{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"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) (v0.9)\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`"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First we set up the notebook to display mathematical objects using LaTeX formatting:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%display latex"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Spacetime\n",
"\n",
"We declare the spacetime manifold $M$:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"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": {},
"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": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"Chart (M, (t, r, th, ph))"
]
},
"execution_count": 3,
"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": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"t: (-oo, +oo); r: (0, +oo); th: (0, pi); ph: (0, 2*pi)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X.coord_range()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Metric tensor\n",
"\n",
"The metric tensor corresponding to the Vaidya solution is:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"g = -(r - 2*m(r + t))/r dt*dt + 2*m(r + t)/r dt*dr + 2*m(r + t)/r dr*dt + (r + 2*m(r + t))/r dr*dr + r^2 dth*dth + r^2*sin(th)^2 dph*dph"
]
},
"execution_count": 5,
"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": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"nice_derivatives(False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"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
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"Ric(g) = 2*D[0](m)(r + t)/r^2 dt*dt + 2*D[0](m)(r + t)/r^2 dt*dr + 2*D[0](m)(r + t)/r^2 dr*dt + 2*D[0](m)(r + t)/r^2 dr*dr"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Ric = g.ricci()\n",
"Ric.display()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"Ric(g) = 2*D[0](m)(r + t)/r^2 dt*dt + 2*D[0](m)(r + t)/r^2 dt*dr + 2*D[0](m)(r + t)/r^2 dr*dt + 2*D[0](m)(r + t)/r^2 dr*dr"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Ric.display()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Ricci scalar is vanishing:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"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": {},
"source": [
"The energy-momentum vector ensuring that the Einstein equation is fulfilled is then:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"1/4*D[0](m)(r + t)/(pi*r^2) dt*dt + 1/4*D[0](m)(r + t)/(pi*r^2) dt*dr + 1/4*D[0](m)(r + t)/(pi*r^2) dr*dt + 1/4*D[0](m)(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": {},
"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
},
"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": {},
"source": [
"The derivative of the function $m(v)$:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"D[0](m)(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
},
"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": {},
"source": [
"The future-directed null vector along the ingoing null geodesics:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"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
},
"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": {},
"source": [
"## Outgoing radial null geodesics\n",
"\n",
"Let us consider the vector field:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"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": {},
"source": [
"It is a null vector:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"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": {},
"source": [
"Moreover it is a pregeodesic vector field:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"-4*(r*D[0](m)(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[0](m)(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
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"-4*(r*D[0](m)(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
},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"-4*(r*D[0](m)(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
},
"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": {},
"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
},
"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": {},
"source": [
"Let us choose a simple function $m(v)$:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"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
},
"outputs": [
{
"data": {
"image/png": 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HAAIR5QEAAEkvvijt2WPO2HUAABPlAQAAVTwU7uqrpVtvtZMFAAIV5QEAEPbee8/7z7k8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\nqHgQERERERGvqHgQERERERGv/B9ru/fVUaPA0gAAAABJRU5ErkJggg==\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": {},
"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
},
"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": {},
"source": [
"and we perform a numerical integration for $v_0 = 3 m_0$"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"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
},
"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
},
"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
},
"outputs": [
{
"data": {
"image/png": 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zBFpOiw8Gf8C6lFaJAgBDnvaeCG4XjB2JO1iXond8dwIsV5VDqVHqHADSi9IBAB3taShW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\nYRhGh3AAMAzDMIwO4QBgGIZhGB3y//Qpr4GvrWaOAAAAAElFTkSuQmCC\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": {},
"source": [
"The event horizon:"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"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
},
"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": {},
"source": [
"The trapping horizon:"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"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
},
"outputs": [
{
"data": {
