{ "cells": [ { "cell_type": "markdown", "id": "761c1747-adda-4e4f-a2a0-a7556e31d75f", "metadata": {}, "source": [ "# Comparing coordinate systems\n", "\n", "In this example, we will study how the choice of coordinate system influences the behaviour of heyoka.py's adaptive integrator. We will focus on a simple (but nontrivial) dynamical system, consisting of a central Keplerian force field coupled to a force field constant in direction and magnitude. This dynamical system is known as the *Stark problem* or *accelerated Kepler problem*, and it has numerous applications of practical interest (including spaceflight mechanics, the dynamics of dust grains in the outer Solar System, atomic physics, etc.). Note that the Stark problem can be solved analytically via [elliptic functions](https://arxiv.org/abs/1306.6442), but of course here we will consider a numerical approach.\n", "\n", "Without loss of generality, we can choose to orient the constant force field towards the positive $z$ direction. The Hamiltonian of the Stark problem in Cartesian coordinates (and adimensional units) thus reads:\n", "\n", "$$\n", "\\mathcal{H}_\\mathrm{cart}\\left(v_x, v_y, v_z, x, y, z \\right) = \\frac{1}{2}\\left( v_x^2+v_y^2+v_z^2 \\right) - \\frac{1}{\\sqrt{x^2+y^2+z^2}} - \\varepsilon z,\n", "$$\n", "\n", "where $\\varepsilon$ is the magnitude of the constant acceleration field. For this study, we will pick a \"small\" value $\\varepsilon=10^{-3}$, so that the constant acceleration field act as a perturbation on the otherwise Keplerian motion of the test particle:" ] }, { "cell_type": "code", "execution_count": 1, "id": "wireless-tuner", "metadata": {}, "outputs": [], "source": [ "# Value of the constant acceleration field.\n", "eps = 1e-3" ] }, { "cell_type": "markdown", "id": "dc8e56ef-c8e8-4e94-85ca-c736f2799576", "metadata": {}, "source": [ "We will also select a set of initial conditions corresponding to a low-eccentricity, low-inclination orbit with semi-major axis $\\sim 1$:" ] }, { "cell_type": "code", "execution_count": 2, "id": "d42ee668-e1e3-4559-b1c0-6e34fd0cb20e", "metadata": {}, "outputs": [], "source": [ "# Initial Cartesian conditions.\n", "cart_ic = [0.48631041721670787, 0.6097331894913622, 0.05026407424597293,\n", " -0.917207331153677, 0.8411848961939183, 0.10100071061790256]" ] }, { "cell_type": "markdown", "id": "bd8590b0-5bdf-46b5-8e76-62fef9ab62dd", "metadata": {}, "source": [ "We will now proceed to integrate this dynamical system using several coordinate systems.\n", "\n", "## Cartesian coordinates\n", "\n", "We begin, as usual, with the creation of the symbolic Cartesian variables:" ] }, { "cell_type": "code", "execution_count": 3, "id": "f346b5ff-9cfe-426b-9a07-5ad08fe9eae5", "metadata": {}, "outputs": [], "source": [ "import heyoka as hy\n", "vx, vy, vz, x, y, z = hy.make_vars(\"vx\", \"vy\", \"vz\", \"x\", \"y\", \"z\")" ] }, { "cell_type": "markdown", "id": "5b5b4bf0-c240-4301-92b0-631bdb738941", "metadata": {}, "source": [ "Next, we build the Hamiltonian:" ] }, { "cell_type": "code", "execution_count": 4, "id": "8b14b902-dd4d-47c2-9b76-a71a97578e37", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(((0.50000000000000000 * ((square(vx) + square(vy)) + square(vz))) - pow(((square(x) + square(y)) + square(z)), -0.50000000000000000)) - (0.0010000000000000000 * z))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ham_cart = 0.5 * (vx**2 + vy**2 + vz**2) - (x**2+y**2+z**2)**(-0.5) - eps*z\n", "Ham_cart" ] }, { "cell_type": "markdown", "id": "2637d545-c4a6-4bcd-80c2-b2ede49e4943", "metadata": {}, "source": [ "We are now ready to construct the adaptive integrator. In order to implement the equations of motion, we will use heyoka.py's expression system to symbolically differentiate the Hamiltonian:" ] }, { "cell_type": "code", "execution_count": 5, "id": "sound-jenny", "metadata": {}, "outputs": [], "source": [ "# Construct the integrator object.\n", "ta_cart = hy.taylor_adaptive(\n", " # Hamilton's equations.\n", " [(vx, -hy.diff(Ham_cart, x)),\n", " (vy, -hy.diff(Ham_cart, y)),\n", " (vz, -hy.diff(Ham_cart, z)),\n", " (x, hy.diff(Ham_cart, vx)),\n", " (y, hy.diff(Ham_cart, vy)),\n", " (z, hy.diff(Ham_cart, vz))],\n", " # Initial conditions.\n", " cart_ic\n", ")" ] }, { "cell_type": "markdown", "id": "e29f6700-bd70-4f40-a449-733c344ad1e2", "metadata": {}, "source": [ "Let us now integrate the dynamics for a few time units and plot the resulting trajectory:" ] }, { "cell_type": "code", "execution_count": 6, "id": "other-sherman", "metadata": {}, "outputs": [ { "data": { "image/png": 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S6lNKqf1KqR1KqSsmnbtdKbXHO/eR2at68dJa877/3HbWcLWmLUZTNMBrLu3kP999tYQrMe8sbY6w6+O3885rlk55/u13P8Ff3r+bxfgllRBCCCHObE4ELOALwO1nOX8HsMb79V7gXwCUUibwT975jcBdSqmNM1rpItc7lmfFR+/j+7sGpzzf3RAmYBr4TIPP/Z8r+c1b1mIaMiVQzF9/9sZL+c5vXD/luX/5yQFWfPS+KRu7CCGEEGJxmhMBS2v9MDB2lkvuBL6oXU8ADUqpTuAqYL/W+qDWugx8xbtWzICvPnWUG/7qx2c83xILcmyiwC9cvZR//6WXceWyplmsToiZc0l3khc+/mq2LGmY8vyWP3mA+54/PrtFCSGEEGJOmhMB6xx0A72T7vd5x850/DRKqfcqpbYppbYNDw/PWKELUbpY4cNffY7f/frULaxXtUYBt5nFP951OR+5Yz0dydBslijEjIsEfHzz16/jH++6fMrzv/7fz/DOf/2ZTBkUQgghFrn5ErCmmmOmz3L89INa36213qq13traKm2Wz9UL/WnuuvsJ7nn22BmvOTCc466rlvKPd13O67d0EfLLXkFiYVJK8fotXfzgt17BVDNfH90/woqP3sehkdzsFyeEEEKIOWG+BKw+YMmk+z1A/1mOi4ukteaBXQO85lOPsKv/9D2BurwRqoBp8Kd3buL9N65k63KZEigWhzXtcZ762C28+/oVU56/+W9+wlefOiqjWUIIIcQiNF8C1r3A//G6CV4DpLTWx4GngDVKqRVKqQDwdu9acRHKlsM9zxzjvf/59Bmv6U8VuXldK3/8hk284bJuljVHZ7FCIeqvORbko3es58/eeMmU53/368/zf7/yHMXK1G3ehRBCCLEw+epdAIBS6svATUCLUqoP+CPAD6C1/gxwH/AaYD+QB37ZO2cppT4IfB8wgc9rrXfN+h9gAanYDp975OCUm6y2J4IMpkv4TcWr1rdz52VdvHpTB4Z0CRSLlM80eOc1y+huDPMX973I3sHsSefv3d7P00fG+fwvvYx1HfE6VSmEEEKI2SQbDYsay3b4hc/9jCcPn7mh42VLGogFffzu7eu5tCc5i9UJMbftH8ryN9/fw/27BqY8/+X3XMO1q2Rj4gslGw0LIYSYL+bLFEExw2xHs/4P7j8tXDVFA7XbVyxtIB7y8Xdv2yLhSohTrG6L8bdv28KbLp+ykSl3fe4J7t0uS0SFEEKIhU4ClqBYsVn1e/dhOSePZvoMxViuzOq2GB2JECtaYvzbL76MtoS0YBdiKtGg+wXEh165esrzH/rys3z+0UOzXJUQQgghZpMErEUuXayw/g/un/Kc5WiuXNbI/qEs77h6KX/7ti0EfPKfjBBno5Tiw7et49O/MPV+WR//zgt86MvPznJVQgghhJgt8ml5Eds7mGHzHz9w0rFI4MQeVqtaozx9ZJxP3XU5v/GqNbNdnhDz2us2d/H933zFlOfu3d7PZR9/gLLlzHJVQgghhJhpErAWqUf3jXDb3z980rGAaZAv27TFg/gMxYHhHPf8+nW8YUtXnaoUYn5b1xFn15+8espzE/kKa3//e1RsCVlCCCHEQiIBaxH6yZ4h3vlvPzvteNl22NSVYChToi0e5IcfvpErljbWoUIhFo5o0Mf+P7/jjOfXfOx7jOfKs1iREEIIIWaSBKxFRGvNj3cP8Uv//tSU51e2RtnVn+aq5U38169ezeq22CxXKMTC5DMN9v/5HXQ3hKc8f/mf/oAdfROzW5QQQgghZoQErEXkqcPj/PIXTg9XkYBJPOTj4HCOG9a08Jdv2czKVglXQkwnn2nw0O/cxG0b26c8/4ZPP8b3nj8+y1UJIYQQYrpJwFok9g1meNtnf3ra8SVNYfJlm0zR4pYN7fzpnZewoiVahwqFWPh8psE/v+MKfv2mVVOe/7X/foYv/ezoLFclhBBCiOkkAWsRGEgVufWUhhYAK1ui9I4VALhpXSsfuWMdyyVcCTGjfKbBh29dy++/dsOU53/vG8/zTz/ej3PKvnRCCCGEmB989S5AzKxcyeKav3jwtOPLmyMcHMmxoiVKayzIh29dy+q2eB0qFGLx8ZkGv3jdcgyl+Ph3Xjjt/F9/fw9ly+E3b1mDUqoOFQohhBDiQskI1gJmO5pNf/T90463xYMcHs3zsuWNRIMmH75tLZt7Gma/QCEWMb9p8K5rl/HhW9dOef4fHtzHPzy4T0ayhBBCiHlGAtYCpbVm1e/dd9rxoM9gKFPi6hVNjObKfPjWtVyzsrkOFQoh/KbBr920indes3TK85/84T4+/9ghciVrlisTQgghxIWSgLUAaa1Z8dHTwxVAyXK4blUz/akCH751La9cP3VHMyHE7PCbBn/0+k3csmHq/xf/7Lsv8uDuIdkrSwghhJgnJGAtMFprXvbnp6+5qrpyWSP7h7J88ObVvG5z1yxWJoQ4E79p8C/vvILNPckpz3/oy8/yxMFRbJkuKIQQQsx5ErAWmF/896cYyZamPLelJ8kL/Wned+Mqfu6KnlmuTAhxNn7T4H/ffx0tscCU53/tv5/hJ3uGZrkqIYQQQpwvCVgLyB/fu4uH9w5PeW5zT5LtfSl+85Y1vHVrDz5T/uqFmGsCPoNH/t8rz3j+3f+xjd0D6VmsSAghhBDnSz5lLxD//tghvvD44SnPre+Is6Mvxf+7fR13XtZNIuSf3eKEEOcsHDB58mOvOuP52z/5CMdThVmsSAghhBDnQwLWAnD/zgH+5Nun76WjFCxpCrN7IMP/fdUaXr2pg45kqA4VCiHOR1s8xA8//Ioznr/2L35EpliZxYqEEEIIca4kYM1zz/el+Mg9O6Y8t7QpQu9YgQ/cvIqb1rWyqjU2y9UJIS7U6rY4X3vftWc8f+kfP4DW0vRCCCGEmGskYM1jWmv+64kjTORP/ya7pzHMkdE8P791CZt7Grh8aWMdKhRCXIyrVjTxt2/dcsbzt/39w7NYjRBCCCHOhQSseezZ3gm+uq33tONt8SB94wVetb6Ny5c2cNtG2etKiPnqTZd38zuvXjfluX1DWX7zK8/KSJYQQggxh0jAmqcKZZs3//Pjpx1f3hxhKFPipnWtbO5p4I2Xd6OUqkOFQojpYBiK/3PtMn7puuVTnv/mc/3c/fDB2S1KCCGEEGckAWue2vCH9592rDMZ4vBonlesbcVvGrzzmqWE/GYdqhNCTKd4yM97XrGSV61vm/L8X3xvN9967tgsVyWEEEKIqUjAmode94+PnHZsWXOE46ki165sJlOs8Puv3UBzLFiH6oQQM6G7Icyv37yaLUsapjz/dz/YyzNHx2e3KCGEEEKcRgLWPPO5hw+y89jJG42uaIlyZDTPdaua6U8V+MBNq1nWHK1ThUKImXLlskZ+6bpltMQCp507Mprnf7b1cmA4W4fKhBBCCFElAWseeb4vxZ/f9yIAPsNdV7WqNcqhkRyXL23geKrI7Zd0cIs0tRBiwXrjZd284+plU5778pO9bO+doHcsP8tVCSGEEKJKAtY8kSlWeNfnf1a7bzmaNW0xDgzn2NSVIFWo0BoP8pHb19exSiHETFNK8b4bV/L2ly2Z8vyHv7adA8NZ6SwohBBC1IkErHlAa81H73n+pP2uWuNB9g1l6W4IU7IchtIl/ukXrpCOgUIsApGAjw/cvJqrVzRNef6X/v0pnuudmN2ihBBCCAFIwJoX/utnR/nOjuO1+0GfwXCmhM9QNEb97B/Kcve7rqQ1Lk0thFgsljRF+I1XrqErGZry/F2fe4LUFJuQCyGEEGJmScCa4/YMZPjqU0dPOlayHAA2dSXYeSzNR+9Yz3WrW+pRnhCijq5f08Lbr1pKeIrtGIoVh7sfOVCHqoQQQojFTQLWHDaSLfHjPUMndQ2sfpC6akUT2/tS3LaxnbdunXothhBi4fuNV66m4wyjWP/04wM8dXhslisSQgghFrc5EbCUUrcrpfYopfYrpT4yxfnfUUo95/3aqZSylVJN3rnDSqnnvXPbZr/6mbPzWIpPfG937X5LLEihYnPNyiaePDRGT2OYD75yNU3R01s2CyEWB6UU933ohjOef+tnfkquZM1iRUIIIcTiVveApZQygX8C7gA2AncppTZOvkZr/dda68u01pcBHwUe0lpP/lr2Zu/81tmqe6b1juX5//5nR+1+WzzISLbEJd0JdvSliAV9vPXKJVzanaxjlUKIuSAcMPnKe6854/lNf/T9WaxGCCGEWNzqHrCAq4D9WuuDWusy8BXgzrNcfxfw5VmprI6+vaOfkWypdn8oU6IjEeLIaJ582ea2je2885ql0jVQCAHANSubefPl3Wc8/7cP7JnFaoQQQojFay4ErG6gd9L9Pu/YaZRSEeB24OuTDmvgAaXU00qp957pRZRS71VKbVNKbRseHp6GsmfOoZEcf3X/6R+GAj6DTNHipnWt3Ly+jeaYdA0UQpzwt2/bcsZz//ij/ewZyMxiNUIIIcTiNBcC1lRDMGfaIfP1wGOnTA98udb6Ctwphh9QSr1iqgdqre/WWm/VWm9tbW29uIpn2J2ffrR2OxHyAXDF0gaOjuW5YU0LbfEgr9vcWa/yhBBzlFKKh3/n5jOef+2nHiFVkNbtQgghxEyaCwGrD5jcBq8H6D/DtW/nlOmBWut+7/ch4Bu4Uw7nrf/Z1ku66C5IjwRM0kWL9R1xnjk6wcbOBNmSxa9cv0KmBgohprS0OcKfvfGSKc9ZjuZ3/3fHlOeEEEIIMT3mQsB6ClijlFqhlArghqh7T71IKZUEbgS+NelYVCkVr94GbgN2zkrVM0Brze9M+vCTL9t0JUPs9qb1dCZD3LS2jfUdiXqVKISYB950eTcrWqJTnnvswAjfeu7YLFckhBBCLB51D1haawv4IPB94EXga1rrXUqp9yul3j/p0jcBD2itc5OOtQOPKqW2A08C39Va3z9btU+3X/uvZ047Vh3Num5VMxOFCr903fJZrkoIMd9Egz4++fOXTXkuU7T45rPHODSSm/K8EEIIIS6O0vpMy50Wrq1bt+pt2+bWllkvHk9zxz88AoBpKGxHs74jzu6BDDesaWE8X+aDN6/m9ktk7ZUQ4qVprfnSk0f52DemHtR/zw0r+O3b1hHyNi+f65RSTy+krTiEEEIsXHUfwRKuP/n2rtpt29FcvrSB3QMZtixpYDBdZFlzlJvWtdWxQiHEfKKU4pXr27hhTcuU5w8M5/jyk0dnuSohhBBi4ZOANQc8sGuAJw6eaIxoKHj26AQB08BxNIZS/MrLV8ybb5qFEHNDZzLMz79syZTnfrR7iGzR4uBwdparEkIIIRY2CVh1Npotcc8zJy84X9kaA+DWTe3sGczw+i1dbOlJ1qM8IcQ8d8uGdt62tQeAkP/kH/l/+4O9PLZ/hExRWrcLIYQQ00UCVp3t6k9z/66B2v31HXH2D2W5ZmUTP3hhkBvXtnLDmhZ8pvxVCSHOX8hv8vMvW8qGzgTFinPa+ft3DfD8sVQdKhNCCCEWJvnUXkcT+TKf/vH+k47tHsgQ9BmkCm73wFs3tnNpt4xeCSEu3JXLGrmka+rtHR7bP0qxYstUQSGEEGKaSMCqoz0DGZ48dGLt1bLmCADXr27hxeNp3n/jKi7tTsqmwkKIi/Y7r17Hytap98b6lS9sYzxfnuWKhBBCiIVJAladaK35+bufqN1f0xbjyGiey5c28ODuIdZ3xFnaFGFDp2wqLIS4eG2JEDeubaUjEZry/H88foThTGmWqxJCCCEWHglYdfJc78RJ9/cNudNzqmskbtvUweVLG2a5KiHEQvax12w4Y0OLe7f3c3QsP8sVCSGEEAuPBKw6edM/P167vbrN7Rp407pWXjye5raN7SxpDLPK6yYohBDTwWca/Nata2mLB0875zcVb7/7pxQrdh0qE0IIIRYOCVh1sHsgXbvdkQixfyjL5p4kP9kzzJq2GH6fwTUrm+tYoRBioXr39SsYzpbwGSev7azYmoqtuX/nwBkeKYQQQohzIQGrDm7/5CO12wPpIgD5svut8bLmCDeuaWVJU6QutQkhFjalFP/yjiuwHD3l+d/86nM4ZzgnhBBCiJcmAWuW7RnI1G4v9ULUrRvb2T+U5YY1LZQsh5vWt9arPCHEInDLhnZCfoO17adPQ17