{ "cells": [ { "cell_type": "markdown", "id": "585d5c32-0c8d-413e-a2ad-91f8766a229d", "metadata": {}, "source": [ "# Solving the ODE for outgoing radial null geodesics in Vaidya spacetime\n", "\n", "This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://relativite.obspm.fr/blackholes).\n", "\n", "The computations make use of tools developed through the [SageManifolds project](https://sagemanifolds.obspm.fr)." ] }, { "cell_type": "code", "execution_count": 1, "id": "af5f40ce-a96a-43c1-b830-a2f7c77d6bf2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 10.0.rc0, Release Date: 2023-04-23'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "code", "execution_count": 2, "id": "745e8d88-46b2-4080-88ee-b49964052d5d", "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "code", "execution_count": 3, "id": "a3952b06-1be3-47a8-8620-3680316a3a9b", "metadata": {}, "outputs": [], "source": [ "x = var('x', domain='real')" ] }, { "cell_type": "code", "execution_count": 4, "id": "7d0c7d93-6f9a-4297-b5c4-eb3f273f113d", "metadata": {}, "outputs": [], "source": [ "a = var('a', latex_name=r'\\alpha', domain='real')" ] }, { "cell_type": "code", "execution_count": 5, "id": "56a44b6b-3605-4237-b433-9f62c8c84f6c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -\\frac{{\\alpha} x - 1}{{\\alpha} x^{2} - x + 2}\$" ], "text/latex": [ "$\\displaystyle -\\frac{{\\alpha} x - 1}{{\\alpha} x^{2} - x + 2}$" ], "text/plain": [ "-(a*x - 1)/(a*x^2 - x + 2)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(x) = (1 - a*x) / (a*x^2 - x + 2)\n", "f(x)" ] }, { "cell_type": "markdown", "id": "fb746f8d-72f5-43b3-8847-bdb2bb07072d", "metadata": {}, "source": [ "## Case of a high density radiation shell" ] }, { "cell_type": "code", "execution_count": 6, "id": "c8a29227-b1b2-4783-ae1e-31ee0dc70d93", "metadata": {}, "outputs": [], "source": [ "assume(a > 1/8)" ] }, { "cell_type": "code", "execution_count": 7, "id": "f4b54f1b-1cc6-4dec-af02-61f501424cff", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\frac{\\arctan\\left(\\frac{2 \\, {\\alpha} x - 1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}{\\sqrt{8 \\, {\\alpha} - 1}} - \\frac{1}{2} \\, \\log\\left({\\alpha} x^{2} - x + 2\\right)\$" ], "text/latex": [ "$\\displaystyle \\frac{\\arctan\\left(\\frac{2 \\, {\\alpha} x - 1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}{\\sqrt{8 \\, {\\alpha} - 1}} - \\frac{1}{2} \\, \\log\\left({\\alpha} x^{2} - x + 2\\right)$" ], "text/plain": [ "arctan((2*a*x - 1)/sqrt(8*a - 1))/sqrt(8*a - 1) - 1/2*log(a*x^2 - x + 2)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F(x) = integrate(f(x), x)\n", "F(x)" ] }, { "cell_type": "code", "execution_count": 8, "id": "b47c84e5-464d-4871-a730-617ead570bc7", "metadata": {}, "outputs": [], "source": [ "P(x) = a*x^2 - x + 2" ] }, { "cell_type": "code", "execution_count": 9, "id": "14f9200b-39b9-4d31-a06b-4887e9474fa7", "metadata": {}, "outputs": [], "source": [ "x1 = 1/(2*a)" ] }, { "cell_type": "code", "execution_count": 10, "id": "e16f281a-eefb-47f8-90a2-ccdba49c0902", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -\\frac{1}{4 \\, {\\alpha}} + 2\$" ], "text/latex": [ "$\\displaystyle -\\frac{1}{4 \\, {\\alpha}} + 2$" ], "text/plain": [ "-1/4/a + 2" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P(x1)" ] }, { "cell_type": "code", "execution_count": 11, "id": "f492f367-9f82-4979-8cad-5730f17b3743", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -\\frac{1}{2} \\, \\log\\left(-\\frac{1}{4 \\, {\\alpha}} + 2\\right)\$" ], "text/latex": [ "$\\displaystyle -\\frac{1}{2} \\, \\log\\left(-\\frac{1}{4 \\, {\\alpha}} + 2\\right)$" ], "text/plain": [ "-1/2*log(-1/4/a + 2)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F(x1)" ] }, { "cell_type": "code", "execution_count": 12, "id": "d71448f1-9e79-4c8b-8045-edbaa96c6f33", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\frac{2}{\\sqrt{\\frac{8 \\, {\\alpha} - 1}{{\\alpha}}}}\$" ], "text/latex": [ "$\\displaystyle \\frac{2}{\\sqrt{\\frac{8 \\, {\\alpha} - 1}{{\\alpha}}}}$" ], "text/plain": [ "2/sqrt((8*a - 1)/a)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "exp(F(x1)).simplify_full()" ] }, { "cell_type": "code", "execution_count": 13, "id": "7079e1e8-521e-4aed-831f-e4e740d32420", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle 2\$" ], "text/latex": [ "$\\displaystyle 2$" ], "text/plain": [ "2" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P(1/a)" ] }, { "cell_type": "code", "execution_count": 14, "id": "1289a06f-2971-431b-b0f4-cfd7e9029a46", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -4 \\, e^{\\left(-\\frac{2 \\, \\arctan\\left(\\frac{1}{\\sqrt{\\frac{16}{x} - 1}}\\right)}{\\sqrt{\\frac{16}{x} - 1}}\\right)}\$" ], "text/latex": [ "$\\displaystyle -4 \\, e^{\\left(-\\frac{2 \\, \\arctan\\left(\\frac{1}{\\sqrt{\\frac{16}{x} - 1}}\\right)}{\\sqrt{\\frac{16}{x} - 1}}\\right)}$" ], "text/plain": [ "-4*e^(-2*arctan(1/sqrt(16/x - 1))/sqrt(16/x - 1))" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "thb = -4*exp(-2/sqrt(16/x - 1)*atan(1/sqrt(16/x - 1)))\n", "thb" ] }, { "cell_type": "code", "execution_count": 15, "id": "8d79df08-6cfb-4e4f-8ed6-186aa90e6d91", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(thb, (x, 0.001, 15.99))" ] }, { "cell_type": "code", "execution_count": 16, "id": "9b60dbbd-9414-4f35-979d-5d92d130c7b9", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -\\frac{1}{3840} \\, x^{3} - \\frac{1}{96} \\, x^{2} + \\frac{1}{2} \\, x - 4\$" ], "text/latex": [ "$\\displaystyle -\\frac{1}{3840} \\, x^{3} - \\frac{1}{96} \\, x^{2} + \\frac{1}{2} \\, x - 4$" ], "text/plain": [ "-1/3840*x^3 - 1/96*x^2 + 1/2*x - 4" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "taylor(thb, x, 0, 3)" ] }, { "cell_type": "code", "execution_count": 17, "id": "e745d966-6e84-4f46-9b5e-f69efbeaf243", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle x\$" ], "text/latex": [ "$\\displaystyle x$" ], "text/plain": [ "x" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x" ] }, { "cell_type": "code", "execution_count": 18, "id": "a29ca495-c43a-4812-bc65-3a1a407ba565", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\left( {\\alpha}, x \\right) \\ {\\mapsto} \\ \\frac{\\sqrt{2} e^{\\left(\\frac{\\arctan\\left(\\frac{2 \\, {\\alpha} x - 1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right) + \\arctan\\left(\\frac{1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}}{\\sqrt{{\\alpha} x^{2} - x + 2}}\$" ], "text/latex": [ "$\\displaystyle \\left( {\\alpha}, x \\right) \\ {\\mapsto} \\ \\frac{\\sqrt{2} e^{\\left(\\frac{\\arctan\\left(\\frac{2 \\, {\\alpha} x - 1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right) + \\arctan\\left(\\frac{1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}}{\\sqrt{{\\alpha} x^{2} - x + 2}}$" ], "text/plain": [ "(a, x) |--> sqrt(2)*e^((arctan((2*a*x - 1)/sqrt(8*a - 1)) + arctan(1/sqrt(8*a - 1)))/sqrt(8*a - 1))/sqrt(a*x^2 - x + 2)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(a, x) = sqrt(2)/sqrt(a*x^2 - x + 2)*exp(1/sqrt(8*a - 1)*\\\n", " (atan((2*a*x - 1)/sqrt(8*a - 1)) + atan(1/sqrt(8*a - 1))))\n", "f" ] }, { "cell_type": "code", "execution_count": 19, "id": "e9246b40-7c09-4b6a-bc23-0ab21d20a1b6", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -\\frac{\\sqrt{2} {\\left(2 \\, {\\alpha} x - 1\\right)} e^{\\left(\\frac{\\arctan\\left(\\frac{2 \\, {\\alpha} x - 1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right) + \\arctan\\left(\\frac{1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}}{2 \\, {\\left({\\alpha} x^{2} - x + 2\\right)}^{\\frac{3}{2}}} + \\frac{2 \\, \\sqrt{2} {\\alpha} e^{\\left(\\frac{\\arctan\\left(\\frac{2 \\, {\\alpha} x - 1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right) + \\arctan\\left(\\frac{1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}}{\\sqrt{{\\alpha} x^{2} - x + 2} {\\left(\\frac{{\\left(2 \\, {\\alpha} x - 1\\right)}^{2}}{8 \\, {\\alpha} - 1} + 1\\right)} {\\left(8 \\, {\\alpha} - 1\\right)}}\$" ], "text/latex": [ "$\\displaystyle -\\frac{\\sqrt{2} {\\left(2 \\, {\\alpha} x - 1\\right)} e^{\\left(\\frac{\\arctan\\left(\\frac{2 \\, {\\alpha} x - 1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right) + \\arctan\\left(\\frac{1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}}{2 \\, {\\left({\\alpha} x^{2} - x + 2\\right)}^{\\frac{3}{2}}} + \\frac{2 \\, \\sqrt{2} {\\alpha} e^{\\left(\\frac{\\arctan\\left(\\frac{2 \\, {\\alpha} x - 1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right) + \\arctan\\left(\\frac{1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}}{\\sqrt{{\\alpha} x^{2} - x + 2} {\\left(\\frac{{\\left(2 \\, {\\alpha} x - 1\\right)}^{2}}{8 \\, {\\alpha} - 1} + 1\\right)} {\\left(8 \\, {\\alpha} - 1\\right)}}$" ], "text/plain": [ "-1/2*sqrt(2)*(2*a*x - 1)*e^((arctan((2*a*x - 1)/sqrt(8*a - 1)) + arctan(1/sqrt(8*a - 1)))/sqrt(8*a - 1))/(a*x^2 - x + 2)^(3/2) + 2*sqrt(2)*a*e^((arctan((2*a*x - 1)/sqrt(8*a - 1)) + arctan(1/sqrt(8*a - 1)))/sqrt(8*a - 1))/(sqrt(a*x^2 - x + 2)*((2*a*x - 1)^2/(8*a - 1) + 1)*(8*a - 1))" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(f(a, x), x)" ] }, { "cell_type": "code", "execution_count": 20, "id": "69d03276-f958-44f6-9d00-a428f6432a6c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 6 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a_sel = [1/4, 1/2, 1, 2, 4, 6]\n", "graph = Graphics()\n", "for a1 in a_sel:\n", " legend_label=r'$\\alpha = {:.2f}$'.format(float(a1))\n", " graph += plot(f(a1, x), (x, 0, 