"image/png": 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jqQScvncaNx/fxJzYOQxHyBx0S8C13GvYnbKbrP3zDEH97e0b1hdrhq/Bmitr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\nY4yxGEYAMMYYYzHsP6LWArLiJR/8AAAAAElFTkSuQmCC\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
},
"outputs": [],
"source": [
"graph.save(\"vaidya.pdf\", aspect_ratio=1, ymin=-4, ymax=4, axes_labels=[r'$r/m_0$', r'$t/m_0$'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"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
},
"outputs": [
{
"data": {
"image/png": 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rcYZee86cTaq3GfrVC1fjnbF3TJzl5Qy9WNpm6Be2LbRoZl6JM/SVZuib/FlQ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\noHdWdYJ5gKAXjaDXnv2gbw+0I5FOYDI1qXqUoBd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vxJsPQa+98qBv9Fq1Zn66meU0ZwLb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evWCYqzEyb1V4DOyvyMGbJW4t1/zSe+Qi/PV8i2FXpvfU3t/jriK/QTJkwQGaUjbCv03vh9CbvG\nLnrwsyC6+aPe5Gk1SZ6fxbZCL8c17Cv0wl53cdWkjRs3UmVjJUEL+jTjU4/O0Z3uFXp1/H2Jr9BL\n9XMs3reYei/vTSaTyeG0lfK8521x/7OIr9DL87rb5lQh1zCZTBS/PJ5xtiZbNm7cSOPHj7epzNu2\nFYiv0Hv6uq8/s56gBdU01zh41rZC76334meZnxG0oPL6cid7ia/Qy/Oz2OZUOa5hX6F3/7pLV6G/\n6qqrmPrlR40aRTqd69a0pKQkuu+++7ptv+OOO2j48OHdto8cOZIefPBBIjJX6RctWkSnTp0ijUZD\ndXVdixZ+8cUXFBMTIzhWIrW32aSnU3Xq3WaZl7mdRtjXfOKEXr6vkLuEPjV1mkzXsEXYzyJO6BMT\nE0VE6IouoU9N7T5wRWqEvu6j3h5I83cGkadfD8v399Ul9Kmp98hyBWuh75vQV+BRngt9amoq7c7Z\nTdCCLlZI2VJhK/TeaBsRdg1xQi/Vz3H/f++nX6z7Redje6GX7z3fhbCfRZzQy/e6d+XU1NQ73O59\nueYyQQvakbXD4yv+8pe/pNDQUBuZ796qIE7oPX3dbQeaOqJL6FNTf+nRNVhITU2lF/a8QP3/2d/N\nnuKEXr6/r66cKtc1rIU+ISFBwBHihb6srIw0Go3gfvnDhw/T9OnTXe5z/vx50mg0tHLlSpvtbW1t\nFBUVRX/84x+7HRMfH0/vvvsuGY1Gevjhh6m6upp27dpFGo3GZkDs7t27SaPRUH19vaB4iYhC2Or4\n4iAi1NfXC9u5qgo08Xo0thsAdHyBl5AA/OUvwO9+Z26laW83/5MAg8GAujohrRf/BTAbwHQAXwCY\nJMM1WIkAsB3APTAYDqKu7gSAkTJcpwthP0sCgK8A3APgZpjblZJcHjFnxBw039qMp799GpEtkdDr\n9dBoNJLE3MVImF+7+2AwAHV1xQBiJb5GF0J+V41tjcgqKcZT455EXd1HAO4DsB5AuKTX8Yz7ALwH\n4EkYDANRV1cLQNoOvcGRg/HVzK9wz8Z7UN9cj8u6ywKmLnwKQAvMXw+3wvx1sTAMBgMO5hxEtCka\niaGJEv/eXgXQBuBxGAzXyPSadCH8df8AwO8BzATwCYC7ZbiGa05ePokZI2dYnasH/pt6ArO3XI/p\na55AqCFGJb+vCJhz1y8B/Bzm3DVC4mt4QldONef6S3CVU3/K/gloAUZGjfQ4npqaGrTb3WeHDh1q\nd76RMLe23AvgFzDnV9c59dkJz6K1sRXPff0cotqiPIrveP5xXBPr6j32MwCfAvgNDIY41NVVgCWn\nsmIwGHA8z11MAHA/gGYAc2HOFSvBklPl+/vqyqkGw3BZrnF9/PXYkroFD3z2AEzNJuiqdIgMddca\nvRSWnAr8CjExMUxeoNPpkJSUhAcffFDQ/kJabKqqqjBgwACb9hgAqK2tRUxMjMPjV61ahTVr1mDv\n3r2YO3cuevXqherqagQHByMoqOv1DwsLAwDU19cjOjpaUMwaIlkalB1SV1eHuLg4b12Ow+FwOBwO\nh+NH6PV6xMbKU4AzGAwYPnw4MjMzERUVJcs1rNmxYwdmzpxp84F5586dSE1NRWVlJXr3FrYeh1cr\n8zExMdDr9cIPKCxEzWebMHjxUgQ/C3zy62fxPyNeli9AJhpgrtCfBWuFXl4qYK6EVwPYCbkr9MLJ\nhTmuSAip0APA2tNr8fS3T+OJiU9g+e3LZajQA8ApmCvPIyCkmiQXq46uwtIDS1H8l2KEBIXAPFj3\nNwBuA2uFXl42wTx461GwVpOEcu7KOdyz8R4MihuEL+d8KXBxoX8CWAzgeQit0I99byxSR6Ri6e1L\nRUTrCgLwNwAfAlgF8+9MDbTDXKHfBdYKvRi+z/0es7fMxpknz2BIryHdnm9o02H2lutxVlePLx5c\niUkDf++VuNxTAXOFvgasFXp5cZ9TZ22ehSBNED771WceX2X+/PnYsGFD1zlnzcJHH33k4ohTMFfo\nLd+Aus6pRISlB5bi9YOvY9G0RXj6xqcFxZVVmYVJH07C9jnbceuQWwUcIX9OvVxzGde+fy02P7AZ\ndw2/S+BRG2Gu0MuXUz2DPaeysv/yfjzw2QP42aCfYePMjQIq9ARAg5iYGFniAYDdu3djypQpXhF5\nAOjXrx+MRiNaW1sRHm7+m6yvr0ePHj0EizwA3xkAO2NtPwpdDNp+8e9Kh2QFn7aSDb6wlDMe2PIA\n3fzRzXZb1TFncnd8f2Ep6Qe/OoNPW2lBu1dL8cvjXb6PHQ2KVQe+N22lyWSihDcSRC9CN27cOJt+\n+X/+858CjpJu2kpnrDuzzsXgV2fIm1M3n9vsZvCrM/i0lcIXlpKX3/zmN7Rjh+djTFhpb2+nnj17\n0sWLXXll8eLFNG0a2/hHn5H5yuoymrV5ABd6wXChZ0NZoR+0YhA9+92zDp7hQi+H0Msz+NUZXOiJ\niP7n0/+huz9xP+CcCz0rjnNqsb6YoAV9eeFLj8/c2NhIwcHBNjJ/4MABgUfLK/Tzd86nkW+PFBiL\nNfLl1L9+91dKfivZw6O50Cst9A0NDZSSkkIGg8Gr1/3DH/5Ar75qXpfAZDLRddddR1u3bmU6h8/I\nvF6vpzZDIxd6JrjQs6GM0FtWft1ybouTPbjQSy30yw4so5ilMWQ0eeumGdhCbzKZqO/rfenltJcF\n7c+FnpXuOXX7xe0ELaiwttDjs9qv/BoUFEQNDQ0MZ5BP6Cd/OJke2vYQQyzWyJNTb/34Vpq5eaaI\nM3ChV1LoN2zYQPPmzfP6dWtra+mRRx6h5cuX0zPPPBMYK8ByoWeFCz0b3hd6y033cs1lF3txoZdS\n6O//7/007WPvTOPaReAKfX5NPkEL+jrra8HHcKFnxTanvvjDi5TwRoKoXLlixQobmR87dqwHZ5Fe\n6FsNrRT+SjitPLzS4fPCkDanGk1GilkaQ8sOLBN5Ji70Sgn9448/TkeOHPH6daXA52SeiAs9O1zo\n2fCu0L/4w4uU+EaigJ+HC70UQm8ymSjpzSR6Yc8LEkcphMAUeksvsa7B9SIs9nChZ6Urp96x/ueU\nulHcXOG//vWvbWT+scce8/BM0gr9ydKTBC3oYOFBD+OxIF1OPX/lPEEL2pO7R2RMRFzolW+58TV8\nUuaJuNCzoz6h//e//00pKQMoIgI0eXIEHTv2jdN99+7dSxqNpvMfANIEaai8nHWgkVC8J/S3r7+d\n4abrn0L/448/0j333EP9+/cnjUZDX37Zvc9XKqEvqC0gaEHbL25njlMaAk/oH3zzQYocHeny9bWm\n2/tdA4IG9PWpNySNSxzqFXqjaQDFLQuiJT8+J+pMw4cPt5H59957T8TZbIV+6dKlNHHiRIqJiaGE\nhAS67777KCsrq3NvV0L//vH3KXhRMDW2NYqIx4I0OdWzAbmu8F2hd/faOsLZe/5ysatvrDkW1DIH\nEjOhwT2wadYlzBg1ALO3LMVXWS8qHVIH0TBPEzYewJ0ADisbTicJANIAxAOYBuCiotFs3rwZzz77\nLBYtehWnT3+La68Nxp133oOKinMuj8vOzkZ5eTne2P0G6C+EJSeXgGRZKmEizFOZXYT5dZRnIRsT\nmXC85DgmD5gs8Ii7YF6cZTeAB2BeLEkNPALgYwBrYJ660sR0dFNTE6677jq88847AOBwGtJxieOQ\n9mgaCmoLcMeGO1DdXC3gzC/AvODIIgBaAMCR4iMAwPA7lxoNgLdhXqDlcZh/Z2ogFOZF8VIBzAKw\nQ7IzZ5ZmYvDVg12+vo6wvN/zCs9i8opozNn1Nxwu+kCyuMSRAGAvgN4AbgWQpWg0XQxHdtVH0Lea\nMGnAJwDKPDpLTU0NcnJybLbdcMMNIuKaCGAPgAsA7sT+/WlYsGABjh49iu+//x7t7e2YPn06mpqa\nAJj/Rhbduggv/fwlPLfnObx+8PXOMx0vPY5rEq5Bj9AeIuKxIE1OPV5yHCPjR6JnRE8JYgLMU1Wu\nhac5VT6651R79u/f7/K1dYXlPb/t6DZEPBeBx9MeR3N7s5Q/gH+i9KcJdzirzFvgFXpW1FGhnzRp\nEi1YsKDzscl0iQYMCKbXXutDjlpuLJ/aa2trO7f5Q8vNhYoLBC1od85uxiP9s0JPRKTRaGj7dudV\nc7EV+me+fYYGrxzsUWzSEhgV+nZjO/V4tQe9cdBcVXf3+hI5fr/zlhvhdFWJ+xNLG6M1u3fvtqnK\nh4eHU2trqwTROW65qaioII1G0222HEcV+nHvjaM/bv+jBLFYIy6nihuQ6wrfrdBbcPbaWuPoPc9b\nboTjs5V5C7xCz4ryFfq2tjacOnUKt99+e+c2jWYEbr99Bg4fboC5yuW4mjR+/Hj0798f06dPxzWt\n12D1Pavx9rG3sfDbhT5ZoT9YeBBBmiBMGsC66Jh/VuiFILZCf7RkK24ceKPkcbETGBX6CxUX0NTe\n5MHfuO37PeNEHr55KAvjk2Jx5ydP8Aq9C44WH8VVfa5Cz4gfATTBVU51xvHjx20ejx8/vnOZeXHY\nVugtObW2thYAui2UY1+hX7J/CTKvZOKGAWK+JXCE5zm1zdiGM+VnMLH/RIljAny5Qm/B2WvrCOv3\nfHhZOHb+ZicOFBzAfZvv4xV6F/i8zANc6NlRVugrKythNBqRmJhoG1XCcJSXj4Kjm0///v2xevVq\nfP7559i2bRuSk5Nx66234oagG3xa6PcX7sf4pPGIi4jz4Ggu9KxC32ZcjJOlRbhxQI3kMXmG/wv9\nsZJjCNIEYUK/CYKPcfZ+z84s40IvgGOlxzo+PA2HOS52obeXeXEtNvbYCr3JVIunn34aU6dOxejR\no7vtbS30L+19CUYy4ob+Uss84GlOPXflHFqNrTLFBPiy0JtMJpevrQVn7/metT1thJ7jBKW/GnCH\nuzYba3jLDSvKtNyUlJSQRqPpNgXU3/72N5o8eTIJneXmlltuod/+9rdE5LstN4NXDqandz0t8iz+\n1XIjpA3DAmvLzbHiYwQt6EiRvDMysOO/LTdP7HiCrnn3ms7HLK+vNdbvd95y45zm9mYKXRxK7xx7\nx2or+8xh/fv3t2mzWbdunQzRmltunnwygYYMSaGSkhKXe5tMJpq+fjpBC1q6f6kM8Vhgy6mrT6yW\ncECuK3yv5ebJJ5+kIUOGuH1tHWH9nre03HAc4xeVeQu8Qs+KMhX6Pn36IDg4GDqdzma7TqdDv379\nILSadMMNN3QO0PrT9X/yuQp9ob4Ql2sv4+aUm0XGxSv0Qiv0R4qPICw4DOOTFkPI18Pew38r9MdK\njmFSf/YWG3us3+/RYUm8Qu+EM+Vn0G5qt2trYqvQl5aWorS01GabtJV5CxMxf/50fPNNBfbu7Y3+\n/aNd7q3RaBDfIx4DYgbg72l/txkUKy1sOfV4yXGMSRgj0YBcV/hWhX7+/Pn45ptvsHfvXvTv35/5\nrNbv+WlDpmHnb3ZKEq0/4lcyD3ChZ8f7Qh8WFobrr78ee/bs6dxmMpnwww8/YMqUKR1b3N98zpw5\nY5MgfE3oDxQcAADcPEiszANc6IUJ/ZGSI7gu6TqEh7wEof2e3sP/hL65vRkZugyP+uXtsX+/c6F3\nzNHiowgPDse4xHF2zwgXevsWm5iYGIwaNUrSOIkI8+fPx/bth5GW9jlSUvIgJKeeKD2B+6+63+Es\nN9IiPKceLz0uY4uNPeoXeqJ/dLy225GWloaUlBSPzmj/np82ZJo0ofojCn8z4BaWNhtreMsNK95t\nudm8eTNFRETQunXr6Pz58/SnP/2JevfuTVeuXCEioueff54eeeQRsnw9vGJFX9q+fS1lZ2fT2bNn\naeHChRQSEkJpaWndzu0rLTdP7HiCrv731VIGRb7actPQ0ECnT5+m06dPk0ajoRUrVtDp06epsFD4\nUvRCWm5SVqTYtTXJvwgKO/7TcvPj5R8JWtCh3EMuX9+u97uZFStW0Pbt2wW933nLjS2/3vprmrJm\nios93LfcPPfcczYtNtOmSb9a8ty5c6lnz570448/UllZGZWV7aKyshhqbp5EznXJSqEAACAASURB\nVHJqZWMlQQvakL5B0Eqx0uA6pza0NlDQoiBafcLbf3vqbbmZOxfUs2eE1Wtr/tfc3Ny5l5j3PKc7\nfivzRFzo2fGu0JsXjUqh8PBwuvHGG+nYsWOdz/3ud7+zuoFk0+uvx9Hw4aEUGRlB8fHxdNttt9G+\nffucntsXhP7qf19NT+x4QuqgyBeF3nrBkKCgoM7///3vf890BVdCX1hbSNCCtp3fZncUF3rhsAn9\n0v1LKWZpDO35YY/L19f2/U70+uuv0/DhwykyMlLQ+50LfRfD/jWMFu5a6GYv10L/85//3Ebm//53\n6e+f9n8Lln/r1kWSs5y689JOghaUU5VDRO5XipUO5zl1X/4+ghaUUZ4h4/WdoU6hN7+2II0Gdq9t\n17gLse95ji1+LfNEXOjZUcc89N1hH8ClZqHXNegIWtAn6Z/IFJfvCb1UOBP6jRkbCVpQeb2jVYO5\n0AtHuND/8tNf0h3r7/BGUFzoiaiisYKgBW3M2Chgb8c5ta2tjSIjI21kfseOHTJF7AjH89ATEf3f\nD/9HfV/va5PPlRb6ZQeWUfTSaDIYDTJe2xXqFHp15lT/xe9lnogLPTtc6NlgF/pt57cRtKDCWuFt\nJOxwobcW+nlfz6ORb490cZQabz6+K/RGk5F6vdaLtHu1Xosq0IXevnLtnu459cSJEzYiD4AqKipk\nitgZjoX+F+t+QTM2zei2t5JCf++me+m2dbfJeE0hcKEPdPxuAKwj+KBYVpRfWMox7HMmq3VQ7IGC\nAxjcczCS45JliMcCHxRrPSj2QOEBTE2e6uIo4YugeA/fHRR7sfIialpqcNOgm7wWVaAPij1Wcgx9\nevTB0F5DBR7RPaceOnTIZo8RI0agT58+ksbpnu4LSxlNRhwtOYobB3Rf8M1+YSlvDYolasGR4iOY\nMnCKm+PkRv2DYtWTU/2TgJB5gAs9O1zo2WAT+h/yf8Ctg2+VIQ57uNAX1BbgtnW34eyVswKmAVXj\nzcc3hd6yuvHkAZO9GlUgC/3h4sOYPGAyNBoNw1G2OfXw4TSbZ3/2s59JGCELtkJ/vuIYGtoaMCXZ\nsTgrIfSXa++BrlGnkhWludAHNEp/NeAOKdpsrOEtN6zwlhs23LfclNaVErSgTzM+lSkGRwR2y03s\n0liCFnS85LjAo9T49bBvtdw8+sWjdN371ykVVMC13BiMBopZGiNiMSVzTh08OMSmxeb999+XLEbP\nMLfcrD4xhIIWBVFDa4PLvb3ZcrMxI4SgBV1pKJLxOqzwlptAJOBknogLPTtc6NlwLfTrz6wnaEG6\nBp1M13dG4Ar9Y18+RhqtRvBKsWbUePPxHaEfvmo4zd85X8mgAkroz5SdIWhBP17+0eNzlJUd6tYv\nn56eLkl84jhOv/sylMa/34OEjEvyltD/+Zt7afgqDakvp3KhDzQCps3GGt5ywwpvuWHDdcvN93nf\nY3zSeCREJchwbVcEbstNVlUWfjH0F4JXijWjxq+HfaPlRtewHjnVOV7tl3dEILXcHCw6iJCgEEzs\nP9Hjcxw+XG7zOCYmGmPGjBEbmgRMxJHiAZgy0AAhbYzeark5XFyKGwdOg/pyKm+5CTQCUuYBLvTs\ncKFnw7HQExG+z/sedwy9Q4ZrCiHwhL7F0ILjpceROjJV8EqxXajx5qN+oT9U9BgA4KZkZWUeCByh\nP1h0EBP6TUCP0B4en8N+8OukSSYEB18RFZcUVDdX42LlZUwZ+CKsB8W6Qm6hb25vxuny07hxwEyo\nM6dyoQ8kfEbm58yZgxkzZmDTpk2SnZMLPStc6NnoLvTnrpxDeUO5gjIPBJrQHyk+gjZjG24edLPD\nWW7co8abj7qF/mDRUCTHAslxZ5QOCEBgCP3BwoOiPzwdPmx7r5kyJRhCc6qcHC0+CgCYkvwb2M9y\n4wo5hf50+WkYTIaOAblqzalc6AMGZbt83CNHz7w9vIeeFd5Dz0ZXD/0/D71KEUsiqKmtSaZrsRAY\nPfQvp71MvZf3JqOp61yuVop1jhr7PdXZQ3/jmsk0Z+tAErpSrLfw1x76Yn0xQQvamrnV4whaW1sp\nPDzcpl9+584PiTWnysHLaS9Tn9f7WOVo5wtLOUKOHvo3D75JkUsiqc3QZrVVrTmV99D7O1zmO+BC\nzwoXejbMQn/nhji6Y/00t3t7D7XefKQT+qkfTaWZm2d2286FXh6a2poodHEovX10JQldKdab+KPQ\nbzm3haAFldZ5LtxHjx7tNvi1qqqKPMmpUnPH+jvono332G1VVuhnb5lNN390s4Nn1JpTudD7Mz7T\nZiM3vOWGFd5yw8ZEtBi+xv4CPe4YmgshC0t5B7V+PSxNy01jWyOOFh/FtMHTuj3HW27k4UTpCbSb\n2nFT8s/hbmEpJfDHlpuDRQcxpOcQ9Ivp5/HV7VtsrrrqKvTu3Rue5FQpMZEJR0uOOliYqfvCUq6Q\nuuXG+WJRas2pvOXGn+EybwUXela40LNwqKgVzQZg+rAaCF0p1juo9eYjXugPFh1Eu6kdtw25zeHz\nXOil52DRQUSHRWNs4lgIWSlWCfxN6A8WHRQ9c5D94NcpU6xFVTmhP19xHnWtdU4WZlJG6IvrilFc\nV+xisSi15lQu9P4Kl3k7uNCzwoVeKN9kf4Ok6CSMTdwDoSvFeg+13nzECf3e/L1IjErE1X2udroP\nF3pp2V+wH1MGTkFIUEjHFi70bLAJfWNbI06XnRY1+JWI8NNPP9lss5V5QCmhP1R0CMGaYEwaMMnJ\nHt4X+kNF5g8+rld+VWtO5ULvlyjb5eMeb/XM28N76FnhPfSuMJlMNHzVcHr8q8c7trhfKVYZ1Nrv\n6VkP/aQPJ9GcrXME7ct76MXTbmyn6KXRTlYhdbxSrNL4eg99Wl4aQQvKKM/w+Eq5ubnd+uUvXHCW\nx73bQ//w5w/TxA8mCtjTez30C75ZQMP+NUzg3mrNqbyH3p/gMu8CLvSscKF3xoWKCwQt6KuL1hLD\nhZ4NNqGvba6loEVB9MGJDwRfgQu9OI4UHSFoQYeLDjvZgws9G+6FfsmPSyh2WazNbE2srF271kbk\n+/bt6ybveU/oB68cTE/velrg3t4R+uvev44e/eJRwfurN6dyofcXuMy7gQs9K1zoHfH6T69T5JJI\namxrtHuGCz0bwoV+R9YOghaUXZXNdAUu9J6z7MAyino1ym66Pnu40LPhWujv/uRuunPDnaKu8Nhj\nj9nI/MyZ3Wd/6o78Ql+kLyJoQdvOb2M4Sl6hr2upo6BFQfThSdb3lFpzKhd6f4DLvAC40LPChd6e\nqR9NpRmbZjh5lgs9G8KE/i/f/oWS30r26HXjQu8Zd264k+765C4Be3KhZ8Ox0BtNRur5Wk9avG+x\nqLOPGDHCRuZXrFgh8Eh5hX7T2U0ELai8vpzxSPmEfnfOboIWdKHCk3ubWnMqF3pfh8u8QLjQs8KF\n3kJFYwUFLQqiNSfXuNiLCz0b7oV+7LtjGb8Kt4ULPRtthjaKejWKXjvwmtAjiAs9C92FPr08naAF\npeWleXzWsrKybv3yJ0+eZDiDfEI/7+t5NPLtkR4eLY/Qv5z2MsUvjxdR3FFrTuVC78twmWeACz0r\nXOiJiNadWUfQgsrqy9zsyYWeDedCX1pXStCCNmZsFHUFLvTCOVR4iKAFHS0+ynAUF3o2bIV+1ZFV\nFPZKmKgVpbds2WIj8jExMWQwGBjPIo/Qj313LP1h+x9EnEF6ob9t3W1076Z7RcREpN6cyoXeV+Ey\nzwgXela40M/aPIsmfzhZ4N5c6NlwLPQfn/6YNFoNXWm4IvoKXOiF8er+Vylmacz/s3ff8VHU+R/H\nP5uEkIQkBJHeO4giYkFRmieHSPspIJZDLGflxOPw9FDRSSChGTrSpEgHpUnvhCpN6RB6ILQQIaSQ\nsrvz/v0R1mST3ex8p+xusp/X43GPx4/dmdnPD2H2mWV2vjBbzYJ7MujFygP9K4s74LmZz2k62qef\nfmqH+Y4d1V5/ry/ob9+7DZNkwqw/Zmk8kn6gz7HkICQ6BKN2j9I4E+C951RvBz3nKL7PvGB8H3rR\nfPs+9FmWLFp/bj11a9RN4VxPENEm4vvQK83xfeg3nN9ALaq0oAplKmh+Bb4PvbK2XdpGrWu1znd/\neaXxfejFyr0PPVCOdiRspna1HtF0tJ07d9r9uk2bNiqPpO996Pdc2UMgUOuarTUdR8/70B++cZju\nme/RczWf0zgTkfeeU739PvScwzz904SrvO2TeVv8Cb1ovvkJ/bqz60AS4djNY4Jz8Sf0YuV9Qm+V\nzXhw5IP4arO+fy/5E3rnZVuyETw0WOMnlvwJvUjHb8aBJMKm8+VQ1H3oi+rOnTswmUx2n8zv2LFD\n42T6fEL/v03/Q+XvK+u21ocen9CP3jMaQUODkG3J1mkmwHvPqd76CT3nKP5kXmX8Cb1ovvkJ/bJT\ny6hORB1qWqGp4Fz8Cb1YeZ/Q/369FyXfS6aO9Tvq+gr8Cb3z9l/dT5mWTGpXu52Go/An9CLFJRyn\nAL8AeqZ6JVKyUqyj9uzZY3f+CgwMpCeffFLjZPp8Qr/z8k5qXbM1mUwmjfPY0v4J/a4ru6hltZYU\n6B+o00xE3ntO9dZP6DlHMeY1xKAXzbdAb7aaaemppfRq01dVviEx6MXKBf3G8ysoNLAUPV3d2fLv\n6mPQO277pe1UtnRZeqzyYxrnYtArbful7fRUtaeoTGAcET1AakBf8BKbli1bUlBQkA7TaQN9liWL\nDlw7oMMlNgXTBvoN5zbodIlNwbz1nMqgLy4x5jXGoBfNd0C/5eIWup15m3o37a1hLga