SFOb3vvF8HaoSQgghFgYJWLPsTf/8WO320bE83Q1hfvDCIM3RAPmyzdZlTbTFp+7yJYQQ08FnGnzxV65m7+Dpe1/1jhX4ylO9WPbpmxILIYQQ4qVJwJpFTx0eq00FjId8ABje38Ca9hiFss0vXresXuUJIRaRS7uTbO45sYl5wvuZBNAUDfD739xZj7KEEEKIeU8C1iz6xPd2125nihbr2uP0jhXoTIbwmwZXrWiiIRKoY4VCiMUiHDD5nVevA9x9+NJFC4C2eJCxXJknD41xYPj0ES4hhBBCnJ0ErFnyzNFxDnofVqqjVxXHnYJzSXeSJw6O8qFXralbfUKIxWdzdwNvvbKntg/flcsaGfI2Gz48muNr23rrWZ4QQggxL0nAmiUPvjjIeL6CaSgyRYvLljRwcDjH5Usb2N47wdtftpSmqIxeCSFmTzLi58Z1blOdTV0Jnj4yDkAkYOJoODCU48Xj6bM9hRBCCCFOIQFrFhwczvL4gVEAbK/9cXXqTSzoI1uy+IWrl9atPiHE4nXV8ibed+NKdvWfCFLVtaI/fHGQH+0eQmtp2y6EEEKcKwlYs+DhvcM8e3Sidv+q5U1kihavubSD7b0TXL2iifUd8foVKIRYtNoSIZY1Rc94Pl2ssKMvNYsVCSGEEPObBKwZ1juWZ6JQOenYk4fHiAV9HBjKkS5a/Mar1qCUqlOFQojF7oY1LbzvxpWnHV/VGuWzDx1kolChWLHrUJkQQggx/0jAmmEj2RKf/OE+gj73rb60222LvKotxp7BDDesaWFly5m/PRZCiJm2pClCk9fBNBY80a79wHAOgP1DWfYOZqZ8rBBCCCFOJgFrhlXXNZQst2Pg88dSKAXV8ao3bOmS1uxCiLq7YU0rH7h5FdmSddLxrmSIP/3OCziyDEsIIYQ4JxKwZtBgusgf37urdn9ZcwSA123u4rneCa5f3cLGrkS9yhNCiJqNXQkKZeekY6tao/SnigD86MVBKrYz1UOFEEIIMYkErBk0kCpiTfra98honsaIn+d63VbIbYkgGzokYAkh5oab1rVy5bJGAPymqk0RvHZlM5/60X72DMg0QSGEEOKlSMCaQZ9/7FDt9suWux9aNnYl6B0rcMuGNi7pSmIY0txCCDE33LCmhWZvP76K7X451BoP8tOD7jYTx73RLCGEEEKcmQSsGWI7mm8911+7/9ThcZJhP3sHs7XNhm+/pKOOFQohxMmUUtyysZ0b1rTUjg1nSgBs7Ezwni9uw5HFWEIIIcRZScCaIT/ZM1S73dMYBmB5c4ThTIlrVzazrDlCV0O4XuUJIcSU3nx5Nz87OHbSsVWtUV447jbs2XZkvB5lCSGEEPOGBKwZ8vvf3InfdKf/9Y0X3IPeXldt8SCbupL1Kk0IIc7IZxq84bIuljZFaseqa7GuWdnE2z7703qVJoQQQswLErBmgNaa46kiFVvTnggC8JpLO9jeO8Hrt3Sxsz/FrRvb61ylEEJM7U/esImjY3kAur2R9njQxxPeyJbWMk1QCCGEOBMJWDPgK0/11m5XP4c8cXAMpeDYeJ6VLTGZHiiEmLOiQR+t8SC3b+rg2IQ7Am97P8zWd8T55S88Vc/yhBBCiDlNAtYM+PFud/1VyG8w5K25GsuV2dCRIF+2ee3mzjpXKIQQZ/dXb9nM/bsGAOhMhsiXbQKmwe6BDD/ZMyzNLoQQQogzkIA1zVKFCo/uHwGgMeK2O37+WAqA5liAxkiAFS3RutUnhBDn4qa1rYC7xUS1PXskaAKwrj3Ovz166IyPFUIIIRazORGwlFK3K6X2KKX2K6U+MsX5m5RSKaXUc96vPzzXx862Jw+NkS/bgLtnTEssSLZk0RYPojUE/QZr2+N1rlIIIc5OKcV7bljBU4fdroF3XtbFRL4CwGiuzAMvDNSzPCGEEGLOqnvAUkqZwD8BdwAbgbuUUhunuPQRrfVl3q+Pn+djZ4XWmp95G3K2xd3mFkua3LVWr1jbypOHxnjrlUsI+Or+tgshxEu687JuAExD1fb1e+2lnYxkSzgadg+k61meEEIIMSfNhU/6VwH7tdYHtdZl4CvAnbPw2Gl3ZDRPuuh+wzvkbc55cDhHJGCydzBDezJY2xNLCCHmunUd7mh7ZzIEwNr2GN99/jjghq7/ePxwvUoTQggh5qy5ELC6gd5J9/u8Y6e6Vim1XSn1PaXUpvN87KzIFC2+tq2vdv+mda2kChVu39TBjr4Ud27ppjkWqFd5QghxXvymwT/edXltL7+9g1kAbvRG5EuWw1C6WM8ShRBCiDlnLgQsNcWxU9tTPQMs01pvAf4R+OZ5PNa9UKn3KqW2KaW2DQ8PX2itZ1W23bVXYb+7EHz38QwATxwcJegzaEsE6WmMnPHxQggx1yzxNhzesqShduyhve7P0DVtce7zRrSEEEII4ZoLAasPWDLpfg/QP/kCrXVaa531bt8H+JVSLefy2EnPcbfWeqvWemtra+t01l/z7e3uB41CxWZla5SBdJFLu5M4Gnoaw9I9UAgx76xoifIrL1/B9t4JAF7nbTMR9Bn85f2761iZEEIIMTfNhYD1FLBGKbVCKRUA3g7cO/kCpVSHUkp5t6/CrXv0XB47m77w+OHaWoXq0FquZDGQLvKaSztJhv31Kk0IIS5IMuxnRUukdvs7O9wvkq5b1QxAJOjjxePS7EIIIYSo8tW7AK21pZT6IPB9wAQ+r7XepZR6v3f+M8BbgF9TSllAAXi71loDUz62Hn+OXMkC3H2wAA4M5wBoT4Q4OJKjLRFiTZu0ZxdCzD+rWmMAtQ6oN6xp4cd73GmCT3tt3Dd0JupTnBBCCDHH1D1gQW3a332nHPvMpNufBj59ro+th8cPuO3Z82WblS1RDo7keMXaVh7eO8xG74NHOGDWs0QhhLggS5sj3L6pg/t3uXtfPbLP3Uz9NZd28NVtvdy8vpXjqQKdSemSKoQQQsyFKYILwoe/9lxtz6vDo+7oVdQLVJcvbWBVq6y/EkLMTz2NkVqTi9s2tteO/+zgGADNsSCD6VI9ShNCCCHmHAlY0yRTtOgdc1sZOxqaogGe650g6DMYyZboSITqXKEQQly45liAgM/ggRcGAXjLlT2M5soA/OsjBzGm6ukqhJh3lFLvUEo9cJbzP1FK/eoMvG5WKbVyup9XiHqQgDUNbOdEZ/jqRsLXrGzieKrI67d0YTtIB0EhxLx2aXeyNnplKPjfp909/25c28r3dw3iTLlBhhBiLlJKXa+UelwplVJKjSmlHlNKvQxAa/3fWuvbZrsmrXVMa31wtl9XiJkgAWsafPbhAwS9xd/FigOcaHaRLlRY3hzBa4IohBDz0rr2eK15z1Jvb6wlTeHanliHRrIUK3bd6hNCnBulVAL4Du6+ok1AN/AngMzzFWKaSMCaBj89MErJcoPVSLZET2OYx/aPsrknyTNHx3nl+rY6VyiEEBfHMBQrW6Ks74hzeDQPuKEL4NqVzfztA3s54h0XQsxpawG01l/WWtta64LW+gGt9Q4ApdQvKaUerV6slLpVKbXbG+36NCd2oqme/xWl1ItKqXGl1PeVUsumelGl1P1e5+fJx7Yrpd7s3dZKqdXe7aBS6m+UUkeVUoNKqc8opcLeuYeUUj/n3b7ee9xrvPu3KKWem563SYgLJwFrGgxn3C991rS5rYyvWNoIQEssiGkoLulJ1q02IYSYLtesbEJ7UwHb4kF++OIQAA0RP33jBUqWjGAJMQ/sBWyl1H8ope5QSjWe6UKlVAvwdeD3gRbgAPDySeffCPwe8GagFXgE+PIZnu5LwF2THrsRWAZ8d4pr/xI3CF4GrMYdZftD79xDwE3e7VcAB4EbJ91/6Ex/HiFmiwSsi3R0NE/FdkevLG8RwrO945iG4sBwliWNERIh2WBYCDH/veXKJewZzABw/ZoWwF1f+r2dbvv2ii0LsYSY67TWaeB6QAOfA4aVUvcqpdqnuPw1wAta6//VWleATwIDk86/D/gLrfWLWmsL+P8Bl51hFOsbp5x7B3CP1vqkqYnKXVPxHuC3tNZjWuuM97xv9y55iJMD1V9Mun8jErDEHCAB6yI9tG+4trj70EiOpmiA3rECbfEgYb/JmnbZXFgIsTCEAybdDW4jn3ueOQZAY8T9AunqFU3804/31602IcS58wLRL2mte4BLgC7c8HSqLqB30uP05Pu4I1D/oJSaUEpNAGO4Uwi7p3jNDO5oVTUovR347ylesxWIAE9Pet77veMAPwXWeoHwMuCLwBJvtO0q4OGX+OMLMeMkYF0kQ7nBqvoh42XL3ZH25liAfNnmsiUyPVAIsXBctqSBTV3u5unrO+I8c3QCgHjIx6PeBsRCiPlDa70b+AJu0DrVcWBJ9Y43urRk0vle4H1a64ZJv8Ja68fP8HJfBu5SSl0LhIEfT3HNCFAANk16zqTWOubVmweeBv4vsFNrXQYeBz4MHNBayw8iUXcSsC6C1pqy19yiLe7uc/V8XwqAfNkmXaywsVMClhBi4Xjt5k6Op4oAtdGsq1c08cMXhyjbjnQSFGKOU0qtV0r9tlKqx7u/BHdt1BNTXP5dYJNS6s1KKR/wIaBj0vnPAB9VSm3yniuplHrrWV7+PtxRr48DX9VaO6de4B37HPD3Sqk273m7lVKvnnTZQ8AHOTEd8Cen3BeiriRgXYSjY3lGs+5Gm0MZ9wNHv/fBoy0eRGu3jbEQQiwUy5ojjOXKhP0mD+52m1xU9/m7bWM7n3pwXz3LE0K8tAxwNfAzpVQON1jtBH771Au90aC3Ap8ARoE1wGOTzn8DtyHFV5RSae957jjTC3vrre4BbsFtenEmvwvsB57wnveHwLpJ5x8C4pyYDnjqfSHqylfvAuaziXyFbUfGABjPV7hqeRNPHh5jTVuMkWyZnsYwDZFAnasUQojps7zZDVNvvLybLz95FICvPOUuyQgHTB7bL7NzhJjLtNbHgLed5fwXcKcMVu/fj9fa/QzX/yfwn+fx+u8G3j3FcTXpdhG3O+HvneE5vs+kdvFa652c0j5eiHqSEayLYCjFEwfHWNXqfuBwvP7FftNg/1CWOy7pONvDhRBi3okGfVy+tIHHD7hB6taNbuOxhoifbz3XT8lysB3pJiiEEGLxkoB1ETTuh4hqa+JtR8YBCPjct3VzT0Nd6hJCiJn0zquX1TYV/sELg4A7PRBgVWuMh/cN1602IYQQot4kYF2EarA6OpavHQv6DAxvkLohIvtfCSEWnmXNEQDuvKyrduzwiPtzMBIw6Zv0M1EIIYRYbCRgXYQDw9na7atWNAGwtt1tW7y+Q/a/EkIsTNVR+lzJAmBzT5InD7vrUfcPZylZpzUGE0IIIRYNaXJxEe5++CCGAkeD4605GMu5XQU39yRJhGQESwix8MRDft5x9VL++2duk4vuhjA7+lK8an0bD+4e4tqVzaTyFZIyin/OWlpa9PLly+tdhhBCiPPw9NNPj2itW089LgHrIuwfytIQ8TORr7DD2/8q6He/2bUcTU+jtGgXQiw8S5sirG0/MUp//64BAGIh95+UzoYwh0ZzXBZpqEd589Ly5cvZtm1bvcsQQghxHpRSR6Y6LgHrIk3kKwCUbYfWeLC28XDANPCZMgNTCLHwmIbC9Bab/twVPXz9mT4AvvVcPwDDmZL0SxZC1IXW2tv03KFUsSlZ7gboJcuhYjtYjnZ/tzWW41C2HCq2e6xiO5RtjW07aNwZSlrrU57/RJMz9/aJY5Mv1frE/VOv0d6Dq5ebhiLkNwn7TUJ+g42dSaJBE59hYJoKn/cz98TvRu2+YchP27lIAtY02NSVYFd/mq5kiO19Ka5Z2VTvkoQQYlbcv/M4AO99xUrufvggAI/uG+bWDe31LEsIMYcVKzbpQoVUoUK+bFO2HbIli3Shwmi2TLpYoVhxyJUsRnMlsiWbXMmiWLFrocUNUXYtSBUtu9Z8DLwvgpQ6KYhorVFKnXRN0OeGFb9p4DMUPtNtVla97JR8dfp9pg5hk16GoM8g6DMJ+o3a600OSRrccOeFwO/tHDgpnPm8Ov2mga8WuAyUqr628q5UxIIm8ZCfWNBH0G+gJn3d5TfdIBfyglw85KclFiAR9hML+CSsTSMJWBeoPGkRd3XB90jWXX/VHAsSDcpbK4RYuFpiAd5zwwo+98ghAFLeaP5br+zhf57uq2dpQogZ5jia4WyJQyM5jo0XyBQrpIsWI9kSA6kio7kyA6kiw5kSZXtmmt4oBaZyg5PfUIT9JtGgwrZPDjvuCJBBwHTDk888EbzO9Gez0ScFEzgxanUq0zAI+U2CPvd3v6kwlHJfx3DDmu3o2oiZo8G2HMo4k0a23JlP4YBJNOg7ZbRKUbY1+bIbMFMFB0NVX9cgEjBrgdBxNAPpEvuGspQtB60hHvLRFA0QD/kI+Ax8hvuZtWQ5pIsVJvJlDKUI+kzv86zGbxrEgj4vqJlEAj5a4kEawv6TgqNpKDqTYRoj/pOCq5CAdcF+tHuwdrva4KI/VQCgWLZl/ZUQYkHrTIZZ1lyu3b/PG8maKLhBK1+26lKXEOLcFSs2w5kSI9kSfeMFDg7n2DuY4ehYnr2DmTnREbQ6JdlUbtiwta5tZq4U+A1vVMcbgTKD7mhU9THghiNHg+MNCzla43hBrBqbTo8H7hm/6Y46Bb0QZXh1uAFKob3ntR1NyXIoWd4zVrxn8e76TDcETh5Rq9ZuGopixSZXtsmWbCq24/55vXAYDphEvF9aQ6FikyvZjGRLOI4bopJhP0G/SXs8yIqWKAHTfY18yWYsX2YkW66N1E3+88WDfiq2Q9GysR2HlliQWMiHqRQThTJ945Y3eugQCZiEAiaNET+NkQB+06A/1Q8aOpKh2vveGAnQGg8QD/npbggvykGHxfcnnib7h7K1DoKHRnIEfUbtB1Es5CPsN+tcoRBCzJwlTRG+t9NtbvG6zZ18Z4cbsB7bPwLA88dSXL2yuW71CbFYOY6mb7zA4wdGuH/XADv6UrUOx3OVUu40OK3dJmHV+9WpdNVRJ+OUkR3DUOCNAFXDUzXwaFtjn2FUpTqpDkVt5CZoGvh97qhT9TUmd4quONod3aqFqZOf0zQU0YAP0zwRBqv1+kz3z1Yo25Rsh1zZxna0F3jcEa+w3yQR8gHuVMZqiMoUy4zlIBr0kQj7CPoMEiE/HYkQ4YCJoRRlbzSqOsKVK9v4TYXlVNeBua+VK1mULYeAz6A5FqAxEiAa9KG1+6VYpmgxlnOnaFZH+CIBH53JEKZhMJQpun8upTg2UaBYsWv1DmVKtCWCtMVDDKUzPH6gRLpQoWQ5tCdCdDWEakErEfKzpClCQ9hPV0O4NhNsIZGAdYHSRQvvCxTSRYvrV7fw6P4ROpMhhtIlljRF6lugEELMoKZogHHvQ9v+IXdPwGrrdp+h+O7zx/mVl6+QOf1CTJPhTInv7TzOfz9xlD2DmXqXM2385okg5fdGoqo/Nar5SKG89UbuL9sLO+41p6+tAjAM8ClFwDTcAOUzCPpPTJFzp9UpbEfXflm2xnZsKqjalMDqVEG/NwXQZ6gTjSe8qYbVkayK42A7mrLlkC87wIlAaHrTGIPeF/CW7VCo2OTLNiXLJqUUkYC7fspvGkSDPpqjQcIBoxY8SxWbsteQI1tyR8wMpShaNlq7IapQthnLlVFKkQi7X/jHQn6SYT8hn0nJckgVKqQKZcZyZVKFChXbnU4YDph0NoSo2JpcySIZ9hMN+siXLVKFIrajyZbcka7maJDuhjDJSIBMscJYtkwqXyFTtDCVoj0RZE17nBFvmuhQukSunKcp6mfMV+aF42liQR8DqSK21rTHQ1zak6A1Fqr9HS5pCtMQCczQf3kzSwLWBcp6X12sbIlycCRH3GtP3BwLkC5WaveFEGKhCvgMogGT3QPuh73qN8jvvn4Fn334IEXLJhKQn4VCnE2mWOHb24/ze994vt6lTBtDgaFOhCJbn9xh77SueKZRu36y2mOUBn36lzV+n1ELUNWpfNUw5TMMHF3tDlgNPTaOtt01TJNeTym3iUTANGujKbXRMm/kzNFuqKuum7JsTd62UZyYxlhtRuH+3HMDUL5kky1ZtRGrSMAkFvRhKEUs6K6PCvoMbAcsx6212oGwbNs4JY2h3NevrmezHM1EvoKetF7KNBTxkJ+eRh/RgEnGWxNXcTSlisO4U/b+/O74Xdjvq3VRDPlNmqIBQn6DbNEiW3HrHUgVa401mqMBmmNBDEMxnCmRLVqkixbHJgoETIPWeJDGaICxXNn9LFyw6BtP4TcNNJqw32Rde4x00WIgXWSiUCER8rO6LYbfVBxPFbl/5wDxkJ+lTREMQ/Hk4TGiAZPlLVFiQR+r22KE5skMMfmX7wJVvzk5dX5yoWzP27QthBDno6shzJ2Xd/Mlb8PhwXQJgFFvZCtbsiRgiUVtIl/mrZ/5Kfu8Ud7FQHnhyjDc0SO/6a77CXhhaHKIUurkVhKTt4CY6nnd55v8XCeurbZnr9hu98GKrWujUKZhEPYbJIP+E934DIWt3amCatJUQMtxaqNclqMpe6NS1aYVpnIbZ0SD7nqosuWuX6qGKJ+hiAR8RIOm2znQZ9LsTXm0qiNl3jTIagCt2G74CpgGtmNje9Mcx3MWGo3PMGrrv4J+g8aIj5WtURwvaGVLFn7TDZSpQoX+icKkdWrKez8cokEfrbEgyUiAiu2OZNmOO7VwKFPE0W44booEaIoGKNsOg+mSu+xFKfYPZbEcTSLsIxIwyZYsehojhPwmw5kSqUKFkuWOoLUnQmzsSmDZ7vTBTLHCvqEszbEg6zviWI5mPFfm6GgOv2nQ3Rgm7HcbduwZzNAQ9hP0mWituX/nALajiYd8dCRDKNyGcq/a0EbQNzcDl/zLdwGyJauWoI97jS36U0XA/YCxriN+WvcZIYRYaBJhH9aI+yXTypYoP9o9BJzYHzBfsiF+xocLMS9prTkymuemv/lJvUupi+qaIffXiZEqwzj5eDX7VJtLVL+QrjZZUIqT9oKqTtdztK61MAe3OUR1lKoaqBRQcdzpfGXL3bvKsp1aCIsEfO6+UgGTsN/A8RpDlCru9YXKiT1LTePkKYg+06hN/TOUIuBTWLamaDkUym5w83nNIqJBn9v8wm+QDPtrYcnRmmLFIeCrvl9u7SG/++cqW473fmjSxQqOBlO5swJMQ6GUIh700ZEMo3C/zM8UK7W1WkAtWDneOqt0sYJluyNa4YBBSyxIQ8SPoRSZokWmWPHa4dtMFHKULTdwdSZDBH0mw9kSlq1pjgUoWQ77h7NULE04YJIqVHC0pjUepCkaqI2OFcp27XNwWzxET2MYrTUj2TJaa/YMZIiH/HQmQ8S8QFpxNC8cz3idB6E9GULhhjfb0YT8Jus74oxmyxwezRHyG6zvSFCybPYOZvGb7vqxI6N5/u6BvXQ1hGmMBtjSk2RpU2TOdDOUgHUB3A3rbIDaOqyjozlaYu7QaLXjixBCLGSrW2Pc88wxAK5Y1sjBkRxbepL88EW3y2rfeIHlLdF6lijEWWmt6U8V+dvv7+GeZ4/N6msHzBPrgoI+s9YpLuT3fveaL5inTqfz9kDymW4oqIaDqsnrlybvxzT5i98TxyaZFF6qtNa1jXlLluOFGafWSKIanrTWOM4Ux2rXaSqWJl9xu9HZzqQpg6r2YicClBc2qmHuxPor97mqdRjeuqVEyO1uF/abOI7bIKJQsRlKV2qjT9VmFpGgWXvZ6ntpGu7omWXr2roorXVtFM6d1uf+KlvuSJmj3XVKRUvV/q6CPkU44P4dAbXNjXMli4o3ulX9OwT3NTsSIZRSWN57bDmaaMB9Pq01+bLbXRDc0JYuVmrr1QI+g4ZogGQkgKEgU7QYzZYwDYOK49QaUfhNNwAmTT+ZkoXtQLfXXCJVqHA8Vaz9neRKFkG/QWcyTDLsp1hxR6SKFXfN2O6BDInqND6lGEgXiQZMChWbXf0pEmE/DeEA4/kyy5ujlG2H/UPZWifHtniQS7oTjGXL9KcKjGTKdDeG2dCZIF+2GM2WOTicY2lThCuWNpAqVNg3lGF5c5RLuhIMpEv0juXpaggTC/rYO5hhRUuUbz2XYzhT4vZLOogFfXQ1hGmNBy/0f8+LJgHrAoT8Jn3jhdr9FS1RDo3kuGZlE08cHCMaNGUNlhBiwbtsaQPP9U4A8OLxNABXLmtie1+KWza08dmHD3D9mpY6VjgzlFK3A/8AmMC/aq0/ccr59cC/A1cAH9Na/83sV7lwaW80ZDhTYv9wlof3DvOt5/pnrFPepq4EH751LTesaV2Q3c7qoRrcLNsNK5btBovqRrv5su19me14oz3u7VLFvQ7c1uuWrSl6gahQsSmUbSxHE/QbNOAHoGxpbMfBMBTKa15hKrfde7FiUy7ZteAT8ruf3+IhahsdFyru9L+wdy7gM4iH3DVUpuGOvBW9kbFUwapNj/QZJ4JvLOSukZrchdA0FLGg39toWFOs6FqzidFc+aQgFg6YbkAKuy3VR7Jl8mV3CratNb1jeUqWjWkoEiF3ZChftrFsTUciTCzkI1OsMJor1wYIhrMlLEcTD/pY0RIlHDDJl2xGc2UCpiJbsugbL5AI+WiNB7Edd6rfksYIjtYcHslha00y7GciXyES9LGxK0m6UGEgVXDXn5UtWmJB1nbEqVgOYzl3Hdj+oSxLmyJsiibJFC3SxQoHht1jDV5YPDiSpTkaxGcolje7n7P9pkFXQ4hC2WF77wTdjWGWN0d5tneCjZ0JuhvDfGdHPxs6Ezx1eIwrljWSCPlY3Tb