6), color=hue(a1/8), \n", " legend_label=legend_label, thickness=1.5,\n", " axes_labels=[r\"$x$\", r\"$f_\\alpha(x)$\"])\n", "show(graph, frame=True, axes=False, gridlines=True)\n", "graph.save(\"vai_f_alpha_x.pdf\", frame=True, axes=False, gridlines=True)" ] }, { "cell_type": "markdown", "id": "25598cdb-8418-4b91-bf0d-838fa6049387", "metadata": {}, "source": [ "Equivalent form:" ] }, { "cell_type": "code", "execution_count": 21, "id": "ec000ab2-eae5-4233-aec7-96947a786d40", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\left( {\\alpha}, x \\right) \\ {\\mapsto} \\ \\frac{\\sqrt{2} e^{\\left(\\frac{\\pi H\\left(x - 4\\right) + \\arctan\\left(-\\frac{\\sqrt{8 \\, {\\alpha} - 1} x}{x - 4}\\right)}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}}{\\sqrt{{\\alpha} x^{2} - x + 2}}\$" ], "text/latex": [ "$\\displaystyle \\left( {\\alpha}, x \\right) \\ {\\mapsto} \\ \\frac{\\sqrt{2} e^{\\left(\\frac{\\pi H\\left(x - 4\\right) + \\arctan\\left(-\\frac{\\sqrt{8 \\, {\\alpha} - 1} x}{x - 4}\\right)}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}}{\\sqrt{{\\alpha} x^{2} - x + 2}}$" ], "text/plain": [ "(a, x) |--> sqrt(2)*e^((pi*heaviside(x - 4) + arctan(-sqrt(8*a - 1)*x/(x - 4)))/sqrt(8*a - 1))/sqrt(a*x^2 - x + 2)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h(a, x) = sqrt(2)/sqrt(a*x^2 - x + 2)*exp(1/sqrt(8*a - 1)*\\\n", " (atan(x*sqrt(8*a - 1)/(4 - x)) + pi*heaviside(x-4)))\n", "h" ] }, { "cell_type": "code", "execution_count": 22, "id": "fd9643f9-8424-4f48-ae6e-f7cbde23e189", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 6 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a_sel = [1/4, 1/2, 1, 2, 4, 6]\n", "graph = Graphics()\n", "for a1 in a_sel:\n", " legend_label=r'$\\alpha = {:.2f}$'.format(float(a1))\n", " graph += plot(h(a1, x), (x, 0, 6), color=hue(a1/8), \n", " legend_label=legend_label, thickness=1.5,\n", " axes_labels=[r\"$x$\", r\"$f_\\alpha(x)$\"])\n", "show(graph, frame=True, axes=False, gridlines=True)\n" ] }, { "cell_type": "markdown", "id": "d3c1a7e5-9dfe-4221-85b6-e096cdbcbd7f", "metadata": {}, "source": [ "Maximal value of $f_\\alpha(x)$:" ] }, { "cell_type": "code", "execution_count": 23, "id": "46ad577c-6277-4ba1-b4de-2b6080b0df47", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle e^{\\left(\\frac{2 \\, \\arctan\\left(\\frac{1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}\$" ], "text/latex": [ "$\\displaystyle e^{\\left(\\frac{2 \\, \\arctan\\left(\\frac{1}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}{\\sqrt{8 \\, {\\alpha} - 1}}\\right)}$" ], "text/plain": [ "e^(2*arctan(1/sqrt(8*a - 1))/sqrt(8*a - 1))" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(a, 1/a)" ] }, { "cell_type": "markdown", "id": "70544891", "metadata": {}, "source": [ "Expansion for small $x$:" ] }, { "cell_type": "code", "execution_count": 24, "id": "39821c30", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -\\frac{1}{4} \\, {\\left({\\alpha} - 1\\right)} x^{2} + \\frac{1}{2} \\, x + 1\$" ], "text/latex": [ "$\\displaystyle -\\frac{1}{4} \\, {\\left({\\alpha} - 1\\right)} x^{2} + \\frac{1}{2} \\, x + 1$" ], "text/plain": [ "-1/4*(a - 1)*x^2 + 1/2*x + 1" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "taylor(f(a, x), x, 0, 2)" ] }, { "cell_type": "markdown", "id": "cd07fe10-6120-4eb2-bc62-481bdf08cc0a", "metadata": {}, "source": [ "## Case of a low density radiation shell" ] }, { "cell_type": "code", "execution_count": 25, "id": "2bda2f22-48f9-4c0b-b6db-3d4a46714581", "metadata": {}, "outputs": [], "source": [ "forget(a > 1/8)" ] }, { "cell_type": "code", "execution_count": 26, "id": "d178b806-4cef-428e-bb57-d4364f1751c4", "metadata": {}, "outputs": [], "source": [ "assume(a < 1/8)" ] }, { "cell_type": "code", "execution_count": 27, "id": "dda4678b-9f0b-422c-9e5e-35215c8a45d7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\frac{\\log\\left(\\frac{2 \\, {\\alpha} x - \\sqrt{-8 \\, {\\alpha} + 1} - 1}{2 \\, {\\alpha} x + \\sqrt{-8 \\, {\\alpha} + 1} - 1}\\right)}{2 \\, \\sqrt{-8 \\, {\\alpha} + 1}} - \\frac{1}{2} \\, \\log\\left({\\alpha} x^{2} - x + 2\\right)\$" ], "text/latex": [ "$\\displaystyle \\frac{\\log\\left(\\frac{2 \\, {\\alpha} x - \\sqrt{-8 \\, {\\alpha} + 1} - 1}{2 \\, {\\alpha} x + \\sqrt{-8 \\, {\\alpha} + 1} - 1}\\right)}{2 \\, \\sqrt{-8 \\, {\\alpha} + 1}} - \\frac{1}{2} \\, \\log\\left({\\alpha} x^{2} - x + 2\\right)$" ], "text/plain": [ "1/2*log((2*a*x - sqrt(-8*a + 1) - 1)/(2*a*x + sqrt(-8*a + 1) - 1))/sqrt(-8*a + 1) - 1/2*log(a*x^2 - x + 2)" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(x) = (1 - a*x) / (a*x^2 - x + 2)\n", "F(x) = integrate(f(x), x)\n", "F(x)" ] }, { "cell_type": "code", "execution_count": 28, "id": "1c31f6b7-a188-4a1c-9b74-ca58a9bb17fd", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\left(-\\frac{\\sqrt{-8 \\, {\\alpha} + 1} - 1}{2 \\, {\\alpha}}, \\frac{\\sqrt{-8 \\, {\\alpha} + 1} + 1}{2 \\, {\\alpha}}\\right)\$" ], "text/latex": [ "$\\displaystyle \\left(-\\frac{\\sqrt{-8 \\, {\\alpha} + 1} - 1}{2 \\, {\\alpha}}, \\frac{\\sqrt{-8 \\, {\\alpha} + 1} + 1}{2 \\, {\\alpha}}\\right)$" ], "text/plain": [ "(-1/2*(sqrt(-8*a + 1) - 1)/a, 1/2*(sqrt(-8*a + 1) + 1)/a)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x01 = (1 - sqrt(1 - 8*a))/(2*a)\n", "x02 = (1 + sqrt(1 - 8*a))/(2*a)\n", "x01, x02" ] }, { "cell_type": "code", "execution_count": 29, "id": "e65e6a60-4b14-4ceb-94cd-9adcb4eb1780", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\frac{1}{{\\alpha}}\$" ], "text/latex": [ "$\\displaystyle \\frac{1}{{\\alpha}}$" ], "text/plain": [ "1/a" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(x01 + x02).simplify_full()" ] }, { "cell_type": "code", "execution_count": 30, "id": "8a7f1b45-14d0-43bb-9cf4-f264fc0f6fca", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\mathrm{True}\$" ], "text/latex": [ "$\\displaystyle \\mathrm{True}$" ], "text/plain": [ "True" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bool(P(x) == a*(x - x01)*(x - x02))" ] }, { "cell_type": "code", "execution_count": 31, "id": "17101703-5822-4146-b4f1-7071a547b2bd", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\frac{1}{x_{1} + x_{2}}\$" ], "text/latex": [ "$\\displaystyle \\frac{1}{x_{1} + x_{2}}$" ], "text/plain": [ "1/(x_1 + x_2)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x1 = var('x_1', domain='real')\n", "x2 = var('x_2', domain='real')\n", "a1 = 1/(x1 + x2)\n", "a1" ] }, { "cell_type": "code", "execution_count": 32, "id": "e545d1be-e060-44fa-a615-c9f6b1fb0524", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -\\frac{{\\left(x_{1} + x_{2}\\right)} {\\left(\\frac{x}{x_{1} + x_{2}} - 1\\right)}}{{\\left(x - x_{1}\\right)} {\\left(x - x_{2}\\right)}}\$" ], "text/latex": [ "$\\displaystyle -\\frac{{\\left(x_{1} + x_{2}\\right)} {\\left(\\frac{x}{x_{1} + x_{2}} - 1\\right)}}{{\\left(x - x_{1}\\right)} {\\left(x - x_{2}\\right)}}$" ], "text/plain": [ "-(x_1 + x_2)*(x/(x_1 + x_2) - 1)/((x - x_1)*(x - x_2))" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f1(x) = (1 - a1*x) / (a1*(x - x1)*(x - x2))\n", "f1(x)" ] }, { "cell_type": "code", "execution_count": 33, "id": "6202206d-225b-48f6-8be7-a07e66dab797", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\frac{x_{2} \\log\\left(x - x_{1}\\right) - x_{1} \\log\\left(x - x_{2}\\right)}{x_{1} - x_{2}}\$" ], "text/latex": [ "$\\displaystyle \\frac{x_{2} \\log\\left(x - x_{1}\\right) - x_{1} \\log\\left(x - x_{2}\\right)}{x_{1} - x_{2}}$" ], "text/plain": [ "(x_2*log(x - x_1) - x_1*log(x - x_2))/(x_1 - x_2)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate(f1(x), x).simplify_full()" ] }, { "cell_type": "code", "execution_count": 34, "id": "ef452726-0192-41a0-b781-bf12c4d22cd6", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -\\frac{\\sqrt{-8 \\, {\\alpha} + 1}}{{\\alpha}}\$" ], "text/latex": [ "$\\displaystyle -\\frac{\\sqrt{-8 \\, {\\alpha} + 1}}{{\\alpha}}$" ], "text/plain": [ "-sqrt(-8*a + 1)/a" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(x01 - x02).simplify_full()" ] }, { "cell_type": "code", "execution_count": 35, "id": "5e350efa-964d-4830-ada5-8f4615413cbe", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\frac{x_{2} \\log\\left({\\left| x - x_{1} \\right|}\\right)}{x_{1} - x_{2}} - \\frac{x_{1} \\log\\left({\\left| x - x_{2} \\right|}\\right)}{x_{1} - x_{2}}\$" ], "text/latex": [ "$\\displaystyle \\frac{x_{2} \\log\\left({\\left| x - x_{1} \\right|}\\right)}{x_{1} - x_{2}} - \\frac{x_{1} \\log\\left({\\left| x - x_{2} \\right|}\\right)}{x_{1} - x_{2}}$" ], "text/plain": [ "x_2*log(abs(x - x_1))/(x_1 - x_2) - x_1*log(abs(x - x_2))/(x_1 - x_2)" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = x2/(x1 - x2)*ln(abs(x - x1)) - x1/(x1 - x2)*ln(abs(x - x2))\n", "g" ] }, { "cell_type": "code", "execution_count": 36, "id": "fcfaae9b-0bae-4897-88de-b312d2fd3edd", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -\\frac{x_{1}}{{\\left(x - x_{2}\\right)} {\\left(x_{1} - x_{2}\\right)}} + \\frac{x_{2}}{{\\left(x - x_{1}\\right)} {\\left(x_{1} - x_{2}\\right)}}\$" ], "text/latex": [ "$\\displaystyle -\\frac{x_{1}}{{\\left(x - x_{2}\\right)} {\\left(x_{1} - x_{2}\\right)}} + \\frac{x_{2}}{{\\left(x - x_{1}\\right)} {\\left(x_{1} - x_{2}\\right)}}$" ], "text/plain": [ "-x_1/((x - x_2)*(x_1 - x_2)) + x_2/((x - x_1)*(x_1 - x_2))" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(g, x)" ] }, { "cell_type": "code", "execution_count": 37, "id": "ac8d74b8-2859-40c4-8079-99abbf66fb85", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\left(3, 6\\right)\$" ], "text/latex": [ "$\\displaystyle \\left(3, 6\\right)$" ], "text/plain": [ "(3, 6)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X1 = x01.subs(a=1/9).simplify_full()\n", "X2 = x02.subs(a=1/9).simplify_full()\n", "X1, X2" ] }, { "cell_type": "code", "execution_count": 38, "id": "01cdfbe6-1261-4105-a9a6-a305bf34209a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\left(3.00000000000000, 6.00000000000000\\right)\$" ], "text/latex": [ "$\\displaystyle \\left(3.00000000000000, 6.00000000000000\\right)$" ], "text/plain": [ "(3.00000000000000, 6.00000000000000)" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n(X1), n(X2)" ] }, { "cell_type": "code", "execution_count": 39, "id": "3272b8ac-e7dc-451a-9ca4-983efb7e0436", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\left(1, 2\\right)\$" ], "text/latex": [ "$\\displaystyle \\left(1, 2\\right)$" ], "text/plain": [ "(1, 2)" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b1 = (X1/(X2 - X1)).expand()\n", "b2 = (X2/(X2 - X1)).expand()\n", "b1, b2" ] }, { "cell_type": "code", "execution_count": 40, "id": "32019dc3-d956-4cd6-b61a-c50d744f489c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\frac{9 \\, {\\left| \\frac{1}{6} \\, x - 1 \\right|}}{{\\left(x - 3\\right)}^{2}}\$" ], "text/latex": [ "$\\displaystyle \\frac{9 \\, {\\left| \\frac{1}{6} \\, x - 1 \\right|}}{{\\left(x - 3\\right)}^{2}}$" ], "text/plain": [ "9*abs(1/6*x - 1)/(x - 3)^2" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R(x) = abs(x/X2 - 1)^b1/abs(x/X1 - 1)^b2\n", "R(x)" ] }, { "cell_type": "code", "execution_count": 41, "id": "8b8e8602-e2eb-49a8-bce9-535ab09d888e", "metadata": {}, "outputs": [ { "data": { "image/png": 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9+jA9DSW3sbGAszOztZqVxzhjd+MGoNfzjcXGiM2JxTTVNMTmUBkM9KCSG+Lj4+Hu7o74+HjeociGiluqKO1XFHaNEBgYCC8vL4wdO9as76lUKkYRWTHGG4EZXoYFaLk1GICqKqklwa2rmYsHKBTFAAOqa6thAJXBQA8quaFr167w8fFB165deYciGypuqaK0X1HYNYKPjw80Gg1iYmLM+t7zzz/PKCIrxkIzdi3SraVwdobB8c8VkMR9dgJiUMkN7u7u+Pbbb0ntFUvFLVWU9isKOwasXbuWdwiWx0Izdi3SraWws0OFk5P0XtxnJyAGldxQVlaGU6dOoYzQrDgVt1RR2q8o7BjQIrdfsdCMXYt0a0HadOsmvREzdgJiUMkNly5dwkMPPYRLly7xDkU2VNxSRWwpRoAWuf2KhWbsKLkdMgQ4f57QcicA8iorpTeisFOUIV2G4GP7jzGkC6HBQAwquWHIkCE4f/48qeVOqLilitJ+7QwGMrd2c6OkpASurq7QarVof+sN5negoqICrcmsSqsAOh3g4iK9v3YNYHhTcItza2H048bB4fRpICQEePFF3uHYFGLsskX4ZYdwyxY5fs2pQ8SMHQNWrlzJOwTLYtxKrHVraR07hlBym54OzJx58yo1BTKuX5feiBk7RUkvTseEJROQXkxoMBCDSm7IysrCv/71L2QZ8yYBqLilitJ+RWHHgOeee453CJbFWLn07g3Y2TE9FSW3hYXA+vVSS4Uu/fpJb8TDE4pSWFGIP2r+QGEFocFADCq5QavVIiwsDFqtlncosqHilipK+xWFHQPUajXvECyLhe6vA1qgWwuTL+6xExCFSm4YOnQokpKSMHToUN6hyIaKW6oo7VcUdgygtPCkIljoiVigBbq1MI6dOklvxIydgBgiN7BDuGWL0n5FYccAZ2dn3iFYFgvO2LU4txbGzritmJixExCDSm64cOECBgwYgAsXLvAORTZU3FJFab+isGPAlStXeIdgWSw4Y0fJrZsb8NVXUkuFvIoK6Y2YsVMUt7ZueMb1Gbi1JTQYiEElN3To0AEvvfQSOnTowDsU2VBxSxWl/YrCjgETJkzgHYJlseCMHSW3PXsCvr5SS4V+I0dKb8SMnaL0bN8TK19ciZ7tCQ0GYlDJDT179oSvry96EkoMVNxSRWm/orBrhMDAQHh5eWHs2LFmfW/Lli2MIrJCamtvFnYWmLGj5La0FIiKolUjHY2Nld5QCpoApbpS/Pfn/6JUJ7yygkpuqKioQHx8PCqMs+MEoOKWKkr7FQsUy8DcBYpra2thb99Caua8PKB7d2mZk8pKoFUrpqej5FatBry9AZUKGDOGdzTyqA0Lg/3zzwP33QfExPAOx2ZQ56jhvcYbqvdVGONOZDAQg0puUKvV8Pb2hkqlwhgiiYGKW6rI8SsWKObMjz/+yDsEy2G8v65HD+ZFHdDC3HIgOCxMeiNm7ATEoJIbBg8ejD/++AODBw/mHYpsqLilitJ+xYydDMSMXSPs2gW8/DIwbhxw8iTz01FyS3LGTqWC/X33Ae7uQHY273BsBjFjxx5KuYEawi1bxIwdAXx9fXmHYDnS0qS2b1+LnK5FueXAqq1bpTdixk5ADCq5IScnB3PnzkVOTg7vUGRDxS1VlPYrCjsGvPnmm7xDsBwpKVJr3IqKMZTcOjlJT8Q6OfGORD7Pv/GG9KasTHowRqAITvZO6N6mO5zsCQ0GYlDJDQUFBVi3bh0KCgp4hyIbKm6porRfUdgxICoqincIlsPChR0lt8OHA1lZUkuFqFu3tikr4xeIjTHcbTgWui3EcDdCg4EYVHLD8OHDkZWVheGEEgMVt1RR2q8o7BjQv39/3iFYjtRUqfX0tMjpWpRbDnjeey/g6Cj9IC7HKooYu2wRftkh3LJFab+isGOATqfjHYJl0Otv3mNnoRk7Sm4TEoBevaSWCrqqKsB4Y67YfUIxEvISMC16GhLyCA0GYlDJDRqNBiNGjIBGo+EdimyouKWK0n5FYceA/Px83iFYhuxsoLpamuHp1csip6TktroauHpVaqmQn58PiP1iFae6thoFVQWoriU0GIhBJTe0a9cOEyZMQDvjnzMCUHFLFaX9Oip6NAEAkFl0stkY76/r0wdwcLDIKVuMW06MGTPmZmEnZuwEhKCSGzw8PLB8+XLeYZgFFbdUUdqvmLFjQJhxkVdbx8IPTgAtyC0nwsLCbl6KFTN2AkJQyQ2VlZW4fPkyKisreYciGypuqaK0X1HYMeCjjz7iHYJlsPCDE0ALcsuJjz76SMzYCUhCJTdoNBoMHDiQ1D12VNxSRWm/orBrhMDAQHh5eWHs2LFmfc/f359RRFYGhxk7Sm4HDgSOHJFaKvj7+4sZOwYM7DQQ79i/g4GdCA0GYlDJDQMHDsSRI0cwkFBioOKWKkr7FVuKycDcLcVaDA8/LG0jtmOHtK2YwDZ4911gwwZg/nzg6695RyMQCAQtHrGlGGfmzZvHOwTLwGHGjpLbq1eBOXOklgrz5s0TM3YMuFpyFY9+/yiulhAaDMSgkhvy8vKwaNEi5OXl8Q5FNlTcUkVpv6KwY8B7773HOwT2lJcDubnSewsWdpTc5uUBCxZILRXee+89sdwJA/Ju5OGY4RjybhAaDMSgkhtyc3Ph6+uLXGP+JAAVt1RR2q8o7Bjw66+/8g6BPcaFidu3Bzp2tNhpW4Rbjvz6669igWIBSajkhpEjR6KoqAgjR47kHYpsqLilitJ+RWHHAG9vb94hsOfWy7B2dhY7bYtwyxFvb2/xVKyAJCI3sEO4ZYvSfkVhxwBK9040GQ5LnQAtxC1H8vLyAFdX6QdR2AkIQSU3JCUlYdy4cUhKSuIdimyouKWK0n5FYceAqqoq3iGwh8ODEwAtt507Sw+Ydu7MOxL5VFVV3Szsiou5xmJLdG7dGZM6TULn1oQGAzGo5AYXFxcMHToULi4uvEORDRW3VFHaL7nCztfXF2PHjkW7du3QrVs3TJs27a7/8omKioKdnV29V2JiIpMY+/fvz+S4VgWnwo6S2z59gHXrpJYK/fv3v1nYabV8g7Eh+nTogyUTlqBPB0KDgRhUckOfPn2wbt069CGUGKi4pYrSfskVdkePHoWPjw9Onz6NyMhI1NTUYPLkybhx48Zdv5uUlIScnJy6F6sFIo8ePcrkuFbFlStSa+FLsZTcVlQAFy5ILRWOHj0KdOgg/SAKO8WoqK7A9kPbUVFNaDAQg0puqK6uRk5ODqqrq3mHIhsqbqmitF/yCxTn5+ejW7duOHr0KB599NEG+0RFReHxxx/H9evX0cH4l5YZmLtAcXFxcZPOQ4baWqBtW6CyEkhOBgYMsNipKblVqwFvb0ClAqjsoV1cXIwON24AvXoBDg5AdbVFH46xVdQ5aniv8YbqfRXGuBMZDMSgkhvUajW8vb2hUqkU3/ydFVTcUkWO3xa1QLH2z1mFTp063bXv6NGj4e7ujieeeAJHjhy5Yz+dToeSkhKTlzkEBASY1Z8cWVlSUefoCPTta9FT27xbzgQEBNy8FKvXS+sVCgQEoJIb+vfvj3379pG6vEnFLVWU9ku6sDMYDJg9ezYeeeQRDBs27I793N3dsWbNGoSEhCA0NBSDBw/GE088gejo6Ab7+/r6wtXVte7l4eEBAEhJSYGfnx90Ol3dStHz5s1DdnY21q9fj5iYGERERMDLywsajQbLly9HSUmJSd+ioiIEBgYiPj4eYWFhCA8Ph1qtxurVq5Gfn2/St7y8HP7+/khKSsLOnTtx6NAhnDx5Eps2bUJmZqZJX71eD19fX6Snp2PLli04fvw4oqKisH37diQnJ2PRokWorKw0+U5ubi7Wrl2LmJgYHDhwALt378b58+exYsUKaLVak77FxcUICAhAQkICjm/aBACo7NEDazZsQF5enknfiooK+Pv7Izk5GTt27MDhw4dx4sQJbN68GRkZGZg/fz5qa2sxb9481NbWYv78+cjIyMDmzZtx4sQJHD58GDt27EBycjL8/f1RUVFhsjJ3Xl4e1qxZA5VKhf3792PPnj1ISEhAQEAAiouLTWLRarVYsWIFzp8/j927d+PAgQOIiYnB2rVrkZuba9K3srISixYtQnJyMrZv346oqCgcP34cW7ZsQXp6Onx9faHX602+k5mZiU2bNuHkyZM4dOgQdu7ciaSkpLq4jcybNw/5+flYvXo11Go1wsPDERYWhvj4eAQGBqKoqMjkuCUlJVi+fDk0Gg1CQ0MRERGBmJgYrF+/HtnZ2SZ9dTod/Pz8cOXKFWzbtg1RUVE4duwYgoODkZaWhgULFqCmpsbkO1lZWdi4cWPdLQ27du1CYmIi2rZtizKDAbX2UmpY9t//oqCgAEFBQYiLi8O+ffuwd+9exMXFYdWqVSgsLDQ5bmlpKZYtWwaNRoOQkBAcPHgQZ86cwYYNG+rFXV1djYULFyIlJQVbt25FdHQ0oqOjsXXrVqSkpGDhwoWorq6u92dtw4YNOHPmDA4ePIiQkBBoNBosW7YMpaWlJn0LCwuxatUqxMXFYe/evdi3bx/i4uIQFBSEgoICk75lZWVYunQpEhMTsWvXLkRGRuL06dPYuHEjsrKyTPrW1NRgwYIFSEtLQ3BwMI4dO4aoqChs27YNV65caTBH5OfnAwAuXLiAiIgIhIaG2nSO2LNnD/bv3w+VSoU1a9ZYJEfc+mfNmnNEREQEBgwYgHXr1qG8vLzeOLHGHPHAAw/U5YilS5eirKzMpK/IEc3LEQDq1RG35wg/Pz/IxkCYjz76yNCnTx9DZmam2d/9y1/+Ynj22Wcb/F1lZaVBq9XWvTIzMw0ADFqtVtaxf/jhB7PjIcWqVQYDYDBMnWrxU1Nyq1JJmlQq3pHIp85vp05S8Bcu8A3IRlBlqwyYC4Mqm9BgIAaV3HDt2jVDQECA4dq1a7xDkQ0Vt1SR41er1cquQ8jO2H3yyScICwvDkSNH0KtXL7O//+CDDyI5ObnB3zk7O6N9+/YmL3Njs2mM3hg9fNIYlNza2QGtWtG6Ra3Or3gyVlHsYIdWDq1gB0KDgRhUckNWVhZmz56NrKws3qHIhopbqijtl1xhZzAY8PHHHyM0NBSHDx+GZxOfyoyNjYW7u7vC0Uls3ryZyXGtBo6FHSW3o0cDOp3UUqHOr3gyVlFGu4/GYtfFGO1OaDAQg0puGD16NHQ6HUYTSgxU3FJFab+Oih7NAvj4+OCXX37Br7/+inbt2tVtpOzq6orWrVsDAObMmYOrV6/WyVq2bBn69u2LoUOHoqqqCsHBwQgJCUFISAiTGB9//HEmx7UajIXdoEEWP7XNu+VMnV+xSLHiiLHLFuGXHcItW5T2S27GbtWqVdBqtZgwYQLc3d3rXjt27Kjrk5OTg4yMjLqfq6qq8Pnnn2PEiBEYP348jh8/jvDwcLz44otMYrzTJV6bQK+/uTgxhxk7Sm4vXpSWObl4kXck8qnzKy7FKsrF/It4Lvw5XMwnNBiIQSU3JCcnY9KkSWTiBei4pYrSfsnN2BlkLLu36c+nNo188cUX+OKLLxhFVB/jzKFNkpEBVFVJN4/9+bSwJaHktqICiI2ltUBxnV9xKVZRKmoqkFqZiooaQoOBGFRyg6OjI7p27QpHRzp//VJxSxWl/dIZWYToTGlzUHMx/suif39pAVsLY9NurYA6v+JSrIAYVHKDp6cntm3bxjsMs6DilipK+yV3KZYCcXFxvENgB8cHJwAbd2sF1PkVl2IFxKCSG/R6PUpKSqDX63mHIhsqbqmitF9R2DHg2Wef5R0COzgXdjbt1gqo8ysuxQqIQSU3nDt3Dq6urjh37hzvUGRDxS1VlPYrCjsGrFu3jncI7OBc2FFy6+kJ7NwptVSo8ysuxSqKZwdPvGL/Cjw7EBoMxKCSGzw9PbFz584mL9XFAypuqaK0XzuDnKcRWjjmbL5r8wwaJBV3hw4BEyfyjkbAiv/9D3jpJeCRR4Bjx3hHIxAIBC0ac+oQMWPHgFv3f7MpamqA1FTpPacZO0pu8/KAJUuklgp1fsWlWEXJK8vD098/jbwyQoOBGFRyQ2FhITZt2oTCwkLeociGiluqKO1XzNg1QmBgIAIDA6HX63Hp0iXZM3aVlZVwcXGxQIQW5vJlqaBzcQFu3ADsLf/vAkpu1WrA2xtQqaT17ChQ5zcmBrj/fmlJm1vWhBQ0DXWOGt5rvKF6X4Ux7kQGAzGo5Aa1Wg1vb2+oVCqMIZIYqLilihy/YsZOIXx8fKDRaBATE2PW91asWMEoIs4Y768bMIBLUQfYsFsroc6veCpWQAwquWH06NGorq4mtaUYFbdUUdqvKOwYMG3aNN4hsOHSJanldBkWsGG3VkKdX+Ol2NJSoLaWVzgCgWyo5AY7Ozs4OjrCzs6OdyiyoeKWKkr7FYUdA1QqFe8Q2JCYKLVDhnALwWbdWgl1fo0zdgYDUFLCLyCBQCZUcsOVK1fw3HPP4cqVK7xDkQ0Vt1RR2q8o7BjQvXt33iGwwbjp6b33cguBkltXV+DZZ2/WSBSo8+vsLL0AcTlWAVydXfFQ54fg6kxoMBCDUm6ghnDLFqX9ii3FGEBpD0CzsIIZO0pu+/cHwsJ4R2EeJn47dJAe6RWFXbPp36k/Fo5aiP6d+vMOxWahkhv69++PMGKJgYpbqijtV8zYMSDVuCSILXH9+s11OwYP5hYGJbfV1UB+vtRSwcSvWKRYMar11Th3+Ryq9YQGAzGo5AaDwYCamhpQWpCCiluqKO1XFHYMePTRR3mHoDzGy7C9egHt2nELg5LbhASgWzeppYKJX/FkrGIkXEvAx+kfI+EaocFADCq5ITY2Fk5OToiNjeUdimyouKWK0n5FYceAX375hXcIymMFl2EBG3VrRZj4FYsUCwhBJTf06dMHGzduRJ8+fXiHIhsqbqmitF9x4ZwBX3zxBe8QlMcKHpwAbNStFWHiV1yKFRCCSm7o3Lkz3n77bd5hmAUVt1RR2q+YsWOAr68v7xCUx0pm7GzSrRVh4ldcihUQgkpuuH79Onbt2oXr16/zDkU2VNxSRWm/orBjwLfffss7BOWxkhk7m3RrRZj4FYWdgBBUckNqaipefvllUg8kUHFLFaX9isKOATa3YXJlJWBMQpxn7Ci5HTlSqolGjuQdiXxM/BrvsSM0s2CtjHQbiW/sv8FIN0KDgRhUcsPIkSOh1WoxklBioOKWKkr7FYVdIwQGBsLLywtjx44163t/+9vfGEXEieRkaVspV1fAzY1rKJTcOjgA7dtLLRVM/HbqJLWisGs2DvYO+ODtD+BgT2gwEINKbnBwcED79u3hQCgxUHFLFaX9isKuEXx8fKDRaBATE2PW9w4dOsQoIk4YL8MOGQJw3t+QktvkZGDKFKmlgonfjh2lVhR2zSa5MBlP//I0kgsJDQZiUMkNqampmDFjBqlLsVTcUkVpv6KwY8CgQYN4h6AsVnJ/HUDLbWkpcPCg1FLBxK8o7BSjtKoUFyovoLSK0GAgBpXcUFNTg/z8fNTU1PAORTZU3FJFab9iuRMGVFRU8A5BWazkiVjABt1aGSZ+jZdii4r4BCMQmAGV3DBw4ED8/vvvvMMwCypuqaK0XzFjx4DCwkLeISiLRiO1VjBjZ3NurQwTv2LGTkAIkRvYIdyyRWm/orBjAKWnne5KdfXNGbvhw/nGAhtza4WY+DUWdiUlAKHLRoKWCZXcEBsbC2dnZ1JbilFxSxWl/YrCjgH79u3jHYJyXL4MVFUBbdsCVrAFDiW3Hh5AQIDUUsHEr7GwA8TuE83Eo70HXmj1AjzaExoMxKCSG3r16oUlS5agV69evEORDRW3VFHar53BYDAoekQbpKSkBK6urtBqtWjfvv1d+5eXl6NNmzYWiMwC7NwJvPIKcP/9wJkzvKOxLbdWSD2/7dtLT39cugQMHMgvMBtAjF22CL/sEG7ZIsevOXWImLFjwJIlS3iHoBznz0utFVyGBWi5LSoCgoNpPXtQz6+4z04RiiqK8Nbit1BUQWgwEINKbtBqtQgPD4eW0I4uVNxSRWm/YsZOBubO2NkUL