9WG/RhvON\n6Pk6Zgr0709GvPkw6Au37dI2alOrDfn7+eswF4PeVQAoLiGO2tZqS7Zr6NWAfseOHXa/bt1aTzyr\nB/2Bqwcox5pjEJzVgb7fk/0ow5xB19KuGTATkfeeUxn0xSHGvA4x6EXzDdAvPrGYGjzQgJpXbq5x\nLga90lKzU2nPlfPUsd5bZOSbD4M+r2xLNu25skfjJTYFY9AXVfyf8ZSUkXQf80RqQJ+ZmUkHDhyw\ne0xfzBOpBf2uy7soLDCMmlVqpvM8tsRB36JyCyIimnV4lt2XYvXN+86puTHovT3GvE4x6EUr2aDP\ntmTT8lPLqXfT3jpd88mgV9K2i9vIIluoY71vydFdbvSMQZ/bvqv7KMuSRe1rt9d5Lga9s+IuxZG/\nyZ9a1WiV71Ex0O/fv5/MZvNfv/bz86NWrVoVsYfaxM+pOy/vpFY1Wun0Lz3OEgP97iu76ZGKjzi8\ny42+edc5NS8GvTfHmNcxBr1oJRf0G85toLvZd6n3w1ousSkYg95V68+tp3rl6lG9B+qRs9tW6hmD\nnmjLhS1ULqicQZ+iMugdtT1hOz1R9QkKKx1W4BnloN++fbvdr5s3b07h4eG6zpmX8nOqRbbQ7iu7\nDbhe3lHKQW/7Qq6z21bqm/ecU+1j0HttHryTjqK89daURcW3rRSt5N22stGERmgysYlBc/FtKx0l\nyzKqj66Oz9Z9VuAZ5yvF6pUv37bymR+fQc8lPY0cCnzbyrxkWUaV76vgi41fFLGV/UqxjmrTpo3d\nLSkHDhxowLQFc31O3Z+4HyQRdl/e7YZ5bBV928rEu4kgibDk+BIAylaK1Se+bSWnLP5k3oD4E3rR\nStYn9BM6TaD4P+MpvHS4ooWlxONP6B115OYRSkxNpK4NuxZ4hj+hV57YJ/QpWSm07+o+6lC3g8Fz\n8Sf0ts7dPkfX069T29pti9iq6E/o7927R3v32p//n3/+eX0HdZjrc+r2S9sppFQIPVH1CTfMY6vo\nT+jjEuKIiP76PS9qYSl940/oOWUx5g2KQS9ayQF9tbBqRJR7LbHSlWLFY9AXbPWZ1RQWGEatazn6\n53kGvfKUg37bxW0kQ3YD5okY9LnFJcSRn8lPwZ1enIN+9+7ddtfL+/v7G/DlV2cVfU7ddmkbPVfz\nOZ3v5a4k56CPuxRHTR5sQhXLVPzrMQY9g96bYswbGINetJIB+sUnFlOzSs0ULyylPgZ9/ladWUUd\n63csAgEMeuUpA/2mC5uo/gP1qU65Om6ai0G//dJ2alGlBYWXVnJ9u2PQb9u2zW6rJ598ksLCCl5/\nb2SOz6kW2UI7L++kdrXauXGW/DkG/faE7Q7v1sSgZ9B7TR6+zMdltmvmO3XqhK5du2LBggWeHkk4\nvoZetOJ7Df3drLsIHhqMmB0xAPKuof907ac6LkteML6G/kbaDZBE+OnwTwq25mvolVf0NfT1xtXD\nJ6s/cfdQ8NVr6GVZRrXYahi4QfT6dvtr6Fu2bGl3vfxXX3nqfcn+nPrbld9AEmHvlb0emsdW3jX0\n11LjQRJh0bFFTrfma+j5GnpPV2wwX5y+AOsoBr1oxRP00w9Nh0ky4crdK389xqA3/s1n5u8zYZJM\nSEpPUrgHg155jkF//vZ5kERYfmq5h+byPdCfunUKJBHWnV2nYu9c0KekVISfn58d5jdt2qTrnGLl\nnVOH7/wKoTGhyLHkeHAeW7mgX3isPkgiXE+7XuTWDHoGvSdjzLsxBr1oxQ/0rWa0Qse5HQvtwaA3\n9s3n5UUvo9WMVoJ7MeiVVxj0Uw5MgX+kP1IyUzw4l2+BfsK+CSgVVQrp2ekqj3ATq1bVsIN8YGAg\nMjIydJtRXbnn1I5zQ/DivPYeniV/B/DhqkA0nhgEJedUBj2D3lPxNfNujK+hF614XUMfnxxPe67s\noXeav1Noj6JWitUv37yGPtuSTRvPb6QuDboI7snX0Cuv8DX0my5sopbVW1LZoLIenMu3rqHffGEz\ntarRisoEllF5hIq0bVtnu0eeeeYZCgkJ0T6cpuqT2bqRdl3OpPa1j5HSlWKN7wnafqkKta0lk9KV\nYvkaer6G3hMx5t0cg1604gP62YdnU0RQBHVv3N3hHgx6Y9584hLiKMOcQV0aimKeiEEvUh7orfL7\ntOXiOjfdxcZVvgF6i2yhbZe20Qt1X9B0nK1bf7P79fPPG7HYl3gHr6VQhhnUrrYfKb1zmNHdSL9B\n8X8mULva35HSlWIZ9Ax6T8SY90AMetG8H/RWuS3NOTqb3nj4DQoKCHK6B4Ne/zefX+N/pVpla9HD\nFR9WeQQGvfJyQX/gWg9KybpHHepmeXqg+5V80B+6dohSs1M1Yf7PP/+kw4cP2z3Wvv18KmqlWHe1\n7dI2CgsMoxZV4kjkVsBGFnfp/v3la71DSleKJWLQM+jdH2PeQzHoRfNu0G88f5uupd2gdx4ruGBR\n4Rj0+r35yJBp2all9EqTV8hkMmk4EoNeeSZae7YJlQsqTS2rjyBXC0u5r5IN+s0XNlN46XBNiynF\nxcXZ/To4OJhatqxEjhaWcnfbL22n1rVaU4BfYxJd28Oo4hLiqGH5hlQlrAq5WliqYAx6Br07Y8x7\nMAa9aN4L+lmHn6KHKwbQ41X6k9KVYhn02t989iXuo+vp1+mVJq/oMBeDXmnrzq2nv9f7PwrwU7ZS\nrPsquaDffHEzta/dngL8AlTPsXXrVrtft27dmgIDt5OzlWLdVY41h3Zf2U3ta7e//4j4Yn1GtP3S\n9gL3vGfQi8Wgd1se/fqtgkrS3WycxXe5Ec277nLz570/ETgkELF7BsHVfegLxne50XZHhs83fI5K\noyrBYrXoOBff5aao7O/pX/R96D1XybrLTXp2OgKHBGLCvgmaXr9JkyZ2d7IZNmzY/Wfs70Pv7nYm\n7ARJhANXDxR4xvXaHkZl+3O+4KijtW3y7kPPd7lREt/lxugY814Sg1407wH9hH0TEBAVgJvpN6Hm\nzYdBr+7NR5Zl1BlbBx+u+tCAuRj0zvrp8E8gie7/eQcY9GKpAf36s+tBEuHULfXnumvXrtlBnoiw\nb9++fFt4DvRD4oYgfFi4kx/KPQP6JceXgCTC1dSrTrZg0IvFoDcyxrwXxaAXzfOgl2UZzSY3Q/eF\n3fM9yqAXS92bzx/X/wBJhA3nNhg0F4PeUb1/7o0npj1R4FEGvUiioP98w+eoFltN07lh7ty5dpAP\nDw+H2WwusJVnQN9+dnt0WdCliC3cD/qPV3+M+uPru9iKQS8Wg96oGPNeFoNeNM+CfselHSCJsPHc\nxgLPMOjFEn/z+WbLN4gYHmHwapEM+vyZrWaUG14O32791sGzDHqRREDffEpz9F3eV9Pr9enTxw7z\n3bt3d7Kle0GfkZOBwCGBGPfbOBdbuhf0DcY3wEerPlKwJYNeLAa9ETHmvTAGvWieA32vJb3QaEIj\nWGVHJyUGvVhibz4PTXoIby1/y+ihwKDPa1fCLpBE2Htlr5MtGPQiKQF9UnoSSCLMOTxH9etYrVZU\nqlTJDvOTJk0qYg/3gd52CdGJpBMKtnYP6C+nXAZJhJ9P/KxwDwa9WAx6vWPMe2kMetHcD/rEu4nw\nj/R38aU0Br1Yyt58Tt06BZIIK06tcNNcDHoA+HrL1yg/oryLLxwz6EVyBfpFxxa5uHbbdYcPHy50\nvfzZs2dd7OUe0A/cMBBVY6sKnOuMB/2sP2bBJJmQnJEssBeDXiwGvZ4x5r04Br1o7gX9N1u+QWhM\nKO5mufqzyaAXy/WbT/SOaIREh+Bezj03zsWgf2zKY3hj6RsKtmTQi1QU6N//9X08NOkhTccfOXKk\nHeTr1q2rcE/jQd9scjMVlxAZC/o3l76JFlNbqNiTQS8Wg16vGPNeHoNeNPeAPsuchYqjKuJfa/6l\ncA8GvVhFv/k8NuUx9FzS091DwZdBfzX1KkgizD0yV+EeDHqRHIFelmXUGlML/df213TsF154wQ7z\nH32k5FpwW8aB3nb7x3lH5qnY2xjQy7KMyt9Xxhcbv1B5BAa9WAx6PWLMF4MY9KIZD/q5R+aquFUc\ng14sx28+p2+dFryeVe98E/RTD06Ff6S/wDwAg16sgqC3XU629sxa1cfMyMhA6dKl7TC/bNkywaMY\nA/p5R+aBJML1tOsqj6A/6I/fPO7kpgYiMejFYtBrjTFfTGLQi2Ys6FtOb4kOczqo2JNBL1bhNx9p\nm4SwmDA3X2JTMN8Dfef5ndF2VlsVezLoRcoP+v5reyFoaJCmP+vr1q2zg7y/vz9SUlJUHEl/0L+9\n4m088sMjGo+iL+jH/TYOgUMCkZGTofFIDHqxGPRaYswXoxj0ohkD+v2J+0ESYeXplSqPwKAXK+/N\nR5Yz0XhiY/RZ1sfTQ8GXQJ+enY7SQ0ojdk+syiMw6EWygd4/ktByurbr5QcMGGCH+WeffVbD0fQD\nvSzLqBZbDf9Z/x9Nx8lNP9B3XdAV7We312EmgEEvGoNebYz5YhaDXjT9Qf/W8rdQe2xtF3f0cBWD\nXqzcN58/rrcBSYQ1Z9Z4eqD7+Qbol59aDpIIZ5LPaDgKg16kG2nnYZIIpYcoXynWUU2bNrXDfGRk\npMbJ9AH9yaSTIImw7uw6jfPY0g56s9WMsJgwDI0bqtNMAINeNAa9mhjzxTAGvWj6gf562nUEDgnE\nyF0jdZiLQS/WOnyx0R/lR5RCjiXN08Pkq+SD/t0V76LJxCaaj8OgV97q+NUgifDEtFDFK8UWLDEx\nsdAtKffudbZGgEjaQW+7nCU9O12HeWxpA/2ey3tAEuG3K7/pOBPAoBeNQS8aY76YxqAXTR/QD9o8\nCKExobiTeUenuRj0SpNlGTXHVMSHq/zgfW8+JRf0FqsFFUZWwJebvlR9DPsY9Erqt6Yf6oytg9Ss\na4pXii3YzJkz7SAfEREBs9ms04TaQN9lQRe0m91Op1nypx70Q+KGIHxYOMxWvX6P8segF4tBLxJj\nvhjHoBdNG+hTs1JRdlhZDNwwUOe5GPRK2n15N0gibLs4At755lMyQW/7tHL35d2q9nccg76oZFlG\n3XF18cnqTwAoWynWUa+99pod5nv21Pt2rupAn2PJQWhMKKJ3ROs8jy11oG87qy26L+xu0EwAg140\nBr3SGPPFPAa9aOpBH7snFgFRAbhy94oBczHoXfXp2k9RNbbq/e8qeOubT8kD/f82/Q8VRlbQ+B0R\nRzHonRWfHA+SCKviV/31mCjorVYrypcvb4f5adOmGTCtOOh3JuwESYT9ifsNmMeW2Dk1PTsdgUMC\nMf638QbOBDDoRWPQK4kxXwJi0IsmDvpsSzaqj66uYqVCkRj0zjJbzag0qhIGrB+Q71FvffMpWaB/\naNJDeHvF24ITKo1B7yhn15OLgP7gwYOFrpe/ePGiQROLgf7brd+i3PByBvyAWDDl59T1Z9eDJMLJ\npJMGzwQw6EXLD3rOUYz5EhKDXjQx0M/6YxZIIhy7eczguRj0jtp4biNIIuxL3FfgGW998ykZoD/7\n51mQRFh2UnSRIZEY9AV7cd6LeGHOCw6fUwr6IUOG2EG+YcOGRo17P+Wgf+bHZ9BjcQ+D57Gl7Jz6\n+YbPUeX7KgaeQwvGoBfLBnrOUcUG8506dULXrl2xYMECT4/ktTHoRVMGeovVggbjGxh8LWX+GPQF\ne3Ppm2g0oZGT/9+89c2n+IN+xK4RCB4arPMdRxzFoLd1L+cegoYGFXlPfyWgf/rpp+0w379/f6NG\nzpdr0CdnJMMv0g/TD7nzv7Prc+ojPzxi4L9AOYtBL9ZsTw/gtRUbzPMn88pi0IvmGvTzj84HSYSD\nVw+6cS4Gva27WXcRPDQYMTtiitjKW998ijfoW05viVcWv6JxQqUx6AFg7Zm1ii73KAr0SUlJMJlM\ndpjfsGGDkWPnq2jQLzi6ACQREu8mumkeW87PqYl3E0ESYeGxhW6eCWDQc3rEmC+BMehFcw56q2xF\nk4lN8NL8lzwwF4MeAH489CNMkknBF4+99c2neIL+yt0rIIkw78g8naZUEoO+/9r+qDmmpqK/v85A\nP2fOHDvIlylTBllZ7vw74Rz0fZb1QbPJzdw4S/4cn1Nn/j4TJsmE5IxkD83FoOe0xZgvoTHoRXMM\n+iXHl4Akwt4reiy0oiYGfeuZrdFhTgeFW3vrm0/xA/3438ajVFQpHddUtvpshQAAIABJREFUUJpv\ng77B+Ab4cNWHird3BPrevXvbYb57d3ddIpi/wqC3ylad1yxQU+Fz6qs/v4qnpj/lwZkABj2nJcZ8\nCY5BL5o96K2yFY/88IjTL6K5L98F/bk/z6n4dNhb33yKF+jbzW6HF+e9qPOESvNN0Nu+cLzi1Aqh\n/fKDfseFHxAREeGGW1IqyR70B64eAEmE7Re3e2geW3nnVIv1CsoNL4dvt37r4ZkABj2nNsZ8CY9B\nL1oe6Bce+96AxXLU5pug/3brtwiLCUNGTobgnt765lM8QJ+UnuSBLykWzPdAP3rPaJQeUhpp2WnC\n+9pAHzKEQNXtb0mZmOju69Pzlwf6qO39ET4sHDmWHA/OYyv3nLr3Sg0vOs8DDHpOTYx5H4hBL9pN\nmK0PoeEEf7w0v42nh8mXb4HeKltRe2xtvLfyPZVH8NY3H+8H/fRD0+EX6Yeb6TcNmU95vgX6drPb\nafp+Tlr2dVQfHAgalAf65s2b6zaf+nJB/8yPpfDKYqWXzLmjs5C2hSNiuB/M1sueHiZfDHpOLD/i\nSnyl/ENoYY8z1K1RNeq5JIZ+jf/a0yPdL5SI1hJRcyLqSER7PTvOX1WkuUc+oDN/Wmlo+xNEdNrT\nA92vPhFtI6J7RNSOiK673OODxz+gqV2m0oT9E+iz9Z8RAAPmeoKINlHu71NHIkrV5ag7EnbQpZRL\n9Hbzt1Ue4UUiWkFEG4moFxFl6zKX9t4iotlE9CMRfUREsu6v0KxSM9radyslpCRQh7kd6HbmbQV7\nDSKiGCKKpGWnRlDrmq2pYpmKus8mlomIJhBRPyJ6n3J/z7yhUkS0iIi6ElEPIlql+Yi3M2/TzoSd\n1K1hN9XHCA2sTKEraxPdIKI+RFSdqHPnzppn015F+vPeUvot0Uwv1d9HRPGeHuh+9Wn9+br0Qt3S\nFOD3Aik5p7qnJ4hoMxGdIiXnVJPJRJHtImlwm8H05eYvaeTukQbN5a3nVI4x7yMx6JWXY82hyLgx\n1POhrvRYlcpE1J4Y9K7SH/Q/HfmJ6pWrR8/WeFbDUbz1zcd7QX8361vafOEcvdIkWPeZ1OUboF93\ndh1ZYaUuDbuoPsalS5fo9NEzRPPpL9DXfNasaS692nj+DwIRvVi/EuWeuzwP+tuZt2n/1aP0Yr3B\nJHJOdU8Mek55jHkfikGvrOmHptOV1CsU1W4EEW0lovLEoFeSfqBPy06jX07+Qm89+haZTCaNc3nr\nm493gn71mYZklolebryeiCTdZ1JXyQf9qjOr6ImqT1C18Gqqj7FmzZrc/yOHiOYTBSQTfX54JO29\nMk31MfVq3bl11KxSM6oWvouIHiBvAP3mC5tJhkwd6/ch0XOqe2LQc8pizPtYDPqiS81Opci4SOr7\naF9qUqEJEVUkBr1I+oB+4fGFdM98j95p/o5Oc3nrm4/3gX7xicX0dPWnqUbZ3EtuGPSu0g76HGsO\nrTu3TtMlNkT5ME9ElEPUI6sHNa8cTh3nfehR0MuQaf259dSpfifKPaduI28A/YZzG6hphaZUPbw6\nqTmnuicGPacgz16y7zr+Aqwx8ZdiHffV5q8QPDTYweqErleK9Uwl80uxj099HF0WdNF7KHjvF7i8\n40uxdzLvoFRUKYzZO+b+I8pWinVvJe9LsZvObwJJhD+u/6H61TMyMhAUFGR3F5uFCxcWuVKsu3J8\nS8qiV4o1OlmWUTW2KgZuGFjgGfFzqnviL8VyzmPM+3AMevsup1xG0NAgfL3laydbMOjFUgf6g1cP\ngiTCqvhVBs3lrW8+ngf9rD9mwSSZCvwwy6BXnjrQf7r2U9QYXUPT38VVq1bZQd7f3x+3b98G4Hyl\nWHcVtT3KyS0pPQf6YzePgSTCxnMbHTzLoBfLW8+pvhNj3sdj0OfVd3lfVBhZAXezivqzxqAXSxz0\n7//6PqqPrg6z1WzQTID3vvl4FvQvznsRbWY5uh0rg155YqCXZRm1xtRCvzX9NL3qRx99ZIf51q1b\n2z3vSdA/8+Mz6LG4h5NnPQP6UbtHIXhoMDLNmU62YNCL5a3nVN+IMc8x6AH8fu13mCQTJu2fpGBr\nBr1YykF/N+suykSXgbRNMmiW/Hnrm49nQH8r4xb8I/2L+DvAoFeectAfuXEEJBE2nNug+tVkWUb1\n6tXtMD9iRGG4eQL0yRnJ8Iv0w4+HfixiK/eD/oU5L6DTvE4utmLQi+Wt59SSH2OeA+DboJdlGc/N\nfA4PTXpIYGVCBr1YykA/+cBk+EX64crdKwbNUTBvffNxP+inHpwKv0g/3Ei7UcReDHrlKQP9kLgh\nCIsJQ5ZZ/Z+/AwcO2EGeiHD8+HGH27ob9HMOzwFJhGuprs5H7gN9alYqSkWVwoR9ExRszaAXy1vP\nqSU7xjz3V74K+vlH54MkwubzmwX3ZNCLVTToZVlG8ynN0W1hN4Ne31ne+ubjXtC3ntkaf/vpbwr2\nYtArzzXon5z2JHot6aXpVb7++ms7yDdo0KDIv8fuBH3PJT3x1PSnFG7tHtAvPbkUJBEu3L6gcA8G\nvVjeek4tuTHmObt8DfRp2WmoGlu1iOs5XcWgF8s56Pcn7gdJhNXxqw167aLy1jcf94D+geEPgCTC\nmD1jXO8AgEEvknPQX029CpIIc4/M1fQKTZs2tcP8f//7X5f7uAP0WeYshMWEYUjcEIG9jAf9Oyve\nwUOTHhLci0EvlreeU0tmjHmuUL4E+kGbByFoaBAu3rmo4SgMerEcg/69le+h5piasFgtBr2uq7z1\nzcd40A/aNAgkEZpNbub0tpWFY9ArzzHobZc2JWckqz7ymTNnCl1is3v3bkX7Gg36Dec2gCTCkRtH\nBPc0DvRW2YqKoyrii41fqNibQS+Wt55TS16Mec5hvgD6M8lnEDgkEN9t+06HuRj0YtmDPiUzBSHR\nIYjaHmXQ6ynNW998jAV965mt8eyMZ13eh75wDHrlFQZ95/mdndw9SHmjRo2yg3ylSpVgsSj/gdhI\n0Pdb0w+1xtRSeR4xBvS2fwHccWmHyiMw6MXy1nNqyYoxzzmtJINelmW0n90edcbWQUZOhk5zMejF\nygP96D0xKBVVSsGX5NyRt775GAP6S3cugSTCT4d/UrSwVOEY9MrLA/3drEUIHBKI0XtGazris88+\na4f5999/X/gYRoBelmXUHFMTn679VMNR9Af9t1u/Rbnh5TTe+pZBL5a3nlNLTox5rshKKuh/OvwT\nSCKsP7te57kY9GIdgMVaFnXGlsabS1816DXU5K1vPvqDPmZHDEKiQ5CWnQZA2UqxDo4CBr3SckE/\n/6g/SCIkpCSoPtKNGzdgMpnsML9mzRpVx9Ib9IevHy5iUSaR9AV9i6kt8Povr2s+DoNeNG89p5aM\nGPOcy0oa6G9l3EL5EeV1OqE7ikEv0opT34Mkwv7EhyGyUqzxeeubj36gl2UZTSY2wRtL37B7nEFv\ndDl4ZXFVPDnNBJGVYgs2ffp0O8iHhoYiM9PZIkiu0xP0UdujEBYThmxLtqbj5KYP6G1fOJ5/dL4O\nMwEMetG89Zxa/GPMc4oqSaB/e8XbiBge4eJ+2lpj0Cut/ez2eObHRyC6Uqx78tY3H31A//u130ES\nYe2ZtYWeY9AbV3p2OoKHBmPEroehdKVYR3Xu3NkO8716abvFJaAf6J+Y9gRe/VnPf23TDvrph6bD\nL9JP4M+zkhj0YnnrObV4x5jnFFcSQL/lwhaQRJh2cJob5mLQu8q2+uXCYwshslKse/PWNx/toB+w\nfgAqjKzg9PphBr0x/XziZ5BEOPfnKShdKbZgqampKF26tB3mFyxYoMt8WkGv1y03C6cN9N0Xdsdz\nM5/TeSaAQS+at55Ti2/FBvOdOnVC165ddTtZceoqzqBPzUpFrTG10GZWG1hlY27xVzgGfVG9t/I9\nVIutlm/lXQa9WOpBb7aaUfn7yui/tn+R2zHo9e+1X17Do5Mfvf8rZSvFFmzJkiV2kC9VqhRSUlJ0\nm1EL6KcenAr/SH+dPwG3pQ70meZMhESHYPjO4QbMBDDoRfPWc2rxrNhgnj+Z956KK+g/WvURykSX\nwfnb5908F4PeUbcybiFoaBCid0QXeIZBL5Y60NvuAb4/cb/LbRn0+pVpzkRoTGiBhZTEQf/GG2/Y\nYf7vf/+77rOqBX3n+Z3RdlZb3efJSxz068+uB0mE4zePGzgXg14sbz2nFr8Y85yqihvoN53fBJII\nk/ZP8tBcDPqCxeyIQekhpXEr45aDZxn0YomDvs+yPmg4oaHi/4YMen1aeXolSCKcTDpZ4BnloM/O\nzkbZsmXtMP/DDz8YMq8o6NOz0xE0NAixe2INmScvMdD/a82/UHtsbQPvzGWLQS+Wt55Ti1eMeU51\nxQX0d7PuouaYmnj+p+fdeHmNoxj0tnIsOagWWw3vrni3iK0Y9GIpB316djrKRJcRXqSLQa+9t5a/\nhSYTmzh5VhnoN27cWGjV18TERAOmzU0E9CtOrQBJhDPJZwybJy9loJdlGbXH1ka/Nf3cMBPAoBfN\nW8+pxSfGPKep4gD691Z2RWhMKC7euejhmQAGfW6Lji1SuMw7g14sZaCff3Q+SCJVl5wx6NWXbclG\nxPAIDN46uIitXIP+o48+soP8U089ZcC09ikF/bsr3kXjiY0Nnycv16A/fvM4SCKsO7vOjXMx6MXy\n1nNq8Ygxz2nOm0H/84nGIIkw/dD/PD1Mvnwb9LIso8XUFnj+p+cVzsWgF8s16DvM6aDprh4MenWt\nO7sOJBEOXz/sYkvnoLdYLKhYsaId5mNiYgya2D5XoDdbzSg/ojy+3PSlW+bJq2jQR++IRmhMKDLN\n6u/Bry4GvVjeek71/hjznC55I+gvp1xGxPAI9FhcHrIcCjUrxRqX74J+47mNKlaGZNCL5Rz0CSkJ\nMEkmzPh9hqZXYNCL98+V/0S9cfUU/uDrGPRbt24tdInN2bNnDZq4cEWBfuuFrYq/VK1/zkH/5LQn\n0WuJ9nvwq4tBL5a3nlO9O8Y8p1veBHqL1YI2s9qgxugauH3vMtSsFGt8vgn6v/30N7SY2kLFtfYM\nerEcgz5qexRCokOQmpWq+RUY9MozW814cOSDgp9aFwZ9wUtsHnvsMQOmLTpnoO+3ph9qjK7hhi+Z\nOqsw6K/cvaLzqq9qYtCL5a3nVO+NMc/pmreAPmp7FPwi/RB3Ke7+I+Irxbon3wL9/sT9IImw5PgS\nlXMx6MWyB71VtqLuuLp4e8Xbur0Cg15Z6j+1zgO92bzcY5fYFKwg6K2yFVVjq+KzdZ95ZJ687EE/\naf8kBEQF4E7mHQ/PxaAXy1vPqd4ZY57TPU+DflfCLvhH+jv4khmDXiz9Qd9jcQ/UH18fFqtFw1wM\nerHyQL/tYu4KyHk/5OoTg951n6z+BDXH1FT5qXUu6Lds8ffoJTYFyw/6qQe/AEmEHZd2eGyevPJA\n32FOK3SY08HTA92PQS+Wt55TvS/GPGdIngL9jbQbqBpbFc/NfM7JEvUMerH0A318cjxMkglTD4ov\nD184Br1YuaB/a3kDgWu2xWLQO89sNaPiqIr4z/r/aDhKDj76qI7HL7EpmA30gUMI5YaHafxBXc9u\n4va9RgiIIkza/62nh8kXg14sbz2neld+xHEGVMo/hBb2OEPdGlWjnkti6Nf4rw1/TYtsod6/9CYZ\nMi3puYQC/AIcbBVKRGuJqDkRdSSivYbPpayKRLSViMoTUXsiOu3Zcf6qPhFtI6J7RNSOiK673OOD\nxz+gqV2m0oT9E+iz9Z8RACIiGrV7FFUsU5HeevQtHeZ6gog2Ue7vU0ciStXhmHr0IhGtIKKNRNSL\niLI9O85fvUWp2ZPpl5Nn6Z3m5chkgu6v0KxSM9radyslpCRQh7kd6HbmbQV7DSKiGCKKJCJJ95nU\nZSKiCUTUj4jeJ6IfNR9x68WtlJSRRK8/8rrqY1gsJlq6NN3usVdffVXraJoLDaxMa944TSYyUXpO\nGu2/OsPTI92vIq09258sMlG3RpOJKN7TA91P/Jzqnp4gos1EdIqUnFNNJhNFtoukwW0G05ebv6SR\nu0caNFfBcyrnKMY8Z1juBv2gzYNo1+VdtKTnEqoSVqWILRn0YmkH/dXUqzTn6Bwa8PQACgoI0mku\nBr1IS074U6bZRG89epCIPiIiWffXYNA7buHxhVT/gfr0eJXHVR9jx44ddOvWLbvHevV6QNNcenX+\nzk3KtoIaPRhCHed9SHuvTPP0SEREtCJ+Gz1ZtTlVD69AuecuBn3RFQfQcw7z9D8NuIovsyn+ueOS\nm19O/AKSCKP3jBbYiy+5EUv9JTctprRAWEwYUjJTDJiLL7lRUqsZrfD3uX+HyEqxauNLbvLKNGci\nfFi4i4WiXPfhhx/aXWLTokUEXK0U666+2fINyg0vh9v3LiteKdboMs2ZKBNdBtE7oqF0pVj3x5fc\niOXORb+KV4x5zi0ZCfqTSScRFhOGV39+VcW1wAx6scTffMbsHQOSCI9PfdzAW9Yx6Ivq9K3TIImw\n8NjC+48w6JWnDfTLTi4DSYSTSSdVT2A2m1GhQgU7zA8bNhSuVop1Vw9Negh9l/cFoHylWKNbHb8a\nJBFOJJ24/wiDXixvBT3nKL7MhnNLRl1yk3wvmbos7EI1y9akH7v+SCaTSfAIfMmNWOL/PHwn8w4F\n+AXQoeuH7K6h1ze+5Kaopv8+nR4IfoD+r/H/3X/kLSKaTbmXj/AlN0Wn7ZKbhccXUvPKzalJhSaq\nJ4iLi3Nwic1rRLSIiLoSUQ8iWqX6+Fo6nXyaTt46Sa80eYWIcq+hX/tmPDWvHO7RS25WnF5BDR5o\nQE0etP2+V6Tcc9cDxJfcKMlbL7nhHObpnyZcxZ/Ml6z0/IQ+y5yF52Y+h4qjKuLinYsaJ+NP6MVS\n9mnS7Xu3ET4sHP9Z/x/hlWLVxZ/QFyzTnInyI8pjwPoBDp7lT+iVJ/4JfWpWKoKGBmn+pLLwJTYt\n8j3reKVYdxW9Ixplossg05xp97gnP6G3WC2oMLICvtj4hYNn+RN6sfgT+uIQY55ze3qAXpZl9FnW\nB6WHlMaey3rhm0Evlus3n2+2fIPgocG4kXYDgNhKsepj0Odv/tH5IIlw6pazPzsMeuWJgX7ukbkg\niZCQkqD6Fc1mMx588EE7zA8fPrzAVp4DfYupLfDqz686fM5ToN+ZsBMkURHvDQx6sRj03h5jnvNI\nWkE/NG5ogWuA9YpBL5bzN5/kjGSExYTh8w2f2z3OoHcv6NvOaou2s9q62IpBrzzloH9p/kt4dsaz\nml5t8+bNhRaKOn/+vIMt3Q/6C7cvgCTC4uOLnW7jCdAP3DAQlUZVglUu6s8yg14sBr03x5jnPJZa\n0C86tggkEaRtkkGTMejFcvzmM2jzIJSJLoOk9KRCezDo3QP6U7dOgSTC/KPzFWzNoFeea9AnZyQj\nICoAE/dN1PRKH3zwgR3kH3/88SK2di/oY/fEovSQ0kjNSi1yO3eCXpZl1BtXDx/8+oGCrRn0YjHo\nvTXNmB88eDCqVKmC4OBgvPDCCy6Xlp41axZMJpPd/4KDg51uz5gv2YmCfsO5DSgVVQr/WPYPAxEI\nMOhFs3/zuZVxC6Exofhy05dO92DQGw/6AesHoPyI8sgyK30NBr3yigb9lANT4B/pj5vpN1W/QlZW\nFsqVK+fiEpuCuQ/0Lae3RPeF3RVt6y7QH75+GCQR1p5Zq3APBr1YDHpvTBPmhw8fjoiICPz66684\nevQounfvjrp16yIry/kbx6xZs1C2bFncvHnzr/8lJRX+5M4WY77kpxT0ey7vQUh0CDrP74wcS44b\nJmPQi5X35vPlpn4IjQnFrYxbRe7BoDcO9JnmTDww4gEM3DBQcE8GvfKcg77trLb37+uvvuXLlxe6\nxObSpUsK9jQe9LZLbEQudXQH6L/e8jUihkcg25ItsBeDXiwGvbelGvOyLKNy5cqIjY3967G7d+8i\nKCgIixYtcrrfrFmzEBERofh1GPO+kSvQH71xFOWGl0Prma2RkZPhxskY9GKdRVJ6FZSJNuGrzf0V\n7cGgNwb0ti9fxifHq9ibQa+8wqBPvJsIk2TCrD9maTpyz5497SDfunVrgb2NBf3wncMRPDQYadlp\nQvsZCXpZltFwQkO8veJtFXsz6MVi0HtTqjF//vx5mEwmHDlyxO7xtm3b4rPPPnO636xZsxAQEIBa\ntWqhRo0a6N69O06cOOF0e8a87+QM9Odvn0fl7yuj+ZTmBq0g6ioGvUj/3fhPhMWY8Oe9ehBdKZZB\nrx/on5v5HNrPbq/hCAx65dmD3nYtuZbzVUpKCkqXLm2H+SlTpggexTjQN5/S3OldbFxlFOiP3DgC\nkghrzqxReQQGvVgMem9JNeZ3794Nk8mEGzdu2D3+6quvonfv3k7327t3L+bOnYsjR44gLi4OXbt2\nRdmyZZGYmOhwe8a8b1UQ9FdTr6LuuLpoML7BX7c39EwMeiXdSLuB4KHB+GbLJxB982HQ6wf6E0kn\nQBJh0THn/0qqLAa98vJA//jUWnh50cuajjZz5kw7yJcqVQp//qn09yd/+oPetqLwspPLVB/DCNAP\n3jpYxSU2BWPQi8Wg94YUY37evHkIDQ1FaGgowsLCEBcX5xDzvXr1wmuvvaZ4ALPZjPr162Pw4MEO\nn7dhvlOnTujatavd/xYsWKD4dbjiU37QV419ANVHV8elO0quEzU6Br2r+q3ph4jhEbh97zbUvPkw\n6PUBfb81/VBxVEWNqLHFoFeejFO33gBJhJ9PfKTpSH/729/sMN+tWzcNR9MX9JHbIxEWE1ZooSjR\n9AS9LMtoPLEx+i7vq+k4uTHoxWLQezrFmE9LS8P58+f/+t/x48cdXmbTpk0b/Pvf/xYaolevXnj9\n9dcdPsefzPtml+6cRWiMP0giTDnwsafHyReD3lnxyfEIiArAqN2j8j3KoBdLO+jvZt1FaEwoBm91\n/AGJuhj0Svtq8yBEDC+NLLPylWILdvXqVZhMJjvML17s/F7uytIH9DY091nWR+M8uekF+mM3j4Ek\nwqr4VbrMxaAXjUHvyTR9AbZKlSoOvwArctKxWCxo1KgRBg50fMcFxrzvdTX1KhpOaIhqsdXQcW4l\nTSvFGhOD3lE9FvdAzTE1HXxax6AXSxvox/02DgFRAbiaelXnuRj0rrLKVtQYXQMfrfoQIivFFiw2\nNtYO8mFhYbh3754OE2oHve269NXxq3WYJzc9QP/dtu8QPixc4DasSmLQi8Wg91Sabk05YsQIlCtX\nzu7WlPXq1UN2dt4/7fbp0weDBg3669eRkZHYuHEjzp8/j0OHDuG1115DSEgITp1yjA/GvG9lg3z1\n0dVx7s9zmleKNS4Gff52X94Nkghzj8x1sgWDXix1oLfKVjQY3wC9f3b+vSVtMeiLasuFLSCJsOfy\nHoisFFuwFi1a2GG+b9++Ok6pDfRfbf4K5YaX0+kSrry0gv6hSQ/p9q8F9jHoxWLQeyLNi0Z9++23\nqFy5MoKCgtChQ4dCi0a1a9cO77zzzl+/HjBgAGrVqoXSpUujcuXK6NKlCw4fPuz0+Ix536kg5G0x\n6EVzL+hlWUarGa3QfEpzF8unM+jFEgf9+rPrQRJhZ8JOA+di0Dur7/K+qD++fr4/q+KgP3nyZKF7\ny2/atEnnSdWBXpZl1B1XF/9c+U+d58lNLehtX/j+9bRRi2Qx6MVi0Ls7zZg3Osa8b+QM8rYY9KK5\nD/TLTi4DSYRN55WAg0EvlhjoO8/vjOZTmhu8OjLAoC9cenY6ykSXQdT2qALPiIH+66+/toN8lSpV\nYLFYDJhYHPT7E/cL/F1XlxrQS9skAy6xKRiDXiwGvTtjzHMezxXkbTHoRTMe9DmWHDSc0BAvzntR\nYC8GvVjKQH/uz3MwSSbM+H2Gm+Zi0OfPtkjXxTsXHTyrDPSyLKNOnTp2mB8wYIAxAwMQBf3ADQNR\ncVRFmK1mA2cSB/3DPzyMfyz7h6Ez5cagF4tB764Y85xHUwp5Wwx60YwF/Q/7f4BJMuHIjSOuN7aL\nQS+Wa9APWD8A5UeUx70cPb4oqTQGva0Oczqg7ay2RWzhGvS7d+8udInNwYMH9R/WLmWgt8pWVB9d\nHf3W9DN4ntyUgv7UrVMgibDi1Aq3zMWgF41B744Y85zHEoW8LQa9aMaAPjUrFRVHVVS5dDrAoBfN\nOejTstNQdlhZfLnpSw/MxaC/cveKwn8VKRr0n3zyiR3kGzVq5IZLpgAloN+ZsBMkEXZc2uGGeXJT\nAvqo7VG63PNeLAa9WAx6o2PMcx5JLeRtMehF0x/0g7cORtDQIFxOuazhKAx6sRyDfsqBKfCL9PPg\n4mq+DfrhO4cjaGgQ7mYp+bPiGPTZ2dl48MEH7TAfFVXw+nsjKxr0/1rzL1SLrebiS+765wr0zSY3\nwxtL33DrTLkx6MVi0BsZY55ze1ohb4tBL5p+oL945yKChgZh0OZBrjd2GYNeLHvQW2UrGk9sjFcW\nv+LhuXwT9LZFlF7/xfHCh072QkHQL1++vNAlNufOqT8/qssx6HMsOagwsgL+s/4/bp4nN2egP5l0\nEiQRlp9a7pG5GPSiMeiNijHPuTW9IG+LQS+aPqB/edHLqBZbDWnZaTrNxaAXKw/0q+OXgyTCroRd\nnh4Kvgh62xoLm89vFtzTHvTdu3e3g/xzzz2n+6zKKgz61fGrQRLh92u/e2gmx6AfvHUwyg4ra/Bd\nbFzFoBeLQW9EjHnObekNeVsMetG0gd52L/NFxxbpPBeDXqxc0LefXR4tpz/lpmurleRboH9v5Xuo\nPba2ystPckF/8yYhIMDfDvM//vijrnOKZQ/63j/3xsM/POzxP2P5Qb87YSrqjauHd1e869GZcmPQ\ni6Ue9JzjvP53hjFfMjIK8rYY9KKpA32WOQsNxjdA+9ntDXpjZ9CLdOjaBJBE+PnE4xBZKdb4fAP0\nadlpCI0JReT2SA1HkTFmzHN2kA8ODvaC97xc0KdkBiBoaKDXfCoky7WTAAAgAElEQVRqA32ZaFL5\nLyJGxaAXSx3oOcf5EccZ3LW0a9T+p/Z0z3yPtvfdTvUeqKf7a5TyD6GFPc5Qt0bVqOeSGPo1/mvd\nX0NdoUS0loiaE1FHItrr2XH+qiIRbSWi8kTUnohOK9przG9j6MKdCzSh0wQymUwGzFWfiLYR0T0i\nakdE113u8cHjH9DULlNpwv4J9Nn6zwiAAXM9QUSbKPf3qSMRpRrwGuLF7t1LdSIq08uNjxFRLyLK\n9vRI93uLiGYT0Y9E9BERybq/QrNKzWhr362UkJJAHeZ2oNuZtxXsNYiIYogokogkzTP8fOJnysjJ\noL6P9tVwFBPNnp1m90iPHj0oPDxc23CaK0VEi2jpqWaUbcmhNx6p4OF5cgsNrExr34yniKBAMhFR\n6YCznh7pfhUp99z1AOWeu+I9Ok1e4udU9/QEEW0molOk5JxqMpkosl2kG+YqnjHmOUNzB+RtMehF\nEwN9YmoiDdkxhPq37E9NKzY1cC4GvZKu3L1Ci48vpn8/PYj8/VYS0UZi0LsX9DP+mEEv1H2BakXU\nUn2MP/74g44cOWL32NtvV9Q0l36VojlHQun5OhWoeviHRLTK0wMREVFwQAUyy2WpSlggvTT/Y9p7\nZZqnR7ofg14scdBzjmPMc4blTsjbYtCLphz0AzcOpLDAMJLaSW6Yi0HvqvH7xlNY6TB697F3iehF\nIlpBDHr3gT4+OZ52X9lN7z32nqr9bc2ePdvu1zVqhFL79qMp9/fMsyWkJFBcwg7q02wYEXUloh7k\nDaCPS4ijpIxbNP+VFdS8cjh1nPchg95lJQP0nJM8fJmPy/ia+eLZtdRrhl4j7yq+hl60oq+h33Jh\nC0gizDk8x81z8TX0jrqbdRfhw8IdLBLleqVYz1TyrqH/YuMXKDe8nKbFirKzs1G+fHm76+W/+eZr\nuFop1l1F74hG8NBgpGalQulKse7ovZXvod64epBlWfFKse6Pr6EXS+waes4+xjyne/khf/bPsx6b\ng0EvmmPQ51hy8NCkh/DsjGc9dDcLBn3BYvfEIiAqAIl3Ex08y6A3GvQ5lhxUGlUJ/1rzLxVT5rVs\n2bJC95Y/e/YsXK0U645s98+3X5DJ86DPMmchYngEvtnyzV+PMehFY9CXtBjznK55C+RtMehFKwz6\n2D2x8Iv0wx/X//DgXAx6W2arGTXH1ESfZX2K2IpBbyToV55eCZJI89+Jrl27FnFvec+C/sDVAyCJ\nsO7sugLPeBb0K06tAEmEk0kn7R5n0IvGoC9JMeY53fI2yNti0IuWB/qElC0oE10G/db08/RQYNDn\nNu/IPJBEOHz9sIstGfRGgb7rgq54bMpjGiYErl69Cn9/V/eW9xzo+6/tj0qjKsFsNTt41nOgf/Xn\nV/Ho5EcdPsegF41BX1JizHO65K2Qt8WgF+0mZPkhdJ5fGlVjKyIlM8XTA93Pt0Fvla1oOqkpXpr/\nksI9GPR6g/5yymX4RfphyoEpmuaLiYmxg3xISIiT9zn3gz7HkoMKIytgwPoBRW0Fd4M+NSsVwUOD\ni7znPYNeNAZ9SYgxz2nO2yFvi0Ev1uLj00ASYfmpCKhZKda4fBf0tksMdiXsEtiLQa8n6L/b9h1C\nY0LvfylUXVarFXXr1rXD/LvvFrWSqXtBvzp+NUgi/H7tdxdbuhf0c4/MBUmEhJSEIrdj0IvGoC/u\nMeY5TRUXyNti0Cvr9r3bqDSqEl5e9BLUrBRrfL4HelmW8dT0p9BmVhsVezPo9QC92WpGtdhq+ODX\nDzTNtGXLlkJffN27d6+LvdwH+t4/98bDPzys8O+J+0D/0vyX8NzM51xvCAa9eAz64hxjnlNdcYO8\nLQa96/658p8IHxaOq6lX4eq2lZ7Lt0C/+fxmkERYf3a9yiMw6LWC3vbF10PXDmma5/XXX7eDfNOm\nTRX+eTQe9CmZKQgaGlTkpSyFMx70SelJ8I/0xw/7f1C8D4NetOIAes5RxQbznTp1QteuXbFgwQJP\nj8Sh+ELeFoPeeTY0Tj4wOd+jDHqx9Af98z89j8enPq5xZga9FtC/NP8lPDHtCU1zJCcnIzAw0A7z\nY8eOFTiCsaCffmg6TJIJV+5eEdzTWNBP3DcRAVEBSEpPEtqPQS+at4Oec1SxwTx/Mu89FXfI22LQ\nFy41KxW1xtRC+9ntYZULoopBL5Z+oN97ZS9IIiw9uVSHuRj0akB/6c5nMEkmTD+kDdBjx461g3xg\nYCCSk5MFj2Ic6J/+8Wm8OO9FlXsbB/qnpj+Frgu6qtqXQS+aN4OecxRjnhOqpEDeFoPevo9WfYQy\n0WVw4fYFJ1sw6MXSB/TdFnZD44mNHfyApTYGvSjov9lCCIsJRFp2murXlmUZDz/8sB3mX3vtNbVH\ng96gP5F0AiQRfj7xs4aj6A/6U7dOgSTCLyd+UX0MBr1o3gp6zlGMeU5xJQ3ythj0udkur5m0f5KL\nLRn0YmkD/dEbR0ES4afDP+k8F4NeKehzLDmo8n0YPl4ttlJswfbu3Vvoi69btmxRfTy9QT9ww0CU\nH1EeWWatfx70Bf3/Nv0P5YaX0zwXg140Bn1xiTHPKaqkQt6Wr4O+6MtrHMWgF0s96N9Y+gZqjamF\nHEuOAXMx6JWAftnJZfcX6voUIivFFuy9996zg3zdunVhtWr9/08f0GdbslFhZAX8e92/Nc5jSx/Q\nW6wWVIutho9Xf6zLVAx60Rj0xSHGPOeykg55W74M+n+u/KeLy2scxaAXSxz08cnx8Iv0w8R9Ew2a\nCWDQuwb93+f+HS2nt7z/K+UrxeYvJSUFISEhdpiPiYlRO3qBtIN+6cmlIIlw7OYxnWYC9AD9pvOb\nQBLhtyu/6TYVg140Br23x5jnisxXIG/LF0Fvu92eui/2MejFEgP9m0vfRLXYasg0Zxo0jy0GvTPQ\nxyfHgyTCnMNz8j0qDvrx48fbQT4gIADXrukJI22g7zy/M56a/pSO89jSBvp/LPsHGk5oqPvfSQa9\naAx6b44xzznN1yBvy5dAfyPtBiqMrIBuC7tpeLNk0IulDPQnk07CL9JP6L7a2mLQOwL9Z+s+Q4WR\nFRz8QKUc9LIso0mTJnaY79mzp17j538lqAF94t1E+EX6YcqBKQbMBKgFfWpWKkKiQxC9I9qQqRj0\nojHovTXGPOcwX4W8LV8AvSzL6Dy/MyqMrICb6Tc1zsWgF8s16F/75TXUGF1Dhy8jisSgzw/6tOw0\nhA8Lx6DNg5zspQz0cXFxOn/xtajEQR+9IxrBQ4ORkpli0EyAGtDP/H0mTJIJCSkJhk3FoBeNQe+N\nMea5QtkgXy22mk9C3lZJB/2UA1NAEuHX03rdD5pBL5Zz0B+/eRwmyYSpBz2BCwa9DfSTD0yGX6Sf\nC0y6Bv1rr71mB/mGDfW/bMQ+5aC3ylbUG1cPby1/y8B5bImBvu2stnj+p+eNHopBLxyD3ttizHN2\nXUu9hkYTGvk85G2VVNCfTDqJkOgQvP/r+zrPxaAXyzHoey3phVpjaiHbkm3Q67qKQd9iags0ntgY\nLy96WcFezkF/48YNlCpVyg7zo0eP1nlqRykD/faL20ESIe5SnBtmApSC/uKdiwbdktVxDHrRGPTe\nFGOe+yuGvONKGugzzZloNrkZGk9sjPTsdAPmYtCLZQ/6IzeOaPhCsp75NujDh4WDJMKyk8sU7uUY\n9DExMXaQDwoKwp9/Kl2sSmuuQd9nWR/UH1/f4H8pKJhr0Edtj0KZ6DKaFukSjUEvGoPeW2LMcwAY\n8q4qSaDvt6YfSg8pjSM3jhg4F4NerDzQv7K4K+qMrWPQfeVF813QvzDnBfhH+guvFJsf9BaLBbVr\n17bDfN++fQ2Z13nOQZ+SmYLgocGI2aHXLTJFcg56WZZRf3x99F3e1+1TMehFY9B7Q4x5jiGvsJIA\netviN65XedUjBr1YB/D7tVCQRJj5uzv++yjN90CfeDcR/pH+GLRpkNBKsbnlgX7NmjWFvvj622/6\n3S9deY5BP+XAFPhF+uFq6lUPzAQ4A/2uhF0gibDlglFfEi46Br1oDHpPx5j38RjyYhVn0CekJCBi\neAReXvSyG/9JnUEvUreFbVBvnB/M1pYQXSnW2HwL9IO3DkZoTCjuZt0VWik2r1zQd+nS0A7yjz32\nmJsvZ8lfYdA/Oe1JdFnQxUPz2CoM+g9+/QA1x9RUuBq1MTHoRWPQezLGvA/HkFdXcQR9tiUbz/z4\nDGqMriEAEr1i0CtpX+K++1/4kyC6Uqx78g3QZ5mzUHFURXyy+pO/HlMD+vPnP4fJZP+p/LRp0zTP\np6080B+58Z3gdwKMLA/0GTk/o+ywsvhqs+fPrQx60Rj0noox76Mx5LVV3EDff21/lIoqpeuS6GIx\n6ItKlmW0n90eTSc1hcVqgehKse6r5IN+1h+zQBLh9C17JImCfuDAgXaQDw8PR1qa+77M6bxc0H+8\nmlDl+7Je8t0MwAb6OYf9QRLh3J/nPD0QAAa9eAx6T8SY98EY8vpUXEC/8NhCN14nX1QMemetP7ve\nwT3/GfRiaQe9LMtoNrkZOs/v7PB5paBPT09HRESEHeYHDHha1UxGlJadirCYUhi8VWylWOPLQZtZ\nD+L5n0wQWSnW6Bj0ojHo3R1j3sdiyOubt4P+RFIIykQH482lb3rwWt38MegLZpWteHTyo3h2xrMO\njsOgF0sb6Lde2AqSCJvPb3a6jRLQT5kyxQ7yJpMJ5865XinWXU07OO3+YlhvQWSlWKOLT44HSYQF\nR5+EyEqx7ohBLxqD3p0x5n0ohrwxeSvoU7OuofHEYDSd5If0bM/cFcJxDPr8zT86HyQRdiXscrIF\ng14s9aDvuqArHvnhEZf/LYsCvSzLaNq0qR3mO3fuDCUrxbojWZbx2JTH7n/xVflKse7oi41foNzw\ncsg0p0JkpVh3xaAXjUHvrhjzPhJD3ti8DfRW2YpXFr+CsJgwnL71ONSuFGtcDHog94vJdcbWQbeF\n3VxsyaAXSxz0Z5LPwCSZMOP3GYq2dwb6LVu2FLod5YYNG+4/63nQ70/cD5IIq+NX33/EO0CfbclG\nxVEV0X9t//uPKFsp1t0x6EVj0LsjxrwPxJB3T94EemmbBJIIK06tgNqVYo2PQT/+t/Hwi/TD8ZvH\nFWzNoBdLDPT91vRDhZEVkGnOVPwKjkDfvXt3O8g3atQIVmv+1/cs6N9d8S5qjql5/4vWtjwP+qUn\nl4IkwtEbR/M9yqAXi0HvqzHmS3gMeffmDaC3vSkOiRuS71EGvVjGgz41KxUVRlbAOyveEZiLQS+W\nMtDfvncbIdEh+Hbrt8KvkB/0v5/6HX5+fnaYnzhxooO9PAP6O5l3EBIdUuDcYMuzoO80rxNaTm/p\n4BkGvVgMel+MMV+CY8h7Jk+C/uiNoygTXQa9lvRyAEoGvVjGgv67bd+h9JDSuJxyWXAuBr1YrkE/\nctdIBA4JxI20G6pewQb6SoMrgYLzIB8WFobU1FQne7kf9BP2TYB/pD+upTr78+wZ0F9OuQyTZML0\nQ85ek0EvFoPe12LMl9AY8p7NE6C/lXELtcfWxqOTH0V6drqTrRj0YhkD+htpN1Amugz+u/G/Kudi\n0IvlHPRmqxk1RtfA2yve1vQKv138DaYvTaAP6C/Q9+/f38Ve7gO9LMtoOqkpeizu4WpLuBv0kdsj\nUSa6DFKznP3gAzDoRWPQ+1KM+RIYQ947cifos8xZaDurLR4c+SAu3bnkYmsGvVj6g/6T1Z+g7LCy\nGlfjZdCL5Rj0tnUYDl8/rOnoP/zwA6gSgb6gv0B/5swZBXu6B/Q7Lu0ASYSN5zYq2Np9oLdYLag5\npibeW/megq0Z9GIx6H2lYoP5Tp06oWvXrliwYIGnR/LqGPLelTtAL8sy/rHsHwgcEoidCTsV7sWg\nF0s/0B+7eQx+kX6I3ROrw1wMerHsQS/LMlpMbYEOczpoOqrVakWDBg1yL6+5D/rw/4YL/LBmPOhf\n/flVNJzQEFZZ6e063QP6Dec2gCQSWJ2aQS8Wg94XKjaY50/mXXct9RoaT2yMarHVcCZZySdCnDsy\nGvTfbv0WJBEWHlsouCeDXiztoJdlGR3mdED98fWRbcnWaS4GvVh5oN98fiNIImw6v0nTEVeuXGl/\nO8pKhPCh4S5XirXPONAn3k1EQFQAxv02TnBP40Hfa0kvPPzDw4K3dWXQi8WgL+kx5