7UykkBVyAkM/gwKT51J3JEIdGcrTF3c4n7YnQouz5L4RYXII+szbPf1e/G7AKFbcB0PqOBP/y0IG61TZTlFIm8E/ArUAf8JRS6l6t9QuTLhsDPgS8cfYrnF8s2+HwaI79QzmeOTrOC/1ptvdOkDm1B/YMe+NlXbz9qqVsXdaIz5QQNdOUUt7aLAgz8zN+Kl7HvmL5RBizvDVa1Y55uZJFpmRh2ScCHEDJG7nJltxpdhXLXedU3Q/LW66FUhD2mlu43QhPjJxFAm73wYqjyRYtwA2T41bZ67TqvlYs6O5nFfKbpIsVxnLl2uMtW3NoxJ3aZxqKaNBHxXbIFG1vJCxMPOQjV7KYKLjrqgKmQbpYYTBTrDWiSIT9lC2HwXQRv1ffsQk3EDWE/TRG/EwUKli2w6rWKBVb0z9RpFCxCftNjk3kiQX9rGiJYhiKkWwZy3GnX+4bzNCRDLGmPU7ZcgNq2XbYP5ihqyFMcyxAqlAhEghwcDhX29Yo6b3uweEcAI0RP+va4wym3c2sV7fF2NCZYCBVpG+8wIqWKJt7GhjOllAKrl/dwuFR93P4ipYoE/kKjRE/9+8cYH1HnKNjeW5e1zar0wclBVwAn2nQnyrSlQzRnypy3Ft/VfbmFzdHA0TmSZcTIYS4GJGAyW0b2/nmc/0ApLyNhvtThdomnwvMVcB+rfVBAKXUV4A7gVrA0loPAUNKqdfWp8T6Gs+VOZ4qMpAu8NzRCXrHCzzXO8GhkVxd69rck+Q1l3Zyy4Y2VrbEZAuBRcTvNcdIhPzT8nxlb01UqlAhV7LRaBSKiuOGimzRIuuFi2LFbSaR9hpAgBuk4iF3zVaqUKFQsUmEfQRMg0LFZjBTxPIaX1QbV1iO2+2vp9HduDdXsry1URA2DfJli6FMsbbR77LmCIWyzUC6SDLsJx7ykSla9I3nCZgGjdEAjqMZzZZoigZpivpr0wVLlkPIb9A7licc8LGkKYzPNEgXKhTKbqA7MOx20G5PhEiG/YznyrTGgwxnSgyminQ2hLEcTcA0WNYcpd8Lce7UR1jfGWciX6FvvIBpwNKmCGs74qS992okW6YjGaKzIcTR0TxaQ1siSCLs48honuXNEVpiQQ4OZ1nREiUe9HF4JMfK1ihHRvO1KZ+HRnJkihZPHhrn1ZvauWxJw6wELQlYF2F5S5T+VJGhtBuwqgsyjermd0IIscC1xoO1NafxkI/7nnc3H84ULXzmgvw52A30TrrfB1x9IU+klHov8F6ApUuXXnxls6RiOwxlSoxmS+wfyrKjL8VAqsi2I+OMZEv1Lo/bNrZzx6UdbOlpYGlTREakxLRzN+oN0hw7/zU+jqPJli0vSFhYjjstMFO0GM2V3M58RNC4o2CZohukCmX3dbMlm+OpIoZSNEb8dCTD5Etu04mGiJ9EyE+2ZLFnIIMGkmE/ChhIFYkFfaxrj2NrGM2WGM9Xauun9g6WaIoGWNUaRSnFSLaE1nhhKks04IYpv6kYy1VY0RIlV7LYN5QhEnC7Cg6mi3QkwwAMpApkSzZBn4HlaFa0RilbDqPZMiXL4ehYnu6GMBs64xQrNv0TbhBsiQUImO7asIPDOTqSQdoSIYbSRVKFCq3xIF0NIV48nqE5FmBla4ydx1Ksao3SkQxxcDjHqtYYA+kirfGg161REQ2Y7BnIMJYr86oN7dP7H8QUJGBdhNGsO9/bXXzo7l8ghBCLSTzko+R15Lp1Qzv3PHuM7oYwP3hhkOZogGLFnjf7lpyjqVKjnuLYS9Ja3w3cDbB169YLeo6ZVLEd9gxk2DOQ4ehYnud6J+gdy3OwziNRVVctb+KaVc28an0b6zvjc7ZdsxCTGd46qUTID43n/riy5TCaKzGaLdf295rIu9MIQ3632cVErsyxiQJBn8GyZrd9eirvrr2qbpJ8cCRHwDRoSwTpagjXRteWNIXJlmxeHMgQD7nt3FOFCsWyzerWGPmKzZHRHI6GSNCkdzxPWzzE+o4EmaLFYNoNcH3jeVpiQZa3RKlYDjlvPd3+oSw9jREaowHKlrvubt9glu7GMKWKw/LmCMPelzaRoI+2eJCI97iw32R1W4xUocLRsRxr2+Os64gznC3hOJorlzUynCnREHHbuJdth4aIn5DfoH+iwLLmKCPZEgPpIgdHcixrjsz4uqw5EbDOYcHwO4Df9e5mgV/TWm/3zh0GMoANWFrrrbNVd7U1ZVV1aowQQiwWVyxt5PEDowC1BgBvurybT/94P5d0J3nxeJrLl57Hp4i5rw9YMul+D9Bfp1qmhdaaYxMFnu9LcXg0z46+CQ4MZzkwnKstxre9fXt0HWJgeyLIdataePnqFl61vo3GqOw1KRafgM/t7NfpjRCdidaaTMliOFNyt8rAXU+WLlgcTxVo89ZGDaVLFCp5mqMBkhE/A6kS8ZCPDZ0J0gV36p6jNdGgjyNjbmiqrq0ay5WJRXzeKFiZzmSIla1RRrJluhvC3gh3mZ7GcG3/qmTYz9HRXK1HQUPEXcfVO56nULYpWgG6GsKUIjaD6SIDqSKdyRCXdCfJliyGMiXa4kHiIT+HvJDUHg9ycCTHmvY4jnabcDRH3Rbu3Y1hDnrTGPcNZrC1u2HzQCrP/TsHuLSnyCvWtMzYdMG6B6xzXDB8CLhRaz2ulLoD9xu/yVMybtZaj8xa0Z508cQi3KZogIFUEaNO/wAJIUQ9vPbSTr740yMA7Pea/1QXh1+7qpmnDo8ttID1FLBGKbUCOAa8HfiF+pZ0fo6O5hnJlfjJ7iGOp4o8fmDUa3ntflGYDPsZypRojLhbj4R8BrmyjakU1gz/A7e6Lcbm7iTXrGzm2lXNLGmKzOjrCbHQKDVphOwlWLbDaK7MSLZE2evMOZIt1zoWVsNURyLEeL7CcKZEd0OYtkSQoXSJjmSIirfOKRFy13mN5tyQVfRGvEyvC0h7Isjq9jhj2TLZkvtc7YkQq1pj2I5mPF+mb8wNRp3JMPmyxeHRPMuaIwRMg6xj0TteoCUWoDMZYt9Qls5EiK6GME8fHmNDZ8L7s5RpiQXJlyySYT+RoOm1m3fIVyxWtEQpVGyGM6WTtjGYbnUPWJzbguHHJ13/BO43hnPC0qYIR8fyrG6L8eShMVbIni9CiEUkEjjxz0i1Vfu4t9FwplihMbKwRhu01pZS6oPA93FnXXxea71LKfV+7/xnlFIdwDYgAThKqd8ENmqt0/Wqe/dAmqcOj/N83wRjuQrHUwWaooHaB6ZsycIwcD+YlG02dgYZy5VZ3xFnJFuisyHMULpIUzTASLZMQ8TPsPdt8aAXxkayJcJ+dz3HuYgFfVyzspmXLW/kqhVNrO9IyB6SQswin2nQngjRngid8ZpC2aZ3PF9rh388VSBXsmmMBhhIFWiNB1nb7v6c6Bsv0BDxc2yiQGcyxNqOONmihaNhMF2iIeLQFAsQ8hso5e6V2BgJEA26nRIN5W443BoLEvS7Ldn3D2UJ+U2WNUcYy5V5oT/NpT0NrGiOcmyiwNKmCJf2NFAoW3QmQ+TLNsmwn+OpAh2JEKlChZFcubYmeOfxNAeGsnz9166b0X4JcyFgne+C4XcD35t0XwMPKKU08FlvTvtpZmox8fKWKEfH8iS8fa96GsMzloaFEGKuao4GGPX2IRr1Gh0MpksvOZ1lPtJa3wfcd8qxz0y6PcAc+CLw2ESBn+wZ4omDYxTKNulChUTYR9+4+6HoeKpIY8TPSLZEyG+S8/YD0lrXmpSM5coETIPhTIlY0MdwpkQi7D6mORpgOFuiJRZgPFehIeJ+4x0JmAR9BrmSTSzko1ix0RrWdcRZ3xHn1o3tLG+JsqI5Kg2hhJjjwgGTte1Tr1cqWw5943my3rYKtqM5OpZnKF3iyGjebQsf8jGWq7CsOcJAukhmNEdrPEih7LaBPzZRZDxfJuAz6EqGiARMjozm8ZmKZU0RVrfFaqNnrfEgbfEQB4ez9DSGWdoU4dhEgTVtMXrH8kQCPtKFCo6jyZVsxnIVhrNFQj6T4UyJ0VyZh/cOAyca082UuRCwznnBsFLqZtyAdf2kwy/XWvcrpdqAHyildmutHz7tCWdoMfFIxv0gUf2LShUqMkVQCLHorOuI8/iBUZJhPw++OARAtmhdWPcHccEqtsOOvhQP7BpgMF2s7fcT9Bskwn5Kls2a9jiD6SIbOxMMpIusbY8zlivTlgiSL9kYBjiO27jJZxjkKxbdfpOxXJnOhjD9EwU2dibYP5RlQ2eCg8M5ehrDjGRLmIYiYBqM58us60hw9YomrlzWyLWrmmm5gI5rQoi5K+AzWNkaO+lYdUq4ZTscTxWZyFfIFCscHnW7BmaKFr1jBUJ+A9OA7ka3C2Kx4tCfKtLdEGZNe4x82eboWIFlzRGaIu605aF0icZogIaIn8OjeXoaw8SCPnb2p1jZEuOF42mWNUXoTxVY0hRhNFsmEfKTL9vEgr7aZuQtMXf6c2t85n4mzYWAdU4LhpVSm4F/Be7QWo9Wj2ut+73fh5RS38CdcnhawJpOk5tZ5Mtuaq94G9NFAmbtmBBCLBbVL5nesKWL/3zCXZM1litP+Q2amDn37xxgZ3/K6zKmaQi7UzQPjmRZ2hRlOOtuMNocDbB/KEtbIsjxVAHDUORLMJ531y8MpN3pNcfTBZq8tVimociVLMJ+k3zZpikaoFC2aUsEMZSiIxniFWtaWd+Z4I5LOmqL2YUQi4/PNFjSFGFJk3v/utUnzjmO5uBIlj0DWcbyZSJBHxoLv89tYNHTGK7te7VvKENTJEB7IsRgusiu/hSbupK0xhV7BzNs6kpiOQ4V2/Fa0GvWdyRIFSoEfQYad51VybJ5yBu9euh3bp7xn09z4affSy4YVkotBe4B3qW13jvpeBQwtNYZ7/ZtwMdnuuABb2NhAMf7era6yXAy7GciL90EhRCLy75Bt8FFd6M7JXB9R5wnD4/x8y9bQqFsy9qaWfC954/zzWePEfKbaDTxoB+NpmQ5rG6LUaw4NEcDBH0GQ5kSVy5r5HiqyIqWKBVHkytZdDcmOTZe4MpljRwZzbG5u4GBdJElTRHyJRvLcdsfD6VLLGmK4GjNzevauLQ7ycuWN8mUPyHESzIMxeq2+Emt0keyJY6NFyhWbA6P5jg2XqAhEmBFS4zDIzlQivZEyFsHWqI9HmRdR4KRbImlTRF2HkuzqSvB9r4J1rbHyRTdTZgdrXn6yDg7+lIAfOquy2fly5+6B6xzWTAM/CHQDPyz106x2o69HfiGd8wHfElrff9M13x0LE9bPMhQpkT135JjE27L9mjAR758bgt8hRBiIfCbigFvw/W0N8J/+dIGdg9kWN4S4fBojg2diXqWuCg8fmDU3aS0MYyjIV2skC/bhP0mjgNDmSJBn9tRK192WzabhqJ3vEBbPEi2aFEo20SCJi8eT9OeCHFgOEs85CNXssiWbFrjQZqjAd5y5RIu6U6wti0uoUoIcdFaYsHaNOKrVzZTstw9sCxbs6EjziP7RxjPl2mMBPAbiuPpIh2JELmSzbHxAh3JEM/1TrCkKcLzx1K0xoKAZld/uhauwO2VMBvqHrDgnBYM/yrwq1M87iCwZcYLPMVQxp2zPpQ5sWP9IW/jRcvR+OQfGyHEInLDmlZ+tNtdd3V0LO8ddX8OBkyTii2bsM80y3Z4ZN8wh0fzRAImHckw7YkQCsiVLWwHLulOUijbpAoVNvc0MJQuYmu4tDvJkVF3L5l82SJVqHDlskZ6xwts6kqSKVaIBX28+pIOVrREWdMWm7G9Y4QQAiDoM9nUlazdv3ZVM71jBQ6Nup+3hzJFnu9LsWVJAzuPpVjfmaA5FsBxNJu7k6SLFn/3g70nPefhT7x21uqfEwFrvtGa2sK48VOmA+ZKFiHZt0MIsYhcuayxFrAODOfqXI1LKfVzwD1aL462Qz7T4NO/cAWv+8dHefF4hkjQ7aallLs22DQUw5kSJcsh7DcZzZYpWQ4+0yBdqGAaRq3NumVrBtNFAqZifUecV6xtZW27hCohRP0opVjaHGFpc4Qb17YC7t6LP9kzxGVLGzgwlGN5S4SDwzn+9pRgBfCmy7tntd6XDFhKqR8Cv6213j4L9cwLhlL4zRNdA6MBk1zZrvX+v2xJQ30LFEKIWWIaipD/xPqqfYMZgLkwavVfwDeVUu/UWtsASqlf1lr/e53rmjGXdLvf9g6ki3x3x3HefEU3zdEAJcuhYmuaowEqtmY4U3JbIDdHOTKao2xpVrREODzq7nVzxbJGLl/SwE3rWiVUCSHmrNVtMVa3xTieKjCe6+Ov799DpjR1o7nXXNo5q7UZ53DN/wP+Xin170qp2a1ujupsCDGQPjE9sKfRHbFa2x5n90CGoP9c3lYhhJj/Aj7FsXF3DWrANLC8zj8Fby2qXb8BpN3AQ8DXlVJ+79hvTMcTK6VuV0rtUUrtV0p9ZIrzSin1Ke/8DqXUFdPxuufiXdcsq92+55ljfO6RQ4zmyvgMRbpgYTkOS5oiNEYCtX1lOhKhWtOL37xlLR++dS03r2+TcCWEmNNKls1P9gzxu19/nr95YO8Zw9Whv3gNt25sn9XaXnIES2v9DPBKb7rF/Uqpe4C/0loXZry6OaopEmAiX67dry7wTYTcf8PDAZl5KYRYHPymwWDGbXCxoSvB9t4JgNp+IwVv/5E60Frrzyil8sC9Sqk3M/W+i+dFKWUC/wTcirvNyFNKqXu11i9MuuwOYI3362rgX7zfZ9yfvvGSWpv8qu/uOA64zUg2diXpbgihNYT8JoZSNEcDvHXrEjZ1JSRUCSHmvMMjOf7xR/v5+jN953R9PX6undO/esqtbA/uPxJ/BrxHKfVRrfV/zmRxc5VSU+8AHQ2602RCPhnBEkIsDn7TqG1T0Rjx137feczt2jSWK9crYI0DaK2/6IWs7wLTsUD2KmC/12QJpdRXgDuByQHrTuCL3vqvJ5RSDUqpTq318Wl4/Ze0/8/vYPXHvnfa8Yqt2d47wfZeWNESZW17jOtXt/D6LV0E5N8tIcQcNpwp8ZmHDvBvjx46r8e9YUvXDFV0dueyButRYCWwC3gC+CXcqRf/Vyl1g9b6vTNa4RzVHg/Vbse8YFWdGlOy6r72QAghZoXfNGrrrSLeXlcvX93Cd3YcpysZ4rnecVa0RGe9Lq31qybd/l+lVBH4wjQ8dTfQO+l+H6ePTk11TTcwKwFrqi8AT3VoJEdXQ4jDozn+8v7drGiJsrI1yqrWGO2J0Es+XgghZpLWmsOjeb713DH++ScHal/knY/vfuj6kzoRzqZz+Vrx/cCuKTox/YZS6sUZqGnOC/gMIkHzpPsAfd46BNtZFE2rhBDCXXdluz/zqtOkN3Qm+M6O41y3uoUf7xnmfTeuqmeJAGitvwO0TMNTTZVeTv2hfy7XoJR6L/BegKVLl158ZSeelwd+6xXc9vcPT3k+7Dd59aZ2gj6T4yl3euexiQL7h7KM5nrZ1JUgGvThNxTrOxOsa4/LRtFCiBlXsR0efHGIv7p/NwdHLq4j7SvWttYtXMG5rcHaeZbTs9dQfg5Z3hw9qRWxoroGy307ncXRFVgIIfD7VO2bxerofXUkqzkaIFu0aIoE6lbfDOgDlky63wP0X8A1aK3vBu4G2Lp167T+w7G2Pc67rll22nqs9kSQK5c14mgwDMgWbda1x3nm6Dhr2+Osa4/x0J5hljZFWN4S5StPHqVsOUSCJsuboyTCfla1RvGbBp3JMC2xgKzbEkJcENvRPLJvmH/+8QGePDw2Lc9pGoq/e9sWblrXNi3Pd6EuamJ8dQ76YhPym2SKFYI+g5LlMOxtOFydlnFkNH+2hwshxILhNw3GvKY/A95oyEDa/b1sux/MjYW1+fpTwBql1ArgGPB24BdOueZe4IPe+qyrgdRsrb+a7FeuX3FawLq0u4FcyaY17iNftmmPh3h47zA3rm1le98EAZ/BFcsaGM2WOTKaw28aBHwGjZEAR8fylC2HXcdSrGiJMpQZYKJQYWVLlBUtUZpjQQwFsaCPpU0RfKas6xJCnJApVvjZwTG+8lQvP3xxcFqeMxow6UiG2NiV5JXrW3njZd1z4ksfaXd3gbqSYQ56o1jVKYI5rz1ktT2xEEIsdD5DsX8oC0BTzB2pShfcn4XFik3Qt7CmlmmtLaXUB4HvAybwea31LqXU+73znwHuA14D7AfywC/Xo9YVLVHef+MqPvPQgdqx8XyZJY1h9g1lWdkSZeexFFuWNLDtyDhdDSGUUuRKNrajMQ1FZ0OI3rEC+4YybOlpAGDPQIbHDoyysiXKypYovWN5dh5LEfSZJMI+EiE/Q5kSXQ1hYiF3qmF3Y5imaIClTRHiIf8ZKhZCLBRaa46O5Xny0Bj/+3QfPzs0PSNUk0UDJq++pIPrVrWwqSvBhs7EtL/GhZKAdYE2dMZ5dP8IcKJN+0S+AkCmVKFkLbwPFkIIcTbF2pdLJ2a71f97xOmntb4PN0RNPvaZSbc18IHZrmsqH7ljPZ9/7FBtGudQpkixYtPVEKZvPE9XQ5iBdJFYyEfANCjbmr7xAtesbOLgSI4nDo5x9Yom2uJBfrxniM5kmCVNESq2w2C6SLpYIegz6W4MkyvZxEN+BjNFFIr+iQLNsQDJsJ+H9w6TKlSwHE1LLEhbPFhb1xX2m3Q3hIkGfbTEgrTEAjL6JcQ8U7Jsnjkywace3MdPD47OyGvEgj5u29TOTevauHpF05xuyCMB6wJN/gbu1A8QpYpDqlChLS4BSwixsI17XywBPH7g9H9U58BMjUXv3g++nNs/+QgAqXyFgGkwmi2RDPvxGQaj2SKXL23ghf40LbEgGzrj3Lu9n809SS7rSfLEwVFaYkG2LGkgX7JJFyoUyjaJkB+tNe2JEMdTBfJlm5Jls6Ytju1o+sbz7B3MEAn46GoI18Lc8Ykio9kyflORDPtJhP3s6EthGoqQ32A8X0EBrfEgzbEgybCf7oYwAS90mYZyz0UDC236qRDzgtaa53on+Lsf7OWRfSMz9jqrWqNcsbSR69e0cMXSRpY0TcdOG7NDAtYFigZ9+E1Fxda1DTV7vGkXubJFKl+hLT53k7UQQkyHQW+9FUChcvL0aKUU0vOn/tZ3JPj5rUv46rZe0kWLWNBHczRIxdYMpossaQrzxMFRuhvClG2HZ46Os3VZE2O5ErmSTU9jxA3K2p32WbYd1rbHKVkOR0ZzjObKbOxKEPSZ7B/K8qPdQ3QkQ3QmQ3Qkw/SO5+mfKDCcKWIoxfKWKPmShWEoYkEfQ+kiZVsT8hukCxadiRCJsJ+RbIkX+tOUKjYaaIwEaI4FiAZMRnNlRnNlwn6TjkSIaNBH0GfQFAvQGAlgKoXfp2iPh2iI+OfEmgwh5qNixebpI+P8+2OH+OGLQzPyGrGgj809Sa/zX4JrVjbjn+ej2BKwLtDVK5qoeK2Jw353pKr6Ta7taEayZda01608IYSYFdUW7QAhv0GxcmKvkqDPkA1s54i/fMtmrl7ZxIe/tp3hbImg3yQaNKlYGqW8/cwcTbFs0RoLkitZmIZB0bJZ1Rrl8GieQ5kc161qZiBd4pF9w/Q0RtjUlWA4U+KnB0ZpigZoigZ42fImBjNFJvIVRrJlfIaiIeynbDt0JsNkihVyZQvb0aQLFZY1R4kFTYazZYYzRXb1pwn6DVpiQZY2RfCbiqFMieFMiVShQsCnAEUi5CPod1vNlyybRNiPGoZUoYLtaHymwtGgtdvRsjUexGeeCFp+06ApEqApFqDBG0lLhPzy36xYlLTWDKZL/MOD+/jyk0dn5DVWtkS5emUzGzvjbOxKEAn4WNkaXZBLaiRgXaBlzSeGKas/jKvdBBsjAY6M5rh2VXNdahNCiHowaqME7u9Bn1mXTYbF1N58RQ+5ss0ffHMnh0ZytMQCdDeEGc2WaY0H0VpTqNisaImydyjLuvYYSgV4cPcQ16xspi0e5BvPHmNla4xrV7YwkC6w7fA4jZEA6zviFCo2plKM5ko4jsbWmoaIn7ZEiIFUgWzJYuexFMtbIqxrj1OoOPSO53n8wAiJkJ9kxE9rPMTSpiiDaTeg5cs2oNGaWkv4bMmiMeInEvAxkS9TqFhoDSOZEqahaE+EaIkHKZQtRrNlUoUK+4Yy7B5IkwwHiARMkmE/4YBJ31iesXyZVMHC0ZqAaRDyu/+m+wyj1rQjFvJhKkWDN4oWnBTCDOVNdQz5iYd8Mm1RzHkHhrO85V8eP2mK93RojQe5fnULV69oYuvyJjqSIaIBc1GOIEvAukAh/4m0rb0F3bGg+3amixVShen9j1YIIeYiPamhRWcyxIHhXK2hglLuyIGYO951zTJu39TBX96/mwd2DZAv2zRFA2hgJFPm0p4k246Ms7ErwaGRHOP5CtesbGbvQAal4LIlDZRttzuYz1A0RNygEg74yJYsjk0U6GkMs6o1xvFUkUMjWfYOZljdFmNjZ4J0ocKLAxlePJ6hJRYgEvCxdVkT6WKFXMkiXagwki1h25pY0MTWGkO5e245WjOSdcNb71gBDSxpDLO8OUrQZzCWdx/7/LEUFduhJRYk5DeIBX20J0I42h0xy5VtihUbv8/wprBq4t4+lpbtoLX7b3wy7Mc0FCPZEodHc1i2JlWoULYdwn6T1niQeMhH0GdiOZpSxSZbsmp7YUYCbjhLhH0EfAaGUkQCJpGAj2jAJBwwMQ1FwGfUAlpkkX4YFdMvla/w1w/s5r+euPjRKEPBy1e3cOWyRi5f2khXMkR3Y5hIQGLEmcg7c4F8hsJQ4GjIFN2WxA0Rt/FFumDVRrOEEGIhq/788xmKUW89