74I7N4NLF0KfPYZ72hIoVYD3t6ASgWMGcM7miYyejQQFwf89hvw1FO8oyGLOkcN7zXeUL2vwhh3qoNBoARqtRre3t5QqVQYQzYxCCyNmLHjjE1tv5KQILVWMmNnU26tkHp+xYydgAhUcsPw4cORnZ2N4VaSU+VAxS1VlPYr1rFjwAcffMA7BGUoLweuXJHeDxvGN5Y/sRm3Vko9v6KwExCBSm5wcnKCu7s77zDMgopbqijtV8zYMSA0NJR3CMqg0QAGA9C1K/c9Yo3YjFsrpZ5fsUixgAhUckN6ejpmzpyJ9PR03qHIhopbqijtVxR2jRAYGAgvLy+MHTvWrO+Z299qMT44YSWzdQAtt23bAg8+KLVUqOdXzNgpQlunthjecTjaOhEaDMSgkhsqKytx4cIFVFZW8g5FNlTcUkVpv+JSbCP4+PjAx8en7qZFueTk5DCMyoJY2ROxAC23gwcDp07xjsI86vkVhZ0iDO4yGL79fTG4y2DeodgsVHLD4MGDcYpYYqDilipK+xUzdgzQ6/W8Q1AG44MTVjRjZzNurZR6fsWlWMUQY5ctwi87hFu2KO1XFHYM6Nu3L+8QlMEKZ+wouVWrATs7qaVCPb9ixk4R1DlqPB/7PNQ5hAYDMajkhnPnzqFTp044d+4c71BkQ8UtVZT2Kwo7Bhw7dox3CM2nqAjIzpbeDx3KN5ZbsAm3Vkw9v6KwExCBSm7o3r075syZg+7du/MORTZU3FJFab/iHjsGzJgxg3cIzcc4W9e3L9CuHddQbsUm3Fox9fyKS7ECIlDJDW5ubvjXv/7FOwyzoOKWKkr7FTN2DFi5ciXvEJqPFT4RC9iIWyumnl8xYycgApXcUFpaiqioKJSWlvIORTZU3FJFab+isGPAt99+yzuE5hMXJ7VWdH8dYCNurZh6fo2FXXk5oNNZPiCBQCZUckNycjIef/xxJCcn8w5FNlTcUkVpv6KwY4BNbL8SGyu1o0fzjeM2KLn18gKSk6WWCvX8urpKT4AAYtauGXh19cJn9p/BqyuhwUAMKrnBy8sLycnJ8CKUGKi4pYrSfu0MBoNB0SPaIOZsvmvsL6ef1VJTA9xzjzRDk5wMDBjAO6I6yLu1chr026mTVNRpNMCQIXwCswHE2GWL8MsO4ZYtcvyaU4eIGTsGbNq0iXcIzSMxUSrq2rUD+vXjHY0JlNympgJvvCG1VGjQr/FyrHiAosmkXk/FxMCJSL1OaDAQg0puyMzMxKxZs5CZmck7FNlQcUsVpf2Kwo4BkyZN4h1C8zBehh05ErC3riFCye3168DWrbSuYDbo1/hkLKX/ECvjeuV1qKpUuF4pHLKCSm6g+PAEFbdUUdqvdf2tbWU0da/YxMRERhFZCCu9vw6wAbdWToN+xYydgABUcoOXlxfi4+NJ3WNHxS1VlPYrCrtG8PHxgUajQUxMjFnfa0tp1/eGMD4Ra4WFHXm3Vk6DfsVadgICiNzADuGWLUr7FYUdAzoZ/yKkiMFwc8Zu1CiuoTQEabcEaNBvly5SW1Bg2WAEAjOgkhsSEhLQq1cvJBj34iYAFbdUUdqvKOwYEB8fzzuEppOeDhQXA05OVrWVmBFKbt3dge++k1oqNOjXWNgVFlo2GBvC/R53PNvuWbjfQ2gwEINKbujSpQtmzpyJLsY/VwSg4pYqSvsVy53IwNzlTrKzs9GjRw8LRMaA3buBF1+UZuuMM3dWBGm3BGjQb0AA8MknwF//CuzaxScwG0CMXbYIv+wQbtkix69Y7oQzGzZs4B1C07Hiy7AALbclJUBEhNRSoUG/nTtLrbgU22RKdCWYs34OSnSEBgMxqOSGGzduICYmBjdu3OAdimyouKWK0n7FjJ0MzJ2xI81zzwF79wI//QTMmsU7GtKo1YC3N6BSAWPG8I6mGURGApMnS9vLiUsyTUKdo4b3Gm+o3ldhjDvlwSBoLmq1Gt7e3lCpVBhDOjEILImYseMM6e1XrHipE4C4WwI06Fc8PCEgAJXcMGTIEJw7dw5DCO3iQsUtVcSWYhwwd8ZOp9PB2dnZApEpTEEB0LWr9F6rBaxwdpKSW4ozdg36zcgA+vSRHqjR6W7uHSuQjZixYw+l3EAN4ZYtcvza9Iydr68vxo4di3bt2qFbt26YNm0akpKS7vq9o0ePwtvbGy4uLujXrx+CgoKYxfjTTz8xOzZTzp6V2oEDrbKoAwi7JUKDfo0zdtXVQFmZZQMSCGRCJTdcvXoVc+bMwdWrV3mHIhsqbqmitF9yhd3Ro0fh4+OD06dPIzIyEjU1NZg8eXKjN6KmpqZi6tSpGD9+PGJjY/H1119j1qxZCAkJYRLj9OnTmRyXOcaFmM3cacOSUHLr7Az07y+1VGjQb5s2QOvW0ntxObZJODs4o/c9veHsQGgwEINKbiguLsauXbtQXFzMOxTZUHFLFaX9Oip6NAtw4MABk583btyIbt26QaVS4dFHH23wO0FBQejduzeWLVsGQLrH4ezZs1i8eDGTAfvHH3+gf//+ih+XOQQKO0puhw4FLl/mHYV53NFv585AVpZU2Hl6Wj4w4gztNhQLeizA0G7WtzakrUAlNwwdOhSXiSUGKm6porRfcjN2t6PVagE0vnLzqVOnMHnyZJPPpkyZgrNnz6K6urpef51Oh5KSEpOXObhTWpHWiMFAorAj6ZYQd/QrFiluNmLsskX4ZYdwyxal/ZIu7AwGA2bPno1HHnkEw4YNu2O/3NxcuLm5mXzm5uaGmpoaFDRwacnX1xeurq51Lw8PDwBASkoK/Pz8oNPp6p5imTdvHrKzs7F+/XrExMQgIiICx48fh0ajwfLly1FSUmLSt6ioCIGBgYiPj0dYWBjCw8OhVquxevVq5Ofnm/QtLy+Hv78/kpKSsHPnThw6dAgnT57Epk2bkJmZadJXr9fD19cX6enp2LJlC44fP46oqChs374dycnJWLRoESorK02+k5ubi7Vr1yImJgZHgoOB3FwYHByw6vRpaLVak77FxcUICAhAQkIC9uzZg/3790OlUmHNmjXIy8sz6VtRUQF/f38kJydjx44dOHz4ME6cOIHNmzcjIyMD8+fPR21tLebNm4fa2lrMnz8fGRkZ2Lx5M06cOIHDhw9jx44dSE5Ohr+/PyoqKuqOHxwcjLy8PKxZswYqlQr79+/Hnj17kJCQgICAABQXF5vEotVqsWLFCpw/fx67d+/GgQMHEBMTg7Vr1yI3N9ekb2VlJRYtWoTk5GRs374dUVFROH78OLZs2YL09HT4+vpCr9ebfCczMxObNm3CyZMncejQIezcuRNJSUnw9/fHmTMVaNv2BuLjpb75+flYvXo11Go1wsPDERYWhvj4eAQGBqKoqMjkuCUlJVi+fDk0Gg1CQ0MRERGBmJgYrF+/HtnZ2SZ9dTod/Pz8cOXKFWzbtg1RUVE4duwYgoODkZaWhgULFqCmpsbkO1lZWdi4cWPdLQ27du1CYmIiQkJCUFZWZtK3oKAAWZWVAIDYyEjs3bsXcXFxWLVqFQoLC036lpaWYtmyZdBoNAgJCcHBgwdx5swZbNiwoV7c1dXVWLhwIVJSUrB161ZER0cjOjoaW7duRUpKChYuXIjq6up6f9Y2bNiAM2fO4ODBgwgJCYFGo8GyZctQWlpq0rewsBCrVq1CXFwc9u7di3379iEuLg5BQUEoKCgw6VtWVoalS5ciMTERu3btQmRkJE6fPo2NGzciKyvLpG9NTQ0WLFiAtLQ0BAcH49ixY4iKisK2bdtw5cqVBnPE7wm/Y2rUVPxy6BdEREQgNDSUXI44cOAAdu/ejfPnz2PFihVWlyOCg4Prjm/NOcLf3x+enp7417/+hfLycpO+1poj1Gp1XY5YunRpgzkiKCgIcXFx2Ldvn8gRZuaI4ODgenXE7TnCz88PsjEQ5qOPPjL06dPHkJmZ2Wi/gQMHGn788UeTz44fP24AYMjJyanXv7Ky0qDVautemZmZBgAGrVYrK64tW7bI/4+wFkJDDQbAYBgxgnckjULJrUolKVWpeEcinzv6feUV6T9m6VKLxmMrqLJVBsyFQZVNaDAQg0puyMzMNHz++ed3/XvLmqDilipy/Gq1Wtl1CLl77Ix88sknCAsLQ3R0NHr16tVo3+7duyM3N9fks2vXrsHR0RGdjavq34Kzs3OzHu1+5JFHmvxdbhC4DAsQdUuIO/oVa9kJrBwquaFXr15YtGgR7zDMgopbqijtl9ylWIPBgI8//hihoaE4fPgwPGXcyD1u3DhERkaafHbw4EHcd999cHJyUjzG7du3K35M5hAp7Ei6JcQd/Yp77ARWDpXcUFFRgQsXLqCiooJ3KLKh4pYqSvslV9j5+PggODgYv/zyC9q1a4fc3Fzk5uaa/CGZM2cO3nrrrbqfP/zwQ6Snp2P27Nm4ePEiNmzYgPXr1+Pzzz9nEiOr4zLDYLi5hp2VF3bk3BLjjn7FfrECK4dKbrh48SKGDRuGixcv8g5FNlTcUkVpv+QKu1WrVkGr1WLChAlwd3eve+3YsaOuT05ODjIyMup+9vT0xP79+xEVFYVRo0bhhx9+wPLly5mtzbNgwQImx2XG5ctAcbG04Nrw4byjaRRKbgcNAk6elFoq3NGvuBTbLAZ1HoT37N/DoM6EBgMxqOSGQYMG4eTJkxhEKDFQcUsVpf2KLcVkYO6WYuT45Rfg9deBBx4ATp/mHY3AGomMBCZPlgr/+Hje0QgEAkGLwqa3FKMAuQ2TjffX3X8/3zhkQMltVhYwe7bUUuGOfsWl2GaRVZKFh79/GFklhAYDMajkhpycHMybNw85OTm8Q5ENFbdUUdqvKOwY8Pbbb/MOwTxOnZJaAoUdJbfXrgFLl0otFe7o99ZLsWKS32yu3biGk4aTuHaD0GAgBpXckJ+fj8DAQOTn5/MORTZU3FJFab+isGPA7U/gWjWVlYBaLb1/6CG+sciAlFuC3NGvsbCrrgbKyiwXkEAgEyq5YcSIEcjJycGIESN4hyIbKm6porRfUdgxYMiQIbxDkI9aLf1l3a0biT1ASbklyB39tmkDuLhI78XlWIEVInIDO4RbtijtVxR2DCgtLeUdgnyMl2HHjQPs7PjGIgNSbgnSqF/xZKzAiqGSGy5evIgxY8aQWu6EiluqKO1XFHYMKC4u5h2CfE6elFoCl2EBWm67dAE++uhmPUSBRv2KRYqbTJc2XTC542R0aUNoMBCDSm5o27Ytxo0bh7Zt2/IORTZU3FJFab9ktxSzBIGBgQgMDIRerzfre8OtfC24OgwG0xk7ApBxC6B3byAwkHcU5tGoX/FkbJPp7dobP03+Cb1de/MOxWahkht69+6NQGKJgYpbqijtV8zYNYKPjw80Gg1ijMuByOS3335jFJHCZGQAOTmAoyNw3328o5EFGbcAysulWxjLy3lHIp9G/YpLsU2mvLoca/etRXk1ocFADCq5QafTIS0tDTqdjncosqHilipK+xWFHQPee+893iHIwzhbN2oU0Lo111DkQsYtgMREwNtbaqnQqF9R2DWZxIJELLmxBIkFhAYDMajkhgsXLsDT0xMXLlzgHYpsqLilitJ+RWHHgGXLlvEOQR7E7q8DCLklSqN+RWEnsGKo5IYBAwYgMjISAwYM4B2KbKi4pYrSfsWWYjKw2S3Fxo4Fzp4Ftm0DXn2VdzQ2h1otzdipVMCYMbyjUYCVKwEfH+CFF4DQUN7RkEKdo4b3Gm+o3ldhjLstDAaBQGBJxJZinCGx/UpZGRAbK70nNGNHwi1hGvXbrZvUUtpKQ9BioJIb8vLysGTJEuTl5fEORTZU3FJFbClGgA8//JB3CHfn1ClArwf69pUe3yQCCbd/Ym8PtGsntVRo1K8o7JqMvZ097nG6B/Z2hAYDMajkhpycHMydO5fUXrFU3FJFab8iyzDgf//7H+8Q7k50tNQ++ijfOMyEhNs/GTUKKCmRWio06lcUdk1mVPdRWNRpEUZ1H8U7FJuFSm4YNWoUSkpKMIpQYqDilipK+xWFHQMefPBB3iHcHWNhN3483zjMhIRbwjTq181NarVagNBSDdaCGLtsEX7ZIdyyRWm/orBjQFZWFu8QGqeyEjhzRnpPbMbO6t3egkYDDB0qtVRo1G+HDtKah4CYtTMTTb4Gz0U8B00+ocFADCq5ISkpCY888giSkpJ4hyIbKm6porRfUdgxwOofNI6JkWZc3NyAgQN5R2MWVu/2FiorpaKuspJ3JPJp1K+dnbgc20QqayqRWZmJyhpCg4EYVHKDs7MzBgwYAGdnZ96hyIaKW6oo7VdsKcYADw8P3iE0zq3319nZ8Y3FTKzeLXHu6rdbNyA7WxR2AquDSm7o27cvNm3axDsMs6DilipK+xUzdgw4ZdzRwVoh+uAEQMAtce7qV8zYCawUKrmhuroa+fn5qK6u5h2KbKi4pYrSfkVh1wiBgYHw8vLC2LFjzfreyy+/zCgiBaipubnjBMHCzqrd2gB39Wt8gEIUdgIrg0puSEhIQLdu3ZCQkMA7FNlQcUsVpf2Kwq4RfHx8oNFoEBMTY9b3Vq1axSgiBYiLkxYn7tABGDaMdzRmY9Vub6NfP+DXX6WWCnf1K2bsmkS/jv3wmv1r6NeR0GAgBpXc0K9fP/z666/oRygxUHFLFaX9ii3FZGBTW4otWQL83/8Bzz4LhIXxjkZADT8/4MsvgTffBDZv5h2NQCAQtAjElmKcsertV6KipJbgZVjAyt3eRm4u4OsrtVS4q18xY9ckcsty8eT3TyK3jNBgIIYlckOYAv8Yzs/Px+rVq5Gfn69ARJaBUt6liNhSjACffvop7xAaprr6ZmE3cSLXUJqK1bptgOxs4OuvpZYKd/Ur7rFrEtml2fjd8DuySwkNBmJYIjcoUdhlZmbCx8cHmZmZCkRkGSjlXYoo7Vcsd8KA9evX47PPPuMdRn1iYoDSUqBTJ1r7XN2C1bq1Ee7qV8zYCayU5uQGHx8fVFRU3LXfnj17sG7duiadw8iYMWNQU1PTrGNYGpF32aK0XzFjx4DJkyfzDqFhDh2S2okTae1MfwtW69ZGuKvfWws7cXuuwIpoTm546KGHcP78eRgMhkZfdsTW/VQKkXfZorRfMWPHgIsXL8LLy4t3GPX5/XepnTSJbxzNwGrd2gh39du1q9RWVwPFxUDHjhaJSyC4G83JDa+//jpiY2OxePHiRvu9++67TTr+rSQnJ+Pjjz9GQEAABhLZ+UfkXbYo7ZfmtI2V065dO94h1OfGDcC4COITT/CNpRlYpds70KED8Ne/Si0V7urXxQUwPpElLsfKpoNLB4zvNB4dXDrwDsVmaW5uuO++++7a57nnnmvWOQDAwcEB7du3h4ODQ7OPZSko5V2KKO1XzNgxwNXVlXcI9Tl2TJpl6dMH6N+fdzRNxird3oF+/YBdu3hHYR6y/Lq5ASUlQF4eMHgw+6BsgH4d+2HR/YvEOnYMaW5uePXVV+/a5/nnn2/WOQBpHbtdxBIDpbxLEaX9ihk7Bly4cIF3CPUx3l83aRK5/WFvxRrd3ulBuaoqICtLaqkgy2/37lKbk8M2GBuiSl+FY+eOoUpPaDAQwxpzQ0Po9XrcuHEDer2edyiyoeKWKkr7FYUdA5566ineIdTHeH8d4cuwgHW6vVNhd/484OEhtVSQ5dfdXWpbYGHnd8IPfZb1Qdsf2+LprU8jqSCp7nfr1OvgE+6Dt/e8Xe9756+dx79y/oXz1wgNBmKwyg0rVqxQ9Hjnzp3DPffcg3Pnzil6XJZYY961JZT2Kwq7RmjqXrEbNmxgFFETyc+XthIDyK5fZ8SSbn18gHfeufsrNNRiITFHlt8WWtj5n/SH3wk/TOg7AR96f4iK6gqMWTMG4ZfCAQAzx8zEXwb9BVvit3COtGXCKjfExsYqery+ffvil19+Qd++fRU9Lkus7u80G0Npv+Ieu0bw8fGBj49P3VYecvn2228ZRtUEjhyR2uHDby4wSxRLun3oIeCnn4ChQxvvR/jKdj1k+TUWdpS21FCA3y7/hoR/JMC9nXvdZzFXY/DR/o/g4uiCJ/o9AXs78W9lXlhd3r0DnTp1wowZM3iHYRZU3FJFab8iCzHA6rZfiYyUWsLLnBixpNvXX5d2Xtu4sfHXtGkWC4k5svy20Bm7+3rcZ1LUAcDYnmNx9O2j2By/GYdTD3OKTABYYd69A0VFRQgODkZRURHvUGRDxS1VxJZiBPjyyy95h3ATgwE4cEB6bwOLTFrarYwVEKDACghWgyy/LfThCQc7B1TWVCKxIBFhSTdvrGzj1AY/T/sZJzJO4MDlAxwjbNlYVd5thLS0NLz55ptIS0vjHYpsqLilitJ+RWHHgCVLlvAO4SYXLkiPZrq4AI89xjuaZmNptzJWQMCdVkAYNQqorKS1e5ssvy10xu6TBz7Bx/s/xku7XsL7e9+v9/t/P/ZvjOo+Ck72TvV+N6r7KMxznodR3UdZINKWiVXl3UYYNWoUKisrMYpQYqDilipK+xX32DHgpZde4h3CTfbvl9rHHwdat+YbiwJYldu7YG8PODvzjsI8ZPk1FnaFhdJaLq1asQ3KSuh+T3ese24dLhddRluntg32+duov+Ehj4fqfW5vZ48ZL88Q9+AxhEpusLe3hzOxxEDFLVWU9iuyDANOGXd4sAZ++01qn36abxwKYQm3Fy8Cs2bd3KijqVy6BEyYILVUkOW3c2fA6c9ZqRb2AAUADOg0oN69drcysHP9baIuFV7CM7uewaVCQoOBGFaVdxshJSUFL774IlJSUniHIhsqbqmitF/mhV1ZWRlyc3NRRWmV1mbi4eHBOwSJkhLg+HHpvY0UdpZwO38+EBQEvPee6efr1wMzZ0pXtuVQVgYcPSq1VJDl186uRd1ndzH/Imb9NgunMpuefMuqypBYmYiyKkKDgRiscoPBYFD0eLW1tdDpdKitrVX0uCyxmr/TbBSl/TIp7EJCQvDcc8/B1dUVrq6u6NmzJ1q3bo3OnTtj4sSJCLWlhb+smUOHgJoaYOBAYMAA3tGQoWNHIDwcuH0/8HffBRYsAL74gtaiw0xoQUuezD82H0Fng/DeXtNKf716PWaGzURWicxKX0CSRx99VNHjDRgwAOHh4RggcrKAEYrfY+fv7499+/bhhRdewLvvvou2bduiVatWKCsrQ2lpKZKTkzFv3jykpqbi//7v/5Q+vVWQmZnJOwQJG7sMC1jGrZ0dMGiQtK3u7XTpAqxdC/zjH8DmzcxDsTiy/bagGbuOLh0R/lo49AbTLaDeHfMunr/3ecz6bRa+Hv81hnUbxilCAcAuN/z9739nclxKWM3faTaK0n4VL+zy8vJwxLgg7h345ptvbLaoA4Bx48bxDkFa5sQGCztLuF20SHoa1tMTeOop4OGHgba33Cvftq3tPi8g228LejLWzs4OgzoPQp8O9Sv9Lm26YO2za/GP8H9g8ws2WOkTwiryrgzUajW8vb2hUqkwZswY3uHIgopbqijtV/FLse7ud76p2IidnZ2sflTZtWsX7xCAc+ekm8Fat7aJZU6MWMLtL79I+78uWyYVdh07AuPGAXPmALt3A1u2AOnpdz9O797S7F7v3sxDVgzZfltQYbfoyUX4