{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from shapely.geometry.polygon import LinearRing\n", "import matplotlib.pyplot as plt\n", "import matplotlib.patches as patches\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Finding points in an arbitrarily rotated ellipse" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# The ellipse parametes\n", "ellipse_center = (0.5, 0.4)\n", "ellipse_width = 0.5\n", "ellipse_height = 0.2\n", "rotation_angle = 50\n", "\n", "# some test points for matching\n", "x = np.random.rand(1000)\n", "y = np.random.rand(1000)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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HwjUzpb2EJQtmsRJPIC5PMo0hZHNeUffy6YQNqRRE7Vq6XnZI6nwh23VtXCqhol/SGneM3sXVP7Y+3zbNdsjB1/UQx8BQBT0/2ojq2D7/6badVfTcthFA89b1UqHWNxcs3xD5e1VDyNa8itNzQHEOX9XgOlI5yGJxu6hr47L+iepnU6zRokKcAMvb9ri6ZUmCz4e+S0Oz1cLxdT3E0b968zgjqkZ1NGjqul6qdHeWUY6pX6dS59DWvJLpuaUrN+GiH9+HyvAIAuwzsFRqMlKGPVIZyepZcuGyd1mCIU2dE1dtzINsh9fRVsrV9qT5FZezZ+PqIRfoyGPxJdzg63qII07G+R6ytIXMMztn5lQlfWRrXsnGsxbSracIOVpsSGUka9KeK5e9y2RK1c+mnvAZhUywLV04K9f7Js2vIipa0/h2XYyP60HGwFBFetk24HfI0iaydZ9GH9mYV3HJ8VH4bkizIZWRrJ6lZsv1KDqmDBqV+VUkRWsDWyeWfPF62aJmwMqMqFKrIHdAhzJR635Rztwp3cj03P6llsjDOb4b0mxIZURmcQcAXn7RnRgNgsgQC3sSiocJg6aIycausRFWt+318sHAiDthqnJqzzdPoguoyQuZngNQSEcCG1IZiTuOWtt5xcWpm10A+KAA8pD3+dhzqR8bysZmnR5fDIy4u+yGLj0p8e9lfbps1aZCy5A0UJQXcXquaOPGhlRG6i3uuFhwERLpdOOLAsiKjufL67ksuqGaBRvKxuZhEl+KK+Y1YGV9t21ndW+YqGgyJC0mIh2mZEgRHQlsSOWgNiGS7uHzPZFON7oUAFVjQdfzZRU4RTdUs2IjrG4zxGIrVJm3v/IasKqJyxSNSJvoNFCiZMgFyzdg6cpNWLqQC6g2woaUBpIWOue1jEcm6CvDI5jdt0ZJaFM2FlxXpfbFU+EC07vhvEZDGsPFtNGma401GrAd7SUEQZgg3b96c6JxFpdG0QhvWvUgy2sbHqmSkbOU4IKcGogqclbDdZyaIjJBLwDlQm0uCpuqIns+Wwa1a0OumWgsggggc+HQmuGiugZMF1fUuca6O8tY1zsXV555LHZVxzA8UlUuyBhVjLWjrRT5Wt606iFOVlCRs5RgQ0oD9QsdAFqFAFD86stZiVIAURdAxy1YysaC66rUrg25ZkFm+ADAut65eKRvPtb1zlVe/2kNF9PV3k2ssazGWc0Qq/Xp0oWzClf5nRJJsoKCnKUEh/Y0UcQEOlNE5arIQqOyBUvtuG89rktcUDzBU0RUQqhpQnVZDBeTcsfEGtNlnLleY0UnKZxKQc5Sgg0pxgmNCmB235pUQpu6seC6kjzASsY0SUaBLGF32apNkbWTqG0OTKwxnc/Im1dz1Pp12apNEwpoUpKzVGBDSjNUT5JRJ63Q9t1YMD1PWMmYJ8kokCXsbtsZnbBLbXNgYo2ZeEaWuWaoyRDu32REICnbT5Wurq5gcHDQdTMiadyBAqGQ4DwpNZplwfI8KQZJ45hUFqXc0YZ1vXMnvGfR14DOZ+S1ZIdmmJdJCCHWB0HQFfk7NqT0IQtPTWkvKVXwZZoD2TyJUqyMfnQrctl7yca5hgDwSN/8TJ/LhPBaMg8bqyFxhhSH9jQSV4F3YKjSVJOOkRNXR4vniVkGhiro+dFGVMf2XePU86ONALLVxYkLoXLCrnkon94tClyXLhkuf6CROMHIdTeYGnHzJKmmTrPQWJ9JV58sXblprxFVozoWYOnKTVrev55aeYKomkecsKsHLvVhHjZWk2FDSiNxglHXpJMpGFOKh9FPXAFXisXubM+ttIUp0zA8Uk3187x0d5axYclJuOrMY43Ve2pmXNdsawZsGqu+6jEO7Wmku7OMpSs3RQrlvJNuYKgy4b1rCmbw0aewYn2F5HUpzERqY3LB8g2Rv6e003NxFc+yVZsKF0rgU5TpUM1j8/30bg3Kydy2TpNSvvYrCTakNLN04Swjx3tluRYj1VHc8pvHMNpwaICy4qEsNGzR3VlG/+rN2usGNRrcU9pLkTWLVLGdHzEwVJlQt6aGDgNzSnsp8v2ntEdfOcLoQ3Xdp1WoFIzUPDKNugFhy1j1OReLDSnNmJh0sno0NRqNqBqUPBs1qAuNOHQbgLp3eo2J1EB40KHntuzJ1GnzI/L2UVxYU0coYcmCWei5bSOqo/v6qNQqsGTBrNzvbRLfNx9p1r1vCjWvTPPheW0Yqz7nYrEhZQDdky5pIrUKEWlM2U64VBH2PgiNGvXP09FewrO79ow77ZXXAFQxutMo0P7VmyckUgNAdTTI3L9pKlHrMJLj5nqcgVnkUJDPm48aada9bwo1r0zz7XnzELdOqVX2TwMbUh4QdxddW6kVpx1fHpcjVfu5zYRLVWHvi9BofJ6ocJAOAzDO6E6rQOP6MGv/pvGa6TCSZXO9o62krZ8ohILSIOvXpSs3efMcada9bwo1r0zz7XmzkrROqVX2TwOf2vMA2SmvKe0lXH7q0bis+2ijt8CroHqruy/HlZPCqTVMGoCqfVojrg+z9m/tCL/K3NJhJMtOYS1dKA+9pe0n2+Q9iSTrv+GRqjenmtKse2on8ZLGL69Mo/a8pkhap2lkDTXYI+UBKuEI17tsVSXqy64jzW7SdhtkP++ZN2NCjhQQ5gDl6V/VuaVjZ50l9EbZy6kjLBfnkaYYEo8izbqnFH5VGb+8Mo3S85pEZZ261mNZYUPKE6hPMFUl6ovQiFNeNUwbgGkNk1of6jy1lwZdRnLauU45NKIj3Nkzb4YXpTLiSLvuqcg7lfHTIdOoPK9JKK/TvLAhxWgh7Y6TutCIep5Sq8ABkydh+0jVigGYxTBx2beujGTKXk4d3rLuzjKWrdoUmafnkxLyYd03ojp+Pj6bbSiv07ywIcVowRdPkyoUnodCG9LiQqFQ7iddu/AlC/TXp2OSKbIXxTaU12leRCCpQUSVrq6uYHBw0HUzGIZhEokqpisABAiTadMWbiyiEqJM1Pi1lVq9SYJm9CGEWB8EQVfU79gjxTCek6RgWQG7o34XXhke2WtEAekTz12Hj5pxHrn2ojRjn/sIe6QYxmOSdsy8o07GlrKa3bcmMkxU7mjDut652j9PJzyP7JOlz9nwMkecR4rrSDHW8fWG70YoPMfSlfILfgH6NZZcU1NWleERBNjnJTIxlpTLNCTB88g+afvc5lzOCgWZaQI2pBir+LDYVaDwHANDlb1lDhqpKWdV5V1UAZeETQPBl2K0UfhsBPpK2j6nbuxSkJmmYEOKsQr1xa4KhedQueBXRXlHCbgLlm9A5xd+VgghF4dpA6HeQN2xew9KrWLc7305eeezEegrafucurFLQWaagg0pxirUF7sqFJ5D5YJflesnZNfhbNtZLcyOUYZJA6HRQB0eqQJBWCS18QoM6h7BZrnGhBJp+5y6sUtBZpqCT+0xVilKXRYKzyFrw5T2fRf8qpw6ihNkOi5mpkzeIoFxyb1RBmp1LED75EkYuvSkce+R9xoZ07g+vUYVk8ndafucesFLCjLTFGxIMVahvthVofAcsjYsWTD+gt+kY/NJ1+EUYccoI4+BkGQAqe7AdVwjYwPX5ReoYcMATtPnKnPZ5ak+CjLTFGxIMamJW4xJC1XHzlZVGFDaLZpAVxuiBFw9RdgxxpHVQEgygFR34EUOeRQZigZw3Fx27fmkIDNNwYYUk4q4xQhAaaHm2dmqCgNqu0VT6GhD1GXHNYqyYzRBkgGkugMvcsijyPhmAFMw/CjITBNwsjmTirjFaONUhupnFPmEiAm6O8vYsOQkXHXmsSh3tE1IhmYmkpTc291ZxuWnHp3Yn5zI7SfUk7sb4VIo5mCPFJOKLLswnTs01c/3bbdIhaLuGE2g4nFS6c8ihzyKjG85PyqeTxfhvyJUY2dDKidFmARpSFqMpkMUqmEQDpcwptFpABXNgG0Guag6/lT6QsXwS/Lk634O13lbuuC79nLQjPdPxT0zgMT+yCtUVPu8GceGYSjAa28f1PoiSf5O770DMougrdSq/Tl8un8y7q499kjlgELynm1UdmFxJ/ry7j5Ud4EcLmF8hooXIwsU5CKV/qPQF/VkLYXSKoSR5yhKCgYbUjkowiTIInDiFmPc73QJFdUwSNHCJS6gopCaCd/DHa7lIqX+c90XaZGF/2SlUfI+R1FSMPjUXg58O7XRiO1LJH0TKrYxcVomz3sW+ZJRyvh+4tS1XKTUf677Ii2yk6ZlQ8/RM28GSi3j758stQiyCfsy2JCKQFX5+H5s2bbA8U2o2MSE0ZL3PU3NDz5eHY/vGw7XcpFS/7nuiyx0d5axrncuHumbj3W9c9HdWTb7HCLh/x7AhlQDaZSPap0YqtgWOD4KFRm6jQETRkve9zQxP9jLtQ/ZHPJ9w+FaLsr6qUUI68a7677Qhann6F+9GdXR8ent1dHAG+9rDc6RaiBtHo/PeTi249NFSQA3kYNhwmjJ+54m5ge15FtXxM0h3+oTReFSLsquPBp9/oS6i6tRijC3TTyHTBZVhkcwu2+NN3qCPVINUHILm8a2h6goicsmvEcmvBB539PE/Gim9RVHkkFZBC+GKxr7r1VMjBX5lHOmgq/hcpksEsAEr/XFA/eRfUb2SDWQZhfuu2Fg00NE6SRNXkwYAya8EHnf08T8KMopnbwkzaGieDFcUd9/03vviHxNXuOdivz3WbZGySgBTKhlNVIdxU33bNn7c2rPyIZUA6rKx+fJW48tgV2kkI4JY8CE0aLjPXXPjyKErXSgew5RUeoUMbFeKcl/n2VrlIyKGisg2rii8oxGDSkhxMkArgbQCuDbQRD0Nfx+GoDvAeh4/jW9QRDcabJNSagqH58nrwuKFNIxZQyYMGqpeTaKkieXF1kez87n9mBgqJKr2j/fjzYeE+uVkvz3XbY2yihZtfMoqDyjMUNKCNEK4FsA/gHA4wDuFUKsDILggbqXXQzg1iAIrhVC/B2AOwEcYapNqqgoH8qTl6KQK1JIpwjGgMs5Ysq4ozjvZdTatXTlJgyPVPf+fNvOamojKItSz9NXlLwxKphYr5Tkf5FkK6Ae7gPoPKNJj9RrAPw+CIKHAUAI8UMA7wBQb0gFAF7w/PcHA3jCYHu0QnXyUhVyRQvpUPP0pIHqHMmDj8/U3VlG/+rN4wwpIL1nI61Sz9tXlLwxquher5TkfxFlKzDe8J0zcypWrK+QfUaThlQZwGN1/38cwAkNr1kK4GdCiE8COADAWw22RytUJy9VIVcEL05eqHhMqM6RPPj6TDo8G2mVet6+ouSN0UXatUlJ/puSrdS81l0vO4SE/IzCpCEVVZ+00Tt3NoDvBkFwhRDitQC+L4R4VRAEY+PeSIiPAPgIAEybNs1IY9NC1TCgLORMeHHSLnZXwoGSx4TyHMmKr8+kw7ORVqlTrC/mkqS1GSczTMqSNLIqr2xt/KxGDxAFDy/lKIBJQ+pxAIfX/f8wTAzdfRDAyQAQBMHdQoj9ARwK4Mn6FwVBcD2A6wGgq6srKlTqBIoDWzQhF0da48SlMUPJY1LEOeLrM+nwbKRV6nn7ipI3RgdJdeHiZIbJZH5bsirqs+pLDdTwwcPrCpMFOe8FcJQQYroQYjKAswCsbHjNFgBvAQAhxCsB7A9gq8E2FZ4iXcOSRNrCmCbvFhwYquDYZT/DEb134IjeO9D5hZ+NKxhHyWNSxDni6zPpKr7Z3TnxfjQZeftKR5spFZCMW5uuLkC2+blRnyXzVlD38LrCmEcqCII9QojzAKxGWNrgxiAINgkhvgBgMAiClQAWA7hBCLEI4di9LwgCMh4nH6EacjRBWuPElDEzMFRBz482ojq2b+pu21lFz20bAYRjQsljUsQ54vMz2fZsu64vRinMDcR76FxtgGx+btp8PGYiRutIPV8T6s6Gn11a9/0DAGabbEMzQjHkaIK0xokpY6Z/9eZxRlSN2uWb3Z1lcuGQIs6R+meq5XwsWr7BK6OqhulcPt3jn6a9lMLcQHyosn/1ZicbIJsbL9lnNZYc8MHD6wq+a4/xlrQhClPhn7gdXf2VH3x/mh1qHo/Gu7oo3c0Vh2/tv3jgPixavkG5vZTC3ED82nQVMrb5ubLPOufEaSyvFOErYhhvSW2x2u4AACAASURBVBuiMBX+ibvWoH4HWUQvEEVcejx0nCKl5rGJY2CoEpuYDExcb5TC3DVka9NVyNjm5/ocFqeC8C0lqaurKxgcHHTdDIbZS1SOFACUWgX633UMCyTLTO+9IzJZVgB4pG++sc9tzP0Bwp29bCcve32jEVXDdPuzkHSdR+PztJVacdrx5cjiiuzxYCgjhFgfBEFX1O/YI8UwOYm67mNKewlLFswyejxaZQdJpQioTVx5PNJ6kmSvbxUCoxEbXIqJvnHhuFYhIp9v7UNbcfmpRzfdvGTU8U1usSHVZPg2QX3BZthO9dQTtdNRtnCV2K/rtOhoEER6cnS3X4csiEtUjjIGgfC5OczNyPBRbnGyuQNc1VBJk8RKqc4LMx7VGjOuauC4xlVif9xp0TQ/r7XXZPt1JbRHJSoLYG+ichQHt5UytpppBnyUW+yRsowP1bV93BE0E6oeDmqno2xi20NYOyaf5sh4nOfMdPt1JbTHJSrLcgd3PLcHA0MVliUFQXeUw0e5xYaUZVyeyFGdoJRODXEociKqOUAUT0cVjcZNR4B99XfKjk6RqqBTWcWdeFu2ahO27ayO+3l9fTXGb0xsun2UW2xIWcalta06QU22MY1hxJ6xaFRzgKgVAS0isus1yh1tWNc7N/HvXeUK2VJWww1GVA3K3gVGHRObbh/lFudIWSZtvoROVIu8mWpj2hytxbdu9C5WboPGHKAp7SXsN6kFi5ZvGJfPxkVAzUMhDJEln9FWwUeX8o4xj4n576PcYo+UZVxa26qhBFNtTJujFXfqp9mpeTKSvHZ8OsosrsMQWb22tsKKPnoXmoEsKRNRf2Nq/vsmt9iQisFEfo4JAZamnSoT1JSQzZOjVQ/vZvdBKZ+tGXFtKOQZfxvKiqtm20VFF2QxvmV/Iyuu2myGMhtSEkzm5+gUYKbaaULI5s3RAppzkcZBIbTUzLg2FHwYf9+8C76iqguyGN+yv+HiqiFsSEnwZafvSzsB9d27zOBqFYJ8rNw2rkNLjB5DIav3m8efqaGqC7IY33F/w4YyJ5tL8WGnB/jTTkA9iVCWCHvFGcW/ty5t4rCr2+kZfeQpjsnjz9RQ1QVZDgDwoYF42CMlgcpOL2mnSqWdqrjM0aJOljBts/ZVkcib51R7j6iCmDwvmgdVXZAlr89ULmBR5igbUhKyThydE0NFsbpOdjVFM7qLsyrUZuyrIpHXqxw1/lyDrTmo1zcd7SWUWsS4SvJRuiDL5svUIamizFE2pCRkmTi6J4aKYmWPRHHwKUzL6COLVzlpw+ZT7iSTjUZ9s21nFaVWgY62EraPVGN1QZbNl+4NW5HmKBtSMaSdOLonhqpibTSmagUrfZuMrnHtZvYtTMvoIa1XWWXDxkZ5elyv/7RE6ZvqaIAD9puEDUtOctQqdYo0R9mQ0ojKxEizWFUVa15PmG8CxARp+9BEnxU1TMvEk9arrLJhY6M8HT6GmXw3RIo0R/nUnkaSTjakPZ2jeiInTrAmkefEUJFI04cqfRZ3+k72Ox+vRmD00N1ZxrreuXikbz7W9c6NHXMVBcqn+dKRR4a6wveTdEWao+yR0kiSRyFt6E91p5pnZ1KkOHUe0vRhUp/F7W4B8JUuTC5UdvKcO5kOH707vnuwizRH2ZDSSNLEyLJYGxVrzZuh674j0wLEl7Bhmj5M6rOk3a0Ow9WXfmX0o6pAm80oz7MmfAwzuTJEdMqeosxRNqQ0Ezcx8i5WE/cdmRQgPuUdpNndJfWZzsrBUfjUr4x+TCpQXw30vGvCV++O7ar6LHui4Rwpi2SJCdfn0yy+dWPsfUdZcmtMxql9yjtIk5+U1GdxuQs68hp86lfGDGlyqlTxOV8y75po1vzEtGPOsica9khZJO1OstH6Hw2CyNflue/I5O7Wt7wD1T5M6rOk3W3ena9v/cr4gc/5kjrWRFHCTGlIO+ay/ozy0GfFR68oG1KWSbNYoyZ5FHnDcKYEiI95B6rE9ZmKcZpHUOTpVx+FFGMHnw30Issak8gMINmYy/pZIJQtOsKMPoYO2ZAijIoAoxzH9zXvQAdJhlYeoZDn+iIfhVSz4NrI9dkYaWZZk5WBoQoEgKg4h2zMe+bNwKLlGyb8TQBo8Vz66hXlHCnCyCZzqxBexPGLmncQVyPKBln7lfMb6EIhP8llXZ+8a6qossYk/as3RxpRApCOeXdnOfJvAD2eS1+9ouyRIoxsl+WTgCha3gEVr06WfvVVSDUDFHbiLo/T61hTRZM1ppGt+wDx/V7O6LlU8bj66hVlQ4owRSpYVhQoKLys+CqkmgEqRq4LYyTNmnId/iwSMnlQTpAHWcKoFw/ch5vu2bLXmyUzln0N0bIhRRzeZdGCisLLgq9CKg2+Klqfjdy8fa66pqh4g4tCVnmQ5fR5vRFVI8pY9tV5wIYUw6TAZ4Xnq5BSxWdFa8LItWFURvV5z20bsXTlJmwfqSp9rsqaGhiqYPGtGyeUgInzBvtqVCeh67nyyIO0p8/T5FX56DxgQ4phUuC7V4eSkNKt6HwOu+o2cm0ZlVF9Xh0NMDxSVf7cpDVVe5a4OnqN+GxUx6H7uWzIgzhvvQ8bUBXYkGK0UdQdYD1F9+rYwoSi8znsCuhVaraMSpW+TfrcpDWVVE8vShn7bFTH4eNzxdWe8mUDmgQbUowWiroDjIKSV8dXTCgEn8OuurFlVMr6PO3nxq2puL+VeYN9N6pl+PhcUR5HAeCcE6cVRo5yHSlGC1yjiEmDCYXgsg4SNXTc6ahCVJ/r/ty4enr1pWDqa1G1CKG9HTVc1pGzNa46iarxdeWZx+Ky7qNdN00b7JFitODjTikrzRDCNI0J7xGHXfcR5QUotQjsfG4PpvfeIe2btHO7sc872kt4dtceVMf25TPlNWZV6ump3Euqw6h27Xn3NUez6F58NqQYLTRLWMW1IC0KphRC0QW2Ko0GzsFtJex4bg+27ZQngWed2419rnujoXp3ZVQeVasQGAsCbUa16xwl3izQRASSkxBU6erqCgYHB103ozDoEnqNQhjwrwq7CrP71kiL2K3rnTvuZ+y5iof7xx4q8zbN3KbG9N47pNedPNI337vPYeghhFgfBEFX1O/YI9XE6PSuNMtOqQjFA6kYMM3mPXLZ7yrz1ufwvCmPeOOYdbSX9nr1dH4O4zdsSHmGTmGs203dDIpRVWC7DgHIoGzgFRnX/a4yb30Oz5sqaNo4ZqUWgVKrQHVUXw4Y4z98as8jdN8QT30H6vJ0jAzVk2Fp+1blWXX0B5+udIPrfleZtz6feow6GZY3rSCy2OhYgAMmT9L6OYz/sEfKI3R7OSjvQF3v4BvbUu8FPO34MtY+tFXbLeYqz6qrP6gbz0XFdb+rhN59D8+reMTTePRlY7N9pIoNS07K3d68UAnRM2xIeYVuYUz5KC2V0FiUAbNifSVxF5qmb1WeVVd/UDaeiwyFflcxNIocnk+7GVEdMxcGDaWNJsOhPa/QXYzNhDtcF6538DWyhmTS9G3cs9bCebLq0Wn7w+fwjc9wv7uldulxmrWsMma60y1UcR0qtgHF1A4Z7JHyCBMeJKo7UAo7eCCfQafat7JnDQAsWr5BenN67W/T4Hv4phFfwhtF63efyHLpMZC9fpUNzzmVjaYpfPO4sSHlEc0kjKmEHWVGTosQsRWi0xD1rDXijKis/UHVeE6Lb8I2a7/7YiwmUf8cB7eVIAQwvLNq/JmyXHpcI2nMXBk0VDaapqCS2qEKG1KeURQlmAQVo1Fm5NR2tzqUd/2zqlwAW2P/kt7IvG8K2zdhmwXfjEUZjc8xPLKvFpPpZ8py6bEqcd7k2X1rjK0hKhvNtKjKGN88blzZnGESqF/8LUJEhgg62ko4YL9JuY0QWeVkGbqqx/tYmb4Zqkz7XG28nrg8vxqmnkn22a1C4IozjlGe31FGAACpNxkwu4Z82/ikkTEU531cZXNONmeYBLo7y1jXOxeP9M3HmGTjMTxS1ZJwmtY1H5VgmiVJ08fkVd2HLyji285chkp7TT2TLGk8rREVlVQOYO+hkijSrqE0a7deLq3rnUvaiALSyRjfDmewIcUwKVBV0lmNkCgBIhL+pl4BZT1F5KPC9k3YZqEoxqJKe00+U30YvKOtlNpLlBRGXtc7V7pOVdeQqxOAtkgjYyifKI+CDSmGSUGU8paRxQiJEiBXnnks/tg3X7rrrVdAWT1LPips34RtFopiLCatmzTPlMZrMzBUQc9tG8fdj7fjuT3qDX8eFSMg7xqi5BU2UXogbf/45HHjZHOGDK4K26X5zKgk+J3P7dF6kansQIFKgmlWz5KvyatFP3xB5dBFXhqfI+upvbTJ98tWbRp3Lx4AVEcDLFu1SXsh27xriIpX2NQBB19ljApsSDEkkC3ewUefSryORfdnAvECo1F5y5IodQsIFaWa9Vh0URQ2FXRuCopiLOp4jrQnNaM2OHE/l6FiBORdQ1RKGpg6DVtkGcOGFEMC2eK96Z4te09m6T4mrUtg2BQQScooz66vKArbNUUpWUARV14b1TWeZw1R8diY7OOiyhg2pBgSyBZp4xk5nXWCdAoMKgKiyLs+X2iG+laukHltDm4rRb6+o600rmZV/c/TYnqNU1m7VDxjPsGGlEN8qwNiEtnijULX7rOoAoOKUdesUMl1KSI982ag50cbUR0bv8Xa8dweDAxVJsz7pQtnTXh9qUVg6cJZVtqbFhNrN62eoeIZ8wk+teeIqKOui5ZvwBEeXNBogjTH/nUZOkU5EcXQwscTkL7Q3VnGgftP3P9XR4PI023dnWX0n37MuJOd/aer14/yHZmeuXjgPunfUD4NS/UiY/ZIOSLK/W8qF8gHotzac2ZOxYr1FWM7IyqudKZY8I7eLMOSRPG4y4ebdU3L9MxN92xB18sOkfYLxT6jnHvIhpQjktz8zZhTEbV4u152iFFDh6LAYPwmq4HOoX41ihqSN0Fc7qlv+oVy7iEbUoroFnIqOUGcUxFdamB23xpWNgxp0hroJnbbRTXM2OOnTpye8U2/UM495BwpBUyU7lepkM07rPHYvEKBaiyeKSa6q1pTu25E53qinMNDjZ55M4znmtqCcu4he6QUMOFSrHf/V4ZHIDD+qD/vsCZiy7VLORbPFBPdu21KYRAT68nnkLxNT2F3ZxmDjz41rh4f4Kd+oeyJZI+UAqZcirW7hP7YNx9Xnnks77ASsOXapXTnFdMc6N5tUwqD8HrahwtP4WXdRxdCv1D2RLJHSgEbyY0+77BsYSvJlJISYtxiy3uge7dNKSGb19M+XHkKi6JfqD4He6QU4HpDNLA1DpRj8Yw9bHoPdO+2KcksW+vJh7xGNiqLCXukJDTuRE87vmzs8lxGDVt1nyjH4hl72PYe6NxtU6qRZmM9+ZLXaNtTWNSTm9QQQdB4mxlturq6gsHBQaOf0bgogXDhU4nHFgHqC5x6+xjzTO+9Y8Jdj0BYcf+Rvvm2m0MWlbWSZT2l+ZvZfWsiDZRyRxvW9c7N/nCasalbWI/pRQixPgiCrqjfsUcqAkonXoqID7tHqrF4Jh15DGJKeUZUUV3Lputq+RIys+kpZD1mD86RisCXRekrfIqHsUHeHCdKeUZUMbWW076vT3mNtdPaj/TNx7reucaMGtZj9mCPVAS6d6Kqu+JmCSfxAveXxjk6Z+ZUsrmDeXfklPKMqGJqLad9X85rnAh7VO3BhlQEOhelqovah3CXLniB+0nUHP3BPVv2/p7anNWh5DnEG4+utdxooHe0l7At4nJi2fuy0TsRNi7twYZUBDoXpequuJni2bzAaZDWAxo1RxuhNGfZYDePjrUcZaCXWgRKrQLV0X3p/knvm8XoLXIUwIVxWeT+jIMNKQm6dqKqu+JmCnfx7tE9WTygqnORypxtRoPdtiLTsZajDPTqWICOthIO2G+SsWdphiiATY9qM/SnDDakDKO6K866e/Z1B8AhE7dk8YDG3STf+DoK+Gaw513LrhRZ3rUsM7y3j1SxYclJmd83CdkaWHzrRgDFV/66aaaoSiNsSBlGdVecZffczDsAJh9ZPKBRc7QRah4fXwx2HWvZV0XmKgQrm+ujQWBUjvq6+U3CZlSFWh9y+QPDqF79kOWKCC4jwGQly3HxqDn67hOnkbxE1Dd0rGVf0wNclZmIm+um5KiLS4ttMDBUQYsQkb8zcRUQtT5kj5QFVHfFaXfPvgpOxj1Z84d88fD4ho617GtyvasQbJKH1YQc9dVrGEfNsBmNuCXFhEFMsQ/ZkDKIafcjRcFJzeXKRGNLefF8UEPHWvY5uV7FQNc9l2p/u/jWjZFGgAk5amLz63qNyU7ztgphxENN0YHAhlQCWSepjfwlaoLT95wt1wLJNqa9S3HzAfAnCdwGOtayb8n1aTAlW2p/a0uOmij27FrmxuWaLVq+Af2rN2udhxQdCHxpcQx5Ln20dYkmJeXvy8WhUWQZa0p9TxHZfJjSXsKzu/agOrZP9pRaBPpPP6ap+4/nU0hUP/Sv3mxUttjqe90XCVOQubI21KPzsmRXlzHHXVrMhlQMeSZps9wcXy+AZDPJh2dOO9Z8s3oysjUgo6OtZPS4O0Mf2bqS5TG5li1ZDDCdRhsFPRM1ZlHoNO5cbDriDCkO7cWQJxZL0f2oG9UF5MMzpx1rigmP1FCtO1VjeGTilSAmYQ8QPWTrqlUIa3lMqmQNq+kMqVPQM7VnWbZqU+S1PjV05jBRO/TC5Q9iyHOjeDPcHK9yZYgvz5x2rCkmPFJDtgYokOYI9cBQBbP71mB67x2Y3bfG+6PqlInLt6EmTymUn6GiZ7o7y2ifHO+X8WFDnRU2pGLIM0mz1IWiSJwSSTIaprSXvHnmtGOdx8guKo1zBUDkGpjSXor8e9nPTaCqBCnWrCkysvVTmzuU5CmFzRQlPRP33K6NXtNwaC+GvKdgqLkf05Lkuk4K3eyqjllppw7SjjW1E5Oukc2Vy089OjIvoue2jeMupC21CixZMMtae1WVIIdw7RK3rqjJUwphNYCOnpH1h6kyCJRgQyoBKpM0D1lzQZKUSFJBO98UTpqxLvJR8yykMTgo9J2qEqTgdWgmKMwNVVQ3U82Siyfrj6IbUQAbUoUnT52RJCVSL/RknqkiK5wiGNm6kI2/7Oeu+05VCVLxOjQTLudGGqNHxeijUOfJFj4ZwboxakgJIU4GcDWAVgDfDoKgL+I1ZwBYCiAAsDEIgn802aZmI09oQkWJ1ISerHwAK5zmQHaqqlVy/5ZrVIU+h3CbhyxGT5LR12yhYdcbJFcYM6SEEK0AvgXgHwA8DuBeIcTKIAgeqHvNUQAuAjA7CIJtQogXmWpPs5InNJFGibCb2zyU+y7KiIr7OQVUhL6OXXbjuM2ZORVrH9pKchybGRNGD4eGmwOTHqnXAPh9EAQPA4AQ4ocA3gHggbrXfBjAt4Ig2AYAQRA8abA9TUme0EQaJcJubrNQ77uyZJ6VC+CRzLPLjhq3H9yzZe/vtYzjrl3Ab38LPPwwUKlM/LdzJ3Dggfv+HXRQ+PWoo4A3vAF4/euBQw7J9tkFwoTRw6Hh5sCkIVUG8Fjd/x8HcELDa/4WAIQQ6xCG/5YGQfBTg21qOvKGJvIkYNeOktf/vJnc3Dqh3nccAotGpdZa6nH861+BX/8a+O//Dv8NDgLPPRf/N089Ff3zr30t/DprFvDGNwKnnAK87W0A0ZCsSUwYPbwumgOThlTUSmz0808CcBSANwM4DMCvhBCvCoJgeNwbCfERAB8BgGnTpulvaYFR9SrpCBsleU3YzZ0d6n3XzImmcaiOT+zrxsZCw2n5cmDNGuCBB8b/XgjgVa8KjaFyeeK/Aw8EduwAnn0WeOaZ8Ov27cCGDcCvfgX85jfApk3hv2uvBTo7gYsvBrq7gZbmKTVowujhddEcmDSkHgdweN3/DwPwRMRr7gmCoArgESHEZoSG1b31LwqC4HoA1wPhXXvGWlxQkrxKusJGSV4TdnNnx4e+a9ZE0zhUr8mZMI5BEIbrfvjD0IB6rM65v99+wAknhCG5178eeO1rgY6O+A+YOnXiz971rvDr7t3AvfeGRtq11wJDQ8Bpp4XG2ec/D5xxRlMYVN2dZQw++hRu+c1jGA0CtAqB047PP6d5XRQfk6vjXgBHCSGmCyEmAzgLwMqG1wwAmAMAQohDEYb6HjbYJiYCXVcdJHlNqFxn4CO+9l2zX68SNW6NjBvHBx8ELr0UmDED6OoKQ2+PPQYcfjjQ0wOsWxd6k375S+BLXwrDcElGVBL77RcaZJdeGuZZffObwGGHAfffD5x9NvDOdwLDYZCgyOM5MFTBivWVvQckRoMAK9ZXCvWMjBmMeaSCINgjhDgPwGqE+U83BkGwSQjxBQCDQRCsfP53JwkhHgAwCqAnCIK/mmoTE42usFGS14Td3NmJ6zuqp/moJ8jbIGrcJpza+4ej0F0ZAhb/E7B27b4/fvGLQ2/QWWcBJ55oxyvU1gacdx7w4Q8D//qvwEUXAStXAscfj5/334iLhkYKO57U8xB9gao8MokICB9PjqKrqysYHBx03YxCIasBVe5oi7zeQ0aj4gSap7KtKyj3ua55VVh27gS+9z3gqquA//u/8GcHHQSceWZoPL3pTcAkxzWTH344DAEODWG4/QV472lLsPGl472gRRnP6b13TEjiBcJk30f65ttujpdQlkd5EUKsD4KgK+p3xQ98M4noChtRukDTN7KGTCjcQC9rO/UEeWc88USYe3T44cAnPhEaUdOmAVdcEYbxbrgBeMtb3BtRAHDkkeHJwPnz0bHzady0/GK8/K+PjXtJUcaTLyJPJklOUZBHLiCwUhnX6Ay5cWJlekxe42OauLbbTpAnH1L4wx+AL34RuPlmoFoNf3bCCcDixWEeEgXDKYr2duD227H2uLdgzv2/wjdXfhXv/KcrsHvSZADFMTS4VEE8KnLKtTxyBXukGADhQljXOxeP9M3Hut65tBRQwcmzi3O9i45ru80E+ZqQrwyPIMA+IU8iUbhSAT72MWDmzDCUNzoahst+/WvgnnuA00+na0TVKJWw49ob8OiUv8HfPfkIeu/6VwDFMjTYox6PipzKI498PshAfPUyTPGxdY1PDZ2em7i22zxcQDJR+KmngC9/GbjmmrDEQEsL8L73AZdcEobMPOOU18/AXd/8NsrvWYj3r1+FB2e9Bq+74P2FMjSK5FHX7aFVkVNZvXq+H0xhQ6pAkA9tMJHYusYH0C+wVE5q2piDpEIKu3aFJQS+/OW9ZQNw+unAF74QeqU85s3nvB34Ux/Q04Ov3nk18K0LXDeJicCEYaJ6iT2QfvNEciOUAjakCkKWhcOGl1lU+9fmNT66BRaVvBISBUuDALjlFuBznwMefTT82VvfCnzlK8Bxx9lrh2k+/WngttvCiuj/9m9hwjxDChOGiepaz7J5IrURygDnSBWEtHk2pHNKCkCa/rWZm6FbYFHJK3FesPTBB4E3vxk455zQiDr6aOA//gP42c+KZUQBYYjy058Ov//GN8IrbFLgcy6ML5gwTEyudde5nnlhj5Qi1L03smsoZAvHd1cqddL2r60QmAnPTZa2615Pzoq9joyEIbyvfCU8iTd1KnD55WEuVGt8RXMfkI7TO98ZVj/fvDk0Fk8+Wem9lq7chOGR6t6f+ZYL4wumPLSm5BQVz3ZW2COlAHXvzcBQJfKGaEC+cHx3pVKHav8699zA3HqyfvL0P/8z9DxddlloRH3oQ8BDDwEf/GBhjCjpOJVKwLnnhi+8+mrl96o3omo0Q50h21BY52mg4tnOCnukFKDuvelfvVlakVe2cEjklBQYl/0b5+3Jkpyu28uTdj2R8wb/+c9haOuWW8L/v+pVwL/8CzB7trs2GSBxnD784TCB/qc/3XcfYIr3qsf1BqNo+Hgdl88nJtmQUkC2yCvDIxgYqjgffFn7Asjd5b67Uqnjqn9VDh2oCixTR5LTeOtIHYseGwurjn/2s+HFwW1twJIloVFVKtltiwUSx+mFLwTmzAHuvDOsfn722anfqwZv4PTjs2HiGxzaUyBukVMI8cnaV45pt++uVFPoSoR11b86r2gwdd1DmsRSMldObNkSXtvysY+FRtTb3w5s2hQaVQU0ogDFcXrd68Kvd9+d6b0A3sAxcnw5mMAeqRhqIYXK8AgEEBk+oxDiy+r94B3LeHR7P1z0r47crPp5n/e9okgzX0nkmt18c3jEf/t24MUvDgtsnnYaIGSZicVAaZxqhtSvf536vQBgSnsJSxbMYjnETICUNzoBNqQkNA5ilBFVw3V838d4OEWo58KpkDc3K+r29qzvJSPNfHWay7dtW5hQXcuFesc7wtDe1KnmP5sASuP06leHifUbNgA7dgAHHJD9vRjrkMs/rMMnecyGlISk5Mh6KMT30+S9JC0cyovLJCS8HznJc0VDnBcqzXupoDpfneXyrV0LvOc9wOOPh8bB1VcDH/hA4b1QjSSO04EHAsccA/z2t8C994a1tLK+Vx3NKoNsQt3j45M8ZkNKgupgpVFSroWCysKhvrhMUoSTjFl2/ipeKCDM87I9d617MnbvBi6+GLjiirBS+QknAD/4AfCKV2R6Oypr3yjHHx8aUvffH2tIqdLMMsgm1D0+PsljNqQkyAZxSnsJ7ZMnZVZSLoWCysKhvrhMUpSTjGlzs1S8r+WONqzrnZu3aZmwlmt2//1hZfL//d8wXHXJJcDnPw9MyiYmKa19o7zoReHXbdu0vF0zyyCbUPf4+CSP2ZCSIBvEtImRlISCysKhvrhM0qx5HElja6tsg9N+/+53gY9/PLxw+BWvCL1QJ5yQ6y0prX2jHHJI+PWpp7S8XTPLIJtQ9/j4JI/ZkJKgaxApCQWVhUN9cZmmGU8yysYcsBPOc+q52b0b+NSngOuuC///gQ+E+VAHHpjqbaIMQUprboEbbgAAIABJREFU3yiaDalml0G28MHj44s8ZkMqBh2DSEkoqCwcHxaXbZx7SwwjG3NbdcWceW62bAHe9a4wSXq//YBvfSu83iUlMkOwo72EbTsnXolSOINAsyHlWgYVfb3X8MnjQx02pAzjWijUo7JweHGNpxnyXFyPuRPPzc9/jt2nn4H9hrfh8Re8CJe+ZxkWHncyujO8lcwQ3G9SC9pKrSTWvlE0G1Iu52MzrPd6fPH4UIcNKcO4VlJR7Un6bF5c+zDpLaG083U55la9tmNjQF8fxi65BPuNjeGX04/DpxZciOG2F+DujApTZvBtH6niyjOP1TbGlObLOA4+OPw6PKztLV3NR1ve0aSxJDvWTCRsSFmgUSjUyt7zIqGPKW9Js+1847DmtR0eDmtDrVqFFgBXv+5sXD37LIy1tALIrjDjDEFdBgHp+bJrV/i1Lb3hS81gsOEdTRpL0mPNRMJ37VmmtkgqwyMIsG+RUL1DqNlJcy9cGsjcIUcAK/cS3n8/0NUFrFqFp/c/EO9/1xJc+YZz9hpRNbIozJ55M9BWGv8+AsCcmfoqoJOeL08/HX59wQtS/RlFWWhqvdeTNJakx5qJhA0py/Ai8YsoJanDW9I0J7oU6e4sY13vXDzSNx/reufqNaJWrw7vhPvDH4BjjsEp770Ka1/+6siXZlGY3Z1lnHZ8GfU1zwMAK9ZXtBkFpOdLzZCqhfgU0SULdV5sa2q915M0lqTHmomEDSnL8CLxC1PeEhs7XwZhWYP584FnngFOPx349a8xesT0yJcKILPCXPvQ1gn3cercIJGeLxk9Urou2Nbp1bLhHU0aS9JjzUTCOVKWcVkOgVo+gi+YSHyldJqzkIyNAZ/5THjVCwBcdBFw2WVAS0tk3wsA55w4LfM4m94gkZ4vGQ0pHbLQRHK46UT3pLEkPdZMJGxIWcbVInGVwMjGWzTUTnMWip07gXe/G7j99vB6l+uuCwttPo+Jvje9QSI9XxQMqSg5oEMW+ujhTxpL0mNtGV/0hwiCRoc0bbq6uoLBwUHXzchF4+SYM3Mq1j601ehkmd23JlLQm7xDLeoyXJuFHpkm5E9/AhYuBAYHw5ydFSuAt7zF+Mc29Vy/8MLQ89fXB3z2sxN+Hdc3QD6DwYVcY+xAbU0JIdYHQdAV9Tv2SDmg3nVsy1PkYufWNHeNMTS4774wH+qxx4AjjgDuvBN45SsBmN/ZNrUX4f/+L/x65JGRv46TA3kPFnAYrLj4pD/YkJJgy6Voa7K4yM3y0e3O0CHVGly9Okwmf+YZ4MQTgX//d+BFL9r7PjY2K01byPbBB8OvzxutjehKKo+aC01twBYcn/QHG1IRpBW8eYwuW5PFxc6N0j2DjF+kWoM33xwW2hwdBc44A/jud8cVh/RpZ2sDrZvEXbuAhx8GWlqAo46KfEleOZA0F6gbsL7k+WTB5LP5pD+4/EEEaeqb5D1+m/Woa9raKVaKHjZgoyYLU0yU1+C114aJ5aOjQE8PcMstEyps+7SzNY32Ipi//314QvLII8OLnyPIKwd8rr1HseioLkw/m0/6gz1SEaQRvHl3u1k8RVlDFbZ3bux2ZxpR3cEmrsEgCJObP/e58P+SRGfAr52tabR75xLCekB+OeCzIVxkb6jpZ/NJf7AhFUEawZtnkdeUykh1FK1CYDQIUFaYLD4tzijjrciubkZOmg1A7BoMgtBo6u8HhAi9Uh/9qPRzOSF5H9qNEgVDCsi3ifPZEPbZCEwi77Op6AHqYdsaHNqLII1L8eC2UuR7yH5eo94tCgCjQbD3M5ImTpRQifs5JYrs6mbiSROika7Bt74iNJr6+8MaUTffHGtEAW7C2lTRXjW7ZkjNnJmxRcn4FOJppMhVyvM8W9H0ABtSEaQRvEJM/Pu4n9fIE/dvlby57Oe60HGnlc/5Dkw+0uxgo9Zg34IZ6O7vAW64Adh///Bk3llnKX220bv8PEK7UfLb34ZfZ83K2TI5PhvCPhuBSeR5tqLpAQ7tSVB1KQ7vrKb6eY08btFRSRFV2c91oOsIOSVXN4cY7ZI2RDNuDe7cCZx2GvDTn4YVtH/yE+ANbzDZ3EKiNe/kT38Ka0gdcADQ2am5pePxJcTTiKk8HwqyK8+zUdIDOmBDKidZ4/d54v5lyd+WDbqLdeVlucp3iKomv2J9xfqVOdRIEsg6BXbmXKXt24FTTgH++7+BQw8Na0Ydd1ymNjAajZJf/jL8+vrXA6X4VIZmRrcR6Oq6ryiyPpvPeW9RcGgvJ1ndm3ncoi7cxbp2EC7aHhWPv+meLWRcyzpCplk/Ny5PQXceQ6YQzdNPA/PmhUbUYYcBv/oVG1FUuOuu8Oub3+yyFVpwtQazUISwWNFCnuyRyklW92b931WGR9AqxLjFkFTGIMtn5kHXDsJF26MEjywIatu17HJ3meRlNHE6NNUO9plngLe9DfjNb8IrX9auDb8yNCiIIUXJw6NCEcJiPpU2UIENKQ1kdW/W/saHmlA6j5DbbnsaAWPbteyylEWSQHYqsJ99Fnj724Ff/xqYNo2NKGr8+c/A5s1hftTxx7tuTS6yrEGXOUpFCYv5mvcWRWJoTwhxnhBiio3GNCO+uGl9PjkjEzCNZxxduJZdGitJx5edHd3esWNfTtRhhwFr1jSNEeVNiKmWHzV7tvf5UWnXoOuj+0ULixUBlRyplwC4VwhxqxDiZCEMn7FvMnxy0/p6hFwmeM45cZpzw9BlnZkkgexEYO/cCSxYECrql740NKJe/nJzn0cI1wo6FQUJ6wHp16Drza/Pm9qikhjaC4LgYiHEJQBOAvB+ANcIIW4F8J0gCP5guoFFJ6ublsLxV1