{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Circular equatorial orbits in Kerr spacetime\n", "\n", "This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://luth.obspm.fr/~luthier/gourgoulhon/bh16/)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 9.2, Release Date: 2020-10-24'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Effective potential $\\mathcal{V}(r)$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "a = var('a')\n", "r = var('r')\n", "eps = var('eps', latex_name=r'\\varepsilon')\n", "l = var('l', latex_name=r'\\ell') " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( a, {\\varepsilon}, {\\ell}, r \\right) \\ {\\mapsto} \\ -{\\varepsilon}^{2} - \\frac{2 \\, {\\left(a {\\varepsilon} - {\\ell}\\right)}^{2}}{r^{3}} - \\frac{{\\left({\\varepsilon}^{2} - 1\\right)} a^{2} - {\\ell}^{2}}{r^{2}} - \\frac{2}{r} + 1\n", "\\end{math}" ], "text/plain": [ "(a, eps, l, r) |--> -eps^2 - 2*(a*eps - l)^2/r^3 - ((eps^2 - 1)*a^2 - l^2)/r^2 - 2/r + 1" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "V(a, eps, l, r) = (1 - eps^2 - 2/r + (l^2 + a^2*(1 - eps^2))/r^2\n", " - 2*(l - a*eps)^2/r^3)\n", "V" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Constraint $r^2 - 3 m r \\pm 2 a \\sqrt{m r} > 0$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( r, a \\right) \\ {\\mapsto} \\ {\\left(r - 3\\right)} r + 2 \\, a \\sqrt{r}\n", "\\end{math}" ], "text/plain": [ "(r, a) |--> (r - 3)*r + 2*a*sqrt(r)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(r, a) = r*(r-3) + 2*a*sqrt(r)\n", "f" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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4B3nrLYiNhT/+ABkcMAvHSMD27y/c/lJbtujsHDhy5AgjRoxg/fr1JCQkFIx8xcTEXDcBK+lWRMBV/VSUUjfssXL69Gmee+45+vTpw2OPPUZqaiojR46kR48e/Pvvv8XrzyKEEEIAx//5h+N//EGrMWPwr1SpeAf591/4+mv46iuoW9e8Abowx0jA6tXTyVVh7nfBAw88QOXKlZkyZQoVKlTAZDLRoEEDcnJyrvvwyMhIIiMjb3iKBQsWFGzwfaXy5ctfNdoVHx9/1ajYpaKioggMDGTcuHEFt82aNYvKlSuzYcMGWrZsecN4hBBCiGtJP3WKTe+9R9X77qPaAw8U7yCJifDMM3DPPfDSS+YN0MU5RgLm61swslUY586dY9++fUyaNKkgWbp0Q+zrKekUZKtWrfj3338ZNGhQwW2LFy+mdevW131MRkYG7lcMCef/+0b1akIIIcT1mIxG1r39Np5+frQYObL4symvvAJpaTBtGhRns25xXY6RgBVRmTJlCA4OZvLkyYSHhxMTE8PQoUNv+riSTkEOGDCAdu3aMXbsWLp168bvv//OkiVLLkv+vv76a+bPn8/SpUsB6NKlC59//jnvvfdewRTk22+/TdWqVWnSpEmxYxFCCOG69k+bRvzmzXSYNg2vwMDiHeSnn+CHH2DWLCju9KW4LqdMZ93c3JgzZw5btmyhQYMGDBo0iI8//tji523dujVz5sxh2rRpNGzYkOnTpzN37lxuv/32gvskJCRc1g6jffv2/PDDD/z22280adKEzp074+3tzcKFC/Hx8bF4zEIIIZzL+b172fnVV0T07UtYixbFO0hcHPTvD488Ao8/bt4ABQAGpZStzn3NE2dkZLBv3z7q16+P74UVjaJk8n+mBw4cID4+nqeeeqrEiw2EEELYn7zMTBY+8gjuPj50nD0b9+I0S1UKunSBbdtg924IDjZ/oJdzydVmTjkFKYQQQriirePGkR4XR+d584qXfAFMngwLFsA//1gj+XJZTjkFKYQQQriamMWLOfzTTzQbNoygGjWKd5DDh2HwYHjxRbjvPvMGKC4jCZgQQgjh4NJPnWLDu+9SpVMnal7RiLzQjEbo0wfCw+GTT8wboLiKJGBm9ssvvxAREYG3tzcRERHMnz//po/56aefaNy4Mb6+vlStWvWaCwZmz55No0aN8PX1JTw8nGeeeYZz585Z4ikIIYRwIKa8PNYMGYKXvz+3jRpV/JYTH38M69fDjBng72/eIMVVJAEzo3Xr1tGrVy969+7Njh076N27Nz179mTDhg3XfcyCBQt44okn6NevH7t372bChAl89tlnfP311wX3Wb16NU899RTPPvsse/bsYd68eWzatInnnnvOGk9LCCGEHds1YQLndu2i9ccfF7/lxPbtMHIkvPkmtGlj1vjEtTltArZw4ULatm1L6dKlCQ4OpmvXrpe1f7CE8ePHc++99zJs2DDq1avHsGHD6NChA+PHj7/uY2bOnMlDDz1Ev379qFGjBl26dOGtt95i7Nix5K9QXb9+PdWqVeO1116jevXqtG3blhdffJHNmzdb9PkIIYSwb2c2bGDP5Mk0fOUVQho3Lt5BMjJ0q4lbboFRo8wZnrgBp03A0tPTGTx4MJs2bWLp0qW4ubnx8MMP37C7fGRkJP7+/je8rFq16rqPX7duHR07drzstk6dOrF27drrPiY7O5tSpUpddpuPjw8nTpwgOjoa0P3FTpw4wT///INSijNnzvDzzz/TpUuXwvwohBBCOKGsxETWDh1KWIsW1H/22eIf6M034dgx3XTV29t8AYobcog2FHmZmaQcO3bT+wVWr47Hheal3a8oQpw6dSqhoaHs3bv3uptxl3QrotOnT1+172NYWNhV+0NeqlOnTgwaNIinn36au+++m8OHDxeMmMXFxVGtWjVat27N7Nmz6dWrF1lZWeTl5fHggw/y1Vdf3TBWIYQQzkkpxYbhwzHl5tJq7FjcrtjSrtD+/huiovSlfn3zBiluyCESsJRjx1j4yCM3vV/nefMoGxEBwJEjRxgxYgTr168nISGhYOQrJibmuglYSbciAq4qflRK3bAg8vnnn+fIkSN07dqV3NxcAgMDGTBgAKNGjSrYE3Lv3r289tprjBw5kk6dOhEXF8eQIUPo168fU6dOLVG8QgghHM/B2bM5uXw5d06YgG9oaPEOcuYM9O2rm67272/eAMVNOUQCFli9Op3nzSvU/fI98MADVK5cmSlTplChQgVMJhMNGjQgJyfnuo+PjIwkMjLyhudYsGBBwQbfVypfvvxVo13x8fFXjYpdymAwMHbsWCIjIzl9+jQhISEF+0RWq1YNgDFjxtCmTRuGDBkCQMOGDfHz8+OOO+7ggw8+IDw8/IYxCyGEcB6J+/ax7ZNPqPvkk1S8887iHUQpnXwBfPcdFHflpCg2h0jAPHx8Cka2CuPcuXPs27ePSZMmFSRLl26IfT0lnYJs1aoV//77L4MGDSq4bfHixbRu3fqm53Z3dy849o8//kirVq0IvfCpJiMjAw8Pj6vuD2DDraSEEEJYWV5GBmuGDCGoZk0av/568Q80YYLudP/331DcETRRIg6RgBVVmTJlCA4OZvLkyYSHhxMTE8PQoUNv+riSTkEOGDCAdu3aMXbsWLp168bvv//OkiVLLkv+vv76a+bPn18wypWQkMDPP//MXXfdRVZWFtOmTWPevHmsWLGi4DEPPPAAzz//PBMnTiyYghw4cCC33XYbFSpUKHa8QgghHMvmyEgyTp8u2VZDe/fCG2/AK6/A/febN0BRaE65CtLNzY05c+awZcsWGjRowKBBg67Z3NTcWrduzZw5c5g2bRoNGzZk+vTpzJ07l9tvv73gPgkJCVe1w5gxYwbNmzenTZs27Nmzh+XLl3PbbbcVfP/pp58u6A3WoEEDHnnkEerWrcuvv/5q8eckhBDCPhz/+2+Ozp9P83feuazkpkiys3XLiRo1YNw48wYoisRgwymsa544IyODffv2Ub9+fXx9fa0dk1PK/5keOHCA+Ph4nnrqqRIvNhBCCGE9abGxLOjRgwrt2tF63Ljid7t/4w346ivYsAGK2zfM/FyyAM3iI2AGg6GiwWCYZTAYzhkMhgyDwbDdYDA0s/R5hRBCCGdgzMlh9euv412mDLe9+27xk68lS+DTT2HMGHtKvlyWRWvADAZDGWANsAy4D4gHagJJljyvEEII4Sy2ffwxSQcP0vGHH/As7h6N587pjbbvuQcGDjRrfKJ4LF2E/xYQq5R65pLbjlv4nEIIIYRTiFm0iIM//EDz4cOL1A3gMkrB889DVhZMnw5uVij/VkpaW9yEpV+FB4HNBoNhnsFgiDcYDNsMBsPz17tzdnY2aWlpFg5JCCGEsH+pMTFsGDmSKp07U/vRR4t/oO++g/nz4dtv4QatlMzqwHE4fso653JQlk7AagD9gUNAJ+Ab4EuDwfDUte48ZswY2rVrZ+GQhBBCCPtmzM5m9eDBeJcty+2jRxe/7mv/fnjtNXj2WXj4YfMGeT1nE+HMOfCRfSVvxNIJmBuwVSn1tlJqm1JqEjAFnZRdZdiwYaxcudLCIQkhhBD2bevYsSQfOcIdn31W/LqvrCx49FGoUgW++MK8AV5PTi4cjIZypSFUVtvfiKUTsDhg7xW37QOqXOvO3t7e+Bf3fzQhhBDCCUQvWMChuXNpNmwYZUqyQfabb+oRsDlzwM/PfAFej1I6+TIAtatKDdhNWDoBWwPUveK2OkC0hc8rhBBCOJyU6Gg2vPsuVe+/n1qPPFL8A/3xh+739ckn0KiR+QK8kTPn4FwS1KkKXp7WOacDs3QC9jnQ0mAwvG0wGGoZDIbHgReAKAufVwghhHAoeVlZrB40CJ+QEG4bNar4dV8nTsAzz0C3bvDyy+YN8nqysuFwLIQFQ7ky1jmng7NoGwql1CaDwfAwMAYYCRwDBiqlZgOzbvTYzMxMS4bmUuRnKYQQ9m/rRx+Revw4HX/8Ec/iThkajfDkk+DrC1OnWmcaUCm96tHDHWpVtvz5nITFN+NWSv0F/FXY+3t4eODm5sbx48ctF5QLUkqRl5dn6zCEEEJcw/G//uLwvHncNno0ZepeWblTBB9+CKtWwbJlEBxsvgBv5OQZSEqFhnXAw+JphdOwu5+Ul5cXt9xyC3l5ecTFxTF48GD+97//SXF+CRmNRnJzc20dhhBCiCukHDvGxtGjqfbAA9Ts3r34B1q1CkaPhhEjwFotndIz4ehJqBgKZQKtc04nYXcJGOgkzMvLCw8PD2JiYkhMTJTRGzPIzs62dQhCCCEukZeVxerBg/EtX54WI0YUv+7r/Hl44glo0waGDzdvkNdjMsH+o7rfV/VK1jmnE7HLBCyft7c32dnZ5OTkkJqaautwnEJgYCDe3tIcTwghbE0pxeb33yc1JoZOc+YUv+5LKXjuOUhLg9mzrTcNGH0K0rOgSX1wt8L2Rk7GrhMwX19fDh06RK9evQgICLB1OE7B29sbP2v0gxFCCHFDR+bN4+hvv9Hqo48oXbt28Q/0zTd6q6H586GylYrgk9Mg5jRUqwABvtY5p5Ox6wQMIC8vjzJlyhAYKHPLQgghnMO5XbvYHBlJ7UcfpfoDDxT/QDt3wuDB8NJL8NBDZovvhoxG2H8MAv2gSrh1zumEDEopW537pidOSUkhKCiI5ORkScCEEEI4hazERBb26IFPaCj3zJiBu5dX8Q6UmgrNm4OPD6xbp6+t4eBxOHMemkeATylzHNElW+bb/QiYEEII4SxMRiNr33wTY3Y2bT/7rPjJl1Lw4otw6hRs3Wq95OtcEsQl6K2GzJN8uSxJwIQQQggr2RUVxZn167l7yhT8wkswffftt/Djj/pSkvqxosjJ1Q1XywZBeDnrnNOJybIFIYQQwgpOLl/OnkmTaPjaa5Rv2bL4B9qxA159Ffr1g0cfNV+AN5K/0TbovR5lo+0SkxowIYQQwsLSYmNZ0LMnoc2a0e7LLzG4FXP849K6r/XroZSVpgFPnYVD0XBLLShX2txHd8lszi6nIKOiooiKisJoNNo6FCGEEKJE8rKyWDVwIN5BQbSKjCx+8nVl3Ze1kq+MTDgSC+Ehlki+XJaMgAkhhBAWopRi/TvvELNoER1/+KFk+zxOmQIvvKDrvqw19Wgywbb9YDRBs/rg7m6Js7jkCJjUgAkhhBAWcnjePI79/ju3jRpVsuTLFnVfAMdP6f0e61e3VPLlsiQBE0IIISzg3K5dbDFHs9XUVHjkEahXDz7/3HwB3kxiCsTmd7uXHVTMzS5rwIQQQghHlnX+PKsGDaJM/fo0feut4h8ov+4rLs66dV+5ebrbfVAAVC5vnXO6GEnAhBBCCDMy5eay5vXXS95sFWDyZOv3+8pvOWEyQb3q0nLCQiQBE0IIIcxo2yefEL91Kx2mTi1Zs9XNm+G116B/f+vWfZ05BwmJEFEDSpUgeRQ3JDVgQgghhJkc/e03DsyaRbOhQwlt3rz4Bzp3Dnr0gMaNrVv3lZkFh2MgLBhCylrvvC5IRsCEEEIIMzi3axcbR4+mZvfu1C7JiJXJBE8+CWlpsHIleHubL8ibnXffMfD0hFpVrHNOFyYJmBBCCFFCmQkJrBwwgDL169N8+HAMJamb+uADWLQIFi6EKlZMhGLiIDUdmtQDD2k5YWkyBSmEEEKUgDEnh9WDBqGMRu4YP75kRfeLFsGoUTB6NHTsaLYYbyopFaLjoGoFCPS33nldmIyACSGEECWw9aOPOLdzJx1mzMA3NLT4B4qOhscfh86d4Z13zBfgzeTmwf6jEOQPVUuwaEAUiYyACSGEEMV0eN48Ds2dS/MRIwhp3Lj4B8rO1s1WAwJg1iwo7n6RRaUUHDiutxqqX0NaTliRjIAJIYQQxXB22zY2f/ABtXv1olaPHiU72KBBeruhtWuhrBVXH546C+eS4Jaa4C0tJ6xJEjAhhBCiiDLOnGHVwIEEN2xI06FDS3awmTNh4kTddLVZM/MEWBhpGXAkFiqGQrky1juvAGQKUgghhCgSY3Y2qwYMwODuTtvPPy9Z0f2uXXqroaefhueeM1uMN2U0wt6j4FsKalSy3nlFARkBE0IIIQpJKcWmDz4g8cAB7p05E59y5Yp/sORk6N4d6tSBqCjr1l8djoHsHGgWYb16M3EZScCEEEKIQjowcyZHf/2VlpGRBDdoUPwDKQXPPAPx8XrLIV9f8wV5M2fOwelzULeaHgETNmGXaW9UVBQRERG0aNHC1qEIIYQQAJxatYptH39M/WeeoUa3biU72LhxMH8+zJgBtWqZJ8DCyMyCQ9EQWlZvNyRsxqCUstW5b3rilJQUgoKCSE5OJjAw0BoxCSGEEFdJPnKExY8/TkizZrT76ivc3EvQKX7RIrjvPnj7bd313lpMJti+H3KNeurRfrrdu2TvC0nAhBBCiBvITkpi0aOP4u7tTcfZs/H0L0Gn+CNHoHlzaN0a/vgDSpLIFfncsXAyXm81FOBnvfPenEsmYFIDJoQQQlyHKTeXVQMHkpuWRvtvvy1Z8pWeDg8/DOXKwezZ1k2+ziXDiTN6xaN9JV8uSxIwIYQQ4hqUUmyOjCRh2zbaf/cd/pVK0K5BKejbF44dg/XroXRps8V5U9k5cOAYlA2ESmHWO6+4IUnAhBBCiGs4+MMPHP7pJ25//31CS9ogddw4+Okn+OUXuOUW8wRYGErB/mO6xUXd6rLVkB2xy1WQQgghhC3FrVnD1o8+ol6fPtT83/9KdrBFi2DYML3BdkmPVVTRcZCUCvWqg5endc8tbkiK8IUQQohLpBw7xqLHHqNc48bcGRVVshWP+UX3rVrBn39at+4rMQV2HoSqFaBaBeudt+hcclhORsCEEEKIC7KTkljx8sv4hITQ5uOPS5Z8XVp0/8MP1k2+snNg31EoHQBVw613XlFoUgMmhBBCAMacHFYNHEhOcjIdf/wRr4CA4h/MlkX3Sunky2CA+jWk7stOSQImhBDC5Sml2PjuuyRs306H774joEqVkh3QVkX3AMdPQXIaNKordV92TBIwIYQQLm/3N99w7I8/aD1uHCFNm5bsYLYsuj+fDDFxUL2inn4UdktqwIQQQri0Y3/9xa6vv6bhq69SrUuXkh3s4EF49FHo3BlGjzZPgIWVlQP7jkHZIKhc3rrnFkUmCZgQQgiXFb9lCxuGD6d6t27c8uKLJTtYUhI8+CCEhVm/6N5kgn1HwN1Nt5yQui+7J1OQQgghXFJKdDSrXnuNco0bc9uoURhKkrQYjfDYY3DmDGzcaN2ie4BjJyE1Q9d9ecpbuyOQV0kIIYTLyU5KYkX//niXKUO7L77A3curZAd86y34919YsABq1zZPkIWVkHRxn8egEuxVKaxKEjAhhBAuxZiTw8rXXiMnJYWOP/yAV1BQyQ44YwZ8+il88QXce695giysrGy9z2Nwadnn0cHYZQ1YVFQUERERtGjRwtahCCGEcCJKKTaMHMm5Xbto99VXJW83sXYtvPACPPccvPqqeYIsLJMJ9h4FD3eoW03qvhyMbEUkhBDCZeyaMIFdUVG0+eQTqt53X8kOFhsLLVroKcelS6Gk05hFdSga4hKgcT0I9LPuuc3LJTNHuxwBE0IIIczt2B9/sCsqikYDBpQ8+UpPh27dwNtbN1u1dvJ15hycOgu1qjh68uWypAZMCCGE04tbu5b1I0ZQ43//I+L550t2MJMJnnlG9/xaswZCQ80TZGGlZcDBaAgLhvBy1j23MBtJwIQQQji18/v2sWrAAMJbt+a2kSNL1m4CYORImDcPfv0VGjUyT5CFlZcHe46ArzfUrip1Xw5MpiCFEEI4rbQTJ1jerx+B1avT5pNPcPMs4d6I338PH34IY8fCww+bJ8jCUgr2H9NJWEQt3XRVOCx59YQQQjil7KQklvfrh4ePD3dNnIinXwlrpVau1Ksdn30WhgwxT5BFERMH55J1p3sfb+ufX5iVTEEKIYRwOnlZWax4+WWyk5PpOGsWpYKDS3bAQ4f0iNcdd8CECdaf+jufDMdPQdVw3fNLODxJwIQQQjgVk9HI2iFDSDxwgA7ffUdA1aolO+D589ClC4SEwM8/W3/FY1a23mS7TCBUrWDdcwuLkQRMCCGE01BKseXDDzm5YgXtvvqKcg0bluyAOTnQvbtOwjZsgDJlzBNoYZlMsPfCJtv1a0jRvRORBEwIIYTT2DtlCofmzuX2996j4p13luxgSkG/frrb/ZIlULOmeYIsisMxkJYJTerJJttORl5NIYQQTuHo/Pns+OILbn35ZWp2717yA44dC9OmwcyZuvbL2uIS9KVOVQiQZqvORlZBCiGEcHinVq9mw6hR1OzRgwb9+5f8gD//DMOG6Z5fTz5Z8uMVVWq63mqofDkID7H++YXFWS0BMxgMwwwGgzIYDOOtdU4hhBDO79zu3aweOJDwNm1oMWJEyRutbtwIvXvDo4/CqFFmibFIcnJ1s1V/H6hdws3Chd2ySgJmMBhaAC8AO61xPiGEEK4h5dgxlvfrR1Dt2rT95BPcPEpYWRMTAw8+CE2a6OlHaxe95xfdm0xwSy1wk4kqZ2XxV9ZgMPgDs4HngURLn08IIYRrSI+L47/nnqNUcDB3TZyIh69vyQ6YkgJdu4KPD/z2G5QqZZY4i+RILKSkwy01wdvK7S6EVVkjtY4C/lZKLbnZHbOzs0lJSbnsIoQQQlwpOymJZS+8gMHNjbsnT8a7dOmSHTA3F3r0gOho+Ptv62+wDRB3Fk6dhVpVICjA+uc3o507decOcX0WTcAMBsOjQFNgWGHuP2bMGIKCggoulStXtmR4QgghHFBuejrL+/UjOymJu6dMwTcsrGQHVAqefx6WL9cjXxER5gizaFLS4FAMhJeDCo5ddJ+UBA88AOZYC+HMLJaAGQyGysAXwJNKqazCPGbYsGEkJycXXGJjYy0VnhBCCAdkzMlh1cCBJB89yt2TJhFYrVrJD/ruuzBjBkyfDnffXfLjFVV2ji66D/DTo18OLL91WnIyfPyxraOxb5bsA9YMCAW2XLIixR1oZzAYXsnLy8Pd3f2yB3h7e+PtLRuMCiGEuJrJaGTdsGHEb97M3ZMmUdYcI1VTpsD77+ueX48/XvLjFZXJpJMv0HVfDl50//33MHcuzJkDVRw7l7Q4SyZgS4Fbr7htGrAfGOvu7r7LgucWQgjhRJRSbP7gA2IXL6bt+PGE3XZbyQ/69996nuzll2HIkJIfr6iU0tOOaRnQuC54eVo/BjM6dAheeQX69IFevWwdjf2zWAKmlEoFdl96m8FgSAfOKaV2X/tRQgghxNV2fPEFh3/6idvff5/KHTqU/ICbNkHPnnrV4xdf2GaPxVNn4XQC1K0Ggf7WP78Z5eTAY49BeDh89ZWto3EMshWREEIIu7ZnyhT2TplCkyFDqPm//5X8gEeOQJcu0LAh/PADXFEOYxVJqbrlRMVQ3e3ewb39tl75uG4dBDj2Ak6rsWoCppS6y5rnE0II4dgOzJ7NjvHjafDSS9R/+umSHzAhAe67D0qXhj//hJL2DiuOrGzdbDXIH2pUsv75zWzhQvj0U31p1szW0TgOGQETQghhl47Mn8+WyEjq9enDrS+9VPIDZmTo/ghJSXqoppwNRp6MRl107+YGETUcvuj+9Gld89W5MwwcaOtoHIskYEIIIexOzKJFbBw5klo9e9JkyJCS7+9oNMITT+h5suXLoWZNs8RZJErBgeOQkQVN6oGnYxfdm0w6+TIYdBcPB88lrU4SMCGEEHbl5IoVrHnzTaref795NtdWCl57Df74A37/HVq0ME+gRRV9Cs4m6nYT/jaY+jSzzz6DxYv1xRYbBzg6ScCEEELYjTMbNrBq4EAq3nknLT/8EIM5hlXeew8mTNA9v7p2LfnxiiP+PETHQfWKUK6MbWIwo02bYNgwePNNuPdeW0fjmAxKKVud+6YnTklJISgoiOTkZAIDA60RkxBCCBs5u307y557jnJNmnBnVBTuXmbYjHrCBN3nKzJSZwy2kJIGOw7oxKteddu0vDCj1FRo0gTKloXVq8EML5Nj/0CKSUbAhBBC2Fzivn0s79ePMvXr0+7LL82TfP30k+4MOmAADB1a8uMVR/42Q/6+ut+XgydfoPPZ+HhYtMgsyZfLkgRMCCGETSUfPsx/L7xAQJUq3DlhAh4+PiU/6JIl8OSTujvoZ5/ZJvExGmH3YX3uW2o5RZX6zJn6MmuWbdYxOBPH/79BCCGEw0o+epSlffviU64cd0+ejJc5unhu3gwPPwwdOsC0abZJfJSC/cf0iscGtRx+myGAgwfhpZfgqaf0glJRMlIDJoQQwiZSoqNZ2qcPXkFBdJg2jVJly5b8oAcPQps2enhm6VLw8yv5MYvj2EmIidMjX+VK2yYGM8rKgpYtITNT57dm7nbv+POyxSBTkEIIIawuNSaGpc88g2dAAO2nTjVP8nXyJHTsCCEheqNtWyVfZ87p5KtGJadIvgAGDYIDB2DDBtlqyFwkARNCCGFVaSdOsPSZZ/Dw8aHDd9/hY46O9ImJuh27yaSrw4ODS37M4khO081Ww4KhUphtYjCzuXPhm29g8mS9faYwD7usAYuKiiIiIoIWtmqWJ4QQwiLST51i6TPP4OblpZOvkJCSHzQtTW+uHRenu4JWrlzyYxZHVjbsOQwBflCnqlOseDx0CJ5/Xq9leO45W0fjXKQGTAghhFWkx8Wx5OmnMRgM3DN9Or7ly5f8oFlZurnqxo265stWH9zzjLB9v1752KS+UxTdZ2VBq1aQng5btlh06tHxM9VikClIIYQQFpdx5gxLn3kGTCY6zJhhnuQrNxd69YI1a/S0o62SL6Vg3xE9AuYkyRfA4MGwb5/UfVmKJGBCCCEsKuPMGZb27YspN5d7ZszAr0KFkh/UaISnn4YFC/Qej+3alfyYxaEUHI6B8ylwa23wM0MPMzvw008wcaKu/WrUyNbROCdJwIQQQlhMelwcS595BlNuLh2mTcO/UqWSH1Qp3ZBqzhxdId65c8mPWVwnzsCps7rmq2yQ7eIwo8OHdb3Xo4/CCy/YOhrnJQmYEEIIi0g7eZKlffuCUtwzY4b5kq8hQ/SSvOnToUePkh+zuBIS4egJqFwews2wmMAOZGVBz54QFgaTJjnFOgK7JQmYEEIIs0uNiWFp3764eXjQYdo080w7AnzwAXz6KXz1FfTpY55jFkdKGuw7BiFloHpF28VhZm+8AXv3wrp1IGvfLEsSMCGEEGaVcvw4S/v2Lejz5Rtmpn5Y48fDyJEQGak32baVzGy9x6O/D9St7jTDRD//DFFRMGECNGli62icn132ARNCCOGYko8cYUmfPnj6+elWE+ZKvqZO1e3Yhw6FYcPMc8ziyM2D3YfA3V1vM+TuHG+jR47As8/q6cd+/WwdjWtwjv9zhBBC2FzSoUMsfeYZSpUtyz3Tp5unySroYvvnn9eF95GR5jlmcZhMsPcI5OTqFY9O0m4iM1OX0oWGwpQpTjOgZ/dkClIIIUSJJe7bx3/PPYdv+fLc/e23lCpTxjwH/vlnePJJ6N1b133ZKjtQSm8xlJwGDeuAbynbxGEBr7wC+/fD+vVS92VNkoAJIYQokfN79vDfc8/hX7kyd0+ejHfp0uY58Pz5eg+cXr3gu+/AzYaTNkdPQPx5iKgBpZ2nK+nUqfpHO3269PuyNpmCFEIIUWwJO3ey9NlnCahWjfbffmu+5OuPP3RB0v/+BzNm6JorWzlxRl9qVoaQsraLw8y2bYOXX9azu7ZcUOqqZC9IIYQQxRK/eTPLX3qJMnXqcNc33+Dp72+eA//zDzz0EDz4IPz4I3jasNYq/jzsOwqVwnQC5iQSE6F5cyhdWu/kVMq2M6ouWXUmI2BCCCGK7OTKlSx74QWCb72VuyZNMl/ytWiRHvXq0sX2yVdSKuw/BqFloYYZmsjaCZNJj3glJuoSOxsnXy5LasCEEEIUScyiRax5800qtmtHm08+wd3b2zwHXrJEj3x17Ki3GLJl8pWWoXt9BflD3WpOtTRw3Dj480/46y+oXt3W0bguGQETQghRaEd+/ZU1b7xB1c6dafvZZ+ZLvpYt01OO7dvDvHng5WWe4xZHVg7sOgQ+XrrXly2L/81s2TJ45x196dLF1tG4Nrv8vyoqKoqIiAhatGhh61CEEEJcsP/779kwYgQ1H3mEVmPG4GauEaqVK6FrV7jjDvjlFzBXUlccuXmw66Ae8WpQGzxsWPxvZidP6g22774bRo+2dTRCivCFEELckFKK3RMnsisqivp9+9J48GAM5pqSW7MGOnWC22/Xc2I+PuY5bnGYTLDzIKRnQpN64GvDWMwsN1cnXseP69WP5uqRaybOM79bBFIDJoQQ4rqUycTWsWM5MGsWjQYMIOL5582XfK1dC507Q4sWuijJlsmXUnpz7dR0aFjXqZIvgCFDYMMGPdhoZ8mXy5IETAghxDUZc3JYP3w40f/8Q/Phw6nz2GPmO/jKlXD//dCsmU6+fH3Nd+yiUgqOxEJCItxSUxfeO5FZs+CLL/RGAq1a2ToakU8SMCGEEFfJy8hg1aBBnFm/njaffELVzp3Nd/ClS+GBB6B1a/j9d/DzM9+xiyMmDk7GQ+2qUM5MWyjZiW3bLjZaffllW0cjLiUJmBBCiMtkJyWxvH9/kg8f5q5vvqG8OYdNFi3SrSbuvFNvNWTLaUfQidfxU1CtAlRwrrm5hAR4+GG45RaYONGpOmk4BUnAhBBCFEiPi2PZCy+QnZhIh2nTCG7QwHwH/+sv6N5d9/maN8/2HUDjz8HhGKgYBlXCbRuLmeXl6RWP6el6ttfWea64miRgQgghAEg+coRlL7yAwc2Ne2fNIrBaNfMd/Lff9N6OXbvCnDm27fMFcC4J9h+HsGCoWcnphofefhuWL4d//4UqVWwdjbgWu+wDJoQQwroSdu5kyVNP4RkQwL2zZ5s3+Zo3Dx55RE89zp1r++QrORX2HoGyQU7X5R70j/jjj+GTT3TrCWGfJAETQggXd3L5cpb27Utg9ercO2MGvqGh5jv4Dz/oubCePfXXttxeCPQWQ7sOQ4A/RNRwuuRr507o2xcefxwGDLB1NOJGJAETQggXdmjuXFa++irhrVtz95QpeAUFme/gM2ZA79768v334GHjqpfMLN1o1ccbGjjXFkMA58/rovvatWHKFKfLLZ2O1IAJIYQLUiYTO774gr3ffkudJ56g6Vtv4eZuxm13oqLglVd0D4RvvrF9spOdo5MvDw+41bm2GAIwGvWoV1KS3tPclm3VROFIAiaEEC7GmJPDhhEjOP7XXzQZMoR6ffqYr7u9UjBmjN7tedAg+PRT2w/F5Obp5EsBjeqAl42nQS1g5EhdcL9wIVSvbutoRGFIAiaEEC4kJyWFVQMGcHbbNtp8+ql5G6wqBW++qau/33sPhg+3ffKVZ4Rdh3QS1rgelLLxAgAL+OUXiIyEcePg3nttHY0oLEnAhBDCRaTHxbG8Xz8y4+NpP3Uqoc2ame/gRiP06wfffqv3vXntNfMduyQx7T4EGVl65MvXxn3HLGD3bnj6ab3G4Y03bB2NKApJwIQQwgUk7t/P8v79cfPw4N5ZswiqWdN8B8/J0YX2P/8M06frfW9szWSCPUcgNQMa1oEAG293ZAEJCXpHpxo1YOpU2w82iqKRBEwIIZzcqVWrWP366wRUrcpdEybgE2LGLXcyMqBHD72/47x58L//me/YxWUy6T5fyanQoLbTba4NOuft0UN3ul++HPyd7yk6PUnAhBDCSSmlODh7NlvHjqVCu3a0HjcOT3NufJ2crIdgtmzR2wzZQwGSUrD/GJxP0a0mygTaOiKzU0rP8K5dC//9B1Wr2joiURx2mYBFRUURFRWF0Wi0dShCCOGQTLm5bB4zhsNz51L/mWdoNGiQedtMnD0LnTvD0aN6+V3r1uY7dnEpBQeOw9lEuKWm7nTvhCZMgEmTdLld27a2jkYUl0EpZatz3/TEKSkpBAUFkZycTGCg832KEUIIS8hJTmb1669zZtMmWowYQa0ePcx7gthYvaH2+fOweDE0amTe4xeHUnAoGuISoH4NCC1r64gsYulS6NQJXn0VPv/c1tGYjUtWr9nlCJgQQojiSY2OZsXLL5N17hztJ08m7PbbzXuC3bv1yJeHB6xaBXXqmPf4xaEUHInVyVfdak6bfB0+rLfUvOcevdejcGzOtQ+DEEK4sDObNrHoscdQStFxzhzzJ18rV8Idd0C5croAyV6Sr2Mn4WQ81K4C5cvZOiKLSE6GBx+EkBCYM8f2uzqJkpMETAghnMCRX39l2XPPUaZePTr98AOB5q7M/vVXPe3YtCmsWAEVKpj3+MUVEwexp6FmJahgxk3E7Uj+NkOnTsEff0Dp0raOSJiD5NBCCOHATEYjOz7/nH3TplGzRw9aDB+Om6eZt9qZMEHv69izp95g29vbvMcvrug4OH4KqlWASuVtHY3FDB2qtxhasADq1rV1NMJcJAETQggHlZOayto33+TUqlU0ffNN6j71