LOIzzI6YjYNXDuJG1Q2T37dt1RatHBqv9Hu79saLji+ityuhwUAMq8i7MujduzfWrl2L3oQSAxW3VFHar51B4TtDZ82ahS5duuDFF19Enz590LZtW9jbS/WjTqdDSkoKtmzZguzsbGzatEnJUzPDuKWYVqtF+/bt79q/uroaTk7117KyKHPnAv/9r7Qtwu7dfGNREEu4ffppYPVqaem/s2eBw4elXdnOnQNqa4GePaX9Yc3cQpgEsv2uWQN88AHwl78Ae/eyD4wjG2M3YubemXU30TvaO8K7hzcm9JmA+3vej7KqMmyO34zINyMbPY5V5AUbxhJ+Y2Nj4eHhgS5dujT4e51OR24pEzmIscsWOX7NqUMUn7Hz8/PD9evX8eCDD6JDhw5wcnJCq1at0KpVK7Rp0wYPP/ww8vPz8dNPPyl9asUJDAyEl5cXxpr5N/jChQsZRWQGv/4qtXdaPZcolnA7YIA0y9atGzB1qvQQhUoFFBQAW7dKu1HIqO9RUACsWye1VJDttwXN2O3U7ETqp6nI/TwX+17bh1kPzEKVvgqLTi7C9J3T8fXhr/HjxB8bPUZBeQFe8n0JBeWEBgMxLJEbqqqq8O233+Lll1/G3tv+QVNTU4M333wTJ0+ebPQY169fR2hoKK5fv84yVEWxir/TbBil/So+Y2eksrISiYmJyMvLQ1FREdq1awd3d3eMGjUKDg4OLE7JDHNn7LiTng707SutkJubC3TtyjsiUvzzn8CXX958PuB2KiuBDz8E7jbhrFYD3t5SUUjkVhr5nD0rTVn26AFcvco7GqZ8sv8TrJi6ot7nxZXF+C35N+zU7MSCJxZgcJfBdzyGOkcN7zXeUL2vwhh3WxsMLY/a2lps2LABu3fvhq+vL0aMGFH3u7/97W/4+eef7/hdivfYCfjDZcYuPj4en376KQ4dOgQAcHFxwahRozBlyhTMmDEDf/nLX+Dt7U2uqGsK3DdMDvtzH8uHHrK5os4Sbr/7Dpg9G/j99/q/++EHwM8PuOce5mFwQbZfY9Wblyddn7ZhHO0dkVtWf1mXDi4dMGP4DGybvg2+x305RCa4FUvl3eTkZCxatAgqlQpt2rTBQw89hBkzZuCVV17B6NGj0fouO/yMGDEChYWFJsWgtcP97zQbR3G/BoV44YUXDK1atTJ07txZqUNaDVqt1gDAoNVqZfW/evUq44juwhNPGAyAwbBoEd84GGApt1VVBsPy5QZDcLDp5/ffbzDY2RkM771392OoVNL/BpWKTYwskO23qkoSARgMeXlsg+LM9Yrrhhn/m2GIvBJZ73ffR31v+G/Ufw0+4T6NHkOVrTJgLgyqbEKDgRiWyA3ffPONwcHBwWBnZ2fysre3N7i4uBhmzZplKC0tZR6HpeH+d5qNI8evOXWIYjN23bt3R0REBFavXq3UIcly4MABficvLpa2OwBs7v46wHJunZyATz4BXn/d9PPwcGDXLsBW98SW7dfJSVrUD7D5++w6uHTAz9N+xsX8i9gav9Xkd/uS92Fu1FxU6VvOzjrWCuvcsHPnThw5cgQhISG4evUqqqqqUFtbi9raWuj1eixfvhwPPfQQ7rnLdH5qaireeOMNpKamMo1XSbj+ndYCUNqvYuvYOTs7Y/DgwTa9jIlchg4dyu/k+/dLu00MGSLtOGFjcHULqZaZPl1e33vukVaaoXTZ1iy/7u5Afr5U2I0cyS4oK8DJwQmfPPBJvc/DXwvH0bSjmDJgSqPfv6fVPRjdcTTuaUVoMBCDdW44dOgQDh06BBcXlwZ//95772HmzJn4y1/+gra3Lnx5G9XV1cjKykJ1dTWrUBWHd961dZT2q9iM3XfffYdPP/0U586dU+qQZNFqtfxObqNPwxrh6tZMBg0CoqKklgpm+W1BT8beiS5tumC61/S7FmyDOg/CgnsXYFBnQoOBGKxzg6ur6x2LOiP/+Mc/sHXr1kb7DBo0CFFRURhEKDFQyrsUUdqvYoXdiRMncPToUYwdOxYTJ07E999/j+joaFRVtbxLFKWlpXxOXFV1c7cJGy3suLltArW1gE5H69kCs/z27Cm1WWKv1LtRa6hFkbYItQZCg4EYrHNDq1atcOHChUb7eHt7Iy4ujmkcPKCUdymitF/FCrsFCxZg1qxZmDlzJgoLC/Hf//4Xjz/+ODp06ICJEyfihx9+QGJiYrPPEx0djWeffRY9evSAnZ0d9uzZ02j/qKgo2NnZ1XspEcudGDJkCLNjN0pkJFBaKj2xeP/9fGJgDDe3TSAuTlrkmFKeN8uvh4fUisLursTlxmGGZgbicuN4h2KzsM4NH374If7617/etXDT6/WN/j4uLg5t27YlVQBSyrsUUdqvYoWdp6cn5syZg5UrV+LcuXO4du0atm/fjrfffhu5ubn47rvvMHHixGaf58aNGxg5ciQCAgLM+l5SUhJycnLqXgMZ3n928OBBZsduFOO2JH/9q7SGnQ3CzW0LwSy/vXpJrSjsBFYA69zQq1cvzJo1Cw888AB8fHwQHx9fr098fDxqamoaPU6PHj3g6+uLHj16sApVcUTeZYvSfhVboDg+Ph4//fQTevbsienTp2PkbTdT5+XlIS8vT9G1e+zs7LB7925Mmzbtjn2ioqLw+OOP4/r16+jQoUOTzmPuAsWlpaVo165dk87VZHQ6wM0N0GqBY8eARx6x7PkthCXdvvTSzVoZkOrl//1P/vcpLlBslt8DB6T910aMkPZbE9wRsUAxeyyVGwICAvDFF19Ap9Ohe/fuGDNmDLp164aCggIcPXoUhw8ftrmFh7n8ndaCkOOXywLFI0aMwPr16/H222+jvLy83u/d3Ny4Lsg4evRouLu744knnsCRI0eYnovLdmmRkVJR16OHtDCxjWJJt7dvBVZYaLFTc8Msvy1sxu6lXS+Z/PzXnX/lFImgISyVGz7++GPExsbinXfeQUVFBcLDw7Fx40ZkZmbi119/vWtRV1JSgoiICJSUlFgkXiWgsAUoZZT2q9hyJ0b69euHfv36KX3YJuPu7o41a9bA29sbOp0OW7ZswRNPPIGoqCg8+uijDX5Hp9NBp9PV/WzuH8Bvv/22WTE3iZ07pfall2z2MixgWbd2do3/bIuY5ddY2BUVAeXlQJs2bIKyEm7f57WwogVU+oSwZG4YPHgw1q5di7Vr16KoqAhOTk6yZ7QuX76Mp556itSWYlz+TmtBKO3XrArgf//7H5577jns2LEDlZWVigbCisGDB+O9997DmDFjMG7cOKxcuRLPPPMMFi9efMfv+Pr6wtXVte7l8edN4ikpKfDz84NOp6vbAmTevHnIzs7G+vXrERMTg4iICMyYMQMajQbLly9HSUmJSd+ioiIEBgYiPj4eYWFhCA8Ph1qtxurVq5Gfn2/St7y8HP7+/khKSsLOnTtx6NAhnDx5Eps2bUJmZmZdX9/vvoPhz2VOch99FFu2bMHx48cRFRWF7du3122BU1lZaXL83NxcrF27FjExMThw4AB2796N8+fPY8WKFdBqtSZ9i4uLERAQgISEBOzZswf79++HSqXCmjVrkJeXZ9K3oqIC/v7+SE5Oxo4dO3D48GGcOHECmzdvRkZGBubPn4/a2lrMmzcPtbW1mD9/PjIyMrB582acOHEChw8fxo4dO5CcnAx/f39UVFTUHX/SpEnIy8vDmjVroFKpsH//fuzZswcJCQkICAhAcXGxSSxarRYrVqzA+fPnsXv3bhw4cAAxMTFYu3YtcnNzTfpWVlZi0aJFSE5Oxvbt21FcfB3Hjx/Hli1bkJ6ejvT0NOj1epPvZGZmYtOmTTh58iQOHTqEnTt3IikpCf7+/ujXrxyff/4Thg2T+ubn52P16tVQq9UIDw9HWFgY4uPjERgYiKKiIpPjlpSUYPny5dBoNAgNDUVERARiYmKwfv16ZGdnm/TV6XTw8/PDlStXsG3bNkRFReHYsWMIDg5GWloaFixYgJqaGpPvZGVlYePGjTh9+jQiIyOxa9cuJCYmYurUqSgrKzPpW1BQgKCgIMTFxWHfvn3Yu3cv4uLisOqXX2AwrteVlYV58+ahtLQUy5Ytg0ajQUhICA4ePIgzZ85gw4YN9eKurq7GwoULkZKSgq1btyI6OhrR0dHYunUrUlJSsHDhQlRXV9f7s7ZhwwacOXMGBw8eREhICDQaDZYtW4bS0lKTvoWFhVi1ahXi4uKwd+9e7Nu3D3FxcQgKCkJBQYFJ37KyMixduhSJiYnYtWsXIiMjcfr0aWzcuBFZf/632cEO8+bNQ01NDRYsWABdpQ7BwcE4duwYoqKisG3bNly5cqXBHNGpphOmXJiCyoxKREREIDQ01KI5Yt68edDr9fD19UV6erpN5ohJkybVHd9SOSIqKgoajQZ79uxBeno6fH1975ojEhMTERUVhcjISJSXl5v0tdYc8fbbb9fliKVLl8rPEatWobCw0KSvLecIY19jjkhLS5OVIyZNmlSvjrg9R/j5+UEuZt9jd+rUKWzduhX79+/H+PHj8frrr2PSpEmw5zBLJOceu4aYP38+goODcfHixQZ/39CMnYeHh+x77AoLC9G5c2ezYmoWYWHS8ia9egHp6TY9Y2dJtxMnAocP3/lnW8Rsv0OGAImJwKFDkiAbZuLPE3H4b4fv+PPdsHheaGEIv+wQbtkixy/Te+zGjRuHgIAAJCcn4+WXX8amTZswcOBAfPbZZ4iJiTH3cFyIjY1tdIcMZ2dntG/f3uRlDjuNl0UtRQu5DAtwcNsMUlKk/yUpKbwjkY/ZflvYfXZNJeV6Cp5c+yRSrhMaDMSgkhsyMjLwwQcfICMjg3cosqHilipK+23yPXYODg545pln8Mwzz+DGjRsIDQ3Fv//9b2RkZOCVV17Ba6+9xmRJkbKyMly+fLnu59TUVMTFxaFTp07o3bs35syZg6tXr2Lz5s0AgGXLlqFv374YOnQoqqqqEBwcjJCQEISEhCgem5Fx48YxO3Y9KiqkGTsAePlly52XExZ120yKi6WnaOfM4R2JfMz2Kwo7WRRXFiNWF4viymLeodgsVHJDeXk51Gp1gw8ZWitU3FJFab+KTO+0bdsWb775Jg4cOICoqCh07NgRb7zxBh544AEsX74c165dU+I0AICzZ89i9OjRGD16NABg9uzZGD16NP7zn/8AAHJyckz+JVRVVYXPP/8cI0aMwPjx43H8+HGEh4fjxRdfVCym28nMzGR27Hrs3SstSty7N/DAA5Y7Lycs6rYFYrZfUdgJrAQqueHee+9FTEwM7r33Xt6hyIaKW6oo7Vfx63bdunXDrFmzcObMGQQHB6OoqAiPPfYYnnrqKWzZsgU3btxo1vEnTJgAg8FQ77Vp0yYAwKZNmxAVFVXX/4svvsDly5dRUVGBoqIiHDt2DFOnTm1WDHfDzpKPT27ZIrVvvNEiHtu0qNsWiNl+jYWdSPwCzlgyN7z00m1L3/zVtpe+EXmXLUr7ZXpD1sCBAzF37lxcvHgR//3vfxETE4Nhw4ZhxowZ2Ldv3123XqFKL+NfdqzJz5cWiQWAN9+0zDk5YzG3LRSz/YptxQRWgiVzQ8Fti1wWmrHIZXx8PLp27drgzhXWisi7bFHar8XutDdelr18+TLeeustbN++HQMGDICPjw/OnDljqTAswunTpy1zou3bgZoa4L77AELT+s3BYm4VoEcP4McfpZYKZvsVl2Jl0aNdDzx/z/Po0Y7QYCCGJXPD7TMs5sy4dOvWDbNnz0a3bt2UDosZlPIuRZT2q/gCxXfDwcEBTz/9NJ5++mmUl5dj9+7d2LBhAx6wofvDLDYtb7wM20Jm6wBalzy6d6f14ATQBL/Gwq6gAKisBFxclA/KBuh+T3es+9s6dLmnC+9QbBYquaF79+6YQywxUHFLFaX9cl0bo02bNnj99dexevVqnmEoTlBQEPuTJCUBMTGAgwPw6qvsz2clWMStQhQXSw8sFxfzjkQ+Zvvt2BFo3Vp6f/Wq8gHZCMWVxfh01afiqViGUMkNZWVlOH78OMrKyniHIhsqbqmitF/FCrv4+Hh8+umnOHTokFKHJItFtl8xztY99RRAaEq/uVhya5vbl+42bylvaf2655+ntY6d2X7t7MTlWBmkXE/BL7W/iHXsGEJl26tLly5h/PjxuHTpEu9QZEPFLVW4binWGHPnzkVQUBBeeeUVpQ5JFuM2IcyorQWCg6X3LegyLGABt7fw1FOmP0+ZYrFTc6NJfo0PUNj4k7EGGBr9WcAXS+aG5uDl5YXExER4eXnxDkU2VNxSRWm/it1j1717d0RERJj1dJCt8tlnn7E9QVSUtHVY+/bAc8+xPZeVwdztLXz5penPX31lsVNzo0l+W8iSJ0/1N630p/RvAZU+ISyZG5qDi4sLBg8ezDsMs6DilipK+1Vsxs7Z2RmDBw/G9OnTlTokdwIDA+Hl5YWxY8ea9b21a9cyiuhP1q2T2tdeu3l/UwuBudsWTpP89u4ttYS2SGoKXz5iWul/9UgLqPQJQSU3ZGVlYfbs2cgidOsCFbdUUdqvYoXdd999h08//RTnzp1T6pDc8fHxgUajMXsP3KeffppRRAAKCwHjdmgzZ7I7j5XC1K3CuLgAXl60HhRtkt8+faQ2PV3ZYGwIF0cX9G/fHy6OhAYDMajkhpKSEkRERKCkpIR3KLKh4pYqSvtVrLA7ceIEjh49irFjx2LixIn4/vvvER0djaqqKqVOQYaEhAR2Bw8OBqqqgNGjAW9vduexUpi6VRgvL+DCBamlQpP89u0rtWlpSoZiU3h19YJvL194dSU0GIhBJTd4eXnhwoULpO6xo+KWKkr7VaywW7BgAWbNmoWZM2eisLAQ//3vf/H444+jQ4cOmDhxIn744QckJiYqdTqrpkOHDmwObDDcvAzbAmfrAIZuBQCa6PfWGTtzHx1uQYixyxbhlx3CLVuU9qtYYefp6Yk5c+Zg5cqVOHfuHK5du4bt27fj7bffRm5uLr777jtMnDhRqdNZNe3atWNz4DNngPPnpfvqXn+dzTmsHGZub+HiRWDWLODUqeYdJy5Oer4lLk6JqCxDk/wa77ErL5cWKhbUIy43DtPOTENcbhzvUGwWS+QGJTh//jz69u2L8+fP8w5FNlTcUkVpv4oVdp9//jnee+89/Oc//8G5c+fQuXNnvPTSS1i5ciU0Gg1ycnJwwLivqY1z8eJFNgc2zta9/DLg6srmHFYOM7e3MH8+EBQEvPee6efr10sTpXLvea6tBUpLpZYKTfLr7Ay4u0vvbfA+u4v5FzHrt1k4ldn0Sr/WUItyfTlqDYQGAzEskRuMGG6bmb7958bo1KkT3njjDXTq1EnpsJhhSbctEaX9KrbcyYgRI7B+/XqkpKQgLy+v3u/d3Nzg5uam1OmsmieffFL5g2q10t6wQIu9DAswcnsbHTsC4eGAXm/6+bvvSgsOz5oFfP01MGwY81AsTpP99u0L5ORI99ndd5+SIXFn/rH52HlhJw6nHsb5j27OsqxXr8eprFOYO2EuerUXm6TzxhK5wchTty1yOcWMRS579OhBbl04S7ptiSjtV/Etxfr164dx48YpfVhSbNq0icVBgRs3gKFDgYcfVv74RGDi9jbs7IBBg+ovUAwAXboAa9cCfn7Mw+BCk/3a8JOxHV06Ivy1cCyevNjk83fHvIsFkxbgi8gvcP4anctqtoolcoORL29b5PIrMxa5LC8vh1qtRnl5udJhMcOSblsiSvvlulesraL49iu1tUBgoPT+44+lyqOFYomtbRYtAj77DJg9Gzh4UKqnb6VtW6BVK+ZhcKHJfm34yVg7OzsM6jwITw2oX+l3adMFa59dC78TNlrpE4LKtleJiYnw9vYm9TAhFbdUsdotxQQ3UXya/eBBIDlZuq/ujTeUPTYxLHEJ45dfgLAwYNkyadauY0dg3Dhgzhxg925pm145E1P33guoVFJLhSb7teEZu0VPLsJnEZ9hdsRsHLxyEDeqTCv9tq3aopVD45X+vV3uxT/s/4F7uxAaDMSgcnnz3nvvhUqlwr2EEgMVt1RR2q+dwZy7PlsoJSUlcHV1hVarRfv27e/av6amBo6Oit2+CDzzDLB/vzSNtHSpcscliOJuG+Dpp4HVq6WFhc+eBQ4fBo4cAc6dkyZPe/YEQkMBMzckIUGT/R44IIkbPhyIj1c+MI5sjN2ImXtn1t0g72jvCO8e3pjQZwLu73k/yqrKsDl+MyLfjGz0OJYYuy0Z4Zcdwi1b5Pg1pw4RM3YMWLx48d07yeXyZeC336T3Pj7KHZcoirq9AwMGSCt4dOsGTJ0KLF4szbwVFABbt0rPBsio75GRIf0vo7TTVpP92vBadjs1O5H6aSpyP8/Fvtf2YdYDs1Clr8Kik4swfed0fH34a/w48cdGj5GhzcB43/HI0BIaDMSwRG5QguzsbHz77bfIzs7mHYpsqLilitJ+RWHXCE3dK/bVV19VLoiVK6W/KJ9+Wqo4WjiKur0Djo5Abm79zzt0AGbMALZtA3x9736cggLpfx+lpd2a7NdY2JWUAMXFisVjDQzoOAC9XXujW9tumDpwKhZPXgzV+yoUfFGArS9uxX097kN758Yr/YLyApyuPY2CckKDgRiWyA0XL17ErFmzcKoZi1wWFRUhODgYRUVFCkbGFku4bcko7VcUdo3Q1L1ijx8/rkwAN24AGzZI7z/5RJljEkcxt43w3XfSgxO//17/dz/8ID0Re889zMPgQpP9tmkDdO0qvbex++wc7R2RW1a/0u/g0gEzhs/Atunb4HtcRqUvYIolcsP8+fMRFBSE925b5HL9+vWYOXMmsmQscjls2DCkpaVhGKH1kizhtiWjtF9R2DGgj3H2orn8/LO0fl3//oAZ6yTZMoq5bYQOHST1Fy9Kl15vZd8+YO5cabteW6RZfm30ydjvJnyH2RGz8XtK/Ur/h6M/wO+EH+5pZaOVPiEskRs6duyI8PDwepfO3n33XSxYsABffPEFqR0l5GIJty0Zpf2Kwo4B+ttXtm3aQYAlS6T3n30G2Iv/VYBCbmXg5CRNkt6+c1t4OLBr183/NbZGs/waC7vUVEVisRY6uHTAz9N+xsX8i9gab1rp70veh7lRc1Glt9FKnxCWyA12dnYYNGhQvQWKAaBLly5Yu3Yt/O6yyKVGo8HQoUOh0WhYhak4lsq7LRWl/YrHXBiQk5PT/IPs3g1cuQJ06gT8/e/NP56NoIjbZtClCzB9ury+3boB//yn1FKhWX7795faK1eUCcaKcHJwwicP1L8dIvy1cBxNO4opAxqfUe/Wthue7vA0urUlNBiIYYncsGjRIrz66qvw9PTEU089hYcffhht27at+33btm3R6i6LXLZv3x5TpkyRtcKCtcA779o6SvsVhR0D7r///uYdwGCQVskFgI8+klbEFQBQwK0F6dWL3sxes/waH+65fFmZYAjQpU0XTPe6e6Xfq30vrPjLCrH1GEMskRt++eUXhIWFwWAwYNmyZXB0dIS3tzcmTJiA+++/H2VlZUi/yz2mvXr1whJiiYFS3qWI0n7F9T0GhISENO8Ax48Df/whba7+8cfKBGUjNNutBSkrA06dkloqNMuvDc