{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Event and trapping horizons in Vaidya spacetime\n", "\n", "This Jupyter/SageMath worksheet is relative to the lectures\n", "[Geometry and physics of black holes](http://luth.obspm.fr/~luthier/gourgoulhon/bh16/)\n", "\n", "These computations are based on [SageManifolds](http://sagemanifolds.obspm.fr) (version 1.0, as included in SageMath 7.5 and higher versions)\n", "\n", "Click [here](https://raw.githubusercontent.com/egourgoulhon/BHLectures/master/sage/Vaidya.ipynb) to download the worksheet file (ipynb format). To run it, you must start SageMath with the Jupyter notebook, with the command `sage -n jupyter`\n", "\n", "*NB:* a version of SageMath at least equal to 7.5 is required to run this worksheet: " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.0.beta6, Release Date: 2017-05-12'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Spacetime\n", "\n", "We declare the spacetime manifold $M$:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional differentiable manifold M\n" ] } ], "source": [ "M = Manifold(4, 'M')\n", "print(M)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We use coordinates $(t,r,\\theta,\\phi)$ analogous to the 3+1 Eddington-Finkelstein coordinates in Schwarzschild spacetime, i.e. coordinates such that the advanced time $v = t+r$ is constant on the ingoing radial null geodesics:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "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": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t: (-oo, +oo); r: (0, +oo); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X.coord_range()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Metric tensor\n", "\n", "The metric tensor corresponding to the Vaidya solution is:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = (2*m(r + t)/r - 1) dt*dt + 2*m(r + t)/r dt*dr + 2*m(r + t)/r dr*dt + (2*m(r + t)/r + 1) dr*dr + r^2 dth*dth + r^2*sin(th)^2 dph*dph" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m = function('m')\n", "g = M.lorentzian_metric('g')\n", "g[0,0] = -(1-2*m(t+r)/r)\n", "g[0,1] = 2*m(t+r)/r\n", "g[1,1] = 1+2*m(t+r)/r\n", "g[2,2] = r^2\n", "g[3,3] = (r*sin(th))^2\n", "g.display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Einstein equation\n", "\n", "Let us compute the Ricci tensor associated with the metric $g$:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Ric(g) = 2*d(m)/d(r + t)/r^2 dt*dt + 2*d(m)/d(r + t)/r^2 dt*dr + 2*d(m)/d(r + t)/r^2 dr*dt + 2*d(m)/d(r + t)/r^2 dr*dr" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric = g.ricci()\n", "Ric.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The notation $\\frac{\\partial m}{\\partial(r+t)}$ to denote $\\frac{\\mathrm{d}m}{\\mathrm{d}v}$ is quite unfortunate (this shall be improved in a future version). The display of the corresponding symbolic expression is slightly better:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "2*D[0](m)(r + t)/r^2" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric[0,0].expr()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The Ricci scalar is vanishing:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "r(g): M --> R\n", " (t, r, th, ph) |--> 0" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.ricci_scalar().display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The energy-momentum vector ensuring that the Einstein equation is fulfilled is then:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/4*d(m)/d(r + t)/(pi*r^2) dt*dt + 1/4*d(m)/d(r + t)/(pi*r^2) dt*dr + 1/4*d(m)/d(r + t)/(pi*r^2) dr*dt + 1/4*d(m)/d(r + t)/(pi*r^2) dr*dr" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T = 1/(8*pi)*Ric\n", "T.display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Since $v=t+r$, we have $\\mathrm{d}v = \\mathrm{d}t + \\mathrm{d}r$:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "dv = dt + dr" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dv = M.scalar_field({X: t+r}, name='v').differential()\n", "dv.display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The derivative of the function $m(v)$:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "diff(m(v), v)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = var('v')\n", "mp(v) = diff(m(v),v)\n", "mp(v)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T == 1/(4*pi)*mp(t+r)/r^2 * dv*dv" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The future-directed null vector along the ingoing null geodesics:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field on the 4-dimensional differentiable manifold M\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "d/dt - d/dr" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ks = -dv.up(g)\n", "print(ks)\n", "ks.display()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "M --> R\n", "(t, r, th, ph) |--> 0" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(ks,ks).display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Outgoing radial null geodesics\n", "\n", "Let us consider the vector field:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "l = d/dt + (r - 2*m(r + t))/(r + 2*m(r + t)) d/dr" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "l = M.vector_field(name='l', latex_name=r'\\ell')\n", "l[0] = 1\n", "l[1] = (r - 2*m(t+r))/(r+2*m(t+r))\n", "l.display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "It is a null vector:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g(l,l): M --> R\n", " (t, r, th, ph) |--> 0" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(l,l).display()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Moreover it is a pregeodesic vector field:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-4*(r*d(m)/d(r + t) - m(r + t))/(r^2 + 4*r*m(r + t) + 4*m(r + t)^2) d/dt + 4*(r*m(r + t) - 2*m(r + t)^2 - (r^2 - 2*r*m(r + t))*d(m)/d(r + t))/(r^3 + 6*r^2*m(r + t) + 12*r*m(r + t)^2 + 8*m(r + t)^3) d/dr" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab = g.connection()\n", "acc = nab(l).contract(l)\n", "acc.display()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-4*(r*d(m)/d(r + t) - m(r + t))/(r^2 + 4*r*m(r + t) + 4*m(r + t)^2)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acc[0]/l[0]" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-4*(r*d(m)/d(r + t) - m(r + t))/(r^2 + 4*r*m(r + t) + 4*m(r + t)^2)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acc[1]/l[1]" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acc[0]/l[0] == acc[1]/l[1]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Integration of the outgoing radial null geodesics\n", "\n", "The outgoing radial null geodesics are the field lines of $\\ell$; they obey thus to\n", "$$ \\frac{\\mathrm{d}r}{\\mathrm{d}t} = \\frac{\\ell^r}{\\ell^t}$$.