+gHI93WXU7qV+s99vICPCOd4RhvJe8JDSiJBfhFhFvbiwIAuDnPw+/f9Ob3LZFA2nXIIXNb5HCYkVAKUcqCIJACPFnAH8GsAfAFAC3CSH+MwiCz5hsYNGxeddeM5NH8Jg0Wl0beUn9Yk1g79oFnHpqqKBf/OLQiJoRvQZ82kSkaSsFBa3Epk3hZcWHHgqccIL0Zb6MU9o1WJQcJUYfiYaUEOJ8AO8F8BcA3wbQEwRBVQjRAuB3ANiQykEWRSrbuS5duUmL4KIqAF20y4bR2iy7S+n47d4NvOtdYbHNqVOBX/xCendbnvEYGKpg2apN2PZ8sdyOthKWLpyl1PdZ5l7atnqjoG+/Pfy6cCHQ2hr5Et82e2nWIN/dyDQigoRq2EKILyAM4z0a8btXBkHwoKnGRdHV1RUMDg7a/EhyTO+9Q3p8v562Umvq2HmjAMz6Prpx1a7ZfWukxU/X9c419rlFQzZ+fQtfiXdcvihUzi98YRjWO/po6ftkHY+BoQp6btuI6uj4lVNqEeg//ZjIOVQznirDIxAYXzJDZe6lbWtUH5VaBA7cfxKGd1bpbGqOPz68GmbVqvBQQARFXzc6N3VUN67MeIQQ64Mg6Ir6nUqO1KUxv7NqRDEhsp1rI1nyK6jmabhqlzfhFuJEjt9zeyDO/QRw751AR0foiYoxooDs49G/evMEIwoAqmNB5BxqNGoa/1Jl7qVta6N3+uC2EnY8t2evB42EV+fRR0Mj6sADgbe+Vfqyoq8bXV5k3zx3TDRcR8pDolzLMtIKLqoC0FW7XIZboq61WfvQVi93rlHjtPhXP8DCe+8MLyD+yU+AY45JfJ+s4xE3T6J+F2X4pXnPWpui2hoAOKL3DpQjxrBeQc/uW4PhkfF3djrf1Nx6a/h1/vxw3CSYXDdF8uBQ3bgy6eArYjwk6vjrlPboWi5pBZfL4/hx2G5XrZ5PLaxTj418iKij8D+4Z4sfR+MjaByn965fhU/evRx7WlqAH/0orEekQNaSDHHzJOp3KgZ60tzrmTcDpVZ5tZikMSS5qVm+PPx65pmxLzNVOsOrEhEKmBhjb2qRFQg2pDylsabTkgWztAguqsXebLarXlgDoQehpg5t1WxR8YhQLNwqo378Tnnwv7Dk59cDAP730q9J82yiyFpDR2bUlFpE5BxKMpJU5l53ZxkHTI53+seNIblNze9/D6xfDxx0UHh1Twymah25ruGkG91jXDRD0xc4tFcQdB2jd30cn0K7ZHfzNSbKmgwxqO5IXYdcVan1y13X3ISv/uTraEGATedfhOOWLMr0XlnnteqpvajweS3hPCokJ2N7Q2guCtkYkjsdVvNGdXfHhvVqmDiNStJLlwPdY8yhQjewIVUgdAkuisfxbeZFqAhr00miqgcKXIdc09A9+id03/pFYGwPsGgRZl3xJbufHzOvo+bX5acenXvOqYyjbAxJbWqCAPje98LvzzrL/uc/j2rulS95VLrHuGiGpi+wIcWQx/bJFhVhbXrnp3KggELIVZnf/S68hPjZZ4F3vxv42tcAIrdNyebX5acenfuofs+8Gej50UZUx6ILliSNIZlNzV13hWNYLgMnneSsGSoeHN9OwsnGOIsxSPWmDF8M26xwjhRDHtt5EVH5WACwY/eevbkGpnd+jTkmU9pLaCvtW65T2kvOa3sp88QTofLduhU4+WTgxhuBFhqiZ2CogsW3bjQ2v7o7y+g//Rh0tO07DNLyvP3o1R1p110Xfv3Qh4BJ7vbfKrlXRcijyprrlCWX1HReVTPkbbFHismN6d2GbXd1VD4NAAyPVPfubG2URajtVPftsMf2/m5X3fekefbZ8Kj8H/8IvOY14Qm9UvQJU9vU+nVUUpRYp1HshbEk48kngR//ODR+P/hB161J7M8ihLeyerx13pShy7veDHlbbEgxubDhRndRy6m7s4z+1ZvHGVLAPgFgMxHYW0E0OgqcfTawYUN4+fAdd4SFHImQdDLSp/yzerRvbL73PaBaDU9XHn64voYawpurdmLIYwymNdxNG55p39/HMCAN/zrjLTbc6K5KMiQJgP3rQm0dbeZCbd7usC+8MCy0ecghoRF16KGuWzSOuP7zKv+sDu1hlLEx4PqwVAU++lFt7TQJ1RIuabBZ+sL0Z6V5f1/DgGxIMbmwoeRN1aRJQiYADm4r4aIf3zfOW7V7j7lQG7l6Qipcey1w1VVhGO/220OPFDFk/dcqhD+5Sw1o39isXRvWjzrssDC/zQPyygsKBS1NGoONzzdn5lSjhmeaZ/E1v41De01Akqs0jyvVlhs9yV1twh0sC98JAauhNnL1hJL42c+AT34y/P6GG4A3vtFteyTI+tVXIwowsLGpeaMcJ5mnJWteGpUTf6ZKX0Q934r1FZx2fNnY9VNpnsVX77s/K4PJRJJgyCs4KCh5U8JPJgAWLd8Q+XrTye9e5A089BBw+ulhftTnPw+8972uWyTFq35VROvG5sknQ28ikSRzG1DKRzRxSEH2fGsf2pq71Eccqs/ia34bG1IFJ0kw5BUcFJSRSeEXJQD6V292kvxOvq7LU08BCxYATz8NnHYa8IUv6GmsQbw/UdeA1o3Nv/xLmGS+YEEY2msCfPWIqELx+eplUUd7CaUWMa7uGmnv+/OwIZURX04WJC0cHQvLtTKyLRxse+F0zzUjHrxqFTjjjDCf5thjw5NeRGpFNRPaNjY7dgDf+Eb4/ac/rbmVdPHVI6IKtedrlEXbdlZRahXoaCth+0iVtG6thw2pDFCJo6uQtHCoLaws2H4Gm144E3PNiAdv0SLgF78AXvxi4N//HTjggGzvw+RGy8bmO98B/vpX4IQTgDe9SU/DPIBCqoJJqD1flCyqjgZ4ZtceXHnmseT0qQzeMmbAp5MFSScminBU2MUzdHeWsa53Lh7pm491vXONLXgTc027B++664BvfQuYPDnMqZk2LXPbGAJUq8AVV4Tf9/aSucrHBo0n/jraSti/1IJFyzc4O8GXRJpThq5OQMuQyZzRIPCi7EEN9khlgGKcWUaS94RCjlNeivAMMkzMNa0evP/5H+D888Pvb7gBeO1rM7erqESFZgFa87W+je9/+L9x6ZYtwMyZwMKFztrkiok3CtCNPGRpo+tUjHriLvX2oujw87AhlQHfwmFJC4fSwspKEZ6hRr1SaxEi8gqTPHNNm3v/L38JT+g99xxw3nnAe96TuU1FJUrR9fxoIyDCEEbtZy4VdH0bRTCGM9feDAD47ZkfxnFNnOdG6QSfDB/aGEfS5ewUnRNRsCGVAWpx5iLjw25eJ42KN8qIyjvXtHjwRkeBc84BtmwJ82hqoSBmHJE5IGMTxzRK+dk60FLfxrl/uBcz/rIFfzrwhVg0aRZ+qf3T/MGHyIMPbYyjNp8X37pR+4bRJmxIZaDIoSRXyAwm6rt53cjuf2sVAmNBkGuuqShmZeX9xS+GhTcPPTS8iHjy5NTtaQbSKLT619oMK9V/7sfvuQ0A8O3XvBNbnt2j9XOokTTXfYg8+NDGJGp97rNzgg2pjBQplKSDPLtnmdLYv9SSeTfvKzLFOxYEeKRvfub3VVHMysr7P/4jrBElBHDLLaQvsnVdpiQuByTqtTVshmxqbex6fBO6Kg9ieP8Dccsx87xSxmlRmes+RB58aKMKvjsn2JBicpN39yxTGrK4eRS+uLKTMLXDVFHMSsr7j38E3v1uIAiAyy4D3vrWXO0ySWR+0m0bsXTlJms1aqIUXalFjPOqAhOVn82QTa2Nn/z1cgDA9447BcEBB3qnjONoNKh37N6TONd9UO4+tFEVn50TbEgxucm7e9ahHIqyeza1w1RRzImv2bULeNe7wgrm8+cDF12Uq02mkdWoGR4JL5u2ERaWKbqon7kKK3V3lvHC9XfjDY/8Fs9MbsPquWd4fd9gI1EGtYzGNRCn3F17O2v4bIAUBTakiENlscaRd/csUxodbSXs3jOWejfvM6Z2mCqKOfE1F1wArF8PHHEE8P3vk69crjL/bISFZYou7jOthmyCAG+48esAgIM+34s7L32n/s9wiCzvMApVQ9WH0ggq+KBfGqHYZjakCOPLYs27e5YpjaULZwFIv5v3HRM7TBXFHPua730vLLy5337AihXAlCla22cC1fwkimFhqyGbVauAu+8Gpk4NK9QXhJrCVc1RS2Oo+l52ANCvX2wYOFR1IhtShPFlsebdPasWDY36GyaexgtB95vUIs0Pko5D2zPAxz8evuhb3wKOO87Fo6QmqUZNDaphYSshm9FR4HOfC7+/+GLgoIPMfp4lGhVuFFPaS2ifPCmT4lf1wlP0ntTQqV9sGThUdSIbUoTxpUaIjt0zx/n1E3UhaFupNfYOqwnj8NxzwIkLgJER4J/+CfjgB200XQuN87KjvYRnd+3x7mZ5o9x0E7BpE/CylwEf/ajr1mgjKZzXVmrFkgWzUp0srpdvHe0lbNtZnfC6eqOcqvekhk79YsvAoaoT2ZAijE81QkwaQpR3dZTRItwuuQQYGgKmTweuucZAK83SOC95LtWxezdw6aXh98uWhWHbghCnWMsayrOUWgRKrSI2V5Oq96SGTv1iy8ChqhPZkCKM6xohFJQOtV0dhT5RJbdwW7MG6O8HWltDz8ULXqD0Z5T7iD2fdVx3HfDoo8Df/R0GZs1Bf98akmOWBZnCLXe0YV3v3FTvJatO39FWwgH7yUODVL0nNXTqF1sGjmudKIMNKcK4rBGi04DJo1hd7uoa2z1n5lSsWF8hY9QlkUu4PfVUeHdeEIReKcXLiKkZvoyEZ54J64ABuOdDi3HRvz9AbszyyA2dCldm+GwfqWLDkpOkf0fVe1JDp36xZeBQrZvFhlQGbO64Xe2gl67cpMWAyatYXe3qotp90z1b0FhXnZKrvpHMwi0IgI98BKhUgNe9Dvj855U/k3o4g3meK68Etm4FTjwRi3e9DCPVXeN+7XrM8soNnQo3q0FE1XtSjy79YsvAoertZkMqJc2w4x4YquwtWthIWgMmr2J1tauLavfEy2lCqLjqG8ks3P71X8MSBwcdBPzgB8AkdTFBPZzBAHj8ceArXwm/v/xyPPHTHZEvSxozk0pNh0Guy0jIahBR9Z6YwvSmn7LuZUMqJbIFvvjWjQDcD6gO+ldvlv4urQGTV7G62tWlUfxUXPVRpBZuv/sdcP754ff//M9hknkKVA3f+ho/rUJgNAj2JgEDzaN8nNDTA+zcCZx6KvDmN+Ol96xJvVkxHfqnZJAnGURxBiXn5OmDsrebDamUyBbyaBCQsY7zEies5sycmuq98nqUXO3qZO0WGO+ZouaqjyPRg1CtAuecA+zYAZx9dvh9SlQM30YlPBqEPVq7Cw/Bvsupbe06qYYMtHPXXcAPfwjsvz/w9bCaeZbNii6lJjPIDm4rRXrFXW1aZAYRZS9J0aBkXDdC+44HgsQt5Jog8Z24Z1yxvoKBoYrye/XMm4G2Uuu4nwmEAmd23xql9+ruLGNd71w80jcf63rnWhFQUe1uK7XinBOnodzRBoHwBJAvd5LVBH5leAQB9gn8cf2/bBlw773AtGmhN0qI1J/T3VnG5aceHdtHcTV+qqPBuDpPgPl1pdQ3RWDPnn3exosuCmtHQW3MGtGl1GQGmRCIXH/UNi1xBiWjF5leohARYI9USpKqJateR0CZuGfMkqcAYG8Yp96jQ3n3VrT8hkQPwm9/C/T1hcbT978PdHRk/qykcEaWHaTJXSflkIFWrr0WuO++8K7Enp5xv0obgtKVuygb1+GdVVx55rHk118RKpz7AuXkfTakUlKb/Bcs3xD5+9YMu3hqJD1jWqVWE9Kz+ybmYlBWWEXKb4gV+NUq8IEPhNeFXHAB8MY3Gm2L6h14jX+ji0alJmtLHuONnOJ88sl9xTevugpoy9efupRanEHmw/pTMSg5/CcnzTqhvLnl0F4G4gaulu/hO92dZZQ1u1Ipx7iLTqxb/KtfBTZuBI48cm9toXoGhiqY3bcG03vvUA7HxhEVNq1RahUotYzfjOjcdUaF8WRbn6zznGSo8HOfA4aHgXnzgIULc79dlnBgFLIQOgUvgwoq7efwXzRZ1omLNA8V2COVkXJM5VwVyO1YI9DtSqVeoK7IyMbyjAOexnOLlmEygE/O/QTe8n/D6O48YO9rTOymG8O9Nk/tycpa6DxEQC5UeO+9wI03AqUScPXVmXLfotDhMaLsZVBBpf28gYyG3DrJgVFDSghxMoCrAbQC+HYQBH2S170LwI8AvDoIgkGTbdJFHiPDF1dvFiEXZyBm7TMfjE7qRI3l3KMOwZs+dTYmj1Zxy9+fhFUvnImfN8xDU8IuSQmbGl+Z8goQboJ0zDFSinNsDDjvvLDI6qJFwAx6nh4fQnhxJLWfN5DRkFonOTFmSAkhWgF8C8A/AHgcwL1CiJVBEDzQ8LqDAJwP4Dem2mKCPDspnyzxNEIuyUDMapj5YHT6QONYXrXgXBxbeQh/PvAQfHnuBwFMnIcUhV0ew1rnHWxpP8OJ4rzxRuB//gf4m78BLr7Y/uczpJOkG7G5aSW1TnJi0iP1GgC/D4LgYQAQQvwQwDsAPNDwui8C+CqACw22xQhZd1IUlZMOVAzEtH3mk9HpFQ8/jI+s/g4A4PPzzsUz++0L59XPQ2rCLq9hbUOpkVGcTzwBXPi8WP3618NK9Yx1fAlf2t60klknGjBpSJUBPFb3/8cBnFD/AiFEJ4DDgyD4iRDCO0MqK9SUky5MGIhFNTqd8vxdeu3V3Vj5yjfiF68YtyzHzUMqwq6+EnojaQxrG0qNhOIMAuDjHwe2bwdOOQU480x7n00cF6kCPoQvbW9aSawTTZg0pKIyGvfmcwohWgBcCeB9iW8kxEcAfAQApk2bpql57qCinHRjwkBM+56cT6XAjTcCv/gFdnccgr6TPz7uV43zkIKwa9wpR5HGsLah1NKGxLX37/LlwMqVwAteENaPKkBZFh1wqoAcWRkQk7URfTAwVTBpSD0O4PC6/x8G4Im6/x8E4FUA7hLhIn8JgJVCiIWNCedBEFwP4HoA6Orq8r6+AAXlZAITBmKa92QhqcD/+3/A4sUAgP3++Rp8ZuYbEueha2EXVwm9hq/eXCNz9i9/AT75yfD7/n7gsMN0NNU5OgxOThWQUzs9G/VzJh6ThtS9AI4SQkwHUAFwFoB/rP0yCILtAA6t/V8IcReAC305tZcX18rJBCYMxLj3rBesHe0lDO+solEMsJBsoLc3DPe87W3AWWehWwjyfZPkbfLZm2tEsX/qU6ExNWcO8OEPa2ile3QZnJwqIEdWA7EotRFNYsyQCoJgjxDiPACrEZY/uDEIgk1CiC8AGAyCYKWpz2bcYcJAjHrPRsG6befEC05rUBeS1sKRd98NfPe7wOTJwDe+4U24J676eNlzb652xf6TnwA33xxWLr/hBm/GOAldBqfP+amm5UTe2oimoZy2YbSOVBAEdwK4s+Fnl0pe+2aTbfEByhNFBZvtVwn31KAsJK2FI0dH94V7LrwQeMUr9L23YWThXZ0XRrtae1oV+/btwMc+Fn5/2WXAy1+es3V00GVw+pqfakNOUO4b6mkbfEUMEUheK5EC2+1XFaB5BYHu61EasXZ9xI03AuvXh/kyn/uc3vc2jK7rSGS4XHtar0j5zGeASgU44YQwvFcgYq84SoHpuWQKG3KCct9Qv2aHr4ghwrJVm7xOgrSdxKly8W2rELkEgY1dkJWcjaeeAi66KPz+a18DDjgg/vUEMZlT6DIBWVte4dq1wPXXh9fAfOc7QGv0XYa+otNb4mN+qq3cLqp9Qz23jQ0pAgwMVaQ5PnETJU04QvW1WUMctid6lGCtR0fox4aCtZKzcemlwF//Crz5zcAZZ+h734KQZ+7qCAnmVl7btwPvf3/4/cUXA7NmZX8vomQ1OH1Pl6hhWk5Q7yfquW1sSBEgzj0ZVy9J1Vui8tqBoQqWrtyE4ZF9Bl0aD4ztiV5rz7JVmyYYoQLAacfn31nZMA6N5yVs3BjWEWptBb75zcIkH+sk69wlk7dx7rnAo48Cxx8fnsosKGkNTjLjowGTcsKHfqKcvwVwjhQJ4hSzbKKkiRkLUQBlAAAgAElEQVQnvba2kOqNqKT3jGqntlwPRbo7y2ifPHEvEABY+9DW1O/XmA91cFsp8nU6jUOjeQlBECaYj42FyvZVr8r/ngUky9wdGKpg8a0b3edt3HRT+K+9Pfw6ebK9zyYO9byaNJiUEz70E+X8LYA9UiSQ7Yg72krSiZLGW5L02qQTcCoeGFdFRnV5jaJ2ZaVWgVKLQHVsXx0VE8ahsbyEW24BfvUrYOpUYNky/e9fENLO3dpckdXXsZa38cc/Ap/4RPj9VVcBM2jszqkgG4fK8Aim995BMoRVQxZqM9FW6vlHNajmbwFsSJFA5rZculCe65AmHJH02qQFo+KBMZ2DJaOjvRSZX9bRHu1NkhFlTFZHA0xpL6F98iSyuQNSdu0CPvvZ8Pu+PqCjw217iJNGSCdtPKzkbezZA7z73cDTTwPd3cCHPmT+Mz1iYKiCFkmlbgDjTmcCdEJYgP1QG/X8Ix/g0B4Bsrgt04Qjkl4bt2BUPDCqx8dNHDOXFd1NW4xXZkwO76xiXe9cPNI3H+t655ISuLH88z8Djz8O/P3fA+97n+vWFIq4jYfpcHYt/Pz1Oe8D1q3DyKEvLlThTR0keQzroRbCAuyH2lykZRQN9kgRIa3bMk04Ium1shNwU9pLWLJgVmK7VE+3mTgFtz0iryvu5zUaPWMyz5aXu7Knnwa+/OXw+8svB1ri90uNBw1Ux71Zke3g85bbaKRxjs6ZORUr1lcw84+bcP66WwAA5510PhY8thvdhya8WRORplgvQC+EZTvUVtS7X23ChpTHpDG+4l6bdyGpLnwTAiKLWzoyH6pFoNQqUB01mw9lhSuuCMsdvP714Z16MQwMVdDzo43j8sC27ayi57aNANyFPCgfx5aF4k87voz+1ZuxaPmG3G2OmqM33bMF7bt34qqffA2TgjHc8Opu/OLwY/CQJ7XmbJFWnlDbLLkItVHOP/IBNqQYAPkWkurCNyEgshyLjcyHGgvQ0VbCAft5mA9Vz5NPhoYUEHqjEkI+/as3jzOialRHA2fFYKkfx47aeNS8RbraHDVHAwBLf349Xjb8Zzzwounof+N7AeirNVcUZHJmSnsJu6pjZI/Q16B+1J+ZCBtSTG5UF74JAZHFmyZTPNtHqtiw5KTMbSHBl74E7NgBnHJK6JGKYWCoElsd3lXIw2WlcVUaNx6z+9ZobXNU35/y4H/h9Pt/jl2TJuP8BT14blJ4oEJHrbkiIZMzSxaEh3eoG5Y2Qm3NaGCbhA0pJjeqC9+UgEjrTbPhOnciqP74x7D4phChQZXQvppSleEq5KE7BGxjLHS3uXGOvvyvj6Hvp98EAFw254P4/aHTAMRvRHwwSE2QJGd8eHaToTZdBjYbY/tgQ4rRgurCpxCLN+06d+YJWLIEqFbDY/F///exL01KyC21CmehBJ2Grq2x0G2c98ybgQuWbwAAtD83gmtvvxwHPjeCVTPfgB90vh3i+feOU14u6gNRUa4U5AxVdBjYzertlMGGFBMJFYFogu7OMgYffQq3/OYxjAYBWoXQcqVMDSeegPvvB77/fWDSJKXim3HK1MSpvTTzSaeha2ssdBvn3Z3l8PqjHc/h8p9eg7/96xb87oWH47NvOx/lKe1Y1zs38T1sJy3HKVcgnSe6yPLHNToM7Gb1dspgQ4qZQNF3GwNDFaxYX9lbZ2Y0CLBifQVdLzsE3Z3l3ELcSaXgSy4Ji2d99KPAkUcmvlymZMsdbUpKOg2qdz3W9/lpx5ex9qGtuRVp1rFIOweSwklZ5tSSBbNw30Vfwjse/CV2lPbHx7o/h+CAA5WNM9tJyzLlumzVpnFJ3knypOjyxzU6DGxfqqHbgg0pZgJF3m3U7khrLNZXX/AurxC3fnz5/vuBgQFg//2Biy9W+hObSjZpPkUpzhXrK1pqMukqj6EyB2ThpMzvt2sLFv7i2wCAz77tfOx6xd/i8hQGpa6cRFUjUKZEo+qzxcmTIssfCuhY+1wNfTxsSDETKOpuQ+WONB1CvGfeDPTctnFcTSqjOUf9/eHXD3wAeMlLlP7EZhG+LHc96lKcuspj5GlPpvfbuhU4/XS07KkCn/oUrrnqK6k/F8ifK5TGCJQpVxlp5Qzlwwa6MdlmHWvfuowjDhtSzASKuttQuSNNmxBvtNVSXlmjzKOPAjffDLS2AhdemOpPbSXkZr3rUYfhrrM8Rtb2pH6/0VHg7LOBSgV43euAr3410+fqII0RKDNa95vUsrdqfj0yeWLzsAFFI8tGaFPL2rcl4+qgOF4A37VHntrdWtN778DsvjW57qVTpah3L6nckRYn3FWJKnJZHQvM3JX19a+HF9ieeSYwfbr+99dA1rsedRnu3Z3lVPcl6m6P6vvV1vo1bzgH+MUvsHvKC4FbbwUmT870uTpIYwR2d0bfGbp04axU8kSn/IkzBE3c/akD23ftZcGmjKutiyN678Ci5RvIjRfAhhRpXC10mUCkYPnnQabQ6u9I0yHErYVG//IX4NthDg0++1m9762RpPlEzXDX3R6V96ut9RmDv8R5dy/HqGjBR99+IQaezPSR2khrVEYZrWnliU75E7cWqRosPqRW2GpjvQ4EJjq9KIwXwKE90rhMujQV9nHpmpWFHuqFtI78AWuh0WuuAXbuDO/TS6gb5Zq4+WQzX0sF3e1Reb/+1ZvxN39+FFf9JLze52tv/CfcddjR+J3jBGtdhxIax7/mZZD1hy75E7cWqRosKvIjjxzVIYNtyTiVC6hdjxfAhhRpqC70rLg+1pymAnue9lg5Effss8A3w0rX6O3V977PY9vgpVZAUXd7kt7v2T9vxfdXfAEv2L0DP/3b1+JfTjgNgPu1nteojJpHQP6TsarErcX+1ZvJ5YIODFWwY/eeCT+vlx955KguGWzr1K/K/KeQu8uGFGGKlvRN4VizDYVtxcPy7W8DTz0FvPa1GDjwSPTH7O7T4trgbTr27MG37/gqjtz2BB540XR8ev6nEYgw64LCWs+6ZmTzaP9SizU5kLQWKV0O3NhfNRoL5OaRo7pksC0vctJJUCq5u2xIEcbGVSY2vQ5F87DFYdRgq1bDJHMA95z+IVx0+/1ajR6ZsF1868Zc78tIWLwYr/79b/GXAzrw4VMvwc7JofFERUlkZenKTZHzSBaqMSUHZGuRWkhZFsZqnzxpXJvyyFGdMjiNjMuqa6J0oECYK1UmdGqPDSnCmFzoLrwORfOwOeP224HHHgNe+UpcODINI9Xd436dd3cvE6qjQcCeKd1cfz3wjW8AkyfjgWu+C/z5IAgCSj0vA0OVyJIHcbiQA5RCyqpGTh456kIG59E11IxdGWxIEcfUQncRZrN9ZUVhue668Ou556Ly2O7Il+TZ3ce507nCtEZ+/nPg3HPD76+7Dm983zuwzm2LtBF3kqqjrYTde8ZYDjSgauTkkaMuZHBeXUPJ2JXB5Q+aFBdhNt/LKvz/9s49zqriyve/6uYA3Who8BVzBMRHdIIoLR0hYkbBGE28agdUJGpibsZHXjeiw0znxlE0JJAwDpM7ahLNwxtBRGVscUgGJ4FkMhgYmwAqCgZFwDZGFBqj3cKhu+aPzWlPn961n7V3rdp7fT8fP9iHQ+/a9fzVWqtWmcjp1Y8//hFYuRKoqwOuvDKRHExux/Urea2ji0Zd2MwLLwCXXurkAPu7vwOuucZ0ibTiNY/MvniM1fNAUgRNuxFnHjUxB+chpIMtUjnFlJvNht2FG27m6ZlLNqBt+27MaR6bXkHuvdf584orgIaGRHaY5fZxu5MQAIbWFTgYvYpQMSC7dgEXXgjs3QtMnQrMnZtuYVNANb8Mqy/0SzXCOIRxY8WZR9Oeg/MQ0sFCKqewmy0cbuZpCWDRmh1oGjU8nYlp3z7g/vud/7/+egDJxRB4nWoSAoFM9VSvc9BNqBiQ994DmpuBbduApibggQeAmuw5BlTzy20XjTFYKvpQ2mi2rm/H7U9s6r10uqGugNkXjwldvjysNSykckrUBTgvi2M1KjO0BNKLGXrsMSeb+amnAmec0ftxUpOvqo/MXLLB9fuVdZSnFAqBY0B6ehwX3lNPAcccAyxbBtTXp1vYlFD1HQCeiTgZGrSub+93KXFHVwmzHgl/cteWgPE4sJAigClxEnYBztPiWI1XAHZqvv5ykPn11wNCpPJItz7il8iwdX27q1swq4HqgWJApARuvBFYsgQ45BDgiSeAo49OqYRmcMtmntf5wzbmr9jSR0SVKd+nF7a9KFnakiB7NmXLoHpxphtU76bShVcA9azzT4JKuqTi69+yBfjNbxwLxpVXJv88D7yCYsv92S22CshWgGmZQAH/c+c6megHDgRaW4Fx41IqHR2yPn9kCa9xmsUxHBcWUoaxaXLJ8ukLP0Hb3FjElRNH9hNTqfn677vP+fOKK4ChQ5N/ngdeJ3/87sbKUoBpGd/TVj/+MfDNbzpWxIULgXPPNVBK82R5/sgaXuM0i2M4LuzaM4xNk0uWT18EiXOZ0zwWTaOGa3fD+rp2DxwAfv5z5/+vuy7Ws3ShMtV79dusBZiW8YwBefzx3oMBuOsu4LLLDJbULFmeP7LGrPNPws2PbER3T1/LcqFGZHIMx4WFlGEoTy7VC/zkk4/A0nXtmTx9oRIA7R1d/YJjV7dMCfx7/URSoLiRVaucI/Mf/nCfIHOKqPpzrRCZzhXkKix/9zvHgtjTA9x6K/DlL5spHBHycHorS9QAqLYtTz9jRGbHcBzYtWeYoEnYohI1caKbq2vpunZMG1/MZCI9lXAVQOT4tSDxb4Fcu0uWOH9On55akHlUVP35zstPy0Q/CcyzzwIXXeSkO7juOmD2bNMlciXNxKpll3BDXaH3s8EFu5egrCamnb9iC0o9/eMcV23eZaA09GGLlGGo3qenWuBXbd4VyiJDgSCnIieffAQWrtnR799WTyVhTp4FcRf6unb37weWLnX+f/p032eaJg9HnX155RXg/PPfT7h5zz0kBbCpU3T7DvT0/v+ezpK1J/eyfAoxqZCTrKbPYSFFAIr36dkUu+VF0MkuzE4raB0EqUNf1+6vfgV0dACnnAKMsSOZYdaPOnuya5cjov70J+Ccc4BFi4Ba9XU7JjFx36aJZyZFlt6lmiRCTrIsPO22q1pImqbgOGIoiTvcTBD0VGQYgRi0DoLUoa9rt2yNSihIOauuCSPs2QNccAHw4ovAaac5aQ4GDzZdKiUmNkt+sYjU+2HleDGeVy5Bkgg5semEelhYSKVI2jmj4oihpGO30iLoYuEVI1VJmDoIUoeel4h2dzvZrwHgM58J9Mww2JTDjDwdHY4l6g9/AI4/HvjlL42nqfDDxGYpiVjEtKgeLyps22y6kcTlxl4ietztT5IX0V6way9F0jYFxzklUxnr0t7RhVoh+uwebDHFBjVRq2Kkzjx+OF55qyuSTz9ovJDSFbZ6tXMlzPHHO669CHjFJGTZNZEqb7/tWKKefhoYPdo5ZWlB1nITp+jcnikQLxYxLfxypAF2bjZV6HbRe90O0dHl3Odnq7uPhVSKpG1Kjxv463ZxrW0dPehioYqReuWtrljB9bEmo8cec/78zGciBSv7xSRkJQ4ubSrF6Ql1Eg89djsO29gGjBrliKgRI4yXq3Ksqz43cTDA7Zm2uMi8yiOATAVPJ4HbXOwGRRHtBwupFDGRMyruriKO1YLCCY2giwVJUfHv/+78ecklkf65X9tRzmFGlUpxWr+/C99edBsOe/V5dH7wQ6hftcoRU4bLBbwvmtu27+6T+61aTEeZH+KO6+pnTpq30op+qBovxYY6604ym6Dc5jcqLj2vhJqI9oNjpFLExrijqAKDUvxNc2MRq1umYNu8C7G6ZYrrpE8uuP7114HNm5279SZMiPQr/NrOxv5omrI4rdv/Hn726O0449Xn8dqhh+Oaq77ruPUMl6uSrlI3Fq/dqSXAtxxkfWzLcsxcskHruLalH9pSTso0Nzp5CP2gJqL9YItUitiYY8fPalG5Ox1aV4AQQEdnCTVC9Lu4lrLJllzW5d/+1vnzrLOAQsH7uwr82s7G/mia1zq6MLj0Hn6y9A5M2PkcXj9kOD57xbexvXaY8XK5oePy6Gprl+54Jlv6oS3lpI6fi89GccpCKmVsy7HjJTCqJ9hywCCgZwJPk7QmycBukbKQOvvsyL87yJU+tvVH0xw7pAZ3/GQOztzxDN4YMgyfveI7eGV4sF12knhdzeM2FsPs+IMEWccd17b0Q1vKSZnqubahvgApgb1dJWvFKQupnBA1rsFLYEyat9J3gq2Gssk26UkyVEK63/zG+fOccyL/7vKVPqs270oka37uduadnXjol9/FUds3YFd9A2Zc8R28fNgxJHbQqg3PtPHF2Pdjxsk7xzBuZE2QspDKAXEzyqo6fdhdqO47BG1byAMH7v/5z8ALLzjxUU1NsX53Elf6ZDlDsZK9e4GLLsJRv/8d9jUMx8xr5uPlQUehSKTveW14mkYNjzVWvE7WAXa6YhhGJyykckBS+YL8JljAcS30SEnmDkGTBA7cL7v1Jk0CBg7U+7s1kLv8U7t2OXmi/vAHoFjEoCefxMKPfMR0qfqh2vDE3f175X6iIiSTwMbNGmMGFlI5IM4i6zWZBAkajJsN1w1bF/LA6QbKQiqgWy/U79YAyVQRSbFzJ/DJTzonKI8/3rn78NhjTZcqVfIYZB10s8ZiiwFYSOWCqIus32RSPcFWntpLclKxdSEPfDJw9Wrnz7/+a/2/WwO5yT/1xz8Cn/gEsGMHMHYs8OSTwAc/aLpURqAe06Jb0ATZrNlqGWf0w0IqB0RdZINMJiYmWNsW8spJvqG+gEEDatQnVLq7HesHAJx6auBnpGk1IJcqIgk2bnTuzvvzn4GPfQxYvhwYZjbFQRJkwaKShKAJslmz1TLO6IeFVA6IushStfzYtJBXT/J7OkuoK9RiwfRxri6CAdtexm/37UPXkR9E3Qc+EOpZaYnazLt6nnoKuPBC5yLi885zruoZMsR0qbSTFYtKEoImyGaN6vzIpA8LqZwQZZGlavmxaSEP6yKY8tZOAMD6IUfjjfXtJN8JoO/qicyTTzp3G3Z2AlOnAg8+CAwalNjjTFqEbLeolOsuibv6gmzWqM6PTPqwkGKUqE7rTD75CHOFOogtC3lYF8EJB4XUi8OKuM+SBS0zPPQQ8LnPAaUS8IUvAPfeCwxQT5FxRZBpi5DNFpXqunMjjqAJslmzyTLOJAsLKUZJc2MRbdt3Y9GaHb3XQkgAS9e1o2nUcF7kAxDWRXD8W68CALYeNsKKBS0TSAl85zvALbc4P8+cCfzjPwI16qtIdYgg0xYhmy0qftnWdQgav82aTZZxP7IQK2cSFlKMJ6s279J+t1aeCGLVq1zQyhaplw4bYcWCZj379wPXXw/cfz8gBPBP/wR8/evO/3ugQwSZtghFsahQWXC96ijN3Fa2WMa9MG0ZzQLqLRfTe+P56JblmDRvZawbzm3F9GQfBort1dxYxLTxRVQuy2WrXrl8vbfKS9krpF794Ch2ESTNnj1Oos3773eyyD/2GHDjjb4iCtAzLlRCOS0B3dxYxNypY1FsqIOAI0C88r6VF9z2ji5IvL/gmhhnqjoqNtRhdcsUFgAh8NoUMMFgi5QCVukOtpj/KbeXn1WvXL67lm3A0H3vYt+Agbj56r82Xu5M89JLzsm8LVuAo48GnngCGD8+8D/XMS4oxNiEsaioFtybH96ImUs2JG6hqk4jUqgRKPW8P7I4PikaNm2WqcIWKQWs0h16rSUVUJywKLdXkImqubGIX13bCAAYdPhwNJ9+TCplyyWrVwMTJzoi6tRTgbVrQ4koQM+4CGsRMo2qH3dLmbiFqtoatqezBAigoa4Qqe4oWq9NYdoymgXYIqWAVbqDLQGVlNsrsPXi7bedP0Pmj6LELa3PYvHaneiWErVCYMaEEZjTPDbQv00l/mbxYudE3r59wKc+BSxZAhx6aOhfE2VcqN6P2lhSEeRuzTBxYmHa222jVOqWGDJoADbc9sngL3HwubMe2dhrzWrv6MKsRzYCMG+9NgEFy6jtsJBSYItLKw2oTfZuEzDl9go8UVkupG5pfRYL1+zo/blbyt6f/cRU4q7Znh7g298Gbr3V+fnLXwa+/33P9AZ+hBkXlF3PQfG7W7NM0Ds8w9SHzo3S7GWb+rgEAaDUI/GNf30GAP1No25s2SxThl17CtxM9wLOgM+iKdgWU7cq4HXyyUeEcrWk+b6BXTiWC6nFa3eG+rySRF2zHR1Oks1bb3UCyRcsAO66K5aICgtl13NQqvtxrSIoP8jmJWx96HQ/dXSVXD/vKvVg1iMbSQTTp01zYxGrW6Zg27wLOVg/AmyRUlCp0ts7uiCA3oBhG3eTXti0W1ZNwKs278LcqWMD7apMvG8g60VZSA0dmkgZkqZbVofUe39eSWKu2WefdTKUb90KNDQACxc6QeYpQ9n1HIbKfuyWFDOoSyhsfaTlfqq2VHGqFyYILKQ8KE8ak+at7Oc2ytIAM50YMAxeE3BQVwvZ97XcIlUrhKtoEgAmzVvpKXATcc0uWgRcey3Q1QWcdhrwr/8KHHdc9N8XA8qu56jEcQmFrQ+d7qdh9QUnWD0gaYjdyutuyuMozXxYtkEln1kZFlIByMpuUoVN76djQSL7vqWDk3ttrff3iDJjwog+MVJlampEb5uprH9aLQ779wM33+y47wDg858H7rnHyRVliKwG9EaNn4xSH7piNW+7aAxuXLIh8PeTFrvVlr3yZoSyZyAoSQgeih4UjpEKQNaPh9r0fjqOnZN932HDnD/37DFbjojMaR6LqyaO7I2dqRUCQwbWolvhLqlEWyqA9nbgnHMcEVUoAD/8IfCznxkVUYB9qQ6SxmR9NDcWcdXEkaiO8CrUChRq+n6ahtj1uu7Gtji6SpJK4Eox3pAtUgHI6m6yDMX3q97JTD75CKzavAuvdXRhaF0Bgws16OgsRdrlUHxfAMDw4c6fu3ebLUcM5jSP7XNCb3TLctfvuVn/4lgcWte341c/WILZi76Fwzs70HnU0ah//DFgwoRIvy8JqJ1+NY3J+pjTPBZNo4b3s5YA6Z9e87OEG7eURySpEAqKHgUWUgHI+vFQau/nZrqtdBl1dJVQV6jFgunjIpWR2vv2kgEhVU0asUGPP70dO2b9A/75PxdhgOzB6lGnYtbUb+DvBh6DZm1PYbKGSsilPQ/45ecybimPSFKCh2K8IQupgGR9N0np/fxudgfi72wovW8vGRRSiVv/XnoJx116MS7Z8TwA4J6Jl+LOj1+N7ppa84cHGCYAXvm5VGOFWrC1G0kJHooeBRZSDDmC7lhsNXkrKQspS2OkqilP9l2lbv0nkaR0Yp++/nWMfecdvH7IcNx84U1Yfey43q9krn8wrtggKryoTrXjN1bcLPazHt2I2cs2YW9XtHCHJEhK8FD0KLCQYsgR5CqK8vcyxZAhwKBBQGcnsHevtfmkAPeTSOVJNMo1Kn14803guuuAxx4DAPx67Nm4afIN2FvX96qXzPWPHKPqFxRPcEUh7uXRpW7Zm2i0XAdt23f3xpWaEBtJCh5qHgUWUpqxfXdEgSBXUZg25SaCEMC4cc4luv/938B555kuUWSiBJoGWhRXrACuuQZ4/XXnjry778ZfxkzG/seeAwiZ+hl9ePULsjnhEiSIpbWr1I1Fa3YYTyJNTfAkBac/0EhSxz3zRvlotOoKilohsnt0/MwznT+fespsOWISJdDU81hzVxfwta8BF1zgiKizzgKeeQa4+mo0n35M4kfpbblCKYt49QtVfwpi0baVoJbW6tS4plMEZBm2SGkkj7ujoNzS+iwWr92JbilRKwRmTBjheZFtc2MRMxVJ83qkzER9ulovzzzTuQvOEiGlssBGCTRVLYojN64Fxn0JePFF5368b30LmDWrT+LSJHe+WXEf2YqXKFf1MwGn3bLYPkEvj3aD4waTgS1SGqGY34ICt7Q+i4VrdvRm7O2WEgvX7MAtrc96/juyiTM1oLJe/vsHRjtfWLMG6A4/UaaJlwU2SuLU6nYd3rkXdy7/Jyx+6P86Iuqv/spxe7a0pJr9nWICQEokba3zmgdmnX9Sv8SagGONyWr7VCczHVZf6JdI1N2Wn425kyIspDSS5YU/DovX7gz1eRkdWcypolqcv/WHvcCoUc69e889Z6h0wfCzwIZ1t5XbW8geXL7xSfz6vhsw7bmV6B44CLjjDmD9euD00xN+q/7wBklN3HCGICLMax5obiz2c2GVyXL7NDcWsbplCrbNuxDrb/0k5l92Wp+xduXEkZmdOynCrj2NUMxvQQG3i2y9Pi9D8ZirLjwX5ylTnKP9Cxc6l+0SodqNp4pDKb9bWHdbc2MRh760BYfPmoXTXnFE5BsTPo4jH/gJcOKJ8V8gIhQTAPqR1qGXOOEMQV2mfvNA0cL20Y3bWHPL3J6FuZMiLKQ0YnLhp3xasJwXxe1zP7J66sNzcZ72JUdI/fjHwOzZTloEzXgdJw96zFygf0Br7zuEpbMTmDMH586fDxw4ABx5JLBgAY6cMcM5zWgQVUzKu/sOkIzDSTOmK461LowI85oHeAPrTlbnToqwkNKMic5LPRh2xoQRfa54qfw8r3hO/o1F4GMfA37/e+DnPwe+9CWtz1b1l7btu7F0XXvgY+YS6CemQi9gUgKPPgr8/d8D27Y5n11/PTB37vuXOBumPIZuf2IT9nSWej/v6CqRGmdlVALl5oc3YuaSDVo3WnGsdbpcplQt15Q3t5Sxsd5YSGUA6qcFy6fzwpzaywqqScF38v/614Hf/x6v3DYPU145BkcPG6JtQlH1l3L7VH/udcxcwnGtRJr0Vq8G/vZvncB6ABg7FvjRjxwRSZC3uw70+0znONO1gKjaqty2OjdacaxBcV2mJhbcoM+kurmtLJH/gVAAACAASURBVH9DfQFSglQ2dKr15gcLqQxgQzDsnOaxuRBOlfhNCl7Wy8dHT8CEQw/Dsbt24LwX12DFSWdqm1D8Flq376sWvWJDHVa3TAlXgBdeAL75zd7M5DjySOD224G/+RsnvQExyu3oVT+6nqFjAQlyM4AuARjHGhRHhJlYcMM8k+Lmtrr8ldZVKoKFYr0FgU/tZYC8nBa0LSlinGPz31v5Mn50xlQAwHdW3IUj3tmt7ci9ql+oYtbKi2PsU0DbtjlZyU85xRFR9fXAP/wDsHUrcMMNJEUU4H+Jto5xpjPFgltbuaFro1V5gmx1y5TAC16Uk51lTKSkCPNMiptbv35MIaUHxXoLAs2ZK6dENVXbGmwZ5n1tNPnGmRRe6+jC/eMvwpStT+Pj2zdgwb/diaunf0vLhKLqL9PGF/vESJU/r2yXSK6UV14B5s8H7rsPKJUcwXTddY6I+tCHYr9P0njVua5xpnMBqW6rGsVhDwobragxpSYW3DDPpHjSM0i2d9OChWK9BYEtUkSIk48lzs7OFGHf18akiHEshR9qqIMUNbjpf92EN+uH4qztG3HD2qVaJhRVf5nTPNazH4W2PKxZA1x+OXD88cA99zin8a6+GtiyBfjBD6wQUYC3BU/XONNtVa5sqzsvPy1zOYVMWOHDPJNaDrzW9e3KJJ2VmBYs1OotKEL65PKhRlNTk2xrazNdDO1MmrdSXwyKBYR939Ety12P2gsA2+ZdqL+AGqi2ogHOpBBk8a38t+e81Ib7H52NA6IGbXfeh4kz/3fSRY/OgQOO227BAufUIeBYoGbMcE7mjRljtnwRiNOOcZ5RPhFZ1BAIbONJKC/SaJO4z4xa52EC2oP+ftV8W0nS9RcUqn1VCLFOStnk9nfs2iOCrb7hqIR936F1BXR0lfp9bnoH5UUcd1jlv/3t8U144OwZuPq3izHxb68FDu1xArNDkugE9fbbwE9+Anz/+8D27c5nw4Y5sU9f+QpQND8RRiWN4/WVz6jO0aXDjZ21nEImUh6EfWaUOg8awhA21MFrHRGAMcHid6rZFtgiRYQ8WaRa17fj5oc3usZtuL1v6/p2zHp0I0rdfb9fqBGYf9lp1g26SEjpnGy7/Xbn5698BbjzTmDQoED/PJEd/P79wIoVwEMPAY8/Drz7rvP5CScAM2cCn/98IslEs06e5gKmL0HbPmwfodinTFgV4+BlkUo0RkoIcYEQYosQYqsQosXl728SQjwvhHhGCPFrIcSoJMtDGVt9w2HxOkquet/5K7b0E1EAcMjgASQHXCII4WQ5v/deYOBA4O67gQkTgGXLHJHlg7YYs+5u4Fe/cixiRx0FXHwx8OCDjog6+2xHUG3ZAnz5yyyiIpI36zTzPkHbPmwfobi+BJmTbDmpnZhrTwhRC+BuAOcBeBXA00KIZVLK5yu+th5Ak5SyUwjxJQDfAzA9qTJRhmp2Xt2ojuB6Be6qJoc9nSVMmrcyk/Wk5NprgXHjgMsuAzZuBC65BDjtNPz3lV/CTaXj0f72Pte+E2txfvNN4KmngP/4D+CRR4A///n9vxs71ol/mj4dOO64uG/HwN6TS0x8grZ92D5CcX3xm5NsOqmdZIzUGQC2SilfBgAhxEMALgHQK6SklKsqvr8GwFUJloc8NvqGw6IaPD1SKt/dK8Eg5cEVF2VM00c/Cjz/vJNO4HvfAzZuxBkbb8DPDhuBJ0+ciKePGYNvv7UHwMTeOvGaePs8Z+hg3DZmMD65ZyvwX//lZB9/4YW+/+iEE94XTxYGj1PH1nQmTHyCtn2UPkJtffETgzYl50xSSBUB7Kz4+VUAEzy+/0UAv0ywPAwBouy2VZfGlkl7cKVxqsRtNzZzyQa0bd/tZIivr3eukbn+evzj9L/HjFWLceJbO3HiWzsBPIJuUYOtDx4HTL0AOPpo/KDjAB56oQMdtYPw7sA69AiBY7o6MOUDJex6dBtue/tNHPWXt1B8+w0c3rm3b2EGD3bciGedBXzmM8Dppxu/SDjLULQeJAHV01kmCdr2WegjfmLQJhd3YsHmQojLAJwvpfybgz9fDeAMKeXXXL57FYCvAjhbSrnP5e+vA3AdAIwcOXL89vKpIMY6ogYYliddlWVKAFgwfVzqAido+cOiCg4tv2fls0a3LMeA7hI+vm09znh1Ez66cxNOff2PKPSosxh78VbdB/Dc6LE4+wvNjng6/XQnLothNGFboDGTDF5imlqAvFeweZJC6mMAZkspzz/48zcAQEo5t+p7nwDwL3BE1Bt+vzerp/byRJydqGpwDasv4L1SjzGBo3twq/JmuT3LrUyDS+/hvLdfwb+ccADo6ADeeQf4y1+cP995x8kwfvTR+OHW9/D6IYfh9UMPwxuHDMefDj0cfzr0cAghyObnsgm2urhDbZFk6EFNbJvKI/U0gBOFEKMBtAO4AsBnqwrWCOBHAC4IIqKYbBDHV68yB0uJVPzpaZmbveLCqp/lVieifgjOveoKwOfdH1AsaGkENmddZNgULJsGle2t2iRQdNswZrDJfZmYkJJSHhBCfBXACgC1AH4qpdwkhLgDQJuUchmA+QAOAfCIcGIudkgpL06qTIz9qAbXzCUbXL+flsDRLTzK7+S24FQ/K86EYyqwOW2RYUK02RQsmzRu1gU3+GQiPUxueKgFyKtINLO5lPIXAH5R9dmtFf//iSSfn2Wyvpv3wm1wqeKnkhA4aQiP5sYi2rbvxqI1O/qIKdWzok44pnZ9aYoMU5YhKsGyFOYKVdqTSvhkIj3YqhoMviLGQrhz9ydNgQOkIzzmNI9F06jhiT/LxK4vSA4ZXe+tQ7RFKQ+FfFBU5gqqV5Qw3rBVNRgspCyEO3d/0hQ41c8qZ+JN6llZbFO/vFY6F/+4lqGo5aGQD4rKXKFqbw4upw0Vqyp1WEhZCHdud9ISHVR2+TbjJTJ0L/5xLUNRy0MhWJbKXJGWqKTgxswSFKyqNsBCykKod+6sT2ZUdvk24yUydB8ciLuIxxEjpi2KVOaKNEQlb3D0Q8GqagMspFJCp7jw69wmhQz1yUxH3VDZ5duOSmToXvzjLuJUxEgUKC2ESYtK3uDoo3KebKgvYNCAGuztKmFoXQFCADOXbMD8FVsyt0mOCgupFNAtLrwWBtWz2rbvxqrNuxIXV5QnM13tYPPCagNJLP5J5C6zYVdOwb0YhzAbH97g6KF6ntzTWUJdoRZXThyJpevayW6STcJCKgWSEBeqhUH1rMpj9EkOAMqTmapubn54I4DgdWHzwmoD1BZ/auWpJIjQMO1ejErYjQ9vcPSgmicXr92J7qqbUKhskk3DQioFkhYXQTIGV3+e1ACgPJmp6rtbylDCkvLCmhWoLf7UygPQd6PHJewGlDc4evCaJ8N8P0+wkEqBJMVF0IzBbiQxAChPZl7XroQVlhQXViZfUHaj6yDsBpQ3OH2JGg+qmidrhXAVUxQ2yaZhIZUCSYqLIBmDBfpbpIBkBgDlycytHSrhnRWTBEkd/qDsRtdBlA1o2hscqieU41grVevVtPHFPjFS5c8pbJJNw0IqBZIUFyoLC/B+xuDJJx+R6gCgaq0pl+nmhzfyziogVBcKW0jS/UbZja4DytZtgLZrNY610mu98rppIc9zBQuplEhKXKjMrbVC4KW5n+79OY2rRmyg/M6UJ2gqUF4obEHXAQc3qAuNuFC2bgO0XatxrJVegki1juV9rmAhZTmqAMDqz6laiUzgN0HneWdVCeWFwhZ0HXBwg7rQ0EH1vNW6vh2T5q0k8b6UXatRrZVRBVHe5woWUpZT9LjDKmlsFhx53lkFbbckFgqb+0wUdB5wcCNPGyRqY5OyazWqtTKqIKIsKtOgxnQBmHjMOv8k1BVq+3yWhnm/PKm1H0y5UJ7UWte3J/rcpPGaSLJAmHZTLQhRF4qs9hkv3MZnJXlZaHSQ9tgsW79GtyzHpHkr+/VTU3NvEJobi5g7dSyKDXUQcDbWc6eO9RWcqv7Y3tHlWRe65wrbYIuU5Zgy7ycZ++FF0haNrO+swuw4dcfg5NH8b/MBB2rWwzTHppv1a+aSDWjbvhtzmscCoO9ajWKtVFnZBN4/2ORmCcx6vJ4fLKQsxG2CW90yJdUyJBn7oSIN0z4lc30SC1mYxUj3QpEFkRqlTWw84OA21mY9uhGzl23C3q6SEdGQ5th0E/0SwKI1O9A0arhv8LWtuAkit/Q51Rsg6qIyaVhIWQaVOIGkYz/cSMOiQWVnlVQ7h12MdC4UqmcPrSuQCSD2Ik6beC001Cw/5XJWj7VSt0RHVwmAmXknzbGpEvcSyIUFtbI/qub56jrKmqgMA8dIWQaVGB4TsR9pWDSixhboJql2NhnX4fbsQo3Au/sPWBE3FbdNmhuLWN0yBdvmXYjVLVN6RRTFuLEgYyrteSfNsell5bLJghqF6n6qOrhE2S2dNmyRsgwq7hETsR9pmfYp7KyitrOfdcOkCd7t2Z37D2BPZ6nP95KMm4pj/Uli7FGNG/OyRFQS5d3jtEFaY3PW+Sdh5pINqd0IQRkqVnrKsJCyDNMxPNWT4IwJI1LLmp6nAR2lnYO6nkwKxepnj25Z7vq9JFIsxHWXJjH2qGyMqvG7TqlM2HdXtUHb9t1YtXkXGfdmc2MRbdt3Y9GaHX3EVFbnGy/yHv8UBHbtWYZJ14ybG2LpunZMG19MxdxOxe2WBlHamYrbNwxppliIWz9JjD2qx8arx9qw+gIKNaLPd6K8u6oNFq3ZQc69Oad5LBZMH5eL+cYPN7c08z5CKjJjU6WpqUm2tbWZLoZRTAWnTpq3Upn8M+1Tg3kgbDuPblnu6ooQALbNuzCxcsah2kIBOAt01AXLq4++dnChriZM/egee6r3nza+mIiFJk75dby7qo+6wfOKmjTWAIqHIEwihFgnpWxy+zt27VmIKdcMVTdEVgnbzqbdvmXCTMBppljQUT+6x57b+1dfMh7GBelV93FdmzrePWjsVbl8revbc714u5HGyW0qp8NtgV17TGCouiHi4pfB2BYoZFqOcgpNp9vAq49SqB83qt9/1eZdkVyQfnVPwfXrd9q3GgouPmqk0Y4U+opNsJBiAkNpIdIlfqgeP48ChRgy0xOwVx+NUj8mRHZUy69f3VOwKFe2AeC4Vb2gvnjb1D+oPSNLsGuPCQyV0xs6zc5Uj59HxXTqBtMTsF8fDVM/Xv3M6xlhcHPFRXVB+tU9FddvuQ1U8WzVUF28Tbm/0mhHKn3FFlhIMaEwuVCXFx23AR5V/Jhe+LMGhQlYVx9Viezbn9iE90o9sRdQ1UI8bXwxUkoRv7qnlj4k6Bijunib2oSl0Y7U+gp1WEhFhE80BEdHXbmdbqomivihsPDbhld7ZmkCVvWn6gSiQLQFVLUQL1yzAw11BQwu1KCjM/i9dn51H8eirHO+K/+uIKf3KPcdU5uwNDwDVLwPtsBCKgJ8oiEYrevbMXvZpt77uYDodeW26FQTRfxkaeFPA7++n6UJOMwJM8Cpi9EtywO/s9eC29FVQl2hFgumjwuV9Rvwrvso1jqd853fhqhQKzBk4ABjFyOHweQmLA3PgOoZbEToDwupCFCIq6Hemb0mzCh15bfLiyp+srTwp0GQvm86TksXbiJbAJ6WlMoDC4C30PATalHGSRJ1r3O+89oQFS0be3nchLERwR0WUhEwHVeTVh6ROOLCz4IUtq68Fp24E7CuxYe6uNWB6b6fJpUiu72jy1dEVRJEaAS5hoVCvepsc9W/EYB1yTfzuAmjYESgCAupCKRp0nVbnJPuzG5CbeaSDbhxyYbAosVvkg1bV6rdH5UrG/KyU8tbTFnYE2aV+I2BaqHmBoV6jdPm1fNXQ33BNcasob6gpaxpk5b1lcomLU8bqTBwHqkIpJVPSZXjSDXp6urMbkKtvBMPmmfJa5KNUlcUciR5YTp/km5U+XEo5RJLEy9LSlHR14MIjXIyzn+ePo5svUZtc7f56533DqC2pn/2qHfeO2Bl7rY0oJTrLqtJmePCQioCaS3qqsW5VrinsdPVmf0EWRCBoMpgPKy+ELmudGbA1k2WdmpeEzd1QZsUSWdMp1yvUcvmNn+VeiR6evo7SEs90ppNR9pJOClt0vK6kfKDXXsRScOkq1qEu6VEXaE2sSDHIKeVwrgtTJuj0yBLLi8/13FWgsmB4C4Tr8BiXX2dcr1GKZtqjlDFmdmw6TDhwqe0SQvS16m4IdOEhRRhVItzOU4pqc4aJAg2qNuiukxZHWRZOsFDaeJOkjCLos6M6XlBNX/VCoFu2V9O2bDpMBFsTW2T5tXX8xIrWg0LKcL47YKT6ph+p5VUAsFPJGV5kGXJAkdt4k6KsIsii6VwqOavqJnbKWBik2HTJi2vp/pYSBHG5OJcuWgEsSIFEUlZH2RZWWhtmrjjkBfLmym85q+mUcOt3HSY2GTYtEnL65hiIUUcCotzkDIEEUl5HWS2YdPEHYe8WN5Mopo7KMxrUTC1ybClvvI6plhIMVoIIpLyOshsxJaJOw5Zt7xlNR7RJHnZZEQl62NKBQspRgtBRFJeBxlDkywvilmORzRNHjYZUcnymPJCSJfTE5RpamqSbW1tpothDKq7TLe79dwyj1MtP+MPt509qDKxFxvqrLuKhUkWHtfBEEKsk1I2uf0dW6QsQscuM6lBE3Qnwrs5O2ELh11wPCITBB7XemAhZRFxT70lPWhYJGUXHScueeebHhyPqJes9t2sn6ROC74ixiLi7jIpXTXA2EXcvkfpvjBKJHXdCF/loY8s9122XOqBhZRFxL0wkgcNE5W4fY9FfH+SXKAp391nG1nuu3wJsR7YtWcRcU+9sbmfiUrcvhdWxGfVlVJJ0m4VdrXrIasb0Nb17Xh334F+n1OyXNoyD7CQsoi4R0s5/QATlbh9L4yITzsA1tRkndUFmhI62jaLG1C3U9YAMKy+gNsuGkNCrNgUCM9CyjLi7DLzmuOjjC27G6rE6XthRHyaAbAmJ+ssLtCU0NW2WdyAuo0xAKgfOEBrv48z59oUCM9CKmdkwdwfZXBS2t3kUdCFEfFpWmpMTtZZXKApoattqy9xrxWiT4yUjWM3jTEWd861yWLLQoqxiqiDk8ruhpKgS5ugIj5NS43JyTrvFmI/4m44dLZt+blZGbtpjLG4c65NFls+tcdYRdQTNFR2N1k+AaSLNI/uxzm1pCN1QXNjEatbpmDbvAuxumWKdQtyUug40aj7RFqWxm4aYyzunGtTCg8WUgZJKodMlok6OKkc86Ui6CiT5tH9qJN1lnMLUUCHaHFrWwGnraLMt1kau2mMsbhzrk0pPNi1Z4g8u3jiENXcSyUexSZztUnSiuWL6l6j4irOKjpES3VskwBQvlk2ynybtbGb9BhTzbmTTz4Ck+atDDTebInpZYuUIbJkJk6TqBYEKrsbm8zVeSGKey1L1gmK6LIgl9u22FDXK6LK6LBw8dhV4zbnThtfxNJ17Zmz5LJFyhA8EUcjToAuhd0NBxhng7DWCZ0nNfNw6lO3BVlnQtis171OqufcSfNWZtKSy0LKEFkzE6dFFhYRCoKOiUeYhV6nG1/H77JhDOkWLToTwlKrK5vIqgGBXXuGYDNxeDjAl6FCGFexTjd+3N+lYwyldUhG54nGMPMth10kB5VDP7phi5QhmhuLaNu+G4vX7kS3lKgVAtPG827HC5sCfCnu+imWyWaCWid07sLj/q64Y8jWQzJUE8LmDSqHfnTDQsoQrevbsXRdO7qlEwLZLSWWrmtH06jhZFL0U8OWCY7iYhO1TFnqP6bQ6caP+7tMCzGTUEwImzeyGmfGrj1DpGE+zporTDWRSYBUHi6KroEoZcpa/zGFTjd+3N8V17Viy2YmDNWuysknH8FhFwmSxSS0LKQM4Tch6YhDCLJ42pQU1G0RKUNpkae42EQpE0VBSBWvcaQz9Ubc32VaiFHDbbOwdF07po0vGk+VwtgDu/YM4WU+1uUaUi2S5cy+k08+AkvXtZNyQXlRnWCvGiouBoqugShloigIKRJkvOo87RXnd8V1rWQtxkW1WVi1eRdWt0wxVCrGNtgiZQivnaEuS4DXItne0YVFa3ZYZ3Eom4WF4u8pLPLUTmS2rm9H5/4D/T73K1PWrA9JYZvlLo5rhUpiW13wZoHRAVukDOG1M5y5ZIPrv3GzKHjhtnuspDrTbxkbJhGKVp8ylAIqq60lZRrqCph98RjPMmXN+pAUJhZjk4cAspRLifI8wtgDCymDqCYk1eAWcCbQoJOYnytMhQ2TCPVFnspi42YtAYAhgwb4lo+SIKRM2osxxVOhtkJ9HrGVvJ32ZSFFkFnnn4SZSzb0sxhJIHQMUHlBnzRvpVKcVT7HlkkkyiKft8ENxLeW6BKEWa77tBdjyikIbGtnm+YRW+o2j0JfSKly8NCkqalJtrW1mS5G4hzbstz1cwFg27wLQ/8+NxdPXaEWp48cijUv7+lNCjrxuGF45a2uWIP1ltZn+yQanTFhBOY0jw1dZp2o3t/m+I4gqAR0saEutWDaPNR9mouc7rkhDF7vGbWdbREIgLm+7PbcQo3AIYMHoKOzRKreKMw5SSCEWCelbHL7O7ZIJYCOiaGo2V3gtvMqn9qrTAq6+qXdvf8myk7iltZnsXDNjt6fu6XEwjU7sG3XO7EFWhwo7+KThILrIg91n5Yrt3V9ez8rcpnKuSEJceJnaYjSzkGtF1TEVlJ92e/93J5b6pHY01kCQMvqk8cAfj61pxldSQyTOPlVfVpn1eZdykD0MmFPHy1eu9P189Uv7Taa2DGPgxugccoqr3WfBPNXbHEVUQLonRuSSqTqdzoxqVxlbu9z45INaLzjydTzxiXRl4O0V5DfT+WkaB5P+7KQ0oyuo9BpLIBBB3+YSaI7oKs47UGfx8FdxnQm4TzXvW5UY1Gir9U5iXQMfiIiSjsHESaqAxN7Okupb8iS6MtB2itu5vk0oZb+JQ1YSGlG544l6QUw6OAMM0nUClWGp/6kOejzOLipwHWvD9VYLFZ8npQF0E9ERGnnIMLEq9xdpW7c/sSm1G5nSKIvB2kvr1sdKqGwOaFgBU8bFlKasWn3HWRwhp0kZkwYEfi7adZJHgd3WJK6LojrXh9BFvKk5iC/Z0dp5zjvU2ZPZym1sIEk+nKQ9qp+bkNdAYXavptWSpsT01bwtOFTe5qx7YRSdZDj5JOPwKrNu7Se2pt43DD8Ycdea+okj9jWb/OMX2Bykm2ZVBB72Pfxw6YTYnk47ZgFvE7tsZBKAO7g/eE6oU1WjyznlayNt9b17Zi9bBM6ukqBvp9GKgid2NBeNpQxSVhIMQzjyeiW5crTYDYtSEy2qV7M3913wFVc8QZAL2yx5jxSDMP4kLU7x/K+e84q1fm6VAs8lVihrJCHXHBxYCHFkIcXxWSorNehB4NXS93v26VsXZBMX1Hh1l8BvrNQB251O3fq2EzVLcX5jnPBecNCiiGN6UUxq1TXa0dXCYUagWH1BXJXToTF5O7Zrb/OemQjINArUrkPR0M1F8ydOjYzbjyq813WLNa64fQHDGlUi+LND29MJW9MVlFdOVE/cID1R5ZN7p5V9Vpp6QPoZKG2iaQSjVKC6jtyLjhv2CLFkEa1+JUzqFO/m4sqccQG9bo1uXsOI9baO7owad5KsvWYBHH6DjX3UhLjgNo7lnG7qzUP/TUoLKQY0qgWxUqq3TZUzeOUiCo2bml9FovW7Og94Uexbk1e1Bykv5YRQO93KdajbqKMy0qxUiOE6xVUcQRyVDGU1BxD2YWW1sXcNsKuPYY0Qa9G8Lubi4J5nBJRTPWt69v7iKgy1OrWZCZ1t3ot1Ih+WagFQL4edRN2XFZf5usmouII5DiXO3uFHMQJNWAXmp2wRYohTXnx80vGF+RurrIrJQ2TNHX3VxRT/fwVW1xzTQHmXQ/VmNo9q+q1+jOV1SqNejTVN8O6rVSXFdcKgR4pY5c9zqEEr5CDWY9sBBDNMmWjC436XJcGLKSIwJ1RTXNjEfNXbFEKKbe7uVQLVRouFFtci2HFhtciT8H1QAVVvVZ+psokn3Q9muybXm4rt/lP1d96pNSSJDZOPJLXHFPqkZi9bFPk+rTJhWbLXJc07NojQBwTc17wijupdtv4uQOTdqFEdS2qLg3WdZlw3N+jWuQFwK6HkJhy4Zh0e6veefLJR7jOf0PrCq6/R5fYjHO5s98cE/QqG9vhMAoHFlIE4M7oT60Qys+rdz6VMTIqknShRNnpqsT0La3PahHZOsS62+IhAFw5cWSk3acugWgjpuK4TJ4KU73zqs27XOc/IRBKbIbtT3HEbPld8g7VU4Zpw649AnBn9Mct0NTr87J53IQLJcrJG5WYXrx2Z793DBLHUe0q6dx/IHaSSp3xG+wSMOPCMX0qzO2dZy7Z4Prdjs4SFkwfF6i/+fUnr9CJqP25ubGI25/YhD2d/a1Pw+rdrWlZw3R/okKiQkoIcQGA7wOoBfBjKeW8qr8fBODnAMYDeAvAdCnlK0mWiSLUOiPFeK2ioo68rE6AmaPwfs8MEw+iEopBrFuVi4qKsGJd1+LPd3cFQ/dYNJkaQoXX/Be0v/lZ9b1EVpz6vO2iMZj16MY+CVcLtQK3XTQm8u+0CYr9yQSJufaEELUA7gbwKQAfATBDCPGRqq99EcAeKeUJABYA+G5S5aEMpSOvVOO1otaRCReK1zNV9auKB1G5NMNat1SYEutshfUnibFoMjWECh3zn1d/SjJ0ormxiPmXntanPudfelpuNgMU+5MJkrRInQFgq5TyZQAQQjwE4BIAz1d85xIAsw/+/6MA7hJCCCkV2/CMQunIK1VLQZw6MuFCUT1TVb+DCzWoK9T229lNG1/E0nXtoXZ8QcWIyZ0jNSssRZIai9ROhemY/7z6U9KinVp9pk3e3x9IVkgVAeys+PlVABNU35FSHhBCPxKXQgAAB7NJREFU7AVwGIA3EywXSah0RsqWAip1FAdVPXrFgzSNGh5qkVEtKg11BQwZNMC4WAfYJRAEymNRN3HHtld/mr9iC4t2JlGSFFJuPolqS1OQ70AIcR2A6wBg5MiR8UvGKGFLQbJEiQcJu8ioFpXZF48hI0QpWWGpwmMxOH79iUU7kyRJCqlXAYyo+PkYAK8pvvOqEGIAgKEAdlf/IinlvQDuBYCmpqZcuf3Shi0FyZJG/doiUrJgYUwSHovh8EuESn08MPYikgpHOiiMXgRwLoB2AE8D+KyUclPFd74CYKyU8gYhxBUApkopL/f6vU1NTbKtrS2RMjMOFE/tZQmuXyYo3FcYhgZCiHVSyibXv0syrlsI8WkA/wwn/cFPpZTfFkLcAaBNSrlMCDEYwAMAGuFYoq4oB6erYCHFMAzDMEyaeAmpRPNISSl/AeAXVZ/dWvH/7wG4LMkyMAzDMAzDJAVfEcMwDMMwDBMRFlIMwzAMwzARYSHFMAzDMAwTERZSDMMwDMMwEWEhxTAMwzAMExEWUgzDMAzDMBFhIcUwDMMwDBMRFlIMwzAMwzARYSHFMAzDMAwTERZSDMMwDMMwEWEhxTAMwzAMExEWUgzDMAzDMBFhIcUwDMMwDBMRFlIMwzAMwzARYSHFMAzDMAwTERZSDMMwDMMwEWEhxTAMwzAMExEWUgzDMAzDMBFhIcUwDMMwDBMRFlIMwzAMwzARYSHFMAzDMAwTERZSDMMwDMMwERFSStNlCIUQYheA7Sk97nAAb6b0LEYNtwMNuB1owO1gHm4DGqTZDqOklEe4/YV1QipNhBBtUsom0+XIO9wONOB2oAG3g3m4DWhApR3YtccwDMMwDBMRFlIMwzAMwzARYSHlzb2mC8AA4HagArcDDbgdzMNtQAMS7cAxUgzDMAzDMBFhixTDMAzDMExEWEgBEEJcIITYIoTYKoRocfn7QUKIJQf/fq0Q4tj0S5l9ArTDTUKI54UQzwghfi2EGGWinFnHrx0qvnepEEIKIYyfmskaQdpACHH5wfGwSQjxYNplzAMB5qSRQohVQoj1B+elT5soZ9YRQvxUCPGGEOI5xd8LIcT/O9hOzwghTk+zfLkXUkKIWgB3A/gUgI8AmCGE+EjV174IYI+U8gQACwB8N91SZp+A7bAeQJOU8lQAjwL4XrqlzD4B2wFCiEMB/B8Aa9MtYfYJ0gZCiBMBfAPAJCnlGAA3pl7QjBNwLNwC4GEpZSOAKwDck24pc8P9AC7w+PtPATjx4H/XAfhBCmXqJfdCCsAZALZKKV+WUu4H8BCAS6q+cwmA/3/w/x8FcK4QQqRYxjzg2w5SylVSys6DP64BcEzKZcwDQcYDAHwLjpB9L83C5YQgbXAtgLullHsAQEr5RsplzANB2kEC+MDB/x8K4LUUy5cbpJT/CWC3x1cuAfBz6bAGQIMQ4uh0SsdCCgCKAHZW/Pzqwc9cvyOlPABgL4DDUildfgjSDpV8EcAvEy1RPvFtByFEI4ARUsp/S7NgOSLIWPgwgA8LIVYLIdYIIbx260w0grTDbABXCSFeBfALAF9Lp2hMFWHXD60MSOtBhHGzLFUfZQzyHSYegetYCHEVgCYAZydaonzi2Q5CiBo47u1r0ipQDgkyFgbAcWOcA8cy+zshxClSyo6Ey5YngrTDDAD3SynvFEJ8DMADB9uhJ/niMRUYXaPZIuUo1xEVPx+D/ubZ3u8IIQbAMeF6mRmZ8ARpBwghPgHgmwAullLuS6lsecKvHQ4FcAqA3wghXgEwEcAyDjjXStA56XEpZUlKuQ3AFjjCitFHkHb4IoCHAUBK+XsAg+Hc/8akS6D1IylYSAFPAzhRCDFaCDEQTsDgsqrvLAPw+YP/fymAlZITcOnGtx0OupR+BEdEcUxIMni2g5Ryr5TycCnlsVLKY+HEql0spWwzU9xMEmROagUwGQCEEIfDcfW9nGops0+QdtgB4FwAEEL8FRwhtSvVUjKA0y6fO3h6byKAvVLKP6X18Ny79qSUB4QQXwWwAkAtgJ9KKTcJIe4A0CalXAbgJ3BMtlvhWKKuMFfibBKwHeYDOATAIwdj/XdIKS82VugMErAdmAQJ2AYrAHxSCPE8gG4As6SUb5krdfYI2A43A7hPCDETjivpGt5k60cIsRiOG/vwg/FotwEoAICU8odw4tM+DWArgE4AX0i1fNzmDMMwDMMw0WDXHsMwDMMwTERYSDEMwzAMw0SEhRTDMAzDMExEWEgxDMMwDMNEhIUUwzAMwzBMRFhIMQzDMAzDRISFFMMwDMMwTERYSDEMk2mEEB8VQjwjhBgshBgihNgkhDjFdLkYhskGnJCTYZjMI4SYA+f6jjoAr0op5xouEsMwGYGFFMMwmefgXWlPA3gPwJlSym7DRWIYJiOwa49hmDwwHM49jYfCsUwxDMNogS1SDMNkHiHEMgAPARgN4Ggp5VcNF4lhmIwwwHQBGIZhkkQI8TkAB6SUDwohagE8JYSYIqVcabpsDMPYD1ukGIZhGIZhIsIxUgzDMAzDMBFhIcUwDMMwDBMRFlIMwzAMwzARYSHFMAzDMAwTERZSDMMwDMMwEWEhxTAMwzAMExEWUgzDMAzDMBFhIcUwDMMwDBOR/wEftav+Bf3cjwAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(10,10))\n", "ax.set_aspect('equal')\n", "ellipse1 = patches.Ellipse(ellipse_center, ellipse_width, ellipse_height, angle=rotation_angle, fill=False, \n", " edgecolor='red', linewidth=2)\n", "ax.add_patch(ellipse1)\n", "ax.scatter(x, y)\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "cos_angle = np.cos(np.deg2rad(rotation_angle))\n", "sin_angle = np.sin(np.deg2rad(rotation_angle))\n", "\n", "# transforming the coordinates along the major and minor axis of the rotated ellipse\n", "xc = x - ellipse_center[0]\n", "yc = y - ellipse_center[1]\n", "\n", "xct = xc*cos_angle + yc*sin_angle\n", "yct = -xc*sin_angle + yc*cos_angle \n", "\n", "# normalized ellipse equation\n", "norm_equation = ((xct**2)/(ellipse_width/2)**2) + ((yct**2)/(ellipse_height/2)**2)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "colors_points = []\n", "\n", "for r in norm_equation:\n", " if r <= 1:\n", " # point in ellipse\n", " colors_points.append('red')\n", " else:\n", " # point not in ellipse\n", " colors_points.append('black')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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nz0Kv15s+VjzPo2rVqnj8+HGh67pz5w46dOgArVYLrVaLwMBAh6ywu3z5MgYPHozXXnsN06ZNK3ScmAkTJkCj0UCj0UCtVsPT09Psni6JnDlzRlbBUKlUpqk+lmVRrlw5py+DT0tLw969exEWFmaW/mf27NmSq/vyUk6dP39e0iJFCCm2wjN69GhJpYNhGMTGxha3y/myYcMG+Pj4QKfTgWVZDB8+3CZpkYxGo2TMt7x+lVYSEhJw8uTJIr3XXnaoImVDOnbsKPuyzbs5RVHEhx9+KDviYVkWixcvdmo/bMnTp09Ro0YNsxEzx3ElTll88OABZs6ciY8//hirV68uUhofo9GI6tWrQ61WWyja9+7ds4PUz9i3b5+ZfwzLsihfvjzu3r1r1fF79+61mP7KUyhL8hL89PT0fFP3PL/JxX4TBAGXL1+2u6zbtm0zm7pzd3c3pRWaNGmSpHxKpRLTpk2DKIqoVq2aRRme54sdy+y1116TPC9ubm7YvXt3oeq6du0a5s2bh0WLFuHOnTv5lg0LC7OwELIsi8GDBxenOybat29voUypVCr07NnTJvVTShdUkbIh4eHhkg93v379zMrIjQ7zRjzWfuBKArNnz5acdmBZ9qXLMXbo0CHJKOQMw5j50UlhNBpx4sQJ7Nu3D0lJSVa3aTQaUaFCBYs2NRqN1f4e7dq1k71fQ0NDLcrn5uZi0aJFCAoKQtWqVTFmzBiHOWcXlsWLF5s9s1IKY36bXq+36bSSFHFxcZLPUF6evhMnTsgm765duzZEUURMTAwqVaoEvV5vmr7573//m2+7d+7cQc+ePU3W0169euH+/ftmZb766itZi9S1a9es7uPUqVPBMIzJusQwDNatW4czZ86gVatW0Ol0KF++PGbPng2j0SibHYJhGJs4hMfGxsLLy8t0Xnmeh4+PD+Lj44tdN6X0QRUpG7N161aUL18eDMOAYRgMHjzY7EU7atQo2dGtWq3GunXrTGVv3bqF7t27Q6fTgeM4hISEuOwHSY5WrVpJ9tVgMODQoUPOFs+hhIaGyirRH3zwgexxUVFR8PX1NX0EC2O1vHHjhuxH1trEpHJT1oQQ9O3b16J83759zdrU6XTw9/d32WTcBw8eRKdOnRAcHIwBAwbkO9B5ftNqtVi4cKHd5Zs2bZqksiIIAtasWQNRFNGsWTNZi1neVLrRaER4eDh27NhRoAU0MzMTlStXNrOeqtVqVKtWzSwNk5yPVGECVkZGRkoqilqtVjIh+RdffAFfX1/J/vI8XygFLj8SExOxYMECDBo0CIsXLy51K/asxWg0ml1ziiVUkbIDRqMR9+7dk/xwjB8/3mJqJ+9j8/wqidTUVJQvX97MeV2r1aJu3bolygnwnXfekVQceZ7H+fPnnS2eQ7lw4YJshOtly5ZJHpOXp+/Fc8gwDE6fPl1gmw8fPpSNjl2nTh2r5O7Xr5+sMvHtt9+alb1y5YrkR5HneUnrlauRk5MDT09PqxWpvDQ8WVlZ+O9//wsfHx/o9Xq8/fbbNkuz8dVXX8laX/IUuREjRhRYpjBs2LBBctpTr9fj119/NSt78eJFtGnTBiqVCnq9HqNGjSqUlW7cuHGSi3RUKpXkuyNPUZP6zREWQmdz9epVfP311xg4cCC2bdtmNyUnKSkJ/fv3h1arhVKpRLNmzWiIHhmoIuVgLl++LLvC5vkpmxUrVkiOjAVBwOHDh53Yg8IhNd2pVCpRq1atEqUQ2orOnTubXX+NRoMqVarILqMPDw+XnA4khMDb29uq1EQdOnSQXOK/fPlyq2S+c+eO5EdLo9FYKAtr1qyRteg8P8VtDaIoIjU11eH3SZ5PWZ4VSG6673kFuGfPnmbXValUwsvLyyaO6IcOHZINX5CX4Pynn36SVNL1er1VyaD//PNPvPnmmwgMDMTIkSPx+eefS/ZZpVJh+vTpxe7T84wZM0bSuVvOcm8wGLBlyxaLc8LzvMsn6i4uW7duBcuypntSEAS0bNnSJk72zyOKIpo2bWphCTUYDHb15yypUEXKCfz0009gGAaCIECv14PjOOzdu9eszPDhw206wnQmCxcuBMuyplVQtWrVQlxcnLPFcgpZWVmYOnUqqlSpAh8fHwwZMgQPHjyQLZ9f5neFQoHq1asXqGg8fPgQDRs2BM/zcHNzg06nw/DhwwuloOzatQs6nQ5qtRoajQY6nQ7r16+3KDdmzBhZ682kSZOsbm/x4sXw9vaGWq2Gt7c3Fi1a5FCFKi4uDt988w0++ugj9OjRQ/JDzzAMFixYgKtXr8r6ARbk+2YNoiiiR48eZooDz/Nm4TeSk5Mtgv2q1WrUqFGjwFAVq1atsvAT43leUnmTskgVl4iICEklUKlUSipTeSslL1y4gDfffBOenp4ICgrChg0bbCqXq5GRkSE5qCrMoMhaIiIiJK8/wzCYMmWKTdsqDVBFykncv38fa9euxaZNmyTn3n/++WdZi9TBgwftIlNCQgJWr16Nbdu22TzQ4NOnT3H48GFcuHDB9EF8GS1ShUUu8/vz98Px48etquvChQvYvXt3gSui5EhLS8POnTvx7bffYvHixRbhD/bu3Svrj8XzvNWOuitWrJD0jZGb/rQ3f//9t2S/8mK+bdu2TVbZ7dKli01kMBqN2LZtG/7zn//g3Xffxb59+yyen9jYWLRt2xYqlQpqtRrdu3e3cA5/kezsbLi5uUlannieN3ND0Gg0Fj5StmLs2LFgWRYqlQoajQYMw2DcuHGSi3cGDhxo8/ZLAkeOHJG9z9q1a2fTtjZs2CBrCX/nnXds2lZpgCpSLkpKSgrKli1rNsLUaDQICgqyy5LzadOmmVnJDAYDjh07ZvN2RFHEnDlz4O3tDUII/P39sWvXLpu3U5qYPXu2bFybvGkOR3D79m34+/tDr9eb4it1794d2dnZAIAmTZrIKnwHDhywuh05R+Ly5cvbq2sFMnz4cHAcB4VCAaVSCY7jTCNzOd83rVaLsWPHOlzWrKwsq5Wd6Oho2RAQlSpVwjvvvAOtVgudTofevXvnaz0tLpGRkZg8eTKmT59uchg/dOgQAgICoFQqwfM8xowZY7rfXjb++usvWeXGVgp7HhcvXpS8p1mWxaxZs2zaVmmAKlIuzI0bN9CpUyeoVCpotVr07dvXLsHSTp48KfnQuLm52dxxc+rUqZLWhrCwMJu2U9oYNWqUpEMuwzC4efOmQ2TIs3a8eO3yXqw+Pj6SL3mO48ysUbm5uVi6dCnq1auHWrVqYcqUKUhJSTH9Lqc0KhQKp1gxN23aBB8fH2g0GqhUKtStWxd//fWXWZnmzZtb+JMIguDyy+UfPHgguxihefPmzhbPRFZWlsOv/caNG1G9enXodDrUrl0be/bscWj7L2I0GlGxYkVJa+/vv/9u8/Y6dOhgZg3P8/ujATstoYpUCUAURbu+RD766CNJX4S8/H+VK1fG3Llzi20Jy87Olh1RNWvWzEa9KZ2kpqaiatWqZh89juMwZMgQh7T/+PFj2SCy1apVAwB06dJF8j5yc3MzsyL07t3bTJlmGAZ16tQxOcz6+/tLtlO1alWH9PV5Dh8+LDm9FBISYlYuKSnJlJ9NpVKhXr16OHPmTKHays7OxqJFi9CgQQPUr18fCxYskHQizs3NxZIlS1C3bl3UqFEDkyZNKtbS/K5du1ooUxzH4bfffitynSWd1atXSw74nK1MnT9/Hl5eXiarsD3TuaSnp2P06NHw9PQ0WZ9p+jJpqCJFQZ8+fWSnZJ5/iYwYMaJY7dy7d0/W38fT09NGvSm9PHnyBOPHj0f16tXRsGFDrF692mGj9Lt378paLipUqADg2Ute6uOzYMECUz2XLl2SDS6Z5yy8c+dOyXq2bduGe/fu4eTJk3adYnoeucjdOp1OMqZbdna2pH9hWlpavlNSoijijTfeMOs3x3F47bXXLK6xlCIaGBhYZOtxcnIyOnXqZMq1xnEcZs+eXaS6SgOiKKJ8+fKS17127drOFg9ZWVn47bffsGrVKpuF2KAUD6pIuRA5OTkICwvDjh07Cp0LrTjkZY4vSJliGMYUN6co5OTkFDt5am5uLn799VeMHDkS06dPl3WcvnjxIsaMGYORI0fi8OHD1LG9mIiiiBo1alhctxeTN589exYdOnSAp6cnateubeG/tXz5clmH9EGDBpnK7d69G3Xq1AHLsqhduzZ27NiBAQMGgGEYuLm5gWEYDBo0yO7Jk/38/CRl1ev1iI6OLvD406dPIzg4GCqVCjqdDv3795e0Hh09elTyGeR53izcSVRUlKwi+nww36Jw+/ZtRERE2HyhSUkjMzNTdnpZp9M5WzyKC0IVKRchIiIC3t7eplxajgpzcO/ePVM6D7kP3PNTNNauEJNj5syZklMlf/75Z4HHZmRkoGnTpibnWIZhLD40APDjjz+aVgApFArwPI/+/fu/NMpUTk4Ojh07hqNHj9rUMfevv/6CIAgmyxTP8/Dz8ytUrKTdu3dLTu/qdLp8l1WPGTPGQoF43uHbXrz33nuSH1We5wuM1H79+nULR26dToe2bdtalP3+++8lfeAUCgUmT55sKpdfdPwXpxspRUMURdNimBe3GjVqOFs8igtCFSkXIDs7W/LB5Tiu0H4WhWHDhg1gWRYcx4FhGGi1WjRq1Ai1atWSjShsTQDI/BBFEYsXL0bFihWhVqtRu3Ztq1d0zZkzR3I07uPjY7JM3L17V3L6kOf5Ep2SJisrC4sWLULjxo3RvHlzrFq1StIaEx4ebvKh0Ov18PDwsGm4jNu3b2PKlCl4//33sWzZskJbL3JyclC+fHkL5YTneSQkJEgeI4qirG+dl5eXLboly+XLlyEIgtnzwHEcZsyYUeCxn3/+uWQwT5ZlERUVZVZWTkHiOA5Lly41ldu3b5+sIvq8wkUpHgsWLLC4HizL4uuvv8Z//vMfvPbaawgNDbV5IExnkZOT89IMNO0BVaRcgP3790tOeSmVSptlM3+Rhw8fSiocLMti69atFlYjhmHQvXt3u8hiLQ0aNJD8mAqCgAsXLgB45iQq9UFSKBRWJ+l1NYxGI9q2bWt2TXiex7vvvmtWLjExUXIpO8/zDvMpsobY2FjUqVMHOp0OOp0O5cqVM+WDk8JoNOabn9LeXLx4EV26dIGnpycCAwPxyy+/WHVchw4dZC27L66ySk5OloznZDAYzHyxcnJy4OvrWyhFtLDExMRg/fr1OHbs2Ev7cRVFEQsXLoS3tzcUCgUqVKiAzp07WwRFbdWqlSnUxMmTJ9G1a1fUqFED77//PmJiYpzci2dcuXIFp06dQkZGhsVve/bsgb+/PxQKBdzd3TF16lS7hNcp7VBFygWQy2tFCLH4WNoKuRGwSqXC119/jYMHD8Lf3x9qtRoMw+Djjz92etLZpk2bSp4jjuNMI/yNGzdKjthVKhW++OILh8l67do1zJ8/H0uWLCl2SoX9+/dL3h8cxyEiIsJUbvny5bKpRJ53+HY2ly9fRsWKFU3Rs3U6Hb7//vt8j6lfv77ktXfl1Z6TJk2SHKzkBfJ8kYiICPj5+ZnOS+XKlSXzKf7777+oX78+GIYBx3Hw9fVFeHh4seXNzc1F7969wbIs9Ho9BEFAQEBAkQO4lgZEUURWVhbi4uJkLd3bt2/H77//bjbQUalUEAQBFy9edJrsN2/eRHBwMDiOg8FggF6vx5o1a0y/S6Xv4jjOKbHPSjpUkXIi169fR/v27SV9I/Ie0s2bN9ulbTmnX6VSidGjRwN49hJ5+vRpof1scnNz7TKSXblypaTM1apVM7WXnJwsq0w4KknylClTwDCM6UPHsiw2bdpU5PryS7syd+5cnDhxAv369UONGjVkc5a9mFzYWRiNRlSuXNnCwsRxXL5TrydOnADHcaZnJS/y9vOKpKtx7949eHh4mF0TlmXRq1cv2WNEUURUVBQuXbpU4DMUHx+PmJgYmz1r8+bNs3i+1Gq1zaNml0TkLN2EPPNNq1SpkuRz16lTJ6fIK4oiAgICJOO+5bmLtGnTRnZg6uxBc0mDKlJOIjU11SJy+YtKVJs2beyW2fvOnTuSIyyO4/D3338Xqc5z586hSZMmUCqVYFkWn3zyiU0fSKPRiD59+rMYxEAAACAASURBVJh8uvR6Pby9vS0ykuclnRUEwWTxcNRy7nPnzslGBC5qILt58+ZJXitBENC/f39TxG2p+yjvmtojSn1RyHNYl5KzoNQTUVFR6N+/P+rWrYuQkBBTwt7ikJSUhHXr1mH58uXF9v+T4tq1a+jRowcEQUC5cuUwefJkl43MXb16dVmF/WUOwpieno7JkydL+mdqNBp8+umnsjHW3NzcnCKzXK48pVKJAQMGAIBsiAee52lYhUJCFSknERoaKvlB0Wg0aNq0KTZu3Gg3JSqPJUuWmDKJ5yk/X375ZZHqiouLs5hSYxgGb775po2lfuazsmjRImzbtk02dk5ycjLWr1+P0NBQ3L592+YyyDF69GhJ5VgQBDOzemG4f/++5Esxb3WnnAKVt3l4eLiMr0tYWJhsCIz27ds7VJY9e/aYFO485XzmzJkOlcGVkIqanfcc28r/qqSxfft2CIIge8+yLIt//vlH9jn09/d3itx79+6V9LkjhOC1114DIO/Dx/O8zTNalHaoImVD0tLSkJqaalXZ/KZrHBkMLzY2FlOnTsU333yDc+fOFbmeUaNGya5Qunr1qg0ldm0+//xz2eXyK1euLHK9R44cgY+PDwRBgCAIqFy5Mn788UfZF/yL18AW1htbkJKSImmx4zgOS5YscZgcycnJsnIU5zkoyYwYMULyGa5atarLKOKO5MaNG5JWKEKIKbJ43pT9sGHDJMNzOCvRtlyyc5ZlMW/ePADPrMNSPlJ09WfhoYqUDYiPj8drr70GtVoNtVqNFi1aIDY2FgkJCViwYAFmz55tsYJDzsFcEAT88ccfTulHcWjfvr2saXv37t3OFs9hnDp1SvIDzTAM7t+/X6y6c3Nzce7cOURGRkIURZw4cUI2LMCL18CVQj8sW7YMHMeZFE6e59GgQQPJVUX2Qm5RglKpxKhRoxwmhyvx8OFDVK5c2XT/arVa8DzvMtPCjmbKlCmSU3Ycx2HChAlmbguZmZno37+/KTo8y7KYNGmSQxXQa9eu4cSJE6aAr1OmTDGzZDMMg2rVqpkFhD1y5AgaNmwIjUaDihUrYtGiRS+l0lxcqCJVTLKysuDr62vm1KdUKiEIgsnhWKvVgmVZM4ffzMxMvPLKK2YjQK1Wi7p165bI5adjx46VfOnIrVAqzXz++ecmRUGj0YBlWbNYQLbCaDSiUqVK+fpH5V2DwgTNdAQRERH46KOP0K1bN6xcudImUwkxMTE4d+6cVVPia9askRzIlOQwGbYgJSUFixYtQq9evTB+/HiHJcR2RT799FNZC+9PP/0kecyjR48QGRlploTb3jx69AgtWrQAy7ImJS4vkfiePXvQoUMHNGjQANOmTUNSUpLD5HqZoIpUMdm+fbtVVgGpaYMHDx7ggw8+gF6vh5ubG4YOHerwGz0zMxNLly7F66+/jnfffdciSri1JCQkwM3NzeyjzrIsevbsme9xRqMR165dK9Bak5iYiDVr1mDZsmV2cQq2NWfPnsU333yDL774Am+//TYCAgLQrVs3nDp1yqbtREdHo1KlSqYAnHmK/PNTih988AHGjh2Lb775xqq0JiWNa9euITAwEBzHmYKQ7tq1K99j5PI+SkXKd1WePn1aagJCuiJyYUdczV2hbdu2FlOyPM8X+AzIkV/cKYo0VJEqJj/88IOkX4HUplQqMWbMGIfLKEdWVhYaN25skSh12rRpRaovKioKHTp0gFarhYeHB77++ut8X/T79+9H+fLlwXEcdDod2rRpIxlzaffu3SXSKTgqKgp6vd5krVQoFOA4ziIYY3ExGo04ceIE9uzZg+joaAwfPhwVK1aEn58fmjRpYlrVp1arXS6mVHHJzc1FpUqVLPzSOI4r8GO3aNEisCwLtVptSiX04YcfuvzURnh4OGrWrAm1Wg2dTocPPvjAat9MivUYjUZ06tTJIgjn87klnc2tW7dkHd0rV65cKHeC+Ph4s7hTgiBg9erVdpS+9EAVqWISFhYmu5xbSpHKi9HkCqxZs0ZyNRjDMHaPhH3lyhXJmDV16tQx+5AlJSXJhhNwVFyootKlSxfJaTdfX1+7fawzMjLQsWNHsCwr6yjLMEypCbJ48OBBSYuwRqOx6lmLiorCuHHj8NlnnyE8PNzllajo6GjJrAP2WB1LeRZJfv369ejUqRO6d++O3bt3u9Q9cuHCBdkZEYVCAW9vb6umZ0VRRK1atSTjThU1HM7LBFWkionRaESDBg1MiVzzXuJSH9AXI1G/SG5uLnbv3o1x48bhp59+wpMnT+wqe48ePSQfQIPBgG3bttm17REjRkCtVktOrTyfX3D9+vWSiqpSqSxyqAZHYDQaZWPLaLVau/ksjR07tsCQCDzPY/ny5XZp39HklxUgv8CXJZWPP/5YMoAvy7L4999/nS1ekbl9+za6dOli6hvP8/j2228l80lS/kdmZma+K3dVKhU++OCDAus5e/asbGqt/v3721zuqKgofPTRR2jevDlGjx7t0BA19iA/RUpJKAWiVCpJeHg4+eSTT0iZMmWIp6cn+eijj8i8efMIwzBEq9USlUpFWJYln376KWnYsKFkPRkZGaR58+akd+/eZPr06eSrr74ifn5+5OzZs3aTvUyZMkSptLzMAIiHh4fd2iWEkOvXr5Pc3FyL/SqViiQkJJj+z8nJeabVS8iYmZlpVxmLw6pVq0hOTo7kb0qlkgiCYJd2Q0NDrTovarXaLu07mubNm0veRzzPk06dOjlBIvsSFRVFjEajxX6tVktu3LjhBImKT2pqKmnQoAHZs2ePqW9paWlkypQpZNCgQU6WzrXR6XTkxx9/JCzLSv5uNBrJ/v37C6znwYMHku8EAOT27dvFlvN5/vzzT/Lqq6+S1atXk5MnT5IFCxaQoKAgcuzYMTJ27FjSvn178sUXX5CbN2/atF2nIadhuerm7DhSeYiiiNOnT2PMmDHo2bMnJkyYYBF9+0WmTp0qORXzfPoTW3P27FnJabNy5crZfSQ4e/Zsyf7qdDozZ/L8nILzS3TrbBo2bCg7SnzvvfeKVXdcXBx69OgBlmXh7u6OUaNGmZZiWzPNXJwo667IiBEjLJZ5BwUFlUpn2dGjR8uuji2p07WLFy+WtE6T/7felnRrhSPYv3+/7Ord6tWrY8WKFejevTuGDh2KyMhIi+MfP34sG3dqzpw5NpNTFEX4+/tLWr7UarXp3tZoNBAEocTEdCN0as+2GI1G9OrVCxzHQa1Wm5ykC0oqWrNmTdmPnj1N9itWrDAtm9Xr9fD19cWlS5fs1l4eSUlJ8PX1NfsocByHoUOHWpSVcgoeOHCgS/kqvEhgYKCsqb04L4fExESUKVPGzLmaYRhTVPB3331XNt8ez/NgWdbu07aORhRFbNq0CS1btkS9evUwffr0Qi8/F0UR8+bNQ7ly5aBWq9GgQQMcPXrUThIXnYSEBLi7u5t9NDmOw8CBA50tWpEJCQnJV+k/ePCgs0UsEfTo0cNCyWZZ1pQgPO/9w7IsfvnlF4vjv/vuuwLjThWXxMREqxdnEULQtGlTm7VtT6giZWM2bNggOdfs5eWVb3wbuQ8vy7KIi4uzq8wpKSnYv38/Tp486dAYVg8ePMBnn30GPz8/1K1bFytWrJBVjqKiojB+/HiMGjUKx44dc2klCnj2UpIa4ZUrV65Y53ju3Ln5RuS+efMmypYtayrDMAwEQcCECROwYsUKl4sn5SpMnDhRMsrz8/56rsLVq1fRrVs3GAwG+Pr6YtasWSXal2jmzJmyOUe1Wi3N+2YliYmJaNWqFViWhZubG3Q6nSm+1IvnVa/XS1ps9+zZgzfeeAMNGzbE1KlTbR6OJzMz08yfuKBNqVSWiHubKlI2Ri5/kV6vx4kTJ2SPk5rqUigUCAwMdKD0FFuRkpKC4OBg01SbTqcDz/PFjjDep08fyftLEASsXbsWwLMX6ty5c9GrVy989913kiElKP8jLS1NUjlVKBTo3LmzTdvKyclBfHw80tLSbFpvSSUhIQGVK1eWvKcVCgW6du1qVT1Go9HlB1eO4sqVKzhw4ADu3r2LZs2aSZ5bg8HgtIj177//vtXKFMuyJeK65qdIUWfzIvDsnFpiNBrJpUuXyNWrV8mhQ4fIgwcPzH4fOXIkadmyJeF5nmg0GqLX64mnpyfZunWrI8Sm2BhBEMiZM2fIsmXLyMCBA8m4cePIlStXSPv27YtVb506dQjDMBb7AZDq1asTQghxd3cno0aNIps3byYTJ04kPj4+xWqztHP79m3ZRRcXL160WTtLliwhZcqUIQEBAcTb25uMGDFCdkGCLcjKyiLXrl0jKSkpdmujuPTv31/Wmbl///5ky5Yt+R5/6NAhEhgYSFQqFfHw8CDffvutpDP+y0TNmjVJx44dSbly5Yi7u7tkGaPRSPR6vYMle8aSJUtI27ZtCcuyxM3Njeh0OlKvXj0Lh3mGYcjAgQOJQqFwipw2Q07DctXNFSxSv/zyi+wy0jzztSAI0Ol0GD58uNk0jyiKOH78OH744Qds2LDBLJfTy0RqaiouX76M5ORkZ4tiF1JSUhAaGooJEyZg+/btyM7OtvrYBw8eWESQ12q1aNSoUYkYubkiqampsjG3OnbsaJM2tm3bJjl1+Omnn9qk/heZPXu2KcE1wzAYMmRIoe4zR5CcnCwbIsTX17fA40+fPi17Ts+dO4dPP/0UH3/8Mf7444+X9tnYs2ePxfdIoVCgevXqTj8n//77Lw4dOoR79+4hKysLb7/9NhiGgZubG1iWRadOnUrMN5DQqT3bkpubi549e4Lnedl5/+cfermcTS8joihi/PjxYFkWer0eDMNg+PDhJWKO3FpiYmLg7e1terkJgoDAwEAkJiZaXUdUVBRatGgBpVIJrVaLvn37Fur4iIgIhIaG4ujRo05/mboKo0ePlvwonzx50ib1161bV3bqwtarC9evX2/RF5ZlXSoiN/BspZicIuXj41Pg8XIBb/Mi+D+fFLtPnz4v7b0+ceJEMAxjSiNVuXLlYqe4EUURV69exT///GNTv9rr169jz549iI2NtVmdjoAqUnYgz7LUvHnzApWp6tWrO1tcl2H+/PmSH7OJEycWqp5Lly6hQ4cOYFkWPj4++O6776xKZOsImjZtavHy12q1RbJMZGdnF0rJTE9PR9u2bcHzPHiehyAIqFOnDnVAxzMfmylTpsDDwwOEEAQEBODAgQM2q9/Ly0vy+WcYBnfv3rVZOwBQq1YtWaXNFsmhn+fOnTs4ffp0kZ2SpRRMrVaL4cOHF3isn5+fVX42ecpUWFhYkWQsDdy9exfbt2/HkSNHiq34REdHIyAgABzHgWVZCIKAIUOGvNQJrqkiZUf69+9f4APu7e3tbDFdhgoVKkieo7wVJlu2bMH8+fPx119/yY4u4+LioNfrLZaHh4SEOLg3liQlJcku/S1btqzd2x89erTFSkKNRoO3337b7m2XJOyxcvWNN96Qff6tUYYzMzMxduxYeHl5gWVZdOvWDdeuXZMsm6cMvrjpdDo8fPjQJv1JS0tD9+7dodPpYDAYwDAMxo8fX2irT2RkpGkqJ89CW61aNauU+//85z+ysZOktk8++aSo3aX8P1lZWShbtqzkeWcYBhs3bnS2iE6BKlJ2ZPPmzfkGSFQqlejbt6+zxXQZ8lvJ4e3tDb1eb1r91qlTJ0mfj08//VRSWXGFgIVPnz6VVaTKlStn9/blrCIajcbl/GdKA3/++Se6d++OZs2aYfjw4abk0c8r+KtWrbKqri5dupj5cSmVSnh6ekrmxOzYsaPsPWYrJXHAgAEWSjnP8wgNDS10XY8ePcK8efPQoUMHeHt7gxCCSpUqFZgw9/z58xYWbK1WK/mMqVQql8pzWlL59ddfZXP75Vk9S6tva35QRcqOZGdno3nz5pJLq3U6HTw9PWmMlOdo2rSp5MOp1WotRkAcx2H+/PlW1+Hm5obDhw87oVfmtG7d2mK6V6fT4auvvrJ723IvQJVKVSqjgDuThQsXmj33DMOgQoUK6NixI3x8fNC4cWPs3r3bqrqio6MlneEZhsHUqVMtyp8/fx48z1sobRs2bLBJ39LS0mQHPQEBAUWqc8uWLZLT+itXrsz3uOPHj6NRo0bQaDTw8fHBtGnTZJOcX7x4sUiyUf7Hzz//LHl+8zZH5Gl1RagiZWcyMzOxdOlStGvXDm3btkWHDh3QokULjB071ua+ESWdU6dOWYzaGYaRdUgNCgqyqGPQoEGSSV0ZhnGJOfwbN26gfPny0Ov1UKvVEAQBjRo1Qmpqqt3b7t27t8W5USgUJSZ6cEkhJSVFUvFhWRbTp083lUtOTsayZcvw7bff4sCBA7LWoq1bt8ompn3rrbckj7l48SJ69uwJX19ftG7d2qbRwe/duyerSHl5eRWpTqm0IYQQlC9fvtB1/fHHH+B5Hnq93rRqccGCBUWSi2LOP//8I7vCNU+R2rlzp7PFdDhUkaK4FOfPn0ePHj3wyiuvoHPnzpLLxvO2GjVqWBx/5coVi+W+DMOge/fuTuiNNJmZmdiyZQtmzZqFsLAwh0WTT0hIQLly5UznMy9XnyNSAr1MhIeHw83NTfKezVNaz507Bzc3N9O9qtFo4OHhgR9++MEiJUdkZKSsVXvChAkO758oiqhYsaKFPEqlssj+dnK59gghRVq1m5KSgi1btmDt2rW4f/9+kWSiSNO3b1/JrA2EPJvedcSg0NWgipSDuXDhAjZu3IgLFy44W5QSgSiKeOWVVyQtTN99953kMSdOnECdOnWgVCrBsiyGDRtWYuKR5PHw4UNJ/5fi8vTpU/z0008YMGAAZs2aZTPnY8r/uHTpkqzy3717d4iiiOrVq0v+rtFoUKVKFYvr0qpVKwsrkF6vd1pC399//93MeqxWq2EwGBATE1Ok+mxpkXqR27dv0+j+NsRoNCI0NBQ+Pj5QKBSm/H0cx1k9XV3aoIqUg0hNTUWbNm3AcRz0ej04jkPbtm1fSu29sJw+fRp6vd5sZU/Dhg0LTLORmZnp0NyBtiAmJgaNGjWCVquFVqtF/fr1cfnyZWeLRSkkwcHBFtOoHMfhyJEjuH79er7TI1qtFl9++aVZfU+fPsUHH3wAnU4HpVKJJk2a4Pz5807q3TNOnz6NHj16oE6dOhg6dGix/D2L6iOVHxcuXECtWrXAMAx0Oh0aNGhQ7PhJFHMuX76Mjz/+GP7+/qhSpQpCQkJw/fp1Z4vlcKgi5SCGDBli4eujVqsxbNgwZ4tWInj06BHmz5+PL774Ajt37nSZuFC2JD09HWXKlDHzEVMoFPD09ERKSoqzxSv1GI1GLFq0CDVq1ICPjw9CQkJw69atItV169YtBAcHg+M4GAwGsCyLhQsXAnjmJ5efIkUIgZ+fn6yMpXWF5ebNm/HKK69AoVBYtWovPxITEy2mVxUKBcqWLWvzWFovM0uWLDFTgFUqFdzc3F46ZYoqUg5C7sWp0WicLRrFRfjll18kw2UolUqXi0pdGhkyZIjFR6FMmTLFmv68dOkSwsPDLRThgICAfBWp4ODg4nbnpWbx4sWS06t6vR5btmxxtnilgszMTMmVwCqVCh9++KGzxXMo+SlSNGmxDcnMzJTcn5OTQ1JTUx0sDcUViY+PJxkZGRb7RVEkP//8M9m4caMTpHI9EhMTyYEDB8jZs2efjfhswO3bt8nq1atJenq6aZ/RaCRPnjwhixcvLnK9QUFBpHXr1kQQBLP9W7ZsIZ6enpLJkjmOIyNHjixymxRC4uLizK5lHllZWeTWrVtOkKj0cePGDcnnz2g0kvDwcCdI5JpQRcqGvJjZOg+VSkViY2OLXf+dO3fIu+++SxiGIYIgkIEDB5KkpCRCyDPL4vHjx8m6devIpUuXit0WxT40atRI9j7JyckhY8eOdbBE1pGRkUHi4+NJdna23duaMWMGqVChAunVqxdp06YNCQwMJPHx8cWu98KFC5L7jUYjWbduXbHrf5E6deqQ+Ph4Mm/ePFK2bFnCsiwxGAyEYRjSr18/MnDgQJu3+TLRrFkzC+WVEEI0Gg1p3LixEyQqfZQpU4bk5ORI/ubr62vTtgCQdevWkbp16xJfX18ycODAkqMQy5mqXHVz5am9tm3byk7tFXd5blpaGnx8fMycW7VaLerUqYN79+4hKCjIlAmeZVl07doVWVlZNuoZxVYYjUY0btxYdrpHoVC4lH9Mbm4uvvjiC9OKHb1ej9mzZ9stOez+/fstVq4plUrUrl272HX/888/suedZVkbSC+PKIo4deoUtm3bhri4OLu2VRqIjIzEyJEj0bdvX2zdulXSXzInJwd169Y1W6bPsizatm1bopIXp6enY9myZejevTtGjBiBqKgoZ4tkxttvv23xTHIch71799q0nbFjx5qFtVGpVPDy8nKZWIyE+kg5hhMnTlj4Sel0OvTq1atY9V6+fFk2R50gCGjSpIlFjBaWZTFlyhQb9cz2iKL40ip6aWlpcHd3l7yeXl5exf4IPHnyBKtWrcKiRYvw77//Fquu8ePHW/ih8DxfLCfh/AgODpY8LzqdziYfmPwUWIr9EEUR27ZtQ4cOHdCqVSv8/PPPss//8uXLwbKsadDI8zzatm0rOcBISUnBhAkT4Ofnh2rVqmHq1KlOcTQ/ePAgWrduDV9fX/To0cPqCOspKSmoVauW6RnLCzOwdetWO0tsPampqXjnnXeg0+kgCAIMBgOWLFli0zYeP34sGbdKp9NhzJgxNm2rqFBFyoHs2LEDFSpUgE6nA8MwCAkJKVZ8o4yMDJQpU0b2A5C3VFrqN19fXxv2zDYYjUZMnjwZBoMBCoUCVatWxa5du5wtllX88ccf6NKlC1599VVMnToVSUlJRa5r7dq1kkvB58yZU+Q6d+3aZaZwazQaMAyDSZMmFam+3Nxc2TyS/v7+kseIooiHDx8WKR2NKIqyQRuVSiWOHz9epH48T82aNSXrDwwMLHbd9iQ5ORm//fYb9u/fXyIHIMOGDTOzNnAch1atWlkE4kxOTpZctMPzPH755RcnSZ8/mzZtMnuWFQoFeJ7HuXPnCjx2+vTpkv11c3Nzuev86NEjREdH20WuI0eOyAa4bdKkic3bKwpUkXIwoiji3r17NgkQuXnz5nwTSAqCIJkuJc+64Uhu3bqF7du349SpU7JWla+++kpSgThy5IhDZbWGw4cPo3PnzggODkbr1q3NXngMw6Bq1arFSt75888/w9vbGxqNBu7u7pg1a5bFebt06RK+/vprfPbZZwgPD5c9r2FhYbKrRjmOw8mTJwst39OnT2UVG0EQLMr/9ttv8PX1NQ0iPv7440IpVGlpaZIZ5/M2uecpJiYGvXr1Qrly5VCvXj1s3rxZto0DBw5I3n8HDhywWk5Hs2bNGrAsC4PBAIPBAHd3dxw7dszZYlnN1atXJe9NQRDw66+/mpXdvXt3oVPlOBNRFFGuXDlJeTt06FDg8Q0aNJA8Vq/X4++//3ZADxyHKIpYt24dmjVrhrp162LGjBmmGIvXrl2TvEeUSiX69u3rZMmfQRWpEsy8efNkc14plUrUrFkTQUFBFr+p1WqEhIQ4REZRFPHJJ59Ap9PBYDBAEAQEBAQgISHBrFx6errsx75NmzYOkdVaVqxYkW/iTkKeTZ/OmjWrWO0YjUYkJydLBhVduHAhWJaFWq02jXJDQkIklakmTZrIyqlQKDB48OBCyyaXJoQQgpYtW5qVzcuh+HwZhmHQu3fvQrUnN+Xp4+Mjecy///4Lg8FgZpXleR4zZsyQbefo0aNo3bo1ypYtizZt2uDo0aNWy+hoYmJiJJ8ZjuNKTKDfZcuWyT5LQ4YMMSt7+PBhyYGjQqFAv379nNQDeR4/fiybJ9Td3b3A49u1ayc7+ImOjnZADxzHoEGDzKySLMsiODjYZOFq166dxbnkOA5nz551suTPoIpUCeb06dMWeeWe/5g9fPgQERER0Ov1JoWL4zhUqFDBYU56a9assZBRpVJZJMq9ceOGbF9skSbCVsjFTpHaWrVqZRcZ7t69K+kzwPM8/vzzT4vyHh4e+cpZVKV669atkhacU6dOmZV76623JK1JOp2uUGlw5syZI+lnKBcXKCQkRNIiy/N8gVHxHUFSUhKmTJmCevXqoV27dtixY0ehfODGjRsnaxUsKXF8tm/fLvk8abVafPPNN2Zlc3JyJF0ZOI5DeHi4k3ogn0EhKytLdnAYEBBQYL3bt2+3eCcqlUqXn2ouLLGxsbLvs7wp26SkJHTr1g06nQ4cx8HHx8fCYulMqCJVghFFEV26dDH7mDEMg4YNG5qtZLlz5w4mT56Mvn37YuHChRZJUe1Jo0aNJF8kDMOYWaUyMzNlfW46duzoMHkLIjIy0ipFSqFQFHshgRyrV6+WVDoVCgWGDx9uUb5Zs2aycvI8X6ypq7CwMLRo0QI+Pj544403cObMGYsycsEnDQZDodKciKKIOXPmwNPTEyqVCuXLl8/XsV0un51er7fa4ddepKSkwN/f3+wDwvM8xo0bZ3Udw4YNk72uGo3GwurrimRkZMDT09NCfpZlJVPOnD17Fl5eXjAYDNDr9WAYBlOnTnW84ACOHz+O2rVrm+X0fHG6+rPPPpMcbFjj0yWKIkaPHg2dTge9Xg+9Xo8qVaoUe5GIq7F69WrZd/+AAQPMyiYmJiIuLs7lUn9RRaqEk52djQULFqB27doICAjAtGnTXGK0nYfcx4zneQvz9NSpUy0UBI7jcPr0aSdJb8mdO3dkM5+/KPeJEyfsIsOGDRsklTmlUokvvvjCovzhw4clp0+0Wi369+9v9+XgcpYhlmWLpNSLooj09PQC5e7YsaPktSmsJcweLFiwQPKaMAxjdYLdffv2yVqkWJbFzz//bOde2Ibz58+jYsWKplVfbm5u+S4yycrKwp49e7BhwwanLX+Pjo62uH4sy6JHpTWQ+wAAIABJREFUjx5m5bKzszF06FAwDGMKQVPYKf+EhARs3boV4eHhLqdA2IJ9+/bJWiXHjx/vbPGsgipSFLsyduxYST+usmXLWqzKEUURS5YsQaVKlaDT6fDqq6+6pI/K66+/bjFfr1AoTH5gPM9j6dKldms/OTlZ8iPMcZyshWffvn0IDAyEUqmEIAh4/fXXcfToUYfE1ImNjYVerzeb3uN5vsgrBq3lzz//lPTNevfdd+3arjW8+eabsla63377zao6jEZjvgOV0NBQO/fCdhiNRpw5cwbHjx93uRVpUnz00UeSgwOGYRAfH29R/unTp7h27RrN8ydBTk4OKlSoYDH9z3FcicnZRxUpil15/PgxXnnlFdMHTa1Wg+M47Nmzx9miFZknT56gXbt2YBgGBoMBHMdh7ty5uHz5Mo4fP+4Qi+CePXvAcRwEQQDHcWAYBj/88IPd2y0qUVFReOutt+Dh4YEaNWogNDTUIUrc+vXr4e3tDZZlodPp0L9/f5ew2A4aNEjyQywIAv766y+r67lw4YKkQzPDMMXKEUjJH7nAuW5ubpJ+ipT8uXr1qilmliAI8Pb2xr59