asmyvXMVljXJCNZc0xoP8jdv3cLeV6zkK0/2srM/RcVyyFcsdvRNEPabDGdKpIsWa9pi7D6epjEaqAVngFShzOq2OJGAyb6hLEfH8mxd3siKFsX23hTbe1OsbI2yqSuJ5Wj2D2U4NlEgHnQbVgR9BpmShd9U7pTBkjsKlS5WSIT8LGmNULYchjJFUvkK28bHiAZ9dDaEaIuH8BmK4WyJA8NZihWHaNANRIZSrG2Po5S7dqRYsSlZDhqLsuVgOQ6mUliOJl+y8JsGzV7nwrLtNqjKFC0m8mUOjeRwtCYW9NWacVSDmuVoRrNlBtNF8mUbQ7kNOhIhPz7TQGvNeK7McKaE5Tj4TYOgz0ChME2F31BUHI3WmpLlkC644dJyHKJBH7Ggj4ZIoDYNMugzar8mj5ApqqHNJBb01UIbuCNwQb/7mFDtOUz8ppIQNw9ZtkPRchhIFXjghUE+9/DBixqBWtoU4X03ruQVa1ppjQdPGjgQF08C1gVSSrG5p4HneicmjVy5HzSSYT+HR3P1LE8IIWbFsfECAJaja1tVVBcnW7YmFJB/tOeqte1xPvjK1RwczvLY/lF2D6Q5MJxlaVOEXMkiEfKTK7ut18dyZbb0NLC9b4LmaJBrVjbzxMFRxvMVXra8CZ+heHjvsNcxMMSKliijuRKHR3IE/QYNkQBau0G8ORpgolDB9lrCx4I+1nXE8RnuWqu+8QIvHk/TFA3QngixsjWKaRgMZYocHskBuVpTi9Z4kFB1BMlyCPlNfIaiZNkUyjZaw0SpgmU7xIK+2n5cpYrDeN6dPnhkNMczR8cJmAbJiJ940OeGqWQINFRsd+rkSLZEqeJgmqo2lbDJF6QxosmVbSqWw3i+QjhgEg/5aI0H8ZsGSkG+bJMv2xTKFumsVWtZH62OaAVNWuPuaG/F1li2w0i2RP+E+/+X7ehaQAwHTKIBH5GASdBnUrRsciWLXMkmX7ZAKYKmgeHNYgz63AAW9pto3LU2hqEwlTppTdpkpqEI+sxaOAv4DEI+A78XEqsj16ZSmIb7PKZh4DcUhqEI+02iQffPFQ34iAZ9hP1mrSZww2Httpp8fNLtU4LgyefOfN100VpjO26gth2NZWssx8F2NMWKQ7ZkkZ008jqaK5MtWYxmS7UvKVKFSm394Ez6/ddu4G0vW0JC9pmbEyRgXYT1HXGe652gyZsCU/Q6aCkFR8fy9SxNCCFmRcVxTjtWXcMi5j63MYW7XqJiO+w+nuFnh0b52aExt1Ou5WBrzfqOBN/fNcDmniRawzeePcaq1hir2+IcGHY3ml7e7I5Wli2HTNFtNFGyHAxDsb4jxkS+Qn+qwE8PZlnREmVVWxSF4uBIjvueP07Um8rXFg+ysjVKvmwzlC4ykS8T8rtT55pjQcD9Nt9nGDTH3OCWKlTQWtfaxSdCfpY0hYmH/PhNo/YB+LneCSbyFeIhd4QoGjBpjLpr0Wytqdjuh+dcySZXsgn4FIZSaK2JBHz4TXeUK1eyMJUiFnJrXtLkdlosVRzyZYtM0eLwaM671vY6JrphIxn2054I1t4fy9EUym5IOhEhtDdV0cBnGgRNt2GM7WjyZZtc2WJiokKhYqPR7giazyThTWsEN/wYhqJYsemfKJAputMXT23saXphyw1VbqA6NXg5jjsyXbFPfrSjTw4d1SBSqLiBcvKo57kwJ43O6VNakLrh8LyebsG4pDvBP7z9cla1xupdijhHErAuQqMXrI6MumGqOkWw+kNmJFuixfvHQAghFrpEyEe6aNU6C9qOpiG8cL5NVUo1AV8FlgOHgbdprcenuO7zwOuAIa31JbNZ48XwmwaX9iS5tCfJr96wkp3HUjzbO8HhkRwP7x1mVVuMXMlmOFNiQ2eCsuXQN56nIexnPF/GbxrEQz4GUkX2jmW5emUTsaCPgyM5vvv8cRojAdZ1xFnjhbIfvjhE3Ntc+LIljZiGO9KTLrrrnCq2JhwwKVUccmWbtniQzmSIQtlmNOeOPh0ayaEUdCXDtMaDLG+J4mjNULrEnoEs2VIF01A0hAPEgj46EiGWNEawtTtKZDtukCkph4DPwGcYWLaN31TkyjZDmTKWrYkETNqTIdoTbmfDarAoVGyOTRR4vi9FoWK7I0x+d7peNOhjWVMUw/BGwcrudMXxvDuVNmAa+E13yl8i7AZBv+kGupLlULZOhLWBkjvFcfLIUdBv0hDxE/S5o3ZKuQGkbDuULJtU2R3FsxzvMYbCnDQGVM0qAdOdShgwDUxDYdluwLQch1LFoWjZlCoOjj7xKK2pjYZVg0/1NtoNXoYCv+lOxzzXYGQ7iy9Bhf0mr93cyW0b27l5fdu8b08uXBKwLsKWngYAmmMBjo7l8Xtj3yXLXSTbP1GQgCWEWLAKZbdrXNWKlijb+1K1D27RoI+l82hjyHPwEeBBrfUnlFIf8e7/7hTXfQH4NPDFWaxt2l3SneSS7iTgfnjeP5RlR1/Km8bnBqtDI27zh5ctb2JXf5rneie4fGkDr2hv5fEDI6QLFZY2R7lqRRNo2D+UxXE0LbEgq1qjbsCZNKbiaE2h4jCcKdHZEGZ1a9zb+qREf6rI9t4JQn6Ttri7bmp5sxuohrMldg9kKFk2YS94tMYDNEcD2N40r4rjuOuVgu7UulLFJlOyqFiO27WwUMFQEAv6aYkF6EyGWNEcwdFQsR3GcmX2DGQpWW5Qsh3tTYUz6WoI4zfdfd+Klk22aHlt6ksEfSYhvzsy1BQNEQ6YtWvLlkO+YpMqVBjNuvuOFSp2rVEG4I5g+YxamAr63al4jvf4kmWTLzu1UDb5/fSZCr9p1I4Z3t501fuO4/7ZsiWr9ucCdxxNKeX97h5Ryn18dWqfoU5MzVPqxJQ9Q6lJ43DuVOGK7Y7UVWzHq/n8Rrbmq1jQx6/dtIpLu5N0JEO0ehtnS6fJhU8C1kXoTJ68kXB1fm0kYPJc70QdKhJCiNkzkC7WpkYDHE+5mw5XPxsuwA6CdwI3ebf/A/gJUwQsrfXDSqnls1bVLFBKsaY9zpr2OOBOid8/lMV2NEfG8vz0wAjRoMl1q5rpTxXZ0ZdiSVOEnsYIFdvh2HiBsN+kKRIgVXA77a5td6c7DWfLHB7NUbJsLulKsqYtTtGyOTyS49s7+lFAWzxEY9TPFcsaUbibWvenith2oRZeWuMBypamWLFJFyySYT9tiSCRgM9d+1R0R4P6J7KM5cq17n3JsJ+exggrWw0c7a51ypUs+sbzlCpuGPB5664SYR9BXwBQbjApWmRKFcZy7gheyO+uv1reEiUW9OFoTcULGCXLZqJQ4chYnlzJomI7tSCltTvCFPKdGJUK+d2mFIbyRqW80aRstuJOLZw0Xa8amKrRxjQMzGogUu7x6vTAamhSTP0hv9rEw9Gnjzw53jTKiu2+T2UvMJUtpxaiplINY1M953wUMA02dSf4uSt6eNWGNtrjIQlN4iQSsKbBs0cnAGqLuSOBkzceFkKIhShTrDD581Rh0jpUgGRk4UwP9LRrrY8DaK2PK6XaLubJlFLvBd4LsHTp0mkob/aE/GZtdGvLkgbesKULrTWjuTIDqSJl2+HwSI6JfIXjqQKjOc2R0TzLWyJctaKJwXSR5/pSTOTLdDeEuaQrgWkY7B3M8OThMfyGQWdDiPUdcXyG4TZ4sDXDmVKt21ki5CNXshnLV/AZFksaw6xscafvpQoVxvMVdvWnGc2WQLmbHSe9ToDLmiNoTW0a3Ei2RMmysR1NwOu2lwz7IeyO8uS8qXojIzk3CPlNGiIBOpIhVgXdtWTV4JEvu+GsuubJ0eA4J0JLNUglQm7Xv5A3KlVdk1UNUiNekKrYJ4/2TA4oSlXDlMJnuFP8TG+64FQmN4Nwa3JwHO99sBwKFXc6oBvo3BGtqUablAK/YXjNLdwmFz7DrAXK8ik1O3N8AVUy7Gd5c4RVbTHWtcdZ3RajPRGiuyFMQ8QvXRfFeZOAdRFWtEZZ0hSmd8zt8tORCLIdGEy7Ldp7pdGFEGIBq9hOLVSBO6qfKWZr0waNefihRCn1Q6BjilMfm+7X0lrfDdwNsHXr1rn76fMcKaVoiQVrU+OvWNp40nnLdnjheJqdx9IsbY6wtDmC7Wh6x/Ls7E+TL1u0xkOsa49TrLhT5UxDEQqbhAN+MkWLim1x0GuqsaY9xqauBKahSBct+sbyfH/XAIWKTchv0hgJeJ0IgxhK1aaq5csWuZI7GlMNUz7TbXdesTXpYoWRTIF8xSLkBa1E2M+y5giRgA/bcYNUpuju+1X0pvRVR4ksR+M4ujY9L+w3a0HKMBSW9/9NseKQKVoMlUteK3l9Uoc+cEeZFF6IMU7u2OduF6Om7MCnobbZs+1NzStWHIpe84lCxa6NPJUsG0efHJr8pkHAZxIP+b09vKiNWlVsN4AVyu7UxLkmYBo0RQMsb4mwrCnKitYo69rjrGmP0ZkMn9RIQ4iZIgHrIiRCfjZ1JmsBa++g+0O/PRHk+WPegk+t5ZsPIcSC1DdeOOnb7Uu7G9g7mCXsjeL7DFXrsjpfaK1vOdM5pdSgUqrTG73qBIZmsbR5z2cabO5pYLO3fvlUxYpN33iBfNmiYmsm8mVGs2WOTRQYzpYATXMsyFKvW+Gx8QI/2j3k7UPldkRc1hwl4FO1kZd0oULA53bgC/lNosEAjrf3VMmymchXmMjnai3eI16L9VVtMcJ+E8txaoHk2HjhtJEZ29G1qYFuK3OTgM9d51Sy3BBSqLhTA4unrK0CaoHKUMoLN25w8pnuOqtqoKqtdaK6rsldA2Y7zkktxAteMC2Uba9RiFMb/UO54SPgM2rTHQNekPJ5ocP2RrXKlrsuayhTPK1z4EsJmMZp79P5aI0HafBGGhsifmJBHz5T0RYP0dXgNjOJBU3Cfh8tMTdE+6QxhJhjJGBdpJvXt3L/rgGA2n5YQZ/74SJVqNA3XmDJwlrkLYQQAGRLFk8dGqvdr34xHPC5H3aaogF6GsP1KG2m3Av8IvAJ7/dv1bechSXkN1ndduY21I6jyVfcBhLZkkWhfGL0tGw7jOfKjOZKVGx3DKhQtsiW3PbnmaK7F9FYrkyxYqMURAI+4kEfPY0RYiEfWmt3DZdlM5guUrGdkxo9+E2DRMBP0Ov+V+3aV21JPpEvkyvZtSl91fNVPm9vKb83QuQz3N/9PqM26lsdeaquZypaDnbZ8Vqhu50Pq2u6qlMS3eYWbgv1aiOK6mtEAz4aIyc6BFa/79XaDVPZksVgukS2ZJ3178Y01Ekd/qrNPSLeflzVzncaN3Amw34awn4avFHEZNiPz1TEgj5aY0E6kiESYT+RSSN7QiwkErAu0uR/DJ4/lgJg31AGcPfCGs+XJWAJIRakUsVh31C2dr/6rfWE14a6JR5caCP4nwC+ppR6N3AUeCuAUqoL+Fet9Wu8+1/GbYbRopTqA/5Ia/1v9Sl54XD3kvLVvsy8GI6jyZXdzXmzpQpZLxhVvMYNk0NMtZmDu1eVu5lvrmxhO26IigbdTXXhTKO17rhTdZSpbDu16YpFb6TInXbnTi18Ke50Rr83jc/wfle1tu/uHlan/n+nTzvmMxSJsI+GcICGiLs+LRLw1Ub8fIY7bTIadNeKRfymjBQJcY4kYF2kTV3uIl+foWrdc6q/7x/Kki6c/VshIYSYrw6P5hjJlmpTgoLeyNXkjU4XEq31KPCqKY73A6+ZdP+u2axLnD/DUMRDfuIhPxB6yeuFEOJ8yFcRF6nazWhya9KDwzkaIn6296U4MparV2lCCDGjyt76q4S3mXDS+706al9diyWEEEIsJjKCNU16GsP0jReIh3xkvA0GgZPmiAshxEJhO5q89/OtPRGsbagKUKy4wWtV65nX04iTPf300yNKqSP1rmMKLcBIvYt4CVLj9JkPdUqN02c+1DnXa1w21UEJWNOguyFMNOC+ldVAtaw5wpHRPC/0p6nYTm0BqBBCLARDmSJHvK0oljRG2NWfZjDtbjQ8kHI7q0o75HOntW6tdw1TUUpt01pvrXcdZyM1Tp/5UKfUOH3mQ53zocapyKf+aXD7JR1MFNxF3ctb3Pax1R3WsyWLI6MyTVAIsbDsPJamwZsS6C6qh/aEu5alq2FBdQ4UQgghzsucCFhKqduVUnuUUvuVUh+Z4rxSSn3KO79DKXXFuT52Nrzp8u7a5sLVDkAhv/vWTuQrDGVK9ShLCCFmTO9YnrC3BrUz6Qar2hqsxkhtXx0hhBBisal7wFJKmcA/AXcAG4G7lFIbT7nsDmCN9+u9wL+cx2NnXHUneYC49wGjupN90bLZP6mNsRBCLAQHR7JYjrvWqtq6+cnD7p5YTx8d5w2XddWtNjGt7q53AedAapw+86FOqXH6zIc650ONp6l7wAKuAvZrrQ9qrcvAV4A7T7nmTuCL2vUE0KCU6jzHx844pRSXL2kAIFNwm1uM5twpg03RAD/aPTTbJQkhxIx68tAYzVH3i6Qfez/jjozmMA1FsWyfdcNYMX9oref8hxupcfrMhzqlxukzH+qcDzVOZS4ErG6gd9L9Pu/YuVxzLo8FQCn1XqXUNqXUtuHh4Ysu+lRbvIB1cMRdb7XSW4vlaHcqjRBCLCR7B7NUvBGsI6N5WmIB9g5mWdkS5XiqyCXeHoFCCCHEYjMXAtZUE/VP3cr8TNecy2Pdg1rfrbXeqrXe2to6/c2alrdET/rG9oEXBgHonyhwYDhHviwbDgshFpYf7HJ/zhUqdm3vq2XN7u9r2mUESwghxOI0FwJWH7Bk0v0eoP8crzmXx86KiN/klevbTju+fyhLUzTAd3Ycr0NVQggx/dJFdyp0pmTREHHXnVY7CjZGAsRCPjqT0klwvlBKvVUptUsp5SilztgO+UxNpZRSTUqpHyil9nm/N85AjS/5GkqpdUqp5yb9SiulftM798dKqWOTzr2mHjV61x1WSj3v1bHtfB8/0zUqpZYopX6slHrR++/i/046N2Pv43xpeHYOdb7Dq2+HUupxpdSWSeem/LuvQ403KaVSk/4e//BcHzuLNf7OpPp2KqVspVSTd25W3seLMRcC1lPAGqXUCqVUAHg7cO8p19wL/B/vf65rgJTW+vg5PnZWXL2yqdboosNrVdyecNcnlCo2Pzs4Vo+yhBBi2j2278Sej03RAACt8WDtWKMXusS8sRN4M/DwmS5QZ28q9RHgQa31GuBB7/50e8nX0Frv0VpfprW+DLgSyAPfmHTJ31fPa63vq0eNk9zs1TE50M6J9xGwgN/WWm8ArgE+oE5uIDbt7+NL/PdVVfeGZ+f4WoeAG7XWm4E/5fQmDVP93c92jQCPTPp7/Ph5PnbGa9Ra//Wk/58/CjyktZ78YXpG38eLVfeApbW2gA8C3wdeBL6mtd6llHq/Uur93mX3AQeB/cDngF8/22Nn+Y8AQFcyXNv7JR5yNx2u7oW1tDnKd3bUZWBNCCGm3def6cPv7X21viMOwIoWd0rgmvYYbfFQ3WoT509r/aLWes9LXHa2plJ3Av/h3f4P4I0zUOb5vsargANa6yMzUMuZXOz7MCfeR631ca31M97tDO7nqynXt0+j+dLw7CVfS2v9uNZ63Lv7BO7sqtl0Me/HbL2X5/s6dwFfnoE6ZkzdAxaA1vo+rfVarfUqrfWfe8c+o7X+jHdba60/4J2/VGu97WyPrQfDULWRK1u7waq6BsFnKEqWw/FUoV7lCSHEtNBa88MXh7h5nTslujqCdXDY3Y4i7DfpbJCAtQCdralUuzerBO/30+fLX7zzfY23c/oHsg9607Y+PxPT786jRg08oJR6Win13gt4/GzUCIBSajlwOfCzSYdn4n2clYZn0+B8X+vdwPcm3T/T3/10Otcar1VKbVdKfU8ptek8HztbNaKUigC3A1+fdHg23seL4qt3AQtJcyzAK9e31dqyD3sbDMeC7ts8kCrKugQhxLx2eNTtitriTQkMmO5mwyta3c6pTdEgY/lyfYoTZ6SU+iHQMcWpj2mtv3UuTzHFsSmbSl2os9V4ns8TAN6AO62o6l9wp2tp7/e/BX6lTjW+XGvdr5RqA36glNqttT7j9MzzNY3vYwz3Q+1vaq3T3uFpeR+nerkpjk17w7NpcM6vpZS6GTdgXT/p8Iz+3Z9Hjc8Ay7TWWW8d3Tdxp17O1nt5Pq/zeuCxU6YHzsb7eFEkYE2jZU0RblrXWgtYR7wPItUOgo8fGOXypTPxpZkQQsyOlLfXX7bo/lzbM+h+7uodc0foN/ck+emB0foUJ85Ia33LRT7F2ZpKDSqlOrXWx70pWxe0+ePZalRKnc9r3AE8o7UenPTctdtKqc8B36lXjVrrfu/3IaXUN3CnSz3MHHoflVJ+3HD131rreyY997S8j1O4mIZngXN47HQ5p+ZqSqnNwL8Cd2itaz8Qz/J3P6s1TgrMaK3vU0r9s1Kq5VweO1s1TnLaaPQsvY8XZU5MEVwommNB1rS56xHa4kEsxw3j2/tSAPzPtt5a9y0hhJiPjoy6e/3t6JsA4LH9o7Qngnz5yaNcv7qFkWyJ9Z3xOlYoZsjZmkrdC/yid/sXgXMZETtf5/Map63X8MJE1ZtwG3tMt5esUSkVVUrFq7eB2ybVMifeR6WUAv4NeFFr/XennJup93G+NDx7yddSSi0F7gHepbXeO+n42f7uZ7vGDu/vGaXUVbh5YPRcHjtbNXq1JYEbmfTf6Sy+jxdFAtY0S3qtim0vXFW7aXUmQxwezXNgKFu32oQQ4mIUK3ZtZP7waJ5mb/3VdataALhmZROj2TLNseAZn0PMPUqpNyml+oBrge8qpb7vHe9SSt0HL9lU6hPArUqpfcCt3v3pNuVrTK7Rux/xzt9zyuP/SrltnXcANwO/Vaca24FHlVLbgSeB72qt7z/b4+tQ48uBdwGvVKe3Y5+R93G+NDw7xzr/EGgG/lmd3Eb8bH/3s13jW4CdXi2fAt7u9TuYlffyHGsEN8Q/oLXOTTo2K+/jxVJaz9Q01blr69atetu2mWmbr7VmxUfvY1VrlAPDOVa0RDk0kqMjEWIgXeSv37KZt25d8tJPJIQQc8zzfSk+8KVnODrmhqy3XNnD/z7dx4detYZPPbiPf3j7ZSRCfq5f04LfnN7v75RST8/VdrxCCCHEZDKCNc2UUvznu6/iwLAbtru91u3VjoI7+lKULadu9QkhxIXqTxU4OpZndZv786y6Svn4hLv+qqcxTGM0MO3hSgghhJhP5F/BGbCpK1m7/eh+d0POobTbUfB4qsiegUxd6hJCiIsxmC4CJzZTX9YcAWCdtxeWaRg4i3BWhBBCCDGZBKwZ0BQNEPAZBH0n3t49g26o+uGLgzx9ZOxMDxVCiDlpIFWkULYBt4kPwPd2DgDuF0cADWE/nUnZA0sIIcTiJgFrhly1vIn13re67YnqfjHu2/3AC4MsxrVvQoj5a99QptYF9Z5njwGwqz/NdauauX/nAHddtZSxfFn2+hNCCLHoScCaIZ9915W19uxLm9xpNJd0JwAYy5XZJ90EhRDzyMHhHP/04wO1+2++ohuAS7qTHJso8HNXdNe+RBJCCCEWM/nXcIZEg75ag4unDo8DUPKaW7QlQnz5yaN1q00IIc6HZTvsG3KnOW/odL8oqk6BznijWqah2OidE0IIIRYzCVgz6Oeu7CHsN2v3d/W7G2dvOzzGQ3uH61WWEEKcl139adIFC6AWonoa3ZH56hdJGjAMNeXjhRBCiMVEAtYMurQ7yaU9bkfBeMhXO54v2wymivzs4Gi9ShNCiHO2vW8C21s3+vyxCQDu9xpcONrdYH1lS7Re5Qkh5iCl1I+VUrd6t/9MKfWpetckxGyRgDWDXrW+rdZRqzqtptr4ojEa4H+e7qtbbUIIca6+u+M4P3hhEIC9g1m6G8I8fyzFLRvaue/547z/xlU0RAJ1rlIIMcf8EfAxpdQ7gMuB36pzPULMGglYM8gwFDetawXgyUNua/ZwwJ0yuK49ztef6autXxBCiLloLFfm2ESBsuXUvii687IuADZ1Jdg9kOFVG9rqWaIQYg7SWj+Mux/5h4G3a63tOpckxKyRgDXDVrTEeOuVPbX7zx6dAODB3UNoDU8fGa9TZUII8dL+64kjrGqNAdDljcjnvf2wBlJFVrREWdser1t9Qoi5SSl1KdAJlLTWmXrXI8RskoA1w1a2RrliWSNwYjF4S8zdF6stHuSvv78Hx5E9sYQQc9O92/uJeWtIy7bbCbW64fCWJQ1IWwshxKmUUp3AfwN3Ajml1KvrXJIQs0oC1gxLhPysbXe//T02UQCgIeIH3Fbuu/rTvHA8Xbf6hBDiTIoVm/1DWb674zgAj+wbYUlTmK9u6+WyJQ08e3ScX7tpVZ2rFELMJUqpCHAP8Nta6xeBPwX+uK5FCTHLJGDNgo2dSX7puuW1+/u9TYarHY2fP5aqQ1VCCHF2f/eDvaxqdbsDXrG0AYCb17nrrTZ1JdjRl+IN3nosIYQA0FrntdbXaq1/4N1/WGt9bb3rEmI2ScCaBeGAyeu3dALQFD3RaevAcA6Azz96iN6xfF1qE0KIqWitufvhg1za7W41UW1w4TfdfzYaIn5evrqFoM8843MIIYQQi5EErFlyaXcDALa33mp1mzttsC0eZN9QVkaxhBBzyp5Bd036Tm+D9Ef2jQAwnCkBYCrFilbZ+0oIIYT4/7d33/FxVWf+xz9HvTerWLIsy5Ir7t0YAzY1OAFT0gkBQkIScJYU+IWEZGFDFthkk0CWFHpYkgWHbsA0G4OxAXfLvVuWZcmqVu/S+f0xY0W2xrJkj+ZqpO/79bov