\n", "Hence the value of $\\frac{\\mathrm{d}r}{\\mathrm{d}t}$:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(r - 2*m(r + t))/(r + 2*m(r + t))" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "drdt = (l[1] / l[0]).expr()\n", "drdt" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Let us choose a simple function $m(v)$:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/4*(v*(sgn(v) + 1)*(sgn(-v + v0) + 1)/v0 + 2*sgn(v - v0) + 2)*m0" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v0 = var('v0')\n", "m0 = var('m0')\n", "h(v) = (1+sgn(v))/2 # the Heaviside function\n", "m1(v) = m0* (h(v)*h(v0-v)*v/v0 + h(v-v0)) \n", "m1(v)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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AAKj8oXBdukh33mknCwAEKsoDACDsbdggvf++OXO7JZfLTh4ACFSUBwBA2Cu769C6tTRg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\nIiIiUuT/nwmNEgmbpb8AAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(m1(v).subs({m0: 1, v0: 3}), (v,-3, 6), thickness=3,\n", " axes_labels=[r'$v/m_0$', r'$m(v)/m_0$'])" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We plug this function into the expression of $\\frac{\\mathrm{d}r}{\\mathrm{d}t}$ found above:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-(((r + t)*(sgn(r + t) + 1)*(sgn(-r - t + v0) + 1)/v0 + 2*sgn(r + t - v0) + 2)*m0 - 2*r)/(((r + t)*(sgn(r + t) + 1)*(sgn(-r - t + v0) + 1)/v0 + 2*sgn(r + t - v0) + 2)*m0 + 2*r)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "drdt1 = drdt.substitute_function(m, m1)\n", "drdt1" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "and we perform a numerical integration for $v_0 = 3 m_0$" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-((r + t)*(sgn(r + t) + 1)*(sgn(-r - t + 3) + 1) - 6*r + 6*sgn(r + t - 3) + 6)/((r + t)*(sgn(r + t) + 1)*(sgn(-r - t + 3) + 1) + 6*r + 6*sgn(r + t - 3) + 6)" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "drdt0 = drdt1.subs({m0: 1, v0: 3})\n", "drdt0" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "outgeods = []\n", "tmax = 4\n", "for t0 in [-6, -5, -4, -3, -2.8, -2.5, -2, -1.5, -1]:\n", " sol = desolve_rk4(drdt0, r, ivar=t, ics=[t0,0.01], end_points=[t0, tmax], step=0.02)\n", " outgeods.append(line([[s[1],s[0]] for s in sol if s[1]>0], color='green'))" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "graph = Graphics()\n", "rmax = 6\n", "nl = 20\n", "for i in range(nl+1):\n", " t0 = float(i)/float(nl)*3\n", " graph += line([(0,t0), (rmax, t0-rmax)], color='yellow')" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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U2inWpbSK0APA3dK6LYDUBfDxjiYdhQYaTOw6kXUpgrLtz23QQENz3fU+P/c5\nbE1tsajfItalkFbSSQCYPHkyJkyYgK5du6Jr16746KOPYGlpiYsXL+ri5ZokkUjw7aRvYSIzwYKD\nCwymVfBor9F6sxNA6AGAmgC1zpHkIwjuFAwnSyfWpQiGWqPGd1e/wzM9noGjhSPrcpjLKs3C1utb\n8cagN2BhbMG6HNJKOl8DoFarERERgYqKCgwaNEjXL/cX9ub22Dx1M44mH8V//vwPr6+tKyM8RiCz\nJBPpxemsS2mRzEgGqUSq0wBQpCzSqgmQzEgGJwt6Y2tOrboWx5OPY3K3yaxLEZTjyceRVpxGi//q\nffHHF7A0tsQrwa+wLoW0gc4CwM2bN2FlZQUTExMsXrwY+/fvR/fu3Zu5ulZXZWCKzxQ83+t5LD++\nXC/eNFsy1H0ogLqubPrAVGYq6BGAztadaf72Mc7fPY+SqhJM6jaJdSmCsvHqRvRy7oWBnQeyLoW5\n+4r7+CHmBywbsAxWJlasyyFtoLMA0L17d8TGxuLSpUt4+eWXMW/ePCQkJDRxpQrATF2VAQBYO2Et\n7Mzs8Nyvz+l9l0B7c3v07NgTUelRrEtpFV0GgGpVNSpqKtofAEppC2BLjiQdQUeLjujbqS/rUgQj\nvTgdh+8cxuJ+i6kpEoDV51fDVGaKVwcY1q4rMdBZAJDJZPD29kafPn3w8ccfIygoCOvWrWviSimA\nuk+13bq5wNnZGX379kVISEibDwZqjrWJNbY9uQ1n0s9g/aX1Wt+PtREeIxCdqT8jALo6DrhEWQJA\nu3MAaAvg4x1JOoKJXSe2u9OiIdocsxlWJlaYFTCLdSnM5ZXn4bur3+G1Aa9p1Y+DsMHbv2q1Wo2q\nqubeCJYDAJKSKpCTswgxMTE4ePAgDh48iFmzuPlHNtprNJYEL8GKyBV6PxUw3GM4kh8k68XuBl2O\nAHBxEiCNADQvsyQTN/Ju0PD/I2pUNdh6fSvmBMyBpbEl63KY++r8V5AaSbFs4DLWpZB20EkA+Ne/\n/oVz584hIyMDN2/exLvvvouoqCjMmTOnhWd+AODD+q/c+2TMJ7Azs8PLh1/W610Bwz2GA9CPdQAm\nMhNBBgC1Ro17int0CuBjHE06CqlEiie6PMG6FME4mHgQOWU51PcfdX0Qvr3yLZYEL4GdmR3rckg7\n6CQA5ObmYt68eejevTvGjh2LmJgYnDhxAqNHj27hmcsBfAZdhQArEytsnLQRx5KPIfym/jYIcrZ0\nho+9j15gOcxNAAAgAElEQVSsAxDqCEBeeR5q1bUUAB7jSPIRDHEfQkO7j9gUswkDOw9EoFMg61KY\n+/ri19BAg9cHvc66FNJOMl3cdMuWLVo8+5/1X9+p//qBdsU0MtV3Kmb4z8CyY8swvst42Jvbc3p/\nvujLOgBTmSmUKuEFgKzSLACgANAMZa0Sp1JP4d/D/826FMFIeZCCk6knse3JbaxLYa6osgjrL6/H\ny/1epj4IekygK3v+CV2OBHwz8RvUqGvw5sk3Ob83X4Z7DMft/NvIL89nXcpj6XoEQAIJrE2s2/zc\nhvMUXK1cuS7LIERnRKOipgKTfWj/f4PN1zbDxsQGz/R4hnUpzH1z6RtUq6rx5mD9/R1KBBsAAF2G\nAGdLZ3w57kv8eP1HvTpe91EjPEYAAM5mnmVcyePpOgBYm1i3a4X6PcU9yI3k9OmlGUeSjsDN2g09\nHHuwLkUQqlXV2HZ9G+YFzYO53Jx1OUyVVpXi60tf48U+L8LZ0pl1OUQLAg4AgC5DwAu9X8AIjxF4\n+fDLOtumpktuNm7wtPUU/DoAXQeA9s5PZ5VmoZNVJ9re1ozDSYcxqdsk2ude70DCAeSV5+GlvrT4\nb8PlDaioqcDbQ95mXQrRkkB++518zJ/pJgQ0nBWQVpyGtRfXcnZfPunDOgBd9gHQJgDcU9yDqzUN\n/zclqTAJyQ+Sqf3vIzbFbMIQtyHo0VHcIyJl1WVYc2ENFvReQP9+DIAAAoAK/3tjT2nmGt2EgB4d\ne+C1/q9hVfQq3C25y9l9+TLEbQjicuOgqFKwLqVZplIdjgBUaREASu/R/H8zDicdhrHU+OHx02KX\nVJiEyLRI+vQP4IeYH1BSVUKf/g2EAAKAFMDe+u8nA0hu5jrdhID3R74PK2MrvVwQONhtMNQaNS7f\nu8y6lGbpcgqgRFkCG1Obdj2XegA070jSEYz0HEmnutX7IeYHdDDtgKf9n2ZdClPKWiVWn1+NOYFz\n4GHrwbocwgEBBAAAaFhIYglgJPgMAdYm1vhy3JfYc2sPItMiObknX/wc/WBjYoPzd8+zLqVZugwA\npVWlsDFpXwDIKs2iEYAmlFWXISojiob/61XVVuHH2B8xP2g+zORmrMthavv17cgpy8E7Q95p+WKi\nFwQSAOqEhXVGSEgJwsP7g88QMCdwDoa4DcGrR19FjaqGk3vywUhihEFug3Ah6wLrUpqly06ApVWl\n7doCWFpVirLqMprDbMLvqb+jWlVN7X/r7Yvfh4KKAtF3/qtV1+LzPz7HjB4z4Ovgy7ocwhFBBYCI\niAM4ePAOZs1yAp8jARKJBBsmbUBCQQI2XN6g9f34NLjzYFzIuiDYUw51OgVQVaJVDwCaAvi7I0lH\n0M2uG7radWVdiiBsitmEER4j0N2huaPMxSH8RjjSitPw7tB3WZdCOCSoAFDHBUAkACvwGQJ6OffC\nwj4LsTJ6JQorCrW+H18Guw1GsbIYCQVNHbXMnq6nANoTABq6ANIUwF9pNBocST5Cw//1EgoSEJUR\nJfrFf2qNGp+e+xSTu01GL+derMshHBJgAABYhYAPR36IWnUtVkWv0vpefOnv2h9GEiPBrgMwkZqg\nSsX9NkCNRtPuNQD3FHUjAJ2sOnFdll67lX8LWaVZmNhtIutSBGHT1U1wMHfAU35PsS6FqQMJBxBf\nEI9/DfsX61IIxwQaAAAWIcDJ0gnvDn0X3175FkmFSVrdiy9WJlYIdAoUbgCQmeikD4CyVoladW27\npwAczR1hIjPhvC59djz5OExlphjmPox1KcxV1lRie+x2/CPoH6L+e6LRaPDJ2U8w0nMkBrkNYl0O\n4ZhAAkBzQ8T8h4DlA5fDxdIF/zz1z5YvFojBnQcLNgAYS42h0qigUqs4vW9JVQkAtHsKgBYA/t2x\nlGMY6TlS9KvdAeCX27+gSFmEF/u+yLoUpk6knEDM/Rj69G+gBBAAVABC67/XNPHn/IYAM7kZPh3z\nKfYn7Bd8m90Gg90GI7EwUZBrF0ykdZ+eqlXVnN63tKoUQPsCwD0FNQFqrKKmAmczzmJ8l/GsSxGE\nTTGbMNprNLrZd2NdClMfn/0Y/V37Y4zXGNalEB0QQACQAphW//27EEIImBUwC/069cMbJ94Q7Or6\nRw12GwwAuJh1kXElf2csNQaguwDQnkZA1ATo76LSo1ClqsKErhNYl8Lcrbxb+OPuH6Jf/Hc24yzO\nZp7FiqEr6EwIAyWAAAAAC+u/fgfgdbAOAUYSI3z1xFeIuR+Dvbf3tvwExjxtPeFs6SzIaYCG+VOu\nFwJqMwJATYD+7ljyMbjbuMPXnvZ4b7m2BY7mjpjWfVrLFxuwT859gp4de2Kq71TWpRAdEUgAaLAa\nwNcQQggY7jEcE7pOwP+d/j/UqmvbdQ++SCQSDOoszIZAupoCKFG2bw1AtaoaeeV5tAagkeMpxzG+\ny3jRf9Krqq3CjrgdmB80/+HolRjFZMfgWPIxrBi6gk7MNGAC+392IYBvIZQQ8NGoj5BYmIifYn9q\n1/P51N+1P65mXxXclEXDL1GudwK0dwTgvuI+AGoC9Kj04nQkFibS8D/qtrw9qHyAF/q8wLoUpj49\n9ym6dOiCGT1msC6F6JDAAgAALIZQQkDfTn3xtP/T+CDqA50dacuV/q79oahWILEgkXUpf6HLKQBT\nmWmbP6U19ACgKYD/OZ58HFKJlBZ6Adh8bTOGug8Vdee/+Px47Ivfh3eGvgOZkYx1OUSHBBgAACGF\ngFWjViGrNAubYja1+bl86uvSFwBwJfsK40r+SpeLALXqAkhTAA8dTzmOQW6D2n2yoqFILUrF72m/\nY2GfhS1fbMA+PfcpXK1dMS9oHutSiI4JKgCEhYUhJCQE4eHhEEoI6O7QHfOD5uPjsx+jrLqsTc/l\nk42pDbo7dBfc0cANawC4HkHR5hwAC7lFu08RNDQ1qhqcSj1F2/8AbP1zK6xNrEV97G9aURp+vvEz\n3hr8lqjXQIiFoMZ3IiIiYG396C/1xfVfX6n/ugZA40VKDSFgNOpCwBkATR1k0tDYp+Eoyw9aXdf7\nI97Hzrid+ObSN1gxbEWrn8e34E7BggsAQhsBuKe4B1drV9EvdmtwMesiFNUK0QeAWnUttl3fhmcD\nnoW53Jx1Ocx88ccXsDOzw4I+C1iXQnggkBGAXx/zZ+xHAjxsPbCo3yJ88ccXKFYWt/p5fOvv2h+x\nubGCWq+gyzUA7T0HgOb//+d4ynE4mDugb6e+rEth6ljyMWQrskX9xpetyMbW61uxfOByUYcgMRFA\nAFABWFv//e1mrmEfAt4d+i6UtUpBHxcc3CkY1apqxOXGsS7lIaGNAGQrsukQoEccSz6Gcd7jRL/V\na8u1Lejt3Bt9XPqwLoWZNRfWwExmhsXBi1u+mBgEAfyrlwLYV//9ZAA3m7mObQhwsXLBwj4Lsfbi\nWiiqFK16Dt+CnIMgN5ILaiGg0NYA3Ffch4ulC6e16Ku88jzE3I8R/fa/+4r7+O3Ob6L+9F9YUYjv\nr36PJf2XiH4xqJgIIAAAgF39V1cAoyDUEPD2kLehqFJg45WNrbqeb6YyUwQ5BwlqHcDDPgA6mAJo\nVwAouw8XKwoAAHAy5SQA4IkuTzCuhK3tsdshl8oxO2A261KY2XB5A9QaNZYOWMq6FMIjgQSABgcB\ndIZQQ4CbjRue6/UcvrrwFcqry1u8noXgTsHCGgGQ6e4woLauAVBUKVBWXUYjAPWOpxxHkFMQnC2d\nWZfCjEajwZZrWzDDfwZsTW1Zl8NEeXU5vrn8DRb2WQhHC0fW5RAeCSwA2AE4BSGHgHeHvYsiZZFg\n+wL0d+2P+Pz4h53yWJMbyQHophNgm7sAltV1AaQRAECtUeNEygnRD/9HZUQhpShF1Hv/t1zbgtKq\nUrw+6HXWpRCeCSwAAIA9hBwCPG09MTdwLr48/yUqayofey0LwZ2CoYEGMdkxrEsBUHdOgbHUmNMR\nAI1GgxJl29cANLQBpkWAQGxOLHLLc0W//W/LtS3wsffBUPehrEtholpVja8ufIVZPWfBw9aDdTmE\nZwIMAIDQQ8CKYSuQV56HLde2PPY6Fro7dIelsaWwpgGkJpyuAaisrYRKo2rzYqWHIwA0BYDjKcdh\nIbfAEPchrEthpqiyCL/c/gULei8QbV+I8BvhuFt6F28PeZt1KYQBgQYAQMghoKtdV4T1DMPqC6tR\no6pp4efgl9RIir4ufXE1+yrrUh7iegRAm4OALOQWsDKx4qwWfXUi5QRGeY0Sdbe3XTd2QaVRibbl\nrVqjxud/fI6pPlPRs2NP1uUQBgQSAJprsSvcEPD24LeRWZKJPbf2NHsNK72de+PPnD9Zl/GQicyE\n0zUA7Q0A2Ypsmv8HUFFTgT/u/oFx3uNYl8KMRqPB5mubEeIbAidLJ9blMPHbnd8QXxCPd4a+0/LF\nxCAJIACoADxZ/31TR9kKMwQEOQfhiS5P4MvzX0Kjaeq12Ont0hvJD5JRoixhXQqAuhEALqcAGn6u\n9iwCpOF/4GzGWVSrqkUdAK5mX0VcbhwW9Bbn3n+NRoNPz32KYe7DMNhtMOtyCCMCCABSAHUrcMPC\nAhASMrX+MKBHCTMEvD34bcTmxuJU6qlm7sFGQzez2NxYxpXUMZGa6GQKoK3bAKkHQJ1TqafQyaqT\nqI+83XJtC9ys3UTbA+Fs5llczLqIfw75Z8sXE4MlgAAAAGEAgIiILBw86IRZs2Y2cY3wQsBor9Ho\n7dwbX5z/opnns9HdoTtMZab4874wpgGMpcaCmAKgLoB1TqaexFjvsaJd+FZWXYafb/6M53s/D6mR\nlHU5THx27jP07NgTk7pNYl0KYUggAaDBJgBbAbwIfZgOkEgkeHvI2ziVekowb7YAIDOSIaBjAK7l\nXGNdCoC6NQC6GAFo62K++2X3Rb8FMK88D7G5saIe/v/l9i8ory7Hc72eY10KE7E5sTiafBTvDHlH\ntCGQ1BFYAAgDsB36FAKe9n8anraeWH1hdTPPZaO3c2/BhBKutwGWVJXAVGbaphXslTWVKFYWi34E\nIDItEgAwxmsM40rY2XZ9G8Z4jxHtvvcvzn8BT1tPzOzZ1EgrEROBBQAAmAt9CgEyIxmWD1yO3Td3\nI6M4o/kfi2d9XPrgdv5tKGuVrEvRyTbA9sz/A9QF8GTKSfTs2FO0/zukPEhBdEa0aD/9pxalIuJm\nBN4Y9AZkRjLW5RDGBBEArudcB/Bov3j9CgHP934elsaW+O7qd808j3+9XXpDpVHhRu4N1qXUbQPk\ncASgXW2AFdQESKPR1M3/e41lXQozP17/ETYmNpjefTrrUpj46vxXsDOzw/O9n2ddChEAQQSAwopC\nAMALv76AWnVt/aP6EwIsjS3xQu8XsPnaZlTUVDTzPH4FdAyAVCIVRD8AXSwCbM/8PyDuEYCkB0m4\nW3oXY73FGQBUahW2x25HWM8wmMnNWJfDu9yyXGy9vhVLByyFudycdTlEAAQRAMZ4181HHk46jPkH\n5kOlVtX/if6EgFf6v4KiyiL8fOPnZp7DLzO5Gbo7dBfEOgCutwGWVZfByriNAUBxHyZSE3Qw7cBZ\nHfrmVOopyIxkGOE5gnUpTPye9jvult4V7fD/N5e+gcxIhleCX2FdChEIQQQAoO5Nc+uTWxFxMwKL\nDy9+pLmOfoQA7w7emOIzBesvrxdMY6A+Ln0EsROA60ZAimoFLI0t2/Schh4AYl71fDL1JAZ1HtTm\n/+0Mxbbr2+Dn4If+rv1Zl8K70qpSbLy6ES/1fQkdzMQbgslfCSAAqFD3Bg9M6+6G/4T8Bz9c+wHv\nn3n/kWv0IwS8NuA1xOXGITojupnr+dXbuTficuMemVZhQycjAG2cAshWZIt6/r9WXYvTaadFu/2v\nqLII++P347lez4kyBP4Q8wPKq8uxfOBy1qUQARFAAJAC+G/999Pwj1498PnYz7EqehU2XN7wyHXC\nDwFjvM7Cz8EP31z+pplr+dXbpTeUtUokFiQyrYPrNQCKKkXbpwBE3gUwJjsGJVUlop3/j7gZgVp1\nLeYGzWVdCu+qaquw5sIazA2cC1drV9blEAERQAAAgIYV3d0BjMNbg0di+cDleO3oa40O2xF2CJBI\nVuK1Ad44kHBAEFsCezn3AgBcu892GoDrRkDtmgIQeRfAk6knYW1ijWDXYNalMLHt+jZM6jYJzpbO\nrEvh3U9xPyGnLAdvDXmLdSlEYAQSAOqEhVkjJMQIEREjsfqJmZgdMBtz98/FH5l/PHKVsEPA3MDD\nsDKWC2JLoK2pLbxsvR5us2SF6zUA7VoEKPKDgE6lnsIoz1Gi3Pt9M+8mrmRfEeXiP5VahS/++ALT\n/aaL+uwH0jRBBYCIiL04eDAds2b1hpFkPLY+uRiDOg/CtN3TkFqU+siVwg0BFsaf4YXeVdh87RtB\nNOEJdArEjTy2vQBMpNweB6yoatsIQLWqGgUVBaKdAiirLsP5u+dFO/y/7c9tcDB3wGSfyaxL4d2B\nhANIepBEh/6QJgkqANSxBnAUQA8YSydh7zP/QgfTDpj882QUK4sfuU64IWBRvzfxoLISe2/Pbv7H\n5EmgUyDicuOY1sDlFIBGo2nzIsDcslwA4m0CdDbjLGrUNaJcAFijqsHOGzsxJ2BOm1pHGwKNRoMv\nz3+JER4jRLnzgbRMgAEAeDQE2JvPwG+zP0FuWS5m/HdGoxXtwgwB3ey/xChPb/xwbT+aO0qYLwEd\nA5Bbnov88nxmNXA5BaCsVUKlUbVpBCBbkQ0Aoj0I6FTqKXS27gwfex/WpfDuSNIR5JXn4bne4hv+\nP5d5DpfuXcJbg2nunzRNoAEAeDQE+NgvwN5nPsbptNN459Q7ja4TZgh4se/HiM4AEgqaPkqYLwFO\nAQDAdBqAy22AimoFALRpDUBOWQ4AiHIBGCDu43+3Xd+GPi59EOgUyLoU3n15/kv4O/pjYreJrEsh\nAiWQAPCgmcf/FwJGeb2L1U+8hq8ufNVoZwAgxBAwvft02JvZY3PMUDR1iiBfutp1hanMlOk0AJfb\nAMuqywC07Sjg3PJcGEmM4GDuwEkN+iS3LBc38m6Isv9/XnkeDicdFuXiv/j8eBy6cwhvDnoTRhKB\n/JongiOAvxkqANPqv2+qYc3/QsDSAf9BWM8n8Pyvz+NW3q1G1wkrBJjITPCPXv/A9th4VNV+BFYh\nQGYkg7+jP9NDgUxkJlBpVI+0eG4/RVXdCEBbpgByy3LhYO4AqZFU69fXN2fSzwAARnuNZlsIAzvj\ndsJIYoTZAezX4vDtqwtfwcXSRZQ/O2k9AQQAKYCGOaqFeFwIkEh6YsvUi/Dq4Iyn9jyFEmVJo+uE\nFQIW9lmIwspC7E/ogqZOEeRLQMcAplMADYuvuJgGeDgC0IYpgNzyXDhZOGn92vooMi0S3R26i24H\nhEajwdY/t2Ja92mwM7NjXQ6v7ivu46e4n7B0wFKYyExYl0METCcB4NNPP0X//v1hbW0NJycnTJ8+\nHXfu3HnMM6bWf/0VwBw8LgRYGPfE/pm5yC3LxvwD85vouy+cEODr4IsRHiOwKWYTmjtKmA+BToG4\nlX+Lk0/g7WEirfslxMVCwIY1AG0aASjPhZOlOAPA6fTTGO0pvk//V7Ov4lb+LVEO/6+/vB7GUmO8\n1O8l1qUQgdNJADh79ixeffVVXLp0CadOnUJNTQ2eeOIJVFZWtvDM7QD2oqUQ0NUuED9NV+PXxF+x\n/vL6Jq4TTghY0GcBzqSfQVpRGliFgICOAaioqWjUS4E/OhkBaOM2QDGOAGSVZiHpQRJGeY1iXQrv\ntl3fBlcrV9FtfVRUKfDd1e+wsM9C2Jrasi6HCJxOAsCRI0cwd+5c+Pn5ISAgAD/++CMyMzMRExPT\nwjOnAtiD1oSAqb69sHSAMd46+SZic2KbuE4YIWB69+mwNLbEzrid9dfxHwJY7wRoGIbkYiFgu9YA\niHQK4HTaaQDASM+RbAvhmbJWifCb4ZgXNE906z7+8+d/oKhSYNnAZaxLIXqAlzUAxcXFkEgksLNr\nzVzcdLQ2BHw+tg/8HFQI2zsNFTUVTVzHPgRYGFsg1C8UO+J2PDJdwW8IcLJwgqO5I7OFgFxPAZjK\nTNvU0ja3TJxTAJHpkQh0ChTd7off7vyGYmUx5gXNY10Kr2rVtVh7cS3CeobB3caddTlED+g8AGg0\nGixbtgxDhw6Fv79/K5/VuhBgIjuO8NBAZBSnY/mxOc3ci30ImBs4F8kPknHp3qVHruMvBEgkEgQ4\nBSAuj81WQLlUDqCuK5u22noOgLJWiZKqEtGNAGg0GkSmRYpy/n9H7A70d+0vut73/731X2SWZFLj\nH9JqOg8Aixcvxu3btxEREdHitd26dYOzszP69u2LkJBtCAnphfDw/+JxIcDPMQrrJnTBD9f2Y1/8\nF83cmW0IGOnZGZ2tO+On2J8aXcdfCAjsGMhsBEBuVB8A1NoHgLaeA5BXngcAohsBSCtOQ2ZJpujm\n//PK83A0+SjmBYrr039D299x3uMQ5BzEuhyiJ3R6NNiSJUtw5MgRnD17Fi4uLW9DSkpKgrW1daNH\n9wN4pv77nfh7ydZY0CcGx1O88eKhdzDELRBOlhOauHvDOeDz67/+gL/nn4YQMBZ1IeA0gJ5N3Gtx\n/ddX6r+uAdC4y1pDCBgNqdEYPBswGZuvRWDthLWNepI3HNLR0OHwgyZeT3sBTgFYd2kdKmoqYC43\n18lrNIfrRYDtOQdAbF0AI9MiYSQxwnCP4axL4VXEzQhIIEFYzzDWpfAqMi0Sf+b8iRNzTrAuhegR\nnY0ALFmyBL/++itOnz4Nd/eW5qO+f8yftTwdIJHY4LvJV2AkkWLxkanQaC43cy92IwFzAw/gQeUD\nHEk60sR1uh8JCOgYAA00TTRQ0j0upwAU1Yo29wAAILopgNPpp9HXpa/oVoLviN2BKT5TYG9uz7oU\nXn15/kv0cu4l2hMfSfvoJAAsXrwYu3btws8//wwLCwvk5uYiNzcXSmVTx+OqUNfpDwD+aOaOLYcA\nRwtvbJz8H+yLr8XuWyMBXGnmXmxCQI+OdujjIsdPcd81cy/dhgA/Rz8AQHxBPOf3bknDCAAXUwBl\n1WVt7gIogQSOFo5av7a+aJj/H+UpruH/W3m3EHM/RnSL/+Jy43A85TjeHPSmKM97IO2nkwDw/fff\no7S0FCNHjkSnTp0e/rdnT+Me/kBdJ8Dw+u9DAUQ3c9eWQ8DT/vPwTI/pWHKkBrllYyC0EDCrpy2O\nJJ1AWXVT2xYBXYYAS2NLuNu4Iz6f/wDQsAaAiykARbWizecA2Jvbt2nXgL5LLExETlmO6Nr//hT3\nE+zM7DCp2yTWpfBq9fnVcLN2wzM9nmn5YkIeoZMAoFaroVKp/vbfvHnNJfOGOekBACZCmxCwYeIm\nGElssfiIHBrNWAgpBMzwPwxlLfDbnVFo7hRBXYYAf0d/3C64zek9W4PTKYA2LgIUYxOgyLRIyIxk\nGOI+hHUpvFGpVfgp7ifM6jmr0Robw3a35C7Cb4Zj2cBlD/+dEdJaAjgL4FHhAAZDmxDgaOGIjZO/\nw774BziQ4AJgHIQSAjxsg9HftTf23KrB444S1lUI8HPww+18/gMA11MAbToKuDxHdDsATqefxgDX\nAW0KSvouMi0S2Yps0Q3/r7u0DhZyCyzss5B1KUQPCSwAmKPuPADtQkCoXyim+EzBa8fKUFbdHUIK\nATP8Z+Noci3Kqi3Adwjwd/RHalEqlLVNrcXQHa6nAGgEoHlqjRqn006Lbv5/R9wO+Nr7IrhTMOtS\neFOiLMEPMT9gUb9FbZoWI6SBwAIAwEUIkEgkWD9xPQorHuCDM8EAekAoIeBp/6ehrFXitzvL0Nwp\ngv/DbQjwd/SHWqPGncLHHczEPZaNgMTWBvhm3k0UVhaKav5fUaXAvvh9mBc0T1SL4DbFbIKyVonX\nBrzGuhSipwQYAAAuQoCnrSf+PeLf+Prid4jN+QJCCQGetp4I7hSMPbdO4nFHCf8PdyHAz6FuJwDf\n0wBcTgEoqtq4CFBkbYAj0yJhIjXBILdBrEvhzb74faioqcCcwOa6gRqealU11l1ahzmBc9DJqhPr\ncoieEmgAALgIAa8Peh2+Dr5YdPhNqDWHIZQQ8EyPZ3A0+SjKqq3AZwjoYNYBzpbOvO8E4GoKoEZV\ngypVVaunAKpV1ShSFolqBOB0+mkMdhsMU5kp61J4syNuB0Z5jhJV//vdN3cjW5GNNwa9wboUoscE\nEgBym3lcuxBgLDXG95O/x8Wsi9h+fT/q+g2wDwEN0wB1TYGaP0r4r7gJASx2AkgkEkglUq2nAB4e\nBdzKKQCxtQGuVdfiTPoZUc3/Z5Zk4nTaaVEt/tNoNFhzcQ0mdJ2AHh17sC6H6DEBBAAVgCfrv2/q\ntDjtQsAwj2EI6xmGFZErUFZtBCGEAE9bTwQ6BeLQnUP11/AXAvwc/Jj0AjCWGms9BaCobttRwA1t\ngMUyAnA95zpKq0pF1f9/V9wumMnNEOoXyroU3pxJP4PrOdfx+sDXWZdC9JwAAoAUwMcAgLCwHggJ\nmYLw8PBG12gXAj4b8xmKlcX47NxnaDhKmHUImOozFUeSjqBW3TBlwU8I8Hf0x53CO5wsyGsLuVSu\n9RTAwxGAVq4BeNgGWCQjAFHpUTCTmaG/a3/WpfBCo9FgR9wOPOX3lKhWwa+5uAY9O/aktr9EawII\nAAAwBgAQEVGCgweBWbOeauKa9ocAD1sPvDHoDaw+vxoZxRkQQgiY6jMFDyof4MLdC49co/sQ4Ofg\nhxp1DVKKUtr0PG3JjeRahw5FVd0IQGunABpGADpadNTqdfVFVEYUBrkNEk0jnKvZV5FQkCCqk/8S\nCxLx253f8PrA10W144HohkACQIMI1L2ZhoLr6YB3hr6DDmYd8M9TDafvsQ0Bwa4RcLJwwsHEg42u\n0W0I8Hf0BwDepwGMpcacjQC0egqgPBcdTDuI4g1RrVHjbOZZjPAYwboU3uyI3YFOVp1EteXx64tf\nw+/X+KYAACAASURBVMnCCbMDZrMuhRgAgQWAMQAOQhchwNLYFJ+O+RS7b+3GpaxL9dewCwFGknWY\n4uPwyDqAR+kuBHS06Ag7MzvetwLKpXImawDEMvx/I/cGipXFojn+t1pVjfCb4ZgTMAdSIynrcnhR\nUFGA7bHb8UrwKzCRmbAuhxgAgQUAAHgCugoBcwNnoYdjD6yIXPHINexCwFSfW0gsTMSdwsQmrtFN\nCJBIJHUtgXneCcDFFEB5dTkAwMLYolXXi6kJUFRGFIylxhjgOoB1Kbw4mnQUhZWFmBs0l3UpvNl0\ndRM00GBRv0WsSyEGQoABANBVCJAazcfHo1ciMi0Sp1JPPXINmxAw1nsNTKTAocSFeNwpglyHAH9H\nfybNgLSdAqioqYAEEpjJzFp1fW65eEYAojOiMcB1AMzkrfvfRt/tvLETvZx7oWfHnqxL4UVVbRU2\nXNmAeYHzRHW0NdEtgQYAQFchIMR3NwZ2HoB3f38XGs2jb7r8hwAL4+UY5eWP4yln0dJRwlyGgO4O\n3XGn8A7UmqZq1w0upgDKa8phLjdv9eKnvPI8dDQ3/AWAGo0G0RnRohn+L1GW4FDiITwb8CzrUngT\ncTMCOWU5WDZwGetSiAERcAAAdBECJJJ9+GS0Ga5mX8W++H2NruE/BIzzfgFnM+WorHn8UcJchgAf\nex9U1FQgW5Hd7DVc42oKwFxu3vKF9fLL80XxaSm+IB75FfmiWQC4L34fqlXVmNVzFutSeKHRaLD2\n4lpM6jYJfo5+rMshBkQgAWD1Y/6M+xAwyuscxnk74d9n/t3Ep2B+Q8ATXZ6AsrYG5zKX4HGnCHIZ\nAnztfQGA10OBjKXGqFZrPwXQ2vl/tUaNgooCOJobfgCIzoiGVCIVTf//XTd2YaTnSLhau7IuhRen\n008jNjeWGv8QzgkgAKgAXK3//mQz13AfAj4YWYDb+bfxa0LjUQCAzxDQw7EHXCxdcDLVDC0dJcxV\nCPC09YTMSIbEgqYWH+qGXMrBCEBNOSzkrQsAxcpiqDQqUYwARGVEoV+nfm06Jllf3Su9h8i0SFEN\n/6+5sAaBToGi2u5I+CGAACAFsKP++1moe+NtCrchYLDbfzHKU4KPzr4IjaapNyZ+QoBEIsG4LuNw\nMvUkWjpKuI72IUAulcO7gzfvIwDargGoqKlo9RRAfnk+ABj8CIBGo0FUepRohv8jbkZALpUj1F8c\nrX8TChJwOOkwlg9cTo1/COcEEAAAoKFRy1gA08BXCPjXsPdx7X4RjiWPxaOnCP4PPyFgnPc4XM+5\nXt+5jp8Q4GvvizsP+AsAciPtWwGX15S3egqgoKIAAAx+BCClKAX3y+6LZgHgrhu7MNVnKmxNbVmX\nwouGxj9iWe9A+CWQAFAnLEyNkJAOCA+fCj5CwGivf2NgZx98dDYaGs2zYBUCGnp6/572e/11ug8B\nPvY++jcF0IZFgPkV4hgBiEqPgpHECEPdh7IuRefi8+PxZ86fohn+b2j8s6T/Emr8Q3RCUAEgImIP\nDh7MxKxZk8HHSIBEIsF7w9bg/F0gKuMXPHqA0F/pNgQ4Wzoj0CmwUW8C3YYAH3sfpBWnaf2pvLW4\nmgJo7RqA/PJ8SCCBnZmdVq8pdNGZ0ejl3As2pjasS9G5XTd2wdbUFpO6TWJdCi++v/o9AFDjH6Iz\nggoAdYwB/BfABPARAiZ1m4Rezr3w8dmeaHyK4F/pNgSM9BiJ6IzG9ekuBPja+0KtUSO1KLWZ67nF\n9xRAfkU+7M3tDb5NbFR6FIa7G/7wv0ajwc83fsbTfk+L4tNwVW0VNlzegPlB8+Fg7sC6HGKgBBgA\nAD5DgEQiwT+H/BOnUuNwI/dLsAoBwzw8kFKUgnul9xpdp5sQ4GNfdwgRX9MAnE0ByFq/CNDQh/8z\nijOQUZKBEZ6GvwDwQtYFpBWn4dlAcQz/h98MR255LjX+ITol0AAA8BkCQv1C4WrlinWXbqLxKYJ/\np5sQMMz9YwDA2cyzTVzHfQhwtlwDS2Nj3nYCGBtxNAXQhhEAQ18A2DBiNMx9GONKdG9n3E50tu4s\nisWOGo0Gay6sweRuk9HdoTvrcogBE0gAyGzmcX5CgFwqx5L+S7AzbifyyoeARQhwsnSHr70U0RkH\nmrkXtyFAIvkMvvbVuFMY3sw13JJLOZoCaO0agArDHwGIyohCz449YW9uz7oUnapR1WDPrT2Y1XMW\njCQC+ZWlQ7+n/Y4beTfw+iBq/EN0SwD/mlSoe9MGgPIm/pyfELCwz0IYSYyw6eomND5FkK8QMNzD\nFtEZv6ClUwS5CgE+9kFILPwTrT1KWBt8twIWwxRAVIY49v8fTzmOwspC0az+X3txLYKcgjDKcxTr\nUoiBE0AAkAL4pv77mWAVAuzN7TEvaB42Xt2IqtoqsAgBwz1W4Va+CoUVI8BHCPCxn4bEQku09hRB\nbXC2C4CmAAAA9xX3kfwgWRRD4rtu7EIPxx4IdApkXYrOJRYk4kjSESwbuIwa/xCdE0AAAICGHuYx\nAKaCVQh4bcBryCnLwe5bu+uv4zcEDHOv2950NtMaLR0lzEUI6NKhC/LKy1BevRK6DgHaTgHUqGpQ\no65p1RSARqMx+BGAc5nnABj+/L+iSoFfE37FswHPiuINccPlDXA0d0RYzzDWpRAREEgAaLAPwGWw\nCgH+jv4Y5z3u4f7bOvyFAA9bD3S27owLd6eipVMEuQgBXh28AADpxU+htUcJt5e2UwDlNXV/H1oz\nBVBWXYYqVZVBjwCcyzyHLh26wMXKhXUpOnUg4QAqaysxO2A261J0rkRZgh9jf8SifotgKjNlXQ4R\nAYEFgEEAjoFlCHix74u4kHUBt/JuPXIdfyFggOsAXM6+gdYcJaxtCPC09QQApBWnobVHCbeXsdRY\nqxGAipoKAGjVFIAYugCeu3sOQ9yHsC5D53bd2IVh7sPgYevBuhSd2/rnVihrldT4h/BGYAEAAIaC\nZQgI8e0AR3NHbL62udF1/ISA/q79cTX7KlRqW+g6BHSy6gRjqTHSi9Prr9NdCJBL5VqtASivrvt7\n0JopgIcHARnoCICiSoHrOdcx1M2w2//mluXiZOpJUSz+U6lVWH95PZ7p8Qw6WXViXQ4RCQEGAIBl\nCDCWhuAfvcbgp7ifoKxVNrpO9yGgv2t/lFWXIb4gHi0dJfw/7QsBRhIjeNh4IK0o7ZHrdBMC+JwC\nMPQRgEv3LkGtURt8///dt3ZDKpFiRo8ZrEvRud/u/Ia04jQsHbCUdSlERAQVAMLCwhASEoLw8HCw\nDAEL+hzAg8oH2Be/r4nrdBsC+rr0hQQSXL53uf4a3YYAT1tPpJekN7qO+xDA6xRA/QiAobZQPZd5\nDvZm9gbfJCb8ZjjGdx1v8Oc5AMC6S+swsPNA9Hftz7oUIiKCCgARERE4ePAgZs1qOPqSTQjwsR+K\nER5G2Hzty2bupbsQYGVigR4dezwSAABdhgAvW7tGIwANuA0BDVMAGk1TNbWsTVMAFfmwNbWFXCpv\n12sJ3bnMuvl/Q14Vn1aUhotZF0VxDG5cbhxOp5+mT/+EdwIIABoA7z/mz9mEgIV9/HAm/TpSiyKa\nuZfuQkD/TsGNAgCgqxDgaXsUacUpzdyLuxAgN6p7M1ZpVO16fpumAAx4C2CtuhYXsy5iiJthLwDc\nc2sPzGRmCPENYV2Kzn1z6Ru4Wrki1C+05YsJ4ZAAAoAaQMMBOM21weU/BEzrfhoWcinCb8xDU6cI\n1tFNCOjvegdxuXGorKlsdA33IcCrgyWKlaUoUf7ZzL24CQHGUmMAaPc0QFt3ARjqAsDYnFiU15Qb\n/Px/xK0ITPGZAktjS9al6FRBRQF23diFxcGLDXbEigiXAAKAFEDDvvvnAPzSzHX8hgALY0dM6/40\ndt0whkYzAXyGgN4uf0ClUeFW/o0mruE2BLhafQsAuKeYgNYeJdweDb/c2rsQsGEKwExm1uK1hnwO\nwLnMczCRmqCvS1/WpehMQkECrudcF0UznB9ifgAAvNj3RcaVEDESQAAAAFn911AAYRBKCJgdMA/x\nBeWIzQ1EU6cI/g+3IaCH42ZIAMTlvon/Z++8w5sq2z/+Tbr3HlCg7FKQPRQQBURxUEBeRXD7uhfi\nT9/heg1DBBQRZSsoKhQRylKW7D1aVoG2UKCle690Jjn374+T0CQ9J02ak+YknM919ZKmd06etLX5\n5Bn315woYWskoK1fbwBAXpUHzI0SbokE6JYAWnoUsFrF5gCYs+5dVF3kvBsAs45iSNQQeLh62Hso\nNuP3S7/Dz90Pj3Z71N5DsSkqjQpLzyzFM72fcdrfVwlxIxIB0LEcbB6AOCTgwc4PItQ7FGsv3gO+\nKOFGhJMAH/dX0C0kEhfyj8CcKGFrJEDXSS636l8wN0q4JRIgxBLAnZ4ESEQ4euuoU0//ExHWX16P\nx2Mfd/pueAkpCcipypE2/0nYDZEJgCvYdXBxSICbixsm95yM+EsbwdBmtKYE9I0YgQsFPWBOiqA1\nEuDt5o1Az0DkVtXA3BTBlkiAEEsAZgcBVTvnHoAbZTeQr8x36g2AFwsuIrU4FVN6Of/0/6JTizCq\n4yj0juht76FI3KGITAAAsUnAM32eQU5VDo5kJoEvStgQYSSgT0QfXCwoANHPsLUEtPVrizxlHiyJ\nErZUAnQzANYuATRHraoW1apqp5wBOJZ1DAAwrP0wO4/Edqy/tB7BXsEY03mMvYdiU87knMGJ7BPS\nu38JuyJCAQDEJAH3tLsHUX5R2qZA3CmCTbFeAvpG9EVZXRmyK0fBnChhaySgrV9b5FblamtsIwG6\nPQC2XgK43QXQCWcAjt46irvC70KQV5C9h2ITdNP/T8Q+4fQ74hedWoROgZ0wrvs4ew9F4g5GpAIA\niEUC5DI5JsRMwJa0LdomNq0jAbrs84sFF2FOlLA1EtDGt42eAAC2kACrlwBU5i0BlNSUAHDOLoBH\nbx116v7/p3NOI6M8w+l3/+dV5WHD5Q14Z8g7cJG72Hs4EncwIhGAazy3i0MCHo99HLcqbuF8/nlt\nje0loENAB/h7+CO5UHcU0HYS0NbPWAAAoSXA6iWABvOWAEpqWQEI8Qpp0eOIlZKaEqQUpzj1BsD1\nl9Yj0jcS90XfZ++h2JRlicvg7uKOf/b/p72HInGHIwIB0ADQtfus4Pi6/SXg/uh7EOgZiM2pm/Vq\nbCsBMpkMMSExSCtJ06uzjQS08T2l3QNgjHAS0FpLALoZgBBv5xKA41nHAcBpBUDDaPD75d8xuedk\np35XXKeuw/LE5Xix34sI9Ay093Ak7nBEIAAuANjo3SlTemP8+Ee0YUD62FcC3FymYFz3R7Al1bhT\noW0lICY0BmnFaUZ1wktAqPch1KnrUKPi+n4JIwGucrbXg5rheu7NY+4mwJLaErjKXeHn7teixxEr\nR28dRZRfFDoEdLD3UGzC0VtHkafMc/rp//WX1qOopgjvDnnX3kORkBCDAABAfwDA+vXAtm1lmDqV\nqwGIfSXg8R5pSC5MxvVS4775tpOAmBAfoxkAHcJKQIj3WwCAkpr3YG6KIDf8EqDbA9BSAbBkBiDE\nK8TpgnKOZrHn/53teemIvxSP6IBo3NPuHnsPxWYQEb479R0e6foIYkJj7D0cCQmxCICOrQDSAIyF\n2JYDxna5BHcXOXZc28ZRYxsJiAn5FaW1pSiuKeaoE04CQrxeBACU1K6CJVHC3HBLgNUzAGb2ASip\nLXG66f96dT0ScxOd9vifSqPCxisb8VSvp5xWcAB2Gedc/jlMu3uavYciIQFAdALQH+wLlvgkwMd9\nO+7tQNh9fS5MpQgKKQExod0AAGnFfCFJwkiALm+9tHYaLIkStkQCWnMJwNk2AJ7LP4cGTYPTCsC+\nm/tQUlvi9NP/i88sRrfgbnioy0P2HoqEBADRCQAADIRYJeChzi/hQEYh6tUT0RoS0C14N2QA0kqm\nwdwo4ZZIgO4dc0nNvbAkStgSCbBWACxaAnCyGYATWSfg5eqFvhF97T0Um7D+0np0D+mOfpH97D0U\nm5FXlYeNVzbi7cFvQy4T4Z9diTsSkf4milMCxnZ9FzUq4HjWPpiKEhZKArzcItAhoAPSioNgbpRw\nSyQgwCMALjIX7RE686OELZEAV/kCAK20BOBkMwAnsk9gUNtBTtkcp05dh82pmzGl1xSnnv5fmbQS\nHi4eeKHfC/YeioTEbUQqAIAYJaBPRB9E+ERg9/XHYSpFUEgJ6BLcFTfLh8DcKOGWSIBMJkOQV9Dt\nI3S2kAA3+XwALRMAlUYFFaMybwmgxjkFYGi7ofYehk3Ylb4LlfWVTj3936BpwPKk5Xiuz3PS0T8J\nUWETAThy5AjGjx+PqKgoyOVybNvGtXHOHMQlAXKZHA92eRC7r19Fc1HCQklAdEA0MspzYG6UcEsl\nIMQrBKW1pXp1wkqAq3wWAEDN/M5Tw0+NqgYAzFsCcLJNgFkVWciuzMbQ9s4pABsub0Dv8N6IDYu1\n91BsxuaUzchX5uPtIW/beygSEgbYRACqq6vRr18/LFmyxIxpPQbsCwwf4pKAhzo/hPP551FcMwCt\nIQEdAzsisyIT5qYItlQCgr2CUVpXalQnnAS4yv8DAFBpEmBplHC1tj9Bc0sAakaN8rpyp5oBOJF9\nAgCccgagVlWLbWnbMLnXZHsPxaYsPrMYIzuOxF3hd9l7KBISBthEAB5++GHMnDkTEydO1PbPbw6N\n9r9reb4uHgm4v+P9ANjGJaZSBBuxTgKiA6JRWF2IWlUtbCkBvu7sOntThJEAXXc3NfMPWBolrBtX\nc0sAZbVlAJyrC+CJrBPoFNgJEb4R9h6K4OxK34VqVTWe7PmkvYdiM87nn8fRW0fxzuB37D0UCYkm\niGAPgBzAQu2/3wLwM0+dOCSgQ0AHdAjogCOZR7R1tpWA6MBoANDOAgC2kgBf9yQoG7jaAQNCSIBc\nJodcJoeaeRCWRgmbuwTgjDkAJ7JPOG1znD+u/IHe4b2duinOktNL0M6/HSb0mGDvoUhINEEEAgA0\nDuNFAP+E2CVgRIcROHLriF6d7SSgY2A7AEBmeaZejfAS4OPuA2XDSVgaJWyIaQlwk7tpNwFaFiVs\n7hKAs+UA1KnrcDbvrNNO/2+/ut2p3/2X1pZibfJavDHwjdvHYCUkxIRIBIClW7e/EBnpiYEDX8L4\n8f0xfvx4jlwA+0vAiA4jcDbvLJQNSr0620hAlN/HkMvkejMAOoSVAF+3CahWucHSKOGm8EuAXCaH\nhnTLPeZLgLlLAM42A3A27yxUjMopNwDuvr4bygYlnuzlvALw07mfoCENXh34qr2HIiHBiagE4Nq1\ndOTnK5GU9Bq2bbuAbdsmYerUqRyV9pWA+6IBDWlwIuuEUZ3wEuDmshlt/TxwqyKDo0Y4CfB1D4Wy\noS0sjRK2RAIYYoyaoJgnAWYvAWhnAHSdDR0dZ24