/YNZeyqjIs2bkEZVWEBgMxLJEbdu7cidTUVOTm5mLfvn2YNWsWqqqqsGjRIkyfPh1ff/01fvyx8aVvKisrkZSUhMrKSubxKgWlvEsRpf2KBYplYO4CxTqdDs7Ozk0/4XPPAXv3Au+9B6xZ0/Tj2CDNdmtB1GrA21taA2/MGN7RyKNZfjMzpQUAHR2BigqpFQAA1DlqeK/xhup9Fca4ExkMxLBEbvjkk0+wYsWKep8XFxfjt99+w86dO7FgwQIMHjz4jsdQq9Xw9vaGSqXCGCKJgVLepYgcv2KBYs4sMl5GbQrx8VJRZ2cH/N//KReUjdAst4K70iy/PXtKs8w1NbRWZRbYBJbIDY6OjshtYJHLDh06YMaMGdi2bRt877LI5aBBg3Ds2DEMGjSIVZiKI/IuW5T2K2bsZGDujF2zePll6bHLl18Gduxgey4BUyjO2DUbLy9pnZiDB4Enn+QdjdUgZuxsg+LiYnz00Ud45513MGnSJJPf/fDDDzAYDLh27RoCAgI4RSiwVcSMHWeavKHvxYvA//4nvf/2W+UCsiHEZtRsabZf4wMU4j47gYWxRG7o0KEDfv75Z1y8eBFbb1vkct++fZg7dy6q7rLIZW5uLnx9fRuc+bNWRN5li9J+xU0wDHjnnXea9sX586UnYqdNkzZTF9SjyW454OgoLY9C6VazZvs1PkDRgp6MlYOjvSM6uXSCoz2hwUAMS+UGJycnfNLATkDh4eE4evQoptxlMflr165hyZIleOaZZ9C9e3dWYSoKpbxLEaX9ihk7Bvz222/mfyk5WdqEFBCzdY3QJLecGDECyM+XWio02694MrZBRriNgF8XP4xwIzQYiME7N3Tp0gXTp0/HPXfZb3DEiBHIz8/HCEKJgbdbW0dpv6Kwa4TAwEB4eXlh7NixZn2vSX9gfX2B2lpg6lTpxixBg1BKhhRptl9xKfaOiLHLFuGXHcItW5T2Kwq7RvDx8YFGo0FMTIxZ3ysqKjLvRKmpwJYt0vt//9u877YwzHbLkQsXpDrnwgXekcin2X5vnbETz2XVceHaBTx/6HlcuEZoMBCDSm5ITEzE2LFjkZiYyDsU2VBxSxWl/YrCjgE3btww7wtz50pLRDz5JPDgg0xishXMdssRnU6qb3Q63pHIp9l++/SR9jUuLwcI3RzOGp1ehxxdDnR6QoOBGFRyQ5s2bTBmzBi0adOGdyiyoeKWKkr7FYUdA+699175nS9cuDlbN38+m4BsCLPcCsym2X5btZKKO0BcjhVYFCq5oXfv3li9ejV69+7NOxTZUHFLFaX9isKOAb///rv8zv/5j3TJ6sUXATPv5WuJmOVWYDaK+BVPxgo4QCU3VFVVISsr667LolgTVNxSRWm/orBjwNtvvy2vY0wMEBoq7TLxww9MY7IVZLsVNAlF/IoHKAQcoJIbzp8/Dw8PD5w/f553KLKh4pYqSvsVhR0Dli9fLq/jN99I7ZtvSiv2C+6KbLdWwIABwIEDN+scCijiV8zY1WNApwF4y/4tDOhEaDAQg0puGDBgAA4cOIABhBIDFbdUUdqv2FJMBky2FDt4EJgyBXByApKSAE9PZY4rEPAmLAx4/nlg9GhpXzWBQCAQNAuxpRhn7ro9SE0NMHu29N7HRxR1ZkBpa5ucHOmB55wc3pHIRxG/xhuBk5KktRkFyCnNwcTvJyKnlNBgIAaV3HDt2jUsX74c165d4x2KbKi4pYrSfsWMnQzMnbErKipCp06d7txh9Wrgww+BTp2ky1UdOyoYrW1zV7dWhFotrTWtUgFjiOz7rojf6mqgbVupzcgAPDyUCY4w6hw1vNd4Q/W+CmPciQwGYlDJDXFxcXj44Ydx4sQJjBo1inc4sqDilipy/IoZO85sM24N1hAlJTcXIf7uO1HUmUmjbgXNRhG/Tk4377MjtAirgDZUcsOoUaNw48YNMkUdQMctVZT2Kwo7BowfP/7Ov/zxR2kD0cGDgX/8w3JB2QiNuhU0G8X8Gi/HisJOYCFEbmCHcMsWpf2Kwo4BaWlpDf8iNRVYulR6v3ixNLMhMIs7uhUogmJ+b73PTiCwAFRyw6VLlzBhwgRcunSJdyiyoeKWKkr7FYVdIwQGBsLLywtjzVw42MHBoeFffPklUFUFTJoEPPOMAhG2PO7o1grp2BF4/XVaV9sV8zt4sNSKGTsAQEeXjpjQaQI6uhAaDMSgkhucnJzQq1cvOBH6hz0Vt1RR2q+jokezMXx8fODj41N306Jc3N3d638YGQns2iXto+nvLy1KLDCbBt1aKZ6eQHAw7yjMQzG/4lKsCZ4dPeH/sD88O4on4FlBJTd4enoimFhioOKWKkr7FTN2DIiJiTH9oLIS+Ogj6f0nnwAjRlg+KBuhnlsrprJSeui5spJ3JPJRzK9xxu7qVaC0VJljEqayphLhp8JRWUNoMBCDSm6oqalBUVERampqeIciGypuqaK0X1HYMeDFF180/WDhQulv+B49gO+/5xOUjVDPrRWj0QADB0otFRTz27Ej0K2b9J7QvUSs0ORr8J+C/0CTT2gwEINKboiPj0fnzp0RHx/POxTZUHFLFaX9isKOAatXr775w+XLgK+v9H7pUkCpnStaKCZuBYqjqF9xOVZgQajkBk9PT4SEhMCT0ML0VNxSRWm/YoFiGTR5SzGDAXjqKWn7sMmTpY1Dxb11LQaKCxQrygcfAGvWSOs2tvCZarFAsUAgaA5igWLO1G0PsmuXVNQ5OwOBgaKoUwCxtQ1bFPUrnowVWBAquaGgoADr1q1DQUEB71BkQ8UtVZT2Kwo7BsyePRsoKJAelACAOXOAAQP4BmUjzDbusStggqJ+jZdiKd1kKCALldyQkZGB9957DxkZGbxDkQ0Vt1RR2i+5wi46OhrPPvssevToATs7O+zZs+eu3zl69Ci8vb3h4uKCfv36ISgoiGmMq1atAj79FLh2DRg6FPjqK6bna0msWrWKdwiyGTNGuhpP6TKson6HDZPapCRp/cYWzBj3MVh8z2JxGZYhVHLDmDFjYDAYMIZQYqDilipK+yVX2N24cQMjR45EQECArP6pqamYOnUqxo8fj9jYWHz99deYNWsWQkJCmMX4auvWwC+/SGvWbdwoXYoVKMJf/vIX3iHYNIr69fAAXF2BmhqxAwXE2GWN8MsO4ZYtSvslV9g9/fTTmDdvnuzHg4OCgtC7d28sW7YMQ4YMwcyZM/HOO+9g8eLFbAIsKkKnb76R3v/rX4CZu1YIGufcuXO8Q5BNUhIwbhytmkZRv3Z2N2ftEhKUOy5BkgqS8OyvzyKpgNBgIAaV3HD58mU888wzuHz5Mu9QZEPFLVWU9kuusDOXU6dOYfLkySafTZkyBWfPnkV1dbXyJ/znP9G6uFi6v2juXOWP38Lp3Lkz7xBkc+MGcPq01FJBcb/Gwu78eWWPS4wb1TeQXJGMG9WEBgMxqOQGe3t7ODs7w96ezl+/VNxSRWm/Nr+lWG5uLtzc3Ew+c3NzQ01NDQoKChrcykOn00Gn09X9XFJSIu9kBw4AmzfDYG8Pu40bAReXZsUuqE/r1q15h2DTKO53+HCpbeEzdgL2UMkN/fr1Q2hoKO8wzIKKW6oo7ZfOPxmagd1ty4wYl+67/XMjvr6+cHV1rXt5eHgAAFJSUuDn5wedTlf3ePK8efOQnZ2N9evXQ+Xigoy//AWHRoyApn17LF++HCUlJSZ9i4qKEBgYiPj4eISFhSE8PBxqtRqrV69Gfn6+Sd/y8nL4+/sjKSkJO3fuxKFDh3Dy5Els2rQJmZmZJn31ej18fX2Rnp6OLVu24Pjx44iKisL27duRnJyMRYsWobKy0uQ7ubm5WLt2LWJiYnDgwAHs3r0b58+fx4oVK6DVak36FhcXIyAgAAkJCdizZw/2798PlUqFNWvWIC8vz6RvRUUF/P39kZycjB07duDw4cM4ceIENm/ejIyMDMyfPx+1tbWYN28eamtrMX/+fGRkZGDz5s04ceIEDh8+jB07diA5ORn+/v6oqKioO/7ixYuRl5eHNWvWQKVSYf/+/dizZw8SEhIQEBCA4uJik1i0Wi1WrFiB8+fPY/fu3Thw4ABiYmKwdu1a5ObmmvStrKzEokWLkJycjO3btyMqKgrHjx/Hli1bkJ6eDl9fX+j1epPvZGZmYtOmTTh58iQOHTqEnTt3IikpqS5uI/PmzUN+fj5Wr14NtVqN8PBwhIWFIT4+HoGBgSgqKjI5bklJCZYvXw6NRoPQ0FBEREQgJiYG69evR3Z2tklfnU4HPz8/XLlyBdu2bUNUVBSOHTuG4OBgpKWlYcGCBaipqTH5TlZWFjZu3IjTp08jMjISu3btQmJiIlasWIGysjKTvgUFBQgKCkJcXBz27duHvXv3Ii4uDqtWrUJhYaFJ39LSUixbtgwajQYhISGI+XM/tdJTp+rFXV1djYULFyIlJQVbt25FdHQ0oqOjsXXrVqSkpGDhwoWorq6u92dtw4YNOHPmDA4ePIiQkBBoNBosW7YMpaWlJn0LCwuxatUqxMXFYe/evdi3bx/i4uIQFBSEgoICk75lZWVYunQpEhMTsWvXLkRGRuL06dPYuHEjsrKyTPrW1NRgwYIFSEtLQ3BwMI4dO4aoqChs27YNV65caTBH5OfnAwAuXLiAiIgIhIaGQqPRiByhYI4w3l4zb948q84R27dvR0JCAhYtWoTy8vJ648Qac8Tu3bvrcsTSpUsVzREHDx7EmTNnsGHDhhabIxYvXlxXR8TExDSYI/z8/CAX0gsU29nZYffu3Zg2bdod+zz66KMYPXo0fvrpp7rPdu/ejZdffhnl5eVwcnKq952GZuw8PDxkL1CcmZEBj969zfuPEcgiMzOzrtC2diguUKy436IiwHiZQattsTuviAWK2UMlN6jVanh7e0OlUpF5MpaKW6rI8SsWKL6FcePGITIy0uSzgwcP4r777muwqAMAZ2dntG/f3uRlDj9v3tzkeAWN8/PPP/MOQTZ9+wJbtkgtFRT326mTtEcyAFy4oOyxCdG3Q19Mt5uOvh368g7FZqGSG/r27YstW7agL6HEQMUtVZT2S27GrqysrO5potGjR2PJkiV4/PHH0alTJ/Tu3Rtz5szB1atXsfnP4io1NRXDhg3DBx98gPfeew+nTp3Chx9+iG3btmH69OmyztnkLcUEAoG0rV5EBLB6NfD++7yjEQgEAnLY9Izd2bNnMXr0aIwePRqAtGLz6NGj8Z///AcAkJOTY7Kit6enJ/bv34+oqCiMGjUKP/zwA5YvXy67qGsKYvsVdlBym58v7ST35+1VJGDiVyx5gvwb+Xj2+2eRf4PQYCAGldxQVFSEbdu2oaioiHcosqHilipK+yU3Y8cDc2fs9Ho9HBwcLBBZy4OSW4r32DHx+/PPwNtvAxMmAEeOKHtsIoh77NhDJTdQvMeOiluqyPFr0zN2FDDn6RWBeQi3bGHi99YZO/HvSAEjqOSGkSNHoqysDCNHjuQdimyouKWK0n5FYceA1157jXcINotwyxYmfr28pO31CguB3Fzljy8QgE5ucHBwQNu2bUnNgFFxSxWl/YrCjgHR0dG8Q7BZhFu2MPHbujUwYID0Pj5e+eMLBKCTG1JSUvDSSy8hJSWFdyiyoeKWKkr7FYUdAzw9PXmHYLNQctuuHTB5stRSgZnfPx92Qmwsm+NbOe1atcPYTmPRrhWhwUAMKrlBr9ejpKQEer2edyiyoeKWKkr7tfktxXhQU1PDOwSbhZLbgQOlVT4owcyvtzewY4f0JEkLZGDngfAb7oeBnQfyDsVmoZIbBg4ciAhiiYGKW6oo7VfM2DEgV9xHxAxKbvV6oKREaqnAzK/x6T+1ms3xrRx9rR4pV1OgryU0GIhBKTdQQ7hli9J+RWHXCIGBgfDy8sLYsWPN+p63tzejiASU3J47B7i6Si0VmPk1XopNSQGuX2dzDivmXN45vHv5XZzLIzQYiEElN6jVajg6OkJN6B85VNxSRWm/orBrBB8fH2g0GsTExJj1vT179rAJSCDcMoaZ306dbu6tFhfH5hyCFg2V3ODh4YHAwEBSe69ScUsVpf2KBYplYO4CxZWVlXBxcbFAZC0PSm4pLlDM1O/06UBoKLB4MfB//8fmHFaKWKCYPZRyAzWEW7bI8SsWKObM4sWLeYdgswi3bGHqt4XfZydgC5XcUFxcjLCwMBQXF/MORTZU3FJFab9ixk4G5s7YCQQAzRk7pvz2GzB1KnDvvcDFi7yjsShixk5ghOKWYgL+iBk7zogNk9lBye3w4cC1a1JLBaZ+jX+JJSUBZWXszmOFDO82HF/Zf4Xh3QgNBmJQyQ3Dhw/HtWvXMJxQYqDilipK+xUzdjIwd8YuNzcX3bt3t0BkLQ/hli3M/fbsCWRnA8ePAw8/zO48VogYu2wRftkh3LJFjl8xY8eZvXv38g7BZqHk9soV4LnnpJYKzP0aH+s/e5bteayMK0VXMGXTFFwpIjQYiEElN6SlpeHtt99GWloa71BkQ8UtVZT2Kwo7BowaNYp3CDYLJbdaLbB3r9RSgbnf+++X2jNn2J7HytDqtIjXxUOrIzQYiEElN+h0Oly+fBk6nY53KLKh4pYqSvsVW4oxoLCwkHcINotwyxbmfh98UGpPn2Z7HkGLg0puGDx4MI4fP847DLOg4pYqSvsVM3YMqKio4B2CzSLcsoW537FjATs7IDUVyMtjey5Bi0LkBnYIt2xR2q8o7BgwcKDY6JsVwi1bmPt1dQW8vKT3LexyrIAtVHJDXFwc2rdvjzhCO7BQcUsVpf2Kwo4BR44c4R2CzULJbc+egL+/1FLBIn5b4OXYnu16YlrraejZjtBgIAaV3ODu7o65c+fC3d2ddyiyoeKWKkr7FcudNEJgYCACAwOh1+tx6dIl2cudaLVauLq6WiDClodwyxaL+F27Fnj/feDxx4HDh9mey4oQY5ctwi87hFu2yPErljtRCB8fH2g0GsTExJj1vRUrVjCKSEDJ7fXrwK5dUksFi/g1ztjFxAB6PfvzWQHXK67jg+Uf4HoFocFADCq5oaSkBL///jtKSkp4hyIbKm6porRfMWMnA7GlmKApiC3F7oBeD3ToIO0+ER9Pa2uOJiK2FBMYEVuKCZqCmLHjjNh+hR3CLVss4tfB4eZ6di3oPjsBW6jkhqFDhyI1NRVDhw7lHYpsqLilitJ+RWHHgI8//ph3CDaLcMsWi/k1Xo49dcoy5xPYPFRyg7OzM/r27QtnZ2feociGiluqKO1XFHYMCA4O5h2CzSLcssVifseNk9qTJy1zPoHNQyU3ZGRkwMfHBxkZGbxDkQ0Vt1RR2q8o7Bjw2GOP8Q7BZqHktnVrYPRoqaWCxfw+/LC0UHFSUotYqLi1Y2vc63ovWjsSGgzEoJIbbty4gVOnTuHGjRu8Q5ENFbdUUdqvKOwYcIXSru/EoOR2yBDpAYohQ3hHIh+L+e3Y8eZDE8eOWeacHBnSdQh8+/piSFdCg4EYVHLDkCFDoFarMYRQYqDilipK+xWFHQNatWrFOwSbRbhli0X9Pvqo1EZHW+6cHBFjly3CLzuEW7Yo7VcUdgxwc3PjHYLNQsltbCzg7Cy1VLCo3xZU2MXmxGKaahpicwgNBmJQyQ3x8fFwd3dHfHw871BkQ8UtVZT2Kwo7BqhUKt4h2CyU3BoMQFWV1FLBon7Hj5fa+Hhaqzg3AQMMqK6thgGEBgMxqOSGrl27wsfHB127duUdimyouKWK0n5FYceA559/nncINotwyxaL+u3eHRg0SKp8T5yw3HkFNgmV3ODu7o5vv/2W1F6xVNxSRWm/orBjwNq1a3mHYLMIt2yxuN8WdDlWwBYquaGsrAynTp1CWVkZ71BkQ8UtVZT2K7YUa4TAwEAEBgZCr9fj0qVLYksxgVmILcVksGUL8NZbwNixwB9/8I6GGWJLMYERsaWYoCmILcUUwsfHBxqNBjExMWZ9T2y/wg5KbocMAc6fp7XcicX9TpwotWfPAkVFlj23BRnSZQg+tv8YQ7oQGgzEoJIbhgwZgvPnz5Na7oSKW6oo7VfM2MnAnEoZACoqKtCa0qq0hBBu2cLFr5cXcPEisGsX8Ne/WvbcFkSMXbYIv+wQbtkix6+YsePMypUreYdgs1Bym54OzJwptVTg4vfJJ6U2MtLy57YQ6cXpmLBkAtKLCQ0GYlDJDVlZWfjXv/6FrKws3qHIhopbqijtVxR2DHjuued4h2CzUHJbWAisXy+1VODi11jY/f675c9tIQorCvFHzR8orCA0GIhBJTdotVqEhYVBq9XyDkU2VNxSRWm/orBjgFqt5h2CzSLcsoWL38ceAxwdgZQU6SUQNAEquWHo0KFISkrC0KFDeYciGypuqaK0X1HYMYDSwpPUEG7ZwsVvu3bAuHHSexu+HCtgi8gN7BBu2aK0X1HYMcDZ2Zl3CDaLcMsWbn5bwH12ArZQyQ0XLlzAgAEDcOHCBd6hyIaKW6oo7VcUdgy4cuUK7xBsFkpu3dyAr76SWipw82ss7A4fBvR6PjEwxK2tG55xfQZubQkNBmJQyQ0dOnTASy+9hA4dOvAORTZU3FJFab9iuRMZmLvcSUZGBnr37m2ByFoewi1buPmtqQG6dAG0WuDMGeD++y0fA2PE2GWL8MsO4ZYtcvyK5U44s2XLFt4h2CyU3JaWAlFRUksFbn4dHW8uVnzgAJ8YGFKqK8V/f/4vSnWEBgMxqOSGiooKxMfHo6KigncosqHilipK+xUzdjIwd8autrYW9vaiZmYBJbcUtxTj6nf9emnhv/vuA8zc7cXaEVuKsYdKbqC4pRgVt1SR41fM2HHmxx9/5B2CzSLcsoWr32eekdqzZ4HsbH5xCEhCJTcMHjwYf/zxBwYPHsw7FNlQcUsVpf2KGbtGCAwMRGBgIPR6PS5duiRm7KwASm7FjF0TePBB6R671auB99/nF4fCiBk79nAfuzaMcMsWMWNnQXx8fKDRaBBj5mUhX19fRhEJhFu2cPf77LNSu3cv3zgE5OA+dmWSk5ODuXPnIicnh3cosqHilipK+xWFHQPefPNN3iHYLJTcOjkBPXtKLRW4+zVurfP770B5Od9YFMTJ3gnd23SHkz2hwUAM7mNXJgUFBVi3bh0KCgp4hyIbKm6porRfUdgxICoqincINgslt8OHA1lZUksF7n6HDQP69AEqK21q79jhbsOx0G0hhrsRGgzE4D52ZTJ8+HBkZWVhOKHEQMUtVZT2Kwo7BvTv3593CDaLcMsW7n7t7Gz2cix3tzaO8MsO4ZYtSvsVhR0DdDod7xBsFkpuExKAXr2klgpW4dd4OXbvXpvZhSIhLwHToqchIY/QYCCGVYxdGWg0GowYMQIajYZ3KLKh4pYqSvsVhR0D8vPzeYdgs1ByW10NXL0qtVSwCr+PPQZ06ADk5QHHjvGORhGqa6tRUFWA6lpCg4EYVjF2ZdCuXTtMmDAB7dq14x2KbKi4pYrSfkVhxwAqi05SRLhli1X4bdUKeOEF6f3OnXxjEZDBKsauDDw8PLB8+XJ4eHjwDkU2VNxSRWm/JAu7lStXwtPTEy4uLvD29saxRv5VHxUVBTs7u3qvxMREZvGFhYUxO3ZLR7hli9X4feUVqf3f/6R9ZAWCu2A1Y/cuVFZW4vLly6isrOQdimyouKWK0n7JFXY7duzAZ599hm+++QaxsbEYP348nn76aWRkZDT6vaSkJOTk5NS9Bg4cyCzGjz76iNmxWzrCLVusxu/EiUDnzkB+PnD0KO9oBASwmrF7FzQaDQYOHEjqHjsqbqmitF9yhd2SJUvw7rvvYubMmRgyZAiWLVsGDw8PrFq1qtHvdevWDd27d697OTg4MIvR39+f2bFbOpTcDhwIHDkitVSwGr9OTsCLL0rvd+zgG4sCDOw0EO/Yv4OBnQgNBmJYzdi9CwMHDsSRI0eYTi4oDRW3VFHaL6ktxaqqqtCmTRvs2rULLxjvwQHw6aefIi4uDkcb+Jd9VFQUHn/8cfTt2xeVlZXw8vLCt99+i8cff/yO59HpdCZPqZSUlMDDw0P2lmICgUABfv8dePJJaeYuJ4fWSs8CgUCgIDa7pVhBQQH0ej3c3NxMPndzc0Nubm6D33F3d8eaNWsQEhKC0NBQDB48GE888QSio6PveB5fX1+4urrWvYw3uaakpMDPzw86nQ7z5s0DAMybNw/Z2dlYv349YmJiEBERgRkzZkCj0WD58uUoKSkx6VtUVITAwEDEx8cjLCwM4eHhUKvVWL16NfLz8036lpeXw9/fH0lJSdi5cycOHTqEkydPYtOmTcjMzDTpq9fr4evri/T0dGzZsgXHjx9HVFQUtm/fjuTkZCxatAiVlZUm38nNzcXatWsRExODAwcOYPfu3Th//jxWrFgBrVZr0re4uBgBAQFISEjAnj17sH//fqhUKqxZswZ5eXkmfSsqKuDv74/k5GTs2LEDhw8fxokTJ7B582ZkZGRg/vz5qK2txbx581BbW4v58+cjIyMDmzdvxokTJ3D48GHs2LEDycnJ8Pf3R0VFRd3xJ02ahLy8PKxZswYqlQr79+/Hnj17kJCQgICAABQXF5vEotVqsWLFCpw/fx67d+/GgQMHEBMTg7Vr1yI3N9ekb2VlJRYtWoTk5GRs374dUVFROH78OLZs2YL09HT4+vpCr9ebfCczMxObNm3CyZMncejQIezcuRNJSUnw9/fH5csVePTRE7h6Veqbn5+P1atXQ61WIzw8HGFhYYiPj0dgYCCKiopMjltSUoLly5dDo9EgNDQUERERiImJwfr165GdnW3SV6fTwc/PD1euXMG2bdsQFRWFY8eOITg4GGlpaViwYAFqampMvpOVlYWNGzfi9OnTiIyMxK5du5CYmIipU6eirKzMpG9BQQGCgoIQFxeHffv2Ye/evYiLi8OqVatQWFho0re0tBTLli2DRqNBSEgIDh48iDNnzmDDhg314q6ursbChQuRkpKCrVu3Ijo6GtHR0di6dav0Z+2PP2Do2hUoLAQOH677s7ZhwwacOXMGBw8eREhICDQaDZYtW4bS0lKT4xcWFmLVqlWIi4vD3r17sW/fPsTFxSEoKAgFBQUmfcvKyrB06VIkJiZi165diIyMxOnTp7Fx40ZkZWWZ9K2pqcGCBQuQlpaG4OBgHDt2DFFRUdi2bRuuXLnSYI5QJasw6KNBCD8WjoiICISGhoocoXCOmDRpUt3xrTlHrFmzBl988QXmzp2L8vJyk77WmiPefvvtuhyxdOlSq8kRCxcuRHV1db2/j6nliEmTJtWrI27PEX5+fpALqRm77Oxs9OzZEydPnsS4cePqPp8/fz62bNki+4GIZ599FnZ2dne8YbG5M3Z5eXn1ik+BMlByq1YD3t6ASgVQeajM6vx+9BGwahXw5pvA5s28o2ky6hw1vNd4Q/W+CmPciQwGYljd2L0D586dw+OPP44jR45g5MiRvMORBRW3VJHj12Zn7Lp06QIHB4d6s3PXrl0za9A9+OCDSE5OvuPvnZ2d0b59e5OXOfz6669m9RfIR7hli9X5Ne6hGBIClJbyjUVg1Vjd2L0DI0eORFFREZmiDqDjlipK+yVV2LVq1Qre3t6IjIw0+TwyMhIPPfSQ7OPExsbC3d1d6fDq8Pb2Znbslo5wyxar8/vgg8CgQUB5ubT0iUBwB6xu7NoQwi1blPZLqrADgNmzZ2PdunXYsGEDLl68iH/+85/IyMjAhx9+CACYM2cO3nrrrbr+y5Ytw549e5CcnIwLFy5gzpw5CAkJwccff8wsxry8PGbHbukIt2yxOr92dsDf/ia9//lnvrEIrBqrG7t3ICkpCePGjUNSUhLvUGRDxS1VlPbrqOjRLMArr7yCwsJCfP/998jJycGwYcOwf/9+9OnTBwCQk5NjsqZdVVUVPv/8c1y9ehWtW7fG0KFDER4ejqlTpzKLsaqqitmxWzqU3HbuDLz7rtRSwSr9vvkm8O230np2qamApyfviMymc+vOmNRpEjq3JjQYiGGVY7cBXFxcMHToULi4uPAORTZU3FJFab+kHp7ghTk3LQJAQkIChg8fboHIWh7CLVus1u/kyUBkJPDdd8DcubyjaRJW69ZGEH7ZIdyyRY5fm314ggoNracnUAZKbisqgAsXpJYKVuv373+X2rVrgepqvrE0gYrqCmw/tB0V1YQGAzGsduzeRnV1NXJyclBNaBxTcUsVpf2KGTsZmDtjV1xcjA4dOrAPrAVCyS3F5U6s1q9OB/TuDVy7Jj1EMX0674jMQix3wh6rHbu3oVar4e3tDZVKpfjm76yg4pYqcvyKGTvOBAQE8A7BZhFu2WK1fp2dgZkzpfcrV/KNRWCVWO3YvY3+/ftj37596N+/P+9QZEPFLVWU9itm7GRg7oydQADQnLGzajIypAcnamsBjQYYMoR3RLIRM3YCgaA5iBk7zhi3CREoj3DLFqv227s38Oyz0nsxaye4Daseu7eQn5+PwMBA5Ofn8w5FNlTcUkVpv6KwY8Ann3zCOwSbhZJbOzugVSuppYLV+/XxkdqffwbKyvjGYgZ2sEMrh1awA6HBQAyrH7t/kpWVhdmzZyMrK4t3KLKh4pYqSvsVhV0jBAYGwsvLC2PHjjXre5sJ72lp7VByO3q0dM//6NG8I5GP1ft94glg4EBpe7HgYN7RyGa0+2gsdl2M0e6EBgMxrH7s/sno0aOh0+kwmlBioOKWKkr7FYVdI/j4+ECj0SAmJsas7z3++OOMIhIIt2yxer/29sBHH0nvV6yQ7rcjgtW7JY7wyw7hli1K+xWFHQOSk5N5h2CzUHJ78aL00MTFi7wjkQ8Jv3//O9C+vfQAxb59vKORxcX8i3gu/DlczCc0GIhBYuxCinPSpElk4gXouKWK0n5FYceA1q1b8w7BZqHktqICiI2ltUAxCb+ursA//iG99/UFCDzYX1FTgdTKVFTUEBoMxCAxdgE4Ojqia9eucHSks6MnFbdUUdqvKOwY0JnS5qDEEG7ZQsbvZ59Ja9udPg1ER/OORmAFUBm7np6e2LZtGzwJ7XlMxS1VlPYrCjsGxMXF8Q7BZhFu2ULGb/fuN7cZW7CAbywCq4DK2NXr9SgpKYFer+cdimyouKWK0n5FYceAZ41rbQkUR7hlCym///qX9DDFgQPSNW9Bi4bK2D137hxcXV1x7tw53qHIhopbqijtVxR2DFi3bh3vEGwWSm49PYGdO6WWCpT8ol8/4JVXpPc//sg3lrvg2cETr9i/As8OhAYDMaiMXU9PT+zcuZPUpVgqbqmitF+xpZgMxJZiAoGVcv48MGKE9ADF2bPSHm4CgUBgY4gtxTgjtl9hByW3eXnAkiVSSwVKfgEAw4YBr78uvf/6a76xNEJeWR6e/v5p5JURGgzEoDJ2CwsLsWnTJhQWFvIORTZU3FJFab9ixk4G5s7YVVZWwsXFxQKRtTwouVWrpQkklUpaz44ClPzWkZoKDB4MVFcDhw4BEyfyjqge6hw1vNd4Q/W+CmPciQwGYlAZu2q1Gt7e3lCpVBhDJDFQcUsVOX7FjB1nVqxYwTsEm0W4ZQtJv56ewIcfSu+/+orEunYC5aEydkePHo3q6mpSW4pRcUsVpf2Kwo4B06ZN4x2CzSLcsoWs32++Adq2BWJigN27eUcj4ACVsWtnZwdHR0fY2dnxDkU2VNxSRWm/orBrhMDAQHh5eWHs2LFmfU+lUjGKSCDcsoWsXzc3YPZs6f3XX0uXZQUtCipj98qVK3juuedw5coV3qHIhopbqijtVxR2jeDj4wONRoOYmBizvte9e3dGEQkouXV1BZ59VmqpQMlvPT7/HOjSBUhKAgIDeUdjgquzKx7q/BBcnQkNBmKQHrtWjnDLFqX9isKOAZT2AKQGJbf9+wNhYVJLBUp+69G+vbR3LAB89x2Qm8s3nlvo36k/Fo5aiP6dCA0GYlAZu/3790dYWBj6E0oMVNxSRWm/orBjQGpqKu8QbBZKbqurgfx8WlcFKfltkHfeAcaOBUpKpAcprIRqfTXOXT6Haj2hwUAMKmPXYDCgpqYGlBakoOKWKkr7FYUdAx599FHeIdgslNwmJADdukktFSj5bRB7eyAgQHr/88/AiRN84/mThGsJ+Dj9YyRcIzQYiEFl7MbGxsLJyQmxhLbBo+KWKkr7FYUdA3755RfeIdgswi1bbMLv/fcD774rvX/vPUCn4xuPwCJQGbt9+vTBxo0b0adPH96hyIaKW6oo7VcsUCwDcxco1uv1cHBwsEBkLQ9KbikuUEzJb6MUFQFDhgDXrgH/+Q/w3/9yDUcsUMwemxm7VohwyxY5fsUCxZzxNd7ALVAc4ZYtNuO3U6ebl2R//BGIj+cbj4A5VMbu9evXsWvXLly/fp13KLKh4pYqSvsVM3YyMHfGTiAAaM7Y2RQGA/DCC8CvvwIjRgB//AE4O3MJRczYCYxQ3FJMwB8xY8cZsWEyOyi5HTkS0GqllgqU/N4VOzsgKEha2y4+Hvj3v7mFMtJtJL6x/wYj3QgNBmJQGbsjR46EVqvFSEKJgYpbqijtV8zYycDcGbvMzEx4eHhYILKWh3DLFpv0++uvwLRpUqF3+DAwYQKXMGzSrRUh/LJDuGWLHL9ixo4zhw4d4h2CzULJbXIyMGWK1FKBkl/ZPP+89JSswQC8+SZQUGDxEJILk/H0L08juZDQYCAGlbGbmpqKGTNmkFobjopbqijtVxR2DBg0aBDvEGwWSm5LS4GDB6WWCpT8msWyZcCgQUBWFvD664Beb9HTl1aV4kLlBZRWERoMxKAydmtqapCfn4+amhreociGiluqKO1XFHaNEBgYCC8vL4wdO9as71VUVDCKSCDcssVm/d5zDxASArRpI1Xb33/POyKBwlAZuwMHDsTvv/+OgQMH8g5FNlTcUkVpv6KwawQfHx9oNBrExMSY9b3CwkJGEQmEW7bYtN9hw4DVq6X3P/wA/PYb33gEimLTY5czwi1blPYrCjsGUHraiRrCLVts3u8bbwD/+Id0v92rrwLnz/OOSKAQVMZubGwsnJ2dSW0pRsUtVZT2Kwo7Buzbt493CDYLJbceHtIauZQeJqPkt8ksXQqMHw+UlADPPAPk5DA/pUd7D7zQ6gV4tCc0GIhBZez26tULS5YsQa9evXiHIhsqbqmitF+x3IkMzF3upLy8HG3atLFAZC0P4ZYtLcZvURHw0ENAUpK0evTRo9J9eAxpMW45IfyyQ7hlixy/YrkTzixZsoR3CDYLJbdFRUBwsNRSgZLfZtGpE7B/P9C1q7RFyKuvAgyfUiyqKMJbi99CUQWhwUAMKmNXq9UiPDwcWq2WdyiyoeKWKkr7FTN2MhBbigmagthSjABnzkgLFldWAu+8A6xdC9gr/+9dsaWYwIjYUkzQFMSMHWfE9ivsEG7Z0uL8PvAA8MsvUjG3YQPwwQdAbS3vqARNgMrYHT58OLKzszF8+HDeociGiluqiC3FOGDujF1+fj66du1qgchaHpTcUpyxo+RXUX75RdqVorYWmDlTWhZFwZk7MWOnENXVQHk5UFFR71Wck4MOrVrV/11lpfS9pr70eukp6tram69bf5b7OyN2djdft//c1M/s7QEHh5uv239u6DMzvlNeVYU299xTv4+j451fTk6N/765feztb3ogjpy8a04d4qhkcAKJ0NBQfPDBB7zDsEmEW7a0WL+vvSa1b74JrFsnvVe4uGvxVFdLN5wWFkqvggLg+nXp6WQ5r9LSRu+D7GC5/5JmkQ7gBwD/BtCHcyxysdrHJpQqEp2cbv6uobax3ynQJ/zXX/H27NnKaVHsSII6zN2pQiAfSm7btgUefFBqqUDJr+LcXtzV1krFnWPz02Rbp7YY3nE42joRGgxyKCsDsrNNXzk5QH7+zeLN2Cr9sEDr1iavCgCtO3WSfm7T5ubvnJ2BVq1u/sVq7ss4c3XryzhLZs7PdnaAwYDK1FRc+O47VH73HdDnz9LOYKj/Mufz2lppZlGvN31/t59l9s29ehXdu3at/3u9Xiq2ja/qatOf7/SS08/Yp7r6zmPA2Jc4T7/+uqLHE4UdA3IssC5WS4WS28GDgVOneEdhHpT8MuHW4m7DBqkg2bZNKhSaweAug+Hb3xeDuwxWIEgLUVsrFWppaUBq6s1Xejpw9apUwJm7EbKdHdCxI9C5M9Cli/Te1RVo3/7ur3vukf6VZCzWbrsMdzg8HM8884xy//2MGDxqFE698ALvMMxCxdttbW3TC8TG+t1aPN7eNvY7pfr8+b60uhpuCuoShV0jBAYGIjAwEHozNww3t79APsItW4RfSMVd69bAjBlAWBgwaRKwezfg1rzUa5VuDQYgKwtITAQuXpTaK1duFnBVVXc/Rrt2QI8eN1/u7tIyMl263Czgbi3kHByY/KdYpV8bgbtbe3tp1rVVK75xMEITFoYBCh5PFHaN4OPjAx8fn7qbFuXSt29fdkG1cCi5pfjwBCW/THnhBeD334Fnn5WmXe+7Tyru7ruvSYdT56jxfOzzUI3l+PDE9etAXBwQGyu1Go1UyN24cefvODgAvXsDnp5A37432169bhZx7dpZJv67QGXsnjt3Do8//jiOHDlCZqsuKm6porRfUdgx4NixYxgxYgTvMGwS4ZYtwu8tPPIIcPo08Pzz0g4V48dL994pfD8ME4qKpIJUpZIKudhYaQauIRwdgQEDgHvvBYYMkd57ekqvXr0UucfQElAZu927d8ecOXPQvXt33qHIhopbqijtVyx3IgNzlzspKipCp06dLBBZy4OSW4ozdpT8WgytVirmwsOln//v/wBfX+nGepkwXe7EYAAuXwZOnLj5unix4b6ensDo0cCoUcDw4VIx17+/Wf8t1ooYu+wQbtkix69YoJgzK1eu5B2CzSLcskX4bQBXV+DXX4Gvv5Z+9vcHHn1UeqiAF1lZ0sMdM2YA3bsDgwYBf/+7NKNoLOoGDwbeegtYuhQ4ckS6FJuSAoSEAP/+NzBtmlTY2UBRB9AZu6WlpYiKikKpuQ+ecISKW6oo7VfM2MlAbCkmaAoUZ+wEdyE0VNp6TKuVntRcskT6+S4LpTZ7xq6qCoiKkva3PXiw/oxcq1bA2LHAww9Lr4cekh5WEFgdYksxQVMQM3acEduvsIOSWy8vIDlZaqlAyS8XXnxRevDgoYekRXNnzgSmTpVm0BrBq6sXPrP/DF5dzRgM5eXSAxtvvgl06wZMmQL89JNU1NnbS4sk/uc/QHS0FMvx48DChcBzz7XIoo7K2PXy8kJycjK8CCUGKm6pIrYU44C5M3YlJSViZo8Rwi1bhF+Z6PXSJc5vvwV0upuzd3//+x13q5DlVqcD9u2Ttjj77TdpSywjbm5S0TZlCjBxorR0iKAOMXbZIdyyRY5fMWPHmU2bNvEOwWah5DY1FXjjDamlAiW/XHFwAD7/XJq9e+CBm7N3jz4KnDtXr3vq9VRMDJyI1OsNDAaDAThzBvDxkZYP+etfpUu+FRXS0iKzZ0uzcVevAmvWANOni6KuAaiM3czMTMyaNQuZmZm8Q5ENFbdUUdovycJu5cqV8PT0hIuLC7y9vXHs2LFG+x89ehTe3t5wcXFBv379EBQUxDS+SZMmMT1+S4aS2+vXga1bpZYKlPxaBffeKz2FunixtCvCiRPSU6dvvw1kZNR1u155HaoqFa5X3jIYKiqAtWuBESOky6orV0qDpWdP4MsvpSVKUlKkhzUefpjZwr62ApWxS/HhCSpuqaK0X3KF3Y4dO/DZZ5/hm2++QWxsLMaPH4+nn34aGbck0VtJTU3F1KlTMX78eMTGxuLrr7/GrFmzEBISwizGxMREZsdu6Qi3bBF+m4CDg7QESmIi8PLL0gzczz9LT6p+/rm0V+qtXL0KfPMN4OEBvP8+cP68tNPFG29ID0akpwMLFkhLktzloQzBTaiMXS8vL8THx5O6x46KW6oo7ZdcYbdkyRK8++67mDlzJoYMGYJly5bBw8MDq1atarB/UFAQevfujWXLlmHIkCGYOXMm3nnnHSxevJhZjG0p7fpODOGWLcJvM+jVC9ixQ7qsOmGCdL+cv7+0TtzGjVKfr7+WLq/++KNU8PXtK92bl5MDbNkCPPmkmJlrImLsskO4ZYvSfkkVdlVVVVCpVJg8ebLJ55MnT8bJkycb/M6pU6fq9Z8yZQrOnj2L6urqBr+j0+lQUlJi8jIHsZAjO4Rbtgi/CnD//cDhw9LDDyNGSEujBARIv4uIkDYAf+wx6T66y5eBf/5TWitP0CyojN2EhAT06tULCQkJvEORDRW3VFHaL6nCrqCgAHq9Hm63bcbt5uaG3NzcBr+Tm5vbYP+amhoUFBQ0+B1fX1+4urrWvTw8PAAAKSkp8PPzg06nq3s8ed68ecjOzsb69esRExODiIgIbNy4ERqNBsuXL0dJSYlJ36KiIgQGBiI+Ph5hYWEIDw+HWq3G6tWrkZ+fb9K3vLwc/v7+SEpKws6dO3Ho0CGcPHkSmzZtQmZmpklfvV4PX19fpKenY8uWLTh+/DiioqKwfft2JCcnY9GiRaisrDT5Tm5uLtauXYuYmBgcOHAAu3fvxvnz57FixQpotVqTvsXFxQgICEBCQgL27NmD/fv3Q6VSYc2aNcjLyzPpW1FRAX9/fyQnJ2PHjh04fPgwTpw4gc2bNyMjIwPz589HbW0t5s2bh9raWsyfPx8ZGRnYvHkzTpw4gcOHD2PHjh1ITk6Gv78/Kioq6o7/448/Ii8vD2vWrIFKpcL+/fuxZ88eJCQkICAgAMXFxSaxaLVarFixAufPn8fu3btx4MABxMTEYO3atcjNzTXpW1lZiUWLFiE5ORnbt29HVFQUjh8/ji1btiA9PR2+vr7Q6/Um38nMzMSmTZtw8uRJHDp0CDt37kRSUhL8/f3h6lqOxx+Phru71Dc/Px+rV6+GWq1GeHg4wsLCEB8fj8DAQBQVFZkct6SkBMuXL4dGo0FoaCgiIiIQExOD9evXIzs726SvTqeDn58frly5gm3btiEqKgrHjh1DcHAw0tLSsGDBAtTU1Jh8JysrCxs3bsTp06cRGRmJXbt2ITExEYsXL0ZZWZlJ34KCAgQFBSEuLg779u3D3r17ERcXh1WrVqGwsNCkb2lpKZYtWwaNRoOQkBAcPHgQZ86cwYYNG+rFXV1djYULFyIlJQVbt25FdHQ0oqOjsXXrVqSkpGDhwoWorq6u92dtw4YNOHPmDA4ePIiQkBBoNBosW7YMpaWlJn0LCwuxatUqxMXFYe/evdi3bx/i4uIQFBSEgoICk75lZWVYunQpEhMTsWvXLkRGRuL06dPYuHEjsrKyTPrW1NRgwYIFSEtLQ3BwMI4dO4aoqChs27YNV65ckXJEVRXmnT0LxMZiz/Tp6NquB749CrR64AmcDAhA6KxZ0AwejOWBgSJHKJQjfvzxx7rjW3OOOHnyJKZNm4b//e9/KC8vN+lrrTli27ZtdTli6dKlIkcokSNuqSN+/PHHenVEaGioSR3h5+cHuZBa7iQ7Oxs9e/bEyZMnMW7cuLrP58+fjy1btjR4nXrQoEH4+9//jjlz5tR9duLECTzyyCPIyclpcL8+nU4HnU5X93NJSQk8PDxkL3eSnZ2NHj16mPufJ5CBcMsW4ZcRBgOyr15Fj169eEdis4ixyw7hli1y/NrsciddunSBg4NDvdm5a9eu1ZuVM9K9e/cG+zs6OqJz584NfsfZ2Rnt27c3eZnDhg0bzOovkI9wyxbhlxF2dtggloxgihi77BBu2aK0X1IzdgDwwAMPwNvb22RvNS8vLzz//PPw9fWt1//LL7/E3r17odFo6j77xz/+gbi4OJw6dUrWOcWWYgKBQCAQCHhhszN2ADB79mysW7cOGzZswMWLF/HPf/4TGRkZ+PDDDwEAc+bMwVtvvVXX/8MPP0R6ejpmz56NixcvYsOGDVi/fj0+//xzZjGK7VfYIdyyRfhlh3DLFuGXHcItW8SWYpAWKPbz80NOTg6GDRuGpUuX4tFHHwUAvP3220hLS0NUVFRd/6NHj+Kf//wnLly4gB49euDLL7+sKwTlYO6MnU6ng7Ozs9n/XYK7I9yyRfhlh3DLFuGXHcItW+T4tekZOwD46KOPkJaWBp1OB5VKVVfUAdLWHLcWdQDw2GOPQa1WQ6fTITU11ayirin89NNPTI/fkhFu2SL8skO4ZYvwyw7hli1K+3VU9Gg2inFSU+56dpMnTzZ77TuBPIRbtgi/7BBu2SL8skO4ZYscv8bfy7nIKgo7GRj39DOuZycQCAQCgUBgaUpLS+F6lwXNSd5jZ2lqa2uRnZ2Ndu3awe4uezca17zLzMxU/AnasWPHIiYmRtFjsjoui2MKt2yPS82vcCtByQOr47LyS8kBq+OKscv2uHL9GgwGlJaWokePHrC3b/wuOjFjJwN7e3v0MnNh0aasf3c3HBwcmCy3wuK4rGIFhFuWxwXo+BVuJah5oOSXmgNKbgF6Hnj7vdtMnRGSD0+0VHx8fMgcl1WsrKDkluVxWUFpjAm3NI/LAmoOKLkF6Hmg4ldcilUYsZgxO4Rbtgi/7BBu2SL8skO4ZQsLv2LGTmGcnZ3x3XffiTV/GCDcskX4ZYdwyxbhlx3CLVtY+BUzdgKBQCAQCAQ2gpixEwgEAoFAILARRGEnEAgEAoFAYCOIwk4gEAgEAoHARhCFnYKsXLkSnp6ecHFxgbe3N44dO8Y7JJvA19cXY8eORbt27dCtWzdMmzYNSUlJvMOySXx9fWFnZ4fPPvuMdyg2w9WrV/HGG2+gc+fOaNOmDUaNGgWVSsU7LPLU1NTg22+/haenJ1q3bo1+/frh+++/R21tLe/QSBIdHY1nn30WPXr0gJ2dHfbs2WPye4PBgLlz56JHjx5o3bo1JkyYgAsXLvAJlhiNua2ursaXX36J4cOHo23btujRowfeeustZGdnN/l8orBTiB07duCzzz7DN998g9jYWIwfPx5PP/00MjIyeIdGnqNHj8LHxwenT59GZGQkampqMHnyZNy4cYN3aDZFTEwM1qxZgxEjRvAOxWa4fv06Hn74YTg5OeG3336DRqOBv78/OnTowDs08ixcuBBBQUEICAjAxYsX4efnh0WLFmHFihW8QyPJjRs3MHLkSAQEBDT4ez8/PyxZsgQBAQGIiYlB9+7d8eSTT9ZtuSm4M425LS8vh1qtxr///W+o1WqEhobi0qVLeO6555p+QoNAEe6//37Dhx9+aPLZvffea/jqq684RWS7XLt2zQDAcPToUd6h2AylpaWGgQMHGiIjIw2PPfaY4dNPP+Udkk3w5ZdfGh555BHeYdgkzzzzjOGdd94x+ezFF180vPHGG5wish0AGHbv3l33c21traF79+6GBQsW1H1WWVlpcHV1NQQFBXGIkC63u22IP/74wwDAkJ6e3qRziBk7BaiqqoJKpcLkyZNNPp88eTJOnjzJKSrbRavVAgA6derEORLbwcfHB8888wwmTZrEOxSbIiwsDPfddx9eeukldOvWDaNHj8batWt5h2UTPPLIIzh06BAuXboEADh37hyOHz+OqVOnco7M9khNTUVubq7J33HOzs547LHHxN9xDNBqtbCzs2vyzL7YK1YBCgoKoNfr4ebmZvK5m5sbcnNzOUVlmxgMBsyePRuPPPIIhg0bxjscm2D79u1Qq9VMNs1u6aSkpGDVqlWYPXs2vv76a/zxxx+YNWsWnJ2d8dZbb/EOjzRffvkltFot7r33Xjg4OECv12P+/PmYMWMG79BsDuPfYw39HZeens4jJJulsrISX331FV577bUm70QhCjsFsbOzM/nZYDDU+0zQPD7++GPEx8fj+PHjvEOxCTIzM/Hpp5/i4MGDcHFx4R2OzVFbW4v77rsPP/74IwBg9OjRuHDhAlatWiUKu2ayY8cOBAcH45dffsHQoUMRFxeHzz77DD169MDf/vY33uHZJOLvOLZUV1fj1VdfRW1tLVauXNnk44jCTgG6dOkCBweHerNz165dq/cvHEHT+eSTTxAWFobo6Gj06tWLdzg2gUqlwrVr1+Dt7V33mV6vR3R0NAICAqDT6eDg4MAxQtq4u7vDy8vL5LMhQ4YgJCSEU0S2w7/+9S989dVXePXVVwEAw4cPR3p6Onx9fUVhpzDdu3cHIM3cubu7130u/o5Tjurqarz88stITU3F4cOHm7VvrLjHTgFatWoFb29vREZGmnweGRmJ/2/n/kHa2gI4jv/avCZaEdEsIUPSFAJSxUFCwFikIJSG0q0IVUTsVKy0RlDQDOpgNouDQrkI3QpdCmKHDqUhS6F/aCPZjCB27RDQVGloPG94PEFqC21T7st53w/c4YaQ++MOOT/OPfckEgmXUtnDGKPx8XE9ffpUL1++VCQScTuSNfr7+1UoFJTP54+PWCymoaEh5fN5St1v6u3t/WZrnq2tLYXDYZcS2ePg4EBnz54cwjweD9ud/AGRSESBQODEGFepVJTL5RjjauDfUlcsFvXixQv5/f7f+j1m7GpkcnJSw8PDisVi6unpkeM4+vjxo+7cueN2tLp39+5dPX78WOvr62pubj6eGW1paVFjY6PL6epbc3PzN2sVm5qa5Pf7WcNYA6lUSolEQplMRgMDA3rz5o0cx5HjOG5Hq3s3btzQ4uKiQqGQOjo69OHDBz148EC3b992O1pdKpfL2t7ePj7f2dlRPp9XW1ubQqGQJiYmlMlkFI1GFY1GlclkdP78eQ0ODrqYuj786N4Gg0HdvHlT79+/17Nnz1StVo/HuLa2Nnm93p+/4C+9S4tTra6umnA4bLxer+nu7mY7jhqRdOrx6NEjt6NZie1OamtjY8N0dnYan89n2tvbjeM4bkeywt7enrl//74JhUKmoaHBXLx40aTTafPlyxe3o9WlbDZ76v/syMiIMeafLU/m5uZMIBAwPp/P9PX1mUKh4G7oOvGje7uzs/PdMS6bzf7S9c4YY8zP10EAAAD817DGDgAAwBIUOwAAAEtQ7AAAACxBsQMAALAExQ4AAMASFDsAAABLUOwAAAAsQbEDAACwBMUOAADAEhQ7AAAAS1DsAAAALEGxAwAAsATFDgAAwBIUOwAAAEtQ7AAAACxBsQMAALDEX24HAAAblUolLSws6OvXr9re3tbAwIAGBwc1NTUlY4xKpZLS6bQuXbrkdlQAFqHYAUCNVSoVjY2NaWlpScFgULu7u4pEIlpfX9fy8rKKxaKuX7+u1tZWraysuB0XgEV4FAsANfbw4UONjo4qGAxKkhoaGmSM0YULFxSJRFStVhWNRnXr1i2XkwKwDTN2AFBjra2tunr16vH5u3fvJEnXrl2TJCWTSSWTSVeyAbAbM3YAUGPDw8MnzrPZrDwejy5fvuxSIgD/F2eMMcbtEABgs+7ubp07d06vX792OwoAyzFjBwB/UKlU0ubmpq5cuXLi87W1NXcCAbAaxQ4AaujTp0+Kx+NaWFiQJD1//lxHR0eKx+MnvvPq1Su3IgKwGMUOAGool8vp7du3Msbo8PBQT548UTAYVLlcliR9/vxZ9+7d0/z8vLtBAViJNXYAUEP7+/tKpVLyer0ql8uamZnR3t6eZmdnFQ6HValUND09ra6uLrejArAQxQ4AAMASPIoFAACwBMUOAADAEhQ7AAAAS1DsAAAALEGxAwAAsATFDgAAwBIUOwAAAEtQ7AAAACxBsQMAALAExQ4AAMASFDsAAABLUOwAAAAsQbEDAACwBMUOAADAEn8DeSyTqK0p9KQAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 8 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = plot(R(x), (x, 0, 2.6), thickness=1.5, color='red',\n", " axes_labels=[r\"$x$\", r\"$r/r_0$\"]) \\\n", " + plot(R(x), (x, 2.9, 12), thickness=1.5, color='red')\n", "graph += line([(X1, 0), (X1, 4)], color='blue', linestyle='dashed') \\\n", " + text(r'$x=x_1$', (2.7, 1.5), fontsize=16, color='blue', rotation='vertical')\n", "graph += line([(X2, 0), (X2, 4)], color='green', linestyle='dashed') \\\n", " + text(r'$x=x_2$', (5.7, 1.5), fontsize=16, color='green', rotation='vertical')\n", "graph += line([(X1 + X2, 0), (X1 + X2, 4)], color='black', linestyle='dotted') \\\n", " + text(r'$x=\\alpha^{-1}$', (8.7, 1.5), fontsize=16, color='black', rotation='vertical')\n", "show(graph, ymax=3, frame=True, axes=False, gridlines=True)\n", "graph.save('vai_r_x_naksing.pdf', ymax=3, frame=True, axes=False, gridlines=True)" ] }, { "cell_type": "code", "execution_count": 42, "id": "7561d621-fbf3-4311-bf0d-2c8d1a946249", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\frac{2 \\, {\\left(x_{1} + x_{2}\\right)}}{{\\left(x - x_{1}\\right)} {\\left(x - x_{2}\\right)} x}\$" ], "text/latex": [ "$\\displaystyle \\frac{2 \\, {\\left(x_{1} + x_{2}\\right)}}{{\\left(x - x_{1}\\right)} {\\left(x - x_{2}\\right)} x}$" ], "text/plain": [ "2*(x_1 + x_2)/((x - x_1)*(x - x_2)*x)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f2(x) = 2 /(x*(a1*(x - x1)*(x - x2)))\n", "f2(x)" ] }, { "cell_type": "code", "execution_count": 43, "id": "d6855336-72a7-4d7c-9fc2-acade303a6f7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\frac{2 \\, {\\left(x_{2}^{2} {\\left(\\log\\left(x - x_{1}\\right) - \\log\\left(x\\right)\\right)} - x_{1}^{2} \\log\\left(x - x_{2}\\right) + x_{1}^{2} \\log\\left(x\\right) + {\\left(x_{1} \\log\\left(x - x_{1}\\right) - x_{1} \\log\\left(x - x_{2}\\right)\\right)} x_{2}\\right)}}{x_{1}^{2} x_{2} - x_{1} x_{2}^{2}}\$" ], "text/latex": [ "$\\displaystyle \\frac{2 \\, {\\left(x_{2}^{2} {\\left(\\log\\left(x - x_{1}\\right) - \\log\\left(x\\right)\\right)} - x_{1}^{2} \\log\\left(x - x_{2}\\right) + x_{1}^{2} \\log\\left(x\\right) + {\\left(x_{1} \\log\\left(x - x_{1}\\right) - x_{1} \\log\\left(x - x_{2}\\right)\\right)} x_{2}\\right)}}{x_{1}^{2} x_{2} - x_{1} x_{2}^{2}}$" ], "text/plain": [ "2*(x_2^2*(log(x - x_1) - log(x)) - x_1^2*log(x - x_2) + x_1^2*log(x) + (x_1*log(x - x_1) - x_1*log(x - x_2))*x_2)/(x_1^2*x_2 - x_1*x_2^2)" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = integrate(f2(x), x).simplify_full()\n", "s" ] }, { "cell_type": "code", "execution_count": 44, "id": "3fcd12ae-41cc-4937-a8fa-e961fc7255d0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\frac{2 \\, {\\left(x_{1} + x_{2}\\right)}}{x_{1}^{2} - x_{1} x_{2}}\$" ], "text/latex": [ "$\\displaystyle \\frac{2 \\, {\\left(x_{1} + x_{2}\\right)}}{x_{1}^{2} - x_{1} x_{2}}$" ], "text/plain": [ "2*(x_1 + x_2)/(x_1^2 - x_1*x_2)" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s.coefficient(log(x - x1)).simplify_full()" ] }, { "cell_type": "code", "execution_count": 45, "id": "ce0d6011-7a2b-40ed-a5a1-0161204a9aa8", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -\\frac{2 \\, {\\left(x_{1} + x_{2}\\right)}}{x_{1} x_{2} - x_{2}^{2}}\$" ], "text/latex": [ "$\\displaystyle -\\frac{2 \\, {\\left(x_{1} + x_{2}\\right)}}{x_{1} x_{2} - x_{2}^{2}}$" ], "text/plain": [ "-2*(x_1 + x_2)/(x_1*x_2 - x_2^2)" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s.coefficient(log(x - x2)).simplify_full()" ] }, { "cell_type": "code", "execution_count": 46, "id": "3fb02863-391f-41ac-9afa-7458286b1d0e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle \\frac{2 \\, {\\left(x_{1} + x_{2}\\right)}}{x_{1} x_{2}}\$" ], "text/latex": [ "$\\displaystyle \\frac{2 \\, {\\left(x_{1} + x_{2}\\right)}}{x_{1} x_{2}}$" ], "text/plain": [ "2*(x_1 + x_2)/(x_1*x_2)" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s.coefficient(log(x)).simplify_full()" ] }, { "cell_type": "markdown", "id": "2d828906-19b7-40e3-9349-d5d115decc5f", "metadata": {}, "source": [ "## Marginal case: $v_0 = 16 m$" ] }, { "cell_type": "code", "execution_count": 47, "id": "ab2c9b77-7092-4c90-a910-fc872da92546", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -\\frac{x - 8}{{\\left(x - 4\\right)}^{2}}\$" ], "text/latex": [ "$\\displaystyle -\\frac{x - 8}{{\\left(x - 4\\right)}^{2}}$" ], "text/plain": [ "-(x - 8)/(x - 4)^2" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(x) = (8 - x)/(x - 4)^2\n", "f(x)" ] }, { "cell_type": "code", "execution_count": 48, "id": "cba6cc0a-e418-4112-9c41-55a11df61447", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$\\displaystyle -\\frac{4}{x - 4} - \\log\\left(x - 4\\right)\$" ], "text/latex": [ "$\\displaystyle -\\frac{4}{x - 4} - \\log\\left(x - 4\\right)$" ], "text/plain": [ "-4/(x - 4) - log(x - 4)" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate(f(x), x)" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 10.0.rc0", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 5 }