3bnn3JnHVwMzj865zzmZEiwfCQkK4OmbplNZ7yrLfnyaYJb7C8qhsjqqVLJdRPqId7e51r3aV1xDSkwoeeV1XHZOCktyCpiZmUBWUhQp0aEORykiItL3KMHyoXmjXPcuDI4Jaz/22QHX+ljPfZrLhlyVbBcR5x2pqOcPy/ZwxfjBACyY4JriPDzR9QehoQkRHKtr4uKxKY7FKCIi0lcpwfKhgADD7KwEjlY1AHCO+56G1NgwCiob2HS4QiXbRcRx+90j7GHBrvurcktd94uGBLk+MmZnJZAWF05ggIq0i4iInEwJlo89/53Z7fvHy7OnudfHMsDGPI1iiYhzqhua+WhPCQCvbjoCwIrdJczIjOf5tXmEBgWQEBlCamxYV08jIiIyYCnB8jFjXH/xze5wc/iGQ66k6pHle1m1r9SRuEREwLVsxFOrDjJreAIAV01ylWGfMCSO0pombj5vOOOHxBIUoI8PERERT/QJ6YA3Fs1tL9E+Kd1VAjkjIQKAvUU1HCqrdSw2ERm4Wtssuwpd1QMTo1wFLOLdC6MnRLp+Dk+MIK+8jrGp0c4EKSIi0scpwXLAhPRYUmJcX15y8l3l2Ztb2wAor23i7W1HHYtNRAaunPwKtuRXAPDW1kJiwoJ49tNDJEeHsuagqyDPuVmJJEeHto/Gi4iIyImUYDnkyolpTM2IAyAyJJDCSlfhi08PlPHqxiMq2S4iPrc5r4LXNhcwNMF1X+jnJ7qmB147NZ2P95Zy1+WjKapuYNggrX8lIiJyKkqwHPKzBWNpaHaNWkWFBQEw1l1VsL65lVc3HnEsNhEZePYV11Db2AJAWmz4CW3WuqqbzskexKhkTQ0UERHpihIshwQGGOaPSWJieixFVY0A7HRXFaxpbOG/3tlFq0q2i4iPfLy3hGU7XYsLrzlYTnp8OM+vzePcrEHkuu8LbbMQ674nS0RERDxTguWgK8anMm1YPABZ7qqC0WFBlNc2UdfUyv+tzXMyPBEZIEprGskrryMnv5Ih7mUjLj3HtYjw0IRw3t1exP0LxzF5aJyDUYqIiPgHRxMsY0yCMeZ9Y8xe9894D32GGmNWGGN2GmO2G2Pu6NB2nzHmiDFms3tb4Nt/wdkZPySW5OgwIkICOeCuKnh84c7RKdH88rVtToYnIgPE0q2FxIa7Rqba3NMBjy8uPHqwa+ry7KxBWlhYRESkG5wewbobWG6tHQksdz8+WQvwE2vtWGA2cLsx5pwO7X+w1k52b0t7P2TvmpEZz52XjQYgITKEijpXcYvdRa5SyS9tyHcsNhHp/xpbWtl8uIKHl+0FoLCygYnpsazYXcKc7EEsySlg8tA4Rqbo3isREZHucDrBWgg8695/Frj65A7W2kJr7Ub3fjWwExjiqwB727Rh8USEBAKuEu0AmYNca2INjgnjzhdzaNO9WCLSS17ecITspCjgX9MC52QnAjB9WDw5hyv4yzemOhafiIiIv3E6wUqx1haCK5ECkrvqbIzJBKYAazocXmSM2WKMedrTFMO+zhjDqMHRPPr1Ke3HcsvqADha5Srd/s52rYslIt5nreWDXcX87r3dALy/owhj4LlPcwEIDXb98Sf1pKqCIiIicmq9nmAZY5YZY7Z52Bb28HmigJeBH1prq9yH/wJkA5OBQuB3XZx/qzFmvTFmfUlJyZn9Y3rJpPQ4IkNdpdqj3SXbMxJco1gRIYHc9o+NWhdLRLxuSU4BMWFBtFnIdhfauWH2MGqbWrlyUhrPfXqIx26Y5nCUIiIi/qXXEyxr7SXW2vEetteBImNMKoD7Z7Gn5zDGBONKrv5hrX2lw3MXWWtbrbVtwBPAzC7ieNxaO91aOz0pKcmb/8SzFhhgOCc1hoe/MpnqBtc6NHnlrlGscPdfkFfs8nhpRETO2OJ1h9vv96xraj2hbVpGHEerGrh83GAnQhMREfFbTk8RXALc6N6/EXj95A7GGAM8Bey01v7+pLbUDg+vAfy27F5KTFh7qfaEyBAAYsODKXPfl3XHC5s55F6LRkTkbK3cU8KBklq2F1QRHxFMYWUDUzPi+N9PDzEzM4FtBVV894Isp8MUERHxO04nWA8Blxpj9gKXuh9jjEkzxhyvCHgecANwkYdy7L8xxmw1xmwB5gM/8nH8XjUxPY6/XD+1vdhFZb1rWmBKTCgAH+4uwVoVvBCRs/eL17a1r8M3bVgCAHNHuIpbzMpKYEdBFXdcMtKx+ERERPxVkJMvbq0tAy72cLwAWODeXwV4XHzFWntDrwbogDnuLzhD4sI5UlFPaFAARVWNANy7ZDujUqI5N3uQkyGKiJ/bkl9BXnld+1TkZTuLmDk8gT9+sA9wjZ5nJ0cREeLoR4SIiIhfcnoES04SGx7M23ecz5GKegAaW9oAGOYu3f7J/lKqVfBCRM7CVY+ubi/JfuWkNADGp8UCcM2UIZTWNHHr+ZoeKCIiciaUYPVBY1NjiAoNIjnaNTUwJDCAQ+7S7f/zwT7e2aay7SJyZtYcKANcJdkB3sgpIDDAcLC0BoB5o5OorG9mQnqsYzGKiIj4MyVYfdSan19McbVramBTq2sUKzHKlXC9saWQ3FIVvBCRnrHW8pXHP+MLE131ga6e7Bq9uvHcTFbsLuGmOZkAXDAy0akQRURE/J4SrD4qMjSIz09I/dcoVlAApTWuhGvlnhL++MFeFbwQkR55eeMRAN7cUgjAa5sLANrX2TsnNYby2qb26YMiIiLSc0qw+rBHvz6FmkbXulhN7nuxji9EvC63nPfcU3xERE6ntKaRO1/M4bwRriI5l7mTqG/PHc5LG/K5dsoQzs0eRIAxBAXqo0FERORM6VO0DzPG8OC1E8h2r4+VFB3avhDx4fJ6fvryFmrdCZiIyKlYa3li5QEAVu9z3YN1/A80ocGuj4EvTk9n6dZCrp+V4UyQIiIi/YQSrD7uqklpzMh0rVFT4r4n67iQwAB+tHizA1GJiD/Jya/ksZUH2te9+tpMVxJ17ZQh/GnFfr44LZ2IkCDGD4nV6JWIiMhZ0idpH2eM4SszhvKV6UMBSIwKaW8rrm7kvR1FrNxT4lR4ItLHlVQ38siyPQBsOHQMgJc35gMwODYMgFvmDqehuZXRg6OdCVJERKQfUYLlB6ZkxDNjeAIjkqMorWk6oS3AwDefXtt+j5aIyHHWWj7aU8KK3SVkutfSu2bKEJpa2vjehdn8+cP9/OCiEQAEB5r2SqUiIiJy5pRg+YkLRiayaP6IE47FRQTT5i4keMuz6xyISkT6srUHy/nD+67Rq1z3WnqvbnJVEgwwrj7nj0yitc2SlRjlSIwiIiL9jRIsP5EcE8bQhAjuvmJM+7GKuub2/Y/3lvLJ/lInQhORPqi4uoGNeRUcqahvn1p883mZAHx1xlD+/OF+fnLpKBKjQoiLCCY+MqSLZxMREZHuUoLlR6YNi2fikNgTjoUEuX6FkSGBfP2JNRRW1jsRmoj0IdZalm4p5L/e2QVAaU0TwwZF8MzqXADiIlzJ1IKJqbS0WdLjI5wKVUREpN9RguVnZmcN4qkbpwMwKDKk/d6r2qZWAO5+eSsNza2OxScizvtgVzF55a4/toS4qwLOH50MwB0Xj+SvH+3nuVtmUlXfzKgUFbYQERHxJiVYfiYgwHD+yCTuvGwUZbVNndo/2lPCGzkFDkQmIn1BcVUDaw+W8/TqgwA0tbYxIzOev32Sy9wRiRytbCAsOIDAAMOUjHiHoxUREel/lGD5oZCgAG6ck3nCsdjw4Pb9u17awif7dD+WyEBjreWpVQdZvP7wCccDjKuixdjUaBavP8wfvjyZWcMHORGiiIhIv6cEy09FhwWz9p6L2x9X1jef0P7YygMcLq/zdVgi4qDXNh+hrLaJirpmUmJcJde/OC2dNQfLmTYsngMltczIjOeCUUkEHi8jKCIiIl6lBMuPJUeH8bebZ3Q6HmBcUwWf++wQdU0tDkQmIr6WV1bHKxuP8NIG1yLCRVWNhAYFsNo9mn3x2GSW7yrmT9dPJTI0yMlQRURE+jUlWH5u3uhkxgz+103qgQGmfW2sx1ce4OlVB7HWOhSdiPiCtZZfvr6N/cU1gKsADsA3Zg+jsLKB712YzYe7Srj7ijEkR4c5GaqIiEi/pwSrH1j6b+e377e2nZhMrdxTyhtbCn0dkoj40G/f3U19UysFlQ0kRYdSVtvEZeek8NSqgwxNCCchMpi88jq+e0GW06GKiIj0e0qw+oGAAMNnP7vYY9va3HLe2VbItiOVPo5KRHxhw6Fj/PWj/azNLQegpLoRgDb3yPU1U9J5ZnUuSxadhzG670pERKS3KcHqJwbHhvGLz48lNKjzr3Tp1qP85t3dnQphiIh/a2lt47q/fEJStKugRVZSJAC3zB3Osp3FfH5iKiXVDXz3giySYzQ1UERExBeUYPUj3z4/i5nDE8hKjOzUtnJPCT99aYvuxxLpR865912mZMRRVNVIcnQoB0pqGZUSxVOrXGtgpcaEkRAZwjdmD3M4UhERkYFDCVY/88Q3pxPTYU2sjj47WMbv3tvj44hEpDf89KUtNLW0sSmvAoBi99TA8UNiAbhpTibThsUza/ggggL1v3oRERFf0aduPxMWHMj9C8dzzZQhndoq6pp5dMU+3tmmohci/mzF7mIWrz/cvpbVkLhwAG48dxivbDzC9GHxXD5uMEcq6rlgVJKToYqIiAw4SrD6oQnpsUzPjOennxvjsf17f99IXpkWIRbxR3uKqrn5mXVMHxZPa5tldEo0RyrqmZmZwPPrDgPwnQuy2FdSwzfPzXQ2WBERkQFICVY/9bUZGTQ0t/L9edke2y/47YpOJd1FpG/LLa3lsj+sxBhYf+gYALuLqgHITo6kqaWNB66ZQEJkCFMz4gjxUPRGREREepc+ffupgADDbfOzSYgIaZ8+dLLsny/1cVQicqYKKuq566UcAI7Xqjn+3/ai+SN4fu1hbpg9jOmZrpGtcWmxToUqIiIyoCnB6sdCgwL53PjB/PIL55yyz4R73/VhRCJyJkprGvnbJ7msyz1GdGgQAFMz4jhSUc83Zmfw6Ip9ANw4ZxhlNU2MS4txMlwREZEBTQlWPzc0IYLMxAieuXmGx/bqxhZuematj6MSke6qrG/mtU1HeHzlAVJjw6hubGF0SjQb8yoYMziao5UNALyxaC5FVY1MGxZPdJjnSqIiIiLS+5RgDQBjBscwfFAkf75+qsf2D3eX8PAylW8X6Wsamlt5YW0ev35rJwCF7mTq+H1Xl48bzLKdxfzj27OoaWxhTvYg3XclIiLiMH0SDxCZiZFMz4znoWsneGx/eNleXlx/2MdRiciptLS28dSqgzz49q4Tjg93LyS+aP4IHlm+l7suH014SCDnZg/CGONEqCIiItKBEqwBJDk6jC9MSmPR/BEe2+96aQuvbsrHWlUXFHGStZbHVh7o9EePGZnxHCyt5YbZw3hm9UFSYkKZPzqZqRnxDkUqIiIiJ1OCNcBEhQbxo0tHccnYFI/tP1qcw4sblGSJOOmvHx1gzcFycjusV3fJ2GTW5R5jSkYcJdWN1Da18o9vz+YcFbQQERHpUxxNsIwxCcaY940xe90/Pf4Z1hiTa4zZaozZbIxZ39Pz5USBAYYnb5zO9GGeL9f/e2kLf1+TpyRLxAFPfnyAXUerWLmnpP3YpKFxLNtZDMB52Ym8s/0oq+++iBHJUU6FKSIiIqfg9AjW3cBya+1IYLn78anMt9ZOttZOP8Pz5SQvfX8Ok4fGeWz75WvbeOLjA0qyRHzo2U9y2X20mtc3F7QfCwkKIOdwBQC3zcvm0RX7ePMHc0+5vp2IiIg4y+kEayHwrHv/WeBqH58/4L16myvJCg7sfHP8A0t38fCyvUqyRHzg/9bksTHvGC9uyD/heHCA67/N62dl8NjKA/xq4TjGD9EiwiIiIn2V0wlWirW2EMD9M/kU/SzwnjFmgzHm1jM4H2PMrcaY9caY9SUlJafqNuAYY3jl+3OYMjSe6LCgTu2PLN/LA0t3KskS6UUvbcjnvR1HTxi5ApiYHkttUytXTkpjU14FX5s5lG+em+lMkCIiItItvZ5gGWOWGWO2edgW9uBpzrPWTgWuAG43xlzQ0zistY9ba6dba6cnJSX19PR+LSDA8MKts5mTPYhQD2voPPHxQX78zxwlWSK94PXNR3hi5QE+3H3iH36unJTGlvxK5o9Ooq3NkpEQwa+v9rzMgoiIiPQdvZ5gWWsvsdaO97C9DhQZY1IB3D+LT/EcBe6fxcCrwEx3U7fOl9MLCDD84SuT+cqMoaTFhnVqf3XTERb+abWSLBEveiOngB//M6d94eDjrp6cxhs5BVw4KokxqTE0NLfy6NenOBSliIiI9ITTUwSXADe6928EXj+5gzEm0hgTfXwfuAzY1t3zpfsiQoL46efGcN20dKZmxHVq35Jfydh/f0dJlogXvJFTwA+e30Rr24n/PS2YMJjXNhcwOiWaqyalsftoNQ9eO4GgQKf/dy0iIiLd4fQn9kPApcaYvcCl7scYY9KMMUvdfVKAVcaYHGAt8Ja19p2uzpczFxkaxO3zR3D1lCHMzEzo1N7Q3Mbwny3t9KVQRLrv1U35/OD5TZ2OL5ycxtKtRwG4e8EY3thSwH9eM57kmM6jyiIiItI3mYE4GjF9+nS7fv3603ccwCrrm/nsQBnv7yjipZOqmh236ZeXEh8Z4uPIRPzb4yv388DSXZ2OXzI2uX2tq2e/NZMPdxdz/axhWuvKzRiz4aRlOkRERPokp0ewpI+KDQ/mwlFJfGlaOrfNy/bYZ8r977P7aLXHNhHp7BevbfWYXJ0/MrE9uXr8hmlU1jdz0ZhkJVciIiJ+SAmWnFJYcCCzsgZx3bR0/u2iER77XP7wSl7Z6HmES0RcWtssX37sU/7+WV6ntgtHJfHx3lIA/u/bswgOCiDQGM4fqWqnIiIi/kgJlpxWdlIUt80fwV+un+qx/cf/zOGnL22hqaXNx5GJ9H3ltU2Mv/dd1h4s79Q2b3QSH+1xlWd/+47zqaxvJtAYPj8x1ddhioiIiJcowZJuCQsO5IoJqbx2+3ke2xevP8zsB5dTXN3g48hE+q59xTVMvf996ptbO7VdOCqpfe2rt/5tLtUNLSRFh3LBKI1ciYiI+DMlWNIjk4fGsf4Xl3hsK69tYuZ/Lmddbue/1IsMJG1tlve2H+WS33/ksX1+h5GrxbfOJiYsmJa2NqYNi/dlmCIiItILlGBJjyVGhXLwwQUkRoV6bP/SXz/lyY8PaL0sGZAq65p5/OMD3PrcBo/t104ZwordJQQFGN78wVzCQwKpamhmTnYixhgfRysiIiLepgRLzogxhnX3XMwtc4d7bP/1Wzu57R8bqaxv9nFkIs7ZdbSKe17bykNvd64UCHDd1HRe2XSEpOhQliyaS11TKyOToxmXFuvjSEVERKS3aB0sOWtv5BR4XDQVIDw4kOdumcl0D4sWi/QX1lpe31zA/3ywl/0ltR77XDc1nZc35vO5cYP51tzhpMWFkR4f4eNI/ZfWwRIREX+hESw5a1dOSmPlXfNJiek8ZbC+uZUv/vVTfv/ebgciE+l9lfXN/OrNHfxw8eYTkqvosKD2/W+dN5yXN+Zz3dR0bpufzYzMeCVXIiIi/ZRGsMRriqoauOfVrRRUNLCjsKpTe0ZCBO/88HwiQoI8nC3ifzYcKufpVbm8tbXwhONhwQE0NLuWLfjuBVk8tvIAN83J5CeXjSI6LNiJUP2eRrBERMRfKMESr3vw7Z0UVjSwJKfAY/vTN03nojEpPo5KxHustTyyfC8f7CpmS37lCW0ZCRHkldcRGGC4eU4mT646yN9vmcXckYkORds/KMESERF/oQRLesUHu4pYva+Mp1Yd9Ng+d0Qif//2LB9HJXL2iqsb+P7fN7Lh0LFT9pmSEcfQ+AhW7yvljR/MJS0u3IcR9k9KsERExF9orpb0iovGpJAWF05MWDDH6pr42ye5J7Sv2ldK5t1vsebnF5MSE+ZMkCI99NKGfO58MafLPgsmDCYxKpTcsjrevuN8kvX+FhERGVA0giW9qrXN8vKGfOqbW7l3yXaPfRZMGMyfr5/m48hEuq+5tY05D31ASXVjp7bRKdHsLqoG4MvT0wkKDCAhIoQ7Lx/t6zD7NY1giYiIv1CCJT6x+XAFRysb+POH+zrds3KcRrOkL3p5Qz4/OcWoVVZiJAdKXZUDf3bFGCJCAhkUFcqCCam+DHFAUIIlIiL+QlMExScmD42jLqWF5JhQPtpdwiPL93bqM+uB5WQlRvL+jy8kMMA4EKXIv1Q1NDPxvve67HOgtJZ5o5O49YIsdhRUkZ0cxZxsFbMQEREZyLQOlvhMREgQUzPiWXTRCBbfOvuEdYKOO1BaS/bPl/LWlkIPzyDS+5pa2nhg6c5TJldTM+La9++8bBSL5o9g+5EqvjYzQ8mViIiIaIqgOMday5KcAu54YfMp+yz78YWMSI7yXVAyYFlrWb2vjG88teaUfYYmhHO4vJ7Y8GAev2EaUWFBVNY1M3N4AkGB+ntVb9IUQRER8RdKsMRxlfXN/PyVrZ0Waz0uNTaMJYvmkhQd6uPIZKDYkl/BLc+u91jEAiA2PJjK+mYA7lkwlgtHJ1HT2EJQgGHCkFiM0ZTW3qYES0RE/IUSLOkzCivr+dzDH7d/kT3ZtVOG8MC1EwgLDvRxZNJf7Smq5o/L9/JmF1NSLxmbzLKdxQA8c/MM4sKDiQwNYmRylBIrH1KCJSIi/kIJlvQpLa1tLMkp4N4l26luaPHY5/b52dx52Wh9uZUzlldWx98+yeXp1Z4XwgZIiQmlqMo1ovUfV41jYnos6fERGkl1iBIsERHxF0qwpE9qbGnlobd3se1IJetyj3ns87MrxvDdC7N9HJn4s+LqBv68Yn+nha9PduGoJD7aU0JiVCiPfHUyMzITCAnSPVZOUoIlIiL+QgmW9Gk7C6t4c0sBm/Iq+GR/mcc+9y8cxw3nZvo2MPErVQ3N/OebO1m8/nCX/WZmJrA2txyA33xxIl+ePtQX4Uk3KMESERF/oQRL/MLHe0vYfbSaFbuLWb3Pc6L14LUT+NrMDB9HJn1ZXVMLP1q8mXe3F52275jB0ew6Ws1t81xTUAO0FlufogRLRET8hRIs8RtNLW3k5Few62g17+8oYuWeEo/97rp8NLfPH+Hj6KQvqW1s4Vt/W8eag+Wn7fulaem8s+0oY9Ni+PXV4xmVEu2DCKWnlGCJiIi/UIIlfqeppY09RdWU1DTyH0u2k1tW57Hf+SMTee6WWT6OTpxUWtPIVx//jH3FNaftO21YPKNSovh0fxn//aVJTM9M8EGEcqaUYImIiL9QgiV+rbXN8un+Mv60Yh+fHvA8dRBg239cTlRokA8jE1/aUVDF1X9aTVNr22n7Xj05jYvGprBsRxHjh8Rw/axhROq90ecpwRIREX+hBEv6jfLaJv64fG+XFeJ+/+VJXDs13XdBSa969pNc7l2yvVt9Z2clcPv8EXy8t5Saxhbuumw08ZEhvRyheIsSLBER8RdKsKTfaWppY/G6PH75etdfvHf86nIiQjRy4W9Kaxq54pGPKalu7Fb/z09M5TvnZ5FXXsfRynouPWcwwxMjezlK8TYlWCIi4i+UYEm/1dTSxur9pTzw1k72dnFPzk1zMrnvqnE+jEx6qrKumf/5YC9Prjr1wsAnu2lOJheOSiIwwLCnqJqxqTHMzhpEoKoD+iUlWCIi4i+UYMmAcLi8jr98tJ8X1ubR1sVb/rlbZnL+yCTfBSanVFrTyOubC7j/zR09Ou8HF43gkrEpBBhDbVMLCZEhqgzYDyjBEhERf6EESwaU/GN1rMst59VNBacs837ckkXnMTE9zjeBCQB5ZXW8saWA3767u0fnxYQFcesFWUzNiCcyNAjjHqQaMziGkKCAXohUfE0JloiI+AtHEyxjTAKwGMgEcoEvW2uPndRntLvPcVnAv1trHzbG3Ad8Bzj+Tfnn1tqlp3tdJVgCsL+khjdzCnl+bR5Hqxq67PuHr0zimikqjtEbPtlfyovr83l105EenzskLpxfLRxHYlQoESGBZCVFaQpgP6UES0RE/IXTCdZvgHJr7UPGmLuBeGvtT7voHwgcAWZZaw+5E6waa+1/9+R1lWBJR61tlg93F7O/pIbCygaeWZ3bZf+YsCDW/+JSjYycoYbmVh5ZvpfF6w5TXtvU7fMCDLRZ18+b5gznumlDGJcW24uRSl+iBEtERPyF0yXUFgLz3PvPAh8Cp0ywgIuB/dbaQ70blgwkgQGGi8emcPHYFI5U1HPNlCFYC2/kFHgsqlDV0MKoX7zd/vi6qen89osTCdDIiUdtbZZXNx3h4eV7OFxe36Nzhw2KICo0iIKKer4wMY1bL8hiaEJEL0UqIiIicvacHsGqsNbGdXh8zFob30X/p4GN1tpH3Y/vA24CqoD1wE9OnmLY4dxbgVsBMjIyph06pBxNuqegop63tx3tdrGF0KAA1t5zCbHhwb0cWd9U19TCva9v58UN+Wd0/sT0WC4Zm0JtYwtltU2cPzKRacPiSY9XYjWQaQRLRET8Ra8nWMaYZcBgD033AM92N8EyxoQABcA4a22R+1gKUApY4H4g1Vr7rdPFpCmCcqZa2yw7C6t4Z9tRHl2xr9vnpcWG8fqiuSRFh/ZidL7V2mbZfbSah97ZddqCIV2JDAnk5vOGM2pwNBV1rimDseHBzBo+iMGxYd4KV/ycEiwREfEXTo9g7QbmWWsLjTGpwIfW2tGn6LsQuN1ae9kp2jOBN62140/3ukqwxFuaWtrYWVjFC+vyeH7t4R6fHxRg+Pu3ZzEzM6HPTjEsq2nk5Y35PL7yAKU13b9nqiuXjE1mdtYgRqZEExoUQEFFPSkxYUxMjyU6bGCO/EnXlGCJiIi/cDrB+i1Q1qHIRYK19v+dou8LwLvW2mc6HEu11ha693+Eq/jFV0/3ukqwpLdYa9mYd4z3dhTx2EcHvPKcydGh3Dgnk8vHpTA0IYLQoMCzfs7WNktxdQO7jlazOa+C93YUsbOwygvRejZzeAIzMxPITIxkVErUCW3hwYGMSI7CmL6ZYErfoARLRET8hdMJ1iDgn0AGkAd8yVpbboxJA5601i5w94sADgNZ1trKDuc/B0zGNUUwF/ju8YSrK0qwxJfqmlrYV1xDblkdy3YUsSSnwOmQelVydCjXTk1n1vAEhiaEk52k5EnOnhIsERHxF1poWMRBtY0tHCippay2kadWHaSgop79JbVOh+XR+CExtLRa4iNCOFbXxKCoEJpa2pg8NI6RKdGMTI4ic1Ak8ZEhTocq/ZASLBER8RdOl2kXGdAiQ4OYkO5ay2ne6ORO7dZa8o/VU1bbxNHKBlbuLeFweR2x4cE0NLeybGexV+IYEhfOlIw4EqNCGZ4YSWhQABkJEeSV19HQ3Epzq6WhuZWUmDAGRYUwJD6chIgQkmNUhEJERESkI41gifihltY2DpbWEhYcyKCoEBqb2zh8rA6DIS4imPCQQI5WNtBmLYOiQhkcE0ZNQwultY0MjY84YZHktjZLVUMzpTWN1DW1AmAthAYHkJ0URXCgFlQW52kES0RE/IVGsET8UFBgACNTotsfR4TQaWpeYtSJJeFjI4KJjehcoS8gwBAXEUJchKb2iYiIiJwt/WlaRERERETES5RgiYiIiIiIeIkSLBERERERES9RgiUiIiIiIuIlSrBERERERES8RAmWiIiIiIiIlyjBEhERERER8RIlWCIiIiIiIl6iBEtERERERMRLlGCJiIiIiIh4iRIsERERERERL1GCJSIiIiIi4iVKsERERERERLxECZaIiIiIiIiXKMESERERERHxEmOtdToGnzPGlACHnI7jJIlAqdNBdIM/xKkYvccf4lSM3tHXYxxmrU1yOggREZHTGZAJVl9kjFlvrZ3udByn4w9xKkbv8Yc4FaN3+EOMIiIi/kBTBEVERERERLxECZaIiIiIiIiXKMHqOx53OoBu8oc4FaP3+EOcitE7/CFGERGRPk/3YImIiIiIiHiJRrBERERERES8RAmWiIiIiIiIlyjB8iFjzJeMMduNMW3GmFOWQzbGfM4Ys9sYs88Yc3eH4wnGmPeNMXvdP+N7IcbTvoYxZrQxZnOHrcoY80N3233GmCMd2hZ4O8buxunul2uM2eqOZX1Pz+/tGI0xQ40xK4wxO93vjTs6tPXatTzVe6xDuzHG/NHdvsUYM7W75/owxuvdsW0xxnxijJnUoc3j792hOOcZYyo7/B7/vbvn+jDGuzrEt80Y02qMSXC3+exaioiI9AvWWm0+2oCxwGjgQ2D6KfoEAvuBLCAEyAHOcbf9BrjbvX838F+9EGOPXsMd71Fci4AC3Afc6YNr2a04gVwg8Wz/nb0VI5AKTHXvRwN7Ovy+e+VadvUe69BnAfA2YIDZwJrunuvDGOcA8e79K47H2NXv3aE45wFvnsm5vorxpP5XAh/4+lpq06ZNmzZt/WXTCJYPWWt3Wmt3n6bbTGCftfaAtbYJeAFY6G5bCDzr3n8WuLoXwuzpa1wM7LfWHuqFWLpytteiT1xLa22htXaje78a2AkM6YVYOurqPXbcQuB/rctnQJwxJrWb5/okRmvtJ9baY+6HnwHpvRDH6ZzN9egz1/IkXwOe74U4REREBgQlWH3PEOBwh8f5/OsLd4q1thBcX8yB5F54/Z6+xlfp/GVskXva1tO9MfXOrbtxWuA9Y8wGY8ytZ3C+L2IEwBiTCUwB1nQ43BvXsqv32On6dOdcX8XY0S24RtyOO9Xv3du6G+e5xpgcY8zbxphxPTzXVzFijIkAPge83OGwr66liIhIvxDkdAD9jTFmGTDYQ9M91trXu/MUHo55tZZ+VzH28HlCgKuAn3U4/Bfgflwx3w/8DviWg3GeZ60tMMYkA+8bY3ZZa1eeSTyeePFaRuH6UvtDa22V+7DXruXJL+fh2MnvsVP16fX352lev3NHY+bjSrDmdjjcq7/3Hsa5EdcU2hr3fXSvASO7ea439OR1rgRWW2vLOxzz1bUUERHpF5RgeZm19pKzfIp8YGiHx+lAgXu/yBiTaq0tdE/XKvZ2jMaYnrzGFcBGa21Rh+du3zfGPAG8eSYxeitOa22B+2exMeZVXNOlVtKHrqUxJhhXcvUPa+0rHZ7ba9fyJF29x07XJ6Qb5/oqRowxE4EngSustWXHj3fxe/d5nB0SZqy1S40xfzbGJHbnXF/F2EGnEWkfXksREZF+QVME+551wEhjzHD3CNFXgSXutiXAje79G4HujIj1VE9eo9O9Gu5E4rhrgG1eje5fThunMSbSGBN9fB+4rEM8feJaGmMM8BSw01r7+5PaeutadvUe6xj7N93VBGcDle5pjt051ycxGmMygFeAG6y1ezoc7+r37kScg92/Z4wxM3H9f7esO+f6KkZ3bLHAhXR4n/r4WoqIiPQPTlfZGEgbri/J+UAjUAS86z6eBizt0G8Brmpy+3FNLTx+fBCwHNjr/pnQCzF6fA0PMUbg+pIYe9L5zwFbgS24vsSl9tK1PG2cuKqm5bi37X3xWuKa1mbd12uze1vQ29fS03sM+B7wPfe+Af7kbt9Kh6qXp3p/9sL1O12MTwLHOly39af7vTsU5yJ3HDm4inHM6WvX0v34JuCFk87z6bXUpk2bNm3a+sNmrO2NKf8iIiIiIiIDj6YIioiIiIiIeIkSLBERERERES9RgiUiIiIiIuIlSrBERERERES8RAmWiIiIiIiIlyjBEhERERER8RIlWCIiIiIiIl6iBEukHzDGrDDGXOre/7Ux5o9OxyQiIiIyEAU5HYCIeMW9wK+MMcnAFOAqh+MRERERGZCMtdbpGETEC4wxHwFRwDxrbbXT8YiIiIgMRJoiKNIPGGMmAKlAo5IrEREREecowRLxc8aYVOAfwEKg1hhzucMhiYiIiAxYSrBE/JgxJgJ4BfiJtXYncD9wn6NBiYiIiAxgugdLRERERETESzSCJSIiIiIi4iVKsERERERERLxECZaIiIiIiIiXKMESERERERHxEiVYIiIiIiIiXqIES0RERERExEuUYImIiIiIiHjJ/wd1cNI9xQuICQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Define a time grid for the integration.\n", "import numpy as np\n", "t_grid = np.linspace(0, 250, 1000)\n", "\n", "# Integrate.\n", "_, _, _, nsteps_cart, out_cart = ta_cart.propagate_grid(t_grid)\n", "\n", "# Plot.\n", "%matplotlib inline\n", "from matplotlib.pylab import plt\n", "\n", "fig = plt.figure(figsize = (12, 12))\n", "\n", "ax1 = fig.add_subplot(1, 2, 1)\n", "ax1.set_aspect('equal')\n", "ax1.plot(out_cart[:, 3], out_cart[:, 4], linewidth=.2)\n", "ax1.set_title(\"Top view\")\n", "ax1.set_xlabel(\"$x$\")\n", "ax1.set_ylabel(\"$y$\")\n", "\n", "ax2 = fig.add_subplot(1, 2, 2)\n", "ax2.set_aspect('equal')\n", "ax2.plot(out_cart[:, 3], out_cart[:, 5], linewidth=.2)\n", "ax2.set_title(\"Side view\")\n", "ax2.set_xlabel(\"$x$\")\n", "ax2.set_ylabel(\"$z$\")\n", "\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "03081059-a228-4ea7-83e1-3277d19028f1", "metadata": {}, "source": [ "The plot shows how the initially-Keplerian orbit is slowly being deformed by the constant acceleration field.\n", "\n", "Let us also plot the time evolution of the Cartesian coordinates:" ] }, { "cell_type": "code", "execution_count": 7, "id": "dbca3334-db50-4d38-8674-6c2455e2bd42", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_t_evol(out, labels):\n", " fig = plt.figure(figsize = (12, 6))\n", " \n", " max_abs = 8\n", " \n", " ncoord = out.shape[1]\n", " ncols = 3\n", " nrows = ncoord // ncols + (ncoord % ncols)\n", "\n", " for i in range(0, ncoord):\n", " ax = fig.add_subplot(nrows, ncols, i + 1)\n", " ax.plot(t_grid, out[:, i])\n", " ax.set_xlabel(\"Time\")\n", " ax.set_ylabel(labels[i])\n", " ax.set_ylim(-max_abs, max_abs)\n", " \n", " plt.tight_layout()\n", "\n", "plot_t_evol(out_cart, [\"$v_x$\", \"$v_y$\", \"$v_z$\", \"$x$\", \"$y$\", \"$z$\"])" ] }, { "cell_type": "markdown", "id": "fourth-walnut", "metadata": {}, "source": [ "Note that the oscillatory behaviour in these plots is a quasi-Keplerian motion driven by the central-force field. The additional constant acceleration has a longer-term secular effect which is however not immediately recognisable in these plots.\n", "\n", "## Spherical coordinates\n", "\n", "Let us now switch to a [spherical coordinate system](https://en.wikipedia.org/wiki/Spherical_coordinate_system). Because we are operating in the Hamiltonian framework, we cannot use directly the time derivatives $\\left( \\dot{r}, \\dot{\\theta}, \\dot{\\phi} \\right)$ of the spherical coordinates as new momenta, and we have to use instead a set of canonical momenta $\\left( p_r, p_\\theta, p_\\phi \\right)$. The coordinate transformation $\\left(v_x, v_y, v_z, x, y, z\\right) \\rightarrow \\left( p_r, p_\\theta, p_\\phi, r, \\theta, \\phi \\right)$ reads:\n", "\n", "$$\n", "\\begin{aligned}\n", "p_r & = \\dot{r}, & r & = \\sqrt{x^2+y^2+z^2}, \\\\\n", "p_\\theta & = r^2\\dot{\\theta}, & \\theta & = \\arccos \\frac{z}{r}, \\\\\n", "p_\\phi & = r^2\\dot{\\phi}\\sin^2\\theta, & \\phi & = \\arctan \\frac{y}{x}.\n", "\\end{aligned}\n", "$$\n", "\n", "The Hamiltonian of the Stark problem in spherical coordinates becomes:\n", "\n", "$$\n", "\\mathcal{H}_\\mathrm{sph} = \\frac{1}{2}\\left( p_r^2+\\frac{p_\\theta^2}{r^2} + \\frac{p_\\phi^2}{r^2\\sin^2\\theta} \\right) - \\frac{1}{r} - \\varepsilon r \\cos\\theta.\n", "$$\n", "\n", "Let us define a couple of functions to convert a state vector between Cartesian and spherical coordinates:" ] }, { "cell_type": "code", "execution_count": 8, "id": "prostate-physiology", "metadata": {}, "outputs": [], "source": [ "# Cartesian to spherical.\n", "def cart2sph(state):\n", " from numpy import sqrt, arccos, arctan2\n", " vx,vy,vz,x,y,z = state\n", " r = sqrt(x**2+y**2+z**2)\n", " th = arccos(z/r)\n", " phi = arctan2(y,x)\n", " vr = (vx*x+vy*y+vz*z)/r\n", " vth = (z*vr-vz*r)/(r**2*sqrt(1-z**2/r**2))\n", " vphi = (vy*x-vx*y)/(x**2+y**2)\n", " return vr,vth,vphi,r,th,phi\n", "\n", "# Spherical to Cartesian.\n", "def sph2cart(state):\n", " from numpy import sin, cos\n", " vr,vth,vphi,r,th,phi = state\n", " x = r*sin(th)*cos(phi)\n", " y = r*sin(th)*sin(phi)\n", " z = r*cos(th)\n", " vx = vr*sin(th)*cos(phi)+r*(vth*cos(th)*cos(phi)-vphi*sin(th)*sin(phi))\n", " vy = vr*sin(th)*sin(phi)+r*(vth*cos(th)*sin(phi)+vphi*sin(th)*cos(phi))\n", " vz = vr*cos(th)-r*vth*sin(th)\n", " return vx,vy,vz,x,y,z\n", "\n", "# Spherical to Hamiltonian spherical.\n", "def sph2spham(state):\n", " from numpy import sin\n", " vr,vth,vphi,r,th,phi = state\n", " return vr,r**2*vth,r**2*vphi*sin(th)**2,r,th,phi\n", "\n", "# Hamiltonian spherical to spherical.\n", "def spham2sph(state):\n", " from numpy import sin\n", " pr,pth,pphi,r,th,phi = state\n", " return pr,pth/r**2,pphi/(r**2*sin(th)**2),r,th,phi" ] }, { "cell_type": "markdown", "id": "bc0ecc24-1b85-4302-80d9-26edb02fd878", "metadata": {}, "source": [ "We are now almost ready to numerically integrate the Stark problem in spherical coordinates. There is one additional complication however that we need to take into account.\n", "\n", "Because now we are operating in spherical coordinates, two of the coordinates are angles $\\left(\\theta, \\phi \\right)$ whose numerical values can grow in principle unbounded even if the motion remains bounded. In this specific example, the angle $\\phi$ will keep on growing as the particle orbits around the origin.\n", "\n", "This constant growth can become a problem because heyoka.py uses the largest absolute value in the state vector to transform the relative integration tolerance into an absolute error allowed within the integration loop: in other words, if (the absolute value of) $\\phi$ keeps on growing, the integrator will progressively become less accurate.\n", "\n", "We can avoid this undesirable effect by periodically reducing $\\phi$ modulo $2\\pi$. One possible way of implementing this is to define a callback function to be called at the end of every integration timestep:" ] }, { "cell_type": "code", "execution_count": 9, "id": "eee6986e-a10a-4a03-b925-c89cc9b44c54", "metadata": {}, "outputs": [], "source": [ "def mod_cb_sph(ta):\n", " # Fetch the current value of phi\n", " # from the state vector.\n", " phi = ta.state[5]\n", " \n", " # If phi is outside the [-pi, pi] range,\n", " # bring it back to [-pi, pi].\n", " if phi < -np.pi or phi > np.pi:\n", " ta.state[5] = (phi + np.pi) % (2 * np.pi) - np.pi\n", " \n", " return True" ] }, { "cell_type": "markdown", "id": "360f746e-070c-4033-a30d-ae881ffe64f5", "metadata": {}, "source": [ "We can now proceed to the numerical integration:" ] }, { "cell_type": "code", "execution_count": 10, "id": "bearing-pepper", "metadata": {}, "outputs": [], "source": [ "# Create the spherical symbolic variables.\n", "pr, pth, pphi, r, th, phi = hy.make_vars(\"pr\", \"pth\", \"pphi\", \"r\", \"th\", \"phi\")\n", "\n", "# Define the Hamiltonian in spherical coordinates.\n", "Ham_sph = 0.5 * (pr**2+(pth/r)**2+(pphi/(r*hy.sin(th)))**2) - 1./r - eps*r*hy.cos(th)\n", "\n", "# Convert the initial Cartesian conditions.\n", "sph_ic = sph2spham(cart2sph(cart_ic))\n", "\n", "# Create the integrator object.\n", "ta_sph = hy.taylor_adaptive(\n", " [(pr, -hy.diff(Ham_sph, r)),\n", " (pth, -hy.diff(Ham_sph, th)),\n", " (pphi, -hy.diff(Ham_sph, phi)),\n", " (r, hy.diff(Ham_sph, pr)),\n", " (th, hy.diff(Ham_sph, pth)),\n", " (phi, hy.diff(Ham_sph, pphi))],\n", " sph_ic\n", ")\n", "\n", "# Run the integration.