A9MeVP3BX+F3oEdrD3kOxCQwxWJq4FJN7TUa4\nT7i9hyMhwYmoBIBFDmAZgFch1uWAHqHvItTbX7sR0BjhJaCNby3ylethboogN6YlwMfdB9UNdbA0\nStgSCSAQRxe05iXA7CWA2hL4e/g7TcMcZ20AVKeuw/Y0557+35W+CzfKbkib/yREjc2OAV64cAHn\nz58HANy4cQMXLlxAVlaWBcMSrwTIZI9gSFQVzuTu4LmWsBIQ4TsIBdUZsCRKmBt+CfB199UuaVgW\nJWyJBDSdAdBhWgJ0SwCerp48Y2FxpiZAROS0DYB2p+9GVUOVUwvA4tOLMajtIAyJGmLvoUhI8GIT\nAUhMTET//v0xcOBAyGQyfPDBBxgwYAA+//xzC4cmXgkY2KYbkvISQWR7CYj06Yd8ZWdYEiVsqQTo\nBIA9tmkbCWBIDRmKeK7FLwE1qhp4u3k320PdmZoAZVVmIbcq1ynX//+48gd6hfVy2uY/6aXp2Jm+\nE+8Mfsep2xtLOD42EYD7778fDMNAo9EYfKxevZrnHskmhidOCRjUdg4Kq4HsyuajhK2VgEjfSBQo\nG2BJlLClEuDl6gUNafRa9QovAUSAXPYNLI0SrlZVm98F0ElmAHT7S5xtBqBOXYdtaduc+t3/0jNL\nEeIVgqfuesreQ5GQMIkI9gBoALyk/XcJx9fFKQGD2rJ/mBNz+6G5FEFrJSDCNwIF1QUgmghbSYCb\nC9uoR8Wo9GqElQACIJN5wtIo4eoGM6OAnSgJ8ES2czYA2nN9Dzv976S7/6sbqrH63Gq8OuDVZpes\nJCTsjQgEwAXAb9p/xwEo5qgRnwS09WuLSN9IJOU9AHOihK2RgEjfSDRoGlBeVw5zo4QtlQA3+U8A\n2OAdQ4SRAF1HSLnsX7A0SrhGVXPHJQGeyD7htNP/PcN6omdYT3sPxSasTV6LqoYqvDHoDXsPRUKi\nWUQgAACgOwpUAOABOIoEDGo7CGdyz8KcKGFrJCDCh30XmK/M19YJLwFuLvsBACqGa1zWSwBD7F4D\nGYJgaZRwteqweUsATrIJsE5dh3N555xu+r9eXe/U0/9EhMWnF2N8zPjbHTwlJMSMSARAx18A8uEo\nEtAvoh+SC5JhTpQwS8skINQ7FACM0vqElQBX+fsAADUzHZakCDaFWwJ0SwtsRzTLooSrVWfh7VbI\nU8NCRE6zCTApN4ltAORkArDn+h5U1lc6rQAcuXUEyYXJ0tE/CYdBZALQA8ABOIoE9ArvhTxlnjaE\nxnYSEOiZCgDaJQB9hJMAN/lYAIBKEw9Lo4Sb0lQC6tR1AAAvNy9tjfkSUKPqCR/3TJhqFlStqkaD\npsEpZgBOZp+El6sX+kT0sfdQBOWPK38gNjQWvcJ72XsoNmHJmSWICYnB6E6j7T0UCQmzEJkAAEBP\nOIoE6NYxrxRd0dbYRgICPJ8BAFTUc41fGAnQNZtRMV/D0ihhbgwloF4rAIYbo8yTgOqGKPi49Yap\nZkHOlANwOvc0BrQZ4FQNgOrV9diattVp3/3nK/ORkJKANwe9KR39k3AYRCgAgKNIQPeQKMhlcj0B\nAGwhAV6uw+AmB8rr+KbwrZcAN7lWADTjYGmUsDkSUKf+BABXM5/mJaCqoQp+7oNhqlmQM+UAnM45\njbuj7rb3MATl7xt/o7K+EpN7Tbb3UGzCqrOr4CZ3wwv9XrD3UCQkzEZUAjBlyhS9ACDxS4Cn65Po\nEtTZSAAAoSVAJtuGAE83VNQtgSVRwk1pfiaAffdiWZSwORJQp2Z7QHi6enDUmJaAyvpK+Hv4w1Sz\nIGeZASisLkRGeYbTdZBz5ul/DaPByrMrMfWuqQj0DLT3cCQkzEYkAsBuFFu/fj22bdumFwAkfgno\nFV6Oy0UXOWqElYBAzw4or2sLS6KELZEA3S79xm57wkpAnfojAICn6zJYmiLYKAAAnwQ4ywzAmRz2\n5+FMAlCvrsfWVOed/t9xbQduVdzCm4PftPdQJCQsQgQCoAH74s2HuCWgR0gF0kqOwdwoYW6al4AA\nj0BU1I+BJVHClkhA4zE9/fVL4SSgTj0BAODpGg9LUwSr6qvg5+GnV9dUAkpqSuAmd4Ovuy/n4zsK\np3JOIdQ7FB0DO9p7KIKx7+Y+VNRX4ImeT9h7KDZhWeIyDG47GIPaDrL3UCQkLEIEAiAHEKn99wqe\nGvFKQOeg6ciurIdK8xhsKQEBngEor1PCkhRBSySAkAIAHP32hZGAutubAD+HJQFCRNdQ1VClNwOg\nw1ACdEcAHX0D1umc0xgSNcThn4c+CSkJ6BbcDXeF32XvoQjOjbIb2JW+C28Okt79SzgeIhAAGYBZ\n2n//G8BinjpxSkDHwAfBEHCrwrwo4ZZKgKerp/ZF1LIoYXMlgKF/A+ASAEAICdAJgIfLy7AkQKhG\ndT8YYjgEANCXgJKavxx++p+InG4DoJpRY2vaVkyKneRUUqNjReIKBHgGSH3/JRwSEQgAgNvTzu9q\nPxxHAjoFdQIAZJTPgTkpgi2VAE9XT9RrdEIgvAQwxHYuk8v4gpmsk4CqhioA0E7Rmx8gVFnPdgD0\nc6/iGRcrASW1pxHireSpcQyul11HWV2ZU63/H711FMU1xZgUO8neQxGcenU9Vp9fjRf7vmhWVoWE\nhNgQiQDomAXgQziSBHQI6AAZZLhZ7gtzo4RbIgEeLh6oV+svCwgrAQyxszBy2dOwNErYEG4JqKhj\nv7eN7+TNk4DK+tXa+30MU82CSmq7I8TLdLMgsXM65zQAYHDbwXYeiXAkpCSgnX87p1wf33hlI4pr\niqW+/xIOi8gEQAZgPhxJAtxd3NHOvx0yyjNgbpRwSyTAw9VVbwZAh3ASoGHY43lyWQwsjRJuSlMJ\nqKyvhI+bD1zkLnp1zUtART07Ln8PX5hqFlRc449Q7yEw1SxI7JzKPoUuQV0c/iijDoYYJKQk4PEe\nj/MsLTk2yxKXYXSn0YgJjbH3UCQkWoQI/690PAnoGNhRKwCArSTAw+XQ7W56hggjAbXqWgCAl9sm\nWBolbI4EVNRfQ4BnAEedaQnQne8P9d4EU82C2CCg0TDVLEjsnM497VTT/4m5icipynHK6f/kgmQc\nyzombf6TcGhEKACAo0lAG782yFPm6dUJLwEeLjmo11yDpVHChvBLQK1KKwCuEbA0StgcCais/wkB\nHnz56PwSUFzD/kxDvHvCVLOgxiAg/mZBYqZB04BzeeecagNgQkoCQr1DcW+He+09FMFZlrgMbXzb\nYELMBHsPRUKixYhUAABHkoAInwgUKAuM6oSVAA/XSahXK2FplHBTuCWgTl0HGWRwd3GHpVHC5khA\nRZ03/D1uwdIUweKaYvi4+WhbCHP3CVBpVKisr9Q7BeB4EpBckIx6Tb3TzAAQETalbMKEmAnaBEjn\noaq+Cr9e/BWvDHjFqfIaJO48RCIAp3ludwwJiPApQkG1sQAAQkqAm7wb1EwELI0S5qapBNSqa+Hp\n6ql3VEtYCaioH44ATy9YmiJYUltyOw6ZpakE6GKSDdfOHUsCTuechqvcFf0i+9l7KIJwuegyKYQQ\nnwAAIABJREFU0kvTnXL6f23yWtSoavDqAFMNzCQkxI8IBEAD4G0AwJQpE/WyAHSIXwIifH9HSU0J\n1AzXDnthJIAhBjKZNyyNEjZXAmpV1XpRvTqEk4DK+jr4e4yCpSmCxTVFRgIAGEtAUU0SAHDUOY4E\nnMo5hT4RfTh+Bo5JQkoC/Nz98ECnB+w9FEEhIixLXIa47nFoH9De3sORkLAKEQiAC4DfAQDr12di\n27blelkAOsQtARE+I0AgFFX/xHMt6yWAQNqd1JZFCZsrAbXqtRxJfYBQElBRX4EAjzBYmiJYXLOf\n44Ud0JeAvKrn2Vt823DUOYYEnM45jSFtnWP6H2AFYFz3cfDgDH9yXE5kn8DFgovS5j8Jp0AEAgAA\nnbX/rQc7rZvLUSNeCYjw/RIAUFD9BsyNErZUAhhi9Pr0Cy8Bdeor8HKtREtTBFn4JaC4plj7Qm5Z\nimBxTTpCvDNgqllQntKd/cyvhuda4paAiroKpBan4u52zrEB8HrpdVwouOCU0//LEpehS1AXPNjl\nQXsPRULCakQiADr+BFAHR5OAYK9wAEBZ7SiYmyJoqQQwxBidpRZWAqrqx8LPQwlrooRZuCWgsLoQ\nYd5h2hrzJaC4pg1CvdJgqllQXtVLCPSUw9N1LEw1CxKrBCTlJYFATrMBcHPqZni6euLhrg/beyiC\nUlRdhA2XN+CNQW84ZV8DiTsPkf0Wdwb7wu1YEqBLoKtqeBuWRAlbIgFExNFLXTgJKK8PRoBHL7Qk\nSrgphhJQq6qGskGJcJ9wvRrzJKCwWo0wn3Ew1SwoT1mNNr5dYKpPAIs4JeB0zmn4ufshJsQ5Gsok\npCRgbJexDp/MaMxP53+CDDK81O8lew9FQkIQRCYAANAFjiYBfu5sVG1VfQ0siRK2RAIYumEU1atD\nGAkorytHoGdXtCRKmJtGCSiqeRkAjAQAaE4CGjQNKKopQpTfJJhqFpSnzEMbv/Yw1SegEfFJwKmc\nUxjUdpBRl0THJLcqFyeyT+Afsf+w91AEhSEGK5JWYHKvyU7TqVFCQoQCADiaBHi7eUMuk2sDb8yP\nErZEAhjaBrmMb43beglgBSAQLYkSbk4CCqvZTZ5hPlx/OPklIK+Kba7U1q8tTDULyq3K1W4A5O4T\n0BRxScDpnNNO0/9/S+oWuMpdMa77OHsPRVD239yPG2U38PrA1+09FAkJwRCpAACOJAEymQy+7r5Q\nNujS6ISXgHpNe3i63kJLooQb4ZeAiroKrQAAQktAUfUHAIBwnwWwJEAot4r9mbMCAPBJQF5Vnt4J\nAMeSgLyqPORW5TrN+n9CSgJGdxqNIK8gew9FUFYmrUTPsJ4Y1n6YvYciISEYIhEADc/tjiMBfu5+\nqKrXj6wVVgJqVPfC2y0ILYkSNoRbAhpnAHQIJwGF1b0BAGHe62FJgJBOAKL8o/TqDCWAiNEuAegf\nAXQcCUjKY3sYDGw70C6PLyQlNSU4mHEQk3o41+7/AmUBNqduxmsDXuPYhyMh4biIQAA0AJ4x8XXH\nkABvN0/UqIyn6IWTgBpVHbzdBqIlUcJNaSoB5XXlCPAwDusRRgKKaorg7+EPD9dfYEmAUE5VIjxc\nPBDkafxuslECKurfRo2qBlF+UUY1jiEBSblJCPYKRnRAdKs/ttBsv7odDDGY0MO5+uOvubAGLjIX\nPNf3OXsPRUJCUEQgAC4AdO1Pv+KpEb8EuMhzoCGuNXphJKBGVQNvN1+0JEq4OQlo0DyMalW10QyA\nDusloEBZoD0CaFmAUG7VIrT1C+V518VKQGb5cgBAdGAHjhrxS0BiXiIGtR3kFO8sN6duxrD2wxDp\nG2nvoQgGQwx+OPsDJveajGCvYHsPR0JCUEQgAADwX+1/ZwP4gqdG3BLgImsAQwmwNErYEH4JYAXA\nGy2JEm5OAgqr2ennCN8inmtZJwE5VTlo599O+5n5EpBb5Yko/wKY6hOQUf4aAKBj4E8w1SxIrBKQ\nlJuEgW0cf/q/uqEae67vwcQeE+09FEE5mHEQ6aXpeG3ga/YeioSE4IhEAHR8BOBTOKIEyGWdwVAp\nLI0Sbgq3BDQKACC0BBQo5wIAInw+R0uihBvhloCsyiyjvunmSUBuVW+09fOFqT4BmRW94OHiinCf\nH2CqWZAYJSC3Khd5yjynEIC/b/yNOnWd08XjrkhagdjQWAxvP9zeQ5GQEBxRCcCUKecxfnwM4uMd\nTwLkMh9omAmwNEqYm6YSUNVQZdRYRTgJyFeWAwAifQehJVHChjSVgOzKbLTza2dU17wEZFbkop3f\nVJhqFpRZnonowM6Qy/j7BLCITwKSctkNgIPaDrLp47QGW9O2IjY0Ft1Cutl7KIJRWF2IzSmb8dpA\nafOfhHMiKgFYv349tm1LxdSpM+BoMwEuchcwpFu/Fl4CSmtL9PLudQgjAboo43CfP9GSKOGmNEoA\nQ2OQU5nNk5zGLwEaRoPM8kx0DuoFU82CMioytBvo+PsENCIuCUjKS0KIVwg6BHDtX3AcNIwGf179\n0+ne/a85vwZymRzP9ZE2/0k4J6ISgEb+B/aPr+NIgAwyMMTA0ihhcySA6BRKa4sR7OXDUWO9BOQr\n8xHiFQI3lwC0JErYlAQUVneHilGjvX8dz7W4JSC3KhcqRoVOQZ1gqllQZnmm3g56x5KApLwkp9gA\neDzrOIprip1q9z8RYeXZlXii5xNS5z8Jp0WkAgA4mgQ0aBrg7uKu/UxYCVA2bIaaIQR7/YCWRAk3\nwi0BBcoCRPhGaGssjxI2JQFZFfMBAO38P4clAUI3y28CADoFdtLWcEtARnkGOgZ21LuW40hAYm6i\nU6z/b03bikjfSKdpZgRIm/8k7gxELACAI0lAnboOnq6eenXCSUBpLRsSE+x1Ay2JEjakqQTkV+cj\nwidCr0Y4CciuZPcXtA+IhSUBQjfLrgOA0Yu7oQRUN5xGSW0JogONz9CLXwJyq3KRr8x3+AZARISt\naVsR1z3OqRLyVp5diR6hPTCiwwh7D0VCwmaI5P/Ygya+5hgSUK+pNxIAQCgJKK0tBQAEey1GS6KE\nm2IoATmVWXrtdnUIIwEZ5RnwdvNGiNffsCRA6EbZ94j0jYSXm5dRTaMEXC8bC0B/lkAfcUtAYm4i\nAMffAJhSnIL00nSnWv8vqi5CQkqC1PlPwukRgQBowB7/A4AMnhrxS0Cduhwerh4cddZLQHEN+/gh\n3g+gJVHC3DRKQGbFOXQMNN6lDwghAdfLrqNzUGfIZAGwJEDoZvk5dA5iYKpPwNUStnFRTChXDSBm\nCUjKTUKodyja+3NtjnQctqZuhbebN0Z3Gm3voQjGmgtrAADP933eziORkLAtIhAAFzS+4D0G4CZP\nnbgloFZVCU/XZJ5rWScBOVU5AKANvLE8StiUBDRoNiGnsg7RATvQ0ihhFm4JuF52HV2CumhrzA8Q\nulneHZ0CC2GqT8DVkmcQ7OWCUO9JMNUsSIwS4CwbALembcXYLmM5ZmocEyLCyiRp85/EnYEIBAAA\ndH3c3cH+AXYsCdAwi1HVAAR6boClUcKGcEtAblUuQrxC9GYYhJOA7MpYEICOgaloaZRwI00lIL00\nXU8AAHMl4GZZNToFjoepPgFXS7LRPaQ/TPUJYBGXBBCRU2wAzKvKw6mcU041/X8o8xCulV7DawOk\nzX8Szo9IBEDHn3BECSivqwQABHmOgaUpgk1pKgE5lTlGiXiAUBKQWZ4JAIgOXI6WRgkb0igBauZp\nZJRnoEtwF6Ma0xKgbFAipyoH3UL+AVPNgq6WXEX3kJ4w1SegEfFIQG5VLgqqCxxeALZf3Q65TI7H\nuj9m76EIxsqklege0h33Rd9n76FIOAkbN/Kd8LI/IhOAKLAvto4lAWV1ZQCAIK//oCVRwk0xlIBc\n5RmOTXqAEBKQUZ4BAOgQ8DRaGiXcFFYCsioSoGbU6BLUkaOGXwLSitMAALGhsTDVLOhqyVV0D+4O\nU30CDBGHBOgigB19A+DWtK24t8O9CPUOtfdQBKG4phibUjZJm/8kBOPEiRP45Zdf7D0MXkQmAAD7\nR9yxJKCslhWAYK9QtCRKuDkJyKk8gyi/Bp5rWScBmRWZiPSN1J5gaFmUMDeP43rZpwCALsFLYEl2\nQGpxKgAgJjRGW9dUAkpqSlBSW4LuId21NY4jAYm5iQjzDtMLSHI8lA1K7Luxz6mm/3+5wP6hfqHf\nC3YeiYSzsHbtWjzzjKm4e/siQgEAHE0CdMf02Nx6y6OEm5OAnCovtPU7gJZGCbNwS0BGeYZRFr1w\nEpBeGgkXmRzRAbthSXZASnEK2vq1hb+Hv16doQRcLWEloVEAAEeRgKS8JAxsO9Ch32XuTt+Nek29\n0wiAbvPfpNhJTjOjIWFfNBoNduzYgQkTxPv/iKgEYMqUKRg/fjzi4+PhSBKQp8wDAL0cdOEkoFal\nQm5VLToH3Y2WRgk30lQC0krS9N5p6xBGAlKKUtA1uBvcXP6AJQFCqcUntNP/xjRKwNWSjwEAXYO7\nGtWIWwKICEm5SRjUxvGn/3uF9eLY3+GYHMs6hrSSNLw64FV7D0XCSdi1axdGjBgBT0/j/jDiQSQC\nwE5vs2FA2zB16lTt7Y4hATmVVxHmHWbUB0AYCbhRdgMA0DX4S7Q0StiQRgkgmoDU4kvoEdKDo856\nCbhSfAU9w3rC0gChlOKD6BEazPMcWQm4XHQY0QG+8HHnOn4mXgnIqcphNwA6cAdANaPGX9f+cpp3\n/wCw6twqdArshJEdR9p7KBJOgtin/wFRCIAGwJPaf3P9ARa/BGRXrkCUfwRHjfUSkF7KvuB0CYpB\nS6OEm8JKQGH1KJTXKdEjtIbnWtZJwOXCy+gV1kv7mXkSoGa241oJITZ0O0z1CbhY0Bt9IpQw1SdA\njBJwNu8sADj0CYCjt46itLbUacJ/KusrseHyBvyz/z+dqp2xhP2orq7GqVOnMGbMGHsPxSQi+G13\nAfuiB7B/NB1PAnKqlGjnn4mWRgmzcEvA9bLr8Hbz1i4vtCxKmE8CUov/BQDoEToPLY0SZmkqAWW1\nZchT5mlnAHQ0LwE3yoqhYgg9QjvDVJ+A5MIS9A6Pg6k+AWKUgKTcJIffALg1dSva+LZx+FMMOn6/\n9Dvq1HV4sd+L9h6KhIg4e/Ysnn/+eYwYMQJ//fUXysvL8f777+Ott97CpEmTcPHiRd77JiQkIC4u\nDnK54UvsoUOH8MILL2DYsGHYuXMniAhLly7Fe++9hzfffBMjRozA6dOnAQDx8fF466238NZbb2HE\niBE4cOCA8E+SREBFRQUBoIoKENF/iIjhqcwioq5E1IGIbpi44gwiAhHNNlGTTkTtiagbEeXw1DBE\n9KH2Wt/zXqnf8h70+nZPIupDREU8VRoieo2IZET0k4lxJRJRIBHdTUTl9Oafb1KfZX2MalRE9DQR\nuRDRHyaudYSIfIhoFBEpm3x12Zll5DrTlRrU44jInYh2mLjWbiLyIKLHiKiOp6aaiMYQkTcdu7WE\noACdzzvPUZdARK5E9JT2uTSyJWULQQHKrkghomFEFEBEpw1qSmpKCApQfHI8Ef1C7Pf0ZWK/x1wU\nE1E/IgolomQTz3EJsT/r6cT/O5hLRD2IKIqIrpm41lzttT43uHXcunE09texJu4nbhiGoc6LOtPr\n21+391AE4+4f7qZHfnvE3sOQEBlTpkwhjUZDs2fPpvDwcHryyScpNzeXDhw4QO7u7jRt2jTe+44d\nO5ZOnzb8u8UwDD355JNERPThhx9SeHg4TZs2jQ4ePHi75vXXX6fOnTvTrFmzaPPmzbdvnzt3LoWE\nhAj8DIlEMAOgz5cA5oHNBnCMmQAiQnppNroGv4OWRgkbYjgTkF6ayrHRTZiZgNTiVHQJ6gI3l01o\naZSwIY0zAZcL34dcJufYYAiYmgm4WHARwV7BaOsXA74+AckFbMvlPhF9YKpPQCPimQk4m3cWA9oM\n4LmP+EktTsWNshsYHzPe3kMRhEuFl3Aq5xRe7v+yvYciISJu3LiBbt26QS6XIycnB2VlZfjkk0/Q\npk0blJSUwM/PD+PHc/8/UFhYiFu3bmHw4MEGt585cwbDhw8HAOTk5KC4uBjjxo3D/ffff7vG398f\nGRkZiIyMxMSJE2/f7ufnh7KyMhQVFd2+ra6uDtOmTcPChQvx73//GwsWLLD8iQquFC2gcQaggogW\nEvvOyTFmAnIqcwgK0NbUrUR0mYjCydKZgHXr1nHUsTMBUQvc6KO9/8dzLetmAsb+OpYmxE/QflZP\nRONJqJmA6TvbU7fvZER0yMS1EmjdOjnpzwRM+n0SjV4zWq+mgoxnAr4/9T25z3KnBnWDXp34ZwLy\nqvIICtAfl9mfFffPXdzMPzqfvGZ7UU1DjVXXEctzn75zOoXND6N6dX2rPq5Ynr89cITnfvz4cTp/\nnp297NOnD40aNcrs+y5atIgUCkWT248cOUKZmZlERNS+fXt65JGms05jx46lLl26NLn97bffJh8f\nH9JoGv+2TZ8+nWbMmHH785EjR9LGjRvNHicR+5fJ7hgKAJEjScD+G/sJClBqUar2FsslIC4ujrOq\npGafdqq7KxGV81yr5RIQtSCKPtr7kV6NcBLwwJqR9Pj6MCLyJlMSEBc3iPSXA7os6kLv73rfqMpQ\nAl7d9ir1XdaX42riloAdV58mKEA3StnfV76fu5i576f7KG6d9eMWw3OvU9VRyLwQ+mD3B63+2GJ4\n/vbCkZ57cXExyeVygxfa5hgyZAhdvXqV9+vp6ekkk8nom2++MbhdrVaTn58fvfzyy03u0717d3r4\n4Ydvf15bW0s+Pj6UnNz4N2zRokUWf29FtgSgYzqAhXCE5YC0kjS4yl3ROaizts7yKGEgi3NUyQUu\nAIA+EQVoaZRwI4bLAUXVGcipykG/yH56NZZHCXMtBxARzuZdwIA2b6L5joFtoFsOqKx/CtfLrhuN\nCTDuE5BceAK9I3pzXEvcywFJeesQ6OmJjoEdeerETWltKY7dOoZx3cfZeyiCsC1tG0pqS6Tpfwle\n9u/fDwAYOXKkWfXXrl0DAHTr1o23Zt++fZDJZE2ueebMGSiVyia3Jycn49q1a3jyySdv35aamora\n2lpERzc2cYuOjsahQ4fMGqcOkQoAYI4ExMcfgSUSEB9vuQSwTYl0NJWAtOI0dA7qDDcXN716yyQg\nJ+c8uPYEXCy4CHcXd3QP+RvGpwMMx9W8BLD1jRJwPp9dX+of2d+oslEC4uPjYKkExMfHI7MiE2V1\nZegfOQTNNQvKycmBbk/AxYKtAIB+kXdxPB4rAQz1xLm/L6F3eCDPuJpKgOH3CjBHAtj7WCYB8fFD\nYEoCzub1woA2dZDJZgDQPXfLaPpchL8PX/3u9N3QkAaPdWsa/mPpY4jhua86twpD2w1FbFisWfVC\njsvS599a4xLqd8UUYn3uXBw4cAAeHh645557zKo35+z/wYMHERgYiP79Df/2HjhwgFMM1q1bB09P\nT/zjH/8AAKxevRoFBQUAAB8fn9t1Pj4+UCqVUCqVZo0VgBj3ABjDvxzQON1h3nJAXFwMWbocwD2l\n0rgccP9PXemJDU9wjInI3OWAiAgv4jod8MrWV6j/8v7azwxPB3CPi385wLD+CM076ka+c1xIw1Ty\njKue4uIiyNLlgLi4ONp0ZRNBAcqtzNXWNJ4OMF4OiIiIuP3vxadeJfdZoHr1E2R8OkBHalEioTvo\n7+s+ZHw6wJDG5YC4uHE8NfzLAYbfL/OWA+LifMnUckD0wmj6cPd9pNsToP/czaUl06eW3oev/ulN\nT+v9Plr3GPZ+7pnlmSRTyOjHpB9t9himsPT5t9a4hPpdMYVYnzsXsbGxFq3/9+jRgwoKCkzWtGnT\nhiZOnNjk9oceeoi6du3a5PaYmBiaMmUKERElJyfTzJkzad26deTm5mZQd+jQIZLL5ZSbm9vkGny4\nmq8KLYeIUFVVxfv1yspN2v9Wcnz1n2DflX8E9l2mAuw7cUCtVmvv4w/23eg4APcB+AtAxyZXUqs7\no7JyEtjlgDoA/+J4vDC9a42AWh3NM65PwVAdkm4uxgfDut6uaRwTwL7D3A7gMbCzCtvBvvs0hMgX\nlZVPAXgJQC0A1iDPZZ5DTEiM9nrdAGwBMAHAA1Crg3jG9T0AFdjZgJ/ATuUbj6sPTt8Yhl7+h6Gs\negzA7wB8mlxJre6Hykq59jHjwe7GN+Ye7demABgPtVqGE+knEO4aDh/y0XvMXwFMBbu8sAnAcO1z\np9s1p2/UI8Y3GnXVm1GHpwD8AHZ2o5HDV88CDNDNpwcqK8dovydcTXUmAFgO4HWo1e1QWVmOphNe\nbgA2AxgP4H6wvzc9Ob5fz4L9uXwI9nfwS+h+BxvxgVo9GJWV2Wj8HWxsk1taU4rMgkz0uPszVFaO\nBqAAkTfPz5Afw3HZ5j5c9WpGjR3JO/DawNc4r2XpY+j/3K0ZV0vvs/zYcnhpvPBw+4cNvt4a31/A\n8uffWuMS4nelOez13P38/CzK3ygoKEBqaqpeZ1rTnDp1CtHR0QgPD+etSU1NRX5+PkaNGtVkvMeP\nH+d8rOLiYtx3330gIsybNw/fffcdjh071qRO987fw8Ojydd4MVsVrED3Dl/6kD6kD+lD+pA+7PHB\nPcPMz4ULF6hNmzaUkpJiVv27775Lv/zyi8mao0ePUrt27ejWrVsGtxcVFVFkZCQdOtR0w/S6deto\n9OjRNHnyZNq/fz8RESUmJpJcLqe6usZN2OvXrycfHx+zxqpDRkQEG0PNzgDcQPv2/ZGVFQJ//10A\nuvNULgU7EzAd+jMBhuSAfffeAL6ZAJa5YN/JfQrumQAAuKG9lgeAHWDXexvZcHkDXt32Km6+9yqC\nvX8Auz/gdZ5rpYKdCYgA30wAu2ntfQA/43z+f3H/T3Ox57k9uLvd3UZ158C+w+0K9h1sAMe11ADe\nAPtu+yfoZgIANso1akEUFj+6GM/17QpgEth30dwzAez38nmw6+Z8MwEAsA/AFHT7Hnihz9v49H4F\nR00N2JmAU9CfCahV1SLqmyh89eBXeHnAy2C/Ry9on2fjTMBDvz6Edv7tsHrCagCVYPcfpIJ/JgAA\n1oP9uTwH4Dtwb30pBTsTkAP9mYCm/AB2JuBNcM8EAOzej3EAlNDNBCw8sRBfHf8K2f+XrddudiHY\n3+P/gv29Fi//2/8/rL20Ftfevebw7XL339iPx39/HH8/9zeGtBti7+FItBKWzgBYgkajQdeuXXHp\n0iWDdXlbodFoEBYWhpMnT6J7d/b1cvbs2di/f//tjYtmYZEu2IjGPQCxRBRBRKaMSzxHBN/f9T51\n/LYjmdsx0JIjgktOg9xmupg4b224J4Ab7j0B+26wxwsvFVzS3mK6YyCLeUcEcyrXERSgTVcGkDkd\nA3V7Ao5mHiUoQGdzz+rVGXYMVGlU5DXbi74+9rVeTdM+AdzY94jgkxuepHtX38tRx90xUGz0XNKT\nXtrykr2HIQhP/fEUxS6OJYbh+9lJSFjGjh07bq/TtxavvPIKzZkzh4jYLoP9+/enTZs2WXQNkQlA\nOhHdRY4iAQNXDKRnNj2j/UxYCXguoRsNXgmypG0wN00lYPah2RTwZQBpGP0XQmEkQLcBMKvCncxt\nG0x0iBYcX0Bes72MmvsQ6UvAxfyzBAXoUIbxNJn4JSB6YRT93y6+hk7iloDrpde1UmfZHxcxUlxd\nTO6z3I0kUkLCOp555hnavn17qz5meXk5vfDCCzR//nx6//336euvLf+dFpkAVBBRATmCBJTWlJJ8\nhpxWnV2lVyOcBHT/vju9u6MXWZodwI2hBDy69lF66NeHOOqsl4APdn9AHRZ2IEuzAyb/MYqGrxrO\nU8dKwOqzg0mmkFFlHdfJBfFKQF5VV4ICtOHSdyauJV4J+O7kd+Q2043n++5YLDq5iFxnulKB0vRO\nbQkJc6murqaOHTuSWq2291AsRoSLeeFg15LDwO6cT+Wps2+zoMOZW8AQg1Ed9XdzWh4lzNUnoLC6\nEFdLruKedv+FNVHCjTT2CSB6CiezD2NYu2EcdeZHCfM1CzqedRzD2g+DpdkBp7IP4u6oKJ7nyPYJ\nOJWTiB6hfvDz8OKoMWwWZCpKuLWbBZ3K/hgAcE+7L2BNlLC9+PPanxjZcST8PPzsPRSrICKsOrcK\n42PGI9yHf6e2hIQlbN68GY8++ihcXFzsPRSLEaEAAI4gAQcy/g8dA9ujU1AnoxrrJeBgxkEAwMiO\no2FNlLAhrARcLXkUpbVKDG3fNIqXpeUSUKeuQ1Jekp5cmCcBBcqVyKwg3N1uC/g7Bj6OY1ntMbx9\nFfiihMUqASezr6KtXyTa+QfCmihhe6BsUOJgxkGn6P6XlJeEiwUX8Ur/V+w9FAkn4vDhw3j++eft\nPYyWYe8pCCJTjYDEuxxw11I3+ucWf2pplPDhw4cpLi6O2rYNJ5kMtHVrNOmWA97Y/gbFfB+jV92y\nKGEufjr3I8kUoPJaOVkTJcxiuBxw7NYxggKUmJNoVGe4HDBnzhwaPHgw+fn5UXh4ON095m7CO6CM\nsuHElx1QWlNKUIB+Pvcu8UUJNyKu5YCRP4+kSb9PIqJcWrYsgvr0cSV/f1/y9/enoUOH0s6dO42u\nJZ7lgM0pmwkKUHpJuuDXnjNnDslkMnr/fePsB9vwxvY3qN037Uitaf2pWoVCQTKZzOAjNja21cdh\nL3JycujZZ5+lkJAQ8vLyoj59+lBSUpK9h3XHI9IZAB3inAnIKHfBpUIVxnZ1Q0ujhKurq9GvXz8s\nWbICMpkcQDl0MwH7M/YbLS20LEqYaybgQMZh9InogwDPKbAmSpjFcCbgeNZqeLt5a2N69TGcCThy\n5BDeffddnDp1Cnv37kVRVRFc1rogzH0L+NoGn8g+AQAY3mEa+KKEGxHPTICaUeNMzhncE3UPgDZo\n3/4rzJsXiaQkHyQlJWD06NGYMGECUlJS9K4lnpmAP6/+idjQWHQJ7tJ8sQWcOXMGP/xoB93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qM6YSWguBrkN8eDPtj9AU+N9RLwXMJz2s6Cl0iIKGEWVgIYZgh1WdSJXtzyIkeNaQl45LdHtL3Z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\n", "text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for geod in outgeods:\n", " graph += geod\n", "show(graph, aspect_ratio=1, ymin=-4, axes_labels=[r'$r/m_0$', r'$t/m_0$'])" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The event horizon:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "t0 = -2.6\n", "sol = desolve_rk4(drdt0, r, ivar=t, ics=[t0,0.01], end_points=[t0, tmax], step=0.02)\n", "hor = line([[s[1],s[0]] for s in sol if s[1]>0], color='black', thickness=3)\n", "graph += hor" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "ingeods = []\n", "rmax = 6\n", "for t0 in range(-6, 10):\n", " ingeods.append(line([(0,t0), (rmax, t0-rmax)], color='green'))\n", "for geod in ingeods:\n", " graph += geod" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The trapping horizon:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "trap = line([(0,0), (2,1), (2,tmax)], color='red', thickness=2)\n", "graph += trap" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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ori6GWCSGh4Nl5YRLa0pRKi/lRAAA65OAPal7MKnTJKMOs9m6BMzuNhsAcKvkFukdoIXN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TtG26R/QxIghedvSwxJgDM99+TkZMrlcp0P2vJo3749//33X9H7b9y4QZlMxmnTpuncXlRURH9/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\nCXDj3OzuGJiak4rO0zrDL8rPKcKfIpUEHL19VLHhT5FCAvKLm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iujAQDYj4BSxl+yHQGl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\nRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 51 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for t0 in [0.5, 1.5, 2.5]:\n", " graph += line([(0,t0), (rmax, t0-rmax)], color='green')\n", "show(graph, aspect_ratio=1, ymin=-4, ymax=4, axes_labels=[r'$r/m_0$', r'$t/m_0$'])" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "graph.save(\"vaidya.pdf\", aspect_ratio=1, ymin=-4, ymax=4, \n", " axes_labels=[r'$r/m_0$', r'$t/m_0$'])" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "A zoom on the trapping horizon in its dynamical part: notice that the \"outgoing\" null geodesics cross it with a vertical tangent, in agreement with the cross-sections of the trapping horizon being marginally trapped surfaces." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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4Kr7522/i9kdu51Icw3PmTaiRYL9h8Qa8OPyiyVvxEfbaqw77wbZB+Dw+kx+W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3OUp+Ko9b1c9v5l9F/f/hcRuVfF0eb33Rm270N5Ko42771zTGV5xo6CHTKqO3WxdOlSys/Pd+sk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\n+tDQUHTt2hULFiwweiTuXiUV9JYY9vb7IvILBA4KxPm75wt9l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