{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Schwarzschild horizon in Eddington-Finkelstein coordinates\n", "\n", "This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://luth.obspm.fr/~luthier/gourgoulhon/bh16/).\n", "\n", "The involved computations are based on tools developed through the [SageManifolds](https://sagemanifolds.obspm.fr) project." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*NB:* a version of SageMath at least equal to 9.2 is required to run this notebook: " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.5.rc1, Release Date: 2022-01-12'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spacetime\n", "\n", "We declare the spacetime manifold $M$:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "M = Manifold(4, 'M', structure='Lorentzian')\n", "print(M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and the **Eddington-Finkelstein coordinates** $(t,r,\\theta,\\phi)$ as a chart on $M$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M,(t, r, {\\theta}, {\\phi})\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(M,(t, r, {\\theta}, {\\phi})\\right)$$" ], "text/plain": [ "Chart (M, (t, r, th, ph))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X. = M.chart(r't r:(0,+oo) th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "X" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mass parameter and the metric tensor:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "var('m', domain='real')\n", "assume(m>=0)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{2 \\, m}{r} - 1 \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\frac{2 \\, m}{r} \\mathrm{d} t\\otimes \\mathrm{d} r + \\frac{2 \\, m}{r} \\mathrm{d} r\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, m}{r} + 1 \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{2 \\, m}{r} - 1 \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\frac{2 \\, m}{r} \\mathrm{d} t\\otimes \\mathrm{d} r + \\frac{2 \\, m}{r} \\mathrm{d} r\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, m}{r} + 1 \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "g = (2*m/r - 1) dt⊗dt + 2*m/r dt⊗dr + 2*m/r dr⊗dt + (2*m/r + 1) dr⊗dr + r^2 dth⊗dth + r^2*sin(th)^2 dph⊗dph" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = M.metric()\n", "g[0,0] = -(1-2*m/r)\n", "g[0,1] = 2*m/r\n", "g[1,1] = 1+2*m/r\n", "g[2,2] = r^2\n", "g[3,3] = (r*sin(th))^2\n", "g.display()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m}{r} - 1 & \\frac{2 \\, m}{r} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r} & \\frac{2 \\, m}{r} + 1 & 0 & 0 \\\\\n", "0 & 0 & r^{2} & 0 \\\\\n", "0 & 0 & 0 & r^{2} \\sin\\left({\\theta}\\right)^{2}\n", "\\end{array}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{2 \\, m}{r} - 1 & \\frac{2 \\, m}{r} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r} & \\frac{2 \\, m}{r} + 1 & 0 & 0 \\\\\n", "0 & 0 & r^{2} & 0 \\\\\n", "0 & 0 & 0 & r^{2} \\sin\\left({\\theta}\\right)^{2}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ 2*m/r - 1 2*m/r 0 0]\n", "[ 2*m/r 2*m/r + 1 0 0]\n", "[ 0 0 r^2 0]\n", "[ 0 0 0 r^2*sin(th)^2]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[:]" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "-\\frac{2 \\, m + r}{r} & \\frac{2 \\, m}{r} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r} & -\\frac{2 \\, m - r}{r} & 0 & 0 \\\\\n", "0 & 0 & \\frac{1}{r^{2}} & 0 \\\\\n", "0 & 0 & 0 & \\frac{1}{r^{2} \\sin\\left({\\theta}\\right)^{2}}\n", "\\end{array}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "-\\frac{2 \\, m + r}{r} & \\frac{2 \\, m}{r} & 0 & 0 \\\\\n", "\\frac{2 \\, m}{r} & -\\frac{2 \\, m - r}{r} & 0 & 0 \\\\\n", "0 & 0 & \\frac{1}{r^{2}} & 0 \\\\\n", "0 & 0 & 0 & \\frac{1}{r^{2} \\sin\\left({\\theta}\\right)^{2}}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ -(2*m + r)/r 2*m/r 0 0]\n", "[ 2*m/r -(2*m - r)/r 0 0]\n", "[ 0 0 r^(-2) 0]\n", "[ 0 0 0 1/(r^2*sin(th)^2)]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.inverse()[:]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, t} \\, t \\, t }^{ \\, t \\phantom{\\, t} \\phantom{\\, t} } & = & \\frac{2 \\, m^{2}}{r^{3}} \\\\ \\Gamma_{ \\phantom{\\, t} \\, t \\, r }^{ \\, t \\phantom{\\, t} \\phantom{\\, r} } & = & \\frac{2 \\, m^{2} + m r}{r^{3}} \\\\ \\Gamma_{ \\phantom{\\, t} \\, r \\, r }^{ \\, t \\phantom{\\, r} \\phantom{\\, r} } & = & \\frac{2 \\, {\\left(m^{2} + m r\\right)}}{r^{3}} \\\\ \\Gamma_{ \\phantom{\\, t} \\, {\\theta} \\, {\\theta} }^{ \\, t \\phantom{\\, {\\theta}} \\phantom{\\, {\\theta}} } & = & -2 \\, m \\\\ \\Gamma_{ \\phantom{\\, t} \\, {\\phi} \\, {\\phi} }^{ \\, t \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} } & = & -2 \\, m \\sin\\left({\\theta}\\right)^{2} \\\\ \\Gamma_{ \\phantom{\\, r} \\, t \\, t }^{ \\, r \\phantom{\\, t} \\phantom{\\, t} } & = & -\\frac{2 \\, m^{2} - m r}{r^{3}} \\\\ \\Gamma_{ \\phantom{\\, r} \\, t \\, r }^{ \\, r \\phantom{\\, t} \\phantom{\\, r} } & = & -\\frac{2 \\, m^{2}}{r^{3}} \\\\ \\Gamma_{ \\phantom{\\, r} \\, r \\, r }^{ \\, r \\phantom{\\, r} \\phantom{\\, r} } & = & -\\frac{2 \\, m^{2} + m r}{r^{3}} \\\\ \\Gamma_{ \\phantom{\\, r} \\, {\\theta} \\, {\\theta} }^{ \\, r \\phantom{\\, {\\theta}} \\phantom{\\, {\\theta}} } & = & 2 \\, m - r \\\\ \\Gamma_{ \\phantom{\\, r} \\, {\\phi} \\, {\\phi} }^{ \\, r \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} } & = & {\\left(2 \\, m - r\\right)} \\sin\\left({\\theta}\\right)^{2} \\\\ \\Gamma_{ \\phantom{\\, {\\theta}} \\, r \\, {\\theta} }^{ \\, {\\theta} \\phantom{\\, r} \\phantom{\\, {\\theta}} } & = & \\frac{1}{r} \\\\ \\Gamma_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\phi} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} } & = & -\\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right) \\\\ \\Gamma_{ \\phantom{\\, {\\phi}} \\, r \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, r} \\phantom{\\, {\\phi}} } & = & \\frac{1}{r} \\\\ \\Gamma_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} \\end{array}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, t} \\, t \\, t }^{ \\, t \\phantom{\\, t} \\phantom{\\, t} } & = & \\frac{2 \\, m^{2}}{r^{3}} \\\\ \\Gamma_{ \\phantom{\\, t} \\, t \\, r }^{ \\, t \\phantom{\\, t} \\phantom{\\, r} } & = & \\frac{2 \\, m^{2} + m r}{r^{3}} \\\\ \\Gamma_{ \\phantom{\\, t} \\, r \\, r }^{ \\, t \\phantom{\\, r} \\phantom{\\, r} } & = & \\frac{2 \\, {\\left(m^{2} + m r\\right)}}{r^{3}} \\\\ \\Gamma_{ \\phantom{\\, t} \\, {\\theta} \\, {\\theta} }^{ \\, t \\phantom{\\, {\\theta}} \\phantom{\\, {\\theta}} } & = & -2 \\, m \\\\ \\Gamma_{ \\phantom{\\, t} \\, {\\phi} \\, {\\phi} }^{ \\, t \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} } & = & -2 \\, m \\sin\\left({\\theta}\\right)^{2} \\\\ \\Gamma_{ \\phantom{\\, r} \\, t \\, t }^{ \\, r \\phantom{\\, t} \\phantom{\\, t} } & = & -\\frac{2 \\, m^{2} - m r}{r^{3}} \\\\ \\Gamma_{ \\phantom{\\, r} \\, t \\, r }^{ \\, r \\phantom{\\, t} \\phantom{\\, r} } & = & -\\frac{2 \\, m^{2}}{r^{3}} \\\\ \\Gamma_{ \\phantom{\\, r} \\, r \\, r }^{ \\, r \\phantom{\\, r} \\phantom{\\, r} } & = & -\\frac{2 \\, m^{2} + m r}{r^{3}} \\\\ \\Gamma_{ \\phantom{\\, r} \\, {\\theta} \\, {\\theta} }^{ \\, r \\phantom{\\, {\\theta}} \\phantom{\\, {\\theta}} } & = & 2 \\, m - r \\\\ \\Gamma_{ \\phantom{\\, r} \\, {\\phi} \\, {\\phi} }^{ \\, r \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} } & = & {\\left(2 \\, m - r\\right)} \\sin\\left({\\theta}\\right)^{2} \\\\ \\Gamma_{ \\phantom{\\, {\\theta}} \\, r \\, {\\theta} }^{ \\, {\\theta} \\phantom{\\, r} \\phantom{\\, {\\theta}} } & = & \\frac{1}{r} \\\\ \\Gamma_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\phi} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} } & = & -\\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right) \\\\ \\Gamma_{ \\phantom{\\, {\\phi}} \\, r \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, r} \\phantom{\\, {\\phi}} } & = & \\frac{1}{r} \\\\ \\Gamma_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} \\end{array}$$" ], "text/plain": [ "Gam^t_t,t = 2*m^2/r^3 \n", "Gam^t_t,r = (2*m^2 + m*r)/r^3 \n", "Gam^t_r,r = 2*(m^2 + m*r)/r^3 \n", "Gam^t_th,th = -2*m \n", "Gam^t_ph,ph = -2*m*sin(th)^2 \n", "Gam^r_t,t = -(2*m^2 - m*r)/r^3 \n", "Gam^r_t,r = -2*m^2/r^3 \n", "Gam^r_r,r = -(2*m^2 + m*r)/r^3 \n", "Gam^r_th,th = 2*m - r \n", "Gam^r_ph,ph = (2*m - r)*sin(th)^2 \n", "Gam^th_r,th = 1/r \n", "Gam^th_ph,ph = -cos(th)*sin(th) \n", "Gam^ph_r,ph = 1/r \n", "Gam^ph_th,ph = cos(th)/sin(th) " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that we are dealing with a solution of Einstein's equation in vacuum: " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Ric}\\left(g\\right) = 0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Ric}\\left(g\\right) = 0$$" ], "text/plain": [ "Ric(g) = 0" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.ricci().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The scalar field $u$ defining the horizon" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} u:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{1}{2} \\, {\\left(\\frac{r}{m} - 2\\right)} e^{\\left(\\frac{r - t}{4 \\, m}\\right)} \\end{array}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} u:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{1}{2} \\, {\\left(\\frac{r}{m} - 2\\right)} e^{\\left(\\frac{r - t}{4 \\, m}\\right)} \\end{array}$$" ], "text/plain": [ "u: M → ℝ\n", " (t, r, th, ph) ↦ -1/2*(r/m - 2)*e^(1/4*(r - t)/m)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u = M.scalar_field(coord_expression={X: (1-r/(2*m))*exp((r-t)/(4*m))}, name='u')\n", "u.display() " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 10 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plm2 = implicit_plot(u.expr().subs(m=1)+2, (r, 0, 15), (t, -10, 15), color='green') + \\\n", " text('$u=-2$', (11,12), color='green')\n", "plm1 = implicit_plot(u.expr().subs(m=1)+1, (r, 0, 15), (t, -10, 15), color='green') + \\\n", " text('$u=-1$', (6.3,12), color='green')\n", "pl0 = implicit_plot(u.expr().subs(m=1), (r, 0, 15), (t, -10, 15), color='green') + \\\n", " text('$u=0$', (3.1, 12), color='green') \n", "pl1 = implicit_plot(u.expr().subs(m=1)-1, (r, 0, 15), (t, -10, 15), color='green') + \\\n", " text('$u=1$', (0.8, 0.5), color='green') \n", "pl2 = implicit_plot(u.expr().subs(m=1)-2, (r, 0, 15), (t, -10, 15), color='green') + \\\n", " text('$u=2$', (-0.2, -2.5), color='green', background_color='white') \n", "graph = plm2+plm1+pl0+pl1+pl2\n", "show(graph, aspect_ratio=True, axes_labels=[r'$r/m$', r'$t/m$'], figsize=8)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "graph.save('def_Schwarz_Hu.pdf', aspect_ratio=True, \n", " axes_labels=[r'$r/m$', r'$t/m$'], figsize=8)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form du on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}u = -\\frac{{\\left(2 \\, m - r\\right)} e^{\\left(\\frac{r}{4 \\, m} - \\frac{t}{4 \\, m}\\right)}}{8 \\, m^{2}} \\mathrm{d} t -\\frac{{\\left(2 \\, m + r\\right)} e^{\\left(\\frac{r}{4 \\, m} - \\frac{t}{4 \\, m}\\right)}}{8 \\, m^{2}} \\mathrm{d} r\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}u = -\\frac{{\\left(2 \\, m - r\\right)} e^{\\left(\\frac{r}{4 \\, m} - \\frac{t}{4 \\, m}\\right)}}{8 \\, m^{2}} \\mathrm{d} t -\\frac{{\\left(2 \\, m + r\\right)} e^{\\left(\\frac{r}{4 \\, m} - \\frac{t}{4 \\, m}\\right)}}{8 \\, m^{2}} \\mathrm{d} r$$" ], "text/plain": [ "du = -1/8*(2*m - r)*e^(1/4*r/m - 1/4*t/m)/m^2 dt - 1/8*(2*m + r)*e^(1/4*r/m - 1/4*t/m)/m^2 dr" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "du = diff(u)\n", "print(du)\n", "du.display()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{{\\left(2 \\, m + r\\right)} e^{\\left(\\frac{r}{4 \\, m} - \\frac{t}{4 \\, m}\\right)}}{8 \\, m^{2}} \\frac{\\partial}{\\partial t } + \\frac{{\\left(2 \\, m - r\\right)} e^{\\left(\\frac{r}{4 \\, m} - \\frac{t}{4 \\, m}\\right)}}{8 \\, m^{2}} \\frac{\\partial}{\\partial r }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{{\\left(2 \\, m + r\\right)} e^{\\left(\\frac{r}{4 \\, m} - \\frac{t}{4 \\, m}\\right)}}{8 \\, m^{2}} \\frac{\\partial}{\\partial t } + \\frac{{\\left(2 \\, m - r\\right)} e^{\\left(\\frac{r}{4 \\, m} - \\frac{t}{4 \\, m}\\right)}}{8 \\, m^{2}} \\frac{\\partial}{\\partial r }$$" ], "text/plain": [ "-1/8*(2*m + r)*e^(1/4*r/m - 1/4*t/m)/m^2 ∂/∂t + 1/8*(2*m - r)*e^(1/4*r/m - 1/4*t/m)/m^2 ∂/∂r" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "grad_u = du.up(g)\n", "print(grad_u)\n", "grad_u.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that each hypersurface $u={\\rm const}$ is a null hypersurface:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(grad_u, grad_u).expr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The null normal $\\ell$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{12 \\, m \\log\\left(2\\right) - 4 \\, m \\log\\left(2 \\, m + r\\right) + 8 \\, m \\log\\left(m\\right) - r + t}{4 \\, m} \\end{array}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{12 \\, m \\log\\left(2\\right) - 4 \\, m \\log\\left(2 \\, m + r\\right) + 8 \\, m \\log\\left(m\\right) - r + t}{4 \\, m} \\end{array}$$" ], "text/plain": [ "M → ℝ\n", "(t, r, th, ph) ↦ 1/4*(12*m*log(2) - 4*m*log(2*m + r) + 8*m*log(m) - r + t)/m" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rho = - log(-grad_u[[0]])\n", "print(rho)\n", "rho.display()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field l on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell = \\frac{\\partial}{\\partial t } + \\left( -\\frac{2 \\, m - r}{2 \\, m + r} \\right) \\frac{\\partial}{\\partial r }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\ell = \\frac{\\partial}{\\partial t } + \\left( -\\frac{2 \\, m - r}{2 \\, m + r} \\right) \\frac{\\partial}{\\partial r }$$" ], "text/plain": [ "l = ∂/∂t - (2*m - r)/(2*m + r) ∂/∂r" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "l = - exp(rho) * grad_u\n", "l.set_name('l', latex_name=r'\\ell')\n", "print(l)\n", "l.display()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 81 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_l = l.plot(ambient_coords=(r,t), ranges={r:(0.01,8), t:(0,8)}, \n", " fixed_coords={th:pi/2, ph:pi}, parameters={m:1}, color='green', \n", " scale=0.8, aspect_ratio=1)\n", "show(graph_l, figsize=8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check that $\\ell$ is a null vector everywhere:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(l,l).expr()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form lf on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\underline{\\ell} = \\left( \\frac{2 \\, m - r}{2 \\, m + r} \\right) \\mathrm{d} t +\\mathrm{d} r\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\underline{\\ell} = \\left( \\frac{2 \\, m - r}{2 \\, m + r} \\right) \\mathrm{d} t +\\mathrm{d} r$$" ], "text/plain": [ "lf = (2*m - r)/(2*m + r) dt + dr" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "l_form = l.down(g)\n", "l_form.set_name('lf', latex_name=r'\\underline{\\ell}')\n", "print(l_form)\n", "l_form.display()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Levi-Civita connection nabla_g associated with the Lorentzian metric g on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g}$$" ], "text/plain": [ "Levi-Civita connection nabla_g associated with the Lorentzian metric g on the 4-dimensional Lorentzian manifold M" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab = g.connection()\n", "print(nab)\n", "nab" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g} \\underline{\\ell} = \\left( \\frac{2 \\, m^{2} - m r}{2 \\, m r^{2} + r^{3}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\left( \\frac{4 \\, m^{3} + 4 \\, m^{2} r - 3 \\, m r^{2}}{4 \\, m^{2} r^{2} + 4 \\, m r^{3} + r^{4}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} r + \\frac{m}{r^{2}} \\mathrm{d} r\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, m^{2} + 3 \\, m r}{2 \\, m r^{2} + r^{3}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( -\\frac{2 \\, m r - r^{2}}{2 \\, m + r} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\left(2 \\, m r - r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{2 \\, m + r} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g} \\underline{\\ell} = \\left( \\frac{2 \\, m^{2} - m r}{2 \\, m r^{2} + r^{3}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\left( \\frac{4 \\, m^{3} + 4 \\, m^{2} r - 3 \\, m r^{2}}{4 \\, m^{2} r^{2} + 4 \\, m r^{3} + r^{4}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} r + \\frac{m}{r^{2}} \\mathrm{d} r\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, m^{2} + 3 \\, m r}{2 \\, m r^{2} + r^{3}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( -\\frac{2 \\, m r - r^{2}}{2 \\, m + r} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\left(2 \\, m r - r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{2 \\, m + r} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "nabla_g(lf) = (2*m^2 - m*r)/(2*m*r^2 + r^3) dt⊗dt + (4*m^3 + 4*m^2*r - 3*m*r^2)/(4*m^2*r^2 + 4*m*r^3 + r^4) dt⊗dr + m/r^2 dr⊗dt + (2*m^2 + 3*m*r)/(2*m*r^2 + r^3) dr⊗dr - (2*m*r - r^2)/(2*m + r) dth⊗dth - (2*m*r - r^2)*sin(th)^2/(2*m + r) dph⊗dph" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab_l_form = nab(l_form)\n", "nab_l_form.display()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( \\frac{2 \\, m^{2} - m r}{2 \\, m r^{2} + r^{3}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\left( \\frac{4 \\, m^{3} + 4 \\, m^{2} r - m r^{2}}{4 \\, m^{2} r^{2} + 4 \\, m r^{3} + r^{4}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} r + \\left( \\frac{4 \\, m^{3} + 4 \\, m^{2} r - m r^{2}}{4 \\, m^{2} r^{2} + 4 \\, m r^{3} + r^{4}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, m^{2} + 3 \\, m r}{2 \\, m r^{2} + r^{3}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( -\\frac{2 \\, m r - r^{2}}{2 \\, m + r} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\left(2 \\, m r - r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{2 \\, m + r} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( \\frac{2 \\, m^{2} - m r}{2 \\, m r^{2} + r^{3}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\left( \\frac{4 \\, m^{3} + 4 \\, m^{2} r - m r^{2}}{4 \\, m^{2} r^{2} + 4 \\, m r^{3} + r^{4}} \\right) \\mathrm{d} t\\otimes \\mathrm{d} r + \\left( \\frac{4 \\, m^{3} + 4 \\, m^{2} r - m r^{2}}{4 \\, m^{2} r^{2} + 4 \\, m r^{3} + r^{4}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} t + \\left( \\frac{2 \\, m^{2} + 3 \\, m r}{2 \\, m r^{2} + r^{3}} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( -\\frac{2 \\, m r - r^{2}}{2 \\, m + r} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\left(2 \\, m r - r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{2 \\, m + r} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "(2*m^2 - m*r)/(2*m*r^2 + r^3) dt⊗dt + (4*m^3 + 4*m^2*r - m*r^2)/(4*m^2*r^2 + 4*m*r^3 + r^4) dt⊗dr + (4*m^3 + 4*m^2*r - m*r^2)/(4*m^2*r^2 + 4*m*r^3 + r^4) dr⊗dt + (2*m^2 + 3*m*r)/(2*m*r^2 + r^3) dr⊗dr - (2*m*r - r^2)/(2*m + r) dth⊗dth - (2*m*r - r^2)*sin(th)^2/(2*m + r) dph⊗dph" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab_l_form.symmetrize().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check of the identity $\\ell^\\mu \\nabla_\\alpha \\ell_\\mu=0$:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = l.contract(nab_l_form, 0)\n", "v.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The null normal as a pregeodesic vector field" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{m}{r^{2}} & \\frac{2 \\, m^{2} + 3 \\, m r}{2 \\, m r^{2} + r^{3}} & 0 & 0 \\\\\n", "-\\frac{2 \\, m^{2} - m r}{2 \\, m r^{2} + r^{3}} & -\\frac{4 \\, m^{3} + 4 \\, m^{2} r - 3 \\, m r^{2}}{4 \\, m^{2} r^{2} + 4 \\, m r^{3} + r^{4}} & 0 & 0 \\\\\n", "0 & 0 & -\\frac{2 \\, m - r}{2 \\, m r + r^{2}} & 0 \\\\\n", "0 & 0 & 0 & -\\frac{2 \\, m - r}{2 \\, m r + r^{2}}\n", "\\end{array}\\right)\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrrr}\n", "\\frac{m}{r^{2}} & \\frac{2 \\, m^{2} + 3 \\, m r}{2 \\, m r^{2} + r^{3}} & 0 & 0 \\\\\n", "-\\frac{2 \\, m^{2} - m r}{2 \\, m r^{2} + r^{3}} & -\\frac{4 \\, m^{3} + 4 \\, m^{2} r - 3 \\, m r^{2}}{4 \\, m^{2} r^{2} + 4 \\, m r^{3} + r^{4}} & 0 & 0 \\\\\n", "0 & 0 & -\\frac{2 \\, m - r}{2 \\, m r + r^{2}} & 0 \\\\\n", "0 & 0 & 0 & -\\frac{2 \\, m - r}{2 \\, m r + r^{2}}\n", "\\end{array}\\right)$$" ], "text/plain": [ "[ m/r^2 (2*m^2 + 3*m*r)/(2*m*r^2 + r^3) 0 0]\n", "[ -(2*m^2 - m*r)/(2*m*r^2 + r^3) -(4*m^3 + 4*m^2*r - 3*m*r^2)/(4*m^2*r^2 + 4*m*r^3 + r^4) 0 0]\n", "[ 0 0 -(2*m - r)/(2*m*r + r^2) 0]\n", "[ 0 0 0 -(2*m - r)/(2*m*r + r^2)]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab_l = nab(l)\n", "nab_l[:]" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{2 \\, {\\left(4 \\, m^{2} - 2 \\, m r - r^{2}\\right)}}{4 \\, m^{2} r + 4 \\, m r^{2} + r^{3}} \\end{array}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{2 \\, {\\left(4 \\, m^{2} - 2 \\, m r - r^{2}\\right)}}{4 \\, m^{2} r + 4 \\, m r^{2} + r^{3}} \\end{array}$$" ], "text/plain": [ "M → ℝ\n", "(t, r, th, ph) ↦ -2*(4*m^2 - 2*m*r - r^2)/(4*m^2*r + 4*m*r^2 + r^3)" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "div_l = nab_l.trace()\n", "print(div_l)\n", "div_l.display()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2 \\, {\\left(4 \\, m^{2} - 2 \\, m r - r^{2}\\right)}}{{\\left(2 \\, m + r\\right)}^{2} r}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2 \\, {\\left(4 \\, m^{2} - 2 \\, m r - r^{2}\\right)}}{{\\left(2 \\, m + r\\right)}^{2} r}$$" ], "text/plain": [ "-2*(4*m^2 - 2*m*r - r^2)/((2*m + r)^2*r)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "div_l.expr().factor()" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{4 \\, m}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{4 \\, m}$$" ], "text/plain": [ "1/4/m" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "div_l.expr().subs(r=2*m)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( \\frac{4 \\, m}{4 \\, m^{2} + 4 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial t } + \\left( -\\frac{4 \\, {\\left(2 \\, m^{2} - m r\\right)}}{8 \\, m^{3} + 12 \\, m^{2} r + 6 \\, m r^{2} + r^{3}} \\right) \\frac{\\partial}{\\partial r }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( \\frac{4 \\, m}{4 \\, m^{2} + 4 \\, m r + r^{2}} \\right) \\frac{\\partial}{\\partial t } + \\left( -\\frac{4 \\, {\\left(2 \\, m^{2} - m r\\right)}}{8 \\, m^{3} + 12 \\, m^{2} r + 6 \\, m r^{2} + r^{3}} \\right) \\frac{\\partial}{\\partial r }$$" ], "text/plain": [ "4*m/(4*m^2 + 4*m*r + r^2) ∂/∂t - 4*(2*m^2 - m*r)/(8*m^3 + 12*m^2*r + 6*m*r^2 + r^3) ∂/∂r" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acc_l = l.contract(0,nab_l,1)\n", "print(acc_l)\n", "acc_l.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The non-affinity parameter $\\kappa$:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{4 \\, m}{4 \\, m^{2} + 4 \\, m r + r^{2}} \\end{array}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{4 \\, m}{4 \\, m^{2} + 4 \\, m r + r^{2}} \\end{array}$$" ], "text/plain": [ "M → ℝ\n", "(t, r, th, ph) ↦ 4*m/(4*m^2 + 4*m*r + r^2)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kappa = l(rho)\n", "kappa.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check of the pregeodesic equation $\\nabla_{\\ell} \\ell = \\kappa \\ell$:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$$" ], "text/plain": [ "True" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acc_l == kappa * l" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{4 \\, m}{{\\left(2 \\, m + r\\right)}^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{4 \\, m}{{\\left(2 \\, m + r\\right)}^{2}}$$" ], "text/plain": [ "4*m/(2*m + r)^2" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kappa.expr().factor()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Value of $\\kappa$ on the horizon:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{4 \\, m}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{4 \\, m}$$" ], "text/plain": [ "1/4/m" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kappaH = kappa.expr().subs(r=2*m)\n", "kappaH" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The complementary null vector field $k$" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k = \\left( \\frac{m}{r} + \\frac{1}{2} \\right) \\frac{\\partial}{\\partial t } + \\left( -\\frac{m}{r} - \\frac{1}{2} \\right) \\frac{\\partial}{\\partial r }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}k = \\left( \\frac{m}{r} + \\frac{1}{2} \\right) \\frac{\\partial}{\\partial t } + \\left( -\\frac{m}{r} - \\frac{1}{2} \\right) \\frac{\\partial}{\\partial r }$$" ], "text/plain": [ "k = (m/r + 1/2) ∂/∂t + (-m/r - 1/2) ∂/∂r" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k = M.vector_field(name='k')\n", "k[0] = 1/2 + m/r\n", "k[1] = -1/2 - m/r\n", "k.display()" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$$" ], "text/plain": [ "0" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(k,k).expr()" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-1\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-1$$" ], "text/plain": [ "-1" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(k,l).expr()" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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ebRMhcMr/lCTHD1gQrkFBXEQmb17O5iVLgLdvTbeXgdvvbyNBnSDpWEcb+f9a/1dkcbcQ0UoDDKgyAAd7H0SZHOJL9TrSyL9crnJ4MOIBpjWZhgwuGUQdm+7n/LWYC/1XzF0RRb2KAuBuLE03NXXs+v+6SBQAUtdLJ2uSpS2NMxf6d3MDvvkm5fGkSVYLgK13t0oqCDPtzDThjVu2tBz6N4erq+CmITEh6LGnh6QQ4An/E5YjGmMt7AUgsxA4H3BekuMHLIz8b98Gkj4vb3z6FPjf/4CCBbnPn42EQLdy3TCu3jhJTsPkyD8qiosS5c0LTJ0KBKau42ALOpbpiFf/e4WpjaemeRHQqUwn3Bt+D8vbLRc1Cna0pX4ZXDLg98a/4+GIh+hUppPg49jI/zMdy3SEq1Pqm22NfDVw9puzOPvtWT688jTsKZpuaor30e9lufby5ctRvnx51KpVS5bzpUKkACAiSSN/VydXdCvXDUOqDxFvo6nQv3aOf8MGLhSuxQoBkKROEj3q13Lm9Rnho3+xoX9datYEFi4U3HzXg12SI1Kvwl9ZFkIVK3JOXQi6QqB0aU4I3BOWg6Dlx9o/on/l/pJW4ph1/q1aAR5Gznnhgs2EgKuzKxa0WoC3P7/F4taLRYVpTY7816/n8kM+fACmT+cKXtWvDyxebHMhkM0jG7ybeMsjAqZN43JJypQBNm60+xblrs6uGFFrBJ6Peo5x9cYJOsZo2P/BA8DfX2brxFEsWzEc7H0QExsK24SNOf/PZM2QFS1LtNR7rlb+Wjg58CSyeWRDIa9C8Bvkh2JZiwEAnoQ9QbNNzWSpJT5y5Eg8fPgQ165ds/pcJhEhAD7EfBC8m5i7szs6lemELV22IOSXEOztuVd6MqRhmNwwuW/8eFkEwI77O+D/SfoXVZRwkBL6r1kT8PEBsmYVfEijIo2QK6P0XBSfFxYyt1UqaX15/pwTApUrA1u2CD4sR8Yc/Gdqd/fd6F6+u2AhEBIbYnrE7OwMDLSwBNJGQsArgxfG1B2Dpz8+xaE+h1AuZzmLx5jsR4cOqZ+7dAn4+We7CQGtCNjc2Ypy3ytWcKtInj4Fvv2Wi/517Ahs3mxXIeCVwQs5MgoLg6eK4GzaxN1fS5QAypcHFi0CAgJsYKVlYhJj9KqvmluKLrS/joDNC0P3LN+T/7tOgTo4MeAEsmbIyj9X2Ksw/Ab5oYhXEQDAo9BHaLa5WZrZGUmoABA66h9WYxiCfwnGwd4H0b9yf3hl8LLOvoYNudr9gOmsfhkEwJ331lXduxl0U3hjsaF/CY4fACrnqYyAnwJwZcgVLG+3HN9V/Q5V8lRJtXOlKQw3YTFKz56W25jj1i3Rh3i6eaJHhR7Y02MPQn4JwXdVhRV1Mjv679VLuAGGQuCvv4CQEOHHG8HZyRntS7WHkyrllmZK2CSoE5CQbCRfoEQJwFyk0E5CgIiw8FJKhKpr2a7iIgGNG+s/TkwEDh8GBg2yqxAIiQnB7HOzAQBOKifs7LYTjYs0Nto21cj/uk79/0ePuCmyIkWAevXsLgRmn5vNl/JuXaI1Ho14ZHIqgI38dehfuT8mNZyEMXXG4L/+/+k5fi1FshaB3yA/FPYqDAB4GPIQzTc3R0iMdTcEuyFAABgLH3u4eKB7+e6Y3iSlIM6bqDfyzvs5OwN79gCDB3MrFUxl9VspAEbXGY3eFXujcZHGaFykMRoVaYRGRRrhq8JfIVuGbHy7OgXqoEGhBmhQqAHqF6qP+oXqo3GRxljebrnwPokJ/VeoIMnxa8ngkgG1C9TGiFojsO7rdbg97Dbej30PFbj63dk9sqNS7kpGBUFghADHICb0b0jJksAvv0g79jOebp54/inFqc9vMd9kRMDsFEijRkBuCdGpCxeAMWOASpWACOsS8fxe+fHL/hoWboh3Y99hUatFRqcEYpNMrPro10/YxWwoBPxe+eFcALcSpGzOstjdY7fJ6QAXJ5fUJ5gwwfTJ7SgEpp2ZhqjEKADA4GqD0atiL/gN8jOaFJjKL/z8s/GTXr5sVyHwNOwpFlxcAIAb8S9tuxTFsxfHwd4HcajPIb3PlqerZ5rZ1AcApzIF/ticFx9fUMFFBQneIHiDKv1diUJiQqw6Z0REBAGgiIgImaw0w717RDlzEnEpWUS1axN9+kRERK/DX1OBhQXIc5Yn9drTi/Y82EPRCdFERKTWqKnAwgIEb5DbDDcKjwu3va2mmDs3xX6AaPZsq0/Zbls7/j0NjQmVwUgiOnRI305TP9mzE925I881P3P+9Xm+P0MODiEiopjEGLoYcJGWXllKgw4MolZbWtHxZ8eFnXDyZGF90f0pWZIoMNDqvryLfEcqbxXBG1RmaRnSaDRERBSVEEW77u+ibru6kcdMDyq8uDAFRQWZP9mwYeL7of1RqYhevbKqL1/v+Jp/X3bf380/n6xOpkNPDlHLzS0J3qAWm1uYPsmbN9L7ABANGED0+X8oBY1GQ1+t/4rvx/a72/Ve/xj7kab6TaXs87JT8b+K04foD8ZOwn0+xNjt5kbUoQPRpk38PcsaHoc8JudpzgRvkOcsz1SfncTkRFp+dTmV+KsENVzfkOKS4lKfpG5d4fbXrUu0cCHR69dW265Fo9FQ6y2t+fdi0slJqdrEJcXRtNPTqOLfFWnJ5SViTi/G99rkx6GcPxHR87DnvCOEN6jKiipWOQy7On8iswKAiPibqyGjj47m+7zlzhb72GoKmQVA261t5Xf+8fFEWbKYvhl4eqb8nTOnrALgr8t/8f1ZcW2F9Se8e1cRx09EtPTKUr4vk09NNtpGrVGb/Nzq4esr3Wla+Rnz/+jPi5iCiwpSYnKi0XaxibGUrE42f7IGDawTAMHBkvtxyv8U/36UXVbWpK0ajcZ8PyZOlG5/hgxE//4ruQ9ERJ12dOL7Mf30dGknWbxYmv1aIWCliNn3cB/fh8KLC/ODNZlQ3Pk73GbQJbKXgN8gP+TPnB8AcOfDHbTc0lJ0uUjFsDAFYGq7xx4VUhK/9j7ca2srzSNTEqAxZNvu0lzov2ZNLlO4Th3ucWgo0Lw5cFee3SJ19yOvmb+m9ScUE/ovUYL7fBUsaP11Aex5mFJBUvczqIuTyknY+yY19D9rFleDwQqWX1vOL2McXnM4XJ2NL+n0cPWAs5OFnA1rdsXs0yelCqhIiAjep735x783+t2krSqVynw/rOlDfDywT0Jhsc+cfnUa/z75FwCQP3N+/FzPRAjfElL2JwFSpgaaNZN2PLgkvzHHx/CPF7de7FCFiOTA4Zw/AJTKUQp+g/yQL1M+AMCt97fQcktLYSVTHQEJdQDqF6rP9/f48+OISoiyg6FmkFEASF1bbhFjNzhtcl+RIsB//9lEANwIugGAW4ZZKbcMO1CKyfovVkyyczEkKCoI515zc8tlcpSxvi/OzkDXruKOmTWL+2xZQUxiDNbd4rahdnd2x9DqQ606n2Sn07Url6UuEcO5/p4VrEgGrVqVywmRQubMXEKmBDSkwbgTKcv7ZjadKd1pFizI5VNI5eNHLhYgAcMkvy5lu0i3w0FxSOcPAKVzlIbvIF/kzZQXAJcN3mprK4feXUwPkQLASeWEruW4G2eCOgGHnx62k6FmsEEEQJsoJwuGWf+GWf1eXrILgOjEaDwKeQQAqJSnEtxdLJewFoSlrH/tyPvkSU4oJEirbqfLvkf7eGHWs0JPeaIyYlYvyOD4Aa64lPa+0LdSX+tLhRcoIH5ny65dgZ07RRWR0kXMqF8QUpeRZs4MHD/O1ZOQwI57O3hxXDlPZQysYnkXTLNIjWB4egJbt6Z8b0RgLMlPtoilA+Gwzh/g1K/vQF/k8eSq1F1/dx2ttrRyuNrcJhEpAHqU1wn9P1I49K9FBgFAEtW3RdzdU7KCGzY0ntUvswC4/f427zBr5Ksh0XAjmAv9lyzJORZtIZ1Dh2QRALsf7Ob/1v3sWYXQ0L9KxWXKWwkRYcnVJfzjUbVHWX1OAOKcjpWOH5B51K9FrOPUOn6Jo+24pDhM8k0RcwtbLbROwADSojCenlw/GjYUfSgRYdSxUUjScBUrx9Ubh1I5Som3IQ3g0M4f4Oos+w7y5YutXHt3Da23tha0tapDIEIANCzckC/mc/TZUcFFgWyOjBEA2RX01KnA+/fA2bOml/PJKABkn+/XYmqkVrIk9/np2RM4ckQ2ARAUFYTzAecBcM6mYu6KUi3XR2jon4hbbrZ1q+W2ZvB96YuHIQ8BAF8V/grV8kkbsaZCqNPx9AQWLLDK8cs+6tciJvRvpeMHgL+u/IWACG7ZXduSbdGieAvJ5+IRG/q3wvEDwIHHB/h9OQp7Fcakr6yPTDkqDu/8AaB8rvLwHeTLF1C48vYK2mxto/y8uFAECgBnJ2d0LcvdOOOT43H02VE7G2oGKwSAzeb8teTJYzm8J5MA0IY0AZlH/kDqkLnW8WuT+5o2lU0A6Ib8e5TvIa8oMxf6nzkTGD6c+1ujsVoA2GTUDwgP/cfEcOWNrVjjb5NRPyAu9N+8OVC3ruRLGRb0md9yvuRzpUJoHzJksMrxp4ckP13ShPMHuI2AfAf68rsmXXpzCW23tf3iBIBDZf0bIkMEQNY5f7HIIAC0I383Zzf5RstaKlZMsc3Q8WuRSQDohvxlczZaTIX+Z83i9iRYvlwWAeD/yR+HnhwCABTMUhCdy3a2wmgjmHM6bdtyKy8A4MUL7n2RIABsNurXItRx/vMPMHIk935IwLCgj6zfDaFRGI3Gqqmw9JDkp4eIdYEOwe2g25R9XnZ+/WXD9Q0pKiHKZHu7r/O3hIU6AEnqJMo5PyfBG5RxVkaKSYxRzlZTiKwDoC2uAm8oW8BIS3g4UZ06ousARMZH8mvJa6yqYRvbgoOJdu8msvR59fUl8vBI6UPHjlztAwG8jXzL96PssrLC1vCLxbDgz6xZ+q9rNETDh6e87uREtEVcfYux/43lP1ezz1pfjCoVpgr+dO1KlJjI1VrQLaZTogRRQICoSwhd1y8ZcwV/MmcmmjqV+99rnxs2jEitFnUJSwV9ZKF+fdPr+p2dU/728CA6eVL06Z+EPiHX6a58obWnoU/l74M+bJ2/WKrkrYJTA0/xJWPPB5xH++3tEZMYo7BlArEQAXBxcuEVZ2xSLI49O6aQoWawIgLgEFmzEiMAt97f4kPlss7365IrFzdas7R3gRURgH0PdbL8y8uU5W/IkCHc/D9gPKtfpbIqAhCdGI21N9cC+Ly8r4aVy/uMYSz0r5vcV7Ag913WzquLjACQrUf9gOnQv3aO39ub2xzK6bMrWLlSdATg15O/Qk1qAMD4BuP5FVqyYiqC4enJJfp2+lxrPy6OK1l8SvgW6JSOkvz0EKEUHIob725Q1rlZqVMv0NV8oI2dilBMUGrV7XAjfy1mIgAnnp/gRwO99/ZW1k5zCIwAtNjcgu9PRLwDvQ8iIwCLLi7i+7H6+mo7GmoGCREA3fKx9z7cs51t9+4R3bhhvo3ECMCKayv4Pnz3z3cyGWyE5ctTj/gNkRgBsPmoX8vNm6lH/Bcu6LfZtk1SBMDvpR/fh/wL88tdBS+FwMDUI35PT6Jz57jXExKIOnWSFAGwcSU/Uyg+8k+zzp+I6Prb6xThnvJhSHYCJbdqQbR2LVEoV0bWYZ0/kUkBkJicyE9tZJqdiWITY5W21DQCBICu84+Mj1TASDOIEAD99vXj+3Hz3U07G2oGEQJAN+Rfblk524T8xSJSAGg0Giq3rBz/XtwKumU725KSiKZPJ5o3z7jj1yJSAFiq4S8rGg1RhQqmHb8WkQJArVFTjVU1+D6sv7neRh34jG7oX9fxa5EgAKIToqnQokJ8H/Y/3G/DDujBnL+1xBXKn1oRAkQuLkStW1PE0qWO6/yJTAqA7/75jv9AHnh0QGkrzWNBADi08ycSLADKLC3DzwkmJCcoYKgZBAqAJZeX8O/F776/K2CoCUQIAJ8XPnwfvlr/lZ0NNYMIAWC3Ub+WJ0+4+f2HD823EyEAtt7Zyveh8orKtu/Drl2cTVmypHb8WkQKgEknJ/F9aL2ltT3FMHP+VrN6tXHn//knAuCcf/PmehEBh8KIAPC5sYf/UPbb109pCy1jRgA039TcsZ0/kUUBEBEfwY+Ya62upaChZhAgABqub8i/F/c/3FfIUBMIFAC6m8bsebBHAUPNIEAA2HXULwUBAiA2MZYKLy7M98HnhY99bHv40PI9XKAAUCDJTxfm/K3m40ciV1fLzt8gIkDr1hGFhSltfQoGAkBdqxYVnpqF4A3KPDszxScJy+RWFBMCQNf5m1uZoThmBMDpl6f5Pgw7NExhQ81gRgAYhvwdEgsC4MXHF3q79yWpkxQ01gQWBIDdR/1SsCAA5pybw/eh7da2ChpqAgsCQKPRUKstrfg+/HbqN3tbqLjzd+hs/+TkZEyePBnFihWDh4cHihcvjunTp0Ojm4maLRvQQkQlqeRkLtN78GCuOEynTsDbt/IbLxaDVQBO167Bd7sbvOKAqMQovuqUQ2NiFQDZusiPXJhZBaBb3Mdmmf5yYGYVgF6Wv9xr++XCwiqA5VdTdu8bWWskXJxclLLUNGZWARDZIcNfDvr2NbkKwKYFfeTCzQ3Ys8fkKoD0VMnPJCKUgt2ZOXMm5ciRgw4fPkwvX76kPXv2UKZMmejPP//Ub7h+vfCRv7Gf8eOV6J5xDCIAlwuAvMaDBh4YqLRlwjGIAKzpXpxX2HbKpLUOIxGAX/9oY58EM7kwEgFouqq+44b8DTESAYjbsIa85ngRvEHuM9wpJCZEaSvNYyQCcP78Dscf9etiJALw46ERfB+G/jtUaQvNYyQCEHvskFJJfrooPvJ3aOffvn17+u47/WU8Xbt2pf79++s3NBP6t+j8VSpJRSFsihEBUPj3LI6XZGYOAwEwoXkacv5EqQRAWCZnqjSMczqJyWayvh0JAwFwsDTIbTKo/PLySlsmDAMBoHZSUb8udljeJycGAiAwdwYq+JODzvWbwkAArKipItXvNizoIzcGAiDB3YWaDVQkyU8X5vzNMWfOHCpSpAg9efKEiIhu375NuXPnpu3bjXxp2rYV7/xVKqKNG+3cK4EYCIB/S4OOPj2qtFXiMBAAXXvCMSsWmsJAALz3BDVaZqPKfrbCQAAsqQ2a6jdVaauEYyAAklWgWkPSSPRFi4EAuJMbVHZpGccf9etiIAB+bgWafnq60lYJx0AAxLiAio9ztXeSny7M+ZtDo9HQhAkTSKVSkYuLC6lUKpptqpSsidC/SefvyI5fy717lJAtCxFAwRlB226LK3/qEOgIgOVfZXDMBC1zhIdTUq2afB/+WPWN0haJx9eXEt25yNj1fKCHwRaWezkaBgLgr34llbZIPIGBFFEoDxFAiU6gveccpEiUGLZto2QV9x4crpQh7UTxtCQkUGjLhvznaPOMHkpaw5y/OXbs2EEFCxakHTt20N27d2nz5s2UPXt22mjMaZsI/Rt1/mnB8Wt5+pRu92lGW/4YlHbCzQZ82LyCfLvVoLMXdyptijQiIujuiG70z6hWjlWhUARRl87Q+c41yGeHDWrg2wONhh7M+ZlO9K5N798qNlqzisTA13S+T0M6MXuIYxRXksDj3SvI7+uq9PxyGotCfkYTH09nRn1Np4e2osQ4RaOQijt/FZHgTGy7p2wXKlQIEyZMwMiRI/nnZs6cia1bt+Lx48epD2jXDjimXws/EoAXgAgAfLX0X38F5s2zkdUMBoPBYJhF8U1OHHqpX2xsLJyc9E10dnbWX+qni9DtK5cuFbXxA4PBYDAYXxIO7fw7duyIWbNm4ciRI3j16hUOHDiARYsWoUsXE/ssd+7M7bZlimrVuN8Sdn5iMBgMBuNLwaHD/lFRUZgyZQoOHDiA4OBg5M+fH3369MHvv/8ONzc34wcZhP75sP+KFcjy3XdAz57AwYPcix4eXBGU5s1t3hcGg8FgMD6jeNjfoZ2/JDZsAL77jn/IO/+ICGTJkgVITGQCgMFgMBhKorjzd+iwvyR0Q/8qFbBihf7rbm7A7t3A119zj9kUAIPBYDDSGV+e88+WjasNXqcO5+T79k3dhgkABoPBYKRjvrywvwGRkZHw8vJKCfvrwqYAGAwGg2F/vrywf3RiNJ6HPZf7tLbhS4wAEAH37gEJCUpbwmAwGAwHRVbnH5UQhRzzc6DUslIosLAAZp+bjecfHVwIKCAAjj07hoknJyIh2QYOukULoHJlwNOTm/I4coSLcCjMv0/+RVBUkNJm2ISgqCAsvbIUMYkxSpsiGwnJCZh4ciIOPzmstCmyEB4fjv77+2P51eVKm2I1sYmx6LmnJwYdGAQNmah5kkbYeX8nqqyogpXXVyptilX4vvRF+eXlMejAIKVNEYysYf/7wfdRaUWlVM9Xz1cdvSr0Qs8KPVE0a1FxFlqJ2bC/LnaaAgiLDUPOBTkBAKWyl8Ld4XeRwSWDfBfImxf48EH/OS8vLhGyRw+gZUtO8NiRzjs74+CTg3BzckPIryHI4m7mfUhjhMeHo8DCAohNjkX5XOXxYMQDpU2ymvjkeFRZWQVPw54CAN7+9Bb5s+RX2CrpBEQEoObqmgiJDQEAPBv1DCWzl1TYKmk8Dn2MZpuaISiaE9LL2y3HiFojFLZKPPHJ8Rh/cjyWXFkCAHB1ckXiFOUHKWKJTYqF92lvLLi4gH/u+ajnKJG9hKVDv6ywf4VcFZDDI0eq528G3cT4k+NR7K9iqLu2LhZfWow3kW/kvLT12CkCcOPdDf7vZx+focvOLohPjpfvAgMGpH4uIgLYtAno0AHInRv45hu7RQSCY4Jx+Ck3ekzUJGLe+S+nrLKGNOi1pxdik2MBcDdmm0Rz7Eh8cjy67urKO34AuPn+poIWWcfVt1dRa00t3vEDwKvwV8oZZAXb7m5DzdU1eccPAHFJcQpaJI3r766j+qrqvONPq5z0P4lKKyrpOX4A8g7mbIiszl+lUuH7Gt+bbXPl7RX8fOJnFFpcCA3XN8TSK0sdJxxsBwEQEBmg9/j4i+PouqurfE5DZx8Eo9hZCCy4sABqUvOPV95YiejEaJtcy97MPT8XJ/xP8I81pMHFwIsKWmQdWsd/7Ln+/hhvI98qZJF17H6wG403NkZwTLDe84nqtDXCjEuKw9B/h6L/gf6ISdKfWsqTKY9CVoknSZ0E79PeqLu2Lh6FPtJ7LbtHdoWsEk9YbBi++ecbtNzSEv6f/FO9njNjTgWsEo/sCX/dy3cX3PZC4AWMPj4aBRYVQJONTbDi2gqExYbJbZI4bCwAdEdUWo49P4Zuu7vJIwCKFgVq1RLW1pgQ+O8/LmlQBj5Ef8Dya/pzrB/jPmLFtRUmjkg7+LzwwRS/KameP/HihJHWjk98cjy67OqSyvEDXIQqLUFEmHl2Jnrt7WU0qhYRH6GAVdJ4HPoYddbWwdpba5U2xSoehjxEvXX1MO3MNL3BgJasGbLa3yiREBG239uOcsvLYdOdTUbbZHLLBHcXdztbJg3ZnX+1vNVQLGsxUccQCGden8GIoyNQcUVFhMaGym2WOGwoAEzdSI88O4Lue7rLIwB69hR/jFYItGkDLF5svQ0AFlxcgLjk1GHJBRcXpOnkuICIAPTZ18dospWPv48CFlmH1vEff37c6OsOn7SrQ0JyAgb+M9CoMNMSkZA2nL82zH8v+J7SpkhGrVFj4cWFqL6qOm4E3TDZLpNbJjtaJZ5X4a/Qbns79NvfT28KyZC0MuoHbOD8VSqVqNG/Ie+j36cK0ymCjQSAsZG/lsNPD6PHnh7WhyW7S///AwDeWJ+P8T76Pf6+9rfR10JiQ7DiuoTR/8WLQLlyQNeuwJ07skUoxJCQnIDuu7sjLM54hOpm0E3lxasILDl+IO2M/ENiQtB8c3NsvbvVbDtHH/nHJsViyL9DjIb50xIvP71Es83NMM5nHBLU5gc1nm6edrJKHMmaZCy6tAgV/q5g9juixVjOm6Nikwp/1jj/cfXGoXyu8jJaYwUyCwC1Ro0XH1+YbXPo6SH03NPTOgEgJvRvSJUqwG+/Sb/2ZxZcMD7q1zL/wnzxo/+hQ4HHj4EDB4CqVYGyZYHJk+0qBP53/H+49u6aydcJhFP+aaNOhBDHDwAvPr5w+CVlD0Meos7aOrgQeMFiW0ce+WvD/OturVPaFMkQEdbcWIPKKyvj7Ouzgo7xdHU853/7/W3UXVsXY0+MRWxSrKBj0vXIHwBq5a+FQlkKiT7ul/q/YH7L+TawyApkFACBkYEWFTAAHHxyEL329kKSOkn0NXikhP6rVOH6lcM69fo++r3FkX1IbIj4tb3lDUTh06fArFl2EwIbb2/EqhurLLZLC/P+Qh0/ACSoExw66c/nhQ/qrauHl+EvBbV31JG/Nsx/P/i+0qZIJigqCB12dMD3h78XldjrSCP/hOQEjPcZj5qra5qdqjBGunf+UkL/4xuMx7wW86BSKb78MTUyCYBnYcLDp/88/ge99/WWLgDEhv5lcvwAN6o3N+rn212cL1hRAwCmTjX9mo2FwK2gWxh+ZLigtj7+PhBUP+PlS+D777l6Ehr7jazjk+PReWdnQY5fi6OG/ldcW4G229oiMiFS8DGONvKPTYo1mc2flrj74S4qrqiIo8+Oij7WkUb+089Mx/yL840mJloi3Tt/QFzof1LDSZjTfI5jOn4tMggAc/P9xtj/aD/67OsjTQCICf1XrCib4w+KChI8nx8cEyxu9F+hAufYLSGzEPgU9wnddncTXI8hMDIQT8KeWG7YuDGwZg3QqROQLx8wZgyX12BDIaB1/P+9+E/UcY6W9EdEGHN8DEYcHSH6Ju1ozn/0sdFpPpsfADbd3oSPcR8lHetIzp+s2MYm3c/5A0DdgnWRP7OwqmAVclVwbMevRSsAOnXiHosUAFJGT/se7UO//f2kCQChoX9XV8DZWfz5jTDvwjxRRYvmXxAx+lepxE9n6AqBcuWA8+dFHa4hDfof6C84pKzF54WArH/dz3xwMPDXX0CDBkDhwjYRAlIdPyAgavXHH9xS0YcPpRknksNPD+OvK39JOtbRwv5pKUHUHIOrD0aBzAUkHetIYf+pjadiUsNJcHMWXwmVjfwBOKmc0K1cN0FtB/wzALvu77KVKfLi5gbs2SNJAIgd+WvZ83APNtzeIP5AS6F/rcO/dQto3RoIDxd/DR2CooIEzYnr8iHmA1ZdF3FMjx4irdLhyRNgxgxRh8w8O1NSGFO3+I9Jxo0z/vzbtzYRAiuurZDk+AHg+SczI//z54FffuGWilaoAFSrBsyZAzy3XbQgt2duuDi5SDrW7BTBq1fAffvOua/uuBqDqgyCkypt77BePld5PB31FDOazhA9knekpX7uLu6Y1XwW7g2/h9YlWos6ljn/z5gL/U9tPBXDagwDwI2u+u3vhz0P9tjSHPmQKACsmTf1cPEQf5C50H+VKsDp00CuXNzjq1etFgBzz8+VVKp4/sX5wsuUCg39m0KEeLj69iq8T3tLuszpV6ctr9jo2xdwseDAZBQCuTxziT5Gi9mRf3aD6my3bwOTJgGlSgHVq9tECNQpWAdXh1zFgMoD4OrkKupYk2H/69eBYsWASpW4//XMmZxgtDG5PXNjY+eNeDzysTwiIDkZ2LZNliW7YsnomhGTG03G89HP8X317wX3xZHC/lpK5yiNY/2OYX/P/YIT2HNkZGF/AECDQg2QxzN1+ckZTWfAu4k3lrdfjqHVhwIA1KRGn319sO/hPlmuvXz5cpQvXx61pC55s4RIAZCkTsLLT+JCx56unuhVoRcO9TmEAVWM1OwXgrEwuTa5r2FDwNdXFgHwLuqd6FG/lvfR77H6xmphjaWE/rXMnAkMGSK4+fV31yXP/0UnRuPym8vmG+XIIW7jKEMhMG4cEC08o7p/5f7wGeCDQVUGwcvdS/h1Abz4ZGa5X/nyQOnSxl+7dctmQqBavmrY3GUzAn4KwLQm05A3U15Bx5kM+9+5k/J3YCAwZQonNKtUsYsQKJWjFC8C+lXqJ/1EDRoA/fsDhQpxf69cyU0r2ZG8mfJiVcdVONT7EFQC9rBJFfaPi+PqefTuDTx6ZPwgO6BSqdClXBd0KdtFUHs28v+Ms5MzupbrqvfcrGazMLnRZO7iKies7LASg6sNBsAJgN77euPAowNWX3vkyJF4+PAhrl0zvSbbakQIgJfhLwUlJnm6eqJvpb7Y33M/Qn4Jwc7uO9GhdAfpNhqG/g2z+itWlEUArL25VtAyRlOImr+VEvqfOVN0/YL+lftjdO3RKJeznKAbmCGClvxJncZ4+xZYuND8CggjtCjeAhs7b0TwL8E43OcwBlUZJCjkGp8cb36533ffWb64jYRA3kx58Xvj3/F6zGtBYdrIhEjjqzH69ePyXwy5e9euQqBUjlKonq86/1j0Z+/9+5S/L14Ehg/nEkqbNbO7EFh3ex0voI0NBLWkGvlPmMDV89i1ixOXlSvbLRJjyIPgB3yZcjdnNzQq3MhkW+b8dRhcbTCcVdzc8pzmczDpq0n6BqicsLrjanxb9VsAXEWlnnt74uDjg7Y2TR4ECgBz8/26u0D9VPcnbOu6DV3KdYGHq4RQvyFFi3K1+wEu6c1YVr8MAsDasJ2oethiQ/8SHD8AZHHPgr/a/oWHIx8iYkIEzn5zFotaLUK/Sv34z7Q5/F75Wb5I586WQ//mKGFx61CjuDm7oX3p9tjYeSOGVEuJhpibXjKb8S9WxOgKgWrVgC1bxB1vhITkBH5jJXdnd/Qo38PolICa1MaX1GXIYDmqZAchEJsUi3kXuN0vVVDhUJ9D4qYDRhjZ4lejAfz87CoEzgecx/5H+wFwAu3Jj0+w4esNRhPBU438DT/X9+6l/N/tKASICD8e+5EfuP321W84/c1p7O+5H4W9Cqdqn5ay/VWC1iNzSF7/8DDkIRLViaiat6rJNmqNGoP/HcxvmODq5Ip9PfehY5mOUi8LAIiMjISXlxciIiKQJYsN95FPTORugP/+yz328ODWb38O6x58fBCdd3Xmm2fNkBWdy3ZG93LdUTZnWZRcyu0vXjF3RdwbLnMt79hY4OZNoHZtTqyY4v597qYQ8rl2de3a3EY/WbNavESyJhmn/E/x241qP1cEwp+X/+Trky9uvZgfaWrbuDq7onWJ1siXOZ/wPk2dCkyfbrldy5bACXmL7ryNfIuCiwsCAGrkq4G+lfriRtANXH93XU/kdSjdAYf6HLJ8wjZtuP+zWIYPB5Yv1181IBIiQrG/iuF1xGs4q5wRMCYAN9/fxJ6He3Dw8UG9+XGfAT5oUbyF6ZPVrAncEFcURY/nzyWLGQBYdnUZRh0bBQAYWn0oVndcjffR77Hq+iqsvLES76O5EbGLkwsiJkQgo2vG1Cc5eJATZGKpXJn7/n/3HZBf2ConUyy6tAhjT4wFAPSs0BO7unPJ0M/CnmHWuVnYcncLPwVzvN9xtC5pEO0ICeEcvFrAEkgnJ27Jac+eXJg9d26rbNdCRKi7ri6uvr0KAFjTcQ2GVOdEZmxSLBZdWoS55+fyIuzWD7f0/UNcHJdLEm8hh6hSJc72Hj2AMmVksV2XHfd2oO/+vgCA4tmK48GIB/xgLTYpFrPPzcaCiwuQqE5Eqeyl8HSU4KRu5Ze3EZHQH5uTrE6mAfsHELxB8Aa5Tnelw08OW3XOiIgIAkAREREyWWmGhASiTp2IuBXlRB4eRCdPci8lJ9Bvp36jEYdH0LFnxyghOUHv0Hpr6/H9fhTyyPa2muLePaJcuVL6ULs20adPVp2y3bZ2fN9CY0Lls1Nro6Wf2bPlueZnDj4+yPdnvM94vdfC48LJ76Ufbb+7ncJiw4SdcO1a4X3R/gwfTqTRWN2XK2+u8H1pvaW13mvxSfF06Mkh+uHQD/S77++UmJxo/mRz54rvh/YnTx6iqCjJ/VBr1FRmaRm+L3ff39V7PSE5gbbd3Ua99vSitTfWmj5RXBxR5szS+5E7N1F8vOR+xCTGUO4FuQneIJW3iu59uJeqzdPQp/Tz8Z/J28+bktRJxk/UooV4252ciJo2JVq1iijJxHkFsuPeDv69qPh3RUpWJ6dqExQVRDPOzDD9fvTpI87+SpWIZswgevzYKtu1RMZHUr4/8vH9MOWLnoY+pT8u/CH2vi3G99rkx6GcPxEnAPru68v/w91muNHRp0cln8+uzp/IrAAwx6KLi/g+zzwz0w6GmkFmAdB2a1v5nb9GQ1S2rOkbQatWNhMAU3yn8P3ZfX+39ScMDSVycbG74yciGvvfWL4vZp2iEF68kOYwc+QgunPHqksff3ac70eTjU2s60e/ftKdf8aMROHhki+98OJCvh89dveQ3odVq6T3ASCaOFHypeOS4qjI4iJ8PyTfvw8ckG5/pUpEBw9K7gOR/nej4/aOVp3LCIo7f4dbWOrs5IxNnTehd8XeAIBEdSK67OqC/55LW59sdyQuA+xWPqUmwp6HCi951OYA5PycvCLDMkAtshVzMpf1P3MmF0afOzfluUmTuAQzGdCt910zf03rTygm679nT6tD/VqIiP+suTi5oHPZztadsHhxoEYNccfkyMF91ipXturSS64u4f/+X53/WXUuyUmYzs7Ahg2Al5ekww3n+n9v/Ls0OwCgSxfrCnclJ0s+dNnVZXgd8RoA0LJ4S7Qp2UbaiVq3BjJJXP9/7x4wcCAnBSTwIPgB/rz8JwAuJ+uvNtIKSjkyDuf8Ae5GtKXLFvSswN3cE9QJ+Hrn18KqpjkCEgRAYa/CqF2gNgDgzoc7ovYBsAkVK3IJQjIIAGvKZZrF2E1aN7lv/HjZBQAR4cY7zvln98iOolmLWnU+HqEO59Qp7sYmA1ffXkVARAAAoHmx5vKsURbjOGVy/M/CnvGFmIp4FUHH0tblCaF1ayBzZnHHODsD27dLX4YKYOX1lfx25j0q9EDF3BUlnwu5cgFNm0o7tlEj0atItITFhmHm2ZkAOAGzoOUC6YLfwyPlHiqFxo0liWQi/SS/iQ0noli2YtLtcFAc0vkDnADY2mUrXygoQZ2ATjs7pZntUqUIgB7lU26c+x7JU+/AKmQUAFqkLJkzSYUK+jv9Gcvql1kAvI16iw8xHwBwyX6yRTIsZf1rE7HCwrgowd27Vl9SN8KkFdpWI9T5u7oCx49b7fgB8MuwAGBkrZFwdrKyVHWGDOKcjgyO33DUP6XRFMnn4pESwWjUCDh6FPCUtnpn+pnpfJLot1W/RZW8VSSdh0dqFKZhQ2DrVkmH7ry/E6dfnQbAJfn92uBXaTY4OA7r/AEuC3x71+18rYD45Hh03NERvi99FbZMICIFgG45ZMVD/1pkEAAkMfRmEZWK2xinTRvut6nlfDIKAO2oH5Ap5K/FXOh/+HBuWVOdOtzj0FCrBYDsIX8tQkP/SUncao0E6bUhACAqIQrrb60HwC1THFx9sFXn4xHqdJycrHb8gMyjfi1iQ/9WOv5nYc/w9/W/AXCV/qY3FbAaxxJSQv8NG3L9EBu9AVcDQrvSAgCWtFmitxT7S8KhnT/ACYAd3XbwN6e45Dh02N6BV2YOjwgBUCxbMdTIx904bwbdhP8nf3taahoZIwCyb+BUvz5w7Jjlyn0yCYDr767zf2vfK9kw5nC0y/myZuXyGGQSALoh/xbFWyC7R3YLR4jAnOPMkgVw/1zT4dAhrq0VAmDTnU2ISowCAAyoPEC+fggN/RNxy3ytwCajfkBc6L9OHascPwBMODUByRouV2BcvXEokEXaJj96iA39W+H4AS5yoV2u3LF0R7Qv3V7SedICDu/8Aa4gya7uu9CpDPchiEuOQ/vt7XH29VmFLROICAGgF/qXqdSxLFghAGw25y8WGQSA7Ml+uhiG/g3X8Xt5ySYAdj/Yzf+t+5mTBVPOP0cO4Nw5Ltzv8bmYkBUCQEMaLL26lH88qs4oKdYax1LoX/ueEAGDBkkOMQM2GvVrERrBCA4GPkrbjhdIXdDnlwa/SD5XKoT2IW9e4PBhyY4/PST56ZImnD/ACYDd3XfzpW5jk2LRbls7nA8Qt0WrYggUAA6V9W+IDBEAWef8pWCFACAifuSfwyOH0QpfVpEjBzBxIjf6+vVX41n9MggAIsLeR3sByBzy12Is9K+b3NekCTc6s1IAnHhxgi+q1LRoU3mdJmDa6Tg7Azt2cOIM4KrnSRQANhv1a7EU+s/wOaT98iUXJQgMFH0JItILlc9oOkPeXfratBEW+n//nisLLGHTq/SS5KeHiHWBDkF8Urxe0ZhMszPR+dfnTba3+zp/SwioA1B1ZVW+f68+vVLIUDPcu0eUM2dKHyzUAWi5uSXfn/A46WugZcWwII2AOgAB4QEmC+LIilptuU14OFGdOin258wpeK385cDLfD/abG1jpbEm0P3/mlrH7+fHff617Tp2FFUgR/c+cODRAdlM5zFW8MfZmWjXLu51jYaruaB9zcmJaMsWUZfQXdffc09P+ftAZLrgT6NGRE+eEJUsmfJciRJEAQGiTi+koI/V9O1rek1/mTJEKlXK42HDhH2HdNh+dzvfh+J/Fae4pDj5+6APW+cvFncXd+zruY9fOxqdGI22W9vgUuAlhS0TiIAIgMNl/RtiRQRA9jl/qUiIANh0vl8XJwFfSysiALoh/57lZcryN+SHH4C6dbmRvqnlfFZEAGRf3mcMw9C/YVa/SsVFZyRGAGw+6tdiLIKhTe4rXZr7LpfkyovjxQtREYD45HhMODmBf7yg5QLrV1sYw1QUpmFD4No17n+u/d6sXAmMHCk4AhCVEJVukvz0EKEUHIq4pDhqtaUV7SkHUgMUmEVFL73HEL15o9fO4Ub+WsxEAJ6EPuFVaN21dRU21AwCIwAtNrfg+xMR72Dvg4gIwG+nfuP7sf/hfjsaaQaREQCNRkOFFhUieINcprsIL0FsSyREAEYfHc2/FwsuLLCdbRcucCN6V9eUEb8hEiMAdhn1ExEFB3MRC90Rf3S0fpvAQEkRgAUXFvB9aLm5JWlkqjyZirg4okyZ9L+rDRsSRUamtNm2jfvfi4wA6Fby67Sjk23sT43iI/806/yJiGITYynWXedDDZBGpeI+FH/9RfT2reM6fyKzAqDS35X4D2RAuLgwnF0RIAB0nX9kfKTx8yiJQAHQektrvh+vw1/b2UgziBAAlwIv8X1ou7WtnQ01gwgBEBEfQZlnZyZ4gzLOykgfYz/a1jZ/f845mkOkABBSw19WBg/m7GrRIrXj1yJSAITGhJLXHC++D7eDbtvI+M/ohv4NHb8WkQLg/of75DzNmeANyjAzA/l/9LdhB/RQ3PmnubC/Lh6uHnBr3EzvORURcP488L//AQULcuFoAAgKUsBCC5iZAtAN/WuzaB0SAVMARA6S7W8KAVMARMRn+ufKmAuFshSyp4XmETEFsOdBShKp7Fn+1iBiCmDT7ZTlff0r9Uc2j2y2ta1YMe5eYg6RUwA2zfA3xurVXFLfiROml/MVLChqCkD2gj6WmD6d22m0Xz/Ty/n69uW2hxYwBUCUDpP8dBGhFBwTX1/9UZvBTwTAjfy1anHJEqK3b5W2Wh8jEYBXe9fxI7QG6xoobaFlzEQAmm9qzvclKkH6zm02x0wE4NWnV7ZPkrMWCxEAtUbNh/xdp7vafsQsBQsRALVGTaWXlubfC5uPmMUiIAJg91G/WAREAJ6GPiWX6S589OVNxBsTJ1MIAREABZL8dGEjf6tp1Ej4HtTnzwOjR3MKt1EjYOlS4N0729onBCMRgCIDfsS3YdxSsguBF/A28q2CBgrATASAHGWdvyXMRAD01vfnk3l9v1xYiABcfXsVgZHcKK5F8Ra2HzFLoUkT4MgRkxEA3eV9zYo1s/2IWSwCIgB2H/WLRUAEwCYFfeTEQgQg3Sb56ZD2nb+zM9Ctm+V2uhBxxUZGj+ZCeseP28Y2MRgRAKtWv0Ozz0X+Djw+oJxtQjEhADxjkvgmiq/zt4QJAaCX6Z/fhpn+1mJGAOiG/GWr5W8LmjY1KQCWXEnZvW907dEKGWgBMwLAbhn+1mJGANi0oI+cmBEA085M4yv5dSrT6Yuu5GcSEWECx8VM6F8v7G/qZ9IkpXuQgsEUQIwLqNlAUKMNjZS2TDgGUwAPi2cmr/FceC06wUSykaNhMAWwrkfJtJGAqcVgCkCTMye1HJfHsUP+hvj66k0BRLVuSm6Tufeg6J9FbbOeXE6MTAEc/b2vfTL85cJgCkBTogR1mFeF78OaG2uUttAyBlMAYYN6kstUJyWS/HRRPOz/ZTj/5GSi3LmlOf9ixRw+B0ArAIKigpS2TDgGAuByAVCWCaCYxBilLROOgQAY3xyUe0Fu2y1nkhsDARCcEVRxOKjdtnZKWyYcAwFwsDTIdbKNl/fJiYEASFaB+nZ10Ll+UxgIgGfZQAV+smFBH1tgIAD+rgnCVNC009OUsog5f9nQVdhCnX+xYkSvXiltuXEMBIB/VtDWW5uVtkocBgLAu3Eac/5EqQTAtwvTUASGKJUAOF0EtOHWBqWtEoeBAPihq1vaiFxoMRAAUa6ggZu7KG2VOAwEwMYqoGPPjiltlTi2bSONjgDo+2M+eyf56aK480/7c/5axO77XKwYN6dVpIht7LGWzzkAMR1aAQBCPYFi2YsrbJRIPucARGfn6nJnLFgUGV0zKmyUSMaPh3ruHGhUQKwL0L5GH6UtEsfnHICQKqUAANHZMqJL2S4KGyWSzzkAMe7c7aphza6Omaxois85AO8Gcv/3SA8VJjb3VtYmsXzOAXiXj/suZy1SBq1LtFbYKJH07YvgFX8gyQlQq4Af23qnuyQ/XVREgjOxHTtlW60G8ufndqfSIRKAF4AIAFm0Tzq649eFCMGXTyGqaH6UyFdeaWskQTExeHrtOIo27AB3F3elzZFE+KNbCFXFo0SZuo5TolgMGg38Tx+AV82GyJElj9LWSCLyQwDevbiNMvU6ps33AEDg5RNwKVwU+fKXVtoUScTFRuL1haMo1aw7nJ1dLB/ggLx/fhtJcTEoVKmBkmYo/gH+cpw/AIwYAaxYofeUUeffrx+webOwGuoMBoPBYMiL4s7/y/J+QkP/27aJ2viBwWAwGIwviS/L+Zsr+FOkCPDXX5J3fmIwGAwG40vhy3L+5gr+HD7MFfWxYutHBoPBYDC+BL4s5w+kDv1rk/oKc6Vy0acPEwAMBoPBSNd8ec6/USOg+OclccWKcSN+Q5gAYDAYDEY6Jm2u1TCHszO3baWPD9C9O7de3hh9Pq/X7t+fc/orV3KPly9nqwAYDAaD8UXz5Tl/AChRgvsBgMhI0+2YAGAwGAxGOkR2D7fw4kJ03dUVFwMuQkQNAeX40qYAbt0C2rYFFi4EYmKUtobBYDDMkib8hADik+OhobTjN2R1/s/CnmGczzgceHwADTY0QKmlpTDFdwrufbjn2G+wHQUAEaHdtnbItzAf/nv+n+znR8eO3BbF48YBOXJwCZC7dysqBO4H30ftNbXhfdpbMRtsybzz81B6aWl+m9MvgZP+J5F/YX603NzSsb+7Atl8ZzMyz8mMSisqpakbtDH2PdwHz9meyDInCwIiApQ2RzKRCZFouL4hnKY7ocF6RavtWUVMYgy67eoGj1keyD4vOxKTE5U2SRCyVvgLiQlB7j+Mr7Mvl7McelXohV4Ve6FszrIiTLSOyMhIeHl5ISIiAlmyZDHfeMeOlCkAABg2TPYpgAfBD1BxRUUAgKuTKy4PuYzq+arLdn5UqAA8fJj6eQ8PoH17Tgy0bw94esp3TQsUWVwEAZHcTera0Guomb+m3a5ta86+PovGGxsDALJmyIpP4z8pbJH13Aq6hbrr6iJRzd3Erg+9jhr5ayhslXTW3FiDHw7/APp8Czv/7Xk0KJz2nI2GNJhzbg6m+E3h++Ld2BtTm0xV2DLxnH51Gv3398fbqLcAACeVE9S/qxW2SjwnXpzA94e+x+uI1/xz94ffR4XcFSwd+mVV+MvlmQt1C9Y1+tqj0EfwPuONcsvLocrKKph1dhaef3wu5+Wtxw4RgGcfn/F/J2mS0GJzC9wKuiXb+TFlivHn4+KAvXuBXr2AXLnsFhG4EHCBd/wAMOvsLJtez568j36P7ru784/D48PxIfqDghZZz62gW2ixpQXv+AHgZfhLBS2Sjlqjxtj/xuL7w9/zzhLgwrNpjeCYYLTd1haT/Sbr9SV/5vwKWiWeuKQ4/HT8JzTd1JR3/ADS3AY7ITEhGHBgAFpvba3n+AEgb6a8ClklDtnn/L+t+q3FNnc/3MVkv8kotbQUaqyugXnn5+HlJwe5wdhYAPh/8td7/Cn+E1psaYE77+/Icn506gRktLBznh2FgPcZb73HB58cxKOQR7Jfx94kqZPQa28vhMSG6D1/0v+kQhZZj9bxf4z7qPe8w3w3RRCdGI0uu7pg0eVFRl9LS5x5dQZVV1bFiRcnUr3m4eqhgEXSuPb2Gqqvro4/r/yZ6rVcGXPZ3yAJEBG23NmCcsvLYevdraled1I5IWuGrPY3TAKyO//OZTvDSSX8tDeDbmLCqQkovqQ46qytgx33dshtknhsKACehj1N9dzHuI9ovrm5PAIgY0YurC8UQyHQpw8QFGS9HQDOB5xP5QwJhJnnZspyfiWZeGoizr4+m+r5E/6pb9BpgVtBt9B8c/NUjh+A40XoLBAYEYiG6xvi0NNDRl+PSIiws0XS0JAGs87OQrPNzRAULc93UgmS1En43e931FtXD49DHxttk9k9s52tEo//J3+03toaA/8ZiLC4MKNtsmXIBmcnZztbJg3ZnX9uz9xoXKSxpGOvvr2Kvvv74kHwA5mtkoCNBIBu2F+XsLgwNN/cHHc/3LXq/ACAnj2lHRcXB+zcCXh7W28DYDLBb8e9HSZvAhZJTAQUTkDb82APFl5aaPQ1nxc+aS5BTuv4P8Ubz1cw9Zl1RK69vYbaa2vjzgfTQjoi3vGdf3BMMNpsbYPJfpPTdILig+AHqLuuLmacnQE1mZ7T93S1Xw6SWJI1yVhwYQEq/l0RPv4+ZtvmzJjTTlZZj00Ws3cv391yIxNkcc/iOHMmNhAAxkb+WrQC4H7wfcnnBwC0a2c59G+OevWsuz6Ac6/P4dTLU0ZfIxBmnpUw+h8/HnB35/o2YgRw6ZLdl2Q+CnmE7/79zuTrQdFBeBDiAOJVIJYcP5B2Rv57H+5Fo42N8D76vdl2jj7y14b5LTkaR0atUeOPi3+gxuoauBl002J7TzfHdP43g26i9pra+PXkr4hLjrPYPt07/y5lu0AlIZkxs1tmHOt3DDky5rCBVRKRUQDEJsXiTeQbs21CY0PRbFMz66IfYkP/ukyZAgwaJP3anzGc6zdkx/0deBL6RNxJD30O48bHAytWAPXrc3s3/PSTXYRAVEIUuu7uanHO2OdF2rhp3wy6adHxA0BgZCDikizf+JSCiDD73Gz02NNDUDKfo478NaTBzLMz03yY3/+TP5puaopffH5BgjpB0DGONvKPSYzBuBPjUGtNLdx6LzwhO907/3yZ86Fh4Yaijsnslhn/9f8P9QvVt4VJ1iGTABA6ggqJDUGzzc3wMMTIkj2hSAn9T5kCTJsGqKxbhXL29Vn4vvQ120ZDGvFz/wMGpH7uzRvgzz9tLgSICIP/HSxouiItzPvfDLqJFptbWHT8WgwTVR2FhOQEfHPwG/zm+5vgYxxx5K8N80/xm5Jmw/xEhNU3VqPyiso4F3BO1LGONPJ/FPIIFVdUxMJLC0W/Fzk8HGjgagGb1bAVE/rP4p4FPgN8UK+Q9eFmmyGDAHgWJnzuNDgmGM02NZOeGS829C+T4weAqaeFrTvefm+72WmQVPzwA+BipiK1DYXA4suLsefhHkFtz7w6g4RkASOe+fOBbNmAxo25vSiSk620UhhiHT/gmPP+obGhaLGlBTbf2SzqOEdz/jeDbqb5MD8ArL+1Hj8c/gExSeJXDTnSyH/ehXl4Ff5K0rHpfuQPAF3LdRXUzsXJBUf7HkWdgnVsZYp8WCkARDk6AB9iPqDppqbSkuPEhP7795fN8Z9+dRqnX50W1FYb5hRM9uxAixbC2hoTApcvC7+WDmdfn8WvPr8Kbh+XHIcLgRcsN5w7FwgPB86eBVq1AvLmBb7/3qZCQIrjBxxv3v9T3CfUXVsX5wPOiz7W0cL+v/r8mqbD/Fos5VqYI5NbJhktsY4uZbvAxUnatjfM+QMomKUg6hW0PJJP1iRjwcUFekVFHBorBICU0ZNWAARGBIo+VnDof+9ewNd8mF4oYkv4bru3TVRERNJ0hlYI1KsHzBQ31fAu6h167ulpNlPZGILm/atU0X8cFgasWWMzIfA07Kkkxw9YcP7x8UCpUoCXF2fz3bs2X5Fx+OlhvPj0QtKxjjbyb1K0idImyMIvDX7BT3V/gquTq+hjHWnk/3XZr3Fn2B00LdpU9LEOla9mAZtuXWcu9J/ZLTPcnd0BcIVfeu/tjSR1ki3NkQ+JAkDsyF/L++j3okObACyH/kuX5n7Hx3N7Apwynp0vlNOvTuPM6zOijtGQBrPOiaj69/XX5kP/lrh2TXDTJHUSeu7piQ8x4qv2CZr3nzzZ9Gs2EAJb726V5PgBC8L1v/+A58+5HTTXrOFETdmyXP9sJARal2wtuUy0yZE/ETB0KFco68oVuy0pndxoMvwG+aFRkUZ2uZ6tcHN2w6LWi/Bo5CP0KN9D1LGONOcPAOVzlcepgaewo9sOUVUU2cj/M93KdTP6fHaP7DjzzRkc6XuEL+t44PEB9NnXRzYBsHz5cpQvXx61atWS5XypkCAApM6b5s2UFx1KdxB/oLnQ/5Qp3I3566+5x3FxVgkAIhI812/I1rtbhYeVxYT+DcmRA5glXGjsuL9DWPjeCDeDbiIkJsR8o8aNucJKlpBJCPQo3wOFvQqLOkaL2fenWbPU+188fcr9r20kBHJ75sbVIVdxauApfF3ma1Gri0yO/DduBNau5VaV1K0LlCwJTJrE7ZRpYyHQpGgTnPnmjDwi4ORJ7v8+bBjw+rXl9jJTInsJ7O6xGxe+u4C6BYyXezfEkUb+WlQqFXpX7I3HIx9jYOWBgo5hzv8zRbIWQa38+s43h0cO+A70RbV81dC8eHP82/tfPgKw79E+9NvfD8ka68OcI0eOxMOHD3FNxEhPNCIEQER8BIJjggWfOrtHdgyuNhjH+h3D6zGvUSVvFcsHGcNYmFyb3OfuzpX1lUEAnH512mjFOyGoSS1u9C8l9J8jB9evihUFH2LtF9lUnQMeFxegq7DcGB5dIVCwIJfQKJBKeSrBf7Q//Ab5YUTNEcjtaXwTLmMERgSaXkaXOTPQwYw4tZEQUKlUaFasGf7p/Q+ej