lPn2dAQ9vTdiBHz4IQwcqPd1tPWm2vmiT+nkq2oFfXFSM2bonZ0+/1wPQArnIQmYEEI4oOSjR1n56qtknTvHXRMnUuGOO8x7grw8ePFF+O47XfH9+uv202r90uSrmvMmX+vWwQsvQN++MGCAraMR5iYJmBBCOJiTy5ez9q238AkNpdPcueav90pPh169YNEimDkTnnzSvMcvifzkq5pzj3wdPw4PPQQtWugZYHvJfYX5SAImhBAOQinFnsmT2fnVV1S86y5af/QRnubegyYhAbp21e0m/v7bvua9jp/SCZiTJ19JSdCli95eaP58+ym5E+YlCZgQQjiA3PR01g8fTuzixTR46SVu7d8fg7nrsQ4e1O/8KSl6pWOzZuY9fkm4SPKVm6t7fZ06pacgzbltp7AvkoAJIYSdS42OZtXAgaSdOMEdX35J5Q4dzH+SlSvh4YchNBTWr4fq1c1/juI6flKveKxWEaqG2zoai1EKXnpJb669eDHUq2friIQl2clyFiGEENdy4r//WNirF8bsbDr++KNlkq9Zs3R79caNdYNVe0y+qjt38gV6rcO338KUKXD33baORliaRRMwg8EwzGAwbDIYDKkGgyHeYDD8ZjAYpIuJEELchCkvj+3jx7Py1VcJu/12Os2dS+latcx7EqVg1Cjo3VtfFiyAMmXMe47iUury5KuKcydfv/wCb70Fb78NTz9t62iENVh6CvJOIArYdOFcHwKLDQZDhA03ARdCCLuWde4ca4YMIX7TJhq//jr1n3nGvP29ALKz4bnn9OhXZKTu9mkvS+2U0jVfMa6RfG3cqBea9uoF779v62iEtVg0AVNKdb703waD4RkgHrCjyk4hhLAfCTt2sGrQIFReHu2nTiXsttvMf5Jz53S918aNemPBXr3Mf47iyt/bMfa0SyRf0dF6j8fGjWHaNPvpcyssz9pF+EEXrs9f65vZ2dlkZ2cX/DslJcUaMQkhhM0ppTj4ww9sGzeOsg0a0Pazz/ANCzP/iQ4fhvvvh8RE+O8/aN3a/OcoLqXgSKzeWLtmZahkgedvR5KT9aJTX1/4/Xfw8bF1RMKarJZrG/T4+WfAaqXU7mvdZ8yYMQQFBRVcKleubK3whBDCZnLT01n71ltsiYyk9qOPcs/06ZZJvpYtg5Yt9TDL+vX2l3wdjNbJV+2qTp985ebqrTVPnNDt1kKdcx9xcQMGa9ViGQyGKKAL0FYpdQK46sTXGgGrXLkyycnJBAYGWiVOIYSwpsT9+1n9+utkxsdz2+jRVLv/fsucaOJEeO01uPNO+OknKFvWMucpDqVg/zGIPw91q0H5craOyKKUgv79YepUvcm2JRa2Ohg7KT60LqtMQRoMhq+AB4F2F5Kva/L29sZbWv4KIVyAUorDP/3Elo8+IrB6dTrPm0dgtWrmP1Furk68vvlGX3/6KXjYUQtIkwn2HYNzSVC/BoTaUWJoIZ9+CpMm6ZYTkny5Lov+Fl6YdvwKeBi4Syl1zJLnE0IIR5CTmsrGUaOIWbiQ2o8+StM338TdEh8+ExKgRw/d22vKFL3q0Z6YTLDnCCSmQERNKFfa1hFZ3Jw5MGSIXnT67LO2jkbYkqU/BkUBjwPdgFSDwVD+wu3J0oZCCOGKzu3ezZo33iA7MZG2n31GlU6dLHOiXbv08rr0dF1s37atZc5TXHlG2H0YUtOhQS0oG3Tzxzi45cuhTx944gn48ENbRyNszdIJWP8L18uvuP0ZC59XCCHsilKKA7Nmsf2TTyhdty7tp0zB31ILjX77TTeWqlVL7+lYpYplzlNcObmw6xBkZkPD2hAUYOuILG7XLnjoIbjjDvjuO2k3IaxYhH8NNz1xSkoKQUFBUoQvhHBoWefPs2HkSE4uW0bd3r1pPHgw7l5e5j+RUnpoZcQI6N4dZswAPz/zn6cksnJg10HIzYOGdcDf19YRWdyJE3rxablyestNeTu7ihThCyGEMK+4NWtY9/bbKKORdl99RaX27S1zorQ0XVT0008wejQMH25/wywZWbDzoP66cT3wLWXbeKwgKQnuuw/c3eGffyT5EhdJAiaEEBZgzM5m++efc2DmTMq3bk2ryEh8QkIsc7KDB+F//9Nt1X/5RX9tb1LT9bSjp4ce+fK2wAigncnO1hsOnDgBa9ZAhQq2jkjYE0nAhBDCzJIOH2btkCGkHDtG07feou6TT2Kw1GjU77/DU09BeLjeWqh+fcucpySSUmH3IfD1gVtr6yTMyZlMelPtdevg338hIsLWEQl7Y2fj00II4biUUhyYPZtFPXuijEY6zZ1LvaeeskzyZTTCO+/oyu577rHf5Otckq75CvDTI18ukHwBvPUWzJ0Ls2frwnshruQavwlCCGFhGWfOsGHkSOJWr6bO44/T+PXX8ShloRqnhAR4/HFYuhQ++gjefBMMdljHfOac7nBfrrRusmpvNWkW8sUX8Mkn+rp7d1tHI+yVJGBCCFECSimO//03mz/8EA9vb+6cOJGK7dpZ7oRbtuh39fR0WLzYPlupKwWxp+HYSSgfDHWq2WeCaAE//giDBsEbb+iNB4S4HknAhBCimLLOn2fT6NHELllC1S5daP7223iXLm2ZkymlG0i9/DLceqvuZ2Bv/b1Ax3kkVm+qXSUcqlVwmeRr0SJdjte7N4wda+tohL2TBEwIIYohdulSNo4aBSaTZTvagx7t6t8fZs6E55+HL78ES01vloTRBPuPQkIS1K4KFSy06tMOrV+vF5927qz3eHSR2VZRApKACSFEEeSkpLBlzBiO/fEHFe++m9tGjcKnXDnLnXDPHnjkEd1iYuZM3eHeHuXm6a2F0jLgllousa9jvr17oUsXaNpUt2Hz9LR1RMIRSAImhBCFdGr1ajaMHEleejotIyOp/uCDGCw5vTZjBrz0ElSvDps32+cqR4CsbN3jK+dCd/sgf1tHZDXR0dCxI1SqBH/+CT4+to5IOAq7HCSNiooiIiKCFi1a2DoUIYQgOymJdcOGsfzFFwmqUYP7f/uNGt26WS75ysiAvn11I6mePWHDBvtNvtIyYNt+3fiqST2XSr7OntXJl7c3LFwIlir/E85J9oIUQojrUEoRvWABW8aMwZSXR9M336TGQw9ZdtRr717o1QuOHIEJE3QSZq8SU2DPYfAppRusernO3FtqKrRvD7Gxust9zZq2jsihucYqjSvIFKQQQlxDelwcm95/n1MrVlClUyeaDRtmua2EQK8enDRJ9zCoXl03Vm3QwHLnK6n4c7D/OJQOgIia4OFu64isJjtb9789eBBWrJDkSxSPJGBCCHEJZTJxaM4ctn/+OZ7+/pbdQDtfQgI895zeVqhfP/j0U/D1tew5i0spiImD46cgLBjqVHWpJX9Go14HsXatbjvRuLGtIxKOShIwIYS4IPnIETaMHEnC9u3U6tmTxoMH4xUQYNmT/vefbhyVlQXz5+uhFXtlMsHBaN3hvloF3efLRXp8gX76L76oX6ZffwVL9tsVzk8SMCGEyzPm5LD322/ZM3kyfhUq0GH6dMIsvQgoNxdGjIBx4+Cuu3SLiYoVLXvOksjNhT1HICVdbysUWtbWEVmVUjB4MEydql+qBx+0dUTC0UkCJoRwaafXr2fzhx+SGh1N/b59ubV/f9y9vS170sOH9V6O27ZBZCQMGQLudlxDlZGl20wYjdCorkutdMw3cqTe23HCBPttxSYciyRgQgiXlHn2LFvHjSP6n38IadqUNp98Qpm6dS17UqXg++/hlVcgLEwvn7vtNsues6SSUvTIl5cnNKwPPhZOTu3QuHHwwQf6un9/W0cjnIUkYEIIl2LKy+PgDz+w8+uvcff2puWHH1Ldkj298iUk6H0cf/oJ+vSBr74CS9eXldTpBF3zFeQPt9QED9d7y5g4Ed56S88WDxli62iEM3G93yYhhMs6u3Urm95/n6RDh6jdsyeNBgzAKyjI8if+80+9h2NODvz4Izz6qOXPWRJKwbGTEHsawstBrSoutdIx38yZeiOCgQNh9GhbRyOcjSRgQginl3n2LDu++IKj8+dTtkEDOs2ZQ7A1emylpOh372nT4P779S7N4eGWP29J5Blh31E4nww1KkGlMJda6Zjv1191D9znnoPPPnPJH4GwMEnAhBBOy5iTw4GZM9k9aRJuHh60GDmSmj164GaNgvf//oNnnoHz53Xi1bev/b+LZ2TpzvbZudCgNgRbYXTQDi1cqAcpe/aEb76x/5dNOCZJwIQQTkcpxclly9g6bhzpp05R+7HHuLV/f7ytsVlfRgYMHaprvO66S7dKr1bN8uctqfPJeuTL0wOa1gffUraOyCaWLIGHH4bOnfV6CXtenCocmyRgQginknToEFvHjuX0unWUb92aO7/+mqBataxz8vXr4amn9AaB48fDq6/af+2UUnDyDBw5AWUCIaKGSxbbAyxbpvt7tW8P8+aBp+tsbSlswDV/y4QQTiczIYHdEydyeN48/CtV4s6oKCrceaflVzcCpKfrZXJffAEtWuiie0u3tDCHSzvbVwrTNV8uOt+2ciV07Qp33AG//AKWbgUnhCRgQgiHlpeRwb4ZM9j33XcYPDxoPHgwdR5/HHcvL+sEsGQJvPACxMXBmDG6XbojjCBl5+j+XukZUK+63tfRRa1Zo9dItGwJv/0GpVxz9lVYmQP8lRBCiKuZ8vI4+uuv7IyKIic5mTpPPMEtzz9vnTovgMREeP11vcLxrrtg8WKw1lRnSSWnwd4j+uvG9SDAz7bx2ND69XDffRcHLn18bB2RcBWSgAkhHEp+gf32zz8n5ehRqnXtSsPXXsPfWvsoKqXnqF55RW+gPXmy7lXgCFN3SsGps3AkViddETXA20ojhXZo0ybo1AkaNdLJl6+vrSMSrsQuE7CoqCiioqIwGo22DkUIYUfObt3Kji++IH7zZsJuv53WY8dSNiLCegGcOqW72f/2Gzz0EERFQYUK1jt/SRiNut4r/jxUDNX1Xva+QMCCtm6Fjh3hllvgn3/A3/W2txQ2ZlBK2ercNz1xSkoKQUFBJCcnExgYaI2YhBB26Nzu3ez86iviVq+mdJ06NB48mPC2ba1TYA+6WH3KFL0nTalS8PXX0L27Y4x6wcX+Xlk5ULcahJa1dUQ2tX27XulYp46eOZa3F5tzkF8k87LLETAhhABIPHCAXV9/zYn//iOwRg3afPopVTp2xGDNkZstW/R+NBs36maqH38MZR0ogTmbCAeO6anGpvXBz7WLnHbuhHvugZo1dcNVSb6ErUgCJoSwO8lHjrBrwgRiFi7Ev3JlWo0ZQ9UuXazTwT5fUhIMHw4TJkCDBrBqFbRta73zl5RScPQEnDgD5crokS8P1+4qum2bTr6qVoVFi8Ba6zWEuBZJwIQQdiPl+HF2T5pE9F9/4RMWxm2jR1OjWzfcrNkRUym9C/OQIbqr/aef6oaqjtBaIl9Orl7lmJzm0vs5XmrTJl3zVbu2Tr7KlLF1RMLVOdBfFCGEs0o8cIA9U6YQu2gRpYKDaTZsGDV79LBeL698u3frIvuVK/VmgJ9+6jhF9vmSU2HvUf11o7pQOsC28diBdev01kK33AILFkCQa25xKeyMJGBCCJtJ2LmTPZMmcXL5cvwqVKD5O+9Q4+GHcbd2G/K0NBg9Gj7/XPfyWrIEOnSwbgwlpRTEnIbjJyHIH+q7douJfKtX6z5fjRvr1Y4Bko8KOyEJmBDCqpRSxG/axJ7Jkzm9bh2B1avT8sMPqdali3WnGkGvbpw5E4YN0zVf77+vO9k72j40Obl6I+2kVKgSDtUquPyUI8Dy5Xp7oRYt4K+/wM91+80KOyQJmBDCKkxGIyeXLWPftGkkbN9O6bp1afvZZ1S65x7rFtfnW7MGBg6EzZuhVy8YO1ZXZzua88mw/5hOuBrW0RtqC5Ys0Rtrt2kDv/8uTVaF/ZEETAhhUbnp6Rz97TcOzJxJWmwsIU2bcueECVRo1856fbwuFR2t+3nNnQvNm+s5qjZtrB9HSZlMcPwUxJ7WSVe96uBl5RFEO7Vwoe6T2749/Pqr7O0o7JMkYEIIi8g4c4aDP/zA4Z9+Ijc9nSodO9J63DjKNWxom4DS0vQo1yef6CVw06dD796O2Q0+K1tPOaakQ/WKULm8TDle8Ndfukdup04wb57jzSYL1yEJmBDCrBL37WPf998T/c8/eJQqRc0ePaj7xBP42Wo1YV6eTrZGjoTz5+GNN2DoUMfdeyYhEQ4cB3d3vZF2kIM+DwuYOxeefBIeeADmzAFrL6IVoigkARNClJgpN5cTy5Zx6McfObNxI34VKtBk8GBqdu+Op60SHaXgjz90gf2+ffDYYzBmjGPWeYHey/FwLJxOgHKloU418JQ/4fkmT4Z+/eCJJ+C778Da6zmEKCr57RVCFFtGfDxHfv6Zw/PmkRkfT0jTprT59FMq33MPbrZsXLpmDbz5Jqxdq1ufz5oFTZvaLp6SSkmDfcf0asc6VaF8OZlyvMTHH+uX++WX4csvHXNWWbgeScCEEEWilCJ+40YOzpnDiaVLcffyotqDD1K7Vy/K1K1r2+D27tUjXn/8AU2a6J2W773XtjGVhFIQfQqi4yDADxrWBh+pKM+nlN4tKjJSX7/3nuSlwnFIAiaEKJTMs2c59uefHJ0/n5SjRwmsUYNmQ4dS/cEHbTfNmO/oUf3uO3MmVKkCs2frTvaOPBSSmaVHvVLToWoFqBou2cUlTCa9Q9SECXoE7I03bB2REEUjCZgQ4rpMubmcXLmSo7/+yqlVqzC4u1P5nntoMXw4obfdZps2EpeKiYEPPoBp0yA4WHeyf/FFx176ppSu8zocC96e0KQeBEqh/aVyc6FvX51nT54Mzz9v64iEKDq7TMCioqKIiorCaDTaOhQhXFLSoUMcnT+fY3/+Sfb585S95Raav/02Ve+7Dy972Ejv5Ek97zRlit7Y76OPoH9/x++2mZ0DB6N1c9XwclCzsl7tKApkZem+uf/8Az/+qL8WwhEZlFK2OvdNT5ySkkJQUBDJyckEBkp3ZyEsKev8eWIWLeLob79xfvduvMuUodoDD1Dz4YcpXaeOrcPTTp3S800TJ+pka8gQPQ9l6ynQklIKzpyDI7F62rR2Vb3SUVwmNRW6ddOba//yC9x/v60jEmZis6F0g8HwiFJqni3ObZcjYEII68hNSyN2yRKiFyzg9Lp1AIS3bcsdX3xBhXbtcLeXRkrHj+smqt99Bz4+utB+4EA9+uXoLh31Ci0LtapIe4lrOH9eb6q9f79eW3HHHbaOSDg6g8HQGugDSAImhLC8vKwsTq1YQfQ//3By5UpMOTmENGtG87ffpnLHjpQqW9bWIV60f7/u3TV7tu5eP2oUvPSScyReV4563VJLRr2uIzYWOneG+HhYtsyxO4oIu/IEMNtWJ5cETAgXkJeRQdyaNcQuXcqJ//4jLz2dsrfcQqMBA6jSqRN+4eG2DvFy27frGq+ff4bwcL190PPPg5+frSMzDxn1KrQ9e3Ty5e4Oq1ZBvXq2jkg4A4PB4AHcDwyxVQxO8RufmZBA8uHDpEZHk3X+PDnJyeSkpIBSGNzcwM0NNw8PPP398QoMxCsoiFJly+Jbvjx+4eF4ly1r+9VcQphZVmIip5YvJ3bpUk6vXYsxO5ugWrWo//TTVL3/fgKrVbN1iJdTCpYsgU8/hUWLoHp1+OYb6NPHsVc1Xip/1OtwLLjLqNfNrFkDXbtC5cp6g21b7WYlnFJnYLVSKsNWAThkAqaUImHHDo7/9Ren160j9fhxAAzu7niXLo1XUBBegYEY3NxQJhNKKUy5ueSmppKTkkJuairKZCo4npuXF75hYfiFh+NXsSIBVasSWL06gdWq4V+liv3UwQhxE+mnTulRrqVLObtlC0opQho3puGrr1KpfXsC7HEbnpwcvXHfp5/Czp26geqsWXp5my276ZtbZjYciobEFBn1KoTff9et3G6/HX77DUqXtnVEwsk8AcywZQAOtwryzIYNbP3kExL37sU3PJwK7doRdtttlKlbF/9KlXArxAZgymQiOzGRjNOnST99mozTp8mIiyP99GnST5wg5fhxclNTATC4ueFXsSKB1asTVLMmQbVrU7pOHYJq1MDdWT6VC4dlzM7m7NatnFq9mrjVq0k+fBg3T0/CWrakcocOVLzrLnxCQmwd5rUlJsKkSfDVV3p14/33w+uvw913O1fDUZMJTpzR3ew9PXTiJaNeNzRlit7X8eGHdS5eSpr/Ozur/sIbDAZ/YBdQWymVZ81zXxaHoyRg/r6+bB03joOzZ1OucWMa9OtHeJs2eorR3IEpRda5c6QeP07KsWOkXLhOPnyY9JMnAT3aFlC1KqVr1y5IykrXro1/pUoWiUmIfKnR0TrhWrOGMxs3YszMxCc0lPC2banQti3hbdrYvjP9jRw4AFFRekVjXh707g2DBkFEhK0jM7+UNF3rlZ4JFcOgegXp63UDSukNDfLXWnz5pfy4XESREzCDwdAIeAOoDnwErAHeBbyB8sBopdT26zz2KaC5Uuq1K25vC7wA1AY+ABYA/YF6gCfQAHhDKbXeYDA8DuSvxb0VGKmU+q9Iz8ERErCkxER2jh7Nif/+o9lbb1G7eXMMa9bAkSNw5oxui5yXB15euht2cDCULw+1akGdOhASYrZP1Lnp6SQdOkTywYMkHTqkLwcPkpOcDICHjw9BtWrphOxCUhZUpw6lypQxy/mF68k4c4b4TZs4s2kTZzZsIC02FjcPD0KaNStIuoJq17bvOsa8PPjrL514LVmifyf79dO7J4eF2To688szwrETcOos+PvqDbQDnGQBgYXk5OhNDKZP15sbvP22cw2EihsqTgL2HTpZGgq8BqwEBgB1gEXAJKXUq9d57CJ0wrThktvcgOnothQfA08Bc4FflVLLLtxnEnDvhfvtVkr9euH294CXgRCl1MX6pptwiAKEvVOncmLJEu645x4qjRypEy+DASpW1ImWlxd4ekJ2Npw7py/nz188QFAQ1K4NjRpB8+bQogXceqt+XBF5+vkR0rgxIY0bF9ymlCLz7FmSDh4k+UJCdn7PHo79+SemnBwAfEJCCKpdmzJ168o0prihSxOu+E2bSI2OBiCoVi3CL4xwhd12G56OsCLw7Fn49ltdTB8TAy1b6v0aH3nEeQrrL6UUJCTB4RidhNWspEe+JJO4oeRk6NEDVqzQ/3s8+aStIxL2zGAw1AROKaXyDAZDBaAsEKmUOmkwGFoBacCf13lsGFD10uTrghbANqWUunDMEODv/OTrghT0iNuZ/OTrgjMXYgi58HXhnocjjIBNbdCAZkrRaP9+XZX52GO6C9+NuuNnZOhE7dAhOHhQT3ts2wa7d4PRqJOvhg11MtamDbRtC2YuUDbl5ZEaHa1HyQ4cKBgxSz9xArhkGvOS0bLSdergV7GifY9mCLMx5eWRdOgQ53bs4OyOHSRs305aTAygE67QFi0Ia9GC0ObNKRUcbONoC0kpWLlSJ14//aR7XD32mB7tatbM1tFZTmY2HImBc8kQHKRrvUo5YZJpZrGxuvzvxAmYPx/uusvWEQkbKNIb3oUGqplKqW0Gg2EncF4pdVchHzsAKKuUeveK29sBMUqp4waDIRbYo5TqfMV9FqGnJ2uqS5Ing8HwNdAXCCxKTZlDJGDf16nDY9nZePz2G1wy8lQsmZmwYwds3qwvGzboZo+g1zq3bQvt2kH79nrUzAKJ0KXTmIkXRs0SDx4kNyUFAA8/v4Jk7NJru9iDTxSbUoqM06c5v3cv53bsIGHHDs7t2YMxMxODhwdl6talXKNGhDZv7lgJV75Tp2DGDF3bdfgw1Kyp55T69tVlAc7KaILY0xAbp1dt5hfZy4eom9q2Dbp00YOh//wD9evbOiJhI8X6ZTEYDOWAeOA9pdSoQj5mI9BbKXXgOt+vBRxC13p9esntHkAiME8p1feKxxwEjimlOhUlfruegsxPDqump+OxYoX+g15SPj56GqRly4u3JSTohjOrV+tOf/Pm6ZqVSpV0Itahg76uVKnk5+cG05hnzlw2WpawfTtHf/0VU55OqH1CQgisXp2A6tUL2mQEVq+OX4UKUvhvZ0xGI6nHj5O4bx+J+/dzft8+kvbvJzspCQCf0FDKNWpEw5dfplyjRpSJiMDDEZd65ebqd86pU/W1p6eeS/r2W/1BxpmTEKX0aNeRGMjOhUphUDVcqsYLacEC6NlTN1b9809dTSJEEd2NTt6WF+bOBoOhDnrg6ZrJ1wXtL1xfecwWgP+VtxsMhlvRo2IfFyaGyx5rzyNgJ7ZupXKzZhzo/gh13hwBORdG9rw9wacUBPpBkL8ubjVnApKaqhOx//6DpUt1V27QBf35Cdndd1vlU70xJ0dPYx44QPLRowUrM1OjozFmZwPg7u1d0LssoFo1AmvUILBqVfwrV8YrKEimMy1ImUyknzpF8tGjpBw9SvKRIyQfPkzSwYMYs7IA8A0Pp2z9+pSpX58y9epRpn59fMuXd+zXZdcu3R9gxgy9EKZZM3j2WT3V6AoNmzKydOJ1PgXKBOpRL18HTKBtZNIkPSN9//3w44/Os8GBKLbijoBNQE/9lVZKZRXi/qOBRKXU+Bvc50d0k9bgSwvqDQbDMCASXT8Wc8ntY4BBQLhSKtFgMDyrlJpamPjtegQseeFCAEq3ulP/kSvlrT91ZudCRqbuq2My6U+cZYN03UVwUMmbNwYE6L8M99+v/52QAMuX62Tsv/90QbHBoIv6O3TQlzvuAAss/Xf38tLTkLVrX3a7yWgkIy7usjYZqceOcXbrVjLPni24n6e/P/6VKulL5cr4VaxY8G/f8uXx8PExe8zORplMZJ49S9qJEwWX1OhoUo4eJeXYsYJEy93Hp6BfXJVOnXSyVa8e3s6SkERH63fLH37QCViZMvDEEzrxKmlpgKPIM0JMnO7r5e0Jt9SE4NLOPdJnRkYjDB2qd5Z65RUYP14GDEWJ3A2sL0zydUEv4K6b3OcuYOU1VjPeDRy9NPm64H/AHxeSr1uBQk+V2fUI2NbnX6TZt5NJOnCIoDq1rnEEBWkZehrgXJL+2mDQfxDDgqFsoHlHxvLFxupELH+E7ORJnfTdfvvFhKxly2KtsjSH3LQ0UmNiLksY0mJjSTtxgvRTp1B5F2sEvYKC8A0Lwzc8XF+XL49vWBg+oaGUCg6mVHAw3mXK4OakfyWVUuSlp5N59iyZ8fFknD1L1tmzpJ08SfrJkwU/v/zVrAClypUjoHJlPdJYo4Zu0Fuzph7Vcrap4IQEPSX/ww96it7HB7p1g8cfh06dbPb/uNUpBXFn4fgpXfNVuby+uDvZ621BKSk6X//nH/j8c3j1VclbRYHitKEoD8Sh+32NKsT9W6JrxTre4D71gb3AYKXU55fc7omu/5qrlHr2isecA0YCE4HvgQFKqXOFeg62SMAMBoMhOTn5ql4Z2dnZZF+YVgNY1+NFem74h19/iaHDPYUoQM/OgbOJEH9ej5B5ekC5MhBSFgJ8LfPbrpRebbl8uV5DvWqV7vDt4wOtWsGdd+pLw4Z28VHPlJdH5tmzpJ88ScbZs2SeOUPGmTNkxsfrr+PjC+qU8hnc3PAuXZpSZcviHRxMqbJl8QwIwMvfH8+AAP31hYvHhdu9/P3x8Pe3auKmlMKYmUluZqbeciolhZyUFLLzv05OJvvCdVZCAlkJCWQmJJCXmXnZcTz8/PArXx6/ihXxCw/Hv1Il/CpUwLdCBfzDw/Hw9bXac7KJxES98d6vv+oPGErpqfeePfWocECArSO0rvPJcOwkZGbpLYSqVgBvF0k8zSQ6Wu8sdeIETJsG995r64iEPQkKCgoCUlUREpILjVgXAe2VUnsLcf+vgM1KqetuP3ShEetcoLVSKvqS20OA3cCjV7SlwGAwPAE8ByQA3yillhb6OdgoAQsEkq1+YiGEEELYoyClVIolDnxhBeNh4FalVKolzlEctqoBS01Ovjr/unIELC4ujttuu41HHjnKvHnB9O+vOyTfrMSrRYsWbNq0Sf9DKb357ekE/UnWzQ1Cy0BYiB4Vu/L+hVCk++fkwObNTH7iCV6oUwc2bdKFEOHhepXYXXfpEbKKFQsekpKSQuXKlYmNjS3YA9PscZnx/qa8PHLT0shJTSU3La1g0/OctDTGffghg159FWN2NsacnIJrU/51Tk7Bhul5ubks++8/7rrzTtzd3MBgwM3DAzcPDwzu7vprT8+Cfxs8PfHw9ubbGTN4ZdAg3H188PD1xaNUKbwCA/Xlwsbsl26obumfU1EfY7PX+9gx3Z3+zz91OxY3N/3/ZNeu0LUrLR580O6et6VfC4BO7duzaPI0OH1O151WrwBlS99wBN0ZnrclzjF7Nrz2mq7OmDgxlYYNK7nE876UK73elyrK884fAStSMEXTEdhgT8kX2CgBK8owI8Cnn3py552BDBig2wvNnavrf6/H3d398hc8KAiqVdZTlHEJupbj8Am9ejI8BL9SPkV647vq+DfTuTPfhYXxxrp1kJama2mWLtWXn37SSWLNmvrNr107DE2aABAYGGjRuMx6/7Jlr3nzjo8+4rZXXinU8VNSUngoKIj3JkwoUlwvzJpF8379Cn1/S/+civsYS7/epdzcCNy8WRfh/PMP7Nundznu2FHv//LAA5e9jvb4vC0aU54RTpxmyYef45eZBw3rQ4WQQtWROvTztsA5jEYYNgw+/hiefx6+/hourFVx6ud9I/K8r89SI1+XeAKYbeFzFJldr4LMZzDoJcv16+sdTG67TX9or1fv2vd/+eWXr/0Nby+oVkH36jmXpPdpO3icdZ9/o7cOqRBaqKXk1z1+YR7j7w+dO+sL6G2Tli/XncNXroTp0wlQiljA59lndUH/nXfqJ3uTGraixmXp+xf3MZY+h0s971OnChKuTceO6f+fwsN1LdcHH+jk6zqrd+3xeVskJqMJTsVDzGkwGTmYlkST9q10DakF4yoKa7wW5jpHaqoutv/7b11sP2CA/tOVVdh1ahaIydbnsMbxneF5W4LBYPAD2gJP2ziUq9j1KsgTJ04UDGFWutAE9cgRePBBXcw5Zw7cd18Jo8jM1iNipxMgNw9KB+hEzFadrJOSyFi8mK979WJw8+Z4bNumP06WK6dHyFq31sX9TZvq0Qsnkr/zQXJycpE/ZTkysz7vc+f0YpD8Vbr79ukRnFatLrZWadTILpaf2fz1Npn0NGP0KcjJhfAQ/eHMwgX2Nn/eFnToEDz0kF4oPmfOxU4+4NzP+0bkeRfqeVvsD5LBYHgSaKOU6m+pcxSXXY+AeV/YrNf7kk17a9aEdev0Zq1dusC4cfD66yV4P/HxhhqV9MjY2UT9SXjvEfDy1H+Qw8tZd8VT6dK4d+tGxrvvYhw2DI/cXFi//uII2YgRejslT09o0kS/seZfKle2izfW4vL29ubdd9+97PV2BSV63ikpF5sGL1ummwYrBbVq6WbBI0fqJWd2uBWQzV5vpeDsed1SIjNbr2ysVkE3d7YCZ/3/fMEC3Ye3fHnYuPHqGQpnfd43I8/b5s/7TuA7WwdxLXY9AnajDNpo1LnImDHQu7furGy2nqJpGToRO3Ne/7EOLq1rQUoH2D7Byc3VTTDXrbt4OXpUf69CBd1/rFkzPULWtCmEhto2XmFesbGwdu3FS/4Iaf62We3b68SrShVbR2p/lIKERN3AOT1TN2+uXhH8nbytiIUpBR99BO+8oz8Uz5qly26FKALHHTkoAYdNwPL98INuxF2/PvzyC1SvbsYI8/LgzDldK5aRpevDKoToJq8l7bZvTmfO6FGydev0arZt2yB/lWmlSheTsfzErEIF28YrCicjA3bu1K/t2rX69T1xQn+vZk09Hd2mjU66atWy/YcDe6WU7g0YE6d/j0sH6BGvIBfrZ2YBaWnwzDPw8896sPXddy3T+1o4PZf84+XwCRjoWZf//Q+SknRCll/fbjZKQVKqTsQSEvVfmLCyulbMHj89K6VHxbZuhS1bLl6fP6+/X768nr5s0ABuuUVf6teXDdlsKSlJ/4+8datOoLduhf37dZ2Stze0aHGx/q9VKwgLs3XE9s9kuph4ZWbrnTGqVND7x4oSO3JE13sdPw7ffw8PP2zriIQDkwTMysyWgIFu3v3kk7oOYfRoPRxukU9il7ayyMnVG4JXCIWQMvb90U8piInRb+z5lz17dItq0KMn1apdTMjyk7M6dSQxM6eMDDhwQBfH798Pe/fqhCt/GtnHRxfJN2lyceSyQQPX2fLHHPKL62PjICtHlxBUDddtZ4RZ/P479OkDISH664gIW0ckHJwkYFZm1gQM9N/d99/XCViXLjBzJlhsH2STSe9BeSpej455ekD5cnqKspTNiw4LLy1NJwF79lx+iY29eJ/y5fWUV61aF6/zv75O/y+XZjTq9g/HjsHBgzrZyr9ER+tkGHQ7iPr1dcLVtKlOuurWta/pbUdiNOnVzLGn9QelkDJQJdw+R6kdVF6e/nA7bpwe8Zo2Teq9hFm4ZAKGUspWl5tKTk5WgEpOTi7M3Qv8/bdSpUsrVbOmUjt2FOmhxZOeodShaKVWbVVq+Saldh5UKiFRKZPpug+JiopS1apVU97e3qpp06Zq5cqV173vsmXLFDphveyyb98+CzyZC5KTlVq3TqmZM5V6912lnnxSqZYtlSpXTimdQuhL6dJKNWqkVNeuSvXvr9SHHyr1/fdK/fefUocOKZWeXnDIFStWqK5du6rw8HAFqPnz5980jOXLl6umTZsqb29vVb16dTVx4kSLPeVCS09X6sgRpVau1M/1vfeU6ttXqfbtlapRQykPj4s/Hzc3lVGxotoQGqqi/PzU06CWf/SRUomJ1z28TV5vM4uMjFTNmzdX/v7+KiQkRHXr1k3t37//po8r1uudnaPUsRNKrdmmf//2HlEqLaPkT6IYivO8HeX1jotT6q67lHJ3V+qTTy7/8zZhwgR16623qoCAABUQEKBatmyp/vnnnxsezy5/t4uoqM/bUV7rooqMjFSAGjBgwA3vd4PX3Ja5iM0uTvlR+/77dclT9+56UeDkyXp60mJ8faBWFb2iKv68HhXbfRhKeV1sZeHpWXD3uXPnMnDgQCZMmECbNm2YNGkS9913H3v37qXKDVavHThw4LKRwJCQEMs9p8BA/cNr2fLq7yUn6wKQw4f1dUzMxdV5sbEXa83y+flBaCgNvbwYZzLhExHBD3Fx1PzjD137FBSkzxcYePHroCCOxcVx//338/zzzzNr1izWrFnDSy+9REhICN27dy/5c1RKTwkmJelLYuLVX8fHw+nT+nLmjL5OvWI3i9BQPX1brRo0b37x66pVoUYNli9bxpo1a2jatCnTu3enW926hRqaterrbWYrVqzg5ZdfpkWLFuTl5fHOO+/QsWNH9u7di991prSPHTtWtNc7IwtOnNYLZTDoEehKoVZrJ3EtxXne+ez59V61Sm+mrZTueNKu3eXfr1SpEh999BG1atUCYMaMGXTr1o1t27Zxyy23XHW8Ir/WdqqozzufPb/WRbVp0yYmT55Mw4YNb3g/Z3nNzcmppiCvlJEBL70EM2bAc8/Bl1+asVXFjSgFqem6aD/+QjJSrgyUD4YygdzesiVNmzZl4sSJBQ+pX78+Dz30EGPGjLnqcMuXL+fuu+8mMTGR0habUzWjjAy9Wi82Vics8fFXXY5t3Ehlb288Ltn780pGNzdSgdLly+tCdG9vYs6eJSU7mwZNm958qk4pyM7WLbgzM/V1/iX/39fj7a2TpNBQPQWbfwkLu/h1hQo6yfIt/BSXwWBg/vz5PPTQQ9e9j8O93oVw9uxZQkNDWbFiBe2ufPe+4K233uKPP/5g3759Bbf169ePHTt2sG7dOn2DUpCcphOvc8l66r9imJ76L0LnemspzPO259dbKfjsM3jrLb3gdu5c/b9+YZQtW5aPP/6YZ5999qrvFeq1dlA3et72/FoXR1paGk2bNmXChAl88MEHNG7cmPHjx1/zvjd5zV1yCtL+/mKZka+vrlFo1w5eeUWv5v/pJ112Y1EGAwT660vNSrog+HQC7DqP8vKkyy1NuL3z5S38O3bsyNq1a2942CZNmpCVlUVERATDhw/n7rvvtuSzKD5fX128X6fOde9Sw2Bg/pw5PHT//XpEKTlZNxVNSSn4evy771I7