ktIDHnvzijQ\nz/5jNkgixOyIUXkEBr1Y2kD/6+lfQRJh5emVOs/FoBcrF/R/n1sNzac017w6ctu2be0w36xZMxy+\nftjlSrGFMwb03279FmWiyyAlM0XF3saBPik9CaWiSmHs3rEq9mbQi8WgL8kx5ktADPnikd6g33Jh\nCwKiAvDeyvc0YoRBL5Z60EcMj8Dzs5/XjEfHMehF+uN6FEgiLDjaHqIrxebv4MGDhRaJmj17NoCi\nV4p1nr6gz7Zko9KoSvh49ccajmIM6GP3xCJwSCCSM5JVHoFBLxaDvqTmR1yx7nradXp+zvOUlp1G\n2/puowblG3h6JM5JpfxDaGGPM9StUTXquSSGfo3/WvWxjt48Sq8sfoXa125PkztPJpPJpGGyUCJa\nS0TNiagjEe3VcCw9q0hEW4moPBG1J6LTnh3nr+oT0TYiukdE7Yjouss9Pnj8A+r1UC9KyUqhyqGV\nDZrrCSLaRLm/Tx2JKNWg1xHtRSJaQUQbiagXEWV7dpz7jdpzmmqVfZB6Nd1GRB8RkazqOKNHj7b7\ndZUqVej1118nIqJmlZrR1r5bKSElgTrM7UC3M28rOOIgIoohokgiklTNlL+lJ5fSzYyb1O/JfhqO\nYiKiCUTUj4jeJ6IfNc8FgKb/Pp1eafIKlQ8pr/IopYhoERF1JaIeRLRK81x6FBpYmda+GU/NK4dT\nx3kf0t4r0zw90v0qUu656wHKPXfFe3SavMTPqVyBPP3ThKv4k3nn8SfyxTOtn9Cfv30elb+vjMem\nPIa7WXr+veBP6MVS/mnSrYxbKDusLNrMbKNqpVix+BN6V128cxH+kf4Y/9t4iK4Um7/Lly8jICDA\n7lP56OjoQtt58hP6VjNaof3s9pqOkZd+n9BvvbAVJBG2X9yuw1z8Cb1Y/Al9SYsxX0xjyBfv1IL+\netp11B1XFw3GN8DN9JsGTMagF0vZm4/tVpRJ6UnCK8Wqi0FfVP3X9scDIx7Itx6DOtB/8cUXdpAP\nDg5GcrLjS0Y8AfpD1w6BJMKyk8tU7e84fUDfc0lPPDTpIR3/DjDoxWLQl6QY88UwhnzJSBT0dzLv\n4NHJj6JqbFVcvHPRwMkY9GIV/ebj6FaUDHrPgT45Ixkh0SH4duu3BZ4RA31aWhrKli1rh/mPPy76\nunR3g/7dFe+ixugaMFvNwvsWnTbQX029Cv9If0zcN1HnuRj0YjHoS0qM+WIWQ75kpRT093LuofXM\n1ig3vByO3TzmhskY9GI5fvORZRkvzHnB4a0oGfSeAX3U9igEDQ1CUnqSg2eVg37cuHF2kDeZTIiP\nj3f5+u4CfXJGMoKGBmm405Wr1INe2iahTHQZnS8TtMWgF4tBXxJizBejGPIlM1egzzJn4aX5LyEk\nOgR7LrsT1gx6sQq/+aw8vbLIW1Ey6N0L+oycDFQYWQGfrP6kiK1cgz4nJwe1atWyw3y3bt0Uz+EO\n0I/YNQKBQwKd/NCiV+Kgz7HkoGpsVXy46kMD52LQi8WgL+4x5otJDPmSnTPQZ5mz0Hl+Z5QeUhob\nzm3wwGQMerHy3nwycs6h1pha6Di3Y5FQZ9C7D/Rj946Ff6Q/zt8+72LLokE/b968Qrej3L5d7Iuc\nRoI+x5KD6qOro+/yvkIzqUsM9L+c+AUkEQ5fP2zwXAx6sRj0xTnGfDGIIe8bFQR9ljkLXRZ08SDk\nbTHoxcp98xm0+QGUHlIaZ/8863IPBr3xoM8yZ6FqbFW8tfwthXs4Br0sy3jkkUfsIN+yZUtV/92M\nAv2iY4vcBGZbykH//E/P49kZz7pjKDDoRSsOoOccxZj38hjyvlV+0D8xrT5KDymN9WfXe3osMOjF\nOpm0DqWiCNK28lCzUiyDXv+mHpwKk2TCqVsif04Kg37NmjWFPpVfvny56rmMAP3TPz6t4+0oleYa\n9CeTToIkwvyj8904F4NeLG8HPecoxrwXx5D3zdKybqPK90EgifDdttc8PU6+GPRKkmUZ7We3R71x\nNZFprgY1K8Uy6PUFvdlqRp2xddBrSS8Ve9uDvk2bNnaQb9y4MaxW9SvIAvqCfu+VvSCJ8OtpT8C1\naND3X9sfFUZWQJbZ3XcxYtCL5c2g5xzFmPfSGPK+WbYlG10XdEVgVCCenVFe9cJSxsWgd9X8o/NB\nEmHd2XVQc70ng15/0M85PEfjZSe5oN+zp1uhT+VnzJihy4x6gb73z71Rf3x9WGVtP2CozzHo07PT\nET4sHIM2D/LQXAx6sbwV9JyjGPNeGEPeN8u2ZKPbwm4oPaQ01p1dp3mlWONi0DsrJTMFlUZVQs8l\nPfM9yqAXS1/QW6wWNJ7YGF0WdNF4pJ/Qvbs95KtVq4asLP1+6NAK+oSUBPhH+mPCvgm6zaSuwqCf\ndnAaTJIJl+5c8uBcDHqxGPTFJca8l8WQ981skA8cEnj/E93cGPSieRb0n679FKExoUi8m1jgGQa9\nWPqBfsnxJSCJsPfKXk3HOXHiRKFP5b///ntNx3SUFtD/d2MrlB1WFmnZabrPJV4e6GV5GppPaa7D\nD1R6xKAXi0FfHGLMe1HX066j8cTGqBpblSHvQ2VbstF9YXcEDgnE2jNrCz3PoBfNM6A/dO1QoZVe\n7WPQi6Ud9LIs49HJj+JvP/1N8zRvv/22HeQjIgKRmpqi+biOUgP6tOzvEDGc8PmGZwyZSV25oN9z\nmUASOTy/eSYGvVgMem+PMe8lMeR9s2xLNv5v0f8hcEgg1pxZ43Q7Br1o7gW9xWrBk9OexCM/PIIc\nS04RWzLoxdIG+lXxq0ASYdvFbZqmuHz5MgICAuww//XXBCUrxapNFPQT902Ef6QfElLEVoo1Phn/\nWNYQdcYSrLI3AZVBLxaD3ptjzHtBDHnfLD/kV8evdrk9g14094H+h/0/gCTCzoSdCrZm0IulDvSy\nLKPl9JZ4dsazmn/P+vfvbwf5oKAg3Lw5Aa5WitWaUtBbZSsajG9w/249YivFGl1SehIChwRi5K5n\nILJSrHti0IvFoPfWGPMejiHvm+VYcvDyopcVQz5vPwa9WMaD/nLKZYTFhOGfK/8psBeDXixx0K89\nsxYkkeZ1Gq5fv46goCA7zH/yySf3ny16pVg9UgL65aeWF/hegPeAfkjcEAQNDUJyxi2IrBTrvhj0\nYjHovTHGvAdjyPtmNsiXiiqFVfGrVOzPoBfLONDLsoxO8zqhamxVpGSKXj/NoBdLOehlWcaT055E\nqxmtNP8+ff7553aQDwgIwKVL+e/I4nnQt5rRCq1nti7wqOdBn23JRpXvq+D9X9+//4jylWLdG4Ne\nLAa9t8WY91AMed9MK+TzjsOgF8sY0M89MlfjAj0MerGUgd52rfzm85s1vdqtW7dQpkwZO8y/9957\nDrb0HOh3Jewq4s+gZ0FvW3Ph2M1j+R5l0IvEoOeUxJj3QAx53yzHkoNXFr+iGfJ5x2PQi6Uv6G+k\n3cADIx7A67+8rvFIDHqxiga9LMtoMbUFWs9srfn35quvvrKDvL+/P86dO+dka8+AvvvC7mg8sXER\ni0R5DvRPTX/KyZ2EGPQiMeg5VzHm3RxD3jfLseSgx+IeKBVVStdl1hn0oukH+l5LeuHBkQ8iKT1J\nh7kY9GI5B/2KUyt0uYPN7du3ERYWZof5Pn36uNjLvaD/7cpvMEkm/HjoRxd7uR/0e6/sdfGvVgx6\nkRj0XFEVG8x36tQJXbt2xYIFCzw9kuoY8r5ZjiUHPZf0RKmoUlh5eqUBx2fQi6Ud9MtOLgNJhIXH\nFuo4F4NerMKgt8pWPDr5UbSb3U7z0SVJsoO8yWTCqVNK/ry4D/QPjngQFUdVRJZZyZeC3Qv61355\nDfXG1SviXwwABr1YDHrOWcUG88X9k3mGvG9mNOTzXodBL5Z60N++dxuVv6+Mbgu7GQBoBr1Y9qBf\nenIpSCLEXYrTdNS7d+8iIiLCDvO9e/cWOILxoN9yYQtIIlSNrSq8UqzRoE+8m4iAqACM3TtWwdYM\nepEY9JyjGPNuiCHvm+VYctBrSS+UiiqFFadWuOH1GPRiqQP92yveRtlhZXE19apBczHoxcoFvVXu\ngod/aPr/7d3PS9t3HMfxTzRQeohSQw+FopeePPTWv6DFHQTB1v4CoVB2L716kOi0LGNMWyiD4qHO\nw2yb6k6thzJGGayziGKng3XQCZNBqdgkrMR9TV49tNmi3+i+H/P95puQ5+P4Tb6fvA85PPMhyceX\n015HR0d3hLwxRsvLy5arBBv0A08GdHjksNqSbVYnxVYj6AeeDCh2I6Z0zuv7hKC3QdBjN2I+YIR8\nY3Lyjs7fP6/ocLQqIV9E0NuyC/q5l3MyCePhO8qVIujtPNb9X6IyCaMf176vaKVsNqt4PL4j5Ht7\new+4WjBBn93K6sjnR3R97rr1SbEfBBf07/55p3gyrmuPr1neSdDbIOhRipgPECHfmMIK+SKC3pa3\noE/n0mofa9eZb84EGMulCHqvtvPb6rzdrk+mIrI9KXa3ZDLp2pVfWFioYDr/g378p3E1DzVr7e2a\nJO8nxe4UTNBPLEwokojo9429/vVnPwS9DYIeRcR8QAj5xuTkHV14cEHR4ahmf50NbQ6C3tb/B/2V\n2SuK3Yjp1earKs5F0HsxuTQpkzD6+c9x2Z4UWyqTybh25bu7u/2YUH4F/db2lo5/dVz9M/07rtdC\n0BcKBXXe7lTPtz2VrCKC3juCHhIxHwhCvjE5eUcXH1xUdDiqmdWZsMch6K3tHfSplZRMwuju4t0Q\n5iLo95NzcuoY69DZe2c/XvF+UuxuIyMjrl35+fl5nyb1J6Vzm1oAAAHcSURBVOgnFiZkEkYrr1dc\nj4Ud9I9+eySTMHr6x9MKVyLobRD0IOZ9Rsg3ploL+SKC3pY76Ncz62pLtuncvXNV+npNOQT9Xm4+\nu6mmoSatvl4tuWof9Jubm65/sOnpqWSHuZzKgn47v60Tt06UfHBxCzPoT0+e1qk7p3x6vxH0Ngj6\nxkbM+4iQb0xO3tGl1CVFh6N6uPow7HFcCHpb/wV9vrCirqkuHfvymN78/SbkuQj63TK5jI5+cVRX\nv7ta5lG7oB8cHHTtyi8tLfk8sVRJ0E+/mJZJGD1ff77v88II+sW/FmUSRtMvpg90f3kEvQ2CvnER\n8z4h5BuTk3d0OXVZzUPNSq2kwh5nTwS9rQ9Bf+tZTCZhNPdyLuyBPqqHoH8b0Gu4Df0wpEOfHfr3\nh6Bu3oJ+Y2PDddprX19fABMXFYP+U3kN+kKhoJNfn1TXVJen51c76Ptn+tUx1iEn71jfu7/SoL/j\n89qVIOjtEPRBikiSqWGZTMa0traadDptWlpawh4HAAAAqBk1H/OSTDabNbFYzEQikbDHAQAAAGpG\nzcc8AAAAgPKawh4AAAAAwMEQ8wAAAECdIuYBAACAOkXMAwAAAHWKmAcAAADqFDEPAAAA1CliHgAA\nAKhT7wETGVIuMo1itwAAAABJRU5ErkJggg==\n",
"text/plain": [
"Graphics object consisting of 51 graphics primitives"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"show(graph, aspect_ratio=1, ymin=-0.8, ymax=1.2, xmax=2.5, axes_labels=[r'$r/m_0$', r'$t/m_0$'])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Sage 6.9",
"language": "",
"name": "sage_6_9"
},
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