzNpdPRcyMjK6PReSkpJExLoc+Ouvv2TZsmXi5+cnXl5eMnv2bKcbn97GoaSkpMefGRkZGSIiUlZWJnFxceLn5yceHh4yevRoWbFihdy+fVvZF3aXehsHa88FV8gHkb7PDRGRPXv2iJeXl1RXV1t8fn/lhEpExPrrWURERETUFe+hIiIiIrIRCyoiIiIiG7GgIiIiIrIRCyo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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "max_eles = np.asarray([20, 46, 80, 172], dtype=int)\n", "radius = 10.\n", "sigma_e = 5.\n", "intensity = 1.\n", "distances = np.asarray([50., 20., 15, 12])\n", "\n", "eles_c = 2 * max_eles\n", "markers = ['p', '*', 'x', '.']\n", "plt.figure()\n", "plt.xlabel('$L$')\n", "for counter in np.arange(0, len(max_eles)):\n", " num = max_eles[counter] + 1\n", " p_0 = np.asarray([0., 0., distances[counter]])\n", " l2_norm = np.zeros(max_eles[counter] // 2)\n", " final_length, total_weights, pre_vector = (\n", " quadratures.gauss_legendre_trapezoidal_1d(eles_c[counter])\n", " )\n", " grid_analytic = np.zeros(final_length)\n", " legendre_functions = np.zeros((num, final_length))\n", " full_expansion = np.zeros((num, 1))\n", " full_expansion[:, 0] = (\n", " harmonicex.point_source_coefficients_dirichlet_expansion_azimuthal_symmetry(\n", " max_eles[counter], radius, distances[counter], sigma_e, intensity\n", " )\n", " )\n", " for ii in np.arange(0, final_length):\n", " grid_analytic[ii] = mathfunctions.point_source(\n", " radius * pre_vector[:, ii], p_0, sigma_e\n", " )\n", " legendre_functions[:, ii] = pyshtools.legendre.PlON(\n", " max_eles[counter], pre_vector[2, ii]\n", " )\n", " for el in np.arange(0, max_eles[counter], 2):\n", " grid_expansion = np.sum(\n", " legendre_functions[0:el + 1, :] * full_expansion[0:el + 1],\n", " axis=0,\n", " )\n", " l2_norm[el // 2 + np.mod(el, 2)] = np.sqrt(\n", " np.sum((grid_analytic - grid_expansion)**2 * total_weights)\n", " )\n", " phi_norm = np.sqrt(np.sum(grid_analytic**2 * total_weights))\n", " plt.semilogy(\n", " np.arange(0, max_eles[counter], 2), l2_norm / phi_norm,\n", " marker=markers[counter],\n", " label='$d =$ ' + str(distances[counter])\n", " )\n", "y_label = 'Approximated relative error in $L^2(\\mathbb{S})$'\n", "plt.ylabel(y_label)\n", "plt.legend(edgecolor='white')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c1e6f7fa", "metadata": {}, "source": [ "## Plane wave function" ] }, { "cell_type": "markdown", "id": "2bf9b8ad", "metadata": {}, "source": [ "Defined as\n", "$$f(\\mathbf{r}) = A e^{i \\mathbf{k} \\cdot (\\mathbf{r} + \\mathbf{p})},$$\n", "\n", "with $A\\in \\mathbb{R}^+$, $i=\\sqrt{-1}$, $\\mathbf{k}$ the wave vector, and $\\mathbf{p}$ a vector." ] }, { "cell_type": "markdown", "id": "adf5a011", "metadata": {}, "source": [ "In the case of $\\mathbf{k}=(0,0,k)$ we have the following expansion:\n", "$$f(\\mathbf{r}) = 2 \\sqrt{\\pi} A e^{i k p_z} \\sum_{l=0}^{\\infty} i^l \\sqrt{2l+1} j_l(k||r||_2) Y_{l,0},$$\n", "with $\\mathbf{p}=(p_x, p_y, p_z)$, $j_l$ the spherical Bessel function, $Y_{l,0}$ the complex spherical harmonic of degree $l$, $||\\cdot||_2$ the Euclidean norm.\n", "\n", "And the expansion of its derivative with respect to $||r||_2$ for the same case:\n", "$$\\frac{\\partial}{\\partial ||r||_2}f(\\mathbf{r}) = 2 \\sqrt{\\pi} A k e^{i k p_z} \\sum_{l=0}^{\\infty} i^l \\sqrt{2l+1} j_l'(k||r||_2) Y_{l,0},$$" ] }, { "cell_type": "markdown", "id": "1f5aea62", "metadata": {}, "source": [ "In this case, $f_{l,m}$ decays to zero when $l\\rightarrow \\infty$, but there is not $L$ from which every $f_{l,m}=0$, with $l>L$. Thus, the series has to be truncated, and its accuracy will depend on the value of $k$." ] }, { "cell_type": "code", "execution_count": 8, "id": "111d0707-889d-4b9c-89c1-4fbb920721d3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "max_eles = np.asarray([16, 34, 52, 66, 80], dtype=int)\n", "radius = 1.\n", "a = 1.\n", "k = np.asarray([1., 11., 21., 31., 41.])\n", "\n", "eles_c = max_eles + 10\n", "markers = ['o', 'p', '*', 'x', '.']\n", "plt.figure()\n", "plt.xlabel('$L$')\n", "\n", "k0 = np.asarray([0.,0.,0.])\n", "for counter in np.arange(0, len(max_eles)):\n", " num = max_eles[counter] + 1\n", " k0[2] = k[counter]\n", " l2_norm = np.zeros(max_eles[counter] // 2)\n", " final_length, total_weights, pre_vector = (\n", " quadratures.gauss_legendre_trapezoidal_1d(eles_c[counter])\n", " )\n", " grid_analytic = np.zeros(final_length, dtype=np.complex128)\n", " legendre_functions = np.zeros((num, final_length))\n", " full_expansion = np.zeros((num, 1), dtype=np.complex128)\n", " full_expansion[:, 0] = (\n", " harmonicex.plane_wave_coefficients_dirichlet_expansion_0j(\n", " max_eles[counter], radius, 0., k[counter], a, True\n", " )\n", " )\n", " for ii in np.arange(0, final_length):\n", " grid_analytic[ii] = mathfunctions.plane_wave(\n", " a, k0, pre_vector[:, ii], np.zeros(3)\n", " )\n", " legendre_functions[:, ii] = pyshtools.legendre.PlON(\n", " max_eles[counter], pre_vector[2, ii], \n", " )\n", " for el in np.arange(0, max_eles[counter], 2):\n", " grid_expansion = np.sum(\n", " legendre_functions[0:el + 1, :] * full_expansion[0:el + 1],\n", " axis=0,\n", " )\n", " l2_norm[el // 2 + np.mod(el, 2)] = np.sqrt(\n", " np.sum(np.abs(grid_analytic - grid_expansion)**2 * total_weights)\n", " )\n", " phi_norm = np.sqrt(np.sum(np.abs(grid_analytic)**2 * total_weights))\n", " plt.semilogy(\n", " np.arange(0, max_eles[counter], 2), l2_norm / phi_norm,\n", " marker=markers[counter],\n", " label='$k =$ ' + str(k[counter])\n", " )\n", "y_label = 'Approximated relative error in $L^2(\\mathbb{S})$'\n", "plt.ylabel(y_label)\n", "plt.legend(edgecolor='white')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "a58681df", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.18" } }, "nbformat": 4, "nbformat_minor": 5 }