\n", "_, _, _, nsteps_sph, out_sph = ta_sph.propagate_grid(t_grid,\n", " # Callback to reduce the\n", " # value of phi to [-pi, pi].\n", " callback = mod_cb_sph)" ] }, { "cell_type": "markdown", "id": "50246960-55d9-45aa-9d0a-27d83bdcfa29", "metadata": {}, "source": [ "Let's take a look at the results:" ] }, { "cell_type": "code", "execution_count": 11, "id": "796ba995-39e8-4ad0-b30f-e4c7831cadc1", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_t_evol(out_sph, [\"$p_r$\", r\"$p_\\theta$\", r\"$p_\\phi$\", \"$r$\", r\"$\\theta$\", r\"$\\phi$\"])" ] }, { "cell_type": "markdown", "id": "0d373952-ad09-4da9-a2f9-5c55c6c29ea0", "metadata": {}, "source": [ "Comparing these plots with those for the Cartesian coordinates, we can see how the oscillatory quasi-Keplerian behaviour remains. However, the oscillation amplitude is reduced with respect to the Cartesian case, and one of the momenta ($p_\\phi$, top right panel) has become a constant. This reflects the fact that the $z$ component of the angular momentum in the Stark problem is a constant of motion.\n", "\n", "Note that the bottom right panel, referring to the time evolution of $\\phi$, does **not** represent an oscillatory motion around 0: the sine-like shape is a visual effect of the periodic reduction of $\\phi$ to the $\\left[ -\\pi, \\pi\\right]$ range, but in reality the time evolution of $\\phi$ is linear with a periodic modulation on top.\n", "\n", "The periodic modulations in these plots arise from the fact that the initial Keplerian orbit is not perfectly circular and planar, and thus all coordinates (except $p_\\phi$) oscillate as the motion deviates from a perfect planar circle within each orbit. For a circular planar orbit around the origin, all coordinates and momenta would be constants, except for $\\phi$ which would evolve linearly.\n", "\n", "The fact that the amplitude of the periodic modulations is reduced with respect to the Cartesian case has an effect on the number of timesteps necessary to integrate the system:" ] }, { "cell_type": "code", "execution_count": 12, "id": "a55ce671-925d-4d0d-b7b7-d4a8ac99d527", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of steps (Cartesian): 1002\n", "Number of steps (spherical): 899\n" ] } ], "source": [ "print(\"Number of steps (Cartesian): {}\".format(nsteps_cart))\n", "print(\"Number of steps (spherical): {}\".format(nsteps_sph))" ] }, { "cell_type": "markdown", "id": "a5e2c894-85b9-4382-b3c7-f1890bde33e9", "metadata": {}, "source": [ "The reduction is not dramatic, but nevertheless measurable.\n", "\n", "Spherical coordinates require fewer timesteps because the reduction in the amplitude of the oscillatory motions improves the convergence of the Taylor series that heyoka.py uses internally to propagate the motion at each timestep. In other words, when using spherical coordinates the Taylor series synthesised by heyoka.py at each timestep can describe accurately the solution of the system for longer intervals of time.\n", "\n", "## Delaunay elements\n", "\n", "The results of the previous section suggest that introducing another system of coordinates which further reduces the amplitude of periodic oscillations may further decrease the number of timesteps required by the integrator. Because we are dealing with a perturbed Keplerian system, an obvious choice is to use [Keplerian orbital elements](https://en.wikipedia.org/wiki/Orbital_elements).\n", "\n", "In the Hamiltonian formalism, we cannot use directly the Keplerian elements as coordinates as they are not canonical variables. Instead, we can use the [Delaunay elements](https://en.wikipedia.org/wiki/Orbital_elements#Delaunay_variables), which are closely-related to the Keplerian elements via the following relations (valid in adimensional units):\n", "\n", "$$\n", "\\begin{aligned}\n", "L & = \\sqrt{a}, & l & = M, \\\\\n", "G & = \\sqrt{a\\left( 1 - e^2\\right)}, & g & = \\omega, \\\\\n", "H & = \\sqrt{a\\left( 1 - e^2\\right)} \\cos i, & h & = \\Omega.\n", "\\end{aligned}\n", "$$\n", "\n", "In these formulae, $\\left( a, e, i, M, \\omega, \\Omega \\right)$ are the usual Keplerian elements: semi-major axis, eccentricity, inclination, mean anomaly, longitude of pericentre and longitude of the ascending node.\n", "\n", "When employing Delaunay elements, a major complication is the appearance of the mean anomaly $l$, which is related to the eccentric anomaly $E$ via [Kepler's equation](https://en.wikipedia.org/wiki/Kepler%27s_equation), which, in terms of Delaunay elements, reads:\n", "\n", "$$\n", "l = E - \\sqrt{1-\\frac{G^2}{L^2}} \\sin E.\n", "$$\n", "\n", "This equation cannot be inverted in finite terms using elementary functions, thus, from now on, we will regard the eccentric anomaly $E$ as an unspecified function of $l$, $G$ and $L$:\n", "\n", "$$\n", "E = E\\left( l, G, L \\right).\n", "$$\n", "\n", "The cartesian coordinate $z$ can be written in terms of Delaunay elements as\n", "\n", "$$\n", "z = L\\sqrt{1-\\frac{H^2}{G^2}}\\left[ L\\left( \\cos E - \\sqrt{1-\\frac{G^2}{L^2}} \\right)\\sin g + G\\sin E \\cos g \\right],\n", "$$\n", "\n", "while the two-body problem Hamiltonian is simply\n", "\n", "$$\n", "\\mathcal{H}_\\mathrm{2bp} = -\\frac{1}{2L^2}.\n", "$$\n", "\n", "Thus, the full Hamiltonian for the Stark problem in Delaunay elements reads:\n", "\n", "$$\n", "\\mathcal{H}_\\mathrm{Del} \\left( L, G, H, l, g, h \\right) = -\\frac{1}{2L^2}-\\varepsilon L\\sqrt{1-\\frac{H^2}{G^2}}\\left[ L\\left( \\cos E - \\sqrt{1-\\frac{G^2}{L^2}} \\right)\\sin g + G\\sin E \\cos g \\right].\n", "$$\n", "\n", "In order to write the equations of motion, we will have to take into account that $E$ is a function of $\\left( l, G, L \\right)$ whose derivatives can be explicitly computed from Kepler's equation:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\frac{\\partial E}{\\partial l} & = \\frac{1}{1-\\sqrt{1-\\frac{G^2}{L^2}}\\cos E},\\\\\n", "\\frac{\\partial E}{\\partial L} & = \\frac{G^2\\sin E}{L^3\\sqrt{1-\\frac{G^2}{L^2}}\\left(1-\\sqrt{1-\\frac{G^2}{L^2}}\\cos E\\right)},\\\\\n", "\\frac{\\partial E}{\\partial G} & = \\frac{-G\\sin E}{L^2\\sqrt{1-\\frac{G^2}{L^2}}\\left(1-\\sqrt{1-\\frac{G^2}{L^2}}\\cos E\\right)}.\n", "\\end{aligned}\n", "$$\n", "\n", "We can now proceed to formulate the equations of motion:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\frac{dL}{dt} & =-\\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial E}\\frac{\\partial E}{\\partial l}, & \\frac{dl}{dt} & = \\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial L}+\\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial E}\\frac{\\partial E}{\\partial L}, \\\\\n", "\\frac{dG}{dt} & = -\\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial g}, & \\frac{dg}{dt} & = \\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial G}+\\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial E}\\frac{\\partial E}{\\partial G}, \\\\\n", "\\frac{dH}{dt} & = -\\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial h}=0, & \\frac{dh}{dt} & = \\frac{\\partial \\mathcal{H}_\\mathrm{Del}}{\\partial H} .\n", "\\end{aligned}\n", "$$\n", "\n", "Note that the Hamiltonian does not depend directly on $l$ (only indirectly via $E$). Thus, in the numerical integration, we will be replacing the differential equation for $l$ with the differential equation for $E$:\n", "\n", "$$\n", "\\frac{dE}{dt}=\\frac{\\partial E}{\\partial l}\\frac{dl}{dt}+\\frac{\\partial E}{\\partial L}\\frac{dL}{dt} + \\frac{\\partial E}{\\partial G}\\frac{dG}{dt}.\n", "$$\n", "\n", "The value of $l$ for a given $E$ can be obtained via Kepler's equation.\n", "\n", "On the implementation side, let us begin with a couple of functions to convert between Cartesian coordinates and Delaunay elements. We will be using [pykep](https://esa.github.io/pykep/) for the conversion between cartesian coordinates and Keplerian elements:" ] }, { "cell_type": "code", "execution_count": 13, "id": "57fa693f-3d97-46fa-8961-3b713480d5be", "metadata": {}, "outputs": [], "source": [ "# Cartesian to Delaunay.\n", "def cart2del(state):\n", " import pykep as pk\n", " \n", " vx,vy,vz,x,y,z = state\n", "\n", " a,e,i,Om,om,E = pk.ic2par([x, y, z], [vx, vy, vz])\n", " \n", " L = np.sqrt(a)\n", " G = np.sqrt(a*(1-e**2))\n", " H = G*np.cos(i)\n", " \n", " g = om\n", " h = Om\n", " \n", " return [L, G, H, E, g, h]\n", "\n", "# Delaunay to cartesian.\n", "def del2cart(state):\n", " import pykep as pk\n", " \n", " L,G,H,E,g,h = state\n", " \n", " a = L**2\n", " e = np.sqrt(1-G**2/L**2)\n", " i = np.arccos(H/G)\n", " \n", " Om = h\n", " om = g\n", " \n", " ret = pk.par2ic([a, e, i, Om, om, E])\n", " \n", " return [ret[1][0], ret[1][1], ret[1][2], ret[0][0], ret[0][1], ret[0][2]]" ] }, { "cell_type": "markdown", "id": "47407cff-e083-41fe-8634-e4cc64fdb695", "metadata": {}, "source": [ "Next, we formulate the Hamiltonian and the equations of motion:" ] }, { "cell_type": "code", "execution_count": 14, "id": "0e44e17b-4b7d-495c-a7d7-b9b3167d967f", "metadata": {}, "outputs": [], "source": [ "# Symbolic variables for the Delaunay elements.\n", "L, G, H, E, g, h = hy.make_vars(\"L\", \"G\", \"H\", \"E\", \"g\", \"h\")\n", "\n", "# The Hamiltonian.\n", "Ham_del = -0.5*L**-2 - eps*L*hy.sqrt(1.-H**2*G**-2)*(L*(hy.cos(E)-hy.sqrt(1.-G**2*L**-2))*hy.sin(g)+G*hy.sin(E)*hy.cos(g))\n", "\n", "# Derivatives of E wrt l, L and G.\n", "dE_dl = (1. - hy.sqrt(1.-G**2*L**-2)*hy.cos(E))**-1\n", "dE_dL = G**2*hy.sin(E)/(L**3*hy.sqrt(1.-G**2*L**-2)*(1. - hy.sqrt(1.-G**2*L**-2)*hy.cos(E)))\n", "dE_dG = -G*hy.sin(E)/(L**2*hy.sqrt(1.-G**2*L**-2)*(1. - hy.sqrt(1.-G**2*L**-2)*hy.cos(E)))\n", "\n", "# Equations of motion.\n", "dL_dt = -hy.diff(Ham_del, E) * dE_dl\n", "dG_dt = -hy.diff(Ham_del, g)\n", "dH_dt = hy.expression(0.)\n", "dl_dt = hy.diff(Ham_del, L) + hy.diff(Ham_del, E) * dE_dL\n", "dg_dt = hy.diff(Ham_del, G) + hy.diff(Ham_del, E) * dE_dG\n", "dh_dt = hy.diff(Ham_del, H)\n", "dE_dt = dE_dl * dl_dt + dE_dL * dL_dt + dE_dG * dG_dt" ] }, { "cell_type": "markdown", "id": "455eb1ec-d130-4a2e-88a3-b5c9fa51c172", "metadata": {}, "source": [ "Like in the case of spherical coordinates, we will also need to prevent $E$ from growing indefinitely:" ] }, { "cell_type": "code", "execution_count": 15, "id": "4200061c-7506-4837-986f-c7b8627d9183", "metadata": {}, "outputs": [], "source": [ "# Callback to reduce E to the\n", "# [-pi, pi] range.\n", "def mod_cb_del(ta):\n", " E = ta.state[3]\n", " if E < -np.pi or E > np.pi:\n", " ta.state[3] = (E + np.pi) % (2 * np.pi) - np.pi\n", " \n", " return True" ] }, { "cell_type": "markdown", "id": "a52cf7b4-dc66-40b6-a049-a72e07929167", "metadata": {}, "source": [ "We are now ready to create the integrator object:" ] }, { "cell_type": "code", "execution_count": 16, "id": "6a19bc78-a99b-42bf-a6f3-7e9ac60c0a11", "metadata": {}, "outputs": [], "source": [ "# Convert the initial conditions\n", "# into Delaunay elements.