LIwHO3YsSKTy9u1j46JFRFSqhFthPjx4e+sdA0qV0tn3lV/7+emNRUuX1pf8r+1glwGHeb0LIflCW5SyN6gZXLduHR07drzstk6dOjF16lRys7PxTEzVo8upGbolTN1quomqHS9+Kczzzmdvr3dyMvTtC7/+Cm++CR9+WLjyRKPRyLx580hPT6dVq1bXvM8NX+vcXDwvmTFwFIV53vns7bUurpdffpkuXbpwzz338MEHH9zwvjd6zQ0Gg6dSKteSsdojp07AQOdCffvq/SN79tQzRBMnwlNPWSkAT0+oXB4qhUFKOhlHYxj0yGME+PrBjgN62qRcGcLCwjh9+vQ1DxEeHs7kyZNp1qwZ2dnZzJw5kw4dOrB8+fLrfqp2GF5eukv7NTq1Txo9mqe7dOHBt98uuO302rU8u3Ah933yCeHh4daM1Gqc7fVWSjF48GDatm1LgwYNrnu/06dPE3ZFe40qoWG837cf7hv36IUvZQLh1tr62s77nhX2edvj671pk+5qf/YszJ+v203czK5du2jVqhVZWVn4+/szf/58Iq6zPPJar3VYWBh5eXkkJCQ41O92UZ63Pb7WxTVnzhy2bt3Kpk2bCnX/G73mQDkgzuxB2jmnT8DyNWig/6i8+qpePr1sGXz9tRU7LBgMEORPclhparduxo5/l1FLKdh/DNxj6FSjHlur1dBj/le8sdStW5e6desW/LtVq1bExsbyySefONwvbVEZrvhZ5E+ZX3m7M3G21/uVV15h586drF69+qb3NRgM+ncgMQVOnaVpnic1H/wfmUG++NWqpke+HERhn7c9vd4mk95Ae+hQaNwYFi3Si50Lo27dumzfvp2kpCR++eUX+vTpw4oVK66bjDjL73ZRnrc9vdYlERsby4ABA1i8eDGlijBbcL3XnEKUJDkjuxy7j4qKIiIighYtWpj1uH5+8N13umngTz/p3pa7d5v1FDdVrlw5snNz2XU2DhrXgxYNoGIINUuX4+e334fNe3TjyKycGx6nZcuWHDp0yEpR20b58uWvGhWMj4/Hw8ODYDvc29CSHPX1fvXVV/njjz9YtmwZlSpVuuF969esRURAWdi0G3YdgqxstqcnUvXRB/GqX9Ohkq+iPO9rscXrHR+v2/e88QYMHAhr1hQ++QLw8vKiVq1aNG/enDFjxtCoUSO++OKLa97XmX63i/K8r8URf7e3bNlCfHw8zZo1w8PDAw8PD1asWMGXX36Jh4cHRqPxqsfc6DUHzlkncvtilwnYyy+/zN69ews9tFlUvXvrVZIeHjoJmzr1YmsmS/Py8qJZs2b8+++/+gbfUlC9Em1f78+0zavBzxeiT8GGnbD9gG74qodoL7Nt2zaHGqYvjlatWl38OV2wePFimjdv7pA1IiXhaK+3UopXXnmFX3/9lf/++4/q19sjTCk4lwR7DvPrm6PoXO9W3TC1cV1oFsHkP+cT0aCBw7zehX7eN2Ht13vpUt2ObssW3cz6449L3vtXKUX2dRbZOPPv9o2e97U42u82QIcOHdi1axfbt28vuDRv3pwnnniC7du34+7uftVjbvSau2L9F+CcfcAKKyNDqeef1+2aHn9cqaQki5zmKnPmzFGenp5q6tSpau/evWrgwIHKz89PHT9+XCml1LvvDFeTRn+o1Pb9Si3fpHL/26BOLF6hTu3Yo/bs2qWGDh2qAPXLL79YJ2AzSU1NVdu2bVPbtm1TgPrss8/Utm3bVHR0tFJKqaFDh6revXsX3P/o0aPK19dXDRo0SO3du1dNnTpVeXp6qp9//tlWT6FYivq8P//8czV//nx18OBBtXv3bod8vfv376+CgoLU8uXLVVxcXMElI+NCf66MLLXk2+9Vwl//6d5dm3arszv2qAqhoQ79et/0eSv7er1zcpR6+22lDAalOnRQ6tSp4h1n2LBhauXKlerYsWNq586d6u2331Zubm5q8eLFSinn/d0u6vN2ht/t67nzzjsv6wNWxNfc5j25bHFx6QQs348/KhUYqFTVqkqtWmXRUxWIiopSVatWVV5eXqpp06ZqxYoVBd/r06ePuvPOO/U/srLVfzN+ULtn/KTU8k0qdcFK9e+Xk9Tmhf8qlWe0TrBmcr0mhH369FFKXfG8L1i+fLlq0qSJ8vLyUtWqVXPIZo1Ffd5jx45VNWvWVKVKlVJlypRRbdu2VX///bdtgi+maz3f4KAgtfbn35Xaulep5ZtUxuI16rePv1AqJa2gq6ejv97Xet6AmjZtWsF97OX1PnZMqVatdGPVyEiljCX4c9K3b9+Cv2chISGqQ4cOBUmIUs77u13U5+0Mv9vXc2UCVsTX3ObJkC0uTt0HrCiOH9dTk2vXwttvw8iRl/VOtQ8ZWXA2Ec6eh/RMcHfT+9yFlNUbDdvxcnzhoowmPcUYfw7Op+gpx7JBEBYMwUFwjakKYXlz5kD//rrv8Y8/6v3dhbAhx1p5YSaSgF0iLw8++ghGjYJmzWD2bL3loV3KyIT4C8lYRpZ+IwsO0glZ2SDwkDc2YSMmk94f9ex5/YHBaNJ1XWHBen9GL3v7ZOM6EhN1c+o5c3Rn+2++seB+uUIUniRgVmZ3CVi+DRvgiSd0E/cvv4RnnrHzlkPpmfrNLiFJf20wQOkAKFdaJ2TeJaymFeJmjCZITNb/D55Lgjyj3pQ+rCyEBjvUCkZn9e+/+m9ZejpMmKD7fAlhJ+z5HdZiJAG7jtRUGDBAd9J/4AG9n2Rht+Cwqazsi2+CSRf2LAzw04lYcBD4+dh5NikcRp4RzidDQqLeFshk0olWuTJ6pEv+X7MLGRm6r9dXX8E99+i/acXojCGEJbnkHwpJwG7i99/hhRf09OTEibqbvsPIzbvwBpmkr00mPf1TNkh3Ei8TaJf75wk7lpWta7nOJ12s6fL3vZB0ldYb0wu7sXkzPPkkREfDuHHw8stSKirskiRgVuYQCRhAQoIuWP35Z3j0Ud1B38F6BerkKzlNJ2Lnk3XdGECgH5QJ0kX8AX4yYiEup9Tl/9+kZ+rbg/z1qGq5MuDjbdMQxdXy8iAyEt5/X/f3mjUL6tWzdVRCXJdLvvFIAlZISunC1Zdf1vs7f/ut7hrtsLJydM3O+RS97YvRqAv3SwdAUIC+likk16OUHuVKTIWkFP3/h9GoR0rLBl0cPZWRU7u1Z4/e/3bLFnjnHRg+3A5XdAtxOZd8o5EErIhOnYLnntPdop99Fj79VC/ldmhKQUqafrNNToWUdH2bh/vFZEwSMueVnaPrBZNSdOKVfWEbrEA/nWyVLQ0BvvLa27ncXD3N+N57UKMGTJ8Ot99u66iEKBSX/OMiCVgxKKW3Lxo0SCdfEyfqQn2nYTTphCw5Vb8xX5aQ+UOAv35zDvCTdheORik9jZiSpqcWU9Iu7jvq53Mh2Q7U1/LaOozt2/UKx1274K23YMQIKMIeyULYmiRgVuawCVi+mBjo10+Phj36KHzxBYSG2joqCzCZdBKWlKLftFMz9LQU6DftAL+LCZmMktkXo1G/dgUJV/rF1y7AFwL9dVIdFCD9uRxQdrau8xo7FiIi9ArHpk1tHZUQReaSbxqSgJWQUvDDD7plBegk7PHHnTwHUUoX8aemX3xzzy/OdnfTq+L8fXUyln8tS68sz2iEtAydIKdl6Ncnf7GFuzsE+emEK/DCCKZ0oXdoGzboWq9Dh/SI11tvlXwDbSFsxJnfMa9LEjAziY/XSdicOXD//brDdOXKto7KioxG/cafkqbf/NMyITPr4vd9S11Mxnx99L99vJ08U7UQpfTPNj3z8ktmtv6+wQD+PuDvp0e5ZGTSqaSl6a3SvvhC79jx3XfQoIGtoxKiRFzyj5MkYGb2xx+6ZUVKCnz4oV416bIDDUajTgzSMiH9wqhMeqauMQOdEPiWupCMXUjISl24eHu6dsKgFOTk6qQqM1snXPnXGVn6+6BXI/r5XLwE+Omfp4w4OqXffoNXX4Vz52D0aF2H6iELUoXjc8k/9naZgEVFRREVFYXRaOTgwYMOlYABJCfrztOTJkGTJno0rEULW0dlJ/ITi/RMnUhkZOl9LTOz9e35DAYo5aWTsfzEzMtTX7wvXLu7O26Slv9zyM7Rl6yci1/nJ10m08X7e3vpn4OPtx5BzE+4pG7LJcTE6MTrjz/0CPvXX0P16raOSgizcdA/5CVjlwlYPkccAbvUhg26SH/HDj0q9uGHsvHtDRlNuqo4M1snJFn5X1+4GE2X39/N7fKkzMNDr9zzvHB96b/d3XV9mptBP85gKHnyppS+GE16Wx6jUV9f9nWe3pEgJ0/3CcjJ1f/Ozbv6uZTyupholfK+OCro4y0jWi4qL09PNb77LgQG6r1pu3d33M8dQlyHS/4fLQmYheXlQVSUbobo56f7hjl9kb6lGI0XRo0uJDI5OZd8nXsh2bkkAboZdzed2Li5Xfj1v/CiFLw2hotfmxQok76+9OsbMRguJoCenuDloZPF/H97e+qEy9tL30/+pxCX2LgRXnxRf4B7+WX44AMn6DkoxLW55B8/ScCs5ORJXa8xbx60bw8TJkDduraOyokpdckI1IWEzGTSo1Um0xVfq4s1VfmPLfj6wn/yR83yR9DcDGC4cO3urhOo/Ov8r93MMMomXM7ZszBsmC6ub9xYlzJICYNwci75h1ISMCtbuFB/mo2Nhdde08vH5VOtECIvTzd1HjlS//u993TpghTZCxfgkgmYFJZYWefOsHu3rumYOBHq1NFd9QszYyaEcE4rVugGqgMGQI8ecPCgLrqX5EsI5yUJmA34+OhNcg8ehI4d9d6St90Gq1fbOjIhhDWdOKF30bjrLl0junEjTJkCISG2jkwIYWmSgNlQxYowcyasXatLhu64Ax57TC85F0I4r9RUXX5Qpw4sX643zl6zBpo3t3VkQghrkQTMDrRqBevX6z/Cy5dDvXq6yWJGhq0jE0KYU16e7gtYqxZ88olemHPwIPTpI51GhHA18itvJ9zc9B/hgwd1cX5kpP4jPWWK/qMthHBcSsFff0HDhrqwvnNn/bv+4Ye6v5cQwvVIAmZnAgLgo49g/364+2544QX9R/v33y/vjiCEcAxbt0KHDvDAA1C+PGzZAjNmuNhesUKIq0gCZqeqV4fZs/Uf64oV4aGHdI3Y2rW2jkwIURgxMfDUU3rD7NOn9QjY0qV6taMQQkgCZueaNoV//4VFiyA9Hdq0gYcf1iNkQgj7Exenywhq19a/t998Azt3Qpcu0pdXCHGRJGAOomNHPRo2cyZs2wa33KJrxg4ftnVkQgiAhAQYMgRq1tS/p+++C0eO6O2EpJ+XEOJKkoA5EDc3ePJJOHBAb9D77796xeRzz8Hx47aOTgjXlJSkW0pUr65Hu954A44dg7ffBn9/W0cnhLBXkoA5IG9veOUV/en6k0/gzz/1dEe/ftJDTAhrSU3VqxirV4dPP9WrG48d01sIlS5t6+iEEPZO9oJ0AunpelujsWMhJQWefx7efBOqVLF1ZEI4n6QkiIqC8eP179uLL+rNs8PDbR2ZEA7LJasjJQFzImlp8PXX8PHH+o3hySfhrbf0NKUQomTi43XSFRUF2dnw7LP690s+6AhRYi6ZgNnlFGRUVBQRERG0aNHC1qE4FH9/GDoUoqP1aNjixRARAd27w+bNto5OCMcUG6s3ya5WDb76So94HTumEzFJvoQQxSUjYE4sOxtmzdLJ2KFDuhnksGHQvr0shxfiZg4d0r8733+vP9wMGACvvgply9o6MiGcjku+I9nlCJgwD29vPU2ybx/89BOcPw/33AMtW8Kvv4LRaOsIhbAvSsHKlbrXXt268Pffeluw6GjdVkKSLyGEuUgC5gLc3eGRR3QfsUWLwNdXT0vWrg2ffaaLioVwZbm58OOPcNttcOedutXL5Ml6qvGNN/QWYUIIYU6SgLkQg0E3dF22TNeEtW2ra8YqVdJtLQ4etHWEQlhXUpJetFKjBjz+OJQpAwsWwO7dur9eqVK2jlAI4aykBszFxcXp5pHffKNXed13n6516dhR6sSE89q6FSZM0KNeeXnwxBMwaBDcequtIxPCJbnku40kYAKArCyYO1cvs9++XbeuePFFvZmw1L0IZ5CZqWshJ0yAjRv1yO+LL+qRrvLlbR2dEC5NEjArkwTMDikFq1bpJfbz51+sH3vxRWjdWkbFhOM5dEiP8E6bBomJ0KmT7lrfpYvs0SiEnXDJdxZJwMR1xcfrN63Jk+HoUb0B+Asv6FqZcuVsHZ0Q15eRoT9ATJsGS5fqUdy+ffUHiVq1bB2dEOIKkoBZmSRgDsJk0m9ikybB77/r27p0gT599LWXl23jEwL06O2GDTrpmjNH7wbRrp1uxfLII+DjY+sIhRDXIQmYlUkC5oDOntWFy99/r9talC0Ljz2ma8VatJApSmF9sbHwww8wfTrs3w+VK+sPB08/DTVr2jo6IUQhuOQ7hyRgotj27NGJ2KxZcOqULtx/6ik9RVm1qq2jE84sPh5+/ll/GFi9Wjcd/t//4Jln9E4P7u62jlAIUQSSgFmZJGBOwmjUU5QzZui6m8xM3dDykUegRw+9h54QJZWUpP//mjNH//8Gul3Ko49Ct24QFGTT8IQQxScJmFkPbDBUA0YA7YHywClgFvChUioHScCcUmoq/PknzJunG1pmZ+upyfxkrHp1W0coHMm5c/DPP3rrrH/+0R3r27XT097du8tiECGchCRgZj2wwdAZ6AX8CBwGGgBTgJlKqTeQBMzppabqvfTmzdNvnllZ0KyZnip64AFo0EBqxsTVjh7Viz1+/11PLxqNcPvt0KsX9OwJFSvaOkIhhJm55DuBVacgDQbDEKC/UqoGkoC5lLS0i8nYwoWQng5VqkDXrnol5d13yyo1V2Uy6a2x8pOuPXt0TVeHDnpq8YEHIDzc1lEKISxIEjCLn8xg+ADorJRqzjUSsOzsbLKzswv+nZKSQuXKlSUBczLZ2bBiBfz1l56uPH5cJ1/33KOTsXvv1XvzCecVFwdLlsDixfr69Gm9orZrV510dewI/v62jlIIYSWSgFn0RAZDTWAr8LpS6luukYCNGjWK0aNHX/VYScCcl1Kwb59Oxv76C9as0SMi1avrEZB77tGr2kJCbB2pKIn0dFi5Ev79V19279a3N26sE+4uXaBNG+lML4SLkgSsUA8wGEYB797kbi2UUpsveUwFYAWwQin13IWbZQRMXCUpSY+OLV2qR0b27dO3N26sE7G2bfUbdWioLaMUN5OWBuvX66Rr1SpYuxZycnT91r336hGuDh3kdRRCAJKAFfIBBkM54GZrj44rpbIu3L8CsAzYADytlDJduI/UgImbOnkS/vtPJ2PLl0NMjL69Vq2LyVibNroHmRT024ZScOIEbNqkE62VK2HrVl08HxwMd9wBd92lky55nYQQ1+CSfxUsOgVpMBgqopOvLcCTSinjJd+WBEwUWWysnqbMv+zYoacsy5aF5s31KstmzaBpU91/TN7sze/cOZ1s5V82boQzZ/T3KlfWCVe7dvq6Xj1wc7NtvEIIu+eSf6kt2YYif9oxBngKKEi+lFKnkQRMmEFqqp7qWrtWr6TbulV35QcoU0YnYs2aQZMmejPxOnX0Cjtxc0ajbgmxa5e+7NwJ27fr2wBKl9Y93m67TV+3aAEVKtgyYiGEg5IEzKwHNhieBqZd63tKKQOSgAkLOX1aJ2JbtujL1q165Az0aEyNGhARAfXr60tEhB6pCQiwbdy2kpoKhw/DwYNw6JC+7N2r20FkZur7lCsHt94KjRpdTLpq1pQRRiGEWbjkXxLZiki4hPPndUH/3r36Ov/r/Joy0Cstq1bVU5fVql38Ov/aURO0zExdoxUbe/Fy7NjFZOv06Yv3LVsWatfWCemtt+pLw4YQFibJlhDCYlzyr4skYMKlpaXB/v36cvy4vkRH6+uYGL1yL19QkF61d+klJOTi18HBOkm79OLvb77WCkrpdg6pqZdfzp/Xm1OfPXv15eRJXbN1qfxEs3btqy9ly5onViGEKAJJwKxMEjBh10wmPTqUn5CdOKETnfxkJ//rM2cuT9SuVKqUTsZ8fHQy5u6ur6/82mSCvDy932H+JS9PHzs1VSdf1/t1dXPT04QhIZdfKlTQhfH5l0qVdDxCCGFHJAGzMknAhFNQSidICQl6RC1/ZOrSr1NT9V6YRqNOqvKv87/OzdVJlKenTsY8PS9+7eWlR9IuHVW7dJStbFm94EBWGwohHJRLJmDSd1qIEjIYIDBQX4QQQojCkM/MQgghhBBWJgmYEEIIIYSVSQImhBBCCGFlkoAJIYQQQliZJGBCCCGEEFZmyzYUN2UwGAKBZCBIKZVi63iEEEIIIczB3hMwAxAApCp7DlQIIYQQogjsOgETQgghhHBGUgMmhBBCCGFlkoAJIYQQQliZJGBCCCGEEFYmCZgQQgghhJVJAiaEEEIIYWWSgAkhhBBCWJkkYEIIIYQQVvZ/2ly6LORyT5cAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g1 = plot(f(r, 0), (r, 0, 4), legend_label='a = 0', axes_labels=[r'$r/m$', ''])\n", "g2 = plot(f(r, 0.5), (r, 0, 4), color='pink', legend_label='a = 0.5')\n", "g3 = plot(f(r, 0.8), (r, 0, 4), color='red', legend_label='a = 0.8')\n", "g4 = plot(f(r, 0.98), (r, 0, 4), color='brown', legend_label='a = 0.98')\n", "g1 + g2 + g3 + g4" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( r, a \\right) \\ {\\mapsto} \\ {\\left(r - 3\\right)} r - 2 \\, a \\sqrt{r}\n", "\\end{math}" ], "text/plain": [ "(r, a) |--> (r - 3)*r - 2*a*sqrt(r)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(r, a) = r*(r-3) - 2*a*sqrt(r)\n", "f" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g1 = plot(f(r, 0), (r, 0, 6), legend_label='a = 0', axes_labels=[r'$r/m$', ''])\n", "g2 = plot(f(r, 0.5), (r, 0, 6), color='pink', legend_label='a = 0.5')\n", "g3 = plot(f(r, 0.8), (r, 0, 6), color='red', legend_label='a = 0.8')\n", "g4 = plot(f(r, 0.98), (r, 0, 6), color='brown', legend_label='a = 0.98')\n", "g1 + g2 + g3 + g4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Existence of circular orbits: boundaries $r_{\\rm ph}^\\pm$ and $r_{\\rm ph}^*$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 4 \\, \\cos\\left(\\frac{1}{3} \\, \\arccos\\left(-a\\right)\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "a |--> 4*cos(1/3*arccos(-a))^2" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r_min_p(a) = 4*cos(acos(-a)/3)^2\n", "r_min_p" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 4 \\, \\cos\\left(\\frac{1}{3} \\, \\arccos\\left(a\\right)\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "a |--> 4*cos(1/3*arccos(a))^2" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r_min_m(a) = 4*cos(acos(a)/3)^2\n", "r_min_m" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "rp(a) = 1 + sqrt(1 - a^2)\n", "rm(a) = 1 - sqrt(1 - a^2)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(r_min_p(a) - rp(a), (a, 0, 1), \n", " axes_labels=[r'$a/m$', r'$(r_{\\rm ph}^+ - r_+)/m$']) " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}a \\ {\\mapsto}\\ 4 \\, \\cos\\left(\\frac{4}{3} \\, \\pi + \\frac{1}{3} \\, \\arccos\\left(-a\\right)\\right)^{2}\n", "\\end{math}" ], "text/plain": [ "a |--> 4*cos(4/3*pi + 1/3*arccos(-a))^2" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rs(a) = 4*cos(acos(-a)/3 + 4*pi/3)^2\n", "rs" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(rs, (0, 1), axes_labels=[r'$a/m$', r'$r_{\\rm ph}^*/m$']) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Discrepancy between $r_{\\rm ph}^*$ and $r_-$:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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5MzT9u525FkyWicjjIpIDfBJM+6uvvjrEI1JNaeb2aeZ2ad7uSU11ZpbOPBOWL3fuXWqOZr63o46Cfv2gjetHBs3tzLVgsswYM8YYcypwQTDtc3NzQzwi1ZRmbp9mbpfm7Y7UVLjhBrjgAnj//dYvK2nmzbvjDli5EoqL3e/b7cy1YApz3bt393oIMUczt08zt0vz7rjVq+HGG+Gii2DhQggUqWbevNtuc36GYk0mtzPXginMHRIrW1mHEc3cPs3cLs27Yz75xJlZOvdcmD8f9tsv8Hs08+b17OmsyRSKy3JuZ64FU5jLzs72eggxRzO3TzO3S/Nuv3Xr4Lrr4Oc/D25mqYFm3rI77nCWYfjmG3f7dTtzLZjC3A033OD1EGKOZm6fZm6X5t0+n38O11zjrFQd6J6lpjTzlt16K3Tq5Cxm6Sa3M9eCKcwlJiZ6PYSYo5nbp5nbpXm33RdfwNVXO+ssLVkCbV1SSTNv2SGHON80dPuynNuZ68KVHtGtUZRSKjLk5jorePfq5XyjS29Hct/Eic66TMXFza9jFQq6cGWU0eX07dPM7dPM7dK8g1dQ4Mws9egBH3zQ/mJJM2/d9deDMc4q6W7RrVGiRLAzTNXV1XTr1s3ewJRm7gHN3C7NOzjffAOXX+78d1qas/dZe2nmgZ15Jpx1Frz9tjv9BcpcZ5jCXFtX+h4xYkSIR6Sa0szt08zt0rwD27XLua+mqsqZWepIsQSaeTCuv965P6y+3p3+3M5cZ5g8EuwM06ZNmzj++OPtDUxp5h7QzO3SvFtXUeFchvv6a2dm6ZRTOt6nZh5YSgr84heQmQnnnNPx/gJlrjNMUeaTT4KaiFIu0szt08zt0rxbVlUFt9wCOTmwdKk7xRJo5sG45BI44ABnyQY3uJ25FkxhrndH54FVm2nm9mnmdmnezauthTvvhPR0Z1HKc891r2/NPLCuXZ2ZvSVL3OnP7cy1YApznTp18noIMUczt08zt0vz3lt9PTz4ICxa5OxrdsUV7vavmQfn+uvh449h9+6O9+V25lowhbktW7Z4PYSYo5nbp5nbpXn7Mwb+8hdISnIeN97o/jE08+Bcfz3U1TnrXXWU25lrwRTmLrvsMq+HEHM0c/s0c7s0b3+vvAKjR0NCgrOvWSho5sE55hjnkZ7e8b7czlwLpjA3Y8YMr4cQczRz+zRzuzTvH40bB//+NwwcCI88ErrjaObBu+QSdwomtzPXZQU8EuyyArW1tXTu3NnewJRm7gHN3C7N2zFvHtx2Gzz6KIwaBSKhO5ZmHrwxY+Dpp6G0FPbbr/39BMpclxUIc21duHLQoEEhHpFqSjO3TzO3S/OGVavgrrvgt7+FESNCWyyBZt4Wl1wCNTXw6acd68ftzHWGySO6+a5SSnljwwZny5OzznLW/Nl3X69HpBqrrYWf/hReeAGeey50x9EZpiijGzbap5nbp5nbFct5b93qfBPrmGOcS3K2iqVYzrytOneGCy+E1as71o9uvhslgp1h2r59O0cddZS9gSnN3AOauV2xmveuXXDZZVBZ6az1Y3MtyVjNvL1efhnefBO+/bb9l0sDZa4zTFFm+fLlXg8h5mjm9mnmdsVi3pWVcNNNzl/AS5faLZYgNjPviEsugZISyMtrfx9uZ64FU5g7xa2NjFTQNHP7NHO7Yi3vhi1PPv/cWcn7pJPsjyHWMu+oiy5yZpY6sryA25lrwRTmysvLvR5CzNHM7dPM7YqlvI2B/v2dm7vffde5N8YLsZS5G37yE/j5zzt2H5PbmWvBFOZ2u7GhjmoTzdw+zdyuWMr7pZdg4kTnccMN3o0jljJ3y6WXdmyGye3MtWAKc6effrrXQ4g5mrl9mrldsZL32LEwYAAMHgz33eftWGIlczddcgl8+aVzs357uJ25FkyWtXXhyvfffz/EI1JNaeb2aeZ2xULeCxfCn//sbKr7zDNejyY2MnfbpZc6P9esad/73c5clxXwSLDLClRUVHDAAQfYG5jSzD2gmdsV7XmvW+csTHnddTBrFnTq5PWIoj/zUDAGevVy9vh79dW2vz9Q5rqsQJQZPny410OIOZq5fZq5XdGc97ZtzvIBp50GSUnhUSxBdGceKiJw9tnOtxvbw+3MdYbJI7o1ilJKuauszFmYsqwM1q6Fww/3ekSqo557DmbMgC1b3O9bZ5iijC6nb59mbp9mblc05l1TA7ff7mx9snhx+BVL0Zi5DWec4fw/bc8X3nRrlCgR7AxTSUkJPXr0sDcwpZl7QDO3K9ryblhrKTERliyBq67yekR7i7bMbdmwAU4/HT76CK64om3vDZR5zM0wichjIrJZRKpEJFNELg/Qvp+vXZWI5ItI/yavPywiaSLyne/xgYhc0KTNv0XENHkUhuL39+6774aiW9UKzdw+zdyuaMt76FAYP955hGOxBNGXuS0nnQRdu7bvPia3M4/ogklE7gCGAwOBs4E04H0R6dNC+77AYl+7s4HXgJEiclujZlcC04FfABcDW4FlInJkk+6+AHo3eoRkkY2LLrooFN2qVmjm9mnmdkVT3rNmOfe5/Otf8Ic/eD2alkVT5jZ16eLcwN+egsntzCO6YAL+Ckw0xrxljPnSGPMUsA14tIX2/YGtxpinfO3fAhKBvzc0MMbcY4x50xiTZYzJBR7Gyanpv1tqjTGFjR7Fbv/mwNltWdmlmdunmdsVLXl//DHcey/cdVf7vnZuU7Rk7oUzz2xfweR25hFbMIlIV+BcYFmTl5YBl7Twtoubab8UOE9EurTwnv2BLkDTtUZPEJEdvsuBM0TkuADj7SYiBzU8gANba99A7zGzTzO3TzO3Kxry3rQJfvMbOP98mDTJ+Qp6OIuGzL1yxhnOvUy1tW17n9uZR2zBBPQAOgFFTZ4vAnq18J5eLbTv7OuvOYOA/wIfNHpuLXAfcB3ODFQvYLWIHNrKeJ8HShs9tgPk5+czZMgQqqur/3dH/4ABA9ixYwcTJ06krKyMpUuXMmfOHHJychg5ciRlZWV+bXft2sWYMWPIzs5m/vz5LFq0iHXr1jFu3DiKi4v92lZWVhIfH8/GjRuZOXMmK1asYPXq1UyePJlt27b5ta2rqyMuLo4tW7YwdepUVq1aRUpKCjNmzCAvL4+hQ4dSVVXl957CwkImTJhARkYGS5YsYe7cuWzYsIFRo0ZRWlrq13b37t2MHj2a9evXM2/ePBYvXkxmZibjx4+nqKjIr+2ePXuIj48nLy+P5ORkVq5cSXp6OlOmTGHr1q0MHDiQ+vp6BgwYQH19PQMHDmTr1q1MmTKF9PR0Vq5cSXJyMnl5ecTHx7Nnzx6//ouKihg/fjyZmZkUFBQwb9481q9fz+jRo9m9e7df29LSUkaNGsWGDRuYO3cuS5YsISMjgwkTJlBYWOjXtqqqiqFDh5KXl8eMGTNISUlh1apVTJ06lS1bthAXF0ddXZ3fe7Zt28bkyZNZvXo1K1asYObMmWzcuJH4+HgqKyv92hYXFzNu3DjWrVvHokWLmD9/PtnZ2YwZM4Zdu3b5tS0rK2PkyJHk5OQwZ84cli5dSkZGBhMnTmTHjh1+baurqxkyZAibNm1i+vTppKSkkJaWRlJSEgUFBQwaNIja2lq/92zfvp1JkyaxZs0ali9fzqxZs8jNzWXYsGFUVFT4tS0pKSEhIYGsrCwWLlxIfn4+WVlZjB07lp07d/q1LS8vZ/jw4eTk5DB79myWLVvG2rVrSUxM3GvcNTU1DB48mPz8fKZNm0ZqaiqpqalMmzaN/Px8Bg8eTE1NzV5/1hITE1m7di3Lli1j9uzZ5OTkMHz4cMrLy/3a7ty5k7Fjx5KVlcWCBQtYuHAhWVlZJCQkUFJS4te2oqKCYcOGkZuby6xZs1i+fDlr1qxh0qRJbN++3a9tbW0tgwYNoqCggKSkJNLS0khJSWH69Ols2rSp1c+IjIyMNn9GFBQURPRnxLBhb3P99bUYs5N582DoULufEYsXL27zZ0RZWZl+RrTzM6Ky8mOqqmD+/C/b9BmRmZnZ6mdEcnIybWKMicgHcARggIubPP8vILeF93wFPN/kuUt9/fRqpv2zODNLZwQYS3egEPhrK226AQc1ehwJmNLSUtOaN998s9XXlfs0c/s0c7siOe+qKmOuuMKYQw81Ji/P69EEL5Iz91pJiTFgzPTpbXtfoMxLS0uN7+//g0wQdUckzzCVAHXsPZt0GHvPIjUobKF9LbCz8ZMi8nfgn8C1xpjs1gZijPkeWA+c0EqbamNMWcMDKG+tzwa///3vg2mmXKSZ26eZ2xWpeRsDf/yjsyjle+/Bz37m9YiCF6mZh4NDD4Ujj4TsVv8m3pvbmUdswWSM+QHIBK5p8tI1wOoW3vZxM+2vBT41xtQ0PCEizwAvAtcbYz4NNBYR6QacAnwT3OiDN3bsWLe7VAFo5vZp5nZFat7//rez3cnbb/+4MWukiNTMw0V7bvx2O/OIXrjSt6zAVJxvv30MPIJzT9FpxpgtIhIHHGmMuc/Xvi+wARgHTMC5CTwBuMsYM9vX5lngVeBuIL3R4SqMMRW+Nq8DC3CWHDgMeAHoB5xujAlqAXfdGkUppYL39tvwwAPw2mvw/PNej0bZ9txzkJwMBQXu9RlTC1caY5KBp4CXgCzgCuDGRkVLb6BPo/abgRtx1lrKwplFerKhWPJ5DOgKvIszY9Tw+HujNkfhrNW0EZgD/ABcFGyx1Ba6nL59mrl9mrldkZb3hx/Cww/DQw/BP/7h9WjaJ9IyDzcnn+xskVJZGfx7dGuUKBHsDFN5eTkHHhjUCgTKJZq5fZq5XZGU95dfwsUXwwUXwKJFzkKGkSiSMg9HH38Ml1wCWVnO5blgBMo8pmaYYsHEiRO9HkLM0czt08ztipS8i4rgxhvh6KOdFb0jtViCyMk8XJ10kvMzNzf497ideWdXe1Ouu/baa70eQszRzO3TzO2KhLwrK52FKauqnI1XnYmAyBUJmYezQw6Bnj1h48bg3+N25jrDZJmIPC4iOcAnwbT/8ssvQzwi1ZRmbp9mble4511f72x5smEDLFwIfZrdHTSyhHvmkeDkk9s2w+R25lowWWaMGWOMORW4IJj2es3bPs3cPs3crnDP+7nnYO5cmD4dzj3X69G4I9wzjwQnndS2gsntzLVgCnM/ifR56AikmdunmdsVznknJMDrr8Pw4c4luWgRzplHipNPdi7J1dcH197tzLVgCnNffPGF10OIOZq5fZq5XeGa9/vvw+OPwxNPwJNPej0ad4Vr5pHk5JOde9v++9/g2ruduRZMYe7666/3eggxRzO3TzO3Kxzz/vxz+P3v4Ve/gmHDvB6N+8Ix80jT8E25YG/8djtzLZjCXGJiotdDiDmauX2auV3hlvf27U6hdOKJ8M470KmT1yNyX7hlHomOOQb22Qfy84Nr73bmunClR3RrFKWUgvJyuPxy2LXL2VS3d2+vR6TCWd++cMcdMGhQx/vShSujjC6nb59mbp9mble45F1b6/zll5/vrOIdzcVSuGQe6Y4/HjZtCq6tbo0SJYKdYaqpqaFLJC9vG4E0c/s0c7vCIW9jnBu8x4+HxYsh2td1DIfMo8Ejj0BmpvMIJFDmOsMU5tq6cOUbb7wR4hGppjRz+zRzu8Ih7zfegLFjnWUEor1YgvDIPBocd5wzwxTMXI/bmYd8hklEHgSOBEYbY74L6cEiSLAzTPn5+Rx33HH2BqY0cw9o5nZ5nffs2XD77c4ClXFxng3DKq8zjxazZjnfpty509kupTWBMvd8hklEeorI//o1xiQCc4GRIvILt48X7T7++GOvhxBzNHP7NHO7vMx77Vr4v/9z/tIbONCzYVin57g7GuqfYO5jcjtz1womEfmFiJQAhUCZiLwvIg+KyE+MMRuA+4D+bh0vVhx99NFeDyHmaOb2aeZ2eZX35s3w61/DOefA5MnOV8RjhZ7j7jj+eOdnMEsLuJ15Zxf7egUYAxQBpwLXAG8Bo0XkPSAV6OHi8ZRSSkWI776DG2+Egw6C996Dfff1ekQqEh18MPz0p8F/U85NbhZM640xLzd+QkROB+4GbsUpoJ5w8XgxYdu2bV4PIeZo5vZp5nbZzvuHH+C22+Dbb+Hjj6FHDP7TWc9x9xx/fHAzTG5n7mbBtBdjzHrged9DtcPFF1/s9RBijmZun2Zul828jYGHH4b0dPjgA2c171ik57h7+vZ1Lu8G4nbmbl5BThORW1zsTwGzZs3yeggxRzO3TzO3y2beAwbAlCkwaZKzones0nPcPX36QDCTR25n7uqyAiLyAlBojHnLtU6jlC5cGb40c/s0c7ts5T1tmvONuFdegRdfDPnhwpqe4+4ZMcJZkmLPHhBpuV3YLlwpIhcAfwDGicjXIvKWiPyfiBzl1jFi0eDBg70eQszRzO3TzO2ykXdqKjz4IDzwALzwQsgPF/b0HHdPnz5QXQ3Fxa23cztz12aYRCQN+AIoA84ALgEOAAyQD3wIJBljUl05YIQSkceBx3GK1ZN0812lVLTZuBEuvhjOPhvefx+6dvV6RCqaZGbCeefBp5/Cuee2vx8vF67cYIzpb4x51hhzPfBTnKLpBZyC6S4g2cXjRSRjzBhjzKnABcG01w0b7dPM7dPM7Qpl3sXFzvIBvXo5K3prseTQc9w9ffo4P7dubb1d2G6+KyIjjDF/aeX1zsDBxpgSVw4Y4YK9h2nHjh0cccQR9gamNHMPaOZ2hSrvPXvgqqucNXLWroVjj3X9EBFLz3H3GAP77w+DBsFfWqw6Amfu5QzTRhHp19KLxphaLZbabsmSJV4PIeZo5vZp5naFIu/6erj/fsjKggULtFhqSs9x94jA0UcH/qac25m7WTCNBX4rIte42GfMO+2007weQszRzO3TzO0KRd7//Ce8+67zzbgLgrrhILboOe6uPn0CX5JzO3M3C6brgTuBJSKyWESeFpGzXew/JpWWlno9hJijmdunmdvldt4TJsDgwfD663Drra52HTX0HHfX0UcHLpjcztzNlb5fBKYARwKX4RRQRkR24+wj9yEw1xij68O3QXl5uddDiDmauX2auV1u5r10KTz6KDz2GDz9tGvdRh09x93Vp49z7rXG7czdLJjyjDHPNPxCRI4HrgKu9D1uBp4BdMvmNjjllFO8HkLM0czt08ztcivv7Gy4/Xa47jpnMcHWFhGMdXqOu6tPHygsdPYpbOmbmG5n7uYlufEi8raI/EVE+hhjNhljxhtj7jbGHAGcinPJTrXBsmXLvB5CzNHM7dPM7XIj7x074Fe/cjZCTU6GziHdmTTy6TnurqOOcr4t9803LbdxO3O3t0YR4HygqzFmlWsdR5G2LlxZXl7OgQceaGt4Cs3cC5q5XR3Nu6ICrrgCvv3WWT7gyCNdHFyU0nPcXdnZcOaZ8PHHcNFFzbcJlLmXywpgHJ9osdSyti5cOWLEiBCPSDWlmdunmdvVkbzr6uCuuyAvDxYt0mIpWHqOu6t3b+dnazNMbmfephkmEfkdcB8wDXjPGFPl6mhiSLALVyqlVLgwBp58EsaOhYUL4frrvR6RilX19dCtm3Pv3GOPta+PkM4wGWPeBeKAy4Ec3z1L14qIqzNV6ke6nL59mrl9mrld7c17xAgYPRrGjNFiqa30HHfXPvvA4Ye3PsMUNlujiEgnnKUD7gEuBBYA04wxGe4NL3oFO8O0c+dODj30UHsDU5q5BzRzu9qT93vvOWss/e1vMHRoiAYWxfQcd9/55zv3Mb31VvOvB8rc2j1Mxpg6Y8wiY8zdwBlAJvCqiOSIyMsickJ7+24LEXlMRDaLSJWIZIrI5QHa9/O1qxKRfBHp3+T1h0UkTUS+8z0+EJG97jdq63Hba+bMmaHoVrVCM7dPM7errXl/+incfTf89rfOApWq7fQcd1/v3q3PMLmduSuX0owx3xtjphpjrsdZc+k7IElE1orIkyJymBvHaUpE7gCGAwOBs4E04H0R6dNC+77AYl+7s4HXgJEiclujZlcC04FfABcDW4FlInJko37adNyOuPjii93uUgWgmdunmdvVlrwLCuCmm+D002HqVOdSiGo7PcfdF6hgcjtz1099Y8y3xpiRxpgLgf8DDgE+EpElInKviHR38XB/BSYaY94yxnxpjHkK2AY82kL7/sBWY8xTvvZvAYnA3xuN/x5jzJvGmCxjTC7wME5OV3XguO22LdDugsp1mrl9mrldweb93Xdw443QvTvMnw/77RfigUUxPcfdF6hgcjvzkP5bwRiTZ4z5tzHmFOBlnDWaNojIdBG5yXcfVLuISFfgXKDpylTLgEtaeNvFzbRfCpwnIl1aeM/+QBdgVweOi4h0E5GDGh5AUAtyiC6da51mbp9mblcweVdXO5fgiopg8WI4LCTXCWKHnuPu693bWQusrq75193O3NrkqjFmrTHmSeBnOHvO3Ql8LSJjROTCdnTZA+gEFDV5vgjo1cJ7erXQvrOvv+YMAv4LfNCB4wI8D5Q2emwHyM/PZ8iQIVRXV//vjv4BAwawY8cOJk6cSGlpKUuXLmXOnDnk5OQwcuRIysrK/Nru2rWLMWPGkJ2dzfz581m0aBHr1q1j3LhxFBcX+7WtrKwkPj6ejRs3MnPmTFasWMHq1auZPHky27Zt82tbV1dHXFwcW7ZsYerUqaxatYqUlBRmzJhBXl4eQ4cOpaqqyu89hYWFTJgwgYyMDJYsWcLcuXPZsGEDo0aNorS01K/t7t27GT16NOvXr2fevHksXryYzMxMxo8fT1FRkV/bPXv2EB8fT15eHsnJyaxcuZL09HSmTJnC1q1bGThwIPX19QwYMID6+noGDhzI1q1bmTJlCunp6axcuZLk5GTy8vKIj49nz549fv0XFRUxfvx4MjMz2bx5M/PmzWP9+vWMHj2a3bt3+7UtLS1l1KhRbNiwgblz57JkyRIyMjKYMGEChYWFfm2rqqoYOnQoeXl5zJgxg5SUFFatWsXUqVPZsmULcXFx1NXV+b1n27ZtTJ48mdWrV7NixQpmzpzJxo0biY+Pp7Ky0q9tcXEx48aNY926dSxatIj58+eTnZ3NmDFj2LVrl1/bsrIyRo4cSU5ODnPmzGHp0qVkZGQwceJEduzY4de2urqaIUOGsGnTJqZPn05KSgppaWkkJSVRUFDAoEGDqK2t9XvP9u3bmTRpEmvWrGH58uXMmjWL3Nxchg0bRkVFhV/bkpISEhISyMrKYuHChWzatImsrCzGjh3Lzp07/dqWl5czfPhwcnJymD17NsuWLWPt2rUkJibuNe6amhoGDx5Mfn4+06ZNIzU1ldTUVKZNm0Z+fj6DBw+mpqZmrz9riYmJrF27lmXLljF79mxycnIYPnw45eXlfm137tzJ2LFjycrKYsGCBSxcuJCsrCwSEhIoKSnxa1tRUcGwYcPIzc1l1qxZLF++nDVr1jBp0iS2b9/u17a2tpZBgwZRUFBAUlISaWlppKSkMH36dDZt2tTqZ0RGRkabPyM2b97c6mfE66/Hc/vtZaSn1/Hii5+yc6d+RjT+jFi8eHGbPyNKS0v1M6IDnxELFizY6zOid29neYH8/IpmPyM+/fTTVj8jkpOTaRNjjGcPnNmbe4Bx7XjvEYABLm7y/L+A3Bbe8xXwfJPnLvX106uZ9s/izCyd0ZHj+l7vBhzU6HEkYEpLS01rxo4d2+rryn2auX2auV2B8v7Xv4wBY2bMsDSgGKDnuPs++cQ5TzMzm389UOalpaXG9/f5QSaIusPT3X+MMZU4i2BOa8fbS4A69p7VOYy9Z38aFLbQvhbY2fhJEfk78E/gamNMdgePizGmGqhu1H9LTf387ne/C6qdco9mbp9mbldreb/1Fgwc6Hwb7o47LA4qyuk57r5Aq327nXnEft/BGPMDzlIG1zR56RpgdQtv+7iZ9tcCnxpjahqeEJFngBeB640xn7pw3HZLSEhwu0sVgGZun2ZuV0t5L10K/fs7j2eesTyoKKfnuPsOPxxEWi6Y3M7c1c13bfN9vX8qzrffPgYewflW22nGmC0iEgccaYy5z9e+L7ABGAdMwLkJPAG4yxgz29fmWeBV4G4gvdHhKowxFcEcN8ix69YoSqmw8fnncNll0K8fzJsHnT29/qBUcA47DJ54Al58se3v9WzzXRHpKSJXi8gfReRvIvJP3xpMt4nIz906TmPGmGTgKeAlIAu4ArixUdHSG+jTqP1m4EactZaycGaRnmwolnweA7oC7wLfNHo0Xnog0HFdo8vp26eZ26eZ29U07+3b4Ve/ghNPhBkztFgKBT3HQ6N3bygsbP61sNkaBUBEjgMeAm4FTgIE5/6eUpz7dQ7BudkZ33OLgSnGmKUdGHNUCHaGqaKiggMOOMDewJRm7gHN3K7GeZeWwuWXOz/XrPnxvhDlLj3HQ+Pqq+HQQ6G5L7wFytzKDJNvNult4FOcQikBZ22iQ4wxXYwxPYwxRxpj9gMOAI4HHgfKgTdF5HMR6deeY8eaCRMmeD2EmKOZ26eZ29WQd00N3H47bN3qrLWkxVLo6DkeGj16QHFx86+5nXmbJ15F5DogHmf7kOOMMbtba+/7Jtxm3+Mdcb4edjvwhoisAJ4zkXwjVYjdcMMNXg8h5mjm9mnmdt1www0YA3/6E6SkODd7n3aa16OKbnqOh0aPHpCT0/xrbmfephkmEfkV8ARwuTFmYKBiqTm+5Q9mGmPOxVnjaGJb+4gl69ev93oIMUczt08zt2v9+vUMGACTJsHEifCLX3g9ouin53ho9OgBJSXNv+Z25m29JHcK8BtjzHduHNwYMwiYEaqbwsORiDwuIjnAJ8G0P/jgg0M7ILUXzdw+zdyujIxTeOklePVVuPder0cTG/QcD42ePZ2CqbnrVG5n3qaCyRjzujGm3s0BGGOWGWM2uNlnODPGjDHGnApcEEz7Aw8Mass55SLN3D7N3J6VK+GNN07loYfgX//yejSxQ8/x0OjRw7kXr6yZW7bdzjxiF66MFV9++aXXQ4g5mrl9mrkdX3zhbKh78snfMHass+ifskPP8dDo4dsFtrnLcm5n7nnBJCJnej2GcHbNNU0XFFehppnbp5mH3jffwI03wjHHwKxZ0KWL1yOKLXqOh0bPns7P5gomtzO3WjCJSDcROVpE+jQ8gFdsjiHSTJ482eshxBzN3D7NPLQqKuCmm6CuDhYtgtmzJ3k9pJij53hotDbD5Hbm1rZGEZEncZYj6NTkJWOMafpc1NOtUZRSNtTWws03Q1qa8zhT5/RVFKmuhn33db7x+cADbXuvZ1ujBOEU4HBjzD6NH8AMi2OIOLqcvn2auX2aeWgYA48+CsuWwbvv/lgsad72aeah0a0bHHhg8zNMYbU1SpsOJNLfGLPX1sEicqwxpsDKIMJIsDNMtbW1dNaNnazSzO3TzEPjP/+Bf/8b3n4b7rvvx+c1b/s089A5/nhnxfpBg/yfD5R5OM8w7RSRM5p5/lmLY4g4r7/+utdDiDmauX2aufveesspll57zb9YAs3bC5p56LS0eKXbmYdshklEXgUubfwUcBqwE2dPuQanGmNiZkdCEXkcZ1+9fYCTAs0wFRQUcOyxx1oanQLN3AuaubsWLoRbbnG2Phk9eu/lAzRv+zTz0PnVr5xvfc6b5/98oMxtbb77hO+SEiLyYgvNjgJSgbd9j8nAM8AgYIzv8SawsT1jiFRtXbhy1apVIR6Rakozt08zd8/atfD738Ovfw0jRza/1pLmbZ9mHjotbcDrdubtvaBaBvxZRD4DftpCm8XGmFmBOhKR79s5hphwzDHHeD2EmKOZ26eZu+Orr5zlA845B955Bzq18P1jzds+zTx0evaENWv2ft7tzNu6+e5PfAtNfoAzg3QLMFxEzhCRgxu3balYEpF9RKSniPPvnmCKqlhWV1fn9RBijmZun2becUVFcP31zr+258+H/fZrua3mbZ9mHjot3cPkduZtvSR3OvAI8DBwDHAScL/v16cHerPv8l0xUAh8KyJPtfH4Meebb77xeggxRzO3TzPvmPJyZxXvqipYsgQOOaT19pq3fZp56PToAd9956w51pjbmbfpkpwxZhWwSkSOB44E8oB1xpgPAr1XRF4Afgs8D+QDxwEPi0iNMWZMm0ceIy64IKhbnZSLNHP7NPP2q6lxvlKdl+csTBnMVQjN2z7NPHR69HDWHNu1Cw477Mfn3c68vcsKvAqMAhJ8/x2MvsA5xpjxxpgPjDHjgUsIYmYqls2ePdvrIcQczdw+zbx9jIGHH4aVK2Hu3OBX8da87dPMQ+envjupd+/2f97tzG0uXPmoMWZsM88/aIxJtDKIMBLswpXV1dV069bN3sCUZu4Bzbx9XngBBg6EadPg7ruDf5/mbZ9mHjrZ2c4/FtasgQsv/PH5QJmH88KVnUTkJ42fEJEDgP0b/XqUxfFEhKFDh3o9hJijmdunmbfd2LFOsTR0aNuKJdC8vaCZh87BBzs/m84wuZ25zRmmJcCJQEGjp/vi3ARe4fv1ucaYnxDF2rpwpVJKNTVnjnPf0hNPwLBhza+1pFSsKC+Hgw6C6dPhzjuDf184zzAdAQzgx4Us3wb+jbOA5dvAFJybwaNaWxeu1A0b7dPM7dPMg/fhh3DXXU7B9MYb7SuWNG/7NPPQOeAAZ82xpjNMkbz57h3GmOQAbX5vjJlpZUAeC/Yeph07dnDEEUfYG5jSzD2gmQfns8+gXz+46CJn+5OuXdvXj+Ztn2YeWj16wN/+Bs8//+NzgTL3bIbJt3jlCBG5qrnXAxVLvjYxUSy1xfvvv+/1EGKOZm6fZh7Y1187C1OefDLMnt3+Ygk0by9o5qF18MF7zzC5nXl7t0Zpzr+BXwH3AD1c7DemnXHGGV4PIeZo5vZp5q375hu49lrn69OLFsGBB3asP83bPs08tH76U2fxysbcztzNgqkQuA441MU+Y96uXbu8HkLM0czt08xbtns33HAD/PCDc/9Sz54d71Pztk8zD63mZpjcztzNgqka2GiM0fXfXfT997o3sW2auX2aefP27IGbb4atW4NfxTsYmrd9mnloNTfD5Hbmbn5L7j/ACN/mvMolJ598stdDiDmauX2a+d5qa51vw2VkOJfhTjvNvb41b/s089BqbobJ7czdLJguBfoBGSKyUkReEpErRKQDtyaqDz4IuE2fcplmbp9m7s8Y+NOfnEJp9my4+GJ3+9e87dPMQ6u5GSa3M3dtWQERSQOW4GzKeynwc99L1cAa4ENgljEm15UDRrhglxUoKyvThS0t08zt08z9Pf88DBoEU6fC//2f+/1r3vZp5qE1aBC8/jqUlPz4XKDMvVy4cjMQZ4x5zBhzJnAYcCcwGeiFc8lupYvHi0gi8riI5ACfBNN+5MiRIR6Rakozt08z/9GwYc6H/xtvhKZYAs3bC5p5aDVckms8B+R25m7OMJ0B/AX4LzDbGPN5k9cPBw43xmS7csAIF+wMk1IqdiQlwb33wj/+AXFxXo9Gqcjxzjtwzz1QUQHduwf3Hs9mmIwx2caYh3BmlPZv5vUiLZbaTpfTt08zt08zh8WL4Q9/gAcfhNdeC+2xNG/7NPPQaph3KGtU9kTs1ijKX7AzTLt27eKQQw6xNzClmXsg1jNPT4drrnEWp3z3Xejs5oIvzYj1vL2gmYdWaqqzbdDGjXDiic5zgTIP5813VTtMnz7d6yHEHM3cvljO/LPP4MYb4YILnN3WQ10sQWzn7RXNPLQaVr9vPMPkduYRXzCJyGMisllEqkQkU0QuD9C+n69dlYjki0j/Jq+fJiKzRaRARIyIPNVMH//2vdb4Uejybw2Ayy9v9bejQkAzty9WM8/Nheuug5NOggULYL/97Bw3VvP2kmYeWs1dknM784gumETkDmA4MBA4G0gD3heRPi207wss9rU7G3gNGCkitzVqtj+QD/wDZ7uXlnwB9G70OL0jv5eWFBQUhKJb1QrN3L5YzHzLFucy3GGHwfvvd3x/uLaIxby9ppmHVkPBVF7+43NuZ25h8jek/gpMNMa85fv1UyJyHfAo8Hwz7fsDW40xT/l+/aWInAf8HZgNYIzJADIARGRQK8euNcaEZFapsU6dOoX6EKoJzdy+WMu8sBCuvhq6doVly+BQyztwxlre4UAzD63mLsm5nXnIZphE5IJQ9e3rvytwLrCsyUvLgEtaeNvFzbRfCpwnIl3aOIQTRGSH73LgDBE5LsB4u4nIQQ0PIKh/T/bu3buNw1IdpZnbF0uZf/edc3N3ZSV88AEccYT9McRS3uFCMw+tbt2gSxf/gsntzEN5Sa612Rk39AA6AUVNni/CWSizOb1aaN/Z11+w1gL3AdcBD/v6XS0irf078XmgtNFjO0B+fj5Dhgyhurr6f1+BHDBgADt27GDixInMmjWLpUuXMmfOHHJychg5ciRlZWV+bXft2sWYMWPIzs5m/vz5LFq0iHXr1jFu3DiKi4v92lZWVhIfH8/GjRuZOXMmK1asYPXq1UyePJlt27b5ta2rqyMuLo4tW7YwdepUVq1aRUpKCjNmzCAvL4+hQ4dSVVXl957CwkImTJhARkYGS5YsYe7cuWzYsIFRo0ZRWlrq13b37t2MHj2a9evXM2/ePBYvXkxmZibjx4+nqKjIr+2ePXuIj48nLy+P5ORkVq5cSXp6OlOmTGHr1q0MHDiQ+vp6BgwYQH19PQMHDmTr1q1MmTKF9PR0Vq5cSXJyMnl5ecTHx7Nnzx6//ouKihg/fjyZmZkkJiYyb9481q9fz+jRo9m9e7df29LSUkaNGsWGDRuYO3cuS5YsISMjgwkTJlBYWOjXtqqqiqFDh5KXl8eMGTNISUlh1apVTJ06lS1bthAXF0ddXZ3fe7Zt28bkyZNZvXo1K1asYObMmWzcuJH4+HgqKyv92hYXFzNu3DjWrVvHokWLmD9/PtnZ2YwZM4Zdu3b5tS0rK2PkyJHk5OQwZ84cli5dSkZGBhMnTmTHjh1+baurqxkyZAibNm1i+vTppKSkkJaWRlJSEgUFBQwaNIja2lq/92zfvp1JkyaxZs0ali9fzqxZs8jNzWXYsGFUVFT4tS0pKSEhIYGsrCwWLlzIxIkTycrKYuzYsezcudOvbXl5OcOHDycnJ4fZs2ezbNky1q5dS2Ji4l7jrqmpYfDgweTn5zNt2jRSU1NJTU1l2rRp5OfnM3jwYGpqavb6s5aYmMjatWtZtmwZs2fPJicnh+HDh1NeXu7XdufOnYwdO5asrCwWLFjAwoULycrKIiEhgZKSEr+2FRUVDBs2jNzcXGbNmsXy5ctZufITzj//W7Zvr+O22xLo29dpW1tby6BBgygoKCApKYm0tDRSUlKYPn06mzZtavUzIiMjo82fEYmJifoZ0YHPiMWLF7f5M2LWrFn6GdGBz4gFCxa0+hkxYsRwunevZfXqDf/7jBg+fHirnxHJycm0RciWFRCRD40xvwhJ507/R+AsknmJMebjRs//C7jXGLPXrnsi8hUwyRgT1+i5S4FVQO+ml9hEpAAYbowZHmAs3YFNwBBjzBsttOkGdGv01IHA9kDLChQXF9OzZ8/WDq9cppnbFwuZV1XBTTfBJ5/AypVw3nnejSUW8g43mnnoHXcc3Hnnj+uYBco8nJYVCPUCTyVAHXvPJh3G3rNIDQpbaF8L7GzvQIwx3wPrgRNaaVNtjClreADlLbVtbNy4ce0dlmonzdy+aM+8psb5IE9Ph4ULvS2WIPrzDkeaeegdeKD/JTm3Mw/lDNNKY8wvQ9L5j8dYC2QaYx5r9FwO8J4xZq+bvkVkMPBrY8ypjZ4bC5xljNlrP/A2zDB1w5lhGm+MeSXIsevWKErFgPp6uP9+mDED3nvPWXNJKeW+yy+Hvn1hypTg2ofTDJMNbwB/FJEHReQUERkG9AESAEQkTkQaR5cAHCMib/jaPwg8BLze0EBEuorIWSJyFtAVONL36581avO6bz2nviJyIfAucBDwttu/QV1O3z7N3L5ozdwYeOIJmDbN2ScuXIqlaM07nGnmoXfQQRG6NYqNGSbfcR4DnsVZC2kD8LQxJtX32mTgWGPMlY3a9wOGAacBO4DBxpiERq8fC2xu5lAfNfQjIjOAK3BuFC8G1gAvGmNy2jDuoGaYKisr2X//vbbmUyGkmdsXjZkbA//8JwwaBBMmwB//6PWIfhSNeYc7zTz07rwTiothxQrn14Eyj7UZJowxbxpjjjXGdDPGnNtQLPlee6BxseR77iNjzDm+9n0bF0u+1wuMMdLM48pGbe40xhxhjOlqjDnSGHNbW4qlthg7dmwoulWt0Mzti8bMX33VKZbi48OrWILozDvcaeah13SGye3MI75ginY33XST10OIOZq5fdGW+dCh8PLLMHAg/PWvXo9mb9GWdyTQzEOvacHkduZaMIW5zz//3OshxBzN3L5oynzUKHj2WXjhBeeSXDiKprwjhWYeek2/Jed25lowWSYij/u+yfdJMO0Ptb1ngtLMPRAtmY8fD08+CX//O7wS1PdlvREteUcSzTz0uneH77//8dduZ64Fk2XGmDG+ZQ2C2jpmP1vbl6v/0czti4bMp06F/v3hz3+GIUNAxOsRtSwa8o40mnnode/ubDnU8F02tzPXginMffXVV14PIeZo5vZFeuYzZ8IDD8BDD8GIEeFdLEHk5x2JNPPQ694d6urghx+cX7udeSgLph9C2HfMuOqqq7weQszRzO2L5Mzfew/uvtt5JCTAPhHwz9BIzjtSaeah17CCQGWl89PtzEP5R/t3Iew7Zrz9tutrYaoANHP7IjXz99+H22+H3/4WJk2CTp28HlFwIjXvSKaZh1737s7PhvuY3M48ZAtXqtbp1ihKRbaVK+FXv4Jrr4V334UuXbwekVKxLTUV+vWD3Fw46aTA7WNu4cpop8vp26eZ2xdpmaekwK9/7Xw4z5wZecVSpOUdDTTz0Gt6SS5itkZRrQt2hqmuro5OkTLPHyU0c/siKfOPPnL2hLv0Uuf+pUj88lMk5R0tNPPQ+/JLOPVUSEuDyy4LnLnOMEWZIUOGeD2EmKOZ2xcpmTcUS5dcErnFEkRO3tFEMw+9pjNMbmeuBVOYu/vuu70eQszRzO2LhMxTU51i6eKLI7tYgsjIO9po5qHX9KZvtzPXgsmytq70nZqaGriRcpVmbl+4Z56W5hRLF10E8+f/+C/ZSBXueUcjzTz0GgqmhhkmtzPXgsmytq703bdv3xCPSDWlmdsXzpmnpcENN8CFF8KCBZFfLEF45x2tNPPQ23dfZ9HYhhkmtzPXginM1dbWej2EmKOZ2xeuma9a5RRLF1wQPcUShG/e0UwzDz0R589oQ8HkduZaMIW5wsJCr4cQczRz+8Ix8/R0p1g6//zoKpYgPPOOdpq5Hfvv/+MlObcz14IpzJ177rleDyHmaOb2hVvm6elw/fVw3nmwcOGP90ZEi3DLOxZo5nZ07/7jDJPbmVstmETkCZvHiwbz5s3zeggxRzO3L5wybyiWzj03OoslCK+8Y4Vmbkf37j/OMLmdudWFK0Uk0RjzoLUDhrFgF66sqqpi3333tTcwpZl7IFwyT0mBm25yZpYWLYrOYgnCJ+9YopnbccEFcOaZMGFC4Mx14coo8/rrr3s9hJijmdsXDpkvX/7jopSLF0dvsQThkXes0cztaDzD5HbmOsPkEd18V6nwsXgx/Pa3cNVVMHu28/VkpVTkuekm6NwZgrkapzNMYa6tC1fqho32aeb2eZn5vHlwyy3ON+LmzImNYknPcfs0czsaLysQ0Zvv6gzTj4KdYSosLKRXr172BqY0cw94lfnMmXDPPc7sUlISdOlifQie0HPcPs3cjj/8Ab76yvnyRqDMdYYpyixYsMDrIcQczdw+LzJPSoK77oI774Rp02KnWAI9x72gmdvReIbJ7cy1YApzZ511ltdDiDmauX22M09MhPvugwcegMmTnXseYome4/Zp5nY0vunb7cxtF0xi+XgRb+fOnV4PIeZo5vbZzDwhAR56CPr3d7563KmTtUOHDT3H7dPM7Wi8cKXbmdsumHS75jbas2eP10OIOZq5fbYyHz4cHn0U/vIXGDMG9onROXY9x+3TzO3Yd1+ornb+2+3MrX5cGGMm2TxeNDjhhBO8HkLM0cztC3XmxsArr8DTT8Nzz8GwYc5GnbFKz3H7NHM7unWDqirnv93OPEb/fRU5PvzwQ6+HEHM0c/tCmbkx8Pe/w8svw2uvwaBBsV0sgZ7jXtDM7dh33x8LJrczt7qsgPpRsMsKlJaWNnztUVmimdsXqszr6px7ld56C0aPhscfd/0QEUnPcfs0czsmT3aWFqipge+/bz1zXVYgzLV14cpRo0aFeESqKc3cvlBk/sMPzhpLkybBlClaLDWm57h9mrkdDQvPVle7n7lrM0wicgbwEDDfGLPClU6jmG6NolTo7NkDv/sdfPABzJgBt97q9YiUUjbMnessRFtSAoce2npbL2eY/g30B5Jd7DPm6XL69mnm9rmZeVmZs81JSgosXKjFUnP0HLdPM7ejYYapqiqMt0YRkTeBmcChxpjZrnQaxYKdYdq9ezcHH3ywtXEpzdwLbmVeUuIUS3l5zoa6l1zS8bFFIz3H7dPM7fjwQ/jlL2HTJjjkkNYz93KGqRrYqMWSu5KSkrweQszRzO1zI/MtW+Cyy5yfKSlaLLVGz3H7NHM7Gs8wuZ25mwXTf4ARInKmi30GJCKPichmEakSkUwRuTxA+36+dlUiki8i/Zu8fpqIzBaRAhExIvKUG8dtr379+oWiW9UKzdy+jmb+xRdw6aXOjd7p6aC7ULROz3H7NHM7unVzflZVuZ+5mwXTpUA/IENEVorISyJyhYh0dfEYfkTkDmA4MBA4G0gD3heRPi207wss9rU7G3gNGCkitzVqtj+QD/wDKHTjuB2xadMmt7tUAWjm9nUk8/R0Z2apRw/nv3V9wMD0HLdPM7ej8QyT25m7WTD9AxgJvAUcCrwMfAjs9hVQL4rIyS4eD+CvwERjzFvGmC+NMU8B24BHW2jfH9hqjHnK1/4tIBH4e0MDY0yGMeYZY8wMnMuMbhy33bp2DVm9qVqgmdvX3swXLICrr4Yzz4SPPoLevV0eWJTSc9w+zdyOxssKuJ25mwXTZiDOGPOYMeZM4DDgTmAy0Avnkt1Ktw7mm7k6F1jW5KVlQEt3L1zcTPulwHki0iWEx223ww8/3O0uVQCauX3tyXzSJOcbcDfeCEuWgK4JGDw9x+3TzO1ofEnO7czdLJheByaIyCsicqYxZqcxZpavgDoV6A1c7+LxegCdgKImzxfhFGjN6dVC+86+/kJ1XESkm4gc1PAADgzmYJmZmUEOS7lFM7evLZkb42xv8uCD8NBDMHPmj/+qVMHRc9w+zdyOxpfk3M7ctYLJGJNtjHkIZ0Zp/2ZeLzLGZLt1vMZdN/m1NPNcoPbNPe/2cZ8HShs9tgPk5+czZMgQqqur/7dmxIABA9ixYwcTJ06kT58+LF26lDlz5pCTk8PIkSMpKyvza7tr1y7GjBlDdnY28+fPZ9GiRaxbt45x48ZRXFzs17ayspL4+Hg2btzIzJkzWbFiBatXr2by5Mls27bNr21dXR1xcXFs2bKFqVOnsmrVKlJSUpgxYwZ5eXkMHTqUqqoqv/cUFhYyYcIEMjIyWLJkCXPnzmXDhg2MGjWK0tJSv7a7d+9m9OjRrF+/nnnz5rF48WIyMzMZP348RUVFfm337NlDfHw8eXl5JCcns3LlStLT05kyZQpbt25l4MCB1NfXM2DAAOrr6xk4cCBbt25lypQppKens3LlSpKTk8nLyyM+Pp49e/b49V9UVMT48ePJzMyke/fuzJs3j/Xr1zN69Gh2797t17a0tJRRo0axYcMG5s6dy5IlS8jIyGDChAkUFhb6ta2qqmLo0KHk5eUxY8YMUlJSWLVqFVOnTmXLli3ExcVRV1fn955t27YxefJkVq9ezYoVK5g5cyYbN24kPj6eyspKv7bFxcWMGzeOdevWsWjRIubPn092djZjxoxh165dfm3LysoYOXIkOTk5zJkzh6VLl5KRkcHEiRPZsWOHX9vq6mqGDBnCpk2bmD59OikpKaSlpZGUlERBQQGDBg2itrbW7z3bt29n0qRJrFmzhuXLlzNr1ixyc3MZNmwYFRUVfm1LSkpISEggKyuLhQsXst9++5GVlcXYsWPZuXOnX9vy8nKGDx9OTk4Os2bN5rbbtvD88/DrX3/GSy/tIC7ux7Y1NTUMHjyY/Px8pk2bRmpqKqmpqUybNo38/HwGDx5MTU3NXn/WEhMTWbt2LcuWLWP27Nnk5OQwfPhwysvL/dru3LmTsWPHkpWVxYIFC1i4cCFZWVkkJCRQUlLi17aiooJhw4aRm5vLrFmzWL58OWvWrGHSpEls377dr21tbS2DBg2ioKCApKQk0tLSSElJYfr06WzatKnVz4iMjIw2f0bsv//++hnRgc+IxYsXt/kzok+fPvoZ0YHPiAULFgT1GbFkyTwANmz4mu+//36vcTf+jEhObuOykcaYoB/A4UD3trwnyH5Pasd7ugK1wK1Nnh8BfNTCe1KBEU2euxWoAbo0074AeKqjx/W93g04qNHjSMCUlpaa1rz66qutvq7cp5nbF0zm1dXG3H23MSLGjB5tYVBRTM9x+zRzO2pqjAFjJk0KnHlpaanBmeg4yARRd7Rp4UoR6QmM9hUR37StNGuxz3uBi4wxbd7pSUTWApnGmMcaPZcDvGeMeb6Z9oOBXxvnEmHDc2OBs4wxFzfTvgAYbowZ3pHjtjB23RpFqSCVlztbnXz4ISQlwe9/7/WIlFLhqnNnZ7Pt/v1bbxfShSuNMcXAc8BMEXlQRNp9SU9EjhGRicAvgSfb2c0bwB99YzlFRIYBfYAE3zHiRGRKo/YJwDEi8oav/YM4+9+93mhcXUXkLBE5C2c26Ujfr38W7HHdpMvp26eZ29da5v/9L1x+OaxZA++/r8WSG/Qct08zt2fffcNoaxQROQCnaLgSmISztlG2CdCZb1blMuAu4DrgBWPM+DYPwL/Px4BncW4q3wA8bYxJ9b02GTjWGHNlo/b9gGHAacAOYLAxJqHR68fifOOvqY+a9NPicYMcd1AzTHv27GG//fYLtlvlAs3cvpYyX7/e+RYcOFudnH665YFFKT3H7dPM7enRA555Bp58svXMrWyNYoypMMY8AtwBnA58DJSKyAoRmSIiI0XkVREZLCITfCtnrwN24qzTVACc2tFiyTeWN40xxxpjuhljzm1ctBhjHmhc5Pie+8gYc46vfd/GxZLv9QJjjDTzaNpPi8d105tvvhmKblUrNHP7msv8gw+cBSkPPdSZXdJiyT16jtunmdvTMMPkduadO/JmY8xnwN0iciBwDc46R6fgFFEHAHXAbpwC6V2cS2/pgWai1I9+85vfeD2EmKOZ29c088mT4eGHnUUpZ86EA4NahEMFS89x+zRze7p1cwqmu+92N3NXlhUwxpQbY+YYZ4Xsm4wxZxtjTjDGnGyMucgYc6cx5jVjzCotltpm3bp1Xg8h5mjm9jVkbgz85z/whz/AAw/A/PlaLIWCnuP2aeb2NBRMbmfeoRkmFXo9e/b0eggxRzO3r2fPnvzwA/zpT87s0sCB8PzzIBLwraod9By3TzO3p2tXqKlxP3MtmCwTkceBxwlydq9bwzrvyhrN3L6amv258UZITYVp0+Duu70eUXTTc9w+zdyeLl2cgsntzN3cGkUFwRgzxrcO1AXBtNcdru3TzO3asgX++MeTyMyEZcu0WLJBz3H7NHN7GmaY3M5cC6Ywd+WVV3o9hJijmdvz8cdwwQUAB7J6NWj0dug5bp9mbk+XLvDDD+5nrgVTmJs6darXQ4g5mrkdSUlOgXTSSXDvvaM45RSvRxQ79By3TzO3p+GSnNuZt2vhStVxwS5cWV9fzz77aF1rk2YeWvX18MILEBfnfBtu7Fjo0kUzt0nPcfs0c3t+9Svnstzs2a1nbmXhSmXPa6+95vUQYo5mHjoVFXDbbTBoEAwdChMnOl8B1szt0rzt08ztaZhhcjtznWHyiM4whS/NPDS2bYPf/Aa+/hqmT4ebbvrxNc3cLs3bPs3cnt//HnbvhiVLdIYppsTFxXk9hJijmbtvzRo4/3z47jtYvdq/WALN3DbN2z7N3J6GGSa3M9eCKczde++9Xg8h5mjm7nrnHefm7uOPh08+aX5POM3cLs3bPs3cnoZvybmduRZMlonI4yKSA3wSTPuUlJTQDkjtRTN3R12ds1r3PffAHXfAypVw2GHNt9XM7dK87dPM7WlYh8ntzLVgsqytC1cef/zxIR6Rakoz77jvvnMuuw0Z4jwmT3Zu7m6JZm6X5m2fZm5PwwyT25nr1ihhrrq62ushxBzNvGO++AJuvhl27YIlS+CaawK/RzO3S/O2TzO3p2GGye3MdYYpzBUXF3s9hJijmbffnDlw4YWw//7w6afBFUugmdumedunmdvTcNO325lrwRTmzjnnHK+HEHM087ZrWIzyttvgxhudLU+OOy7492vmdmne9mnm9nTt6lyScztzLZjC3Pz5870eQszRzNvmu++c9ZVee81ZkDI5Gbp3b1sfmrldmrd9mrk9DTNMbmeuC1d6JNiFK/fs2cN+++1nb2BKM2+Dzz5zZpV273aWD7j++vb1o5nbpXnbp5nb89prMGwYbN3aeua6cGWUiY+P93oIMUczD87EiXDxxXDIIbBuXfuLJdDMbdO87dPM7Wm46dvtzHWGySPBzjApFW727IE//xkSE+GRR2DECNh3X69HpZRSjhEjnDXgKitbb6czTGGurQtXDhgwIMQjUk1p5i3Lz4dLLnEuv02aBOPGuVMsaeZ2ad72aeb2NMwwuZ25zjB5JNgZpqKiIg4//HB7A1OaeQsWLID77oNDD4V334WzznKvb83cLs3bPs3cnrfegocfhm++KaJXr5Yz1xmmKPPee+95PYSYo5n7q611prd/8xu44gpnfSU3iyXQzG3TvO3TzO3p0sX5OWfOAlf71ZW+w9y5557r9RBijmb+o61b4a67YO1aZ8mAZ56BfULwzyzN3C7N2z7N3J6uXZ2fp5/ubuZaMIW5oqIir4cQczRzx7x58OCDcOCBkJrq3LsUKpq5XZq3fZq5PZ06OT8LC3Wl75jyww8/eD2EmBPrmVdXw5NPwq23Qr9+zlpLoSyWQDO3TfO2TzO3p7NvKqiqqsbdfl3tTblOd7i2L5Yzz8uDO+5wNtAdNQoefxxEQn/cWM7cC5q3fZq5PQ0zTEcf3dfVfnWGKcx99NFHXg8h5sRq5u+8A+ecAxUVsGaNs9aSjWIJYjdzr2je9mnm9jQUTOnpa1ztV5cV8Eiwywrs3r2bgw8+2Nq4VOxlXlEBf/mLsxDlPffA2LHOfUs2xVrmXtO87dPM7VmyBG64ATZsKOW0037SYjtdViDKjB492ushxJxYynzNGjj7bJgxwymYpk61XyxBbGUeDjRv+zRzexpmmBITp7jar84wWSYijwOP4xSrJ+nWKMoLtbUwYIDzOO88p1A64QSvR6WUUh23ciVcdRV8/TW0duuYzjCFOWPMGGPMqcAFwbTX5fTti/bM8/LgssucYunFF2HVKu+LpWjPPNxo3vZp5vY0fEtu1Kg3Xe1XZ5g8Euw9TKWlpQ0VsLIkWjM3xtky4Kmn4IgjICkJLrzQ61E5ojXzcKV526eZ25Oe7vyjcM2aci68sOV7DHSGKcpMmeLuNVgVWDRmXlwMt9wCjzzi3Nj92WfhUyxBdGYezjRv+zRzexruYZo3T7dGiSm/+MUvvB5CzIm2zBctgocegro6Z/Xum2/2ekR7i7bMw53mbZ9mbk/DJblzzw3qzpegRfwMk4g8JiKbRaRKRDJF5PIA7fv52lWJSL6I9G+mzW0ikiMi1b6ftzZ5/d8iYpo8Ct3+vQHk5eWFolvVimjJ/Lvv4IEH4Kab4NxzYf368CyWIHoyjxSat32auT0NM0ybN29ztd+ILphE5A5gODAQOBtIA94XkT4ttO8LLPa1Oxt4DRgpIrc1anMxkAxMBc70/ZwpIk0vYHwB9G70ON2131gj++23Xyi6Va2IhswXLIDTTnNmlBITYeFC6NXL61G1LBoyjySat32auT0NBVOXLvu62m9EF0zAX4GJxpi3jDFfGmOeArYBj7bQvj+w1RjzlK/9W0Ai8PdGbZ4Clhtj4owxucaYOGCF7/nGao0xhY0e7u7y53PooYeGolvVikjOfNcuuO8++M1vnPWVNmyAP/zB3ord7RXJmUcizds+zdyehktyBx54sKv9RmzBJCJdgXOBZU1eWga0tFXoxc20XwqcJyJdArRp2ucJIrLDdzlwhogcF2C83UTkoIYHENTygFlZWcE0Uy6K1Mznz3dmlRYsgLffdmaVjjrK61EFJ1Izj1Sat32auT0NM0y5uV+72m/EFkxAD6ATUNTk+SKgpYsPvVpo39nXX2ttGve5FrgPuA542PfaahFp7Z8QzwOljR7bAfLz8xkyZAjV1dX/W6djwIAB7Nixg4kTJ3L00UezdOlS5syZQ05ODiNHjqSsrMyv7a5duxgzZgzZ2dnMnz+fRYsWsW7dOsaNG0dxcbFf28rKSuLj49m4cSMzZ85kxYoVrF69msmTJ7Nt2za/tnV1dcTFxbFlyxamTp3KqlWrSElJYcaMGeTl5TF06FCqqqr83lNYWMiECRPIyMhgyZIlzJ07lw0bNjBq1ChKS0v92u7evZvRo0ezfv165s2bx+LFi8nMzGT8+PEUFRX5td2zZw/x8fHk5eWRnJzMypUrSU9PZ8qUKWzdupWBAwdSX1/PgAEDqK+vZ+DAgWzdupUpU6aQnp7OypUrSU5OJi8vj/j4ePbs2ePXf1FREePHjyczM5P999+fefPmsX79ekaPHs3u3bv92paWljJq1Cg2bNjA3LlzWbJkCRkZGUyYMIHCwkK/tlVVVQwdOpS8vDxmzJhBSkoKq1atYurUqWzZsoW4uDjq6ur83rNt2zYmT57M6tWrWbFiBTNnzmTjxo3Ex8dTWVnp17a4uJj4+MnceOMubr4Zjj66kFmzcigvH8N33+3ya1tWVsbIkSPJyclhzpw5LF26lIyMDCZOnMiOHTv82lZXVzNkyBA2bdrE9OnTSUlJIS0tjaSkJAoKChg0aBC1tbV+79m+fTuTJk1izZo1LF++nFmzZpGbm8uwYcOoqKjwa1tSUkJCQgJZWVksXLiQbt26kZWVxdixY9m5c6df2/LycoYPH05OTg6zZ89m2bJlrF27lsTExL3GXVNTw+DBg8nPz2fatGmkpqaSmprKtGnTyM/PZ/DgwdTU1Oz1Zy0xMZG1a9eybNkyZs+eTU5ODsOHD6e8vNyv7c6dOxk7dixZWVksWLCAhQsXkpWVRUJCAiUlJX5tKyoqGDZsGLm5ucyaNYvly5ezZs0aJk2axPbt2/3a1tbWMmjQIAoKCkhKSiItLY2UlBSmT5/Opk2bWv2MyMjIaPNnxH777aefER34jFi8eHGbPyOOPvpozz4jxo0bx7p161i0aBHz588nOzubMWPGsGtX5HxGLFiwIOjPiNWr0wD4/vuqVj8jkpOTaRNjTEQ+gCMAA1zc5Pl/AbktvOcr4Pkmz13q66eX79c/AHc1aXMPUNXKWLoDhcBfW2nTDTio0eNIwJSWlprWvPrqq62+rtwXKZnX1xszc6Yxhx9uzE9/aszUqc5zkShSMo8Wmrd9mrk9mzcbA8Y88EBSq+1KS0uN7+//g0wQdUfELlzpuyRXCdxujJnb6PkRwFnGmH7NvCcV+MwY85dGz90KzAT2N8bUiMhWYJgxZlijNk8DTxljjmllPMuBr40xLd0/1bR9UAtXKtWcLVvg8cedJQNuuQXefBN69/Z6VEop5b1t26BPH3j/fbj++pbbxczClcaYH4BM4JomL10DrG7hbR830/5a4FNjTE2ANi31iYh0A04Bvgk88rbR5fTtC+fMa2vhjTfg1FMhKwvmznUekV4shXPm0Ujztk8zt6fhHqZp02a42m/EzjDB/5YVmIrz7bePgUdw7ik6zRizRUTigCONMff52vcFNgDjgAk4N3gn4FyCm+1rcwmQinNp7z3gZmAAcJkxZq2vzevAAmArcBjwAtAPON0YsyXIsQc1w1RVVcW++7r71UjVunDNPDPTWan7s8/gz3929oKLlsnJcM08Wmne9mnm9nz7LRx+OMya9QO/+13XFtvFzAwTgDEmGefr/i8BWcAVwI2NipbeQJ9G7TcDNwJX+tq/CDzZUCz52qwG7gT+AGQDDwB3NBRLPkcB04GNwByc+54uCrZYaotRo0a53aUKINwyLy+Hp5+GCy5wVuteswZGjoyeYgnCL/Nop3nbp5nb0zDDNH/+Ylf7jegZpkgW7AxTXl4eJ3i9lXyMCZfMjYHp0+GZZ5xVu//zH2fj3C5dAr414oRL5rFC87ZPM7dn92746U9hxIhvePLJlu9XiKkZpliQmZnp9RBiTjhk/vnn0K+fs1HuRRdBTo5TOEVjsQThkXks0bzt08ztaVi48uuvN7varxZMYa5XOO9nEaW8zPy775z7k845B4qLYflymD0bjj3WsyFZoee5XZq3fZq5PQ2X5A488Keu9tvZ1d5UQCLyOPA4QRarnTvr/yLbvMi8rs7Z8+2f/4TqahgyBJ54Arq2fL9iVNHz3C7N2z7N3J6GgslZ29o9OsNkmTFmjDHmVOCCYNpv3uzulKIKzHbma9c6l90eeQRuvBE2boS//S12iiXQ89w2zds+zdyehoLp229LXO1XC6Ywd8UVV3g9hJhjK/MdO5yNcS+6COrrIT3d2QMu0tdUag89z+3SvO3TzO3Zx1fZnHDCSe7262pvynXvvPOO10OIOaHOvLwcXnoJTjjB2SA3IQE++QQuaWnL6Big57ldmrd9mrk9Is7PNWvWtt6wrf3qsgLeCHZZgbq6Ojp1cvc6rGpdqDKvrYWJE+Hll6G01Fki4B//AOdbrbFNz3O7NG/7NHO7OnWC0aPrefTRlueFdFmBKBMXF+f1EGKO25kb48wknXEG9O8P117r3KcUF6fFUgM9z+3SvO3TzO3aZx94//0lrvapM0we0c13Y0NGBjz3HHz4IfzylzB0qLNkgFJKqdDp1s3Zd/Pxx1tuozNMUUY3bLTPjczXr4dbbnG2MykqgkWL4IMPtFhqiZ7ndmne9mnmdoVihkkLpjB3//33ez2EmNORzL/6Cu66C8480ymapkyB7GxnuYCGGxHV3vQ8t0vztk8zt2uffeC88y50t09Xe1OuW7FihddDiDntybygAB58EE45BVatcr75lpsL997beBE11RI9z+3SvO3TzO3aZx/YuDHP1T516VHL2rrS94knnhjaAam9tCXz7dvhtdfgrbfgkENg2DBnAcp99w3hAKOQnud2ad72aeZ27bMP9OhxmKt9asFkmTFmDDCm4abvQO337NkT+kEpP8FkvnkzDB4MkyZB9+7w6qvOHnDdu1sYYBTS89wuzds+zdwuEaiurnG1Ty2YwtzOnTu9HkLMaS3zhuUAkpKcGaVXXoFHHwX9omPH6Hlul+Ztn2Zulwh8/32lq31qwRTmzjzzTK+HEHOay/zzz51CaeZMZ+uS+Hh4+GHYf38PBhiF9Dy3S/O2TzO3SwR69z7C1T71pu8wt3DhQq+HEHMaMjcGli1zFpo86yxYswbGjoX8fPjLX7RYcpOe53Zp3vZp5naJwJdffulun7pwpTeCXbiysrKS/fVvZqt2765kwYL9ef11Z0mAs8+GZ56B22+HzjonGxJ6ntuledunmdvVowc8+eQPvPRS1xbb6MKVUeaNN97weggxo7TUWYn7mGNque8+OPJIWLkSMjOdtZW0WAodPc/t0rzt08ztS0tb5Wp/OsPkEd0aJXxs2ABjxsDUqfDDD/B//wd//Sv8/Odej0wppVR79OwJTz8N//xny210hinK6HL6oVFTA+++C7/4BZx+OsybB3//O2zZAscdN0CLJcv0PLdL87ZPM7dLBD788EN3+9QZJruaLFx5UqAZpuLiYnr27GlreFGvqAgmTHBW4v7vf+Gyy5z1k269Fbr6LnVr5vZp5nZp3vZp5nYdfjg89ND3vPZay4vj6QxTmDPGjDHGnApcEEz7OXPmhHhE0a+2FhYudIqio45yVua+4Qb47DNIS4M77vixWALN3AuauV2at32auV0i8MUXX7jap97GGubOP/98r4cQsfLyIDER3n4bvvnG2RD3jTfgnnucRSdbopnbp5nbpXnbp5nbd8QRR7nanxZMYe6bb77xeggR5fvvnXuTJk50Zo8OPtgpkB58EM45J7g+NHP7NHO7NG/7NHO7RKC8vNzVPrVgCnN1dXVeDyHs1dbCBx/AO+/A3LlQUQFXXQXTpjmX4fbbr239aeb2aeZ2ad72aeZ2iUB9vbv3aGvBFOaOPfZYr4cQloyBjz92iqSZM6G4GE46CZ591lkWoG/f9vetmdunmduledunmdslAgcffLCrfepN32EuLS3N6yGEjbo6+OgjeOopOPZYuPRSZzmA+++Hdevgyy/hxRc7ViyBZu4Fzdwuzds+zdwuESgo2Opun7qsgDeCXbhy165dHNLaHcpRrrraudw2dy7Mn+/MJB1xhHOp7Xe/gyuugH1cLvtjPXMvaOZ2ad72aeZ2HXUU3H33HoYMafmeDF1WIMq8+eabXg/BurIy5zLbnXc6q7XedBOkpjo3bq9ZA9u2wejRcOWV7hdLEJuZe00zt0vztk8zt0sEMjIy3O1TZ5jsauvClbHAGPj8c1iyBN5/H1avdm7kPuccZybp1lvh1FOdPwBKKaVUIH36wAMPwCuvtNxGZ5jCXFsXrozW5fS3bYOkJPjDH5xLbGefDQMGOMsAjBoFBQXOprcvvACnnWa3WIrWzMOZZm6X5m2fZm6XCKSmunvfmM4weSTYe5jKysqiYgZq2zbnhu2UFOexaZPz/Omnw/XXO4/LLvNfcdsr0ZJ5JNHM7dK87dPM7Tr2WLj99mqGDu3WYhudYYoykydP9noIbVZXB1984Swe+dBD8LOfOdOj994Ln3wCN94Is2c7N3BnZ8OQIfDLX4ZHsQSRmXmk08zt0rzt08zt+/zzbFf703WYwtzVV1/t9RBaZYyzie1nnzk3ZK9d6xRF5eXOlOjPf+7s2/aLXzjfaOvRw+sRBxbumUcjzdwuzds+zdwuEejb91hX+9SCKczl5uZy6qmnej0MwPmKf06Oc4N248euXc7rhx8OF14Izz8PF10E550HBx7o7ZjbI5wyjxWauV2at32auV0iUFKyC+jpWp8RXzCJyGPAM0Bv4AvgKWNMi3d6iUg/4A3gNGAHMMQYk9CkzW3Aq8DxwCbgX8aYuR05bnt1797d7S4DKimBr77yf+TmwsaNzrfXwLnMdsYZ8Je/OJvannWWc9ktGr7J5kXmsU4zt0vztk8zt0sEOnfu4mqfEV0wicgdwHDgMSAd+BPwvoicaozZa4lPEekLLAYmAP8HXAq8KSLFxpjZvjYXA8nAi8Bc4FZgpohcZoxZ257jdoTbC53V18O338LWrc6N2E1/fv31jzNGAEcf7Ww5csUV8PjjTnF0+umROXMULF1czj7N3C7N2z7N3C4R2HffNm4kGkBEF0zAX4GJxpi3fL9+SkSuAx4Fnm+mfX9gqzHmKd+vvxSR84C/A7Mb+gCWG2PifL+O881KPQXc1c7jttvnn2dzzjnnU1vLXo/vv3c2mm36KCuDnTudm6obP0pKnEfDLBHA/vs7RVGfPs79RjffDCee6Dx+9jPn9ViTnZ3N+eef7/UwYopmbpfmbZ9mbpcIfPvttzgXgdwRsQWTiHQFzgUGNXlpGXBJC2+72Pd6Y0uBh0SkizGmxtdmWDNtnurAcRGRbkDj7zcGnKMZNw7693+Ihx8O1NJf167OzdU9ejgrZR9+uLOWUc+ezuPII50C6eij4ZBDouMymptuuOEGr4cQczRzuzRv+zRz+4477jhX+4vkZQV6AJ2AoibPFwG9WnhPrxbad/b111qbhj7bc1xwZp5KGz22A+Tn5zNkyBCqq6v/t7DZgAED2LFjB99++y5XXDGVv/51PU8+mcHQodt54IHFJCVVcs89yaxcCX/600RWr97Nq6++TVraF7z77gLmzFnEggXreOyxcUyfXsxppw1g1CjYZ58B3H9/JXl58ey330ZWrJjJypUrWL16NZMnT2bbtm1+Y6irqyMuLo4tW7YwdepUVq1aRUpKCjNmzCAvL4+hQ4dSVVXl957CwkImTJhARkYGS5YsYe7cuWzYsIFRo0ZRWlrq13b37t2MHj2a9evXM2/ePBYvXkxmZibjx4+nqKjIr+2ePXuIj48nLy+P5ORkVq5cSXp6OlOmTGHr1q0MHDiQ+vp6BgwYQH19PQMHDmTr1q1MmTKF9PR0Vq5cSXJyMnl5ecTHx7Nnzx6//ouKihg/fjyZmZn84x//YN68eaxfv57Ro0eze/duv7alpaWMGjWKDRs2MHfuXJYsWUJGRgYTJkygsLDQr21VVRVDhw4lLy+PGTNmkJKSwqpVq5g6dSpbtmwhLi6Ouro6v/ds27aNyZMns3r1alasWMHMmTPZuHEj8fHxVFZW+rUtLi5m3LhxrFu3jkWLFjF//nyys7MZM2YMu3bt8mtbVlbGyJEjycnJYc6cOSxdupSMjAwmTpzIjh07/NpWV1czZMgQNm3axPTp00lJSSEtLY2kpCQKCgoYNGgQtbW1fu/Zvn07kyZNYs2aNSxfvpxZs2aRm5vLsGHDqKio8GtbUlJCQkICWVlZLFy4kGeffZasrCzGjh3Lzp07/dqWl5czfPhwcnJymD17NsuWLWPt2rUkJibuNe6amhoGDx5Mfn4+06ZNIzU1ldTUVKZNm0Z+fj6DBw+mpqZmrz9riYmJrF27lmXLljF79mxycnIYPnw45eXlfm137tzJ2LFjycrKYsGCBSxcuJCsrCwSEhIoKSnxa1tRUcGwYcPIzc1l1qxZLF++nDVr1jBp0iS2b9/u17a2tpZBgwZRUFBAUlISaWlppKSkMH36dDZt2tTiZ8TEiRPJyMhg6dKlzJkzh5ycHEaOHElZWZlf2127djFmzBiys7OZP38+zz33HOvWrWPcuHEUFxf7ta2srCQ+Pp6NGzcyc+ZMVqzQz4imnxGLFy9u82fEK6+8op8RHfiMWLBgQZs+I+6/P48NG15t9TMiOTmZtojYhStF5Ajgv8AlxpiPGz3/L+BeY8zJzbznK2BSo8ttiMilwCqgtzGmUER+AO43xkxv1OYenEtw+7bnuL7Xm5th2q5boyillFL2xdLClSVAHXvP6hzG3rM/DQpbaF8L7AzQpqHP9hwXY0y1Maas4QGUt9S2MV1O3z7N3D7N3C7N2z7N3D63M4/YGSYAEVkLZBpjHmv0XA7wnjFmr5uvRWQw8GvfXm4Nz40FzjLGXOz7dTJwoDHmxkZt3gd2G2Puas9xWxh7UFujVFdX061by0u7K/dp5vZp5nZp3vZp5vYFyjyWZpjAWU/pjyLyoIicIiLDgD5AAoCIxInIlEbtE4BjROQNX/sHgYeA1xu1GQFcKyLPicjJIvIccDXOMgJBHddNI0aMcLtLFYBmbp9mbpfmbZ9mbp/bmUfst+QAjDHJInIo8BLOdwc3ADcaY7b4mvTGKWQa2m8WkRtxvgX3OM7ClU82rMHka7NaRO4EBuAsXrkJuKNhDaYgjxu0srLWi9prr702YBvlLs3cPs3cLs3bPs3cvkCZt/X/R0RfkotkInIkvm/KKaWUUsozRxlj/huokRZMHhERAY6g9Zu/D8Qpqo4K0K69PgEuCEG/NvoPVd+RnHmk/v/UzO32Heq8ITJzCWXfeo7b7z/YzA8EdpggiqGIviQXyXz/c1qtaOXHFSXLg7khra1EpD4U/droP1R9R3Lmkfr/UzO323eo8/YdI+JyCWXfeo7b778NmQd97Ei/6Vt1zJgI7j/UYw+VSM5EM4+evkMtUnOJ1MwjOZOIyVwvyYWxhqUHCPIrj6rjNHP7NHO7NG/7NHP7QpG5zjCFt2rgP76fyg7N3D7N3C7N2z7N3D7XM9cZJqWUUkqpAHSGSSmllFIqAC2YlFJKKaUC0IJJKaWUUioALZiUUkoppQLQgsljIvKYiGwWkSoRyRSRywO07+drVyUi+SLS39ZYo0VbMheR34rIchEpFpEyEflYRK6zOd5o0NbzvNH7LhWRWhHJCvEQo0o7Ple6ichAEdkiItUissm3ObkKUjsyv0dEPheRShH5RkQm+fYoVQGIyBUiskBEdoiIEZFbgnhPh//u1ILJQyJyBzAcGAicDaQB74tInxba9wUW+9qdDbwGjBSR26wMOAq0NXPgCmA5cCNwLvAhsEBEzg79aKNDOzJveN9PgCnAilCPMZq0M++ZwFXAQ8BJwF1AbmhHGj3a8Vl+Gc65PRE4DbgdOB94y8Z4o0B34HPgz8E0duvvTl1WwEMishZYZ4x5tNFzXwLzjDHPN9N+MPAbY8wpjZ5LAM40xlxsY8yRrq2Zt9DHF0CyMeaVEA0zqrQ3cxGZAeQBdcAtxpizQj3WaNCOz5XrgRnAccaYXfZGGj3akfnfgUeNMcc3eu4J4FljzNE2xhwtRMQAtxpj5rXSxpW/O3WGySMi0hVnxmJZk5eWAZe08LaLm2m/FDhPRLq4O8Lo087Mm/axD85mjfoXSxDam7mI/AE4HmfhORWkdub9G+BT4FkR+a+IfCUir4vIfiEcatRoZ+argaNE5EZxHA78DlgUupHGNFf+7tTNd73TA+gEFDV5vgjo1cJ7erXQvrOvv2/cHGAUak/mTf0NZzp4povjimZtzlxETgAGAZcbY2obbaKpAmvPOX4ccBlQBdzq6+NN4BBA72MKrM2ZG2NWi8g9QDKwL85n+HzgiRCOM5a58nenzjB5r+k1UWnmuUDtm3tetaytmTuNRO4C/g3cYYz5NgTjimZBZS4inYB3gJeNMV/ZGFiUass5vo/vtXuMMZ8YYxYDfwUe0FmmNgk6cxE5FRgJvIIzO3U90BdICOUAY1yH/+7UGSbvlODcm9H0XyCHsXcl3KCwhfa1wE5XRxed2pM58L+bOicCtxtjPgjN8KJSWzM/EDgPOFtERvue2wcQEakFrjXGrAzVYKNAe87xb4D/GmNKGz33Jc5fKEfh3EemWtaezJ8H0o0xQ32/zhaR74E0EXnBGKNXC9zlyt+dOsPkEWPMD0AmcE2Tl67Bub7dnI+baX8t8KkxpsbdEUafdmbeMLM0GbjbGKP3GLRBOzIvA04Hzmr0SAA2+v57bUgGGiXaeY6nA0eIyAGNnjsRqAe2uz7IKNPOzPfHybexOt9PvQbtPnf+7jTG6MOjB3AH8APOfQKnAMOACuAY3+txwJRG7fsC3wNv+No/6Hv/bV7/XiLl0Y7M7wJqgMdw/oXS8PiJ17+XSHm0NfNm3v9vIMvr30ekPNpxjh8AbANmAafiLKXxFTDB699LpDzakfkDvs+VR3HuIbsUyADWev17iYSH75w9y/cwwNO+/+7TQt6u/N3p+W881h++v4gLgGqcf6Vc0ei1yUBKk/b9gHW+9puB/l7/HiLt0ZbMgRTfH8imj8le/z4i6dHW87zJe7VgCnHewMk4641V+oqneGA/r38fkfRoR+ZPAF/4Mt8BJAFHev37iIQHcGVrn8uh+rtT12FSSimllApA72FSSimllApACyallFJKqQC0YFJKKaWUCkALJqWUUkqpALRgUkoppZQKQAsmpZRSSqkAtGBSSimllApACyallFJKqQC0YFJKKaWUCkALJqWUagcRud3rMSil7NGCSSml2khELgHu93ocSil7tGBSSqm2uweY5vUglFL26Oa7SinVBiLSGcgDTjPGVHo9HqWUHTrDpJRSbXM9sEqLJaViixZMSinVNno5TqkYpJfklFIqSCJyALAeOMEYU+v1eJRS9nT2egBKKWWbiBwIvAycCBQCu4B84LfGmOtbeetvgQVNiyURuQx4BDgBGAC8DzwKnAx0AX4O/N0Ys0ZE7gYu9731dOAlY8xKt35vSqnQ0EtySqmYIiKHAKlAL+BmY8wjwFdAPNA7wNv3uhwnIvvgFEv3A+nAJGAEkGOMecIY0x/4AnhHRF4CqowxjxpjHgVWArN8fSilwpj+IVVKxZpZwE+AP5kf70lYABwAfNTSm0TkcOAYY8zaJi+dD3zm6+sIoCewyBjzYaM2ZUBfoMgYM6fR80XAIb73KKXCmBZMSqmYISJ3Ar8E3jTGfN/opTN9P1NaefudQHIzz3cD5vr++3JgqTFmSZM2ZwCbgfFNnj8F2APsDDh4pZSntGBSSsWS/r6f85o83w8wtDLDhHM57p2mTxpjUo0xBSLyM+AoYHnj133rNl0CpJi9v2VzLZCmN5ArFf60YFJKxQRf4XIZsM0Y83WTl68E1htjmp3pEZETcb5VvLGVQ/zS9zOlyfPn41zu83teRE7HuUn83SCGr5TymBZMSqlYcSjQCfis8ZMish9wAb6CRkRu9y0f0Fgway/9AtjdtH+cYgz2LqTuBqrxFUwi8lCA/pVSHtKCSSkVK74Fvmfv+4XuALoCq3y/vtkYU9FMmxkB+r8SSDXG1Dd5/hdAvjFma5PnfwvMN8Z855ttOirwb0Ep5RUtmJRSMcF3/9BbwDkiIgAicg3we1+THSJyEs56TP8jIhcBW40xhS31LSKn4CxTkNLk+S747l9q5m09gI98Swo8B4xu++9KKWWLLlyplIol/wQSgAUi8g2wEbgJ+I/vUQT8ucl7grkcdyiwA5jT5PmDcWa1kpp5z5PAH3FmphJaun9KKRUedGsUpZRqge9G8a+B040x5V6PRynlHb0kp5RSLbsWWKvFklJKCyallGpZMJfjlFIxQC/JKaVUM0SkO5AD/MwYU+P1eJRS3tIZJqWUat6twGItlpRSoAWTUkq1pB8wxetBKKXCg16SU0oppZQKQGeYlFJKKaUC0IJJKaWUUioALZiUUkoppQLQgkkppZRSKgAtmJRSSimlAtCCSSmllFIqAC2YlFJKKaUC0IJJKaWUUioALZiUUkoppQLQgkkppZRSKgAtmJRSSimlAvh/zGUtq+2Qq+kAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(rm(a) - rs(a), (a, 0, 1), \n", " axes_labels=[r'$a/m$', r'$(r_- - r_{\\rm ph}^*)/m$'], \n", " frame=True, gridlines=True, axes=False) " ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 9 graphics primitives" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = plot(r_min_p, (0, 1), axes_labels=[r'$a/m$', r'$r_0/m$'], \n", " color='green', thickness=1.5, legend_label=r'$r_{\\rm ph}^+$', \n", " fill=4.1, fillcolor='lightgrey',\n", " frame=True, gridlines=True, axes=False) \\\n", "+ plot(r_min_m, (0, 1), linestyle='--', color='green', thickness=1.5, \n", " legend_label=r'$r_{\\rm ph}^-$', fill=4.1, fillcolor='grey') \\\n", "+ plot(rs, (0, 1), color='green', linestyle=':', thickness=2, \n", " legend_label=r'$r_{\\rm ph}^*$', fill=0, fillcolor='lightgrey') \\\n", "+ plot(lambda x: 2, (0, 1), color='orange', thickness=1.5, legend_label=r'$r_{\\rm ergo}$') \\\n", "+ plot(rp, (0, 1), color='black', thickness=1.5, legend_label=r'$r_+$') \\\n", "+ plot(rm, (0, 1), color='peru', thickness=2, legend_label=r'$r_-$') \n", "graph.set_legend_options(handlelength=2, loc=(1.02, 0.3))\n", "graph" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "graph.save('gek_circ_orb_lim.pdf')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ISCO" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}{\\left(-a^{2} + 1\\right)}^{\\frac{1}{3}} {\\left({\\left(a + 1\\right)}^{\\frac{1}{3}} + {\\left(-a + 1\\right)}^{\\frac{1}{3}}\\right)} + 1\n", "\\end{math}" ], "text/plain": [ "(-a^2 + 1)^(1/3)*((a + 1)^(1/3) + (-a + 1)^(1/3)) + 1" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Z1 = 1 + (1 - a^2)^(1/3)*((1 + a)^(1/3) + (1 - a)^(1/3))\n", "Z1" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = plot(Z1, (a, 0, 1), axes_labels=[r\"$a/m$\", r\"$Z_1$\"],\n", " thickness=1.5, frame=True, gridlines=True, axes=True)\n", "g" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "g.save(\"gek_Z1.pdf\")" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\sqrt{{\\left({\\left(-a^{2} + 1\\right)}^{\\frac{1}{3}} {\\left({\\left(a + 1\\right)}^{\\frac{1}{3}} + {\\left(-a + 1\\right)}^{\\frac{1}{3}}\\right)} + 1\\right)}^{2} + 3 \\, a^{2}}\n", "\\end{math}" ], "text/plain": [ "sqrt(((-a^2 + 1)^(1/3)*((a + 1)^(1/3) + (-a + 1)^(1/3)) + 1)^2 + 3*a^2)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Z2 = sqrt(Z1^2 + 3*a^2)\n", "Z2" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "r_isco_p(a) = 3 + Z2 - sqrt((3 - Z1)*(3 + Z1 + 2*Z2))\n", "r_isco_m(a) = 3 + Z2 + sqrt((3 - Z1)*(3 + Z1 + 2*Z2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Energy and angular momentum as functions of $r_0$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "sAp = sqrt(r^2 - 3*r + 2*a*sqrt(r))\n", "sAm = sqrt(r^2 - 3*r - 2*a*sqrt(r))\n", "eps_p(a, r) = (r^2 - 2*r + a*sqrt(r))/(r*sAp)\n", "eps_m(a, r) = (r^2 - 2*r - a*sqrt(r))/(r*sAm)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{r^{2} + a \\sqrt{r} - 2 \\, r}{\\sqrt{r^{2} + 2 \\, a \\sqrt{r} - 3 \\, r} r}\n", "\\end{math}" ], "text/plain": [ "(r^2 + a*sqrt(r) - 2*r)/(sqrt(r^2 + 2*a*sqrt(r) - 3*r)*r)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps_p(a, r)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{r^{2} - a \\sqrt{r} - 2 \\, r}{\\sqrt{r^{2} - 2 \\, a \\sqrt{r} - 3 \\, r} r}\n", "\\end{math}" ], "text/plain": [ "(r^2 - a*sqrt(r) - 2*r)/(sqrt(r^2 - 2*a*sqrt(r) - 3*r)*r)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps_m(a, r)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "l_p(a, r) = (r^2 + a^2 - 2*a*sqrt(r))/(sqrt(r)*sAp)\n", "l_m(a, r) = -(r^2 + a^2 + 2*a*sqrt(r))/(sqrt(r)*sAm)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{a^{2} + r^{2} - 2 \\, a \\sqrt{r}}{\\sqrt{r^{2} + 2 \\, a \\sqrt{r} - 3 \\, r} \\sqrt{r}}\n", "\\end{math}" ], "text/plain": [ "(a^2 + r^2 - 2*a*sqrt(r))/(sqrt(r^2 + 2*a*sqrt(r) - 3*r)*sqrt(r))" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "l_p(a, r)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{a^{2} + r^{2} + 2 \\, a \\sqrt{r}}{\\sqrt{r^{2} - 2 \\, a \\sqrt{r} - 3 \\, r} \\sqrt{r}}\n", "\\end{math}" ], "text/plain": [ "-(a^2 + r^2 + 2*a*sqrt(r))/(sqrt(r^2 - 2*a*sqrt(r) - 3*r)*sqrt(r))" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "l_m(a, r)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "num_l_p(a, r) = r^2 + a^2 - 2*a*sqrt(r)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "al = [0., 0.5, 0.9, 0.98, 1]\n", "ah = -2\n", "g = Graphics()\n", "for a1 in al[1:]:\n", " g += plot(eps_p(a1, r), (r, 0.01, 0.999*rs(a1)), color=hue(a1/ah), \n", " linestyle='-', thickness=1.5,\n", " axes_labels=[r\"$r_0/m$\", r\"$\\varepsilon_\\pm$\"], \n", " frame=True, gridlines=True, axes=True)\n", "g" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 25 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_max = 10\n", "for a1 in al:\n", " g += plot(eps_p(a1, r), (r, 1.001*r_min_p(a1), r_max), color=hue(a1/ah), \n", " thickness=1.5, legend_label=r\"$a = {}\\, m$\".format(float(a1)))\n", " ri = 1.00001*r_isco_p(a1) # 1.00001 to avoid 0/0 for a1=1\n", " g += point((ri, eps_p(a1, ri)), color=hue(a1/ah), size=60)\n", "for a1 in al:\n", " g += plot(eps_m(a1, r), (r, 1.001*r_min_m(a1), r_max), thickness=1.5,\n", " linestyle='--', color=hue(a1/ah))\n", " ri = r_isco_m(a1)\n", " if ri < r_max:\n", " g += point((ri, eps_m(a1, ri)), color=hue(a1/ah), marker=r'$\\circ$', size=60)\n", "g += line([(0,1), (r_max, 1)], color='grey')\n", "show(g, ymin=-2, ymax=2.5, xmax=8)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "g.save('gek_eps_circ_orb.pdf', ymin=-2, ymax=2.5, xmax=8)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = Graphics()\n", "for a1 in al[1:]:\n", " g += plot(l_p(a1, r), (r, 0.001, rs(a1)), color=hue(a1/ah), \n", " linestyle='-', thickness=1.5, \n", " axes_labels=[r\"$r_0/m$\", r\"$\\ell_\\pm/m$\"],\n", " frame=True, gridlines=True, axes=True)\n", "show(g, ymin=-10, ymax=10)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 24 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for a1 in al:\n", " g += plot(l_p(a1, r), (r, 1.001*r_min_p(a1), r_max), color=hue(a1/ah), \n", " thickness=1.5, legend_label=r\"$a = {}\\, m$\".format(float(a1)))\n", " ri = 1.00001*r_isco_p(a1) # 1.00001 to avoid 0/0 for a1=1\n", " g += point((ri, l_p(a1, ri)), color=hue(a1/ah), size=60)\n", "for a1 in al:\n", " g += plot(l_m(a1, r), (r, 1.001*r_min_m(a1), r_max), thickness=1.5,\n", " linestyle='--', color=hue(a1/ah)) \n", " ri = r_isco_m(a1)\n", " if ri < r_max:\n", " g += point((ri, l_m(a1, ri)), color=hue(a1/ah), marker=r'$\\circ$', size=60)\n", "show(g, xmax=8, ymin=-10, ymax=10)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "g.save('gek_ell_circ_orb.pdf', xmax=8, ymin=-10, ymax=10)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 24 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(g, xmin=4, xmax=r_max, ymin=-4.5, ymax=4)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "g.save('gek_ell_circ_orb_zoom.pdf', xmin=4, xmax=r_max, ymin=-4.5, ymax=4)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 24 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_max = 30\n", "g = Graphics()\n", "for a1 in al[1:]:\n", " g += parametric_plot((l_p(a1, r), eps_p(a1, r)), (r, 0.01, 0.99*rs(a1)), \n", " color=hue(a1/ah), linestyle=':', thickness=1.5, \n", " axes_labels=[r\"$\\ell/m$\", r\"$\\varepsilon$\"],\n", " frame=True, gridlines=True, axes=True)\n", "for a1 in reversed(al):\n", " ri = 1.00001*r_isco_p(a1) # 1.00001 to avoid 0/0 for a1=1\n", " g += parametric_plot((l_p(a1, r), eps_p(a1, r)), (r, 1.01*r_min_p(a1), ri), \n", " color=hue(a1/ah), thickness=1.5, linestyle=':')\n", " g += parametric_plot((l_p(a1, r), eps_p(a1, r)), (r, ri, r_max), \n", " color=hue(a1/ah), thickness=1.5)\n", "for a1 in al:\n", " ri = 1.00001*r_isco_m(a1) # 1.00001 to avoid 0/0 for a1=1\n", " g += parametric_plot((l_m(a1, r), eps_m(a1, r)), (r, 1.01*r_min_m(a1), ri), \n", " thickness=1.5, linestyle=':', color=hue(a1/ah)) \n", " g += parametric_plot((l_m(a1, r), eps_m(a1, r)), (r, ri, r_max), \n", " thickness=1.5, color=hue(a1/ah), \n", " legend_label=r\"$a = {}\\, m$\".format(float(a1))) \n", "g += line([(-6,1), (6, 1)], color='grey')\n", "show(g, xmin=-5, xmax=5, ymin=-0.4, ymax=1.2, aspect_ratio='automatic')" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "g.save(\"gek_ell_eps_circ_orb.pdf\", xmin=-5, xmax=5, ymin=-0.4, \n", " ymax=1.2, aspect_ratio='automatic')" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 24 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(g, xmin=1, xmax=5, ymin=0.5, ymax=1.2, aspect_ratio='automatic')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Orbital angular velocity" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\frac{1}{r^{\\frac{3}{2}} + a}, -\\frac{1}{r^{\\frac{3}{2}} - a}\\right)\n", "\\end{math}" ], "text/plain": [ "(1/(r^(3/2) + a), -1/(r^(3/2) - a))" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "omega_p(a, r) = 1/(r^(3/2) + a)\n", "omega_m(a, r) = -1/(r^(3/2) - a)\n", "omega_p(a, r), omega_m(a, r)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 24 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_max = 10\n", "g = Graphics()\n", "for a1 in al[1:]:\n", " g += plot(omega_p(a1, r), (r, 0.001, rs(a1)), color=hue(a1/ah), \n", " linestyle='-', thickness=1.5, \n", " axes_labels=[r\"$r_0/m$\", r\"$m\\, \\Omega_\\pm$\"],\n", " frame=True, gridlines=True, axes=True)\n", "for a1 in al:\n", " g += plot(omega_p(a1, r), (r, 1.001*r_min_p(a1), r_max), color=hue(a1/ah), \n", " thickness=1.5, legend_label=r\"$a = {}\\, m$\".format(float(a1)))\n", " ri = 1.00001*r_isco_p(a1) # 1.00001 to avoid 0/0 for a1=1\n", " g += point((ri, omega_p(a1, ri)), color=hue(a1/ah), size=60)\n", "for a1 in al:\n", " g += plot(omega_m(a1, r), (r, 1.001*r_min_m(a1), r_max), thickness=1.5,\n", " linestyle='--', color=hue(a1/ah)) \n", " ri = r_isco_m(a1) \n", " g += point((ri, omega_m(a1, ri)), marker=r'$\\circ$', color=hue(a1/ah), size=60)\n", "show(g, xmax=8)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "g.save('gek_omega_circ_orb.pdf', xmax=8)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 24 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(g, xmin=4, xmax=r_max, ymin=-0.15, ymax=0.15)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "g.save('gek_omega_circ_orb_zoom.pdf', xmin=4, xmax=r_max, ymin=-0.15, ymax=0.15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Linear velocity with respect to the ZAMO" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{a^{2} + r^{2} - 2 \\, a \\sqrt{r}}{\\sqrt{a^{2} + r^{2} - 2 \\, r} {\\left(r^{\\frac{3}{2}} + a\\right)}}\n", "\\end{math}" ], "text/plain": [ "(a^2 + r^2 - 2*a*sqrt(r))/(sqrt(a^2 + r^2 - 2*r)*(r^(3/2) + a))" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "V_ZAMO_p(a, r) = (r^2 - 2*a*sqrt(r) + a^2)/((r^(3/2) + a)*sqrt(r^2 - 2*r + a^2))\n", "V_ZAMO_p(a, r)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{a^{2} + r^{2} + 2 \\, a \\sqrt{r}}{\\sqrt{a^{2} + r^{2} - 2 \\, r} {\\left(r^{\\frac{3}{2}} - a\\right)}}\n", "\\end{math}" ], "text/plain": [ "-(a^2 + r^2 + 2*a*sqrt(r))/(sqrt(a^2 + r^2 - 2*r)*(r^(3/2) - a))" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "V_ZAMO_m(a, r) = -(r^2 + 2*a*sqrt(r) + a^2)/((r^(3/2) - a)*sqrt(r^2 - 2*r + a^2))\n", "V_ZAMO_m(a, r)" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 24 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_max = 10\n", "g = Graphics()\n", "for a1 in al[1:]:\n", " g += plot(V_ZAMO_p(a1, r), (r, 0.001, rs(a1)), color=hue(a1/ah), \n", " linestyle='-', thickness=1.5, \n", " axes_labels=[r\"$r_0/m$\", r\"$V_\\pm^{(\\varphi)}$\"],\n", " frame=True, gridlines=True, axes=True)\n", "for a1 in al:\n", " g += plot(V_ZAMO_p(a1, r), (r, 1.001*r_min_p(a1), r_max), color=hue(a1/ah), \n", " thickness=1.5, legend_label=r\"$a = {}\\, m$\".format(float(a1)))\n", " ri = 1.00001*r_isco_p(a1) # 1.00001 to avoid 0/0 for a1=1\n", " g += point((ri, V_ZAMO_p(a1, ri)), color=hue(a1/ah), size=60)\n", "for a1 in al:\n", " g += plot(V_ZAMO_m(a1, r), (r, 1.001*r_min_m(a1), r_max), thickness=1.5,\n", " linestyle='--', color=hue(a1/ah)) \n", " ri = r_isco_m(a1) \n", " g += point((ri, V_ZAMO_m(a1, ri)), marker=r'$\\circ$', color=hue(a1/ah), size=60)\n", "show(g, xmax=8)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "g.save('gek_v_zamo_circ_orb.pdf', xmax=8)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a1 = 0.9\n", "plot(r^2 - 2*a1*sqrt(r) + a1^2, (r, 0.98, 1.02))" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(r^2 - 6*r - 3*a1^2 + 8*a1*sqrt(r), (r, 0, 3))" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(r^2 - 6*r - 3*a1^2 - 8*a1*sqrt(r), (r, 0, 10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Behaviour of the function $\\mathcal{V}(r)$ near a circular orbit" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}2.32088304176189\n", "\\end{math}" ], "text/plain": [ "2.32088304176189" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a1 = 0.9\n", "r_isco_p(a1)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r1 = 2.\n", "eps1 = eps_p(a1, r1)\n", "l1 = l_p(a1, r1)\n", "V1(r) = V(a1, eps1, l1, r)\n", "g = plot(V1, (1, 5), color=\"red\", thickness=1.5, legend_label=r\"$r_0 = 2m$\",\n", " axes_labels=[r\"$r/m$\", r\"$\\mathcal{V}(r)$\"],\n", " frame=True, gridlines=True, axes=True)\n", "g += point((r1, 0), color=\"red\", size=60)\n", "r1 = 3.\n", "eps1 = eps_p(a1, r1)\n", "l1 = l_p(a1, r1)\n", "V1(r) = V(a1, eps1, l1, r)\n", "g += plot(V1, (1, 5), color=\"blue\", thickness=1.5, legend_label=r\"$r_0 = 3m$\")\n", "g += point((r1, 0), color=\"blue\", size=60)\n", "show(g, ymin=-0.04)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "g.save('gek_V_stability.pdf', ymin=-0.04)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Stability of orbits with $r_0 < r_*$:" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": 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eGP8xibi6/XarJyuoBDWvWlISuePtig62UIHOXV3RpTshoNTcQWfyKkHc8GWKJg04GJ3ha+iUoLp6+21ryYFEepoScTVqFBQUQGNAR1WCmlctOdV8gQxgSCfrM3Xm6squ0WUHAppMLTB5lRhu+DJFkwZ88pOf9DoE3xBUV2+9ZT0n0tOUiKtRo6yi7O9/TzAwTQhqXrXkVPMFBmd2pat0/GulM1eDM7vSFaHYzGsyeZUgbvgyRZMGzJs3z+sQfENQXR05AgMGwODB8R+TiKtRo6znN99MMDBNCGpeteR06AJDOpnPBJ27yhRhRNduvGt6mkxeJYgbvszilmmM2UbFYBePPw7vvAO7djl3jREj4Nvfhj/8wblrGNKXfy99m0GZXfnvwe9J+Vy/Pv0OYRTjhrzXhsgMBguzuKUBMEvtJ0JQXUVXA0+ERF2NGhXcnqag5lVLzoSaGBrHfnPxuBrapSunm5vsCMvXmLxKDLONSsCJt6epsbGR7t3N5pbxEERXSlnrKD3zDPzsZ/Efl6irp5+GV1+Fo0cTDtH3BDGvWhJWik/Euf1JPK6WVp1mYVUZ60begojYGaqvCHpeJUpnvkxPkwGA559/3usQfEMQXZWVwfnzcN11iR2XqKtRo6y79BoaEruODgQxr1pyLtRMM4ohmZ33NMXjamiXbtSpMLXhkB3h+Zag51WiuOHLFE0a8MUvftHrEHxDEF0dO2Y9X3ttYscl6mrUKAiHg9nTFMS8asnpkDWU1tlyAxCfq+gwX1ko2EN0Qc+rRHHDlymaNOCNN+Laos5AMF0dP249X3NNYscl6urmm63nIM5rCmJeteR0ZCHKIZmd3z0Xj6uhkfOUBXyBy6DnVaK44csUTRowfPhwr0PwDUF0dewYDBsGie4wkKirfv3giiuCWTQFMa9acjrURHcR+mRkdto2Hlf9M7vQFQl80RT0vEoUN3yZokkDMjM7/6IyWATR1bFj8N4k7txOxlVQ76ALYl615HTzBYZkdotr0nY8rjJEGNyl68Vhv6AS9LxKFDd8maIpDRGRp0QkH4irr/HkyZMOR6QPQXR1/Hji85kgOVdBLZqCmFctOR1qims+E8TvamiXboHffy7oeZUobvgyRVMaopSarpS6Gbg7nvb333+/wxHpQxBdHTuWXNGUjKtRo6zr1dcnfj0/E8S8asnp5iYGx3HnHMTvamhmV8oCvlZT0PMqUdzwZYomDVi6dKnXIfiGoLk6f95aciCZ4blkXI0aZa0LdeRI4tfzM0HLq7aciXMLFYjf1dAu3TgdCnZPU9DzKlHc8GUWt0xj4l3csrm5mS5durgXmI8JmqtDh+C226ztU+67L7Fjk3FVXQ19+8LChdbWLUEhaHnVkiYV5hOFh/jpgCv5VO+BnbaP19WrtRVMOFvEpqtupVsnmwDrSpDzKhk682UWtzQAMG7cOK9D8A1BcxVdbiCZnqZkXPXpAyNHBm9eU9DyqiXlzU0oiLunKV5XQyPDfUHeTiXIeZUMbvgyPU1pjNmw15Aqzz0Hv/kN1NSAW7tRfPKT0K0bvPKKO9czeMuhhvP8qOxt5g2/gWu69bDtvO82NfJ4yRH+OOS93JXV27bzGoKL6WkyAGZTx0QImqvocgPJFEzJurr+evj735M61LcELa9acjayLMDAzPiGkeJ1NfjiquDBndcU5LxKBjd8maJJA77xjW94HYJvCJqr48eTG5qD5F1df71VrIUCtG1Y0PKqJWdDTXRF6B3HwpYQv6tuksHAzC6BHp4Lcl4lgxu+TNGkAVu2bPE6BN8QNFfJLjcAybu67jpoaoIgLTETtLxqSUWomYGZXeNa2BISczU0s1ugVwUPcl4lgxu+TNGkATfddJPXIfiGILkKheDEieSLpmRdXXed9VxQkNx1/UiQ8qot5aEmBiZwh1cirgZ16Up5gFcFD3JeJYMbvkzRpAE1NTVeh+AbguSquNjq8Ul2eC5ZV1ddZU0ED1LRFKS8aktFqImBcS5sCYm5GpTZlfJQczJhaUGQ8yoZ3PClddEkIv1FZKGIVEUeC0WkXyfHiIg8IyIlIlIvIrkiMqpNm+4iMlVEykXkvIisEZErW7x/tYjMFZF3Iuc4JiK/E5H47slNkMrKSidOqyVBcpXKcgOQvKvMTKt3K0hFU5Dyqi1nQ81xTwKHxFxZRVNwe5qCnFfJ4IYvrYsm4M/AHcAjkccdwMJOjvkF8BPgB8AHgFJgi4i0vOd1MvAo8GXgfqAXsE5EojMhb8Ry+11gFPBj4HvAsyl+npjceuutTpxWS4LkqrDQer7qquSOT8XVddcF6w66IOVVW84m2NOUiKtBmV2pDYdoCIeTCc33BDmvksENX9oWTSJyE1ah9B2l1OtKqdeBJ4BPi8gN7RwjwNPAGKXUSqXUYeDrQDbwWKRNX+DbwE+VUn9RSv0NeBy4FXgQQCm1USn1TaXUZqXUcaXUGuCPwBec+KyvvvqqE6fVkiC5KiyEIUOgR5JL56Ti6rrrgtXTFKS8askFFaY6HEqoaErEVbQH62xAe5uCmlfJ4oYvbYsm4F6gSim1N/qCUmoPUAW0t6HENcAwYHOLYxqB11occxfQtU2bEuBwB+cF6AtUdBRwZNivT/QBxLWi2xNPPBFPMwPBclVYmHwvE6Tm6vrrrUnoFwJy41OQ8qolFZH5RgMSGJ5LxNWgyFpNZwJaNAU1r5LFDV86F03DgNMxXj8dea+9YwDK2rxe1uK9YcAFpdS5Dtq0QkSuBX4IzOwk5l9hFXXRRzHA8ePHmTBhAo2NjRcX7xo9ejQlJSXMnTuXn/3sZ2zatImVK1eSn5/PlClTqK6ubtW2oqKC6dOnc/DgQdasWcP69es5cOAAs2bN4syZM63a1tXVkZOTw9GjR1m2bBlbt25l9+7dzJ8/n6KiolZtQ6EQY8eO5eTJkyxcuJCdO3eSm5vL0qVLKSgoYOLEiTQ0NLQ6prS0lDlz5rBv3z42btzIqlWrOHz4MFOnTqWqqqpV28rKSqZNm8ahQ4dYvXo1GzZsYP/+/cyePZuysrJWbevr68nJyaGgoICXXnqJbdu2sWvXLhYsWEBhYSFjxozhueeeY/To0YTDYcaMGUNhYSELFixg165dbNu2jZdeeomCggJycnKor69vdf6ysjJmz57N/v372bBhA6tXr+bQoUNMmzaNysrKVm2rqqqYOnUqhw8fZtWqVWzcuJF9+/YxZ84cSktLW7VtaGhg4sSJFBQUsHTpUnJzc9m5cycLFy7k5MmTjB07llAo1OqYoqIi5s+fz+7du9m6dSvLli3j6NGj5OTkUFdXx+jRoykshLq6tzhz5gyzZs3iwIEDrF+/njVr1nDw4EGmT59ORUVFq/NWV1czZcoU8vPzeeKJJ9i0aRP79u1j7ty5lJSUtGrb2NjIhAkTOHbsGEuWLCE3N5cdO3awaNEievcuJRSCgoLmVscUFxfz4osvsmfPHrZs2cLy5cs5cuQIkyZNora2tlXb8vJyZs6cSV5eHuvWrWPt2rXk5eUxY8YMzp4926ptTU0NkydPJj8/nxUrVrB582b27t3LvHnzLou7qamJ8ePHc/z4cRYvXsz27dvZvn07ixcv5vjx44wfP56mpqbL/q3NmzePvXv3snnzZlasWEF+fj6TJ0+mpqaGz3/+8xfbnj17lhkzZpCXl8fatWtZt24deXl5zJw5k/Ly8lbnra2tZdKkSRw5coTly5ezZcsW9uzZw4svvkhxcXGrts3NzYwbN44TJ06waNEiduzYQW5uLkuWLOHYsWMdfkfs27fPke+Ivx0/BsCxvx6I+zvixz/+cdzfESf/7xAAG/fsdu07IhwOp813xOTJkx39joi2TfY7YuXKlUl/R5w4cYJx48bR3Gzfd8T3vve9Dr8jXnjhBVLFd9uoiMgzwG87afYB4GHg60qpVkNxIlIAzFVKXbZJjYjcB+wCRiilTrV4fQ4wUin1iIg8BryolOre5tgtwDGl1PfavD4Cq6fqNaXUdzr5bN2BluftDRSbbVQMyXDTTfDIIzBpkvvXLi629qBbuxY+/Wn3r29wh+11lfz2zElWXzmKvgn0NiXCpwoP8bW+Q/mXvkMcOb8hOAR1G5VpwE2dPA5jTeAeGuP4wVzekxSlNPLctsdoSItjSoFuItK/gzbAxYLpf4HXgSc7+lBgDQUqpaqjDyCu+yfNUvvxExRXSkFRUWrDc6m4GjECsrKCM68pKHnVlopQM5kQ92rgkLirIN9BF9S8ShY3fDnzXwMHUUqVA+WdtROR14G+InK3UuqNyGsfxJpbtLudw97BKooeAv4WOaYb8ADwy0ib/UBTpM2ySJvhwC1Yd95Fr38FVsG0H/imUsqx2z++973vdd7IAATH1blzcP681duTLKm4ysiAa66Bd95J/vp+Iih51ZZzoWb6Z3YhI4HNDRN1NTDAC1wGNa+SxQ1ffuxpigul1FvARmCOiNwjIvcAc4B1Sqmj0XYickREHo0co7CWE/i1iDwqIrcA84E6rOULUEpVAXOBHBH5uIjcCSwCDgF/iZxzBJALFAE/AwaLyDARaW8uVUq8/PLLTpxWS4LiKtXlBiB1V1dfHZyiKSh51RaraIr/zjlI3FWQe5qCmlfJ4oYv3/U0Jci/AlO4dKfbGqz1l1pyA1bvU5QJQBbwAtAf2As8rJRqOVT2Y6AZq6cpC9gKfEMpFd2i9GHgfZFHcZvrJbHffMfcc889dp9SW4Liyo6iKVVX11wDr72W0il8Q1Dyqi2VoWb6ZyT2ayRRV4Myu3C48XxCx+hCUPMqWdzwpW1PE4BSqkIp9bhSqk/k8bhSqrJNG1FKzW/xs1JKPaOUGq6U6qGUeiCyXlPLYxqUUj9USg1USmUrpT6jlCpq8f78yHkvezjxOYuL29ZlhvYIiqvCQmsrkyEpzJ1N1VV0eM5n95okRVDyqi0V4Sb6JTgBPFFXgzK7Ut7chN9uWrKDoOZVsrjhS+uiKSgE8cskWYLiqrAQrrzSmluULKm6uuYaa15VeaczEP1PUPKqLZWROU2JkKirgZldaUJRHQ513lgzgppXyeKGL1M0acDIVGb7BoyguEp1YUtI3dU111jPQZjXFJS8asu5UHNCC1tC4q4GRxa4DOK8pqDmVbK44csUTRrw+uuvex2CbwiKq8LC1O6cg9RdBaloCkpetaQxHKZOhemX4JymRF0NiEw0j64+HiSCmFep4IYvUzRpwD//8z97HYJvCIqrd9+1hudSIVVX/fpZjyAUTUHJq5acC1tFTKJ3zyXqKtqTVRHAnqYg5lUquOHLFE0aMGPGDK9D8A1BcBUOw6lTcMUVqZ3HDldBWaspCHnVlnOhaNGUWE9Toq66SQY9JSOQPU1BzKtUcMOX77ZRCRKRTXurzDYqhkQ4c8a6a27lSnj0UW9j+eIXoaYGNm/uvK3BX7xeV82vz7zDy1fczMAuifU2JcrX3j3CB7N689SAFP8nYAg0Qd1GxdAGs9R+/ATB1bvvWs+p9jTZ4SooC1wGIa/aEh0uS3TJgWRcDcjscrFnK0gEMa9SwQ1fpqcpjYm3p6mmpobevXu7F5iPCYKrDRvgU5+y9p5LZV6THa6mTYOf/ATq6yEz/u3JfEcQ8qoti6rKWF59hldG3pLQccm4+v2Zk1SGm3lu6LUJHed3gphXqdCZL9PTpCki8pSI5ANvxNN+7ty5DkekD0Fw9e67IALDUty0xw5X11wDTU1QUpLyqdKaIORVW5JZowmSczUgs0sgJ4IHMa9SwQ1fpmhKQ5RS05VSNwN3x9P+4YcfdjgifQiCq5ISGDoUuqS4SZIdrqLLDpw4kfKp0pog5FVbzoWaGZCR+FymZFz1D+jwXBDzKhXc8GWKJg146623vA7BNwTB1bvvwogRqZ/HDldXX2096z6vKQh51ZZz4eaE5zNBcq4GZHalOhyiSYUTPtbPBDGvUsENX6Zo0gAz5h0/QXBVUpL6JHCwx1V2ttXrpXvRFIS8aktVKLmiKRlX0bWaKgPW2xTEvEoFN3yZokkDIhPbDHEQBFclJfb0NNnlKghrNQUhr9pSFW6mb0bis/uTcXVpgctgFU1BzKtUcMOXKZo04M033/Q6BN8QBFfvvmtPT5NdroJQNAUhr1qilKIqFKJvEj1NybiKzp0KWtEUtLxKFTd8maJJAx555BGvQ/ANurtqaoLTp+3pabLLVRCKJt3zqi3nVZhmFH0T3HcOknPVL7MLQvC2UglaXqWKG75M0aQB8+bN8zoE36C7q1OnrGc7eprscnX11VBcDBcu2HK6tET3vGpLVaTHJ5nhuWRcZYrQN6PLxf3ugkLQ8ipV3PBlFrdMY8w2KoZE2bMH7r0X/u//4LbbvI7G4i9/gYcegoICeN/7vI7GYAf5jed5qvRt/jT8eq7tluXKNb9dcpTbe/TkRwNS3InaEFjM4pYGwCy1nwi6u7JrCxWwz1V0rSadh+h0z6u2VIVCAPRLYnguWVfWApfB6mkKWl6litlGJeDE29PU1NRE167ObpipC7q7mjoVfvYzaGiwVgVPBbtcNTVBjx4wYwY8+WTKp0tLdM+rtmysrWD82SI2X3UrXSWx/3sn6+rZ8kJKmy8wZVhwuiuDllep0pkv09NkAOC5557zOgTfoLur6HIDqRZMYJ+rrl2tPfB0XhVc97xqS1WomZ6SkXDBBMm76p/ZJXDrNAUtr1LFDV+maNKAf/qnf/I6BN+guyu7lhsAe11dfbXeRZPuedWWqnBzUssNQPKu+mV0oTJgE8GDllep4oYvUzRpwOuvv+51CL5Bd1enTsHw4facy05XI0dCUZFtp0s7dM+rtlSFQ/RJYj4TJO+qb2YmNeEQzQGaUhK0vEoVN3yZokkDRo4c6XUIvkF3V6WlMGyYPeey05XuRZPuedWWylAz/TITX24AknfVP7LAZVWAhuiCllep4oYvUzSlISLylIjkA294HYvBX5SV2Vc02cnIkdbQYeSmK4PPsbZQSa6nKVn6Roq0oA3RGdILUzSlIUqp6Uqpm4G742lfpPN/4W1GZ1fNzVBebm2Qawd2uho50oqvrMy2U6YVOudVLKqT3EIFkncVXd4gSJPBg5ZXqeKGL1M0acC9997rdQi+QWdXZ86AUvb1NNnpKtprruvvAJ3zKhbJbtYLybvqHynSgtTTFLS8ShU3fJmiSQOWL1/udQi+QWdXpaXWs109TXa60r1o0jmv2hJSiupwKOnhuWRd9ZAMuokEqqcpSHllB274MotbpjFmcUv70dnVxo3wyU9CYeGlIiUV7HSlFPTsCWPGwI9/bMsp0wqd86ot50JNfKE4nz8Mvpr7s/smfHwqrv6lOJ9P9OrPt/rZdItomhOkvLIDs7ilIS7Gjx/vdQi+QWdX0Z6mIUPsOZ+drkT0voNO57xqS3QLlWSH51Jx1S+zC+cC1NMUpLyyAzd8mZ6mNMZs2GtIhPHjrUdFhdeRxObBB6F/fzAjDv7mUEMtPyo7xvwRN/Cerj1cvfYvy47TXTL4/ZCrXb2uQQ9MT5MBMJs6JoLOrkpL7ZvPBPa70rmnSee8akt12Opp6p1kT1MqrvpmBmtV8CDllR244csUTRrwrW99y+sQfIPOruxeo8luVzoXTTrnVVtqUiyaUnEVtP3ngpRXduCGL1M0acDGjRu9DsE36OzK7p4mu12NHGlt89LUZOtp0wKd86ot1eFmspLcrBdScxW0/eeClFd24IYvUzRpwKhRo7wOwTfo7Mrunia7XV15pXUXXUmJradNC3TOq7ZUh0L0SbKXCVJzFbT954KUV3bghi9TNGlAVVWV1yH4Bp1d2d3TZLcrnddq0jmv2lITDtEnydXAITVX0VXBg7L/XJDyyg7c8GWKJg2oqanxOgTfoKurCxesu+bs7Gmy25XORZOueRWL6nBz0vOZIDVX/QK2KniQ8soO3PBliiYNuOmmm7wOwTfo6ur0aevZzp4mu1317Qu9e+tZNOmaV7GoDodSKppScRW0/eeClFd24IYvUzRpwObNm70OwTfo6iq6Ea6dPU1OuNL1Djpd8yoWNSlsoQKpuQpaT1OQ8soO3PBlFrdMQ0TkKeAprKL2hs4Wt6ypqaF3795uhedrdHW1fj18+tPw7rswYoQ953TC1SOPQI8esHq1raf1HF3zKhZfLs7nwZ79+U7/5LYyScWVUopHig7xZL/hfLHP4KTO4SeClFd20Jkvs7ilpiilpiulbgbujqf9888/73BE+qCrq2hP02Abf4844UrXniZd8yoW1kTw5IfnUnElIvTL6EJVQHqagpRXduCGL9PTlMaYbVQM8fLsszBpEpw543UkHfP738O0aZfmYBn8RZMK83DhIX45cCSP9BrgSQxPnvo7N3bL5icDr/Tk+gb/YnqaDIBZaj8RdHV1+rR9G/VGccLVyJFWYdfQYPupPUXXvGpLqquBQ+qu+mcEZ1XwoOSVXZhtVAxx8f3vf9/rEHyDrq7OnLF3aA6ccRVdduDdd20/tafomldtiRZNqSxumaqrIO0/F5S8sgs3fJmiSQOWLVvmdQi+QVdXp0/bXzQ54UrXtZp0zau2VIeiPU3J3z2Xqqu+GZlUB6RoCkpe2YUbvkzRpAH33nuv1yH4Bl1dOdHT5IQrXYsmXfOqLdFiJZWJ4Km66pPR5WLxpjtBySu7cMOXKZo0oEi330AOoqsrJ4omJ1xlZ0P//lBcbPupPUXXvGqLHXOaUnXVNzOTqnAzQbiJKSh5ZRdu+DJFkwaIiNch+AYdXSnlTNHklKsrrtBvTpOOeRWL6nCILMmgqyT/qyNVV30yuhAGzqtwSufxA0HJK7tww5cpmjTgyivNrbfxoqOr6mpoarK/aHLK1RVXQEmJI6f2DB3zKhY1oeaUJoFD6q6i1w/Cpr1BySu7cMOXKZo0YM+ePV6H4Bt0dBVdm8nuJQeccjVihH49TTrmVSxqVYheKRZNqbrqG9lKJQgLXAYlr+zCDV9aF00i0l9EFopIVeSxUET6dXKMiMgzIlIiIvUikisio9q06S4iU0WkXETOi8gaEYlZ4kba5omIEpE77Pt0l/jSl77kxGm1REdX0aLJ7p4mp1zpODynY17FojacetGUqqs+kTv3qsP6TwYPSl7ZhRu+tC6agD8DdwCPRB53AAs7OeYXwE+AHwAfAEqBLSLSckObycCjwJeB+4FewDoRifVtMgFwdDBi5syZTp5eK3R05VTR5JSrK66A0lLQ6QYoHfMqFjU2FE2puuobuXOvOgDDc0HJK7tww5e226iIyE1APnCPUmpv5LV7gNeBG5VSR2McI1gFzmSl1PjIa92BMuCXSqlZItIXOAN8VSn1UqTNCKAI+H9KqU0tzvdJ4Dngi8CbwJ1KqbwEPoPZRsXQKX/6EzzxhDWvqUvyy+e4xpo18LnPWfOahie356vBI35QWsCVXbrzH4Ou8jSOTxYe4lv9hvFPAdi012AfZhuVjrkXqIoWTABKqT1AFXBfO8dcAwwDNrc4phF4rcUxdwFd27QpAQ63PK+IDAXmAF8F6uIJODKU1yf6AOLa3tostR8/Oro6cwYGDLC/YHLK1RVXWM86DdHpmFexsGN4zg5XfTMyA9HTFJS8sguzjUpqDANibQt6OvJee8eA1bPUkrIW7w0DLiilzrXXJtJjNR+YqZT6awIx/wqrqIs+igGOHz/OhAkTaGxsvJgUo0ePpqSkhLlz5/KhD32ITZs2sXLlSvLz85kyZQrV1dWt2lZUVDB9+nQOHjzImjVrWL9+PQcOHGDWrFmcOXOmVdu6ujpycnI4evQoy5YtY+vWrezevZv58+dTVFTUqm0oFGLs2LGcPHmShQsXsnPnTnJzc1m6dCkFBQVMnDiRhoaGVseUlpYyZ84c9u3bx8aNG1m1ahWHDx9m6tSpVFVVtWpbWVnJtGnTOHToEKtXr2bDhg3s37+f2bNnU1ZW1qptfX09OTk5FBQU8NJLL7Ft2zZ27drFggULKCwsZMyYMfzoRz9i9OjRhMNhxowZQ2FhIQsWLGDXrl1s27aNl156iYKCAnJycqivr291/rKyMmbPns3+/fvZsGEDq1ev5tChQ0ybNo3KyspWbauqqpg6dSqHDx9m1apVbNy4kX379jFnzhxKS0tbtW1oaGDixIkUFBSwdOlScnNz2blzJwsXLuTkyZOMHTuWUCjU6piioiLmz5/P7t272b+/kB49qjl69Cg5OTnU1dW1anvmzBlmzZrFgQMHWL9+PWvWrOHgwYNMnz6dioqKVm2rq6uZMmUK+fn5XHPNNWzatIl9+/Yxd+5cSkpKWrVtbGxkwoQJHDt2jCVLlpCbm8uOHTtYtGgRJ06cYNy4cTQ3N7c6pri4mB07lgKwYUMey5cv58iRI0yaNIna2tpWbcvLy5k5cyZ5eXmsW7eOtWvXkpeXx4wZMzh79myrtjU1NUyePJn8/HxWrFjB5s2b2bt3L/Pmzbss7qamJsaPH8/x48dZvHgx27dvZ/v27SxevJjjx48zfvx4mpqaLvu3Nm/ePPbu3cvmzZtZsWIF+fn5TJ48mZqaGi5cuHCx7dmzZ5kxYwZ5eXmsXbuWdevWkZeXx8yZMykvL2913traWiZNmsSRI0dYvnw5W7ZsYc+ePbz44osUFxe3atvc3My4ceM4ceIEixYtYseOHeTm5rJkyRKOHTvW4XfEvn37bPmOOB8OcWDnrpS+I+6+++6UvyPqTpdTHQ458h0RDofT5jvi6aeftuU7YuvWrSxbtsz274iVK1c68h3x4osvsmfPHrZs2ZLQd8T111/f4XfECy+8QMoopXz1AJ4BVCePfwB+DRyNcXwB8B/tnPu+yPHD27w+B9gY+fNjQGOMY7dgFUkAPwJ2AZmRn6+OnPeOTj5bd6BPi8cVgKqqqlId8dxzz3X4vuESOrp6/HGl7r/f/vM65SoUUiozU6kXXnDk9J6gY17F4pGTB9XyqtMpncMOVz8tfVv99vQ7KZ8n3QlKXtlFZ76qqqqiNUIflWQN4oMZEJcxDVjaSZsTwG3A0BjvDebynqQopZHnYcCpFq8PaXFMKdBNRPqr1r1NQ4DdkT9/DLgHaGyz2NZfRWSxUurrsS6urKHAxujP8S7U9clPfjKudgY9XTmxsCU45yojw5rLpNPwnI551ZYmFaZBhVMenrPDVd+MLpwLwPBcEPLKTtzw5bvhOaVUuVLqSCePBqwJ331F5O7osSLyQaAvl4qbtryDVRQ91OKYbsADLY7ZDzS1aTMcuKVFmx8Bt2PdrXcH8P8ir/8L8J9Jf/h2OHTokN2n1BYdXTlVNDnpSrdlB3TMq7acD1srcKdaNNnhqk9kKxXdCUJe2YkbvvzY0xQXSqm3RGQjMEdEvht5eTawTrW4c05EjgC/UkqtUkopEZkM/FpECrCG8n6NNZH7z5HzVonIXCBHRM4CFcAfgUPAXyJtClvGIiK1kT8eU0rZvutWv3797D6ltujoyqmiyUlXuq0KrmNetaU2si5SqkWTHa76ZHS5uHmwzgQhr+zEDV/aFk0R/hWYwqU73dZgrb/Ukhuwep+iTACygBeA/sBe4GGlVE2LNj8GmoFlkbZbgW8opTxZeaZ377husjOgnyul4PRp+1cDB2ddXXEFbNvm2OldR7e8ioVdRZMdrvpmZFIVCqGU0np/tiDklZ244ct3w3OJoJSqUEo9rpTqE3k8rpSqbNNGlFLzW/yslFLPKKWGK6V6KKUeUEodbnNMg1Lqh0qpgUqpbKXUZ5RS7W6vrJQ6EblOns0fEYC33nrLidNqiW6uamuhsdGZniYnXem2lYpueRULu4omO1z1yexCE4oGzTftDUJe2YkbvrQumoLCQw891HkjA6CfK6dWAwdnXQ0fDpWV0NDg2CVcRbe8ioVdRZMdri5u2qv5VipByCs7ccOXKZo0YP78+V6H4Bt0c+Vk0eSkq2GRVc/K2ruP1WfollexqA2HECBbUvu1YYervtH95zS/gy4IeWUnbvjSdhsVHTDbqBg6Y906+MxnrKGuESO8jiZ+Dh6E22+H11+He+7xOhpDPCytOs3i6tOsHXmL16FQ2nyBr7z7FhOHvJd/yDLzfgzxYbZRMQBmqf1E0M1Vebn1PGiQ/ed20lW0p6m0tON2fkG3vIpFbThEr5h7kieGHa4uDc/p3dMUhLyyEzd8mZ6mNCbenqbm5ma6+GGn1jRAN1fPPQe//S3U1HTeNlGcdBUOQ7duMHUqfP/7jlzCVXTLq1hMPlvMm43nmTPihpTOY4crpRSfKDzE9/uP4NE+DvyPIU0IQl7ZSWe+0qqnSUQGi8iDIvIdEfmpiPxaRH4kIl8UEe/7czXmj3/8o9ch+AbdXFVUWJv1OoGTrjIyYOhQfXqadMurWNixWS/Y40pE6JWRqf1aTUHIKztxw1dKJayIvBf4NvAo1npHAoSwNpttBAZg7aeGiFQBG4AFSqlNqVzX0Jovf/nLXofgG3RzdfYsDBzozLmddjV8OJw61Xk7P6BbXsWiVtlTNNnlqk9m5sU7+nQlCHllJ274SqqnKdKr9D/AX7GKpZnAXcAApVRXpdQgpdQVSqksoBdwLfAUUAO8ICL/JyIP2PMRDDt37vQ6BN+gmysne5qcdjVsmD49TbrlVSzs6mmyy1XvjEyqNS+agpBXduKGr4R7mkTkE0AOsAR4b9vFItuilKrD2tPtHeDPYi3f+k/AcyKyFfilMhOrWiEiT2EVmXEVte95z3ucDUgjdHN19qxzRZPTroYPh7w8Ry/hGrrlVSzsKprsctU7o4v2PU1ByCs7ccNXQj1NIvIp4IfAh5RSYzormGIRWXF7mVLqLqx92+Ymeg7dUUpNV0rdDNzdaWMgFNL7i8NOdHNVUeHc8JzTrnTqadItr2JhV9Fkl6veAZjTFIS8shM3fCU6PHcT8Fml1Dk7Lq6UGgcsNRPFU+OULhNDXEA3V04Ozzntavhwa3HLsAY7YeiWV7GoDYfoaUPRZJer3hmZ1Gje0xSEvLITN3wlNDynlLJ9arpSanPnrQwdcffdcXVIGdDPlZPDc067GjYMmpqsws+JdabcRLe8assFFaZRKVt6muxyFYSiSfe8shs3fNm55MBtIvK8iHzcrnMa4mPFihVeh+AbdHJ14YK1Ya9Tw3NOuxo+3HrWYYhOp7yKxXmb9p0D+1z1zsikJhRC5ymxuueV3bjhy7bFLUVkJfApoEYp5fP/N6YH8S5u2djYSPfu3d0LzMfo5KqszOqteeUV+Oxn7T+/067eeQfe+17YvBn8vi+pTnkVi6KmRr5WcoRJQ6/ljh69UjqXXa621J7j2bOFvDryVnpk6Lm5he55ZTed+UqrxS2BUuATwHdtPKchDiZOnOh1CL5BJ1dnz1rPTg3POe1Kp61UdMqrWNTa2NNkl6s+mVYsNRpPBtc9r+zGDV929jRNAiYopczMNZswG/YaOmLnTvjQhyA/H266yetokqNfP/j1r+EXv/A6EkNH7Kuv4Renj7PkipsY1qWb1+EAkN94nqdK32bu8Ot5b7csr8Mx+IB062n6HfC8iNxu4zkNcWA2dYwfnVxVVFjPTvU0ueFq+HA9epp0yqtYRHuaetvQ02SXq94Z1n1MOi9wqXte2Y0bvuwsmv4ReADYJyLbROQ3IvJhEUmP/5ZozLe+9S2vQ/ANOrlyenjODVfDhumxlYpOeRWL2nCIDCBLUv+VYZeraAGn8wKXuueV3bjhy86i6T+AKcCfgIHAb4H/BSojRdR/i8iNNl7PEOHVV1/1OgTfoJOrigro3Ru6dnXm/G640qWnSae8ikV0jaYMkZTPZZeraNGk8wKXuueV3bjhK6UNe9vwDjBWKRUGEJGBwMeAjwIfwRq++z4wwsZrGoDbbrvN6xB8g06unFzYEtxxNWwYHDjg+GUcR6e8ioVdq4GDfa4yRciWDGo0XjVb97yyGzd82Vk0/RGYIyLvAiuUUv8HLI88EJGhwFAbr2eIUBGd3GLoFJ1cnT3r3BpN4I4rXXqadMqrWNhZNNnpSvcFLnXPK7txw5dtRZNS6iDwbRF5LzGKI6VUGVBm1/UMlzh//rzXIfgGnVw53dPkhqthw6CqCurrIcvHN0DplFexqA2H6CX2FE12uuqT2UXrokn3vLIbN3zZviKYUuq4Uup1u89raJ8bbzRTxeJFJ1dObqEC7rjSZVVwnfIqFudt7Gmy01UvzXuadM8ru3HDV0JFk4gMFZGedgchIjfYfU4/IyJPiUg+8EY87f/yl784HJE+6OSqosLZ4Tk3XEUXuPT7HXQ65VUsalWInjatum2nqz4ZmVovbql7XtmNG74S/VcQBuaJyHC7AhCRrwI/sut8OqCUmq6UuhmIa/fBb3zjG84GpBE6uXJ6eM4NV7qsCq5TXsXCzjlNdrrSvadJ97yyGzd8JVQ0KaXOAL8ElonIt0SSX7RDRN4jInOx7rAzRVMKTJkyxesQfINOrpwennPD1YAB1pIJfu9p0imvYmFn0WSnqz6aF02655XduOErqW1URKQX8BzWUgIvAhuAg6qTk0W2Bbkf+ArWPnX/pZSanXAAAcFso2Joj8ZG6NED5s+Hr3/d62hSY+RI+MY34A9/8DoSQ3s8UniQ7/Qbzpf6DPY6lFYsqTrNkurTrBl5i9ehGHyAZ9uoKKVqlVJPAv8C3Aq8DlSJyFYRWSAiU0TkDyIyXkTmiMgKETkAnMVa/PIEcLMpmOzBLLUfP7q4OnfOenayp8ktV8OH+7+nSZe8ikWTCtOolG09TXa66p2RSW04RMimPVTTDZ3zygnc8GXLhr0i0ht4CLgXuAm4AugFhIBKrCLpILAd2NVZj5TBIt6epoqKCgY4+dtTI3Rx9eabcMstsGsX3HefM9dwy9VnPwvhMKxb5/ilHEOXvIpFVaiZzxe/ye8Gv4cPZ/dL+Xx2unrtfCXPlJ/klStH0SfTzmUH0wOd88oJOvPlWU+TiGSLyL+LyAwR+T3wQWCVUurnSqlPK6XuVEpdp5S6USl1j1Lqy0qpZ5VSO03BZD9LlizxOgTfoIsrpzfrBfdc6dDTpEtexaLe2uSBnjat02Snq+hWKrrOa9I5r5zADV/JTuTeiDWn6cvAEODrwJsi8g2b4jIkwIc+9CGvQ/ANurhyo2hyy9WwYf6/e06XvIrF+UhBkm3T8JydrqK9S7oWTTrnlRO44SvhoimyHcr9kR8fU0p9Tyn1VeAR4BEReUNEzIY5LnLixAmvQ/ANurg6e9Z6drJocsvV8OFQVgZ+3kJMl7yKRV2kILFrnSY7XfXSvKdJ57xyAjd8JfyvILIdykPARGBzi9cLlVJfBqYC/ysi37UtSkOHZGba8z/AIKCLq4oK6NMHujg4jcMtV8OGWQVTtBD0I7rkVSzOR4bnsmwanrPTVZ+LRZOeC1zqnFdO4IavpL5ylVJbga3tvLcwspr1KyLyD8B3lYr8qzM4wvDhtq01qj26uHJ6jSZwz1XLrVSGDHHlkrajS17Fwu6eJjtdZUkGGejb06RzXjmBG75s33sOQCm1H+tOugeAdSLi46040599+/Z5HYJv0MWV01uogHuudNhKRZe8ikVdOIwAPZJfy7gVdroSEfpk6Ltpr8555QRu+HKkaAJQShUBHwWuBdabwsk5vvCFL3gdgm/QxZXTW6iAe6502EpFl7yKRZ0KkS0ZZIjYcj67XfXOyKTazxPiOkDnvHICN3w5VjQBKKXeBR4ErgPWikhXJ68XVGbNmuV1CL5BF1duDM+55ap7d+jf3989TbrkVSzOh8Nk2XTnHNjvqrfGm/bqnFdO4IYvuxa37A5cDwwA+gPZQD1QB5zGWpbgZWB15E47QxyYbVQM7XHHHfCP/wjTp3sdiT2MGgUPPQSTJ3sdiaEt0yveZV9DDfNH3Oh1KDH5j7LjdBFh9JBrvA7FkOZ4trglXNxwd6yIvA5UAXnANmAFsBCrSNoA/DXy3BN4TET+I9lrBgUReSoymf6NeNqbpfbjRxdXbgzPuelq2DB/9zTpklexqFNhsm26cw7sd9UzI/PiWlK6oXNeOUHabqMiIp/EKop6AAIcBfYC7wA1QC3QHHm/LzAYGAFcBVwJfFopddCG+LUm3p6muro6srOz3QvMx+jiqmdPGDMGnn7auWu46erxx6GoCF57zZXL2Y4ueRWLZ86c4Hw4xMSh19pyPrtdTTpbTH7jeeaMuMG2c6YLOueVE3Tmy8ueptlAFrASGKWUukkp9Q2l1O+UUs8ppWYrpeYppV5QSo1VSv0kspXKfUqpq0zBZC8zZszwOgTfoIOrhgaoq3O+p8lNV37vadIhr9qjLhy2bTVwsN9Vr4xMasN6rmqjc145gRu+El6nSUSuwNqQd55S6jv2h2RIlE9/+tNeh+AbdHB17pz17HTR5KarYcOsVcH9ig551R51KsRAsW8VVbtd9crIpFbpOTync145gRu+kulpOg2UAH+0ORZDkvzf//2f1yH4Bh1cRVfOdnqdJjddDRkC1dVWL5of0SGv2sPunia7XfWKzGkKa7gXvM555QRu+EpmG5Um4F6l1BEH4jEkwUCnf3tqhA6u3NisF9x1NXSo9Xz6tGuXtBUd8qo96sIh21YDB/td9crIRGFNWNcNnfPKCdzwldS/hMjClYY0ISvLrBsaLzq4cmOzXnDXVXT7FL8O0emQV+1x3ua75+x2Fd20t1bDO+h0zisncMOXo4tbGtzh73//u9ch+AYdXEV7mvr3d/Y6brrye0+TDnkVC6UUdeEQ2Tb2NNntSueiSde8cgo3fJmiSQM+/vGPex2Cb9DBVUUF9O0LXeybmxsTN10NHmw9+7WnSYe8ikWjUoTB1jlNdruKFk06rtWka145hRu+TNGkAf/zP//jdQi+QQdXbmyhAu666trV+kx+7WnSIa9iURe5K62njcNzdrvqFekF07GnSde8cgo3fNmyjYrBGcw2KoZYPPkk/O1voNsG6DfdBI88ApMmeR2JIUpRUyNfKznC5KHXcnuPXl6HE5MLKswnCg/xHwNH8oleLvxvwuBbPN1GxQ+ISH8RWSgiVZHHQhHp18kxIiLPiEiJiNSLSK6IjGrTpruITBWRchE5LyJrROTKGOf6lIjsjZynXERW2vwRAbPUfiLo4MqNLVTAfVdDh/q3p0mHvIpFXaT3xs45TXa76iYZdBfRsqdJ17xyirTdRsUviMirWNu2PBl5aTZwQin1mQ6O+SXwn8A3gL8D/wV8GLhBKVUTaTMD+EykzVkgB2uz4ruUsvqzReSLwBzg11h78glwq1Lq5QTij6unKRQKkZlpX/e5zujg6uMft+YALV3q7HXcdvXP/2wVhH/5i2uXtA0d8ioWB+pr+Onp4ywacSNXdO1uyzmdcPWl4jf5TK+BfL3fMFvP6zW65pVTdObL9DR1gIjcBDwCfEcp9bpS6nXgCeDTIhJzkyIREeBpYIxSaqVS6jDwdSAbeCzSpi/wbeCnSqm/KKX+BjwO3Ao8GGnTBXge+LlSaqZS6u9KqaOJFEyJMGHCBCdOqyU6uKqshH79nL+O26783NOkQ17FIrr2UU8bJ4I74craSkW/niZd88op3PClbdEE3AtUKaX2Rl9QSu0BqoD72jnmGmAYsLnFMY3Aay2OuQvo2qZNCXC4RZv3Y201ExaRv4nIKRF5te0wX1siw359og+gdzwf9LHHHounmQE9XFVWOr/cALjvasgQ/949p0NexcKJ4TknXOlaNOmaV07hhi+di6ZhWFu+tOV05L32jgFo+9Vd1uK9YcAFpdS5Dtq8N/L8DDAa+DRwDnhNRDqajfIrrKIu+igGOH78OBMmTKCxsfHimO3o0aMpKSlh7ty5zJ8/n02bNrFy5Ury8/OZMmUK1dXVrdpWVFQwffp0Dh48yJo1a1i/fj0HDhxg1qxZnDlzplXburo6cnJyOHr0KMuWLWPr1q3s3r2b+fPnU1RU1KptKBRi7NixnDx5koULF7Jz505yc3NZunQpBQUFTJw4kYaGhlbHlJaWMmfOHPbt28fGjRtZtWoVhw8fZurUqVRVVbVqW1lZybRp0zh06BCrV69mw4YN7N+/n9mzZ1NWVtaqbX19PTk5ORQUFPDSSy+xbds2du3axYIFCygsLGTMmDHk5uYyevRowuEwY8aMobCwkAULFrBr1y62bdvGSy+9REFBATk5OdTX17c6f1lZGbNnz2b//v1s2LCB1atXc+jQIaZNm0ZlZWWrtlVVVUydOpXDhw+zatUqNm7cyL59+5gzZw6lpaWt2jY0NDBx4kQKCgpYunQpubm57Ny5k4ULF3Ly5EnGjh1LKBS6eMypU3VAJfPnz2f37t1s3bqVZcuWcfToUXJycqirq2t1/jNnzjBr1iwOHDjA+vXrWbNmDQcPHmT69OlUVFS0altdXc2UKVPIz88nJyeHTZs2sW/fPubOnUtJSUmrto2NjUyYMIFjx46xZMkScnNz2bFjB4sWLeLEiROMGzeO5ubmVscUFxfz4osvsmfPHrZs2cLy5cs5cuQIkyZNom/fBs6cCRMKWW3Ly8uZOXMmeXl5rFu3jrVr15KXl8eMGTM4e/Zsq/PW1NQwefJk8vPzWbFiBZs3b2bv3r3MmzfvsribmpoYP348x48fZ/HixWzfvp3t27ezePFijh8/zvjx42lqarrs39q8efPYu3cvmzdvZsWKFeTn5zN58mRqamr46U9/erHt2bNnmTFjBnl5eaxdu5Z169aRl5fHzJkzKS8vb3Xe2tpaJk2axJEjR1i+fDlbtmxhz549vPjiixQXF7dq29zczLhx4zhx4gSLFi1ix44d5ObmsmTJEo4dO9bhd8S+ffuS+o44cvIkGeEwVeWtfafyHTFnzhzbvyPKC4spqTxny3dEOBxOm++I7du3J/UdMXr0aIqKihz/jli5cqWr3xG1tbWt2rb9jnj++ec7/I544YUXSBmllK8eWIWI6uTxD1hziY7GOL4A+I92zn1f5PjhbV6fA2yM/PkxoDHGsVuAmS3aKODJFu93B84A3+3gs3UH+rR4XAGoqqoq1RE7duzo8H3DJfzuKhRSKiNDqZkznb+W265WrVIKlCorc/WytuD3vGqPRZWl6rOFh2w9pxOufn/6hPrxqbdtP6/X6JpXTtGZr6qqqmiN0EclWYM4vDyeI0wDOpsCewK4DRga473BXN6TFKU08jwMONXi9SEtjikFuolIf9W6t2kIsDvy5+ix+dE3lVKNInIcuKq9oJU1FNgY/dmaYtU5zc3NcbUz+N9VbS2Ew+7MaXLbVctVwaPbqvgFv+dVe9SFw7bOZwJnXPXKyKSoubHzhj5D17xyCjd8+W54TilVrpQ60smjAXgd6Csid0ePFZEPAn25VNy05R2souihFsd0Ax5occx+oKlNm+HALW3aNAI3tGjTFbgaOJn8p49NaWlp540MgP9dVVZaz24UTW678vP+c37Pq/aoUyGyxd5fE0640nVOk6555RRu+PJjT1NcKKXeEpGNwBwR+W7k5dnAOqXU0Wg7ETkC/EoptUoppURkMvBrESnAGsr7NVAH/Dly3ioRmQvkiMhZoAL4I3AI+EukTbWIzAR+JyJFWIXSzyOXXG73Z73rrrvsPqW2+N1VtGhyYyK42678vP+c3/OqPc470NPkhCtdiyZd88op3PDlu56mBPlXrGJmc+RxEPhqmzY3YPU+RZkATAZeAP6KNa/oYRVZoynCj4HVwDJgF1ZR9RkVWaMpws+xhhEXAvuA9wAfU5dPIE+Z1atX231KbfG7Kzd7mtx21bMnZGX5s6fJ73nVHnXhEFk23jkHzrjqmZHJ+XCIsGbrDuqaV07hhi+tF7f0O/EubtnQ0ECPHj3cC8zH+N3VK6/A5z9vFRZOz/vxwtU118BXvgLPPuvqZVPG73nVHj8pO0b/jC789+D32HZOJ1xtO3+OP5QXsm7kLbb3jHmJrnnlFJ35MotbGgD44x//6HUIvsHvrqI9TX37dtjMFrxwNXSoP3ua/J5X7VEXDtm6RhM446pXpFDSbYhO17xyCjd8mZ6mNMZs2Gtoy/PPw69+BXV1XkfiDJ/9rHV34Lp1XkdiAPjau0e4L7sP3+s/wutQOiS/8TxPlb7Nn4Zfz7XdsrwOx5CmmJ4mA2A2dUwEv7tyazVw8MbV4MFw5ozrl00Zv+dVe5xXIbLF3uEuJ1zp2tOka145hRu+TNGkAd/5zne8DsE3+N2VW/vOgTeuhgzxZ9Hk97xqj7pw2PbhOSdc6Vo06ZpXTuGGL1M0acDatWu9DsE3+N3VuXPuFU1euPJrT5Pf8yoWIaVoUPYXTU64ihZN5zUrmnTMKydxw5cpmjTgjjvu8DoE3+B3V272NHnhavBga9XzhgbXL50Sfs+rWNSrMAA9bR6ec8JVN8mgm4h2PU065pWTuOHLFE0acPbsWa9D8A1+d+Vm0eSFq8GDrWe/9Tb5Pa9iEe21ybb5Fn6nXFkLXIYdObdX6JhXTuKGL1M0aUB9fb3XIfgGv7tys2jywlW0aPLbquB+z6tY1F0smuz9NeGUq16i36rgOuaVk7jhyxRNaYiIPCUi+cAb8bS/7rrrHI5IH/zuys2757xw5deeJr/nVSzqIsNzdt8955QrHbdS0TGvnMQNX6ZoSkOUUtOVUjcDd3faGPjf//1fhyPSB7+7crOnyQtXfi2a/J5XsYgOz/W0uafJKVe9MjKpVXoVTTrmlZO44csUTRrwta99zesQfIOfXYVCUFXlXtHkhausLOjVy39Fk5/zqj3qIvOD7J7T5JQrHXuadMwrJ3HDlymaNGDq1Kleh+Ab/OyqOrJ+rVtFk1euBg/235wmP+dVe0R7mrLE3l8TTrnSsWjSMa+cxA1fZhuVNMZso2JoyTvvwHvfC1u2wIMPeh2Nc3zwg3DLLTB3rteRBJuXq88wt7KUV6+61etQ4mLOuVPk1lWy+IqbvA7FkKaYbVQMgFlqPxH87Cq6Wa/O26iAPxe49HNetcf5cMj2+UzgnKueGRna9TTpmFdOYrZRMcTFD37wA69D8A1+dhUtmtwanvPKlR+3UvFzXrVHnQrbfuccOOeqZ2R4TqfREx3zyknc8GWKJg1YtGiR1yH4Bj+7OnfOenaraPLKlR97mvycV+3hVE+TU66yJZMw0KhR0aRjXjmJG75M0aQBDzzwgNch+AY/u4r2NFlD8s7jlSs/TgT3c161R104TJbNd86Bc6503H9Ox7xyEjd8maJJA44dO+Z1CL7Bz64qK63b8bt0ced6XrkaPBhqaqCx0ZPLJ4Wf86o96lSIbJvvnAPnXEV7xc5rtFaTjnnlJG74MkWTBnTr1s3rEHyDn125uRo4eOfKjwtc+jmv2qM+HLZ9jSZwzlXPSKw6TQbXMa+cxA1fpmjSgKFDh3odgm/ws6vKSveG5sA7V0OGWM9+Kpr8nFftUa/Ctq/RBM65ihZNdRpt2qtjXjmJG75M0aQB+/fv9zoE3+BnV25uoQLeufLjpr1+zqv2qA+HyHJgIrhTrnpGCjyd5jTpmFdO4oYvUzRpwOc+9zmvQ/ANfnZVVeVuT5NXrvw4POfnvGoPp3qanHKVreHwnI555SRu+DJFkwbMmTPH6xB8g59dVVeDmwvDe+UqO9t6+Klo8nNetUe9Q3fPOeUqU4QsyaBO6TM8p2NeOYkbvsw2KmmIiDwFPIVV1N5gtlExALz//dYWIzNmeB2J81x9NTz2GDz7rNeRBBOlFB8vPMhPBlzJp3sP9DqcuPmn4jf5VK+BfKPfMK9DMaQhZhsVTVFKTVdK3QzcHU97s9R+/PjZldvDc1668tuq4H7Oq1g0qDAKHJnT5KSrnhmZWs1p0i2vnMYNX6anKY2Jd8Pe+vp6srKy3AvMx/jZ1aBB8NOfwq9+5c71vHT1qU9Z61G98oonl08YP+dVLCpCTXyxOJ8xg6/mvmx7K3UnXT11qoCrunbnl4OucuT8bqNbXjlNZ75MT5MBgBdeeMHrEHyDX10p5X5Pk5eu/LaVil/zqj3qI7ftO7FOk5OusjP0mtOkW145jRu+TNGkAZ/97Ge9DsE3+NVVfT00N7tbNHnpym9Fk1/zqj3qI4WHE3fPOelKt+E53fLKadzwZYomDThw4IDXIfgGv7qqjnQku3k/gJeu/FY0+TWv2qM+Ung4MafJSVe9NCuadMsrp3HDlymaNGBwdGEbQ6f41VVVlfXsZk+Tl66GDLE+s1/2n/NrXrVHnYM9TU66snqa9Bme0y2vnMYNX6Zo0oDu3bt7HYJv8KsrL4omL11Fv/vKyz0LISH8mlftEZ3T5MQ6TU66ypYMrTbs1S2vnMYNX6Zo0gCzE3b8+NWVF0WTl678tiq4X/OqPZyc0+SkK93mNOmWV07jhi9TNGnARz7yEa9D8A1+deVF0eSlK78VTX7Nq/aoD4foJkKmiO3ndtJVr4xMGpWiWZOldHTLK6dxw5cpmjRg4cKFXofgG/zqKjoRvHdv967ppSu/FU1+zav2qFNhssX+oTlw1lV2hl6b9uqWV07jhi+zuGUaE+/iluFwmAwH7nLREb+6mjQJ/vu/obbWvWt66Uop6NnT2kbl6ac9CSEh/JpX7THn3Cn+t66SP19xk+3ndtLV/voafnb6OItH3MiIrv6fD6RbXjlNZ77M4pYGAJ41G3TFjV9dub2wJXjrSsRfyw74Na/ao16FHZnPBM666hWZuK7LZHDd8spp3PBleprSGNPTZD9+dfXjH8OmTZCf7941vXb1D/9gbVI8e7ZnIcSN167sZnx5IUXNjUwbdp3t53bSVXFTI18tOcKkoddyR49ejlzDTXTLK6cxPU2GuBg7dqzXIfgGv7ryoqfJa1d+6mny2pXdONnT5KQr3eY06ZZXTuOGL1M0pSEi8pSI5ANvxNP+q1/9qsMR6YNfXXlRNHntavBgOH3a0xDixmtXdlMfDjuyRhM46+ri8JwmRZNueeU0bvgyRVMaopSarpS6Gbg7nva5ubnOBqQRfnVVXe3uFirgvatBg+DsWU9DiBuvXdlNnQqR7VBPk5OuukkGXRFtVgXXLa+cxg1fpmjSgGuvvdbrEHyDX1150dPktSs/FU1eu7Ibq6fJmV8PTrvqmZGpzURw3fLKadzwZYomDWj0ywZdaYBfXXlRNHntatAgqKiAkA9+/3ntym6cnNPktKvsjAxthud0yyunccOXKZo04IxfZsumAX515UXR5LWrQYMgHIbKSk/DiAuvXdlNfThMlkOLWzrtSqdNe3XLK6dxw5cpmjTg/e9/v9ch+Aa/uvKiaPLa1aBB1rMfNu312pXd1CvnhuecdtVL9Nl/Tre8cho3fJmiSQPWrFnjdQi+wY+uLlyAhgb3J4J77cpPRZPXruwkpBQNDg7POe0qOyNDmzlNOuWVG7jhyyxumcbEu7hlfX09WVlZ7gXmY/zoqrzcuv1+5Up49FH3ruu1q9OnYehQWL0aPvc5z8KIC69d2UldOMSnig7z34Ou4mM9+9t+fqddjS0vpKS5kakOLMzpNjrllRt05sssbmkAICcnx+sQfIMfXVVVWc9uD8957WrAAOvZDz1NXruyk7rIfKBsh9ZpctqVTnOadMorN3DDl+lpSmPi7Wky6M2BA3DXXfDXv1rPQWLAAPjlL62HwR2Kmhr5WskRJg+9ltt9uBXJvMpTbKo9x0tX3ux1KIY0w/Q0GQAYPXq01yH4Bj+68qqnKR1cDRrkj56mdHBlF/WRSdQ9HJrT5LSrbMmkTunR06RTXrmBG760LppEpL+ILBSRqshjoYj06+QYEZFnRKREROpFJFdERrVp011EpopIuYicF5E1InJlmzbXi8grkTbVIrJLRD7qwMfkiSeecOK0WuJHV14VTengyi9FUzq4sov6SMHh1N1zTrvKzsigLhxCh1EUnfLKDdzwpXXRBPwZuAN4JPK4A1jYyTG/AH4C/AD4AFAKbBGR3i3aTAYeBb4M3A/0AtaJtFrYZD3QBfgYcBeQF2kzLIXPE5NXXnnF7lNqix9dVUc6kd0eoU0HV34pmtLBlV00RIsmh3qanHaVnZFJGGjUoGjSKa/cwA1f2hZNInITVqH0HaXU60qp14EngE+LyA3tHCPA08AYpdRKpdRh4OtANvBYpE1f4NvAT5VSf1FK/Q14HLgVeDDSZhDwPmCcUuqgUqoA+I/IeUZhM3cFbaJLCvjRVVUVdO9uPdwkHVz5pWhKB1d20RCZRO3U8JzTrnpG/u9ap8GyAzrllRu44Uvbogm4F6hSSu2NvqCU2gNUAfe1c8w1wDBgc4tjGoHXWhxzF9C1TZsS4HCLNmeBt4CviUhPEekCfBcoA/a3F3Bk2K9P9AH0bq9tS8rKyuJpZsCfrrxY2BLSw5VfiqZ0cGUX0eG5Hg4NzzntKjsStw530OmUV27ghi+di6ZhwOkYr5+OvNfeMWAVNy0pa/HeMOCCUupce22UNZj+EHAnUAM0AD8GHlFKVXYQ86+wirrooxjg+PHjTJgwgcbGxosT3UaPHk1JSQlz587lzTffZNOmTaxcuZL8/HymTJlCdXV1q7YVFRVMnz6dgwcPsmbNGtavX8+BAweYNWsWZ86cadW2rq6OnJwcjh49yrJly9i6dSu7d+9m/vz5FBUVtWobCoUYO3YsJ0+eZOHChezcuZPc3FyWLl1KQUEBEydOpKGhodUxpaWlzJkzh3379rFx40ZWrVrF4cOHmTp1KlVVVa3aVlZWMm3aNA4dOsTq1avZsGED+/fvZ/bs2ZSVlbVqW19fT05ODgUFBbz00kts27aNXbt2sWDBAgoLCxkzZszFWMLhMGPGjKGwsJAFCxawa9cutm3bxksvvURBQQE5OTnU19e3On9ZWRmzZ89m//79bNiwgdWrV3Po0CGmTZtGZWVlq7ZVVVVMnTqVw4cPs2rVKjZu3Mi+ffuYM2cOpaWlrdo2NDQwceJECgoKWLp0Kbm5uezcuZOFCxdy8uRJNm/eQ58+qtUxRUVFzJ8/n927d7N161aWLVvG0aNHycnJoa6urlXbM2fOMGvWLA4cOMD69etZs2YNBw8eZPr06VRUVLRqW11dzZQpU8jPz+e1115j06ZN7Nu3j7lz51JSUtKqbWNjIxMmTODYsWMsWbKE3NxcduzYwaJFizhx4gTjxo2jubm51THFxcW8+OKL7Nmzhy1btrB8+XKOHDnCpEmTqK2tbdW2vLyct9/eQ1lZM+vWrWPt2rXk5eUxY8YMzp4926ptTU0NkydPJj8/nxUrVrB582b27t3LvHnzLou7qamJ8ePHc/z4cRYvXsz27dvZvn07ixcv5vjx44wfP56mpqbL/q3NmzePvXv3snnzZlasWEF+fj6TJ0+mpqaGxYsXX2x79uxZZsyYQV5eHmvXrmXdunXk5eUxc+ZMysvLW523traWSZMmceTIEZYvX86WLVvYs2cPL774IsXFxa3aNjc3M27cOE6cOMGiRYvYsWMHubm5LFmyhGPHjnX4HbFv3764vyOOFReRoRSbN7zqyHdEXl6eo98RB3a/DsCiFS8n9R0RDofT5jviwoULcX1HjB07llAo5Pp3xMqVKz3/jpg5cyZ5eXmsW7eOXbt2dfgd8cILL5AySilfPYBnANXJ4x+AXwNHYxxfAPxHO+e+L3L88DavzwE2Rv78GNAY49gtwMzInwV4BdgA/CPwfuAFrCJoeAefrTvQp8XjCkBVVVWpjjh48GCH7xsu4UdX3/2uUu9/v/vXTQdXc+cqBUpduOB1JB2TDq7sYkllmfrUSec+j9Ouii80qI+cyFMH6mscvY4b6JRXbtCZr6qqqmiN0EclWYP4sadpGnBTJ4/DWBO4h8Y4fjCX9yRFKY08t+2JGtLimFKgm4i0XSq3ZZuPAZ8GvqyU2qWUOqCU+jegHmuOVEyUUo1KqeroA6uXqlNee+21eJoZ8Kermhr3J4FDeriKbqVSUeFtHJ2RDq7sosHBfefAeVc9I4ty6rD/nE555QZu+PJd0aSUKldKHenk0QC8DvQVkbujx4rIB4G+wO52Tv8OVlH0UItjugEPtDhmP9DUps1w4JYWbbIjz20H1cM44Pzxxx+3+5Ta4kdX1dXeFE3p4Mov+8+lgyu7aFBhxyaBg/OuonOa6jQomnTKKzdww5fviqZ4UUq9BWwE5ojIPSJyD9Yw2zql1NFoOxE5IiKPRo5RWMsJ/FpEHhWRW4D5QB3W8gUopaqAuUCOiHxcRO4EFgGHgL9ETvs6cA74HxG5PbJm00Ssiebr7f6s06ZNs/uU2uJHV14VTengyi9FUzq4sov6sLNFk9OuuiJ0QTivwQKXOuWVG7jhS+ttVERkADAF+GzkpTXAD1SLydgiooBvKqXmR34W4LdYd7v1B/YCTylr+YHoMT2AiVjzm7KArcC/KaWKWrT5B2AM1vyqrsCbwO+VUq8mEL/ZRsXAnXfCfffB9OleR+I+FRUwcCC8/DJ88YteRxMMdNjw9nNFh/mXPoN5rG+sGRqGoGK2UekEpVSFUupxpVSfyONx1ebuNaWURAumyM9KKfWMUmq4UqqHUuqBlgVTpE2DUuqHSqmBSqlspdRnWhZMkTZ/VUp9ItKmj1Lq3kQKpkQwS+3Hjx9dedXTlA6u+vWDjIz072lKB1d24fTwnBuudNm0V6e8cgOzjYohLn74wx96HYJv8KMrr4qmdHCVkWH1NKV70ZQOruyiIRwmq9XmBvbihqssydBicUud8soN3PBliiYNWLBggdch+AY/uvKqaEoXV35Y4DJdXNlBgwo7trAluOOqZ0YmdRr0NOmUV27ghi9TNGnARz/qyD7AWuI3V42NcOGCN0VTurjyQ9GULq7soN7h4Tk3XEU37fU7OuWVG7jhyxRNGlBQUOB1CL7Bb6682qwX0seVH4bn0sWVHTQ4fPecG656SqYWd8/plFdu4IYvUzRpQFZWltch+Aa/ufKyaEoXV37oaUoXV3bg9PCcG66yNOlp0imv3MANX6Zo0oCBAwd6HYJv8JuraNHUO66tm+0lXVz5oWhKF1d20KDCZDnY0+SGK13mNOmUV27ghi9TNGlAXl6e1yH4Br+5qolspONFT1O6uPJD0ZQuruzA6eE5N1xla3L3nE555QZu+DJFkwZ85jOf8ToE3+A3V14Oz6WLq4EDobbWmhCfrqSLq1QJKUUTytHhOTdc6bJOky555RZu+DJFkwb86U9/8joE3+A3V14WTeniKtrjfvast3F0RLq4SpX6yORpJ3ua3HCVJRk0qDAhn+94oUteuYUbvrTeRsWviMhTwFNYRe0NZhuV4DJzJvzgB9DUBCJeR+MNu3fDP/4jHDoEt9zidTR6U97cxD+9m8+zg6/h3mz/fufknq/kd+UnWTvyFnplOLdQp8FfmG1UNEUpNV0pdTNwdzztzVL78eM3V9GFLb0omNLFlR96mtLFVao0RHqashwcnnPDVXYkfr/fQadLXrmFG75MT1MaE++GvQ0NDfTo0cO9wHyM31z913/BwoVw8qT7104XV+XlMHgwrFgBX/iC19HEJl1cpcrbF+p54tTfmTHsOm7snu3INdxw9WbjeX5Q+jbzht/ANd38+/eiS165RWe+TE+TAYCpU6d6HYJv8JurmhpvlhuA9HHVv7/V05bOPU3p4ipV6sPOz2lyw1V2JH6/30GnS165hRu+TNGkAZ///Oe9DsE3+M2Vl0VTurjKzIR+/dK7aEoXV6kSHZ5z8u45N1xlR+Yx+X2tJl3yyi3c8GWKJg3Yv3+/1yH4Br+58rJoSidXAwemd9GUTq5S4eKcJgd7mtxw1fNi0eTvniZd8sot3PBliiYNGDZsmNch+Aa/uaqt9a5oSidX6V40pZOrVGhwYXjODVfRou+8z4fndMkrt3DDlymaNKBLly5eh+Ab/OaqpgZ69fLm2unkKt2LpnRylQr1KowA3Ry8XdMNV5ki9JAM3w/P6ZJXbuGGL1M0acA777zjdQi+wW+uvByeSydX6V40pZOrVGhQ1hYq4mDR5Jar7Az/F0265JVbuOHLFE0a8OEPf9jrEHyD31x5WTSlk6t0L5rSyVUqOL3vHLjnqqdk+v7uOV3yyi3c8GWKJg3485//7HUIvsFvrrwsmtLJVboXTenkKhUaVMjRhS3BPVfZGRmc9/lEcF3yyi3c8GUWt0xj4l3cMhQKkZlptgqIB7+56tEDJk6EH/7Q/Wunk6sZMywH6bqdTDq5SoUpFcX8X8N55o64wbFruOXqJ6XH6J/Zhf8e/B7Hr+UUuuSVW3TmyyxuaQBg7NixXofgG/zkqqkJGhu962lKJ1cDB0IoBFVVXkcSm3RylQr1LgzPueUqOyPD98NzuuSVW7jhy/Q0pTHx9jQZ9OTcORgwAJYvhy99yetovGXrVnjwQXj7bbj2Wq+j0ZffnTlBdThEzlD/S362vJCy5gs8P+x9XodiSBNMT5MBMJs6JoKfXNXUWM9e9TSlk6t037Q3nVylQvTuOSdxy1VPDeY06ZJXbuGGL1M0pSEi8pSI5ANvxNP+61//usMR6YOfXHldNKWTq3QvmtLJVSq4cfecW66yJZM65e8lB3TJK7dww5cpmtIQpdR0pdTNwN3xtN+6davDEemDn1x5XTSlk6t0L5rSyVUqNKiw43fPueVKh7vndMkrt3DDlymaNOD666/3OgTf4CdXXhdN6eQqO9u6kzBdi6Z0cpUK9S4Mz7nlKlsyqff54pa65JVbuOHLFE0aUF9f73UIvsFPrmprrWeviqZ0c5XOazWlm6tkcWN4zi1XWRkZNKFo8vEQnS555RZu+DJFkwacTdffJGmIn1x53dOUbq7SuWhKN1fJ0qDC9HB4eM4tV9mRz+Hn3iZd8sot3PBliiYNuP32270OwTf4yVVNDXTtCt26eXP9dHOVzkVTurlKFjfunnPLVZZYixz6eTK4LnnlFm74MkWTBqxbt87rEHyDn1x5uYUKpJ+rdC6a0s1VMoSVolEpshwumtxydamnyb+TwXXIKzdxw5cpmjTg+9//vtch+AY/ufK6aEo3V+lcNKWbq2RojPTIOD0855ar7Ejx5+eeJh3yyk3c8GWKJg147rnnvA7BN/jJlddFU7q5SueiKd1cJUN9tGhyuKfJLVdZGZHhOR/PadIhr9zEDV9mG5U0xmyjEmy++U04ehR27/Y6kvTguefgN7+5dFehwV5Kmhr515Ij/HHIe7kry8Nq3SaqQ818rvhNnhn0Hh7o2c/rcAxpgNlGxQCYpfYTwU+uamu97WlKN1cDB8L589YmxulGurlKhoZIT5PTi1u65So70tNU7+PhOR3yyk3MNiqGuPjud7/rdQi+wU+uamqgVy/vrp9urtJ5VfB0c5UMDS4Nz7nlqosIXRFfLzmgQ165iRu+TNGkAStXrvQ6BN/gJ1dez2lKN1fpXDSlm6tkiBYXThdNbrrKzsigTvn37jkd8spN3PBliiYN+MAHPuB1CL7BT668LprSzVU6F03p5ioZGly6e85NV1mS6euJ4DrklZu44csUTRpw6tQpr0PwDX5y5XXRlG6u0rloSjdXyXBxTpPDPU1uusrOyKDexz1NOuSVm7jhyxRNaYiIPCUi+cAb8bQPhfz7peA2fnLlddGUbq769QOR9Cya0s1VMjREemS6O1w0uekqKyPD1z1NOuSVm7jhyxRNaYhSarpS6mbg7njaX3311c4GpBF+cuX13XPp5iozE/r3T8+iKd1cJUO9CtNdhAwRR6/jpqtsyfT14pY65JWbuOHLFE0asGPHDq9D8A1+cdXUZN1a7+Xdc+noKl0XuExHV4nixr5z4K6r7IwMX2+jokNeuYkbvkzRpAFf+cpXvA7BN/jFVU2N9exlT1M6uho4EM6d8zqKy0lHV4nSEHanaHLTVZb4e3hOh7xyEzd8maJJA1544QWvQ/ANfnGVDkVTOrrq3x8qKryO4nLS0VWiNKiw43fOgbuusjMyfb24pQ555SZu+DLbqKQxZhuV4HL4MNx6q7WFyr33eh1N+vD441BUBK+95nUk+vHHs0Ucu1DPjOHXex2Kbcw9d4ot58+x9MqbvQ7FkAaYbVQMgFlqPxH84iodeprS0dWAAenZ05SOrhKl3qXhOTddZWVk+LqnSYe8chOzjYohLn70ox95HYJv8IurdCia0tFVuhZN6egqUdwannPTVVaGvxe31CGv3MQNX6Zo0oD58+d7HYJv8Iur2lrr2cuiKR1dpWvRlI6uEsWtu+fcdJUtGTSjuODT3iYd8spN3PBliiYNePDBB70OwTf4xVW0p8nLJQfS0dWAAdDQAPX1XkfSmnR0lShu3T3npqvsjEwA327aq0NeuYkbvkzRpAFHjhzxOgTf4BdXNTXQrZv18Ip0dDVggPWcbr1N6egqURpUmCwXhufcdJUdKQLrfLpWkw555SZu+NK6aBKR/iKyUESqIo+FItKvk2NERJ4RkRIRqReRXBEZ1abNk5HXq0VExTpnMtdOlp49ezpxWi3xiyuvt1CB9HSVrkVTOrpKFLeG59x0FS0C/boquA555SZu+NK6aAL+DNwBPBJ53AEs7OSYXwA/AX4AfAAoBbaISMtfYdnARuBZm6+dFAOiv0kMneIXV+lQNKWjq/79red0W+AyHV0linX3XKbj13HTVbb4e3hOh7xyEzd8aVs0ichNWMXKd5RSryulXgeeAD4tIje0c4wATwNjlFIrlVKHga9jFUmPRdsppSYrpcYBe+y6diocPHjQ7lNqi19cpUPRlI6u0rWnKR1dJYpbd8+56Sr7Yk+TP4fndMgrN3HDl7ZFE3AvUKWU2ht9QSm1B6gC7mvnmGuAYcDmFsc0Aq91cIxd10ZEuotIn+gDiOvX5ic/+ckEQgs2fnHl9Wa9kJ6uoj1N6VY0paOrRFBKuTY856arrMjn8WtPk9/zym3c8KVz0TQMOB3j9dOR99o7BqCszetlHRxj17UBfoVVWEUfxQDHjx9nwoQJNDY2Xly8a/To0ZSUlDB37lx+//vfs2nTJlauXEl+fj5Tpkyhurq6VduKigqmT5/OwYMHWbNmDevXr+fAgQPMmjWLM2fOtGpbV1dHTk4OR48eZdmyZWzdupXdu3czf/58ioqKWrUNhUKMHTuWkydPsnDhQnbu3Elubi5Lly6loKCAiRMn0tDQ0OqY0tJS5syZw759+9i4cSOrVq3i8OHDTJ06laqqqlZtKysrmTZtGocOHWL16tVs2LCB/fv3M3v2bMrKylq1ra+vJycnh4KCAl566SW2bdvGrl27WLBgAYWFhYwZM4Y//elPjB49mnA4zJgxYygsLGTBggXs2rWLbdu28dJLL1FQUEBOTg719fWtzl9WVsbs2bPZv38/GzZsYPXq1Rw6dIhp06ZRWVnZqm1VVRVTp07l8OHDrFq1io0bN7Jv3z7mzJlDaWlpq7YNDQ1MnDiRgoICli5dSm5uLu+8U051dQknT55k7NixhEKhVscUFRUxf/58du/ezdatW1m2bBlHjx4lJyeHurq6Vm3PnDnDrFmzOHDgAOvXr2fNmjUcPHiQ6dOnU1FR0aptdXU1U6ZMIT8/n5/+9Kds2rSJffv2MXfuXEpKSlq1bWxsZMKECRw7dowlS5aQm5vLjh07WLRoESdOnGDcuHE0Nze3Oqa4uJgXX3yRPXv2sGXLFpYvX86RI0eYNGkStbW1rdqWl5czc+ZM8vLyWLduHWvXruXw4Tx69GikqOh8q7Y1NTVMnjyZ/Px8VqxYwebNm9m7dy/z5s27LO6mpibGjx/P8ePHWbx4Mdu3b2f79u0sXryY48ePM378eJqami77tzZv3jz27t3L5s2bWbFiBfn5+UyePJmamhq+9rWvXWx79uxZZsyYQV5eHmvXrmXdunXk5eUxc+ZMysvLW523traWSZMmceTIEZYvX86WLVvYs2cPL774IsXFxa3aNjc3M27cOE6cOMGiRYvYsWMHubm5LFmyhGPHjnX4HbFv374OvyN+P24sCti5davj3xG//e1vXfuOqDlTDlhzmuL9jgiHw2nzHTFv3rx2vyN27tzJwoULPf2OWLlyZVp9R/ziF78gLy+PGTNmcPbs2cu+I+zYZsV326iIyDPAbztp9gHgYeDrSqlWw2EiUgDMjQyvtT33fcAuYIRS6lSL1+cAI5VSj7Rp/xHgf4H+SqnKFq//OtFrR97vDnRv8VJvoNhsoxI8PvEJq6fp5Ze9jiT9uOYa+MpX4NmOZhQaEqIq1Mzni9/k94Ov5kPZfb0Ox1Y+UXiQJ/sN54t9BnsdisFjgrqNyjTgpk4eh7EmcA+NcfxgLu9JilIaeW7bGzSkg2PaO0+i10Yp1aiUqo4+gJp4LmaW2o8fv7hKhzlN6eoqHRe4TFdX8RLdakS3bVTAmgzu161U/J5XbuOGL9/1NMVLZDJ2PvBBpdQbkdc+iDV5+0al1NEYxwhQAkxSSk2IvNYNa1jtl0qpWW3af4TYPU0JX7udzxDXhr2NjY1079693fcNl/CLq1tvhY9+FKZM8S6GdHX10EPW3KZly7yO5BLp6ipeTlxo4JunjjJl6Pu4tYezt2277epf332LB7L78mT/Ea5d0y78nldu05mvoPY0xYVS6i2sZQHmiMg9InIPMAdY17JoEZEjIvJo5BgFTAZ+LSKPisgtwHygDmsJgegxw0TkDuB9kZduFZE7RGRAIte2i+eff97uU2qLX1ylQ09TurpKx56mdHUVLw2Rnhg3Frd021WWZPh2/zm/55XbuOGri+NX8JZ/BaZw6W64NVjrL7XkBqDlIP4EIAt4AegP7AUeVkq1HCr7Hq3nVW2PPH8Tq8iK99pxUV3dcUH88MMPd9rGYOEXV9XV0LWr9ewV6eqqVy84csRbN21JV1fxUt5QS3NNLU29aqnu2uTotdx21eV8HRWNzVR39d+8UL/nldt05ssOl9oOz+mAiFxB5A46g8FgMBgMtnClUurdZA40RVMaE5ljNYKOJ4T3xiqsruykXXu8AdydxHF+PNa4ih/jKn6Mq/gxruIniK5SOT5eX72BEpVk8aP78JyvifyldlgNW3UVADXJTGwTkXCyE+L8dqxxldBx0T8aV50fF/2jcdX5cdE/GledHxf9Y2BcpXJ8Ar5SGqPTdiK4IW6mB+zYVPDj5zWu3Dk2Ffz4eY0rd45NBb9+Xq98xYUZnvM50WUJSOEWyqBgXMWPcRU/xlX8GFfxY1wlhlu+TE+T/2kEfhd5NnSMcRU/xlX8GFfxY1zFj3GVGK74Mj1NBoPBYDAYDHFgepoMBoPBYDAY4sAUTQaDwWAwGAxxYIomg8FgMBgMhjgwRZPBYDAYDAZDHJiiKc0QkX8TkXdEpEFE9ovIhzpoe7+I7BKRsyJSH9l8+Mcx2n1RRPJFpDHy/Kizn8Id7HYlIt8QERXj0cP5T+Msibhqc9w/ikiziOTFeE/LvAL7fZncutj2I+14uLFNOy1zy25XJq9ate8uImNE5GQkb46JyLfatEk9r5RS5pEmD+BfgAvAd4CbgMlALXBVO+3vBL4CjAKuBh4HzgNPtmhzL9AM/Aq4MfLcBHzQ68+bhq6+gbXOx7CWD68/q9uuWhzXFzgGbALy2rynZV456MvkltX+I4ACrm/jIlP33HLIlcmrS8e8AuwBHox8x98N3Gd3Xnkuxzxa/aXvBWa0ee0tYGwC51gJLGzx80vAq23abASWeP1509DVN4BKrz9burgClgJ/AJ6JUQRomVcO+jK5pVoVAv06OKeWueWQK5NX1nuPAJXAgA7OaUtemeG5NEFEugF3AZvbvLUZuC/Oc9wZaftai5fvjXHOTfGeMx1x0BVAr0j3brGIrIu08y3JuhKRbwLXYi0WFwvt8goc9QUmt1ryNxE5JSJbReSjbd7TLrccdAUmrwA+C/wV+IWIvCsifxeRP4pIVos2tuSV2bA3fRgEZAJlbV4vw+pybRcRKQYGY/19PqOU+lOLt4clc840xylXR7D+53YI6AP8O7BLRG5XShXYE7rrJOxKRK4DxgEfUko1y6WNMFuiY16Bc75MblmcAp4E9gPdga8CW0XkI0qp7ZE2OuaWU65MXlm8F7gfaAAejZzjBWAAEJ3XZEtemaIp/Wi7RLvEeK0tHwJ6AfcA40TkbaXUkhTP6QdsdaWU2oM1Jm6dTGQXcAD4IfAju4L2iLhciUgm8Gfgt0qpv9txTp9iqy+TW5GGSh0FjrZ46XURGQn8DNjesmm85/QZtroyeXWRjMh7/6qUqgIQkZ8AL4vIU0qp+iTOGRNTNKUP5UCIy6veIVxeHbdCKfVO5I+HRGQo1pyKaNFUmsw50xynXLVtGxaRfcB1KUXrLYm66g38A3CniEyLvJYBiIg0Aw8rpbahZ16Bc75aEdDcao89WDdmRNExt5xy1YoA59Up4N1owRThLayi6EqgAJvyysxpShOUUhewumEfavPWQ8DuBE4lWF25UV6Pcc6HEzxnWuGgq9ZvWuMsd2D9g/QlSbiqBm7F+tzRx0ys//HegTVBEzTMK3DUVysCmlvtcSetPWiXWw66akWA82oXMEJEerV47XogDBRHfrYnr7yeJW8erWbyR2+z/BbWbZaTsG6zfE/k/bHAghbtnwI+g/W/iuuAb2Ldfjq6RZv7sG6z/CXWbZa/RK/bd+109VvgE1jj43cA8yKu7vb687rpKsbxz3D53WBa5pWDvkxuWT8/DXw+8m9wVOR9BXxB99xyyJXJK+vnXkARsBy4Gfgw8Hdgjt155bkc87gsWf4NOAE0YlXbH27x3nwgt8XPPwQOY603VIU1lv19IKPNOb+ENWHwAlaX5Rfc+Cx+cxX5h3kycr7TWHdW3Ov153TbVYxjn6FNEaBzXjnhy+TWxZ9/AbwN1AMVwA7g/wUlt+x2ZfKqVfsbgS1AHVYBlQNk2Z1XEjmRwWAwGAwGg6EDzJwmg8FgMBgMhjgwRZPBYDAYDAZDHJiiyWAwGAwGgyEOTNFkMBgMBoPBEAemaDIYDAaDwWCIA1M0GQwGg8FgMMSBKZoMBoPBYDAY4sAUTQaDwWAwGAxxYIomg8FgMBgMhjgwRZPBYDCkgIj8k9cxGAwGdzBFk8FgMCSJiNwHfN3rOAwGgzuYoslgMBiS51+BxV4HYTAY3MFs2GswGAxJICJdgAJglFKqzut4DAaD85ieJoPBYEiOR4CdpmAyGIKDKZoMBoMhOczQnMEQMMzwnMFgMCSIiPQCDgHXKaWavY7HYDC4g+lpMhgMgUREbheRhSKyU0Q+LSL9RWSyiMwQkVUickcHh38BWNu2YBKR+0VkgYi8LiKfEpEMEXlKRKaKyMzIte6JtH0scq0Zkdc/5uDHNRgMNmCKJoPBEFT+HfgmsBGYB8wBJgLLgE8B3+7g2MuG5kQkA3gSawmCXcCLwPNAvlLqh0qp7wFvAn8Wkd8ADUqp7yulvg9sA5ZHzmEwGNIU8w/UYDAEDhG5FiiJ9BSNAAYAzyql3gUGArXA2naOHQq8Rym1t81bHwD+pqw5DyOAwcB6pdT/tmhTDVwDlCmlVrZ4vSwSw+CUP5zBYHCMLl4HYDAYDB4wFFgR+fP9WHfBHQBQSr0MvNzBsV8GXorxendgVeTPHwI2KaU2tmlzG/AOMLvN6zcB9cDZeD+AwWBwH9PTZDAYAodSardS6m8iMgi4BchN4PB/Bf4c45zblVInROR9wJXAlpbvR9Z1ug/IVZffgfMwsMNMKjcY0htTNBkMhiDzUUCIs2gSkeux7jo+2kGz6ITutuf8ANCr7esicitwHR33bhkMhjTAFE0GgyHIfBRoBPbE2T6etZk+ClQCf2vz+kciz7ltXn8sEsPLACLS0QR0g8HgIWZOk8FgCDIfBfYopRribP8vXCp+2uMjwHalVDjGtY4rpQrbvP4FYI1S6lyk1+nKOGMxGAwuY3qaDAZDIBGRYcCNxD80dw9QqJQq7aDNTcCwtucUka5E5jPFOGwQ8FpkuYFfAtPiicdgMLiPKZoMBkNQGYp1q/+yONvHMzQ3ECgBVrZ5vR9wHlgU45gfAV/CuiPvRaWUuYPOYEhTzDYqBoPB0AmRO9/eBm5VStV4HY/BYPAG09NkMBgMnfMwsNcUTAZDsDFFk8FgMHROPENzBoNBc8zwnMFgMHSAiPQE8oH3KaWavI7HYDB4h+lpMhgMho55FNhgCiaDwWCKJoPBYOiYB4AFXgdhMBi8xwzPGQwGg8FgMMSB6WkyGAwGg8FgiANTNBkMBoPBYDDEgSmaDAaDwWAwGOLAFE0Gg8FgMBgMcWCKJoPBYDAYDIY4MEWTwWAwGAwGQxyYoslgMBgMBoMhDkzRZDAYDAaDwRAHpmgyGAwGg8FgiANTNBkMBoPBYDDEgSmaDAaDwWAwGOLg/wMbEDfs9/TPCAAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = Graphics()\n", "for r1, color in zip([0.4, 0.5], ['blue', 'turquoise']):\n", " eps1 = eps_p(a1, r1)\n", " l1 = l_p(a1, r1)\n", " V1(r) = V(a1, eps1, l1, r)\n", " g += plot(V1, (0.3, 0.6), color=color, axes_labels=[r\"$r/m$\", r\"$\\mathcal{V}(r)$\"],\n", " frame=True, gridlines=True, axes=True)\n", " g += point((r1, 0), color=color, size=60)\n", "show(g, ymin=-0.01)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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