36OsfXGCnIiJkf+JUroP/b3B+bMAapX56Y17CAEtCJgc2cJkT4tgwZx/99Vq4CiRTkhs3Ch3YVA/UL18XO9nwW1TTXyv3KFG7x4enL31Js3FSvu5enmieefhA1OWLa/Drqh/5wZc8J3kK+eI2tZoiUO9j7IC4A9D/dgwIEBsggAuyBQAAgd9bcp2QYn+p/A+7HvsbbTWrQp2QZuzm7S7TMM/Rtm9bu5ySIADj45KN1GAAceHRDeWGzoX+v4DefYLdCuVDvc+P4G5rWYh54VeqJ4tuKijjdWiz0VPcSFR/X48AHYLM5JODs5o0nRJljefjne/fwOfoP80LJ4S4vHEcj8cr++fYUZYCMhUDxbcfzR6g9BicMxSTHG7y9ffcUJKmO8eGFXIaCb+V80a1FxBxc2iO5cucJt8W1nIZCoTsSEUxP4x4OrDUa2DNmMtk0l2tas4e5FsbHA338DNWpw//eJE+0uBLbc2YKLgRcBAKWzl8aWLltMTgWwkb8O39f4HvUL1UfVvFXhO9AXlfNUTtWmdcnW+Kf3P7yT23l/Jwb9MwhqTRrZ4lGAAHjx0XhyUm7P3GhTog3/OF+mfGhZoiVcncUnzRglY0Zg0SJuVLNggfGsfhkEQNdyXSVXZnRWOWNgFWFhNQDiQv/Zs0ty/Fqq56uOXxv8il3dd+HF6BcI+zUMx/sd57OBzWUFmysxyyM09G8MDw9g8GBpxyJFCHhl8OKf61i6o8mIgFnn3749Z48YdIVAixZc6WYreBTyiK8vUTxrcZzofwKdynQyOiUQmRCZ+gQqlbACVzYWAk/DnmLbvW0AuAjg3WF3xU0HmCvPbUchsPzqcv4z06xYM6zpuAbPRz83mhSYauRv7H148YJbIWNHIRAeH45ffH7hHy9rtwz9K/fH45GPMa7eOL3vf1ra1AcAN1cr8MfmHHl6hNxmuBG8QfAG9d/fn5LVyVadMyIiggBQRESETFaaYft2IicnIu7jSDRsGJFaTUREN97dIOdpzgRvUN4/8tLIIyPp9MvTlKxOprikOMo0OxPBG5RtbjZKTE60va3GSEgg+vrrFPs9PIhOnpR0Ko1GQxqNhtQaNbXd2pZ/Tz9EfaAkdRIlqZMoMTmREpMTKUmdJP4C69en2Gnup2JFok+fJPXBFHfe3+H702tPLwqNCaUTz0/Q7LOzqduublRkcRFyn+FOc87NEXbCH34Q1hfdHw8PIl9fq/sSnRBNHjM9CN6gnPNzUpI6iZLVyeTr70vDDw+n3AtyE7xBrtNd6UHwA/Mn69ZNfD90fx49sqovIw6P4N+XRRcX8c+/+PiCxv43lrzmeBG8QQUWFiC1Rm38JLdvS7e/RAmitWut6gMR0YD9A/h+zD47W+81v5d+1GhDI4I3yGW6Cz0KMfI/S0wkyp5dnO116hD98QfRq1dW209EFBYbRtnmZiN4g1TeKrr57qbe68/DnlP33d0J3iCvOV4UEhOifwKNhqhoUeH/9wkTiG7c4I6TkR+P/Mi/F913d0/1+oPgB9R0Y1OCN6jfvn5iTi3G99rkx6GcPxHRoSeHyHW6K/8PH3hgoFUCwK7On8isAHgY/JCuvrlq9MbTZ28fvs/Hnx23j63GkFEAaNF1/qExofLYGRZG5OJi+oagUqX8Xbu2rAJg/c31fH8WXFhgtI1GzE3o5ElFHD8R0a77u/i+/HDoh1SvJ6uT6VLgJXoc8tjyyXbulO44v/7aqht3eFw4ec7yJHiDPGd50qe4T6naRCVE0bFnx+ht5FvTJ9JoiEqXlt4PgChU+mf8SegTcprmRPAGZZ+XnSLjI422u/v+Lj0NfWr6REOGSLe/Xj2iBxaEngV+Pv6z3j3cFIERgakdv5aJE8XbLqMQuBV0i38vMs7KSAHhASbbhsSEiPvOO4Dzt3nYXywdSnfA3p57+XDK5jubMeTQkLRT8tLMFEC5XOVQq0Ato1se6+ZG7H24117WpkamHABTqGQoJATAfOg/Rw5gzx4g5+f5t6tXgdatuYI6MnD93XX+7xr5ahhtI6qfYkL/Hh7AkSNAU/FrkI2x+8Fu/m9jy7OcnZxRt2BdlMlZxvLJpIT+AS5ZcNcuq4pMbbi9ga8sN7DKQKPh10xumdCmZBvzS7dUKuvyMCpX5qo2SmTm2Zn8vW5svbEmt7qtlKcSSuUoZfpE1vTh0iVg3jzJh/t/8sfSq0sBABlcMmBmU9O1NQpmKWh6nlxKYq/u1MA334g//jMa0mDk0ZH8ezH5q8ko5FXIZPucGXPKd2+zEw7n/AGgU5lO2N19Ny8ANt7eiKH/Dv0iBIAp2pZsyye9HHh8QNmER60A6NSJe2ztMkCQjMbpYOzmoE3u69YN8POziQC4EXSD/7t6vupWn09U1n/fvrI5/ujEaBx9dhQAkCtjLjQu2ti6E2bKxCWYiqFDB67IlLu75MuqNWre2QDAqNqjJJ8LgHTHWbo0cPx46mWPAjGc67eqH02bcgJZKh07Sj50wskJSNJwS7bH1htr1mmapUoVbrmlVP79l4sHSEA3ya9MjjIYW3+sdDscFId0/gDQpVwX7Oy2E84qZwDA+tvrMezwsC9WAHi4eqB9aW5NflhcmOASuTbDzY0bPcskALRI2e3RJIZZ/4ZZ/RUryi4AktRJuP3+NgCgVPZSeslyViHU4axbxyWbycCRp0f4bUq7lusquaSpHmIcpwyOHwCOPT/GJ5a1KtEK5XKVs+p8qFw5pQCWUEqXBk6fBvLlk3xZ3VH/uHrjTI76BeHqKn4ZqZalS4Hu0rZlvxR4id8DI7dnboxvMF6aDQAXhZEy+tcya5akaJJhkt/StkutW3HloDis8weAbuW7YUe3HbwAWHNzDUYcGfHFCoDu5Rwk9K/FRgJANrJnT7lJmVrOJ7MAeBjykN+mVGqFOaOYC/17eHCV57RMmiSLANDdqKhnBStusroIDf27ugJTp1rt+AFgyZUl/N9Wj/oB8aF/GRy/4aj/x9o/Sj4Xj5QIxtKlwI/Srk1EGHsiZYQ8rck06wQMID0Ks3gxMGKEpEOn+E5BSCxXoKt7+e5oWcLyUti0iEM7fwDoUaEHtnXdxs+Tr7qxCj8e/ZHLVkwLiBAA7Uq1g4cLd+Pc/2i/Yyx1lEEA2PS9WrUK2LkTuH/f9HI+GQWAkPl+SZgK/Wvn+Fev5uYytVgpAKITo3Hk2REAXMhfttKyQkP/SUlA27bcGn8reBTyiF8TXyJbCbQrJXLawRRCnY6nJ1fe2ArHD8g86tciNvRvheMHuCJtl95wRafK5iyLIdWHSD4Xj5TQ/+LFwJgxki53+/1t/H39bwBARteMWNRqkaTzpAUc3vkDQK+KvbC1y1ZeAKy4vgKjj43+4gSAp5snf/MKiQ2RXDFPdmSMAMieFJMlC9CrF1f21hwyCQDd+X5ZR/5AaodjmNw3frxsAuDI0yN8xb5u5brJE/LXYs5xtm4NaEtuh4YCzZtbJQCWXV3G//1j7R+NJtNKQmjoPyYGGD0aSBCwhbMJbDLqB8SF/gcOtMrxJyQnYPzJlBD/gpYL5PlMiQ39W+H4DZP8pjSaIj1fIQ2QJpw/APSp1AebO2/mv9zLri3DmONjvjgB4DBZ/4ZYIQBslvAnFhkEgO7Iv1q+avLa17hxygjSVFa/TAJg90OdLP8KVmSGG8NU6L9DB+DgQW5fgjqfK/FZIQDC48Ox6c4mAFyFuG+rfmuN1fpYCv0XLAhk4PYlwaFDXFuJAsAmo34tQiMYW7dyPxL5+9rfegV92pcSuJ24EIT2IUcOLtFXIoZJfkJLE6dZRKwLdAg2395MKm8Vv4Z0zLExZtdX2n2dvyXM1AEgIoqMj6QMMzPwxYCsLXIkOwkJRJ06iaoD0GpLK/79Co8Lt5OhZrh3jyhnTtF1ABKSE8h9hjvBG1R6aWnb2HbpEtGIEUTXr5tvN3eu/vrm2bPNt9chKiGK/4zlXpBbWpElSxgW/OnQgSg+PuX18HCusIz29Zw5ie7cEXWJRRcX8Z+rkUdGytwBMl3wp3RponfvuFoLHh4pz3fsqN9HAQhd1y8ZSwV/GjZM+dvJiWjLFtGXsFTQx2o0GqJSpYSv8w8wvR7fFJ/iPlGu+bn4z9OJ5yfk7UNq2Dp/sQyoMgAbvt7AZ43/eeVP/OLzyxcTAcjsnhltSnLlft9Hv5e8q5zNkBABcLj3RmIE4EHwA9sk++lSty6wfDm3TtkcVkQAdEP+XcvKlOVvSP/+KX8by+r38uLmyiVGANQaNZZd0w/5y46x0L9ucl/Tplx0RhvlkBABsOmoHzAf+l+6FDh7Fhg+nHus0XBldUVGAGadncVvFT2gygD5I2KWojBTp6bkBbx4wb0vgYGiLpFekvz0EKEUHIr1N9eTyltFecaCpjYC/bFykNEIgMON/LWYiQBsvbOVV6Cjjo5S2FATiIgAtNzcku9PRLwDvQ8iIwBrbqzh+7Hw4kL72WkOCRGArru68v3w9ZenUmAqNBqilSuJFi0yPxqWGAE49OQQ34dWW1rJaLgBv/2WesRviMQIgM1H/Vr++y/1CHnp0pTXNRqi4cMlRQCehz3nK7JmmJnBbBU8q7h1y/hIf/Fi7vXAQKKSJSVFAMRU8pMRxUf+adb5ExGtvbGW3mRK+SAEFc1JmtmziZ4/59s4rPMnMikAIuIj+D0O8i/Mb7oOudIIFAAtNrdwTOdPJEoA/HDoB74fZ16dsa+d5hAhAAxD/g4xrSRBAOgKysNPDtvOttBQombNiNq2Ne74tUgQAOZq+MtKYiJRjhzGHb8WiQKgx+4efB9+O/WbDYzXsc8w9K91/FokCAC1Rk3119Xn+yB4Pw7rYc7fWuK8PI0rwmrViObMoYhbtxzX+ROZFAAdt3fkP5DnX59X2krTCBAAus7fZqMbaxAoAGqursnPazpcPwQKgB33dvDvxfDDw+1spBlECIAHwQ/4PpT4q4TjiGMRAsBuo34tBw8SNW5s3qGLFAAXAy7y70PuBblt34eZM007fi0iBcDGWxv5PpRZWoYSkhNsY3tqmPO3mkmTjDv/zz8RAOf8p07Viwg4FEYEwKabG/SSGh0aCwKg+abmju38iSwKgITkBD4aU3ZZWeXsNIcAAWCXkL9UBAqA4YeH833489KfChhqBoECwG6jfrEIFAAajYbqra3H92HFtRW2ty0xkejvv4l8fMy3EygAFEjy04U5f6vx9xfm/LXPVa9ONGeO4wkBAwEQP/RbcvN2IXiDCi4q6DijG1OYEQC6zj8qIUphQ81gRgDceHeD74PIrTvtixkB4JAhf0MsCIBPcZ8o46yM/O59DrF6xBALAsDuo36xCBAAu+/v5r8PZZeVtc2KEWsQIABGHR1ldrteG6O483f4bP+3b9+if//+yJEjBzJmzIiqVavixo2UQisoVgyoKSLz+uZNYOJELju0Rg1g0SIgWcFNdLT06QNs2cKvAnBfswH7z+WHSgO8iXyDq2+vKmygBcysAiBHWedvCTOrAHTX99ss018OzKwCOPz0sF5hH2cnZyUsNI+FVQAbbm1AbFIsAOCbqt/It7eCnFhYBWDzDH9rUam4FScmVgEkJCdgwqkJfHPZCvrIScGC3HfZxCqA2+9vY/m15QC+/Ep+pnBo5//p0yc0aNAArq6uOHbsGB4+fIiFCxcia9as+g2l1n++eRMYOxZYsMBqW2Whb189AdD+VACWHwVUGgcr+GMKEwKg2oOPfBNZN/axBSYEwMOnF/kmspb1tQUmBIDu9r2y1fK3BSYEgPr2Ldsv75MLEwLg2bv7tqnmJzdmBIBNC/rIiQkBoAl4na4q+ZlERJjA7owfP54aNmxouaGZ0H+qsL+xn5Urbd8ZMWzbpjcF8HdNUNGFhc0WM3IoDKYA4tycqNlALrwWnRCttHXCMJgCuFc0I3mN55L9HHrqQheDKYDJLblppDwL8jhmyN8QgymA+GxZqNIw7nPUektrpa0ThsEUwI2aBcltsgPO9ZvCYApA4+RE3/fKaLuCPrbAYAogolBuKviTIkl+uige9ndo51+uXDkaM2YMde/enXLlykVVq1al1atXG29cs6Y05z9kiF6FPYfBQADMbQC6+uaq0lYJx0AAxLiAqn8PikmMUdoy4RgIgIsFQeWXOGiynykMBMCw9qARh0cobZVwDARAcEZQoTGgI0+PKG2ZcAwEwM4KDjrXbwoDAZCsArXvAxp4YKDSlgnHQAA8ywbKNNHuSX66MOdvDnd3d3J3d6eJEyfSzZs3aeXKlZQhQwbatGlT6sbz5ol3/o7q+LVs20ZqJxURQOHuoI031ittkTgMBMCyuk5KqWzp3LtH6hwp5VF//6OD0haJR0cA3MkN8nvpp7RF4jAQALM653D8BFhDfH0pKYMb34fFhyYrbZE4DATAobJO9iqGIx+BgRRTpADfh/lj6ylpDXP+5nB1daV69fTfoFGjRlHdunVTNzYR+jfp/B3d8X8mcfdO8i+WlVb3KE7vIs0UGXFUEhIo8Juu9KCwB21e46DVCi2guXuXHlfKTydrZqen7x8qbY4k3i6YSk8LZqStP7VIO9NHuoSH092WVehmCU+6em6X0tZIIuzYAXpQPAsdbVsqbUXAtGg0dHNYZ3pUMAOdWTFBaWskEffyGV2tnoeuV8xBHwKfKGmK4s5fRSQ4E9vuKdtFihRBy5YtsXbtWv65FStWYObMmXj79m3qA2rVAq5f13sqEoAXgAgAWbRP9u4NbNuWUl+fwWAwGAz7oXjms0N7vwYNGuDJkyd6zz19+hRFihQxfoDQrP+rVwFj4oHBYDAYjHSAQzv/n376CZcvX8bs2bPx/PlzbN++HatXr8bIkSONH2DJ+Wf5PPb395e08xODwWAwGF8CDu38a9WqhQMHDmDHjh2oWLEiZsyYgT///BP9+vUzfoC5gj8DBwL371u99SODwWAwGGkdh57zl8T8+VyRk8/wc/6fPiFL1qxcuL9JE+D5c65BiRJcIYhC6bDIA4PBYDCUgM35y45h6H/gQO63NrmvQAHg9GkWAWAwGAxGuuXLc/7FinFlKFUqYNQo4K+/UrdhAoDBYDAY6ZgvL+yvJSYG8PREZGQkvLy8EBERgSxZsui3YVMADAaDwbA/LOxvMzw9LbdhEQAGg8FgpENkdf7J6mSUWVYGGWdlRI/dPXAx8CK/c5LDooAAiEmMwbOwZ7Y5+YQJgLs7UKoUsH498OmTba4jEhERpjRJXFKc0ibIzrOwZ4hKiFLaDNk4/vw4Xn56qbQZsrDv4T4cfnJYaTOs5l3UO/zi8wsehzxW2hSriIiPwKijo7DnwR6lTRGMrGH/m0E3UWO1/nanhbIUQo/yPdCrYi/Uyl8LKpV9ox1mw/662GkKICE5AVnnZUV8cjx6V+iNHd13yHp+5MrFbYGqxdUVaNEC6NkT+PprIFs2ea8ngNnnZmOy72QUyVoEz0c9d8x95CWiIQ0q/l0Rj0IfoUf5HtjdY7flg9IA/ff3x7Z72+Du7I6wX8Pg6SYgkuagJKoT0XJzS5wNOAsnlRM+jP2AnJ45lTZLEnFJcei6qyuOvzgOADjc5zDal3bQLXUtcPDxQfTc2xOJ6kRkdsuMyImRSpskiWPPjqHX3l6ISuSE8vux75EnUx5Lh31ZYf/KeSrDzdlN77nAyEAsurwIddbWQYklJTDh5ATcCrrleCNBO0UALr+5jPjkeADAzgc7Me30NFnPj0aN9B8nJQHHjgHffgvkyQO0awds3Gi3iEBCcgJmnp0JAuFV+Cusv7XeLte1F7+d+g2PQh8BAA4+Oej4kS4BTD8znd9zPkGdgPMB5xW2SDphsWFouYVz/AAn1m5/uK2sURJ5HPoYddbW4R0/wA240hqRCZH47uB36LyrMxLViQCA2KRYha0ST3BMMPru64t229vxjh8AohOjFbRKOLI6fxcnF/SrZKIAD4CX4S8x78I8VF9dHWWWlcFk38m49+Ge4wgBOwiAN5Fv9B57n/HGjDMzZDs/Jk40/ZoCQmDtzbWIS04Jif9x6Y8vwkECwNFnRzH3wlz+caI6EXc/3FXQIuuZfmY6pp6eqvfch5gPClljHU/DnqLuuro4+/qs3vNp8fO37e421FxdE/eC7+k9XzRrUWUMkojfSz9UWlEJG25v0Hs+i7uZqKyDQUTYeHsjyi0vhx33U0duBYz6HQLZE/56VeglqN2zj88w69wsVF5ZGRX+rgDv0954FPJIbnPEY2MB8Oxj6rn+30//jllnZ8lyftSoARQtarmdHYRAfHI85pyfo/fc07Cn2Ptwr2zXUAr/T/7otz+10PV54aOANfIw7fS0VI4fgO3yU2yI30s/1F1bF88/Pk/1WkR8hAIWSSMuKQ5D/x2K/gf6IyYpJtXr9p5GlUpsUiz+d+x/aLa5GQIiAlK9njNj2piGef7xOVpuaYlvD36Lj3EfU73u7uwOT9e0MUUmu/NvVqwZsmUQN6/8KPQRpp2ZhvJ/l0erLa2UT56yoQB4GvbU6POT/SZj9rnZVp8fKpXwDY606AqB/PmBw/IkEq29uRZvo1JvoDT9zPQ0OfrSEpcUh267uyE8PjzVayf8T9jfIBmYdnoavM94G33t+afUDtSRWXtzLVptbYVP8caFbERC2nD+2jD/2ltrLTd2YK6+vYrqq6pjydUlJts4ek5JkjoJ887PQ6UVlXDq5SmT7XJmzJlmBJnszt/V2RVfl/1a8vE+/j54GPJQRoskYiMBYGzkr+U3398w9/xck68LpmdP6cfGxwMHD1ptgrFRv5YHIQ+w/9F+8SeNiOAKN23dCiQnW2mhNIgII46OwO33t42+fu71OeXFq0jMOX4g7Yz81Ro1fjnxC4YeGopkjenPR1oY+ZsK86clEtWJmOI7BfXX1ceTsCdm2zryaPna22uotaYWJpyawOdrmSKtRDAAG63z716uu+RjGxdpjGr5qslojRXILACIyOTIX8vEUxMx/8J8SefnERr6N0bWrMD//mfd9QGsubEG76LemXx92plp4kf/bdsCy5YBAwYAOXMCP/wAnDxpVyGw5uYabLy90eTrCeoEnAs4Zzd7rMWS4we4UKfD5OWYIDoxGt12d8Mfl/6w2NaRR/6xSbEY8u8Qk2H+tML94Puos7YOZp6bCTWpLbZ3xJF/dGI0fjr+E+quq4s7H+4IOiZHxhw2tko+bOL8WxRvISmBo3GRxjjc9zCcVA5Ue0hGARASG4LIBMvLWcafHI8/Llq+iZlESugf4By/jw9QsaL0a4MLi5sa9Wu5H3wfBx4dEHdiJ53PRUQEsHo10LIlkC+fXYTAtbfXMOrYKIvt0sq8v/dpb4uOH+CcZVhcmO0NksibyDf4asNXOPhEWMTKUUf+2jD/ulvrlDZFMmqNGvMvzEeN1TVMRseM4Wgj/2PPjqHi3xXx55U/RQ1S0v3I393FHZ3KdBJ1TNOiTXGk7xFkcstkC5OsQyYBYGnUr8svPr9g0aVFos6vh9jQv9bxm9oSWQRrbq5BUHSQxXaiR/+//278+dBQmwuB0NhQdNvdjV+aZA7B8/4aDXDxIhBn/2kC79PemHZG+DJTRw3933h3A7XX1BblaBxx5K8N898Pvq+0KZIJiw1D442NMf7keEHfE10caeS//tZ6tNveDq8jXos+NqdHOnf+gLjQf7NizXC472GH+gCkQgYBIPYGOvbEWCy+tFjUMTxiQv8yOn4ho34t94Lv4Z/H/wg/efPmQO7c5tvYQAioNWr02dcHgZHC3uu7H+7iffR7yw0bNOB+MmfmIjX//MPlXNgYsY4fgNGseaXZ/2g/vtrwlSChqYujOf9Flxal+TA/ACy8tBAXAi9IOjaTq+MM+i4FXpJ8bLoP+wNAqxKtBI3iXZ1cMbf5XGR0zWgrU+TDSgEgZuSv5ecTP+Ovy0Z2JrSEmNB/s2ZA9erir2GE1TdWC3N8nxGV+e/sDHTtKtwYQyEwbBjwQfya9amnp+Kk/0lRxwhqr60mqVYDe/cCXbpw4qZfP5sJASmOHzCfqAqA68vJk1w0ww5ce3sN3Xd316shIRRHC/v/++RfpU2QhfqF6kMlsXCdIw38pjWdhgaFGkg6Nt2H/QHAw9UDHUp3sNguSZOE9tvb40HwA1uZIi9WCACLN1ATjPlvDP57/p/4A4WG/vfvB0aOtPrGHZcUp1f0Rgh3PtzBwcciVhdIXckQGgqsWsUJABH8++RfzDonvgbDiRcCQv/9+6d+LioK2L7dJkJg78O9khw/YGHk/+IFULo0J7KyZwd+/hm4dMmmQuBd1DuQxI1GHW3kP6/FPBTPVlxpM6ymQ+kOuPH9DTQr1kz0sY40558/c36c+/YcNnXehNyeFiKNBjDn/xlzof8WxVqgZn4uzBwSG4Jmm5s5RpEfIUgUAFJG/lqEZpvqYS70nzUrMGNGShLdypVWC4CV11eKGvVrmX52uvBs8kaNLIf+zVFc+E02ICIAAw8MlHQZH38fy3368Ufzr8ssBKwJ3ZsVrgEBgLavERHA4sVA/fpAkSI2EwKdynTCsrbLUMSriOhjTY78g4K4vS8yZOD+1+fP2yWSUadgHTwe+Rgbvt4gnwiwUwTGkGr5quHkgJM40vcIyuUsJ/g4Rxr5A1zxpIFVBuLJj08wuvZowUnoOTxY2B8A0LZUW6Ph/Hal2uFQ30PwGeDDC4DgmGA03dQUj0Pl2d1p+fLlKF++PGrVqiXL+VIhUgBoSCPp5psvUz6MrTcWP9a24CiMYSr0r53jnzwZ2LJFFgEQmxSLeRfmibcRwO33twVnaosO/evSvj0wW3ghpX8e/yN5lPg++r3l5K0SJYRPt+gKgVy5OOd0+HCK0xXAmLpjMPmryZIc5rOwZ6bFTJMm3GfKkDdvbCYEVCoVRtYeiRejX+BArwNoWrSp4GNNvqe7dwPh4UBCAve//uorbmOv//3P5kLA1dkV31T9Rh4RMHQo9z3Jlo1Lkn1k30GVSqVCu1LtcHf4XSxqvUjQVIDRkf+uXZzYVUjIAEDWDFnxV9u/MOmrSYLas5H/ZzK6ZkS7Uu30nutQugP299yPDC4ZkDVDVpzofwLV83E3wA8xH9BsUzOrRshaRo4ciYcPH+LatWtWn8skIgTA28i3gucnC2QugNG1R+Pct+fw5uc3+KPVH9JzIgzD5IbJfX37yiIANt7eaFUNeKFJggCkhf7btwf27eO2OxZIh9IdUDlPZfHX+oyPv4Alf1KWZEZHc86pY0fgL+H5IBlcMmBGsxl4+b+XuDrkKsbVGydYCEQkRBgtZwqAE5mDB5s/gY2EgLOTMzqX7QzfQb64O+wuaheobfGYiPgI40Kml5HS5O/eAUuW2E0IaEXAnOYivg+GaCt0hodz0b3y5YFKlYDp0+0qBFycXPA+6j0/PeOsMr2bZ6qR/6JFQO/enNjNmRMYPdpukRhDwmLD8Pe1v/nH5irYMuevg+5GP53KdMLeHnvh7pJyA87mkQ0+A3xQLS9X2CcoOghNNzV12KVFqRAoAITO94+rNw4BPwXgr7Z/oWHhhtbXPKhRAyj3OfxmKqtfBgFgrF63GETtsy429C/B8QNA8WzFcWfYHbwf+x5H+h7B9CbT0alMJxTIXEDQ8YLm/aU4f12Cg0UfolKpUKtALSxotQAv//cSP9YSFlUy+xkW0w9DIfDTT8Bj6yN+5XKV05t2yp85v9F2SZok45Xa8ublkl9NYSchoCGNXp7JT3V/EhcJ6GRkmfX9+8DUqXYVAq/CX+HPK38C4Gren//2PAZVGWQ0EpBq5P9eZ/rw0ydg6dKU/7udhcCkU5N44du3Ul/4/8/f5FRAWnL+KhGVuyRl1xAR1t5ci9ikWAyvNTzVlr9awmLD0Hxzc35uu0DmAjj9zWmUzF5SymV5IiMj4eXlhYiICGTJYsOdo96+5cKf2gzuEiUAPz/uwwpg94Pd6LVXf2RRNGtRdC/XHVXyVsGAAwMAcPUOfAf5ymvb06dcSLNXL6BUKdPttm/nqudpv1TDhgHLl+sX1zFBaGwoFl5cyC+70qp9IoLvS1++xn+P8j34z4C2jauTKwZVGYSmxYSHbjF8OCdSLFGnDnDmjGjHb46I+AhknZcVAPc5rZ6vOm4E3UhV0bBuwbq4NFjAsqEaNYCbErZmrVMH+O8/wMtL/LE61FpTC9ffXQcA7OuxD5feXMLuh7tTCbpDfQ6ZTuIl4vJLAiSKwIwZgVevuCkNiRx4dABdd3NTQu1KtcPB3gdx6MkhLLm6BKdfndZrGz4+HF4ZjPzf1q7lwuZiyJ8f6N6dE0D16wv6vphj/6P96La7GwCgdoHauDz4MpI1ydh2bxtmnJ0B/0/+fNu9PfaiW/lu+id4+hQoU0bYxSpW5Ozu0SNlkCATfff15Xe9G99gPOa24JKBbwXdwjifcfB9mXKf8xvkhyZFm6QcHBzMiTFz/il/fqBbNy4SKMP/3RjX3l5DnbV1QCBkdsuMxz8+5kXlnfd3MPLoSH55Y3aP7Aj9JVRobX/lNwAgIqE/NickJoQqr6hM8AbBG1RwUUF6HvbcqnNGREQQAIqIiJDJSjO8eUNUsiQR95ElKlGCKCCAiIiCo4OpwboGVH55eRrvM56uvb1GGo2GiIg0Gg2VXFKS4A1ymuZEH6I/2N5WU2zbRuTklNKHYcOI1GqrTtluWzv+PQ2NCZXHTl/fFBvN/bi7E508Kc81tZf29+X7M/LISP75d5Hv6NCTQzTVbyp9/+/3dOPdDWEnnDNHWF90f+rUIQoPt7ovLz6+4PtSfVV1/nmNRkNX3lyhsf+NpTJLy1CjDY3oY+xH8ycbO1Z8P7Q/rq5E795Z1ZemG5vyfTn+7Ljea3fe36Gh/w6lPAvy0Lf/fGv6JCEhRM7O0vvRqJFV3xe1Rq13Dzz69Kje64nJibTh1gaqsaoGNdnYhCLiTdzXKlcWb3vFikTTphE9eiTZfi1X3lzh+5BjXg4Kj9P/rGo0Gjry9Ag139Sc+u/vT0nqpNQnadFCuO358xONGkV07pzV9ystyepkqrW6Ft+PhRcXpmqj0Who0+1N1GF7B9rzYI+Y04vxvTb5cSjnT8Q5yYp/V+T/4YUWFSL/j/6Sz2dX509kVgCYY+LJiXyfV15baQdDzSCzAGi7ta38zj85mSh3btM3gzx5Uv7OkEFWATD//Hy+P+tvrrf+hM+fK+L4iYjmnZ/H92XOuTnWnezyZWkOU6Ui2rzZqkvffX+X70fppaVJrbHCAbRqJd35q1ScgJDIvof7+H7UXlObHyCIZuZM6/qwYYPkPmg0Gvpq/Vd8P5ZeWSrtRKtWSbNfKwRevpTcByKiVddX8X2osLwCJSYnWnU+AxR3/g5URJ8jl2cunBp4ChVyVQAABEYGoummpngV/kpZw4QicRlg9/IpyyL3PlJ4v3uZkgCNIdt2l+ay/tu3B549S5n7jI8HOnQATpneilMMN4Ju8H/XyF/D+hOKyfqvWVOWUL+W3Q9283/3KG9l/kHt2kDhwuKOUamAzZu56SYrWHp1Kf/3qNqjrMuVsSYP4+efuQQ1CWhIo1eHYWrjqdK/L9b0gQi4IK1SH8CtktFublU6R2n8UOMHaSfq0oX7novl3TsuR6BpU64vEgiLDcPEUxP5x8vbLYers6ukczkqDuf8ASC3Z26cGniKXyf6OuI1mm5qitfh4mstK4IEAVAtbzUUy1oMAOD30g+hsaF2MNQMMgoAqcVYLGIs61+b3Jc5M7Bnj00EgHZ+PINLBpTPVd7q8wEQfrPWaCTf0Azx/+TPC5nq+aqjRPYS1p1Q7IZSWsdvrNiRCD7GfcTWu1sBAJndMmNQlUFWnQ+dO0tzOqNHAwsWSL7sP4//wd0PdwFwc/1tS7aVfC6ULg1UlrhSJV8+YMIESYcmqhPx68lf+cfzW8yX7jRz5eLum1LxlF47wDDJr3HRxtLtcFAc0vkDQJ5MeeA7yBdlc5YFwGWONt3UFIER0rbTtTsiBYBKpeJHXmpSi6t6ZytsEAGQWv7TKIZZ/4ZZ/W5usguAT3Gf8OLTCwBA1bxV4eLkIvlcelhymi6fr3PzJtC6NbeMy0r2PkyJMPUsL7FyoiFCnb9Mjh8A1t1cxy+j/a7ad8jsntm6E+bMye0jIYbRo4E//+T6JQHDUb93Y2/ro2RSlsTmy8fdt0pIE4Krrq/i65k0KtJI9AZvqZBa0TNPHq5ktoT/4bW317Dm5hoAnJhc0FK6oHNkHNb5A0DeTHnhO9AXpXOUBgC8DH+JJpua4E3kG2UNE4pIAaAb+t/zcI8dDBSADAKAZBqppsLZmVvHnDEjV/TG2HI+mQXAzaCUrPya+azfCInHXOi/Th3g7NmUcPLVq7IIAL2QfwUrQ/5ahIb+iSRti21IsiYZy64tA8AJS0nFsIwhJoJhpeMHUo/625RsI/lcPGJD/1rHX7q0pMuFx4frCZiFrRZaL2CkhP7z5OH6Ubas6MupNWqMODqCj1Z6N/E2uWQ0rePQzh8A8mXOB79BfiiVnVui5v/JH003NcXbyLcKWyYQEQKgZv6afNGVUy9PmS6qYm9kjADINuev5fvvuep3W7eaXs4nowCQfb5fF2M3a+1yvnr1uKWjMgkA3ZB/jXw15Csrayn0r/v+T5oEzLGimA2AQ08O8UsS25Zqa/XSYB6hof8MGYDvvrPK8dtk1A+IC/1b6fgBYPa52QiLCwPA1XfRVm+1ipw5xYX+rXD8ALDu1jp+Wq9CrgoYVXuUpPOkBRze+QNcsQ6/QX78F/v5x+dotrlZqnXVDotAAaBSqfjRf7Im2bF2+7JCANhszl+LkPW9MgkA7Y0BgDw3N10MnabhOv6KFWUTAHsepESWrE70M8SU89eG+ufqbP5kpQBYcnUJ//fo2qMlnycVQkP/8fFAixbA3buSL2WTUb8WoWHzsmW5gksSeRX+Cn9d4apNuju7Y1Yz8ZthmURoH7y8rHL86SHJT5c04fwBoECWAvAb5MePUJ6GPUWzTc0QFCVuL2/FECgAHDL0r0WGCICsc/5ikUEAaEfLHi4efD6KbJQoAbT7XA67Xj3jWf0yCQDdz5ZsIX8txkL/unP848fLIgDufrjLF+8pk6MMWpZoaYXRRjAXwfjhB66fALdjZPPmkgSAzUb9WoSG/v38uLYJCZIuM+nUJCSqEwFwe0gUySpdSKRCaOg/MhK4ft1yOxOkhyQ/PUSsC3QIXoe/pmJ/FuPXX5ZdVpbeR7032d7u6/wtYaEOgFqjpoKLChK8Qa7TXelT3CflbDWFyDoALTe35N8vw2IfipCQQNSpk+g6AB9jP/L9qL+uvm1si40lunqVq2Ngjnv3iHLmTOlD7dpEnz4JuoRuYZ8aq2pYb7MxdAv+qFREW7akbjN3rv767NmzRV1i6L9D+X4su7JMJsN1MFXwZ/RoIo2Gq7VQp07K8zlzEt25I+oSsq3rN4epgj/58hFt2kTk4ZHyXMeORPHxok5vqaCPLLRsaXpdv679Tk7GP2sWuPrmKqm8VQRvUObZmelt5Fv5+6APW+cvlsJeheE3yA9FsxYFADwOfYxmm5shOEZ8jXNFsBABcFI58VshJ2mScOjJIYUMNYMVEQDZ5/ylIDECoDffn0/m+X4tHh5ArVqWRzpWRABsGvLX8v333FIrNzfTWf1WRADCYsP45X1Z3LNgYBVpWy+bxVjoXze5z8uLi87UqcO9JjICYPNRvxZjYXPtHP/AgcCRI9znDgAOHRIVASAijD0xln/s3cTbeNlkazEVwciTB7hxgyv3DXD3oEGDuBwggRgm+U1rMu2LTfLTQ4RScChefnpJhRcXplFtQIGZQUdqZKGwy36cItfB4Ub+WsxEAM6/Ps8r6Y7bOypsqBkERgBabG7B98dkOVIlEBkBmHtuLt+PTbc32dFQM0iIAFRfVZ3vx4uPL2xnW2goUVCQ5XYSIgC6lQn/d+x/1ttqim3bUo/4DZEYAbDLqJ+I6MmT1CP+J0/02/j6SooA7H+4X6+yosxV8FIwFoXJkyelFLFGQzR8uKQIgI0r+ZlC8ZF/mnX+RET+H/0p2k2l94FIKl2SaPJk7sun0Tiu8ycyKQDUGjXlX5if4A1ym+HmWA7TEAECQNf5R8ZHKmSoCUQIgO67u/P9uP/hvp0NNYMIAfA87LntQ/5SECEAktRJVHhxYYI3SOWtomdhz2xnl0bDlR7etcu449ciUgBYquEvOw0bmnb8WkQKgITkBH5PEniD/nn0j42M/4xu6F/X8WuRIABCY0Ip+7zsfB9Ovzxtww7owZy/tcSXLaV/09D9KVOGIn75hXP+MtVClx0TAmDU0VH8B3Lb3W1KW2keCwKg+abmjuv8iQQLAG2uScZZGSlZbWFO3t4IFABzzs3h34t55+fZ305zCBQAuqPN9tva29lIM4gQAHYb9Wt5/56r1//BwqZhIgTAkstL+D402tDI9n3w8eFG/0WLmt58SKQA+P7f7/k+9N3X10aGG4U5f6vZudO08wcoAuCcf8nPEYG7d80reCUwIgAuX9zDfyg77+ystIWWMSMAdJ1/VEKUwoaawIIACI0J5fvQYF0DBQ01gwABoBvyt2bDLJshQAA02diE78N/z/9TwEgzCBAAdh/1i0WAAPgU94lyzMvB9+Ha22v2sS0ykijRQlheoABQIMlPF+b8rSY6Wv+Dasr5G0QEaMoUxxICgYF6AkBTogRV+y0nwRvkPsPdMUfMhpgQAGnC+ROZFQAnnp+wzxyztZgRALoh/5qrayprpznMCIA77+/orfSx+WhTChYEgN1H/VKwIAB+OfEL34d++/opaKgJLAiAZHUy1Vxdk+/DoouL7G2h4s4/zWX7p8LTk6vpLoYnT7iysJUrA1WqAI8e2cY2MRQsyGVvf14FoHrxAv+tT0TBCCBBnYCjz44qbKAAbLgboF0wswpAt7iPzTL95cDMKgC9tf22yvKXAzOrAJZeSdm978daPzrG6hFDzKwCsFuGv7U0bWpyFYBNC/rIhUoFLF9uchWAYSU/2cpCpyHSvvMHrNu+8t49YMMG+WyxBgMBkCsoEn4bgYIRDljwxxRGBMDozU+h+uz/FS3yIwQTAiDxxDG+ieyV/eTGhAA4dn0H38ShnT9gVADETJuCbfe2AbDh8j65MCEAfA/+abtqfnJjQgD8fny87Qr6yIkJARC1bkW6quRnEhFhAsfFTOjfaNhf9ydDBqJrdpqvEorBFMCzbKCS49wpOiFaacuEYzAF8HdNkOp3pJ0+GEwBxLmqqNlAkOcsT8dL9jOFwRTA5QIgr/EOHvI3xGAKYEJzLkw75tgYpS0ThsEUQFgmZ6o0zEHn+k1hMAVwsDTIbbINC/rIjcEUgNpJRf26KD5loXjY/8tw/kRE3buLd/4ZMhD952AJQ1oMBMD5QqD9D/crbZU4DATAkI6gmMQYpa0SjoEAiHIFtVtSV2mrxGEgALZWAs0/P19pq8RhIABaDoBtl/fJjYEAeOUFqreylmPO9ZvCQADM/Aq09MpSpa0SjoEASFaBqo/JSO8i3yllkeLO/8sI+wPiQ/8ZMgAHDwKtWtnGHmv5PAUQV7QgAKBIOEAatbI2ieXzFIDGiQv1V47LDHdnEzvvOSKfpwCSO3A5JZmSgPbZ6yhslEg+TwHEZvUEABSPcELPChL3SFcKgymALh7V5Nu9zx58ngIIq8ztTJo7BphRe4JjzvWb4vMUQLwb5zIqx2XBDzV+UNgoEXyeAgge2A0A4EzAb8UGIl/mfAobphwqIhLaVnBDRYiJAXLlAuLi9J6OBOAFIAJAFu2Tju74dQkNxYM/f4N/1SLo0G1i2rphfCb8nA9uH1yF3MPHoXyJukqbI57ERDxdNh3PncPRfORCuLukIQHzmaRX/ri2ZDzcuvZEzYYOPt9vAv89q/Hylh/qTFyGTJlzKG2OaCgqClfmjQJVrIh6vccpbY4kAq/44MWO5agweiZyFa+otDniIcLVpROgjotF3XF/QiVkwyDboPiN/Mtx/gA3+t+7V+8po87/11+BefPsaxuDwWAwGByKO/8vJ+wPCA/9L1ggauMHBoPBYDC+JL4s59++fcqyFEPc3bk12wCX8jFwIBMADAaDwUiXfFnO31zBnx07gH//BUaM4B4zAcBgMBiMdMqX5fyB1KF/98/JWc2bcxmfy5YxAcBgMBiMdM2X5/zbtwcyZeL+zpCBG/HrwgQAg8FgMNI5X57z9/TkHH7v3sDJk9yI3xAmABgMBoORjvmylvoZITIyEl5eXoiIiECWLFn0XyQCfvwR+Ptv7rFKBWzeDPTvb39DGQwGg5Fe+PKW+j0Ne4rdD3YjSZ0k96nl50uMACQkAOvWAa9fK20Jg8FgMBwUWZ1/SEwIyi0rh157eyHL3CwYemgoTvmfQrImWc7LyIsCAmDplaXosrMLPkR/kP/kdeoAQ4YARYsC9epxu1q9fy//dUSQqE7EtNPTcOXNFUXtsBXX3l3D94e+R2BEoNKmyEZITAi67uqKRZcWKW2KLDwPe4766+rjf8f+p7QpVvMm8g1qra6Fhusb8rvrpUWICNPOTEPeP/Ji/MnxSptjFatvrEbO+TnRaEMjpU0RjKxh/2dhz1B6WelUz+f2zI1u5bqhV4VeaFi4IZyd7FdS0WzYXxc7TQG8jXyLgou5ev25M+bGox8fIbtHdvkuUKgQ8OaN/nMqFdCoEbcSols3IG9e+a4ngAbrGuDim4twUjnh7c9vkTeTfa9vS95EvEGxJcWQrElGYa/CeD0m7UdcPsV9Qrnl5fAhhhOnL0a/QPFsxRW2Sjq3gm6h4YaGiE2KBQDcHX4XlXJXUtgqaZx5dQYddnRAdGI0AGB+i/n4pcEvClslnpCYEAz+dzAOPT0EAHBxckHSlDQQLTbgffR7jD42Wm/L9UcjH6FszrKWDv2ywv6lcpRCYa/CqZ4PjgnGiusr0GRTExRaXAj/O/Y/XAi4AA1p5Ly8ddgpAnDnwx3+7+DYYLTc3BIf4z7KdwHt3tW6EAFnznDiJn9+oEkTu0UEXoW/wqU3lwAAGtJg1tlZNr+mvUhUJ+LrXV/zka3AiEDEJMYobJV1fIr7hBabW/COHwDuBd9T0CLrOPj4oJ7jB2CbiJuN0X53mm1uxjt+AGlyn4mDjw+i4oqKvOMHAGeVYjX2JUFEWHdzHcotL6fn+AEga4asyhglEtnn/L+v/r3Z14Oig7Dk6hI03NAQRf4sgrH/jcXVt1chIgJhO+wgAF6H648Mb76/iVZbWuFT3Cd5LvDdd4CTmbfVzkJg1tlZIJ2g0YbbGxAWG2aTa9mbsf+Nxc2gm/xjAuHM6zMKWmQdn+I+ocWWFrj5/qbe82lxOoOI8MfFP9BlVxc9xw8A8cnxClkljeCYYLTd1haT/SanGjDJGjW0MRHxEfjmn2/QeVdnBMcE672WI2Pa2ajpadhTNNvcDEMODUF4fHiq13N4pI2+yO78u5fvLrjtm8g3WHR5EeqsrYPiS4pjvM94PAt7JrdJ4rCxAHga9jTVczeCbqDV1lZGP0iiyZuXC/ELwZgQWLUKSJYnR+Plp5fYeGej3nMxSTFfxDzytrvbsOzaslTP+7zwUcAa6/kY95Fz/EE3U732/ONzBSySTqI6EUMPDcUvPr/oCU8tEfERClgljTOvzqDqyqo48eKE0qZYxSn/U6i0ohI23dlk9HUvdy87WySeRHUiZp2dhcorKuP0q9NG23i5e8HV2dW+hklEdudfJmcZVMwtfqvHV+GvMP/ifFRdVRXvot7JbZY4bCgAnn00Lm6uv7uOVltayXNjErrBkS5aITBsGODtbb0NAGadm2U02XPJ1SVpevR/78M9DD001OhrJ/zT3k36Y9xHtNzS0qjjB0x/Zh2Rj3Ef0WZrG6y7tc5km4gEx3f+umH+oOggpc2RTGxSLEYdHYUWW1ogMNJ0BMnTzdOOVonnypsrqLG6Bib7TUaCOsFku7QUwbBJkZ/u5YSP/g2JS4pDXFKcjNZIxEYCwNyN9Nq7a2i9tbX1AqBrV/Ohf0uorM9F8f/kj423Nxp9LToxGosvLxZ/0r17gZw5gWrVgAMHgHj7h28j4iPQdXdXxCUb/4w+DHmIt5Fv7WyVdCw5fiDtjPyfhT1DvXX14PfKz2w7Rx/5B8cEo83WNkbD/GmJy28uo9qqakYjZIZ4ujqm849KiMLoY6NRb1093A++b7F9zow57WCVPNjG+YsI/RvyZ5s/USJ7CRmtsQKZBUCyJhn+n/zNtrny9grabGuDyIRISdcAIC70b0jLlsCkSdKv/ZlZZ2dBTWqTry+5skR8ouPkyUBYGHD7NidwcufmVmMcPGgXIaAhDQb9M8iiM/TxTxuhfyGOH+CEnEMv1wVw+tVp1Flbx+i0miGOPPLXhvnTymfIGInqRPx26jc0WN9A0PsBOObI//DTw6jwdwUsvbrU6PSRMdK98y+fq7yQpQ6pWNZ2GUbXGW0Di6xARgHwKvyVoJvo5TeX0WarlQJASui/ZUvOkZraFlkgLz6+MDm3pyUqMQqLL4kc/TdsaHCSKGDbNqBzZ7sIgfkX5uPgk4MW26WFG/fHuI9osdn4HL8hyZpkBEQE2MEqaay/tR4tt7TEp3hhSbNWfa9shIY0mHl2ZpoP89/9cBe119TG7POzRUUtHGnkHxEfgV57e6Hjjo5mpyqMkVaS/QAbOX+VSiU69P93u78xsvZIW5hjPcYEwKBBogWAUBUMAJfeXELbbW0RlRAl6ho8YkP/Mjl+gJvrNzfq17LkqsjRv7mIhI2FwEn/k/jN9zdBbX1e+Ai78V24ADRtCsydy9lvJ7SO/9b7W4KPccTQv4Y0GO8zHoP/HSwqMuFoI//Q2FC02doGU/ympOkw/5lXZ1BrTS295cxCyeSWyQYWSeN3v9+x+8FuScem+5E/IC70v7L9SgyvZWR9uiNhKAA0GtECQOxKhouBF6ULADGh/6++ks3xP//4HJvvbBbUNjIhEn9e/lP4yYsXB2rUsNxOZiEQGBGIPvv6CL4xh8SG4M57ATfArl2B06eBiROBHDk4e7dvt6kQkOL4AfGfXVuTrElG993dMf/ifNHHOtqc/8ijI9NEtMgSh58ellxx0JFG/gWyFJB8LHP+ACrnqYyS2UsKauuIYTijaAWAtpCOSAEgZuSv5ULgBbTb3k5a8Rihof83b4DQUPHnN8LMszMFjfq1/HXlL3E1DsROZ+gKgTx5gH/+EXV4QnICuu/pjtBYcf8fQTfzbNlS/k5K4gRKv35Arlw2EQLh8eGSHD8gYOQ/ZEiKiJRpqag5Djw6gAOPD0g61tFG/u7Oaa9QjzF+qvcTauQTIM6N4Ehz/uPqj8PqDqslhfDTfdgfsBz6V+lUN/z15K9YeHGhrUyRF5WKK4ojQQBIXTJ1PuA81txcI/5AS6F/7Uj/5Usu/BxoXTGX5x+fY+tdcVMhkQmR+OvKX8IPkJLLwF8sElixQtQhY46PwdW3V0VfStC67MmTjT+fkGATIbDi2gpJjh+w8Nn18eE2kzp/nrM1b17ghx+4LbVtJATK5yqPzG6ZJR1rduTv48N9l5PsV2p2RfsVmNp4KrK4myk/ngbInzk/rg69ii1dtqBQlkKijnWkkb+TyglDawzFkx+f4IcaP+j5Kkuwkf9nTIX+VVBh/dfrMbvZbP65cT7jxCeAmWH58uUoX748atWqJds5eSQKACkjf4D7f5XIJmEFhLnQf8uWwJ07QMnP0ZkXL6wWADPOzhA16tfy5+U/hRc4Ehr6N4ZKZbz8sQlO+p/EyhsrJV3qfMD5VJXlUtG5M5Ahg/k2MgqBynkqSy6janbkX9pgP4+wMGD1au4zli+fTYRAhdwV8PjHx5jSaApyZcwl6liTI/9Tp4BWrYABAwAvLy6aceKEzYWAp5snvJt449X/XskjAkJDgV9+4f7ndq6c6qRyQv/K/fHkxyeY3Wy2YIHmSCN/LTky5sDKDitxdehVVM1bVdAxzPl/pnq+6iiatajecyqosLHzRnxT9RtM/GoiZjadyb/284mfseTKElmuPXLkSDx8+BDXrl2T5XypECkA4pPjRWdMF89WHOMbjMetH26hY5mO0uw0NlLWJveVKgX4+ckiAJ6FPRM96tcSkRCBvy7bePSvUgGbNnHOUyCvwl+Jv85nEtQJOPf6nPlGmTIB7dqJOKmBEOjeHXgnvCBW+9LtcX/EfUxtPBXlcpYTfl1YWO5XpIhpQRYaajMhkD9zfkxvOh0BPwVgU+dNgkPOJkf+wTolZ+PiuGhG69aciLaDEMjmkY0XAb/W/1X6ib76CvjjD+5/XrgwMGECcOOGXYWAh6sHJn41Eft67hPUPtXIPyQEqF6d26X08GG7RmIMqZm/JqrkqSKoLXP+nzEM/TupnLC5y2YMrDKQf+63Rr9hWpNp/OP/Hf8fll21XBTCIRAhAF58fCForWihLIUwqeEk3PrhFp6Peo65LeaiSl5hHzyjGIb+DbP6CxaURQBsuL3Bqkzl1TdXC28s1vlrHf+AAaIOG1hlIBa1WoS2JduKHl0CAuf9pU5jJCQA+/YBc+aIOqxszrLwbuKNhyMf4v5wTggU8Spi8bgkTZL5Gv/ffGP54jYSAhlcMmBglYG4NvQa2pWyLKYiEyKNf1Z79AA8jYxAP360qxDI5pFNb8MeVyeR5WJ1/59v3gDz5gE1a3LfcTsKASLC7PMp0d2KuUxXfk018p88Gbh1C7h6FejYMeX//t9/dhcCFwIu8EuXs7hnwcAqA01OBaT7Cn+6DK0xFJ6unnBzdsPmzpvRv3LqLXJ/b/w7pjaeyj8edWwU/r72t61NkweBAsDcnKnuFre9K/TGrOazUDVvVahkqLSHvHk5ewCgfXvjWf0yCABJ0xK6JmQpKLyxmNC/RMcPAG7Obvip3k842u8oPoz7gIAxAdjfcz8mNZwEFycXi8efC7Aw8geADh0sh/7NYVj7QAQVcleAdxNvPYdZILPpTGez8/7duomrDGkoBGbMsNohhcaG4pT/KQBAZrfM+LX+r0ZFG4H0dsbjcXHhoirmsIMQ+Bj3kc+DcXFywfWh18VNB/xqImrg729XIXD46WG+Bn6JbCVw44cb8B3oi+r5qqdqm2qpX4MG+o+1//c2bewqBJI1yRh5NGUJ+uxms7Gp8yZcHXoVtfKnnlJOSwl/ICKhP5IJiw2j91HvzbbRaDQ0+dRkgjf4nxXXVlhzWSIiioiIIAAUERFh9bnMotEQDR9OxH2ViJyciLZs4V8+9uyYXt8qLK9A3n7edP/DfQqJCSHnac4Eb1Dxv4qTRqOR37bAQO63OQIDiUqWTOlDiRJEAQGCL/M45DH5vfQjv5d+5OvvS77+vnTK/xTVXlOb7/f+h/vJ54UP+bzwoRPPT9CJ5yfI76UfxSXFievT3Lkpdpr7adaMSK0Wd24L+H/05/vTdGNT2vdwH006OYlabWlFOebl4F/rv7+/sBN27SqsL4Y/c+da3ZdkdTLlXpCb4A3KMDMDRcZH0r0P9+h339+p7LKyep/ZM6/OmD9Zo0bS+qH9efzYqr7MOjuLt/Xn4z8TEVFcUhxtvLWRqq+qzr/mMdPD9OfNx0ea7dmzEw0eTHT3rlV9ICKa4juFt/X7f7/nn/8Y+5Gm+k2lLHOymH9PIiKI3N2F2168ONH48UTXr1u+RwgkMTmRyiwtw9u598Fe/jW1Rk1b7myhQosK8a8/DjF47xMTibJkEf5/P36cO0Zmll5ZyttYdWVVSlYn6/VjzY01/He+2spqYk4txvfa5Mcuzl8oGo2GJp2cpHfDWX19tVXntJvzJzIrADQaDa25sYbmn59PD4Mfpjq0xeYWfJ9vvLthe1tNYaUAMEa7be34voXGhMpj54sXwm9uw4bJKgB239/N9+d339/1XtNoNPTy00u6GHBRuKDZsUMRx09E5Ovvy/ely84uqfpy78M9mnNuDm24tcGyKF26VLrjL1WKKCFBcj8SkxOpwMICBG+QyltFLz6+SNWXCwEXaLzPeDr27JjpEyUlEeXMKb0fHh5EMTGS+xEWG8Y7d5fpLvTq06tUbT7GfqSlV5bSxlsbSa0x8bnu1Ema/cWLE02cSBQVJbkPRETLry7nP1cN1jUw+tmJTYylLXe2kM8LH+MnGTJEnO0yC4EP0R/Ia44X348LAReMtguLDaO9D/ZSSEyImNMz52+IRqOh8T7j9QTA2htrJZ/Prs6fyGIEwBQrr63k+zvx5EQ7GGoGmQVA261t5Xf+REQ1ahi/CahUnMN3crKJAND9fB58fND6E0ZFEWXIYHfHT0Q07NAwvi/b72637mTv3nH/eykOx0qBuev+Lr4fnXZ0sq4f338v3flnz04UHS350rqj/qH/DpXeh61bpfcBIBo5UvKlw+PCKef8nHw/LgVeknai//6z7n34+2/JfSAi+uafb/g+fPPPN1adywiKO3+bz/mLRaVSYU7zOfil/i/8c0MPDcWGWxsUtEoEEpcBdinXBU4q7u3Y83APp8yUQqYkQGPIksegxViynHaOf8UKYMuWlGTHlSuBkSO598NKbgTd4P+umb+m1ecTlfU/ZAgwfrz11wSg1qix//F+AFzSnOQVJVry5eMyzcVQvDhX5bCQuHXhhiy9upT/e3RtK/cHkZqE6enJ7TZpLGlQAIZz/b99JayctFE6dgTcrSgelC+f5EPnXZjHF8XqVaEX6hasK+1ETZtylS+l8PEjl/sg8T56IeACvytp1gxZMa/FPGl2ODAO5/wBzkHMazEPP9f9GQBAIAz+dzA23Ta/WYzDIEEA5PbMjcZFGgPg1lTf/XDXHpaaRkYBQAJ3xBKN4U3aMLmvb1/ZBQAR4cY7zvnnzZQX+TPnl3wuPYQ6nG3buPXoMnD29VkEx3DL29qVaidPfXUxjlMmx38z6CbOB5wHwBX/aVasmVXnQ5Mm3NbRYvD0BI4elb6bJrh6F9pqp99V/Q5FshaRfC5kycIlJUqhVy/JAjMgIoDfrtvN2Q1zmotbjaKHqyvQpYv043v3lrQ9uWGS38ymM5HbM7d0OxwUh3T+ACcA/mj1B8bUGQOAcyDfHvxW8lpyuyNBAOgWRdr7cK+tLbSMDSIAYqplWaR4cW4dMGA6q19mAfAy/CW/e5wso34tlrL+y31elx8Xx43qZBAAupuX9ChvReVEXYRm/bu7cytPrHT8gP6of1TtUdZHl1xcuCWyQpHB8RuO+id9Zf222ujZU/wxvXpx9ygXy6tZjPGb72+IT+b20BhVexSKZSsm6Tw8UvoAcDUw/pa2Ymzl9ZX85kRV81bFsJrDpNng4Dis8wc4AbCo9SI+jEcgDPpnELbf266wZQIRKQC6luvKO0fFQ/9aZBAANu3Hxo3AsGHAsWOml/PJKACuv7vO/y21jrlRzIX+584Fbt8GOnXiHssgAJI1yXoh/w6lO0g+lx5CQ/8JCcDgwUB4uFWXC4kJwY57OwAAXu5eGFBZ/JJOowiNYLi5We34AZlH/VrEhv6tdPw33t3gB2fZPbJbN22hRUrov3t3rgqmq8j6CAA+RH/AZN+UstvL2y2Hs5O0qpiOjkM7f4ATAH+2+RMja3FhGA1pMODAAOy8v1NhywQiQgDkzZQXXxXhbpxPwp7gQcgDe1pqGhkjALLO+QNA2bLc/L6lEKdMAkAb8gdkHvkDxh3O3LlcCNbNDdizRzYBYJOQvxZzjrNgwZQNja5e5d43KwTAmptrkKBOAAAMqT5EvjKxQkP/iYnc1sxWYJNRPyAu9N+6tVWOn4gwzmcc//j3Rr8jm0c2M0cIxMVFXOjfCscPABNOTeDLP39b9VvUL1Rf0nnSAg7v/AHOYSxtuxTDa3IOVEMa9N/fX/Key3ZHhADQrYjoEKF/LVYIAJvN+YtFBgFwPchGI38gdehf6/i1yCgA9jzYw//ds7zE0KopTIX+ixcHLl4Ezp5NcaxWCIAkdRJfDEwFFUbUGmGF0QZYCv27uaX8PWmS6EqLuthk1K9FaNj8+nXg4UPJlzEs6CPrFu1C+5AvH7Bhg2THb5jkN7fFXEnnSTOIWBqgOGqNmr7/93t++YXzNGfa82CP2WPsvtTPHAKWAb6NfKtXCMjhkLAMsNWWVnyfwuPC7WSoGbZtk7QMUKPR8Ot+8y/MbxvbVq4kKl/e/DKlhAT9ddweHkQnTwq+RJI6iXLNz8UX9olKsG5Nt1EMC/4YLue7d09/PX3t2kSfPom6hO7yvq93fC2r+URkuuCPpyfRmTOpC03Nni36EkLW9VuFpYI/OXKk/J0zJ9GdO6IvYa6gjywkJenbae6nY0ei+Hjxl1AnUZUVVfg+LLuyTN4+pIYt9RODk8oJKzqswJBqQwAAalKjz74+2P9ov8KWCURABCB/5vxoUIgrbfkg5AEehTxSwlLTSIgAkCPkLugiMQLw4tMLPiQo+6hfyw8/AA8emN990MoIwNnXZxESGwIAaF+qvbwhfy26ozVjWf0VK3KfIysiALqbgI2qPco6e41hLPSvm9w3fjwXndEiIQJg01E/YD7036sX8ORJStJsaCjQvDlwV9xKozU31+BJ2BMAQINCDdC1nIhkSSFYisI0apQSMTt0iJt2SkgQdQndJL9qeat9sUl+eohQCg6DWqOm7/75jlNpU0EFxznRgQf7jLZ1qJG/FgsRgMWXFvMKdPrp6QoaagYREYCWm1vy/YmId6D3QWQEYOe9nXw/pp2eZkdDTSAxAvDDoR/4fuy8t9M2tsXFEfXuzdlnLjIkMQJw490Nvg/ll5eXvyS2Ft2CP9oRvyESIwA2H/VrMVbwp1cvbkRNRBQeTlSnjqQIgGFBn8uBl23ThxMnjI/0u3fnqvn5+nKffwkRgPdR7/Uq+V0MuGibPuij+Mg/TTp/Ik4AfPPPN3ShIPdmR7uCXgzoQHTpkl59aod0/kRmBUBAeAD/Qay8orLChppBoADQLV3sUM6fSJQAGPffOL4fh58ctrOhJhApAHRD/h4zPWwT8heLBAGgW31t5bWVtrPt/n3O6efIYdzxa5EgAEzV8Jcdw9C/ruPXIlEATDw5ke9Drz29bNQBMh761zp+LRIFgO5n6dt/vrVdH/Rhzt8aktXJFJvBJbUaLFSI6KefiC5doojwcMd0/kRmBUDdtXX5D+ST0CcKG2oGAQJA1/lHxkcqZKgZBAqAphub8v0IigpSwFATiBAAp/xP8X3otqubnQ01gwgB8CH6A7nNcCN4g7LOzUrRCdLL6QoiNlZYvX4RAsBuo34tU6YQubhw9fINHb8WkQLgdfhryjAzA8Eb5DbDjfw/+tvI+M/oRmEMHb8WkQLgQsAF/vuQdW5W+hD9wYYd0ENx55+m5vwNcXZyhvvX3VK/EBgILF4M1KsHVKjAPXftGvdxcCTM5AA4bNa/IQJyAMjR/u+GCMgB0JCGL+tbIHMBvW2YFUdEDoDuCpmeFWTO8rcGETkAa26sQaI6EQAwpJqMy/tM4eEBZMxouZ2IHACbz/UbMn06EBsLrFljejmflxe3Ta7AHADZC/pYYsYMLpfkt99ML+dr2hQ4ciRl23IzOQDppZKfSUQoBcfkypXUI3+dnwiAG/lrIwI//5xqakBxjEQAQlYu5hWpyK0ilcFMBKD5puZ8XxwizGwKMxGAp6FP5ds4xlZYiAAYhvxtPmKWgoUIgO7ufU7TnOjlp5eKmWoSCxEAu4/6xSIgAnD97XX++5B9Xnb6GPtRIWNNICACoLtdb7WV1fS267UDbOQvhjlz5kClUmHMmDEpT9aqBRQRqJoDA4FFi7iIQNGiwNixwI0bFg+zOUYiADlHjMWUAE5J33p/Cy8+vlDQQAGYiQCQo6zzt4SZCIBuZb+a+WQu7iMXFiIAZ16dScnyL93e9iNmKViIABx4fABvo94CADqV6YSiWYsqY6c5LEQA7D7qF4uFCACRjQr6yImFCEB6quRnijTj/K9du4bVq1ejcuXK+i+oVNJ24QoI4IRAzZrAjh3yGGkNRgSA98ZX6MetPnHs0L8WEwIgV1g830TW2v62wIQAuPlWp7hPfhst85MDMwJgz8OUwj6y1fK3BWYEgM2X98mFCQFgs2p+cmNGABx6esh2BX3kxIwAMKzkV69QPQUNVQgRYQLFiIqKolKlSpGPjw81btyY/ve//+k3MBP61wv7m/qZ5gDLtrQYTAEkq0D9uoBqrq6ptGXCMZgCeJPbgwr+xIXXHDLUbAyDKYB/muYj1e9cH95HvVfaOssYTAFoPDyoy9Asjh3yN8RgCiC6WgXyGp9SAMtmy/vkxGAK4MSQlKRRm2b4y4XBFIAmZ07qOKGI7Qr62AKDKYCwFg3IbbIiSX66KB72TxPOf+DAgTRmzBgiIuPOX6MhKlJEmvOvUUN0ZTGbY0QA9OoG22fTyomBAHiWDZR3LCgmUUDWtKNgIACW1QIVXFRQaauEYyAAYlxAjb4Bdd/dXWnLhGMgAC4XAHlOBK26vkppy4RjIADGtXTQuX5TGAiA4IygciNADdY1SBsCjCiVADhYGuT0u10q+ZmCOX9L7NixgypWrEhxcXFEZML5ExGNGyfe+deoQfTRwRJVtBgIgCBP0KabG5S2ShwGAmBefVBsYqzSVolj2zbS6AiAH/9oprRF4jAQAFfyg3bf3/3/9s46PIqrC+PvxIMkuBMKFAvaIinuUNy1FCjFoZRSKC0fhUCx0gLF3d0luAR3CRAIEjxAIBDint3z/THZye5mZWZ2dmdD5vc8ecjuztw5l5nsee+5554rt1XC0BMAv3bIJJELbbQEQKIjaPSWfnJbJAw9AbDd24oFfayFvz+luqXXOxg5opStk/y0kd352/Wcf0hICH7++Wds2rQJbqb2OgeEz/tXrw6cOJG+w5i9kZYDEDdiMFQMcNPLCVULfyW3VcJIywEIL1MMKQ4AU7Mm3J3d5bZKGL17gzZuQJyrA157AB2ajpTbImGk5QC8bdMQAPCkXH7ptu+1FWk5AO/zuSPeCajbdrh9JiuaYvx4vJn0C5IcgSeFXPBrq6lyWySMtByAR1WKAADc6jaATzEfmY0SSOPGiNi1EeHZGES5MRj03Zwsl+SnDUPEOxPb5inb+/btQ6dOneDomH6DVCoVGIaBg4MDkpKS0j8jAkqWBF6+1GkjGoAngCgAHpo3v/4aOHnSfh2/Hskf3iHZIztyuOaU2xRxECEi9DlyFS4p/Za+NiI5MhwpTg7IniNzPDOGiA59gWwFi8HJQdy2rXKTmpyI+MgP8ChQ3PzBdkrix3egnDnh7prJxEsaRISot8+Rq2gpuU0RTUpcDJKS45Ejd0E5zZD9i9CunX9MTAxe6jnzH374AeXLl8f48eNRqVIl3RPGjQP+/VfnLYPOv0UL4MABwNXVSpYrKCgoKCgYRXbnb9dh/5w5c6JSpUo6P9mzZ0fevHkzOn7AfOhfM+o8fhzo2lXwzk8KCgoKCgqfA3bt/AVjquBPtWrA/v3paz4PHlQEgIKCgoJClsSuw/6i0Av9c2H/Fy/gUaIEu69469Zs8RMAaNsW2LVLmQJQUFBQULAVSthfcvRD/9Wqsf9qkvsaNQIOH1YiAAoKCgoKWZbPz/nXrMlm8wPscr59+zIeowgABQUFBYUszOcX9geA8HDgxg2gUSNEJyXB09MTUVFR8PDw0D1OmQJQUFBQULA9sof9P0/nr0V0dLRx5w8oAkBBQUFBwdbI7vwlD/sP9huMr5d/jbUBa5GYmmj+BLn53KYA/PyAihWBQYOA58/ltkZBwW4QMNCxe5JSk5Ccmiy3GZIQHB4MtVottxkWcyv0Fj4lfJLbDN5I6vzvhd3DylsrEfAuAAMODED+f/Lj+73fw++RH5JS7diZ2lAAEBEqLakE9+nuWHFzheTtY9AgICgIWLUKKFWKzYGYPVtWIXDq2SkUn1ccffb0kc0GazLYbzBy/50b/13+T25TJGNNwBpkm54NFRZVgEqtktsci/E94wunv5xQ4J8Cmd5p/nPxH7hPd0e2Gdlw7/09uc0RTUhUCErPL42yi8qi7KKycpsjmtCYUNRYUQPVV1RHoX8LIS45Tm6TeCGp8/fy9NLZrz02ORab7m5C+23tUfDfgvhh/w84+uQoUlQpUl5WGmwkAG6+vYn7H+4jMTURww4Nw9EnRyVtH15euq9v3GD3FpdJCBAReu3uhdfRr7E5cDP8n/vb7Nq2YGfQTqy8tRKRiZGYeHqi3OZIwvGnxzHIbxASUhPwMPwhLoVcktsk0ahJjf+d+h+mnJ0CNanxIf4DLoRckNssUSSkJGDQgUH47eRvIBBUpMKOoB1ymyUYIsKGOxvgvcQbzyKfAQCeR2a+KKWa1FhxcwXKLy6Pm6E3AQAp6hS8inols2X8kNT5e7h6oHnp5gY/i0qKwrrb69BqcysUmlMIgw4MwslnJ5GqTpXSBMuwgQB4GZVerlhNanTc1hHHnx6XrH1Mnmz8MxmEwOHgw/gQ/4F7Pf3cdKtez5YEhwdjwL4B3Ou4lDi8jHxp4gz75/jT42i/tT3UlB6GfRv7VkaLxBOfEo/uO7tjxoUZOu9nxvD/w48P4bPKB6sCVum8XzJXSZksEkdYXBg67+iMfvv6ITY5lns/u3Pm2uvg4ceHaLSuEYYcHILopGidzwrnLCyTVcKQfM6/b5W+Zo/5lPAJqwJWofnG5igypwiGHxqOMy/O2Ed40coC4MmnJzqvk1RJ6LCtA048PSFJ+2jeHMiVy/xxNhACRATfs7467/m/8Me1N9ckvY4cxCXHofOOzohNidV5/8Qzie6jDGgcf5JK91l/+umpTBaJJzQmFA3XNcTuB7szfKb/ZW3vbL67GTVW1EBgWGCGz5wdnWWwSBx7H+xFpSWVsO/hvgyf5cuWz/YGiSBZlYy/zv6Fqsuq4vyr8xk+d2Qc4enqKYNlwpHc+bct2xYuji68j/8Q/wFLbyxF4/WNUXxeccw4P0Nn1CELVhQAj8MfZ3gvMTUR7be1x6lnpyxuHy4uQMeOws7RFgK1awMPHlhuB4BDwYdw4+2NDO9POTtFkvblgogw+OBg3AvLON+aWZ3/sSfHDDp+IKNgtXduv7uNWqtqGXz2ADYKmRnQhPn77O2DuJTMMY9siMjESPTd2xedd3TWiQJqk8Mlh42tEs7lkMv4evnXmHRmEpJVhvNG8mbLm2l2LpXc+Xu6eaJ5KcOhf3OExobif/7/w933dyW2SgRWEgDBn4INvp+Ymoh2W9tJMyduboMjU1y5AsyZY7EJRATfM74GPzscfFj86D8gAIiWd+S26NoibAncYvCzk89O2kcESwDHnhxDh20dDDp+IHM5/wOPDqDemnp4Hf3a6DFRifbv/I2F+TMbJ56eQOWllbHx7kaTx2V3sd+wf3RSNEYcGoG6a+ri/of7Jo/NLBEMwEoV/rp6dxV9bpGcRVAmTxkJrbEAKwgAQyN/DQmpCWi7pS1OPz8tun0AQLNm/EL/xujQwbLrAzj4+CCXBGOIqWenCm+0b1+2emOuXMC33wJbtwIxMeKNFMGlkEsYc3yM0c8/JXxCwLsAG1pkGeYcP2BcsNoTRIQ5l+ag47aOZkfJ9j7yNxXmzyzEJcdh5OGRaLGphUkhpsFe5/z3P9wP78XeWHJjCYhHqZu87nltYJU0WMX5ty/XHk4OToLPK5yjMPz7+tuXCpRQAEQnReN93HuTxySkJqDNljY48+KMcFs1iAn9a1i5EmjXTvy1YXiuXx9jUwImCQjQXAA4dgzo3RvInx/o1MkmQuB97Ht029nNbJKqpAmcVuTok6NmHT8AvIt9p5OcZW+kqFIw9OBQjD0xltcXtL2O/ONT4jHwwMBMH+a/HHIZ1ZZXw+Lri3mfY1ff+WBzRrru6IqO2zviTcwb3udl+ZF/Hvc8aFqyqaBziuYsirP9z6JcvnLWMMkyDAmAbt0EC4DgcH4jKI0AOPfynEBDtRAT+l+5Ehg4UPw10/B77IdbobfMHid47n/EiIzvJSWx+zdYWQikqlPRY1cPvI0xn/meGZz/0SdH0XFbR7OOX4O9hv4jEiLw7eZvseIW/5oZ9jjy14T5VwesltsU0aSqUzHh1ATUW1tP8PNiT3P+l0IuocLiCgaTRc2R5Z0/ICz0X8yjGM70P4Myee0k3G8IfQHg5ydYAAgJn8anxKP15tY4/zJjRikvhIb+JXL8pub69Tn4+CBuvjU+NZCBPn0ANzfjn1tRCPxx8g+cfXmW17GXQi7xGymPHAk4O7OJlsuXAx8/WmglP4Q6fsA+nf+TT09Qe3VtwXky9ub8Tzw9gRorahhMIM1MLLi6ADMvzBSVsG1PYf+lN5aKfkayfNgfADqW7whHxtHscS6OLvDr6Ycv83xpLVOko1Ej4NAh0QKA78hfQ1xKHFptboULr0QUJRES+v/xR0kcP8AmXAmZ8556TsDcf44cQJs2/I41JAS2bQNUwpPxdgftxr+X/+V9fIo6BWdf8BAKW7YAqansEsuhQ4FChYAWLVghZiUhIMbxAzyfXRuun38T/QbfrPoGj8IfCT7X3sL+085Py9Rhfg1ipno12JPzH1p9qOjlesrIH+x/QqMvGpk9LlmVjGGHh2WetbeNG4sWAI8/GU/2M4ZGADz4IGL5Hd/Q/9q1wKZNwtvXg89cvz4HHh3gNUXAIWY6QyMEevUCxhhP1jPEw48P0X9/f8GX5LXkr0ED3dcqFXDiBDB4sFWEwM23N0U5fsDMyD8qCsidG3ByYiNOBw4Aidbd18P/uT/CE8JFnWtvI//vq3wPBybz764+stZIzP92PvK45xF8rj3N+df1qovHPz3GD9V+EHyu4vzTMBX6L5KjCHK75QYAXHl9Ba02t0JMkm0zt0UjUgAIHflriE2OFTX/ZDb037Ah+69aDfTrZ7EA2P9oP26/uy34PEGZ/23apP+/i+G96YRLbWKTY9F5e2dRyW685v1//934Z1YQAvsf7Rfl+AHgSYQJ53/2LBAZyT5Hp06xq0UKFGCnaawkBDqW7yh6VZHRkX9qKvu3XbUq+7eg2enTygz8eiAejniIflX7ZWoR4MA4YJTPKDwd9RTj6owTVO/Fnkb+AFAgewGs6bAGFwdcRLVC1Xifpzj/NDqV76RT61/DF7m+wKUfL+FM/zPcHMmlkEtovaW1ZFnFixcvhre3N2rWrClJexkQIQBMLfMzRfXC1dG7cm/hJ5oK/a9cCZw+DQwbxr62UACoSc17rl+f/Y/2IyCU51RBjhzsFsxiKFUK+Ocf3odvvrsZDz6KK3j04OMD80ucfHyA4sXNNyaREBjw1QDU86on6BwNJoVrixbsqF+bmBhg82arCYGcrjmxs9tOPB75GD/7/IycLjl5n2t05L9iBbvF9927wPffs3b37g3s3Wt1IVAmbxms67hOGhGwZg37nDRrBpw7J2qqyxJyueXC7Oaz8XDEQ/So2IPXOQZH/klJQIq8+8DUKV4HNwbdwCifUbyOz5tNmfMHABTMURANSuiGNkvlLoWz/c+iRK4SqFKwCk72PcmFiS68uoDWm6URACNGjEBQUBCuX79ucVtGESAAwuPDEZEYwbvpKgWr4K/GfyFoeBBuDL6BUrlLibPRUJhck9zHMMDixZIIgP0P9+PO+zvibITAuX8xof9SpVixw8fZplGpQCW4OroKv1YaZks2M4zwvmgLgWLF2OePJ1/k+gLnfziPZ6OeYXaz2ahRpAbvc0NjQ43vVubmBvTsafxkKwqBMnnL4L9v/8ObMW+wsNVCFM5hvq660ZF/7dq6r2Nj2YTRzp1tJgQ0ImBXt13iG/nf/9gI16lTbHSveHHgp59sLgRK5i6JJiWb8Do2Q7a/Jrna1RVo1QrYs8dmkRh91KTGyWcneR2rjPy10A7Nlc5dGmf6nYGXZ/rOc9UKVcPJ709yUwDnX51H2y1tM822iHwFAN9Rf+9KvfFo5CPcGXoHExtMRIX8FSyzr1kzdj5Wg35Wv0QCgG8mvDEEZWwLDf1rHL/+jodmqOtVF89+fobtXbdjXJ1xaFKyiaBEIF7z/pZUY0xKAo4cEXxaydwlMa7uOFwfdB3PRj1Dtwr8bDA579+D3wjPoBDYv99iIZDTNSdG1hqJ4h7mxV1CaoLhnUW/+gooX97wSTYWAmtvr+V+/6boN8IiAVWq6L4ODQUWLbK5EIhJisGk05O419MbTzea2J0h7L9/P5tASgQcPQp06cIm7vbqZXMhsODqAgR9CAIA1CpaCxd+uGB0KkBx/loM/HogelfujY7lO+JM/zMo7pnxj/Orwl/hxPcnkMstFwDWkbTb2g7xKfHWNk8aeAgA7d38tKlRpAYGfp3ujFMpFWXzSri3tYsLsG4d0LQpsH274ax+CQTAj1/9iG+KfYMSniVQwrMEvDy94OXpheIexeHmlL48r0jOIiiasyiK5iyKIjmLoEjOIijhWQJ/NviTf5+EhP69vEQ5fm17u1fsjtnNZ+NU31P4NP4T7g+7z61kyeacDR6uHgbP5ZWJzjf0b4h8+YBR/MKRxiiZu6TO5kQjao4wGhEw9gwDYDeU8jD8/2AUjRDo2JGt3Bhv2d/7tTfXcO0tWza6SsEqeDjiIUbVGmVwSiAm2Uh+UV/zG5NZWwjcfHsTfo/9AKQvgzY2HWBoWhWTJmV8T4MNhcA/l/7hipp1qdAFExpMwP3h9w0mBeZ01btHw4dnbDAujl2xY0Mh8DbmLZfEzIDB4taLUderLm4MuoFFrRbpDAZcHF0yzaY+ANgMbZ4/Vuf6m+vkOdOT4AuCL6jp+qYUlxxnUZtRUVEEgKKioiSy0gT+/kTu7hq9StSuHVFiIhERPfjwgHLOyEnwBfms9KF/Lv5DzyOeExFRiiqF8v6dl+ALyj49u8V9Fo1aTTRsWLr9Dg5EGzda3Gzrza25e/ox7qMEhhLRtm3pdpr68fIievVKmmumcf3Nda4/fff2JZVaRY8/PqYtd7fQr8d+pYZrG1LZhWVpbcBafg2OGcOvL9o/+fIRBQZa3Jfw+HBymupE8AUVn1uc1Go1ERE9/fSU/r7wN1VfXp3gC/Kc6UnPPj0z3VjfvsL7of0THGxRX/rs6cPdl1U3V3HvRyVG0YIrC6jswrIEX1DlJZW5fmYgOFi8/TlyEP35p0V9ICJqt6Ud148l15bofPb442Pqt7cfOUxxoFyzctHLyJcZG1CpiIoWFWZ74cJEI0cSnT1LlJpqcR9eR70m92nuBF+Q81RnCg7XvbcRCRE07vg4cpvmRiX/K0nRidEZG6lUiZ/t2bMT9exJtHs3UXy8xbZr02tXL+5eDPEbkuHz97Hv6Yd9P1COGTlo/InxQpoW4nut8mNXzp+I6Orrq+Qx04P7D2++oTnFJ4u/oTZ1/kQmBUB4fDi9j31v8LSB+wdyfd4dtNs2thrCCgKg1aZW0jv/mBjd/2f9Hyen9N9Ll5ZUACy9vpTrz/wr8y1v8PJlWRw/EdGaW2u4vvxy9BeDx4TGhFJ4fLj5xvz8xDvOYcMs6kdoTCg5T3Um+ILy/J3H4HeGSq2iBx8eUGxSrOnGqlUT3w+AKCxMdD9uvLnB3Y9ic4tRYkqiweMiEiIoIiHCeEOjRom3v1gxogsXRPeBiKj/vv5cP0YfGW30uOTUZEpKTTL84bRpwm3XFgJJRtrlyennp7k+5P07r8nvLqNi0jiyO3+7W1dSq2gtHO9znAvVnXh2Ah23d0RiqnXXDUuGiSmAPO55UCB7AYOnaedG7AqyINnHUiRMAjTcvETbXZoK/ZcqBVy4AHyZNr/49Cl7X0JCJLm0dlVCIUlzRhES+s+Xj53GqFTJ8usC2BG0g/u9m7fhuf9COQrxW7stJvQPAEOGsKFoC1h+YzlS1Ow8/qCvB8HdOWNOiAPjgPL5yptfU969u3hDmjRh75FItEte/1HvD7g6GU44zeWWi5smNYglfXj9mq04KZLb725j/e31AFg7JzaYaPRYZ0dn40sCxeTDaE8NtG0r/Pw0UlQpGHE4vZz4zKYzTWbyZ5ZtfLWxO+cPAD7FfHCszzEuA/T40+PotL3TZyEAjNGkZBMu6dHvsZ+8fZVYAPDZbEUUhr4cNMl9Pj7sv1YQADdC2Q2JHBgHQWuAjSIk679JE8Db2/Jrgt2BUJPFXNyjOL4p9o1lDbq6Ct9QasgQYMkSwEH8V1GyKhnLbi4DwN6T4TUNzBcLQWwSZp06bDEpkY5Af67/x69+FGcHwK5cKFpU3LlOTkD//qJOJSKMPZ6+wdLE+hPFL38rW5atuSCWO3fYeIAI9JP8fvzagnthp9il8weA2sVr4+h3R7ks0KNPjqLLji5IShW/na5NESgAnB2d0bF8RwBscRnZN4exUgTAYIKSWPSz/vWz+osVk1wAJKYmcjXYvfN7I5tzNtFt6cDX4ezYwW5wpBZeP12f/Q/3czsUdvPuJs3oRYjjlMDxA2yk7F3sOwBsbRHt1USi+PJLoFo1YefUqcNmpefkX29AH+1R/4R6E4yO+nnh4MCOfoXi5MQ+Y034LdHT58iTIzj1/BQAoGSukhhZa6SodjjECjFHR2DpUlFCzFCSX2YuvmQMu+5RXa+6OPLdEU4AHA4+jK47u362AkA79L8zaKctLDSNRAKARKpvs+TIAQwYwP5eurThrH6JBcDd93c5h1m9cHWxlmfEVOg/Xz5g1qx0J7lsmSQCQCfkX9GCJYfa8A39OzqyzslCxw+wozQNfIuxmEVI2FwCx68/6h/w1QDRbXEIDf1rHH+nTqIul6pOxbgT47jXs5rNskzAAOKcv6MjG/rv3FnUJcceH8vVmhlcfbA0U3t2iF07fwCoX6I+Dn93mBthHXx8EN13dUeyKllmy3giQAA0K9WMWypy4NEB+xA5EkcAJJ8bmzcPuHIFuHfP+HI+CQWA9ny/pM7fWOhfM8c/fjywcaNkAkA75O/l6QWfoj5iLdeFb+hfpWLX+p86ZdHlrr25hqtvrgIAqhasivpe9S1qj4Ov08mRg3U0Fjh+QOJRvwYhoX8LHT8ArAlYw4XKfYr6GM0hEYTQ0L/G8XcVV/r5zIsz2HpvKwB2h77pTaaLaiczYPfOHwAalGiAQ70Pwd2JdaAHHh1Aj109DBfqsEd4CgAXRxd0KN8BABCdFM27qpTVsVAAWG3OH2C3xPXxMb3VLyCZALjx9gb3u+QjAn2Ho5/c17u3ZAJg38N9XASja4Wu0ooyU45z4ECgXTv294QE9ncLBMDCawu533+q9ZN0/eAb+o+NZR1NZKToS1ll1A8IC/336GGR49cv6DOnxRzp7gVfIWah4xea5JfZyRTOHwAafdEIB3sf5ArG7Hu4Dz139/zsBEDXCnYW+tcgUQRA0jl/oUggAG6GsiN/B8YBVQtZkIxkCB8foFw59ndjWf0SCQDtZ6t7RQsyww1hLPQ/ZAibRb5rF9C+PfueBQLgXew7bL+3HQCQxz2PuP0vTGEqbF6tGpAnbQXEtWtAy5aiBYBVRv0a+Ib+N28GZs4UfZnZF2frFPSp61VXdFsZ4Ov8s2VjIwUiyQpJfjoIWBdoF5x4eoLcprlx6y+77ehGKaoUo8fbfJ2/OUzUASAiSkhJ4IoB5ZqVy/gaWLkQUQegxcYW3P2KTIi0kaEmCAkh+vJLwXUA4pPjyXGKI1coxio8fkw0ezbRixemj9u8mf2/1/Rh6FC2uAsPtAv7eM3zErNG2Tz6BX+GDNG1LymJqH379M/d3YlOnhR0Cd/Tvtxz9fuJ3yXuABkv+FOnDlF0NFtrIV++9Pdr1SKKiBB0Cb7r+kVjquCPkxNRnz66782YIfgSIVEhJgv6SELVqvzW+efLR3TnjuDm30S/oRwzchB8QYwvQ9ffXJe+D7oo6/yF0qxUM+zvuZ/bcGVn0E702dOHC2HaPWYiAG5Obmhfjh0VRSZGCqt5bwtERADIWgl/YhEZAbj7/i5UxJZBrV5Ewvl+bcqUAcaNA0qUMH2cBREA7ZC/ZFn++mgvFTOU1e/iAuzcKToCkKxKxtIbSwEAjowjhtUcJpHhWhgK/Wsn91WqxD5HmnX9IiIAVh31A8ZD/5o5/o0b2WRSzogJgiMAf57+EwmpbIndETVHGK3fbxHGIhiOjsD69WzUDGB3umzalN2ZUQBZJclPBwFKwa44EnyEXP5yoa8Gg7Z7g+aPrkMpSQkZjrO7kb8GExGAvQ/2cqOBAfsGyGyoEQREAJpvaM71JyrRju6DwAjAoquLuH4surrIhoaaQEQEoOXGllw/roRcsZ5tR44Q7dlj2h6REYBNdzZxfei6o6uERusxc2bGEb8+IiMAVh/1a7hwIeOIf88e3WNmzRIVAQgIDSDGl+EilZJV8NTn8eOMo3xHR6KdO9nPIyOJfHxERQCEVPKTENlH/pnW+RMRHXp8iD66pz8MMdldSDVoEPvlkcJOBdit8ycyKgDik+O5EFSev/NQcmqy3JYahqcAaLahmX06fyJBAuCHfT9w/bgcctnGhppAgACwSchfKCIEgM9KH+5enH1x1nq2xccTDRjAPueGHL8GEQLAVA1/SVGp2D0ujDl+DQIFgFqtpqbrm3J9+Pfiv1YwXgvt0L+249cgQgAkpyaT92Jvrg8rbqywnv26KM7fUhLy586oCDU3fvBgitq/336dP5FRAdBzV0/ugTz+5LjcVhqHhwDQdv4GN/CQG54CoPKSygRfkOMUR4v2m7AKPAXA6luruXvx67FfZTDUCAIEwJWQK1wfqi6tah8ChkiQALDZqF/DpUtE/fqx3zemECAADj0+xPWh5H8lrd+HxYuNO34NAgXAnEtzuD7UWlmLVGp+eTMSoDh/i/nnH8POP+0nCmCdf//+OhEBu8KAANgTsJV7KAcdGCS3haYxIwC0Rwd26fyJzAoA7WS/KkuryGioCXgIAO2Q/9XXV2Uy1Ag8BcB3u7/j+rD61moZDDUBTwFgs1G/GHgIgBRVis6Iefu97da3S60mOnyYKCjI9HE8BYAMSX7aKM7fYkJDiRjGvPPXiwjYnRDQEwApbVpTrilsBm2+2flMrmiwC0wIAG3nH5MUI7OhJjAhAC6HXLb/PAwikwLgY9xHLuRfYl4J+xkxa2NGAGjv3pf377z2F4EhMisAbD7qF4MZAbD8xnKuDz4rfezvWeIhAMxt12tlZHf+mS7bPwOFCgH1BVT1+vgRWLECaNYMKFwY+OknIDraevbxRW8VgNOhwzhxIBdcUoGP8R9x7uU5mQ00g4lVAGTNIj9SYmIVgHZxH6tl+kuBiVUANsnytxQzqwC0d+8bXH2wwd37ZMfMKgCrZ/hLwfjxRlcBxCTF4M/Tf3IfSVrQRyo8PYFjx4yuAshKlfyMkfmdPyB++8qPH9mtRGfPltYesegJgBo3Q7FzB+CSKvM2v3wxIgCaXXyXfoicRX74YEQAPL+bLr7sfhmQEQGw654VavlbAyMCIOX4Ud3lfTWssLxPKowIgNsPzlinmp81MCIAZl+cjbC4MABWKOgjJUYEQErATZ1KfrOazfqsK/kZRUCYwH4xEfrPEPY39LNjh9w90EVvCmB/WVDxmQUoVZUqt2X80JsCSGVA33Viw2uxSbFyW8cPvSmAl/ldqNgvIKepTpSQknFJqV2iNwWwtAZDzCQ7DvnrozcFkOLmQk362mB5n5ToTQE8LJ2LPMfb6Vy/MfSmAP5s7mTdgj5SozcFEJcrO1UeKkuSnzayh/0/D+dPRNSggTjnP3Wq3JYbRk8ArKkGOv38tNxW8ceAAGjcFxSXHCe3ZfzREwCP8oBqLLLTZD9j6AmASY1AY4+Nldsq/ugJgDgnUPkRoHMvzsltGX/0BID/F6Bic4ra51y/MfQEQN+OoNFHRsttFX/0BEBYNlC+cbB1kp82ivOXjEWLhDt/e3X8Gvz9KcXNhQigT26gDbfWyW2RMPQEwOLazvZbs8AYISGUWrok14fp8zPJiFObzZtJ5cBGxm4XlPULTxx6AuCfrkUyR+RCm8BAis+Vg+vD6uOz5bZIOFoC4FAFJ1sVw5GOyEiKqlaB68PSCS3ktEZx/pJhJPRv1Pnbu+NPQ3XxAgXWLUMrf25gfwVy+KBW02vfX+lSrSK0f/8/clsjjtev6W6r6nSgQ3kKjX4rtzWi+LBjPV2vUYR2zxkotyniSEqiO4Pa05l6xenx/fNyWyOK2NvX6Uq9knRwcGP7X71jhNt//0qXaxSiW3uXym2KKFI/hdO5dlXpXMvyFP3pnZymyO78GSLemdj2n7LdsCFwTjcrPhqAJ4AoANw+Y8OHs4lpCgoKCgoKtkf2zOfPI9tfA9+s/+3bBW/8oKCgoKCg8LnweTn/Ll3Y5WbGKFaM/Tc8HGjSRBEACgoKCgpZks/L+Zsq+DNhAnDvHvDNN+xrRQAoKCgoKGRRPi/nDxgP/Y8fzxZ9OHpUEQAKCgoKClmaz8/564f+J0zQ/VwRAAoKCgoKWZzPz/kXKgRMnMj+O2cOO+LXRxEACgoKCgpZmM9rqZ8BoqOj4enpiaioKHh4eOh+GBUFfPstcOUK+zpvXsDfH6hSxfaGKigoKChkFT7PpX5qUlujWen5XCMAKpXcFigoKCgo2DGSOv/E1ETk+TsPnKY6oebKmtgSuAUxSTFSXkJ6ZBAAweHB2H5vO9RqK4ikPn0AJycgVy52+uP+femvIYKQqBAkpybLbYZVSFWn4nLIZQiIomUKtt/bjgcfHshthiSkqFIw8/xMnHh6Qm5TLEZNakw6PQmzLszK9M/c9TfX0X5rexx7ckxuUyziyacn+HbTt5h+LvNsDSxp2P926G18teIrnffcnNzQpkwbdK/YHW3KtEF2l+wizBSPybC/NjaaAohJikHuv3NDRSrUKVYH5wechwMjoQYrUAD48EH3vQoV2FUQ3boBFStKdy2ejDg0AktuLIGnqyfe/foObs5uNrfBWiSmJqL4vOL4GP8R9b3q49wP58yfZOeoSY3G6xrj3KtzcGAc8HHcR+R2zy23WaKJTIxErZW1EPwpGAAQMjoExTyLyWyVOMLiwtBsQzMEhgUCADZ22og+VfrIbJVw1KTGwqsL8cuxX0AguDm5IeF/CXKbJRg1qbH8xnKMOjoKqepUAMDL0S/h5ell7tTPK+xfpVAVZHfWde6JqYnY/WA3euzqgQL/FkDPXT2x98FeJKTY2Y22UQTg2ptrUBEblr/0+hIGHhgo7TSJZg90bR48AKZMYfcY9/YGfH1tFhGITorGqoBVAICopCgsuLbAJte1FUMPDsXH+I8AgMuvL3NfAJkVNakx2G8wzr06x72+8vqKzFaJ51nEM9ReXZtz/ADwMPyhjBaJ5+yLs6i2rBrn+AEgJDpERovE8SrqFZpvbI7Rx0aD0saUmfHvJuhDEBqsbYDhh4fr2J9ZojGSOn8HxgE/fv2j0c/jU+Kx/f52dN7RGQX+LYA+e/rA75EfklKTpDRDPDYQAPp/rGtvr8UQvyHSCYAxY0x/bmMhsPDqQiSr0sP9C64u0HmdmVkbsBbr76znXqeqU3Hj7Q0ZLbIMjeNfHbBa5/23MW9lssgyLry6AJ9VPnj4UdfZZzZHoyY1pp+bjiYbmiA0NlTns+IexWWySjhEhHW316Hy0srwf+6v81lut8wTWUpKTYLvGV9UW1YNF0MuZvg8f/b8MlglHMkT/rp5d+N1XGxyLDYHbkb7be1R8N+C6L+vP44EH0GKKkVqk4RhZQEQHB6c4b1VAasw9OBQaQSAtzf/0L4hIfBAujne6KRozLk8R+e9NzFvsO72OsmuIRe3Qm9h2KFhGd4//vS4DNZYjjHHD7DzmZmNjXc2oumGplxURpuoxCgZLBJHWFwYvt30LSaenph5EqkN8D72PTpu74gf9v+A6KToDJ9nlmmlC68u4KvlX2HK2SlIUWf0VdmcsyGbczYZLBOO5M6/TvE6KJyjsKBzopKisP7OerTe0hrVllcz+HDYFCsKgMefHht8f+WtlRh+aLg0f+Dd+AkwHTRCoGJFYP1688fzYMHVBYhIjMjw/ozzMzL16P9Twid02dEFSaqMEasTzzJfQpma1Bh0YJBBxw9AJ2Ru76hJjYn+E9F3X1+jz1hUUuZw/powf2Z8prTZHbQblZZWwoFHB4weoz9dbG9EJUZh2MFhqL+2Ph58ND5Ayuue14ZWWYbkzt+BcUDnCp1Fnx/0IQjPI55LaJFIrCQADI38NSy/uRwjDo2wfM5IjPPXQARcu2bZ9cH+seiP+jW8jHqJDXc2CG/02TOgZUvgjz/Y+yEDalKjz54+eBH5wuDnl0Muyy9eBaBx/GturzF6TGYZ+SekJKDnrp6Yft50xrW9j/xNhfkzE5GJkfh+7/fourOrwQiMNrZOBBfCngd7UGFxBSy7uczssfmy5bOBRdJglXX+Xb27ij63Z6WeqFLQTorsSCwAiMjsKGrZzWUYeXikZQJASOhfHy8vw1URBbLg6gJEJkYa/Xz6+enCp3i6dAGOHwdmzWJXNbRsCaxaZVMh8NfZv3DkyRGjn6tIhdPPT9vMHkvg4/gB1vnbexLTu9h3aLS+EXYG7TR7rD2P/D+XMP/xp8dRaUklbLq7idfx9jjyfxP9Bp22d0KXHV14i7As7/zre9VH/mzCkx56VuqJjZ02gjG1La+tkVAAvI15i/iUeLPHLbmxBKOOjLLsC1fM6N/LCzh9mv3XAiITIzH3ylyTx7yIfCF89F+gQPrvajUrBAYNAgoWtIkQOBJ8BFPOTjF7XGYI0/J1/AAQlxKHd7HvbGCVOO68u4NaK2vh2ht+ESt7Hfl/DmH+uOQ4DD80HC03tcSbmDe8z8vhksOKVglDTWosvb4U3ku8se/hPkHn5s2WhcP+AODo4Cg49N+7cm9s7LQRTg5O1jDJMgwJgKZNBQuAx+GG5/sNsej6Iow+Olq8ABDq/DWOv1QpcdfTwtyoX4Pg0f8UI45XpbK6EHge8Rzf7fmOW5pkCt5Jf3FxwIIFwBPbhtXVpMbAAwN5OX4N9hr6P/j4IOqtrSdoyZu9jfzVpMa0c9MyfZj/ZeRLVF1WFUtvLBV8rj2F/f+99C+GHx4uavoun3sWH/kDwkL/far0wYaOG+zT8WvQCAAfH/b1x4+CBYDQxKkF1xawRTDECAAhof/ixSVz/JGJkZh72fSoX8PzyOfYeHcj/8Z9fMxHJawgBBJSEtBlRxeDyYuGCP4UbDQnQIfq1YGffwbKlAFq1AD++w94/Vq0nXzQOP61t9cKOs8ek/7+u/IfOmzrgNjkWEHn2Zvz//3k7/jz9J+ZOswPAIuuLcLTiKeizrWnsP/raPF/g1k+7A8ADUs05JX56Mg4ol+VfnB0cLSWKdLh6QkcOyZaAAgZ+WuYf3U+xhwbI04A8B39lykDFC0qvH0DzL8yX9CXq6DRP8MIi2joC4FvvwUeCivwQkQYcXgEAt4FCDqPVxnZaK2Rxc2bwC+/sEKsbl2rCAGxjh/gMfI/fBj45x/dPlkR/+f++OXYL6Icpr2F/W+/uy23CZLQsXxH0cvc7Mn5/9X4L/Su3FvUuYrzB+Ds6IyO5TuaPU5FKnTY3gFnX5y1linSYoEAEDt6+u/qf9h2b5vwE805Sk1uhb8/e2ySZcWWIhMjMe/KPEHnPIt4xjspCID4lQwqFXvffv1V0Gmrbq0S5Sx5zdsOy1gnAABw6ZJVhMCagDWi+gKYeXbv3AHatAF++w3Ikwfo1AnYuhWIsd6+Hpbkw5gUp6mpQGKi6LbFsKTNEjQo0cCm17QGdb3qIvinYPz41Y9gBFavtaewv6ebJzZ33owz/c6gYn5hidNZfs5fg6nQf/+q/dG2TFsAbOW/1lta4/zL89Y0RzpECgBTy/zMEZ4gImxtKvTv5QVs3Ai4u7Ov/fwsFgDzLs8TFVKdfn46/6prtWpZlpBYty7vQ4M+BGHkkZGiLnPy2Umo1GZ2V/zxx3QBZgwJhUBiqninZnLkr/3MqFTAvn1A795sgmbnzlYRAk1LNYVfLz/U96ov+FyjI//Hj9m/B3d3oE4dYNMmm0QyvszzJc72P4vT/U5LIwKI2L4k276WRpGcRbCq/SrcHnobLUq34H2ePY38NTT8oiEChgRgTos5yOmSk9c5ysg/jSYlmyCXW64M7w/8aiBWd1iNXd13oU2ZNgBYAdBqcytcfJWxXKIYFi9eDG9vb9SsWVOS9jIgUACo1CpR82E+RX2wsNVCDKthZJRoDkMjZU1y33ffAYcOSSIAIhIi8N/V/0SZ+DTiKTbf3czvYKGhf20GDwZ+/5334SefnRRdjCgiMQK3Qm+ZPqhIEUFiJIMQWLSIHanyZHjN4VjVbhUalmgoeGQWHB5sfLRdsybbF30SE4G9e60mBNqWbYtzP5zDrcG38EO1H+Dq6MrrPKMC9cSJ9P/Py5eB779n7e7QwSZCoNEXjTgRIEbUcLRtC5QrB2TPzu7yefQokGLbyqlVClbBsT7HsKXzFl7PWoZsf5UK+N//gKlT2U3XZMLZ0Rljao/BiJojeB2vOP80XBxd0KFcB533hlQfguXtlsOBcYCrkyt2dd+FVl+2AsAuKfp287e4FHLJ4muPGDECQUFBuH79usVtGUWAAHgV9Yq3I6lTvA7mtpiLl6Nf4srAKxhZa6T4nAh9R6mf1d+4sSQCYNWtVRYVt/nn0j/8Dxbj/AcPBpYuBRz4P/I9KvZA+3LtRY9KeGX9d+8uqm1cugT89BMwbRrvUzR7b5zpfwZvf32LRa0W8RYCcSlxeB/33vCHDAMMHGi6ASsKga8Kf4U1HdYg5JcQNP6isdnjoxKjDAuZ77/P+HwkJQEHDthUCDT6ohH6V+svvoHbt9l/U1OBzZuBVq3YnJcBA2wuBPyf+3MrZEzlA2QI+0+eDMyYwf6bNy+7YdmmTbIIgVdRrzD/6nwAAAMGpXOXNnpslq7wp0+/qv2434fVGIYlbZbobGHr5uSGPT32oGXplgDYmv/fbvo28+wkxlMAmEr20/7ynVh/Ii4OuIhfav/CZ1tI83h7A7Vrs78bW84ngQDgU7/AFIKEg9DQvwjHDwAFcxTE/p77EfV7FO4Pv48NHTdgVK1RqFu8Li+HefL5SfMX6dLFfOjfFC4uok4rlKMQRtQagTP9z2C0z2jufVP9Mhn6FyLI9IVAp07AmTP8zzeCh6sH7oXdA8AKnVpFahk8TkUqJKQa2FXUw4MdNRvDRkIgRZWCaefSRd3CVguFTQd8/33G9yIigLVrbSoEAt8HcstJPVw9cH/4fUxuONmgCMggsF21ojgqFfudpPl/t7EQGHNsDPe8jKw1Eg9GPMDcFnMNTgVkpjl/RkDijOgMm2NPjiExNRHty7U3WsAnISUBHbZ14BKlPFw9cOL7E6hV1PAfMF+io6Ph6emJqKgoeHh4WNSWSaKi2GVlV6+yr/PlA06dAqqw1Qp3B+1G153pORAOjAMalGiArhW6olqhaqi3th4ANsx/ZaDEwicsjM16b9WKVdHGOH2aTdxKSPtibNcO2LlT9w/RCPEp8dh4ZyO3TlnzXBEIW+9t5RzHmNpj4O7krnOMs6Mzunp3RaUClfj3aexYYI7h8sE6NG4MnDwp2PGb4kPcBxT4ly04VC5vObQo3QI3Q28iIDRAx6k0/qIx/Pv5G2smnfr1gQsXhBvSvj17f0QKAIC9BxWXVMSDjw/AgMGNQTdw+fVl7AjagfMvz+vUNTjc+zBalWllrCFWaApcTcHBMEBIiEWrTjbc2YB++9jBRo+KPbCt6zbcCr2FhdcWYmvgVm4vBgYMon6PQk5XA/O4W7eyokQILi7sSpJu3Vghk92y+es1AWvw4wF2d9QWpVvgWJ9jAIAzL85g8pnJOPfyHHfs/p770b6c3jbeISH8xXHu3EDHjmwEqmlTwNnZItu1+XbTtzj2lLX972Z/47e6vwFgi51NOj0JawLWcM/XpQGXULt47fSTo6PZ7ypT01ouLux3bvfu7HeVp6dktms4/vQ4Wm5iB6YFshfAo5GPuKnstzFvMe7EOGwJ3AIAKJqzKF6P4Z2PI38lOyLi+2N14pPjqen6pgRfEHxBnjM96drraxa1GRUVRQAoKipKIitNEBlJ5ONDxH4VEuXLR3TnDmtHYhR9t/s7ar25NS29vpTexbzTObXq0qpcv19GvrS+rcbw9ydyd0/vQ7t2RImJFjXZenNrrm8f4z5KY+eVK+k2mvphGKKNG6W5ZhpHgo9w/fnl6C/c+ymqFAp8H0hrA9bSjHMz6HnEc34NLljAry/aP+3bEyUlWdyXwPeBXF/qramn89nb6Le08OpCarmxJfXd25fikuNMNzZpkvB+aH5y5CD6KP7ZUKvVVH15da4vF19d1Pk8LDaMpp+bTj4rfWjy6cnGG4qOJnJ1Fd+P8uWJUlJE9yM5NZlK/lfSaD+IiE4/P01dtneh/vv6U3xyvOGGatcWbnvu3EQ//EB07BiRWi26D0REx54c4/rgNc+LElISMhxz590d+nH/jzTx1ERSG7pehw78bXdxYb+rNm5kv4clIDElkcouLMv1Y/3t9QaPO/viLI08NJLOvTgnpHkhvtcqP3bl/ImI4pLjqPG6xtx/eK5ZuejGmxui27Op8ycyKQBM8dfZv7g+z7001waGmkBiAdBqUyvpnb9aTeTlZfzLwNs7/XcHB0kFwLSz07j+bLqzyfIG37xhRYqNHT8R0ST/SVxf5l+Zb1ljgYHiHKabG9HJkxZd+uKri1w/qi+vbtiZ8KVjR/HO39mZKDxc9KVX31rN9aP5hubi+zB3rvg+AET//CP60qmqVKq8pLLlfyObNomzXSMErl8X3QciohnnZnB9qLu6rmXPVEZkd/5Wn/MXSjbnbPDr5YdGXzQCwK4db76xOQJCA+Q1jC8ilwF2806fM931YJc1LTSPREmAhpBs3wZTWf+DB7P/35p19Go10K8fO08oATdCb3C/1yhSw/IGhWT9N29ucahfAxFhR9AOAGwo3JINuQCwy0rLlxd2jpsbcPAg+zdiAQuvLeR+H+UzyrLnTGwSJgDMns3WOhCB/ly/byNf8XZ0tfBevngh+tT1d9YjMCwQAPv30atyL3ENtWvHa8oxA8nJ7HdW69asHBDBq6hX+OvcXwDYKdrFrRfb154zEmB3zh9gMz8P9jrIJblEJEag2cZmmacSlggBUC5fOW7O+1LIJYtKTEqChAKATz18URhy/prkPkdHYPFiqwiAm29vAgByuuREmbxlLG4PAH+H8/Qp8N5I1r1A7n+4j4cf2Tn6el71UCSngeV6QmAYYY5TIsf/JvoNdgWxgjl/tvzoUbGHRe2hbVtxTmfOHGD0aNGX3Xh3I55HPgfAzvXXKV5HdFsoXjw90Vco3t7ApEmiTo1NjsVE/4nc6zkt5ugkeAvCw4PNpRBL2bKiT9VO8htRcwSqFqoq3g47xS6dP8AKgEO9D6GeF5sI9ynhE5ptaIa778Vtp2tzRAiArhXS1fqeB3usbaF5rBABELq+3CT6Wf/6Wf0MI7kACIsL4zaR+brw1+K/2PQxl/WvSSJ79oy9LyH8N7Ixxo77O7jftSNPFsE369/Rkc2ct9DxA8CyG8u4IlFDqg+Bq5MIx61NzpxscqwQ5swBxowRfUn9Uf/khpNFt8UhZkmstzdb8VN7B00BzLk0h0v67Vi+o+VFi8TW9Chfno2QiRitH396HLsf7AbAJvlNbTxVnA12jt06f4At/HC492FOAYcnhKPphqYIfB8os2U8ESgAulXUCv0HyRz61yCBACCRoTezMAy7K1758mxBEEPL+SQWAJpRPwBUL1xdrOUZMRX6b9+efWa+/JJ9/fSpxQKAiLAzaCcAVpB18e4iui0d+Ib+VSpgzx72flhAYmoilt9cDgBwcnDC0BpDLWqPQ0gEw0LHD0g86tcgNPSvcfwFC4q6XGhMKGZfmg2AvRd/N/tbVDs6iAn9ly/P9qNwYcGXS0pNwk9HfuJe/9P8H4OF6j4H7Nr5A0BO15w48t0R1C7GhrA+xn9E0w1NcT/svsyW8USAAPDO740K+SoAAC68uoDQGDvZ3lPCCIDk82YdOgAPHrDFbowt55NQANwMTXf+ksz3a2PI4WiW85UqxS7FlEgASB7y12Au9O/snD4aW7YMGDHCIgGw4/4OfIj/AIAtJ17UQ5oNqniH/p2cgKqWhYStMuoHhIX+NQ5TpOMHgEmnJ3H1PoZWH4qyecWH3TmEhv4tcPwAMPfyXK4mS93idfF9FQM1Ez4T7N75A+ya/yPfHYFPUdaBfoj/gCYbmiDoQ5DMlvFEgADQJF0RyD5C/xosEABWm/MXgkQC4Mbb9GS/6kUkHPkDGUP/+uv4ixWTTABoh/y7V7Qgwc0QxkK1bm7AkSPs/7lGqFkgAIgIC64u4F7/VOsnE0cLhG/oPzWVHZ2eOiX6UlYZ9WvgGzZ3cxOX55CGfkGfyY0kEjAA/z7kz2+R488KSX7aZArnD7A7LR3rcww1i7C1+sPiwtBkfRNu9GL38BQAdpX1r48EEQBJ5/yFIoEA0Iz8PVw98GWeL6W1r0gR1h6AHT0byuqXQABkCPlXkCjkr8FQ6F87ua93b3ZTKQsFwOXXl7n7UaNIDS46KBmmIhh//82KM4AtiiVSAFht1K/BXOjfMa1s+O3bbMGcyEhRlxl3Yhy3vfL/6v9P2hr3fEP/Hz4A69aJvoxOJb+aIz/LJD8dBKwLtAsiEiJ0inkU+rcQPfzw0OjxNl/nbw4zdQDUajVXWMJhikOGYkB2gcA6AM03NOfuV2RCpA0NNYJaTTRsmOA6AO9i3nH9aLSukfVsCwszf1xICNGXX6b3oXRpoleveF3i7ru7XD/qr6lvocFG0C74Y2wd/+bN7P+95rihQ4lUKt6X6LGzh9kCLBZhrODPnDns50lJbM0Fzfvu7oLrFWiv62+xsYX0fSAyXvDH25vo9Gmi/PnT36tViygiQlDzR4OPmi3oYzGmCv5o2w8QzZghuHntokQF/ilAEQkRkndBD2Wdv1ByueXCie9P4OvCXwMA3sW+Q+P1jU3WzrcrzEQAGIbhsv7VpMbeh3vlstQ4FkQA7CKMJjICoDPfX1ji+X5t2/LnN3+cBREAzagfsELIX8OQIWwkI39+48v5LIgAaC/vK5C9gOXL+wxhKPSvndzn4sJGZ0RGAKw+6tdgKGyuSe5r1Ij9N1/aSP3aNUERAJVahXEnxnGvZzadCTcnN8tt1sdYFKZ8eeDOHWDWrPT3JkwAZs7k3XRWSvLTQYBSsCvC48Op2rJqNOcbUKwz6KaXM73ZtIwoQVd12t3IX4OJCEBAaACnQpuubyqzoSbgGQFotqEZ15+oRDu6DwIjAFPOTOH6sTVwqw0NNYHACIBaraZyC8sRfEGML0Nvo99azzaVil9lSBERgImnJnL34k//PyUy2ACHD2cc8esjMgJgk1E/Efs86I/43+lFFAMD2e8ggRGAVTdXcX2osaIGqdT8IzeCMBSFKV+e6K3W8ztrlqgIgJUr+RlD9pF/pnX+REQf4z5SnIvWlwZAqhzZifr0Idq/nyghwX6dP5FRAaBWq6n0/NJc6D8slkcYWC54CABt5x+dGC2ToUYQIADab23P9SM4PNjGhppAgADQDvk3WNvAxoaaQIAASEhJoPyz8xN8QU5TnehN9Bvr2nb2LNHVq6aPESgA+NTwlxSNbRUrZnT8GgQKgJikGCr8b2GuD2dfnLWO7Rq0Q//6jl+DQAHwMvIlZZuejfuuvR162zq2Z0Rx/paS7FND92Zr/+TMSVHdu7PO//17uU01jBEBMP7EeO6PasWNFXJbaRozAkB7sya7c/5EvAVAkTlFuA2nbDQ64A9PAfCn/5/cvVh4daEMhpqApwBYF7CO60OvXb1kMNQIAgSAzUb9GmJj2fl9c5EYAQLA97Qv14eO2zpKbnIGbt4kKlCAqG5dw45fgwAB0GV7F64Pow6PsoLRRlGcv8UcPGjc+QMUBbDOP0cOnYiAXWFAANw/sdW2Xw6WYkIAaDv/mKQYmQ01ghkB8Db6LdeHJuubyGioCcwIAJuG/MViRgCo1Wr6atlX3L249OqSjMYagIcAsPmoXyg8BMDb6LfciNlpqhM9+vjINrap1fx2HOQhAGRI8tNGduef6RL+MtC8Ob99nGNj2YSuDh3Y0pXff8+WF01MtL6N5jCQBFih10/4Np4tvHLq2SmEx4fLaCAPTCQBkj2s8zeHmSRA7WQ/SSv7SYmZJMB7YffwKPwRAKB+ifoonFPcemirYiYJ8FLIJQS8CwDALu/7ptg3cllqGB5JgFZd1y8FlSqxz5GJJMA/T/8pfUEfPjAMv5K948ebTALMskl+Wti18585cyZq1qyJnDlzokCBAujYsSMePXqke5CLC+vQhRATky4EihUDrlyRzmix6AkA5uNH7FwegcrvABWpsP/RfpkN5IERAeCckp69Les6f3OYEADaZX0lr+wnJSYEgE5hH28rZflLgQkBoLN7Xy0Ld++zFiYEgM0y/C3FhAC4+/4u1gRYqaCPlJgQANqV/Op51fusK/kZRUCYwOa0bNmS1q5dS/fu3aPbt29TmzZtyMvLi2JjY3UPNBH658L+JqYG6Lff5OieYfSmAMKygSoPBbXa1Epuy/ijNwVwsVpecpnIhtdik2LNny83BqYA/h1ejQsRPgl/IreF5tGbAlCXLk0Np5biQv6hMaFyW2gevSmAmAF9yGmyAxemTUzhsZJATgxMARxe+mvmms4zMAXQeVkTrg9/X/hbbgvNozcFEDHpN7mS/LSRPexv185fn7CwMAJAZ8/qZZUmJRF5eopz/nnyED2y0XwVXwwIgK+HO9Gn+E9yW8YfPQGwvyzIZSIoLjlObsv4oScAUhnQd51AuWblsr9kP2PoCYDg3KBiv4Aarm0ot2X80RMAS2qAmEmgSf6T5LaMH3oCIN6ZoSZ97XSu3xh6AuBKUZDneCsW9LEGegLg96ayJPlpozh/IQQHBxMACgwMzPhh377CnX+ePEQBATbvBy/0BEBgftC2u3aytpwvegLg1+aZyPkTZRAAyQ6g7v/Vk9sqYegJAL8yoEVXF8ltlTD0BED3Hg7WX94nJXoC4KM7qO1qO67fYQg9AbCwJmjz3c1yWyUMPQHQfFRuWyf5aSO787frOX9tiAhjxoxBvXr1UKlSpYwHCNmCEwDy5GGTcKpVk8Q+yUnLAYj/ujIAwFkN5HbPLbNRAknLAUh2dQIAFHXLB3cnd5mNEkBaDoBqyGAAgAMBrUu2kNkogaTlAEQWZ6sGZoezztbRmYK0HABV2vR+82KNpNuF0Bak5QC8b8rm8zgSMLn+nzIbJZC0HIDInM4AAC/3guhZqafMRglk/Hi8mziaezm2xqgsl+SnDUPEOxNb1pTtESNG4NChQ7hw4QKKFSuW8YDkZDaLPypK5+1oAJ4AogB4aN60d8evTVISnm5dirCKJVC7Zie5rRFF0ounuH10Hb7oMQQFcxu4d/YOEV4f3IKXDjGo3XowHJhMo5k5KCYGARtnw/Pbjihdyk5XK5jh3c2zeHb3LGp9/zucnFzMn2BvqFQI3DQXTuW9UcGnjdzWiCI85DGC961Blb5jkc1Tws17bEjQ0Y1QJcSjcsfB/FYOWAfZM1UzhfP/6aefsG/fPpw7dw4lS5Y0fmC/fsCGDTpvGXT+I0YAixZZx1gFBQUFBQXTyO787XoIQ0QYOXIk9uzZA39/f9OOH+Af+l+8GJgxw3IDFRQUFBQUMiF27fxHjBiBTZs2YcuWLciZMyfevXuHd+/eISEhwfAJpgr+5M4N/Pxz+uv//U8RAAoKCgoKWRK7DvsbK+Cxdu1a9O/f3/BJeqF/Lux//jw86tUDZs9miz9omD6dLf6goKCgoKBgG2QP+9u18xfFoUNA27bcy+jcueEZEYGoqCh4eKTN+isCQEFBQUFBPmR3/nYd9hdF8+ZAfnZZE/LkYev36/Pbb8Dff6e/VqYAFBQUFBSyEE5yGyA5Li7AwYPA3r3AgAFAwYKGj/vtN/ZfTQTgf/9j/1UiAAoKCgoKnzmfX9hfj+joaHh6euqG/bVRpgAUFBQUFGzL5xf2P/joICacmoB3Me+kbto6fG5TAKGh7KqGI0fYIpYKCgoKCgp6SOr8X0W9Qrtt7TDzwkwUmVsEzTc0x+pbq/Ep4ZOUl5EeGwuAn478hK+WfYXA94HSN16/PrBgAdC6NVvaddw4djtOGYXA+9j36LmzJzbf3SybDdZk1/1daLK+Ca6/uS63KZIRFBaEr5d/jWEHh8ltiiScfXEWX/z3BdpsyZyV9bS5/uY6is0thpLzSyIqMcr8CXZKqjoVffb0gds0N/TclclKBWuhUqsw7vg4uP7litILSkNANF1WJA37h0SFwOs/rwzvOzk4oXmp5uhRsQc6lu8ITzcja/GtgNmwvzY2mAJ4+ukpvlzI7rWewzkHAocH4otcX0h3gdKlgWfPMr5fogTQrRv7U7OmTctaVlxSEUEfggAAj0Y+Qtm8ZW12bWsTFBaESksrgUDIny0/wsaFyW2SxbyMfIlKSyshNjkWAHB/2H14F/CW2SrxHAk+gvbb2iNVnQoAuDrwKmoVrSWzVeLYfHczftj/A1LUKQCAvxr/hYkNJspslXAefnyIXrt74fa72wAAR8YRqZNS5TVKBPfC7uHHAz/i2ptr3Hs8/14+r7B/cc/iqJi/Yob3U9WpOPLkCPrv748C/xZA+63tsfnuZsQkxUh5ecuxQQTgwccH3O+xKbFotK4RXka+lO4CY8cafv/lS+DffwEfH6BkSZtFBALfB3KOHwCmnZtm1evZkuikaLTb2g6Upos/xH9AREKEzFZZxsvIl2i4riHn+AHgUfgjGS2yjIVXF6Lt1rac4wdgf987PEhIScCgA4PQZ28fzvEDQB73PDJaJRw1qTH/ynx8tfwrzvEDgLOjs3xGiSAxNRF/+v+Jr5d/reP4ASB/9vwyWSUMyef8B3490OTnyapk+D32Q5+9fVDg3wLosqMLdtzfgbjkOKlNEYeVBcCzCN1R+cuol2i8vjFeRb2S5gK9egHOZv6QbCgEpp6bqvN6271tCIkKkfw6toaIMGD/ADyL1L2fp1+clskiy3kZ+RKN1jfCyyhdMar/OjOQqk7FyMMjMeroKKhJrfNZXIqdfNfw5OHHh/BZ5YNVAasyfObhaiaaaUe8jHyJZhuaYfSx0UhMTdT5LH+2zOEwAXYKqeqyqph2fpqOENOQWXZfldz5d67QmfexiamJ2PNgD3rs6oEC/xZAj109cP7lealNEo4VBUBweHCG955HPkejdY2kcYq5cgEtBGw7qy8E/vgDiI01fx4P7r6/i11Bu3TeS1GnYNaFWZK0LydzL8/F7ge7M7x//OlxGayxnBeRL9BofSO8iHyR4TNDz6w9E5UYhbZb2mLx9cUGP49OiraxReLZfHczaqyogcAwK+QH2QgiwtqAtai8tLJRcZzTNaeNrRJOZGIkBvsNRqP1jfA4/LHBY3K75YaTQ+ZYQS+58/fy9BI1nxafEo8d93eg0fpGGUbHsmAlAfD4k+GH5nnkczRa3wivo19bfA10E7lf+8uXwKxZ6TUPLGTq2akG318VsEqafsrE2RdnMf7keIOfZUbn/yLyBRqvb2zQ8QPAk4gntjXIAp5HPEedNXVw7Okxo8dkhiQ57TB/ZotUaPMu9h06bOuAAQcGICbZ+HRLdufsNrRKGESEnfd3osLiClh5a6XJY/NlyzzbHFulwl/XCl1Fn+vk4ARXR1cJrbEAKwgAU6OoZxHP0GhdI7yJfmPRNdChg/nQvym8MiZtCuXOuzsGR8YAO/UjavQ/fz5bxKlwYWDOHOCNhf9PIngT/Qbdd3WHilQGP38e+RxPPz21sVXiMef4gcwz8r8Ucgk+q3x0ckwMEZVk387fVJg/M7EraBcqLakEv8d+Zo/N4ZLDBhYJJyQqBB22dUD3Xd3xLtb88vW82fLawCppsIrz7+LdRdR5Tg5O2NplK4p6FJXYIguQUAAkpSaZnT99GvEUjdc3tkwACA39a9OvHzB6tPhrp6E/16/Pylsrhfdx6VIgJQV4945NbCxWDKhXjxUFNhACyapkdN/VHWFxpjP6M8von4/jB9g5/2RVsm2MEsnmu5vReH1jfIj/YPZYex75fw5h/oiECHy35zt029kN4QnhvM7J7mJfI3+VWoVF1xbBe4k3L/GiIcuP/EvlLoWvC38t6BxnB2fs7LZTUM6AzTAkAGbOFNzMs4hnGZKPDBH8KRhNNjTB25i3gq/BISb0368fsHo14Ogo/roAbr+7jT0P9pg8RtTov337jO9dvMiKFRsIgXHHx+FSyCWzx514dsIq15eSF5Ev0Gid4Tl+fdSkxvOI59Y3SgREhMmnJ6PP3j68BYo9jvzjU+Ix8MDATB/mP/bkGCotrYQtgVsEnWdPYf+3MW9Rb209/HTkJ51VL3zI8s4fEBb6d3Zwxq7uu9CxfEdrmWM5+gJgwgTBAsBYkoixYxuvb4zQmFBB1+AQGvqXyPEDwJSzU3gdJ3j0/8svpusTWFEIbAncggXXFvA69tTzUzpLy4yyfTtQpgzwww9AsO1C6xrHLySL/8kn+5v3T0hJQK/dvcxGmfSxN+f/LOIZfFb5YHXAarlNsYg9D/bg283fihq02JPz9z3jiyuvr4g6N5+74vx5h/4dGAfs7r4b7csZGNXZGxYKgOBPwr7gNQKAz1xTBoSE/tu3l8zxB4QGYN/DfbyOTVIl4e+Lf5s/UEPhwmwFQz5IKATuhd3DIL9BvI+PTormV+1v+HDgyRNg3TqgbFmgWjV2SsmKQkCM4wfsz/nHp8SjyYYm2H5/u+Bz7S3sP+rIKNwLuye3GRZz8+1N0efaU9jfp6iP6HOz/Jw/AJTNWxZVClYxe5ya1Dj65GimKYmI335jM+I1CBAAQkb+Gh6FP0Lj9Y0RHs9v7kwHvqH/ixeB+/eFt28AvqN+DSturhA2UhAznaERAl5ewIoVgk6NSoxC5+2dEZ8SL+g8XvP+X3yh+/rOHXZKyUpC4G3MW1GOHzAjXFUqoHFjoFQp4J9/gHARz6pA9j7YK3p0Zm8j/9K5S8ttgiT8Vvc3dCrfSdS59jTy//HrH3G8z3FRlUiVsH8apkL/zg7OYNIqHC65sQQ/H/058wiA8eNFCQChI38NDz8+xKpbIjJ/zYX+86U9qOHhQNOmwN27ouzTEBAagP2P9gs6J0mVhNkXZ/M/oUsX8aWJ1Wpg3z7ehxMR+u/vL+q+8Zr3nzzZ+GdWEAIrb64UXbDH5Mj/8GHgzBng+XNWHBcsCLRsCaxaZTUhUNerLop5FBN1rsmR/7x5bB/evxdpmXDmtJyDtR3WolTuUja7pjXwdPPEnh57cK7/OdQsUlPQufY08geA5qWb4+7Qu5jZdCayOWfjfZ7i/NPo6m3Y+bs5ucGvlx82dNrACYCF1xbil2O/SCYAFi9eDG9vb9SsKewh5I0IASBm5A8A2ZyzoXbx2sJPNBX679cPePSILe4DAB8/WiwAfM/6ijpv+c3l/HMbhIT+9XFzY4sY8WTvw728pzD0ufL6ivnwcsuWgLn9JgDJhEDTUk1FL6kyKYC++Ub3tUoFHD8ODBpkNSHwRa4v8HjkY6xuvxpVC1YVdK7Rkf/u3cCYMWz0onBhoFkzNlL0wfwKAktwcnBC/2r98XDEQ2lEQFAQO5X3339AvLCIlRTUL1EfVwZewdYuW1HCswSvc+xxqZ+rkyt+r/c7Hox4gFZftuJ1Tl53JewPAKiQvwK88+tucODm5IYDPQ+g5Zct0adKH6zruI4TAPOvzsevx3+VRACMGDECQUFBuH7dijutCRAAscmxgsLbDowDmpZsiqVtluLZqGdoUKKBOBsNhck1yX158gDHjkkiAG6F3sKBRwdEmZiYmihs9C8m9O/mBvj5CRIO+iVIhaAiFc68OGP6IFdXwysYTKEtBGrUAB48MH9OGvW86uHV6FdY22EtWpdpLagS2YvIF8az6fPnBxo1MvyZFYWAu7M7Bnw1AAFDAnC2/1l0qdAFDoz5rzSjoszNLf13IuDUKWDIEJsJAWdHZ04EzG0xV3xDrVuzz/ovvwB58wI9e7LCxoZCwIFxQM9KPbG0zVJex2cI+wcHA0WKAMWLs9EYKwswU3h5esHRgV8+lDLy10I79O/u5I6DvQ6ieenm3Ht9q/bFmg5rOAEw78o8/Hbit89uCoBvwlTNIjWxou0KvPv1HU72PYmhNYaiYI6C4u3TD/3rZ/V7ekoiAIQu7dFn492N/A8WGvrXOP5mzQTZ1KtSL+zpvgfDagxDzSI14eLoIuh8XvP+3bsLalOHmzfZ7ZsFkNs9N/pX649DvQ8hbGwY1nZYi+qFq5s9T01q08sC+/Y1f3ErCQGGYdCgRAPs6r4LLUu3NHt8THIMVGoDRZpatWIFsSG7bSgEnB2d8TwyfWllLtdcwhrQjiYlJrKrSrp2BQoUsKkQUKlVmOCfvitq81LNjQrODGH/WbOA0FDg9Ws2GlOoEPv/vny5zYWA3yM/HHx8EABQOEdh+Db0NToVoDh/LYbUGIKiOYuiQPYCONj7IJqWaprhmP7V+mNV+/Q57X8v/4s/Tv3xWQkAY87fycFJJ2xZq2gtDKo+SLqdoXLlAn7/na2MN2KE4ax+CQRAPa96gp2jNnW96vI/WEjoX6TjB1in0qlCJyxpswTXBl1DzB8xuDX4Fpa3Xc5r1Hz1zVXzF2nRgl/o3xAODqwQEolGCFQskL4TZ/XC1Y32zaSA7dABcBJQ01xfCPz4I/ueBbyKesWV9S2YvSCWtVlmNOnYYKlZBwfzIsYGQuBN9BusuMkmpmZzzob7w+8Lmw7480/D78fF2VQIbLq7idu576tCX+Fon6O4P/y+waTADCP/Dh10X6vV7P/70KE2FQIJKQn4+ejP3Ou5LedicqPJeDjiocFp7cyyqQ8ANqmJ549oVGoVJaUmmT1uxY0VBF9wP3+c/IPUarUll6aoqCgCQFFRURa1w4tZs4jYgCH7M2MG99G5F+e4fjlPdaY2m9vQuoB19Cn+E0UnRpPrX64EX1ChfwuRSq2S3raUFPPHREYS+fik258vH9GdO7wvEZUYRc8jntPziOf07NMzevbpGT399JQarWvE9f366+sUHB5MweHB9PjjY3r88TE9j3gu/D4vXKj7f23s55tviBIThbVthgcfHnD96bC1A918e5NW3FhBgw8MpurLq5PzVGeCL+jnIz/za7BPH3590f5xcCDavNniviSmJJLnTE+CL8hjpgclpCRQeHw4rbm1hlptakVOU524vt54c8N0Y99+K7wf2j9BQRb1ZfyJ8ZytU85MISIitVpNZ56foS7bu5DDFAeCL8hzpiclpyYbbuTSJXG2OzoSNW1KdOyYRX0gIvrp8E9cP347/hv3fnJqMq0NWEul5pdK/3t6cz1jA/HxRDly8Lc9e3aiHj2Idu0iiouz2H4iorjkOCo6pyhn56lnp3Q+P/fiHNVcUZPgC3Ka6kSvIl/pNqBSERUowO/voGlTomXLiMLCJLFdG9/TvlwfGq9rnOF76viT41R2YVmCL6jJ+iZCmhbie63yYxPnL4Rl15fpCICJpyZaJABs6vyJTAqA40+O0457OygyITLDaR22duD6fO7FOdvYaggLBYAhWm1qxfXtY9xHaex8+5aIYfh9ubVrJ6kA2HRnE9efaWenZfg8MSWR3ka/5f/cHjggi+MnIvJ75Mf1pc+ePhk+D48Pp62BWzN8eRtkzRrxjv+bb9gvfJHEJ8dTnr/zcOL6Xcy7DMe8iHhBS68vpTvvTDzPKhVRsWLi++HgwP4NieR11GtuIJBtejYKi83o0JJTk8nvkR+deX7GeEO9eomzP3t29ty3b0X3gYho2tlp3HPVdktbg8eo1Co6//I8PfjwwHAjP/8s/P9eQiHw9NNT7l44TXWi+2H3DR6XlJpEN97coMQUQd8xivM3xJJrS3QEwOTTk0W3ZXPnT2RSABhj452NXH9HHR5lAyNNILEA0Hb+4fHh0tnZoIHhLwE3N6J//iFyd7eKAPjl6C9cf44EH7G8wcREIg8Pmzt+IqK+e/tyfdn/cL9ljYWHEzk5CXc4NWsSRURYdOlVN1dx/fh+z/eW9WP0aPHO38uLKMl8lNMY2qP+ccfHie/Dnj3i+wAQDRgg+tKhMaGUY0YOgi/IcYojBYWJjOhcuCDefgcHogkTRPeBiKjtlrbcvfj12K8WtWUA2Z2/1ef8xTCs5jAsarWIez3l7BSj28PaJSKWAbYr246bM9/9YDevPQCshkRJgFbHUNa/Zo5/7Fjg0CHA3Z1938+PPT4pyeLL3nh7g/u9RpEaFrcnKOt/yBCgd2/Lrwl2oynNUkYPVw9eyXImyZNHeG5FzZrs3H+uXKIvS0Q6pZd/qvWT6LYAiE/CLFgQOHKEza8Rgf5c/7g648TZAQDffgvksGD5nAVLpH3P+HI18QdXH4wK+SuIa6h2baCoyE3e1Gpg4UJWCohAO8mvSM4imNxwsjg77Bi7dP4AMKLWCMz/dj73evKZyZh2bpqMFglEoADwdPNEi9Lsmvw3MW9w9TWPZDFrIqEAIIj7AzSLfta/fnJf48aSCwCVWoWAdwEAgBKeJaTL7uXrcJYvBzZtkuSSJ56dQHRSNACgQ7kOcHWSYCttIY5TAscPAOdensPd9+xz+U2xb1CzqIW1PXx82LLQQihYEPD3B7y9zR9rhL8v/o0kFftsjqw50rKkX3d3oF07ceeOHcuKTBEEfQji9rzP6ZITvo18xdkAsAmYXcVvD4+ffxZVEEw/yW9OiznI6ZpTvB12it06fwAY5TMK81rO417/efpPzDwvfDc92RAoALSXRe4M2mlNy/hhhQiAZkmnJBQunF7EyFhWv8QC4HH4Y25UU72I+SVyvDGV9e/gwP6/A+yIpl8/SQTAjvs7uN+7eYuonWAIvln/rq7AmjUWO36ALRCmYVStURa3J9jpSOD49Uf9Y+uMFd0Wh5h6GGPHArNni66i+duJ37io5e/1fkeB7AVEtcMhpg8AW857qrho8eyLs7mllo2/aIweFXuIs8HOsWvnDwCjvxmNOS3mcK8n+E/A3xcEbAYjNwIEQPty7eHswK7J3xW0i03KkBsJBIBV+7F2Lfv/e+2a8ZCzhALgZmj65iU1CksQ8tdgLPTv4ABs3AicOAEMG8a+J4EASEpN4koxe7h6cFEni+Eb+k9KAjp2BEJCLLrcq6hX2PtwLwB2DTbfDcXMwjeC4e4OnDxpkeMHJB71axAa+rfQ8Z96dgqHgg8BAIp5FMPob0aLakcHMaH/0aOBuXNF9eNZxDPMvMB+Pzs5OGFR60VgxJYTt3Ps3vkDwJjaYzC7WXoFuN9PUuxELwAALr5JREFU/Y5/L/0ro0UC4SkAcrvnRrNS7BdnSHQIrr+1YnVCIUgYAZD8D6lwYfb/t3Jl08dJJAC05/slHfkDGR2OxvH37s1+kS1eLJkAsErIX4Mpx1m1KlCyJPv706fsfbFAACy5voQbaQ6rMcyiWhM68A39JySw90UtPkfHKqN+QFjov1s3ixy/Sq3Cr8d/5V7PaDJDUE18owiNwljg+AHg56M/cyJstM/oDBVqPycyhfMHgHF1x2FW03QHOu7EOMy9bEEJTFvDUwBoF47Yed8OQv8aLBAAVpvzF4oEAkB75M+nMp4gWrRg/58BXcevQUIBoB3y717RgiqDhjAW+q9Zk90A6Nw54Msv2fcsEADxKfHc/LKLowsGVx9sgdF6mHM6np7pDmbZMraAlkgBYJVRvwa+YXM/P3bqQiSb7m7Cnfd3ALAFfb6r8p3otjLANwpTsCAwaZJox6+f5Dep4SRR7WQaBCwNsAumn5uuswxw3uV5Jo+XZamfKcwsA/wY95EcpzgSfEFf/PeFxUWOJEfEMsAWG1tw98tQjQOb4+8vahlgqiqVsk3Pxt0bq7B/P1Hr1kR+fsaPUauJhg3TXda0cSPvSySmJJLHTA+usI/A9cn80C/4o7+cLySE6Msv0z8vXZro1SujzRli5c2V0i3vM4Sxgj8FCxLdv88uuXRwSH9/6FDBtQr4rOu3CHMFf0qXTv/d3Z3o5EnBlzBX0MdiVCqiokX5LfGrVUvUstH45Hgq+V9Jrg9bA7dK24eMKEv9hDKh/gRMbZSeyPHLsV+w8OpCE2fYGWYiAHmz5eVKIL+IfIFbobdsbaFpREQAyB5yF7QRGQF4FP4I8SlsKVRJlvgZon171ra2bY0fY2EE4PjT41zIv2P5jtKG/DX07Jn+u6Gs/mLFgNOnRUcAiEgn0c/i5X2GMBT6107u692bjc44pH2NiogAWHXUD5gO/Y8dC9y/n55rkpDAHnvqlKBLzL08F29i3gAA2pZtiyYlm1hicUbMRWH69GE3MALY3J+WLYHISEGXyCpJfjoIUAp2habsovP/QO17gJafnG3wOLsb+WswEQHQLnM8/sR4GY00gYAIQPMNzbn+RCXa0X0QGAFYf3s914+Z52fa0FAjiIwAfL/ne64ffo9MRBgsITWV6PffiUaNMj0SExkBOPP8DNeH2qtqS2e3PtoFfzQjfn1ERgCsPurXYKjgz9ix7PNDxBYlat9eVAQgNCaUsk/PbnlBH3NcvGh4pD96NNuPwED2O0hEBIBvJT+JkX3kn2mdPxHRn/5/0sM87M1OBeh5vcpEW7YQRUdzx9it8ycyKgDCYsO40H/p+aXtL/SvgacAaLahmX06fyJBAmDU4VFcP44/OW5jQ40gUABoh/w9Z3paJ+QvFBECoPP2zrYJ0b58SVSqFJG3t2HHr0GEADBWw19y9EP/2o5fg0gBMMRvCNeHYQeHWakDZDj0r3H8GkQKgHZb2nF9GHtsrPX6oIvi/C1BrVZTfHbXjGrQzY2oUyeiLVso6vVr+3X+REYFQNP1TbkHMiA0QF4bTcFDAGg7/+jEaCMNyQhPAVBndR3rlCm2FAEC4MDDA1wf+u7ta2NDTSBAALyIeMFt0lP438LGN+mREj4CXIAAsNmoX8OyZUQlShBNm2a8LwIFwP2w+9x9yDkjJ72PfW8d2zWMHWvc8WsQKAC0/x6KzCliy+8nxflbinro0IzOX+snytWVdf6rVulEBOwKAwJg6fWl3EP5v1P/k9tC05gRANpCxi6dP5FZAZCiSuGS/Ur+V1JGQ43AUwD02dOHuxcHHx2UwVAT8BQA2rv3TT0zVQZDTcBTANhs1C8UAQKg9ebWXB+mn5tufdtiYoh++41o5UrTYoynAJAhyU8bxflbzL17pp0/wDp/vYiA3QkBPQEQPXkCp6rLLixrv6F/DSYEgLbzj0mKkdlQE5gQAIHvA7k+dNvRTWZDjWBGAOiH/Plss21zzAiAuOQ4bvc+l79cDO7eJztmBIDNR/1C4SEATjw9wf09FJtbjOKSpdkKWDJ4CABz2/VaGdmdf6bL9s9AxYpABZ4bRyQmAnv3slm6BQoAnTsDu3ezj4fc6K0CyDllBpYFlgDAlpS9F3ZPLsv4YWIVANnLOn9zmFgFcPOtFdf3S4WZVQD6Wf6SFcSREjOrALYEbsGnhE8AgJ6VeqJgjoJyWWocM6sArJ7hbykuLsDOnUZXAajUKow9nl6ISLKCPlJSqRL7HOVL23tDbxVAVqrkZ4zM7/wBcfWfNUKga1dg6VLpbRKDngAYtOs5fj/P/r4raJdMRgnAiAAo9SqWO0TS2v7WwIgAuP0yfaMlqy3zkwITAmBHkBVq+VsDIwKAXr3CgqsS7t5nTYwIgDeRIdap5ic1JgSAVQv6SIkJATD66OgsU8nPKALCBPaLidC/Ttjf2M8//8jdA130pgB+bwqqsKiC3FbxR28KICKnM1UeyobXYpNi5baOH3pTAOeq5iaXiWwfPsV/kts68+hNAagdHGhgdzf7DvnrozcFEF+iCBX7xQbL+6REbwrgfOtKxEyyw7l+Y+hNAajd3an7kLzWK+hjDfSmAD5VKUue42VJ8tNG9rD/5+H8iYgqVBDn/Fu3JkpIkNv6jOgJgJ9bwlbrT6VBTwCEZQN9+RPsb27QFHoCYG85UOn/SsltFX/0BEAqA+rcHdRvbz+5LeOPngAIzg3KO87myVmWoScA5vnY6Vy/MfQEQJwTqPYAUNstbeW2jD96AuBKUZDLRFmfI8X5S8akScKdv706fg1aAiDcDbT25mq5LRKGngCY9w0oIcWO/78N4e9PKnc3rg/j/mkht0XC0BMAtwrZYZa/OfQEwJ8dPGyzvE9KNm8mlQPDibDJu36S2yJh6AmAveVhvYI+1iIwkJLyeHJ9+N+oSnImUivOXzKMhP6NOn97d/xpJPw7iyKzO9L6+h4UHB4stznCiYykN41r0ofsDC2e1lFua0ShPnWK3uZ3p1vFnej6k/NymyMctZpChvehSDeG1vesQCmqFLktEk5ICD32LkivPRk6uXeu3NaIInTVfHrv4Uhnq+Wm8LiPcpsjnKQkut3qa4pwAx35s5fc1ogi6sZFelzEjZ4VcKZnQZfkNEV2588Q8c7Etv+UbW9v4MEDnbeiAXgCiALgoXmzeXPgwAHAzc229olFrU5PHMqkqFWpcHA0sNNbJoFUKjAODqJ3DLMLPoPnKNP3IbPbD2T+Pmh8nrx/y7J/kWTiO2gAvln/nz6x2f6Zhcz8h5ZGZnb8AMA4Osr9ZWE5n8FzlOn7kNntBzJ/Hxgm8/8tS0Amv4t6mNv32SVtXfPNm+ze6QJ3flJQUFBQUPgc+Lycv6mCP82bA5cuAfnTCmpcv64IAAUFBQWFLMnn5fwB46H/TZuA6tXZvbgVAaCgoKCgkIX5/Jy/fui/eXP2X01yX6VKigBQUFBQUMjSfH7Ov2LFdIffrh1X11wHRQAoKCgoKGRhPq+lfhqSk4Hnz4GyZREdEwNPT09ERUXBw8ND97h794AmTYAPH9jXNWsCx48DuXLZ3GQFBQUFhSyD7MsNPr+RP8Bm9ZcrZ345hxIBUFBQUFDIgkjq/IkITdc3RZE5RfD7yd/xOvq1lM1bB5kEgEqtsk7DS5awfWncGDhzBlBZ6ToKnz1We0ZlIjQmFIkpmai+hwkefnyIJ5+eyG2GxSSlJmHz3c2ISIiQ2xSLUKlVWHlzJW6/uy23KbyR1PnfeX8H/i/8ERobir8v/o3i84qj/tr6WHh1IUJjQqW8lLTYUACo1WoU+KcAnP9yxh8n/5C8ffj6slvpnjnDCoCiRYHhw2UVAuvvrEeOGTlQd01dCJhmyhQQEVpsbAHnv5zx67Ff5TZHMv70/xPOfzkj7+y8SFGlyG2ORRARvt/zPYrMLYLcs3MjNjnW/El2iprUGHpwKCosroAyC8vgwqsLcpskmptvb6LgvwXRZ28flFtUTm5zRHPn3R2U+K8EBh8cjOorqmcaISOp8y+XtxwcGUed9y68uoBRR0eh6NyiaLy+MZbdWIawuDApLysNNhIAl19fxof4DyAQZl2chbUBayVtH1Wq6L5+/x5YulQ2IaBSqzDqyCjEpcThUsgl7H6w2ybXtRWLri3CiWcnkKpOxZLrSz4LcbPu9jpMOz8NBMKnhE84+/Ks3CaJJjE1EX329MGmwE3c6yuvr8hslTjC4sLQalMrLL+5nHvv5LOTMlokjhRVCqaenQqfVT6ISooCAIQnhMtslXASUhLwx8k/UGNlDbyJeQOAFWd26d8MIKnzd3d2R6fynQx+RiCceXEGww4NQ5E5RdB8Y3OsurUKnxI+SWmCZdhAAGgeEg0/HvgR626vk6x9/Pmn8c9kEALb7m1DdFI093rWhVmfhYMEgGtvruHX4+mj/URVIh6HP5bRIstZd3sdBuwfoPPe+9j3MlljGWFxYWi6oSm23NsitykWc/bFWVRbVg3Hnx3Xeb9UrlIyWSSOBx8eoM6aOph8ZjJUlP69k9Mlp4xWCcf/uT+qLKuCWRdnIVWdqvNZ4ZyFZbJKGJIn/PWu3NvsMSpS4eSzkxjkNwgF/y2I1ptbY93tdYhMjJTaHOFYWQDoOwcCYcD+AdhwZ4Mk7aNePaBgQfPH2UAIqNQqTD03Vee9m6E3ceLZCcmuIRcf4j6g646uSFHrhsSPPz1u5Az7Z23AWgzYPwCkt7DnacRTmSwSz/2w+/BZ5YNLIZcyfBaVGCWDReJQkxrTz01Hkw1NEBqbcerUIZPU2VeTGvMuz8PXK77Gjbc3MnyeL1s+GawSzqeETxiwfwCabmhqMOfC2cE50wgZyZ+cb7/8Ftmds/M+PlWdiiNPjuCH/T+g4L8FMdhvsPxzjFYUAMGfgjO8RyD039cfm+4aqEkgFEdHoGtXYedoCwEvL7YMsgRsvbfV4Eh4ytkpmXr0r1Kr0Gt3L4REh2T4LLMKm7UBa/HjgR8zOH7A8DNrzxx7cgx11tTBi8gXBj/XhJrtnbC4MHy76VtMPD0RalLLbY5oXkS+QJP1TTDm+BgkphpOuMzuwt9nyAERYdu9baiwuALW3jY+VZs3W14wmWTTIMmdv7uzO9qUbSPq3GRVMlbeWom77+9KbJUIrCQAjIWFCYR++/ph893NFrUPgP/uhoZ4+xZYvdpiE1LVqfjr3F8GP7sUcgmnnp8S3qhKBaxYAdy5Y6F1lvHn6T+N2n/6xWn5xatATDl+AJkqq3zxtcVovaW1zlSTPplh5K8J82dWMQmwDnP1rdWovLSy2byRHC45bGSVcF5FvULbrW3Ra3cvs/P5mSWCAVhpnX/XCgJHnlpUzF8RlQtWltAaC7CCAAgONz6KUpMafff1xdbAraLbB8A/9G8IFxdgwADzx5lha6DhUb8G3zO+wkf/bdsCQ4YA1aoB5csDM2cCT2zrmPY/3I+ZF2Ya/Tw2OTZTJZSZc/xA5nD+qepU/HT4J4w8MtLsKNmeR/7mwvyZhdCYULTb2g4D/QbyWl0hJFpsK1RqFeZfmQ/vxd44HHyY1zlZ3vm3KtMK7k7ugs/zzu+NU31PwcXRxQpWiURCAfAp4ZPZrFY