\n", "del_ic = cart2del(cart_ic)\n", "\n", "# Create the integrator.\n", "ta_del = hy.taylor_adaptive(\n", " [(L, dL_dt),\n", " (G, dG_dt),\n", " (H, dH_dt),\n", " (E, dE_dt),\n", " (g, dg_dt),\n", " (h, dh_dt)],\n", " del_ic\n", ")" ] }, { "cell_type": "markdown", "id": "76103dc7-ab9a-4b40-8039-b854eb943630", "metadata": {}, "source": [ "Let us proceed to the numerical integration:" ] }, { "cell_type": "code", "execution_count": 17, "id": "c5622eda-bbcd-4c60-bc7e-768dfe0c7c9a", "metadata": {}, "outputs": [], "source": [ "_, _, _, nsteps_del, out_del = ta_del.propagate_grid(t_grid, callback = mod_cb_del)" ] }, { "cell_type": "markdown", "id": "f2839f24-8220-48e3-bcf9-06420cb0eb1f", "metadata": {}, "source": [ "We can now take a look at the time evolution of the orbital elements:" ] }, { "cell_type": "code", "execution_count": 18, "id": "8758a7a5-9250-4d43-9865-492bcb0a5690", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_t_evol(out_del, [\"$L$\", \"$G$\", \"$H$\", \"$E$\", \"$g$\", \"$h$\"])" ] }, { "cell_type": "markdown", "id": "867f0669-43f1-451a-a20e-318befd087be", "metadata": {}, "source": [ "The plots for $L$, $G$, $H$, $g$ and $h$ clearly show how the Keplerian oscillations for these elements have been removed thanks to the use of orbital elements as a coordinate system. These elements would be constant in a perfectly Keplerian orbit, while in the Stark problem they undergo short-term oscillations with amplitude $\\sim\\varepsilon$ and long-term evolution with timescale $\\sim 1/\\varepsilon$. We can see the perturbation induced by the constant acceleration field by zooming into, e.g., the plot for the $g$ angle (the argument of pericentre):" ] }, { "cell_type": "code", "execution_count": 19, "id": "abcdc48c-bc6d-4524-971e-45cfeb3ae2b3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (6, 3))\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.plot(t_grid[:100], out_del[:100, 4])\n", "ax.set_xlabel(\"Time\")\n", "ax.set_ylabel(\"$g$\");" ] }, { "cell_type": "markdown", "id": "facfa4ec-0849-43e1-9611-555236b7f26e", "metadata": {}, "source": [ "Let us now zoom into the plot for $E$:" ] }, { "cell_type": "code", "execution_count": 20, "id": "27210f10-341e-4ecc-b15f-ce6067e464ac", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (6, 3))\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.plot(t_grid[:100], out_del[:100, 3])\n", "ax.set_xlabel(\"Time\")\n", "ax.set_ylabel(\"$E$\");" ] }, { "cell_type": "markdown", "id": "6135ee1f-6525-442d-9a1b-8ee24c47cb50", "metadata": {}, "source": [ "We can see how $E$ is still subject to Keplerian oscillations. Indeed, even in a perfectly Keplerian orbit, the time evolution of $E$ is linear only for circular orbits.\n", "\n", "Because of the presence of Keplerian oscillations in $E$, the reduction in number of integration timesteps after switching to Delaunay elements is measurable but not very large:" ] }, { "cell_type": "code", "execution_count": 21, "id": "b5f2f844-798e-4cbc-8b58-4899dbe07a9a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of steps (Cartesian): 1002\n", "Number of steps (spherical): 899\n", "Number of steps (Delaunay) : 764\n" ] } ], "source": [ "print(\"Number of steps (Cartesian): {}\".format(nsteps_cart))\n", "print(\"Number of steps (spherical): {}\".format(nsteps_sph))\n", "print(\"Number of steps (Delaunay) : {}\".format(nsteps_del))" ] }, { "cell_type": "markdown", "id": "9f980864-f8ba-4d5e-b276-f21ad9167c5b", "metadata": {}, "source": [ "In order to further reduce the number of timesteps, we will have to implement one final trick." ] }, { "cell_type": "markdown", "id": "5f73a4e7-33ec-4167-87b3-6fa8b985fccb", "metadata": {}, "source": [ "## Delaunay + Sundman\n", "\n", "The idea we will be exploring in this section is to replace the time $t$ with a fictitious time $\\tau$ defined by the differential relation\n", "\n", "$$\n", "\\frac{dt}{d\\tau} = r,\n", "$$\n", "\n", "where $r$ is the distance from the Keplerian centre of force (i.e., the origin). This time transformation belongs to the class of [Sundman transformations](https://en.wikipedia.org/wiki/Karl_F._Sundman), which were originally introduced for regularisation purposes: the fictitious time $\\tau$ flows slower close to the centre of force, so that it is impossible for a test particle to reach the gravitational singularity as that would take an infinite amount of fictitious time $\\tau$.\n", "\n", "Here, however, we are not interested in the regularisation properties of this transformation. Rather, what is of interest to us in this context is that, in Keplerian orbits, $E$ evolves *linearly* with $\\tau$. In other words, by replacing the time coordinate $t$ with $\\tau$, we will be able to remove the Keplerian oscillations of $E$ in the Stark problem.\n", "\n", "We can introduce the new time coordinate $\\tau$ directly in the definition of the equations of motion. $r$ can be expressed in terms of Delaunay elements as\n", "\n", "$$\n", "r = L^2\\left( 1 - \\sqrt{1-\\frac{G^2}{L^2}}\\cos E\\right).\n", "$$\n", "\n", "For each Delaunay element $D_i$ we can then write:\n", "\n", "$$\n", "\\frac{dD_i}{d\\tau} = \\frac{dD_i}{dt}\\frac{dt}{d\\tau} = \\frac{dD_i}{dt} L^2\\left( 1 - \\sqrt{1-\\frac{G^2}{L^2}}\\cos E\\right).\n", "$$\n", "\n", "We will also append the differential equation for $dt/d\\tau$ to the ODE system, so that we can track the evolution of the real time $t$ in fictitious time $\\tau$:" ] }, { "cell_type": "code", "execution_count": 22, "id": "56a06947-164a-4f91-b977-e5926e3a1a90", "metadata": {}, "outputs": [], "source": [ "# Expression for dt/dtau.\n", "dt_dtau = L**2*(1 - hy.sqrt(1.-G**2*L**-2) * hy.cos(E))\n", "\n", "# Additional dynamical variable to\n", "# integrate t(tau).\n", "t, = hy.make_vars(\"t\")\n", "\n", "ta_del_e = hy.taylor_adaptive(\n", " [(L, dL_dt*dt_dtau),\n", " (G, dG_dt*dt_dtau),\n", " (H, dH_dt*dt_dtau),\n", " (E, dE_dt*dt_dtau),\n", " (g, dg_dt*dt_dtau),\n", " (h, dh_dt*dt_dtau),\n", " (t, dt_dtau)\n", " ],\n", " # Both t and tau\n", " # start at zero.\n", " del_ic + [0.]\n", ")" ] }, { "cell_type": "markdown", "id": "905d9b86-5cf2-4aaa-b8bd-f42da7d646dd", "metadata": {}, "source": [ "In order to prevent the real time $t$ from growing indefinitely, we will periodically reset its value:" ] }, { "cell_type": "code", "execution_count": 23, "id": "5f2a30a0-6045-4230-a708-f217d7915b97", "metadata": {}, "outputs": [], "source": [ "def mod_cb_del_e(ta):\n", " # Reduce E to the [-pi, pi] range.\n", " E = ta.state[3]\n", " if E < -np.pi or E > np.pi:\n", " ta.state[3] = (E + np.pi) % (2 * np.pi) - np.pi\n", "\n", " # Modulo reduction of t when it\n", " # grows past 5.\n", " t = ta.state[6]\n", " if t > 5:\n", " ta.state[6] = t % 5\n", " \n", " return True" ] }, { "cell_type": "markdown", "id": "9f112023-526d-4dec-8da3-9827b2e2e7d2", "metadata": {}, "source": [ "We can now proceed to the integration:" ] }, { "cell_type": "code", "execution_count": 24, "id": "0249bafb-1cfa-4845-94c0-92e898be650d", "metadata": {}, "outputs": [], "source": [ "_, _, _, nsteps_del_e, out_del_e = ta_del_e.propagate_grid(t_grid, callback = mod_cb_del_e)" ] }, { "cell_type": "markdown", "id": "3f4b7531-bfb3-46e7-8f24-af3b021c24c5", "metadata": {}, "source": [ "Let us plot the results:" ] }, { "cell_type": "code", "execution_count": 25, "id": "1fd0289a-8cbd-41bd-b98e-b543e8a2e4ac", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_t_evol(out_del_e, [\"$L$\", \"$G$\", \"$H$\", \"$E$\", \"$g$\", \"$h$\", \"$t$\"])" ] }, { "cell_type": "markdown", "id": "62f36759-6e45-4cf6-93c0-4a07c65ebd3b", "metadata": {}, "source": [ "And let us zoom into the plot for $E$:" ] }, { "cell_type": "code", "execution_count": 26, "id": "ca36771b-5759-4d07-bf93-3271733062a7", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (6, 3))\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.plot(t_grid[:100], out_del_e[:100, 3])\n", "ax.set_xlabel(\"Time\")\n", "ax.set_ylabel(\"$E$\");" ] }, { "cell_type": "markdown", "id": "48e5d8ba-be06-429a-87d8-489b00d09b44", "metadata": {}, "source": [ "The plot indeed confirms that the Keplerian oscillations for $E$ are gone.\n", "\n", "What about the number of steps?" ] }, { "cell_type": "code", "execution_count": 27, "id": "536551b3-6d01-43c1-b113-a188c0ebf183", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of steps (Cartesian): 1002\n", "Number of steps (spherical): 899\n", "Number of steps (Delaunay) : 764\n", "Number of steps (D + S) : 388\n" ] } ], "source": [ "print(\"Number of steps (Cartesian): {}\".format(nsteps_cart))\n", "print(\"Number of steps (spherical): {}\".format(nsteps_sph))\n", "print(\"Number of steps (Delaunay) : {}\".format(nsteps_del))\n", "print(\"Number of steps (D + S) : {}\".format(nsteps_del_e))" ] }, { "cell_type": "markdown", "id": "af4898ae-72a0-4bcb-b007-9bf3ec92599c", "metadata": {}, "source": [ "We can see how, after the removal of the short-term Keplerian oscillations from $E$, the reduction in number of steps is substantial. Indeed, in the Delaunay + Sundman setup, the evolution of the coordinates in fictitious time deviates from constant or linear behaviour only through the external perturbation, whose magnitude $\\varepsilon$ is small.\n", "\n", "Let us conclude by summarising in a plot the number of steps required by each coordinate system:" ] }, { "cell_type": "code", "execution_count": 28, "id": "01beaa65-65aa-47e8-bb61-2eddb230d312", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (6, 6))\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.bar(range(4), [nsteps_cart, nsteps_sph, nsteps_del, nsteps_del_e], tick_label=[\"Cartesian\", \"Spherical\", \"Delaunay\", \"D + S\"])\n", "ax.set_ylabel(\"N of steps\");" ] }, { "cell_type": "markdown", "id": "ab28c328-df90-4a77-b9cd-2140b21e5fed", "metadata": {}, "source": [ "## Conclusions\n", "\n", "In this example we have shown how the choice of coordinate system and time coordinate can influence the behaviour of a Taylor integrator. Intuitively, the closer the time evolution of a coordinate is to a polynomial, the longer the Taylor series can approximate the ODE solution, and the fewer number of steps is required.\n", "\n", "In these experiments we focused only on the number of steps as a performance metric. Clearly, the use of more sophisticated coordinate systems (such as the Delaunay elements) can lead to more complicated equations of motion, which in turn may lead to overall longer integration times. Nevertheless, the minimisation of the number of timestpes may be of interest in some cases (e.g., to reduce the accumulation of numerical errors in long-term integrations)." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.6" } }, "nbformat": 4, "nbformat_minor": 5 }