1qdFnbx9su7dNhLFpiAn9A6zj37sXqFtX/LXBfhHrz/XrczHkIvyf+wtrOExLdT96BEyYAJQpA3z1lU2EQHB4MPru62v2uMwy778mYI1Zxw8AH+M/2kc+jhGik6LRfmt7LLq+iNfx9jry/1zC/Dvu70ClpZVwKPgQ73PsLex/9/1d1FlTB6OPjUZcShzv8/K657WiVdJiFeefwyUHWpVpJeicSgUq4XS/0yiYQ+SI1ZoYEgAtWwoWAKZG/dqoSY3v9nyH7fe2CzRUC6Ghf43jb91a/DXT2BK4hddo0feswNH/b78Zfv/2basLgbjkOHTZ0cVkOFmDoFBtUhIgQ/7DmoA1GHhgoFnHr8FeR/8vIl+gzuo6OPLkCO9z7HHk/zmE+eNT4tF7d2/02NVD8Couexr5H3h0ANVXVMe1N9cEn5vlR/6AsNB/5QKV4d/XHwWyF7CWOZajLwCuXRMsAIQsA9MIgJ33dwo0NA0hoX8JHb+puX59Lry6gNMvTvNvvGNHQH9/Bn2sIASICEMODkFgWCCv46+/vc6v0EfHjuxuk56ewPjxrO02EAJCHT/AX7jaksshl+Gzygf3P9wXdJ69Of8tgVsyfZgfAOZcmoOt98RNWdqT89/9YHeG5Xt8UZw/gDZl28DV0dXscS6OLtjceTPyZ89vLVOkQyMA8qXdYIECQGjWtIrYrPLdQSIK4wgJ/ffqJYnjB4DNdzcLGiUKyvx3dWUdJl/0hcCsWUB8PP/z01hyfQk2B/JPxFSTmt+Uxvnz7L8xMcDs2ayN5coB//uf1YSAGMcP8Bj5Jyayq0ZsxMOPD9F4fWNRBVXsLey/9MbSTB3m1/BFri9En2tPYf/f6/6OUrnF1U9QnD8AD1cPtPyypdnjklXJ6LKjC97GvLWWKdJSqRJw+rQoASCmAIyKVOi5uyeuvr4q+Fzeof/169kRsoUIGfVrOPfyHM68OMP/BLErGW7fBv74Axg6VNBpl0IuYfSx0YIvx2vev127jO8FBwMzZlhFCJx6dkqU4wfMCNfQUDYiU6gQa/OCBcCbN8aPl4Db724jSZUk6lx7G/n/Vuc3eLiaiWhlAr6v+j3299yPcnmFl+q1p5F/hfwVcH/4fUxpNAVuTm6Czs3yc/4aTIX+KxWohC88vwDAfrE0Xt/Yvuv/ayNSAIhdL52qThW3NM5U6N/FBejfP/31hAkWC4BNdzeJKggz5ewU/gc3b24+9G8KZ2feh36I+4BuO7uJCgEef3bcfETjVzN7AUgsBC68uiDK8QNmRv63bwMpacsbHz8Gfv4ZKFaMff6sJAS6VOiCsbXHinIaRkf+MTFslKhQIWDyZCAkYx0Ha9CuXDu8+PkFJjecnOlFQPty7RE4LBCLWy8WNAq2t6V+bk5umNRwEoKGB6F9ufa8z1NG/mm0K9cOzg4Zv2yrF66Oc/3P4dwP57jwyuPwx2i8vjHexb6T5NqLFy+Gt7c3atasKUl7GRAoAIhI1Mjf2cEZXSp0wcCvBwq30VjoXzPHv3YtGwrXYIEASFGlCB71azj78iz/0b/Q0L82NWoAc+bwPnz7/e2iI1IvIl+YF0KVKrFOnQ/aQqBsWVYIBPLLQdAwstZI9KnSR9RKHJPOv0ULwN1AmxcvWk0IODs6458W/+DNmDeY13KeoDCt0ZH/mjVsfsj798DUqWzBqzp1gHnzrC4Ecrvnhm8jX2lEwJQpbC5JuXLAunU236Lc2dEZw2sOx5OfnmBs7bG8zjEY9r9/H3j2TGLrhFEyd0ns77kff9Tjtwmb4vzTyOWWC81LN9d5r2aRmjjZ9yRyu+dGcc/iON3vNErmKgkAeBT+CE3WN5GklviIESMQFBSE69evW9yWUQQIgPdx73nvJubq6Ir25dpjY6eN+DDuA3Z13yU+GVI/TK6f3Dd+vCQCYOu9rXgWIf4PVZBwEBP6r1EDOHECyJWL9ykNSjRA/mzic1FOPDWTuc0w4vry5AkrBKpUATZu5H1a3mx5uWdqR9cd6OrdlbcQ+BD/wfiI2dER6GtmCaSVhICnmydGfzMaj0c+hl8vP1TIV8HsOUb70bZtxvcuXwbGjLGZENCIgA0dLSj3vXQpu4rk8WPghx/Y6F+7dsCGDTYVAp5unsibjV8YPEMEZ/169vu1dGnA2xuYOxd49coKVponLjlOp/qqqaXofPtrD1i9MHR37+7c7z5FfXD8++PI5ZaLe8/L0wun+51GCc8SAIAHHx+gyYYmmWZnJL4CgO+of2j1oQgbF4b9PfejT5U+8HTztMy+evXY2v2A8ax+CQTAnXeWVd27FXqL/8FCQ/8iHD8AVClYBa9+eYWrA69icevFGFBtAKoWrJph50pj6G/CYpDu3c0fY4qAAMGnZHfJjm4Vu2Fnt534MO4DBlTjV9TJ5Oi/Rw/+BugLgfnzgQ8f+J9vAEcHR7Qp00antKoxYZOkSkJSqoF8gdKlAVORQhsJASLCnMvpEarO5TsLiwQ0bKj7OjkZOHgQ6NfPpkLgQ9wHzDg/AwDgwDhgW5dtaFiiocFjM4z8b2jV/3/wgJ0iK1ECqF3b5kJg+vnpXCnvlqVb4sHwB0anApSRvxZ9qvTBhHoTMNpnNI71Oabj+DWUyFUCp/udhpenFwAg6EMQmm5oig9xln0h2AweAsBQ+NjdyR1dvbtiaqP0gjivY15LO+/n6Ajs3An8+CO7UsFYVr+FAmCUzyj0rNQTDUs0RMMSDdGgRAM0KNEA9b3qI7dbbu44n6I+qFu8LuoWr4s6xeugTvE6aFiiIRa3Xsy/T0JC/xUrinL8Gtyc3FCraC0Mrzkcqzusxu2ht/Hu13dgwDqZPO55ULlAZYOCICSKh2MQEvrX58svgXHjxJ2bRnaX7HgSke7UZzebbTQiYHIKpEEDoICI6NTFi8Do0UDlykCUZYl4/s/9EfQhCABQz6se3v76FnNbzDU4JRCfYmTVx3ff8buYFYXA6Rencf4VuxKkfL7y2NFth9HpACcHp4wN/P678cZtKASmnJ2CmOQYAMCPX/2IHpV64HS/0waTAjP4hTFjDDd65YpNhcDj8Mf499K/ANgR/8JWC1EqTyns77kffr38dJ6t7M7ZM82mPgBYlcnzx+o8/fSUis0tRvAFwRdUeUll+hD3waI2o6KiCABFRUVJZKUJAgOJ8uUjYlOyiGrVIoqIICKil5EvqeicopR9enbqsbMH7by/k2KTYomISKVWUdE5RQm+IJe/XCgyIdL6thpj1qx0+wGiGTMsbrL15tbcPf0Y91ECI4nIz0/XTmM/efIQ3bkjzTXTuPDyAtefgfsHEhFRXHIcXXp1iRZeXUj99vajFhtb0NHgo/wanDiRX1+0f778kigkxOK+vI1+S4wvQ/AFlVtYjtRqNRERxSTF0PZ726nL9i7kPs2dvOZ5UWhMqOnGhg4V3g/ND8MQvXhhUV/ab23P3Zft97Zz76eqUsnvkR8139Cc4AtqtqGZ8UZevxbfB4Do+++J0v4PxaBWq6n+mvpcP7bc3aLz+af4TzT59GTK+3deKjW/FL2PfW+oEfb5EGK3iwtR27ZE69dz31mW8PDDQ3Kc4kjwBWWfnj3Ds5OcmkyLry2m0vNLU7019SghJSFjI998w9/+b74hmjOH6OVLi23XoFarqcXGFty9mHByQoZjElISaMqZKVRpSSVacGWBkOaF+F6r/NiV8yciehL+hHOE8AVVXVrVIodhU+dPZFIAEBH35arPqMOjuD5vuL3BNrYaQ2IB0GpTK+mdf2IikYeH8S+D7NnTf8+XT1IBMP/KfK4/S68vtbzBu3dlcfxERAuvLuT6MvHURIPHqNQqo8+tDv7+4p2mhc/Y009PORFTdE5RSk5NNnhcfHI8papSTTdWt65lAiAsTHQ/Tj07xd2P8ovKG7VVrVaTSq0y3tAff4i3382N6MAB0X0g0hViU89MFdfIvHni7NcIAQtFzK77u7g+eM3z4gZrEiG787e7zaBL5ymN0/1Oo0jOIgCAO+/voPnG5oLLRcqGmSkAY9s9dquYnvi1+4GIoj5SIlESoCEk2+7SVOi/Rg02U9jHh3398SPQtClwV5rdIrX3I69RpIblDQoJ/ZcuzT5fxYpZfl0AO4PSK0hqP4PaODAO/O6b2ND/9OlsDQYLWHJ9CbeMcXjN4XB2NLyk093ZHY4OZnI2LNkVs1ev9CqgAiEi+J7x5V7/2eBPo7YyDAMHxsTXtyV9SEwEdov/Djrz4gwOPDoAACiSswjG1DYSwjeHmP1JgPSpgSZNxJ0PNsnvl2O/cK/ntZxnV4WIpMDunD8AlMlbBqf7nUbhHIUBAAHvAtB8Y3N+JVPtARF1AOoUr8P19+iTo7xqyFsVCQWA2LXlZjH0BadJ7itRAjh2zCoC4GboTQDsMszKBSTYgVJI1n/JkqKdiz6hMaE4/5KdWy6Xt5zlfXF0BDp3FnbO9Onss2UBscmxWHVrFQB2pcygrwdZ1J5op9O5M5ulLhL9uf4eFQUkUepTrRqbEyKGnDnZhEwRqEmNscfTl/dNazxNvNMsVozNpxDLp09sLEAE+kl+ncp3Em+HnWKXzh8AyuYtC/9+/iiUoxAANhu8xaYWdr27mA4CBYAD44DOFdgvziRVEg495r8jltWwQgRAkygnCfpZ//pZ/Z6ekguA2ORYPPjwAABQuWBluDqZL2HNC3NZ/5qR98mTrFBIElfdTpvdD3Zzwqx7xe7SRGWErF6QwPEDbHEpzdr93pV7W14qvGhR4Ttbdu4MbNsmqIiUNvqj/kkNJpmPUJhC7DLSnDmBo0fZehIi2Bq4lRPHVQpWQd+q5nfBNInYCEb27MCmTel/NwIwlOQnWcTSjrBb5w+w6te/rz8KZmer1N14ewMtNrawu9rcRhEoALp5pz/oux7ssoGBPJBAAJBI9W0WV9f0rOB69Qxn9UssAG6/u805zOqFq4s03ACmQv9ffsk6Fk0hHT8/SQTAjvs7uN+1nz2L4Bv6Zxg2U95CiAgLry3kXv9U6yeL2wQgzOlY6PiBjKP+7hUtXAIKCHecGscvcrSdkJKAP06lT9/MaTHHMgEDiIvCZM/O9qNePcGnEhF+OvITUtRsxcqxtceiTN4ywm3IBNi18wfYOsv+/fy5YivX315Hy00t5Q+L80WAAKjnVY8r5nM4+DDvokBWR8IIgOQKevJk4N074Nw548v5JBQAks/3azA2UvvyS/b56d4dOHRIMgEQGhOKC68uAGCdTaUClcRargvf0D8Ru9xs0ybzx5pAf3nfV4XFjVgzwNfpZM8O/POPRY5f8lG/BiGhfwsdPwDMvzqfC5W3+rIVmpVqJrotDqGhfwscPwDsebCH25fDy9MLE+pbHpmyV+ze+QOAd35v+Pfz5wooXH1zFd9u+hYxSTEyW8YTngLA0cERncuzX5yJqYk4HHzYxoaawAIBYLU5fw0FC5oP70kkADQhTUDikT+QMWSucfya5L7GjSUTANoh/27e3aQVZaZC/9OmAcOGsb+r1RYLgAXXFnC/j6o1SnQ7GeAb+o+LY8sbW7DG3yqjfkBY6L9pU+Cbb0RfSr+gz+zms0W3lQG+fXBzs8jxZ4UkP20yhfMH2I2A/Pv6c7smXX59Ga02t/rsBIB2xvWuIDsJ/WuQIAIg6Zy/UCQQAJqRv4uji3SjZQ2VKqXbpu/4NUgkALRD/pI5Gw3GQv/Tp7N7EixeLIkAeBbxDH6P/AAAxTyKoWP5jhYYbQBTTqdVK3blBQA8fcreFxECwGqjfg18Hee+fcCIEez9EIF+QR9J/zb4RmHUaoumwrJCkp8OAtYF2gW3Q29Tnr/zcOsv662pRzFJMUaPt/k6f3OYqQOQokqhfLPzEXxB2aZno7jkOPlsNYbAOgCa4irwhbwFjDRERhL5+AiuAxCdGM2tJa++vLp1bAsLI9qxg8jc8+rvT+Tunt6Hdu3Y2gc8eBP9hutH+UXl+a3hF4p+wZ/p03U/V6uJhg1L/9zBgWjjRkGXGHN0DPdczThneTGqDBgr+NO5M1FyMltrQbuYTunSRK9eCboE33X9ojFV8CdnTqLJk9n/e817Q4cSqUzUDzDAgw8PTBb0kYQ6dYyv63d0TP/d3Z3o5EnBzT/6+IicpzpzhdYef3wsfR90Udb5C6Vqoao41fcUVzL2wqsLaLOlDeKS42S2jCdmIgBODk6c4oxPiceR4CMyGWoCCyIAdpE1KzICEPAugAuVSzrfr03+/OxozdzeBRZEAHYHaWX5e0uU5a/PwIHs/D9gOKufYSyKAMQmx2J1wGoA7PI+UbtemsNQ6F87ua9YMfZvWTOvLjACQNYe9QPGQ/+aOX5fX3ZzKIc0V7BsmeAIwPiT46EiFft73fHcCi1JMRbByJ6dTfRtn1ZrPyGBLVl8iv8W6JRJkvwYhqnKMMxGhmEuMAzTlmGY3AzD/McwzFKGYfYyDFNNUIMClIJdcfPtTco1Kxenmhuta2RwlGx3I38NJiIAx58c5/rVc1dPee00Bc8IQLMNzbj+RCXa0X0QGAGYe2ku148VN1bY0FATiIgAaJePDXwfaD3bAgOJbt40fYzICMDS60u5Pvyw7weJDDbA4sUZR/z6iIwAWH3Ur+HWrYwj/osXdY/ZvFlUBOD089NcH4rMKSJ1Fbx0QkIyjvizZyc6f579PCmJqH17URGA3UG7rVnJzxiCR+oA1gBwAjARQBiAXQCKAmgMIBnAQkHtCTjY7rjx5gZ5zvTkblyT9U0yCAC7df5ERgVAcmoyN7WRY0YOik+Ol9tS4/AQANrOPzoxWgYjTSBAAHy3+zuuH7fe3rKxoSYQIAC0Q/4VFlWwTshfKAIFgFqtpgqLKtjmXqSkEE2dSvT334YdvwaBAsBcDX9JUauJKlY07vg1CBQAKrWKqi+vzvVhza01VupAGtqhf23Hr0GEAIhNiqXic4tzfdgTtMeKHdBBqOMvDWBa2u9LAKQC+DrtdVcAnwC0ENSmgIPtkmuvr5HHTA/u5jXb0EzHWdq18ycyKgAG7BvA9Wnvg71yW2kaMwLArp0/EW8BUG5hOW5OMCk1SQZDTcBTACy4soC7F5P8J8lgqBEECIATT09wfai/pr6NDTWBAAFgs1G/hkeP2Pn9oCDTxwkQABvvbOT6UGVpFev3Yft21iYPj4yOX4NAAfDHyT+4PrTc2NKWYlio868D4Ku03+8COCO0jQxtCjjYbrkSckVHALTY2ILbJcrunT+RQQFw4uZOrj/f7f5ObgvNY0IANF3f1L6dP5FZARCVGMWNmGuuqCmjoSbgIQDqranH3Yt77+/JZKgReAqAdlvacX3YeX+nDIaagIcAsOmoXww8BEB8crzOiPnE0xO2sS0oiOijmc3BeAoAGZL8tBHnsIF8ANQAfMW2ofnJdAl/hvAp5oOj3x3l9lI+/vQ4Om3vhMTURJkt44mBJMAmQ2fDi9ikrwOPDiAp1fJyrlaFZxKgXST8GcJMEmBAaIB1KvtJiZkkwLcxb3Hx1UUAQIV8FVCxQEW5LDUMjyTAZxHPcPDxQQBWWt5nKTySAK22rl8qevc2mwRolYI+fKhQAcib1/QxLi7Azp0mkwCJdJP8xtUZZ5dJfgZoDIABcMbShj4L5w8AtYvXxtE+R5HDJQcAdnOcLju62L/T1KAnAByuX4f/Fhd4JgAxyTFc1Sm7xogA0DhNu8eEANAu7mO1TH8pMCEAdLL87c3haDAjABZfW8z1YUTNEXBycJLLUuOYEABENsjwlwITAsCqBX2kwowA2Ptwb2at5NcYQBKAK5Y29Nk4f4DdGe/Id0eQ3ZmtynQ4+DD67Okjs1UC0BMApYM/4tgmwDPBjmr9m8OAAOjl94J7KWuRHz4YEQDvL53gDqlexE5H/hqMCIC9d7Zxh0hWy98aGBEAietWWX95n1QYEQCXLm2371G/NkYEwBT/ydYr6CMlRgRAwtGDGH10NHfYfy3/QzbnbPLYKJzGAK4QkeVhbQFzBJmGsy/OUrbp2dj5qN9BAOjDpw9ym8UfvRyAK0VBXpM87C/JzBR6OQC/N2XnBm20jMZy9HIAwnM4UuWhINe/XCk51UTWtz2hlwOwvyzIZSLIe7G33JbxQy8HQOXA0Hed2OdowL4BclvHD70cgJACblTsFzud6zeGXg7A0hoMMZOsWNBHavRyAJJcnahJX1mS/LQRM99fCABBgvl+IgKT1qhJGIZhoqKixNV9tDFJSUlISkrClbdX0NevLxLiEoB5wIANAzCvwzy5zeNPUBDQpg27JzWAI6UBp5270Lx0c5kNE8C8eWwRkTT6dAJWrAzNPCo7Kgro1Am4yYb8w7IB/aZUw5HBZ2U2TADnzrFh/0R2oLCsOhAx5Xf8Uf8PMyfaCUTAr78Cq9kRvwpAs77A/InnUaVgFXlt48ubN0DbtsCzZwCAe/mA/r99iauDrtlnyN8QO3YAgwez9wPAhCaA568TML7eeJkN40lyMtC3L3CELZoW7wjUHu6EPWOuoXSe0jY3x9PT0xNADPFxwGkwDFMVwDEATYgoyFIb+Dp/DwCZZB9dBQUFBQUFu8eTiGTbntYuRv41a9bE9evXJWlLM/LX4H/fH/2+7Yed53aiRdUWklxDHyntz8DTpwicMRp/vw7A2sPP4ewofutQU1izD6/WLsa+uRPgvWgxmjW0Xg6G1foQHY37U0Zg6/WT+O3EI3i4mim9KxJr3oPY6xdx59/x+N+DQBy4EAIPc+WDRWK1PhDh4bz/4cT2Veix7zIKFLbOaM2a9yDlTQiu/u8HrLx1HQvOvwI7+JMea/YheO9qnJv2Oxov34JSNawXhbRWHygpCef++A5njp/AT6cfI0/+gpJfAzBvv5iRv+QImCOwGhUqVLBa2yEhIQSAQkJCrHYNa9pvq2tYs31b1VrIzP9HtmjfFvchs/8fKfdA/vatfQ07uQcWz9lb+mMX2f4jRoyQ2wSLsIX91r5GZr8HQOb/P1Luweffvi34HP6PMvt9yAz28wr7p5FJFmvr8vr1axQvXhwhISEopr83uoJNiI6OhqenJ6KioqwWblYwj3If5Ee5B/JjJ/dA9jXPdjHytyaurq46/yrYHldXV0yePFm5BzKj3Af5Ue6B/Cj3gOWzH/nbicpTUFBQUFDQoIz8FRQUFBQUFGyL4vwVFBQUFBSyGELC/pkSrQJFniRjQQUFBQUFBQV7ISs4fwZATshdUEFBQUFBQcFO+OzD/mkFFaIVx297GIb5g2GY6wzDxDAME8YwzD6GYcrJbVdWJu2eEMMw/8ltS1aCYZiiDMNsYhgmnGGYeIZhbjMMY+fbQ35eMAzjxDDMNIZhnjMMk8AwzDOGYSYxDPPZ+0FD2OFm2AqfEQ0BLAZwHeyzNh3AcYZhvIkoTlbLsiAMw9QEMBjAXbltyUowDJMbwEUApwG0AhAGoDSASBnNyoqMBzAUQD8A9wHUALAW7LTwfBntkoXPPuyvYD8wDJMf7BdfQyI6J7c9WQmGYXIAuAVgOICJAG4T0WhZjcoiMAwzC0BdIqovty1ZGYZhDgJ4T0Q/ar23G0A8EX0vn2XykCXDHQqyodnJ5JOsVmRNFgM4REQn5TYkC9IewA2GYXamTX8FMAwzSG6jsiAXADRlGKYswG2RWw/AYVmtkgkl7K9gE9ISL+cCuEBE9+S2JyvBMExPAF8DqCm3LVmUUgCGgX3+ZwCoBWABwzBJRLRBVsuyFn+DHYA8ZBhGBcARwP+IaKu8ZsmD4vwVbMUiAFXAKm0FG8EwTHGw85ktiChRbnuyKA4AbhDRhLTXAQzDVAQrCBTnbzt6AOgDoDfYOf9qAP5jGOYtEa2X0zA5UJy/gtVhGGYh2NBnAyJ6Lbc9WYzqAAoAuMkGXwCwI54GDMOMBOBKRCq5jMsihAII0nvvAYAuMtiSlfkHwCwi2pb2OpBhmBIA/gCgOH8FBalIC/UvBNAJQCMiei6zSVmRUwAq6723FsBDAH8rjt8mXASgv8S1LICXMtiSlckGQK33ngpZNPdNcf4K1mQx2BBbBwAxDMMUSns/iogS5DMr60BEMQB0ciwYhokDEK7kXtiMeQAuMQwzAcAOsHP+g9N+FGyHH4D/MQzzCmzY/ysAYwCskdUqmVCW+ilYDYZhjD1cPxDROlvaopAOwzBnoCz1sykMw7QFMBNAGQDPAcwlopXyWpW1YBgmJ4C/wEYiCwB4C2ArgKlElCynbXKgOH8FBQUFBYUsRpac61BQUFBQUMjKKM5fQUFBQUEhi6E4fwUFBQUFhSyG4vwVFBQUFBSyGIrzV1BQUFBQyGIozl9BQUFBQSGLoTh/BQUFBQWFLIbi/BUUFBQUFLIYivNXUFBQUFDIYijOX0FBQUFBIYuhOH8FBQUFBYUshuL8FRQUFBQUshj/BxshXUMxdTxGAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 153 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_k = k.plot(ambient_coords=(r,t), ranges={r:(1,8), t:(0,8)}, number_values={r:8, t:9}, \n", " fixed_coords={th:pi/2, ph:pi}, parameters={m:1}, color='red', \n", " scale=0.8, aspect_ratio=1)\n", "graph_lk = graph_l+graph_k\n", "show(graph_lk, figsize=8)\n", "graph_lk.save('def_plot_lk.pdf', figsize=8)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\underline{k} = \\left( -\\frac{2 \\, m + r}{2 \\, r} \\right) \\mathrm{d} t + \\left( -\\frac{2 \\, m + r}{2 \\, r} \\right) \\mathrm{d} r\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\underline{k} = \\left( -\\frac{2 \\, m + r}{2 \\, r} \\right) \\mathrm{d} t + \\left( -\\frac{2 \\, m + r}{2 \\, r} \\right) \\mathrm{d} r$$" ], "text/plain": [ "kf = -1/2*(2*m + r)/r dt - 1/2*(2*m + r)/r dr" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k_form = k.down(g)\n", "k_form.set_name('kf', latex_name=r'\\underline{k}')\n", "k_form.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The 2-metric $q$\n", "\n", "We define $q = g + \\underline{\\ell}\\otimes \\underline{k} + \\underline{k}\\otimes \\underline{\\ell}$:" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}q = r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}q = r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "q = r^2 dth⊗dth + r^2*sin(th)^2 dph⊗dph" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q = g + l_form*k_form + k_form*l_form\n", "q.set_name('q')\n", "q.display()" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field of type (2,0) on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{r^{2}} \\frac{\\partial}{\\partial {\\theta} }\\otimes \\frac{\\partial}{\\partial {\\theta} } + \\frac{1}{r^{2} \\sin\\left({\\theta}\\right)^{2}} \\frac{\\partial}{\\partial {\\phi} }\\otimes \\frac{\\partial}{\\partial {\\phi} }\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{r^{2}} \\frac{\\partial}{\\partial {\\theta} }\\otimes \\frac{\\partial}{\\partial {\\theta} } + \\frac{1}{r^{2} \\sin\\left({\\theta}\\right)^{2}} \\frac{\\partial}{\\partial {\\phi} }\\otimes \\frac{\\partial}{\\partial {\\phi} }$$" ], "text/plain": [ "r^(-2) ∂/∂th⊗∂/∂th + 1/(r^2*sin(th)^2) ∂/∂ph⊗∂/∂ph" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q_up = q.up(g)\n", "print(q_up)\n", "q_up.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Expansion along the null normal" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We compute $\\theta_{(\\ell)}$ as $\\theta_{(\\ell)} = q^{\\mu\\nu}\\nabla_\\mu \\ell_\\nu$:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2 \\, {\\left(2 \\, m - r\\right)}}{2 \\, m r + r^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2 \\, {\\left(2 \\, m - r\\right)}}{2 \\, m r + r^{2}}$$" ], "text/plain": [ "-2*(2*m - r)/(2*m*r + r^2)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta = q_up.contract(0,1,nab(l_form),0,1)\n", "theta.expr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check of the formula $\\theta_{(\\ell)} = \\nabla\\cdot\\ell - \\kappa$:" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$$" ], "text/plain": [ "True" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta == div_l - kappa" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check of the forumla $\\theta_{(\\ell)} = \\frac{1}{2} \\mathcal{L}_{\\ell} \\ln \\det q$:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$$" ], "text/plain": [ "True" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "detq = M.scalar_field({X: r^4*sin(th)^2})\n", "theta == 1/2*ln(detq).lie_der(l)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$$" ], "text/plain": [ "True" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta == 1/2*l(ln(detq))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Deformation rate tensor of the cross-sections\n", "\n", "We compute $\\Theta$ as $\\Theta = \\frac{1}{2} \\mathcal{L}_{\\ell} q$:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field Theta of type (0,2) on the 4-dimensional Lorentzian manifold M\n" ] }, { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\Theta = \\left( -\\frac{2 \\, m r - r^{2}}{2 \\, m + r} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\left(2 \\, m r - r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{2 \\, m + r} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\Theta = \\left( -\\frac{2 \\, m r - r^{2}}{2 \\, m + r} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( -\\frac{{\\left(2 \\, m r - r^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{2 \\, m + r} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$$" ], "text/plain": [ "Theta = -(2*m*r - r^2)/(2*m + r) dth⊗dth - (2*m*r - r^2)*sin(th)^2/(2*m + r) dph⊗dph" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Theta = 1/2 * q.lie_der(l)\n", "Theta.set_name('Theta', latex_name=r'\\Theta')\n", "print(Theta)\n", "Theta.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Expansion of the cross-sections along the null normal $k$:\n", "\n", "We compute $\\theta_{(k)}$ as $\\theta_{(k)} = q^{\\mu\\nu}\\nabla_\\mu k_\\nu$:" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2 \\, m + r}{r^{2}}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{2 \\, m + r}{r^{2}}$$" ], "text/plain": [ "-(2*m + r)/r^2" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta_k = q_up.contract(0,1,nab(k_form),0,1)\n", "theta_k.expr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Value of $\\theta_{(k)}$ at the horizon:" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{1}{m}\$" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{1}{m}$$" ], "text/plain": [ "-1/m" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta_k.expr().subs(r=2*m)" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.5.rc1", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 1 }