+5wtltXkp0gpnv1ecmjUqBEiIiKcLQblBVJTU8mqVatIWFgY8fPzI8OHDyc1a9Z0tljFJj4+nty/f58EBgYSnucd3n5ycjLZtWsXyczMJJ06dSIVK1Z0uAwlAaPRSO7cuUM8PDwk04Y4g8jISNKsWTOz3IpKpZJUqVKFREdHE51OZ3Vds2fPJpMmTSIKhYIoFAoCgKxcuZL07t3bHqJTCCEjR44kS5cutUiRotPpSFxcHClXrpyTJCu5ACCxsbEkPT2d1KlTh6hUKmeLZDUKheIsgEaSv1FFikIp2WRkZJAbN26Q8uXLEw8PD4vfz549S2bNmkWuXbtGWrVqRUaPHm3zPFkUabZs2UIGDx5MRFEkmZmZRBRFolariUqlIsOGDSMzZswgarXaqrri4+PJ7t27iUajId27dydlypSxs/T/AwA5efIk2bp1K1Gr1aRfv36kfv36DmvfGcTFxZHg4GCSmppK8r6THMeR3r17k9DQULu3n5qaSlavXk32799PKlWqRIYPH05q165t93Yp0uSnSDl9qq6wG53ao1D+x4wZM8DzvCn8Rf/+/c18NHbt2gWO40y+CRqNBh4eHqVuVVBRMRqNmD17Nnx8fKBWq9GgQQOb++xlZWVh9uzZFgsYOI6TXDjgiowYMcJ0H+WtYHPWSjpHcunSJXTo0AEsy6JcuXKYNm2ahd+nPUhKSoK/v79Z6hiO47Bt27YCj7V2oQalcBDqI0VxFTIzMzFr1iwEBAQgICAAM2bMKFI6EVcgNTUVq1evxuTJk7Fnzx6HvGCfZ82aNRa+MyzL4uOPPwbwTEmQytGoVCrRp08fh8rqqnz99deSS9cjIiJs2k79+vVlV366unPymTNnZFcflhRH4ZLGt99+K7ly2MPDQzapuSiKmD17Njw8PEyhQ9asWeNgyUsvVJGiuASiKKJNmzZmAexYlkWLFi1K3JLf6OhoeHl5QRAEKBQKCIKABg0aICUlxSHtZ2dny0aLZhgG6enpuH37tmwYh7Jly1rUmZOT81KNYlNTUyWDKSoUCpunI/Hy8pK9Vq6S3V6O8ePHS+bzZBgGCxcudLZ4pZI6depI3i96vV42h98PP/wgOSiwxorlCC5evIhWrVqZVhV/9tlnJWoQnZ8ipSzkNCGFUmSOHDlCzp49a+Z8m5GRQSIjI8mhQ4ecKFnhef/998mTJ09M/hOpqank8uXL5Pvvv3dI+1u2bCHp6emSvwEgycnJxGAwPBstSeDl5WX6OyIigjRq1IhotVrCMAwJCAggr776Khk5ciS5efOmXeR3BRISEiSdXQGQixcv2qyNuXPnEnd3d8nfOY5zqK9TUWAYRvI8KZXKQjnMU6zHzc1Ncn9ubq7kb6IokmnTplm8E9LT08mkSZPsImNhuHXrFmnRogU5duwYEUWRpKamkqVLl5J33nnH2aLZBjkNy1U3apEquXz//feSI1uFQoHJkyc7WzyrefjwoWx+rUqVKjlEhu7du0u2T/5/eXaeha9Xr14WMb6ejz90/fp12YjDGo0GBoMBUVFRDumTo0lJSZFN79GpU6di179161ZTSAap9Dkcx5likZ07dw4jRozAhx9+iF27drmUhTY2NlbyPLEsS8Mv2ImtW7dKpt2qX7++ZPmUlBTZwK0cxzlYeku++uoryXcmy7KIjY11tnhWQahFiuIKVKhQgXAcZ7Gf4zi6rL+QeHh4EIVCIfnbyJEjiVL57NEODQ0l7du3JwzDEDc3N8IwDBk+fDgJCQkhhBDy448/kqysLMl6cnJySEpKCvnyyy/t0wknIwgCGTp0qMU9yXEc+e9//2t1PQCIKIpm+1JSUsgHH3xAMjIySFZWlskyqFQqiSAIJDg4mKxbt44MHjyYzJ8/n7Rs2ZIsXryYrF69mvTu3Zv07NnTok5n4e/vT+bNm0cYhiE8zxNBEAjLsmTdunXE29vb2eI5lcOHD5O3336btG/fnvz0009m1vbi8Pbbb5Nhw4YRnU5HDAYDEQSBVK1alfz666+S5XmeN7MyP09AQIBNZCoO586dI9nZ2Rb7tVotuXLlihMksjFyGparbtQiVXJJSUmRTK7r5ubm0NyAtqBRo0YWVgaGYTBhwgSHtH/q1ClJHyl3d3ezHIx53Lx5E8eOHcOTJ0/M9stlnycuNqK1F7m5uZgyZYrpvgwKCkJYWJhVx6ampmLw4MFgGAZKpRItWrQw5ffbsWMHDAaD5Pl8PrfY/fv3Jf3YBEHIN4WKM7h37x5WrlyJtWvXWtxHLyPTp083ewY5jkO9evVs6vdz584d7Ny5E6dOnSrQf3HlypWSPlJ//PGHqa5evXqBZVno9XoMHjwYSUlJNpM1P8aMGVOqLVJOV4wKu1FFyjUQRdFi9UhGRgZWr16NAQMGYNKkSbh586bFcRcvXkTNmjXBsixYlkWNGjUKldQWANLT07Fjxw6sW7cOd+7ckS2XlZWFc+fO2WVlUUxMDMqUKQNBEEzOk6+++ipSU1Nt3pYcc+fOBcMwpmSnZcqUkXVElUPO5P78VqFCBTv1wLUo7HRa+/btLaZN9Xo9bt++jZ07d8oqUh9++KGpDrmcii8qXBTX4uHDh5IKMM/zWLFihdPk2rhxI2rUqAGWZVG/fn2TEpWeng5fX1+z6T+tVot69eo5ZIHJrVu3LJ4HhmFsvqjDnlBFimIzcnNzMWHCBFNeterVq2P//v1ITk5GQECAaV5fq9WC53kcPnxYsp4bN27g+vXrhX6Ijx8/Djc3NxgMBgiCAIZhMGPGDIty69evh5ubG/R6PViWRePGjfNVuopCeno61q1bh6lTp+LAgQNO8Wt59OgRtm/fjrCwMElLVEEkJCTAYDBI+vDkjWilzu/Lzj///CNpEdTpdJg4cSJSUlIsfFzyPrSHDh0y1fPrr79KKlIqlQojRoxwYg8p+fHbb7/JKspdunRxtngWrFq1SvJ+FATB7H60JxcvXkSbNm2gUqmg1+sxatQolw/98TxUkaLYjLzAfC+aZ0NCQiQTF1esWNFmI57MzEy4u7tLfuyfz10WERFhIaNKpUJwcPBLtbzfWi5fvow33ngDWq0WGo0GarUabm5u0Ol0GDRokMPjY5UEtm3bVuCHNC8YKsdx0Gg0YFkWn376qdk9mJ6eLlkPx3E4e/ass7pHKYCjR49KKsBKpRIDBw50tngWfPbZZ5L3qk6nw48//mhR/tKlSzh48CAeP37sBGldk/wUKetyE1Ao5JkD7YoVK0hmZqbZ/oyMDLJ582ZJp+WkpCQSGxtLatSoUez2Dx48KOmAm5mZSUJDQ0mTJk0IIc8cqF+U0Wg0kn///ZdcvHiR1K1bt9iylCZq1apF9u/fb/o/Pj6eXL9+ndSqVYv4+Pg4UTLXJSgoyCIHGyHPQgU0avQsi0TXrl1JXFwc2bZtG0lLSyOdOnUiQUFBZuVZliW7d+8mXbt2Nb2Uc3NzydSpU0mDBg0c0hdK4WnRogVxd3c3Sx9DyLPrP2zYMCdKJk1QUBDheZ6kpaWZ7ddqtWY5UR88eEA6d+5MoqOjiUajIVlZWWTs2LHk22+/tZts8fHxZOPGjSQtLY107dqVNG7c2G5t2Q05DctVN1ezSOXk5ODcuXOIjo4u9daO6OhoWX8OjUYjuZ9hGMTHx9uk/S1btsi2/3yk7rZt20qWcXNzw/79+20iC4XSqVMnMz8ZhUIBd3d33Lt3r9B1paenY+fOnVi/fj3u379vB2kdS3x8PFatWoXt27cjPT3d2eLYhStXrsDPzw+CIMBgMIDjOCxfvtysjCiK+Pvvv7Fq1SqcOHHCad+IlJQUlC1b1iz8jEajQc2aNc1cElq2bGkRRoHneWzfvh0AkJaWhqysLJvJtWHDBrAsC61WC4VCAZ7n8dFHH7nkt5TQqT37sHfvXnh5eUGv14PjOAQEBCAmJsbZYtmNtLQ02UjQdevWtZhOUyqVaNCggVkdSUlJWLx4MUaNGoUNGzYUao780aNHsiucdu7caSo3c+ZMSTkZhsGjR49sdj4oLzcZGRn48ssv4ebmBq1WizfeeKNUP//WMmnSJDAMY8oB6ebmhlOnTjlbLLuQpygdPHjQIqtBamoqWrVqBZ7nTVvDhg2RmJjoFFmvX7+ODh3+j73zDovi+v7/XbZM29kVpCgq9t4LRmOJSiyJRmOLvbdo/MbYosYSe2KLMfbYYy8YOzai2LvRiAU7CgoIaKTDzvv3Rz7sz3VnYPsuuK/n4Xl09869Z2Zn7px77inNIZfLoVAo0KlTJ8TGxuq/f/bsmWQlhOrVq6NWrVqQy+VQKpXo1KmT1ZGbr1+/Fp2nOY7TO8m7Em5Fyg48fPjQSHGQyWTw9/e3yOk3rzBx4kTRENurV6+iZ8+eBhNoQECAQcRceHg4PD099cer1WqUKVPGrH34ZcuWgWEYyOVy/UPXpk0bg1XV69evUbx4cQOfLY7j8OOPP9ryUrhxYzdevHiBQ4cO6dMp5BVOnDgh6oTv5eUlWSPOHly+fBkDBgxA27ZtsW7dOqc4NQ8fPtzIb1SlUqFnz54Ol+VdsrKyRANjbt68KWnxfz+RskqlQu3ata2yHO3cudOkyFZXwa1I2YEJEyaIbmfxPJ+nto8eP36MKVOmYPDgwQgODs5VCRQEAYsWLULRokVBURTq1atnsNq8e/cu1q1bh6NHjxo5KQcGBhpFh6lUKgwbNswsmW/cuIHvvvsO/fr1k8wCHR8fj4kTJ6JKlSr45JNPDCxWbkwnKioK8+bNww8//ICwsDCXNLnnJwRBwIgRI0BRFLRaLViWRZ06dfJMBvHu3buLvhg1Gg2OHz/uEBmWL18OlmX1L3+O4xAYGOhwZUpKSVCpVC75HGVkZIgG83h4eOgXru9bjt4N8jEXqVxrMpnMJR323YqUHejVq5foQ8JxXJ6puH3gwAH9/nS27PXr17fLhPPmzRtJPyofHx+bj5cXSUxMxJIlSzBq1Chs377dJit4QRDw999/49y5c2b7NmRHnWWvqjmOQ8eOHV2qfEl+Y/369UZh6kqlEp9++qmzRTMJqdJFGo3GIQlG37x5I7pdxLKsw/M7SW2TeXh4uGwk7NatW8GyrH7BS9O05HnwPI9NmzZZPJZUihCWZREWFmbDs7INbkXKAgRBQGpqquTKYePGjaI3AU3TePDggUNktAap1QfLsli6dKnNx3v79q2kIlW4cGGbj5fXuHnzJgoUKGCw7VmxYkWrMg/fvn0bpUuXBsdx0Gg00Gq1eqfR3EhNTRU183Mch507d1osU2RkJDp06KBPJPr111/nuaz29qR69eqizwhFUQb+LK7Ktm3bJF+OjvidQ0JCJC1BLVq0sPv47/Lll18aWXJkMhk++eQTh8phLpcvX0aPHj3QsGFDzJgxAzNmzBDdrmUYBv/884/F4wiCgE8//dSo365du9rwbGyHW5EyA51OhxkzZkCr1cLDwwPFixfH7t27jdqlpaWhWrVqBqsfjuMwePBgu8pnK86fPy854Xz88cd2GbNp06ZGEwtN0xg3bpxdxrMn6enpePTokc0ymVerVk305Tlq1CiL+svMzISfn5/RVirDMCY5RB89elTy/rA0G/G///6LQoUKGdwDFEWhbt26LrnVYW+2b9+OypUro0CBAmjWrBkuXbqEgIAA0WvOsmyeWKBlZWWhVatW+kLYCoUCDMNg/fr1Dhn/7NmzogsAmUyGTp06OawkCgA8efIEPj4+eiWEYRh4enri7t27DpPBFiQmJsLX19fguaVp2urC3rt37xZVur28vFzSz9itSJnBDz/8IOpMLVZ/KykpCXPmzEHNmjXRoEEDbN68Oc+8EK5du6af7N7/CwoKssuYz549Q0BAAHieB0VR+q3E5ORku4xnLxYuXAiNRgOO40DTNIYOHWrVNlxcXJxkmRZLy7OEhISIvlCUSiXGjBmT6/GhoaGSilT79u0tkmn58uWS2ZVPnz5tUZ95laVLl4rOM507dxa13BYqVCjPbKnqdDrs378fAwcOxNixY3Hnzh2Hjl20aFGj6yeXy/URZ9WqVTO7lJKlvH79GosWLULPnj0xb968PBs1HBkZia5du0Kj0cDX1xc//PCD1S4grVu3Fp1feJ7H+vXr8X//93/o3LkzNmzY4BIZ0N2KlImkpaWJmjAJIahfv77dxnUGgiCIrn45jsOOHTvsMt7p06cxceJE9O/fH9OnT8epU6fyjOKZzbZt20Qzu48YMcLiPhMSEiQVqYCAAIv63Lhxo6Si3KNHj1yPT09PF9365TgO+/bts0imQYMGSVpbVqxYYVGfeZHMzEzRa0sIQZMmTVC4cGG9X4pcLgfLsjhw4ICzxc4z3Lp1C/7+/uB5Xl/+6H3LLM/zFuX7clXu3buHQYMGoU6dOhg8eHCeKATcsmVL0Wcg22/33cjsmjVr4vDhwxgyZAi++eYbp6TTcCtSJvL8+XNRR0VCxB2iMzMzceLECRw4cABv3ryxm1z24ubNm/D29tbnwaJpGkOGDLG5cqPT6fDVV1+B4zjIZDJQFAWGYVyuur0pVK5cWVIZsGbV1KBBA6MQY4ZhMGXKFIv6e/LkiWTOLVMdRE+cOKHPf5P9mw0ePNji++O3334TXaio1WqcOHHCoj7zIjnNM76+voiPj8esWbPQtGlTDBw40Co/lA+VrKwsnDhxAjNnzpT0ZZ05c6ZVY9y5cwdbtmzBhQsXnLogvHTpEjiO0yseCoUCarUaV65ccZpMprBlyxbR30bsT6FQQKlU6pVilmUxadIkh8rrVqRMJCMjQzKPRrNmzQzaXr16Fb6+vvpVD8MwTq36bSnp6enYs2cPVq9ejYiICLuMsWvXLtEHhud5pKam2mVMe+Hp6Sl6f1jrDPz48WMUKVLEYNuzUaNGVl2f7777zuC6syyL2rVrmxW99/r1a6xduxa//PKL1S/0169fo2DBggYKo0qlQtWqVfOcZdIaUlNTJRWpOnXqmN1ffHw8Bg4cCK1WC61WiyFDhjgt6aOrIRYFmf1naT6njIwMfPnll2AYBjzP6y0mztq2q1u3ruj52cvX1VZkZWWhXbt2+t+HpmlQFCW5KyRmuXKk5c2tSJnBvHnzRLduzp07p2+Tnp6OggULiv6wN27csKt8eZF27dqJPggajQZHjhxxtnhm0aJFC0lLgrU+LBkZGfjzzz+xcOFCnD592mrlQhAE7N69G82bN0e9evWwaNEip5fruH//PoKCgiCXy6FSqdCtW7cPsjDqyJEjRQtr//rrr2b1k5GRgXLlyhlsDatUKlSqVMnuIfZxcXF4+vSpSyvBN27ckMyebWl08owZM4z6VCqVaNu2rY2lzx1BEIws2e/eT66OIAg4efIkfvjhByxYsABHjhyRdEkQW7ya+7xYg9MUKUJIK0LIPULIA0LIeJHvAwghJwgh1wkhNwkhn+fWp70VKUEQsGrVKpQoUQIURSEwMNAop8WhQ4dEHXHlcjmGDx9uV/lyQ6fTYd++fRg4cCDGjBmD27dvO1UeAOjQoYOkIiXmxO/KXLt2Tb9F+a6lx5p8Ks7i9evXiIyMdIoTc1ZWlk1fwMnJyVi9ejUGDRqE+fPnu7xTb2ZmJkaOHGnwEszesjDnBb97927RF49arc5x61yn0yE6OtqiQI8XL16gSZMm+u3egIAAl96abdWqlYHio1AoUKRIEYvTMRQpUkR0PlOpVE5ZqEgFhRQoUMDhsliLIAgoVaqUkU+b2B/Lsli5cqXDZHOKIkUIkRNCHhJCShFCVISQG4SQSu+1+Z0QMvR//65ECHmSW7+ukJBz69atJhXPdTSZmZlo2bKl00KPpdi3b5+oeV2r1dq0AKajuHHjBtq2bQt/f380aNAgz1nVEhMT0bZtW6hUKjAMA39/fxw8eNDZYllMTEwMAgIC9PcYwzDQarUu71uUUy46U7fmpk6dKjoPeXh4YNasWaLHbNmyBb6+vvpki4MGDTLZv08QBFSuXFm0sO275aBcifT0dPz444/w9/eHl5cX+vXrhxcvXljcn5eXl+g1VyqVTtlS/f77740sZAzD4IcffnC4LLbgzp07+mCBbFcHsczqDMM4NOO/sxSp+oSQI+/8fwIhZMJ7bVYSQsa90/5cbv26giL14sULSUdee0S8mYpUMjyGYZya9FAQBAwePFgfjZHtwPzXX385TSZHo9PpsHv3bnTp0gX9+vVzarj/J598YhQlyLJsnt2W7t+/v2jKAEv8jRxJTlvee/fuNamPTZs2iVqkeJ7H9u3bjdqHhoaKui707t3bpPHOnTsnOp5SqcTYsWPNOn9X4urVq1ixYgVCQkJy3RLt1auX6Iu9SpUqDpLWkPT0dHTv3h00TUOr1YKmafTq1cvqyggpKSm4fv06oqKibCSp6WRlZeH48ePYvn07oqKisH79en0S3+zgqD179jhUJmcpUp0IIavf+X8vQsiS99oUJoT8Qwh5TghJJITUzq1fV1CkAGDmzJkGqfQ5jsMnn3zi1ERizi7PkBs3b97EggULsHr1apuu3CIjIxEWFoaYmJgc22VlZWHx4sWoUKECihcvjlGjRjnEP0en0+GLL77QK7nZWzhTp061+9jvExERIeoz4uHhYfLL1NWQshAoFAqXzpreu3dv0S0MnudNXmSkpqYaJTmVy+UoWrSoqLU3KChI9FpRFIWEhIRcx9u2bZukNd7S/GLOJD09Ha1atQLLsmBZFjzPo0SJEnj27BkA4OXLl/juu+9Qvnx5NGrUCHv37kVUVBT8/Pz0CilFUVCr1bh06ZJNZdPpdDh58iSCg4NNStUQFRWFsLAwREdHmz1WXFwc9u3bhzNnzkCn02Hx4sVQq9XQaDSgaRotW7Z0aDJTMeLj47F582Zs377dKVHyzlKkOosoUovfazOKEDIa/98idZsQ4iHS12BCyBVCyBVL8+rYg7CwMHTv3h1t2rTBxo0bHVrdXIwePXqITnA8z+c5XyRTSE1NRfv27Q1WYoMHD5ZcUXbt2tVgNa5SqVCyZEm7JwQ9dOiQ6Cqepmn9hO0ojh8/Dq1WK3qfNGjQwKGy2IpChQpJbrU427k+J86ePSsaoeTr62vWguzJkydo3rw5FAoFFAoFWrZsicjISNG2JUuWFL1WarXaJH/Khw8filrjWZbFb7/9ZrLMrsLs2bONFhZyuRyNGjVCbGws/Pz8DKydHMdh9uzZSExMxC+//IKOHTti0qRJeP78uU3lunfvHooVK6aPCqdp2uJUKLkxa9YsUBQFjUYDtVoNX19fo2uiUqmszmSe13GWImXK1l44IaTYO/9/RAjxzalfV7FIuSInTpwQnZi9vLycruTZg6+//tpoUmdZFj///LNR27t370pG7/z+++9WyZGamoqFCxeiRo0aKFKkCL744guDhHGDBw8WfXlxHIe1a9daNba5xMbGir4IKYrKsz4VEyZMMDonhUKBzz//3Nmi5crcuXNBUZT+henj42Nx1u20tLRcfQ67d+8uGuWlVqtNVjp79+5tMM8olUoEBASYbP0TBAFbtmxBw4YNUbt2bcyfP99p1Q1KlCgh+myqVCqMGjVKX7D73T+GYexqEREEAWXKlDGyVnIch0OHDtl0rGPHjpmcboCiKKt8y/I6zlKkFP9TjEqS/+9sXvm9NiGEkL7/+3dFQkg0IUSWU79uRSpnpkyZApqmwXEceJ6HVqt1ShZYe5OVlSVZlVysCHJOmb67d+9usRwvXrxA4cKFRSfb7ALB33//vZFzLvmfpdCaAsCWMnLkSANfOrlcDm9v7zyb6TklJQVNmjQBx3H67ZmyZcvmmfOJjY3Fzp07ceTIEbsveO7evQu1Wm3wkuY4DnPmzDG5j6ysLCxZsgQVK1ZE0aJF8e2335qVQ23QoEEG9x/DMKhVq5ZTFnv+/v6SSoNUAWmtVmtXH8fr169L5r5q3bq1TceS8tMT++N5Hjdv3rTp+HkJpyhS/41LPieERJD/ovcm/u+z6YSQtv/7dyVCyNn/KVl/E0Ja5NanW5HKnWfPnmHdunXYvXt3nkt4aSopKSmiDp/ZVqn3OXHihKhvh0qlsipD7ldffSUZqptdHy08PFzUGqbRaJyyEhcEAatXr0blypVRuHBh9OvXT3IrKK8gCAIuXryI33//HceOHYNOp8P9+/dx+PBhm2+7OIKsrCxER0fbpcbYrVu30LZtW3h7e6Nq1arYunWr1X1mZWXhzJkzOHr0aI6FvO/fvy8ZqGMLOcxlxIgRouWZKlasiPbt24s+2/ZOBHnq1CnJlAa23n5v2LChWYqUK9S8cxZOU6Ts8edWpNxkU6lSJaOHXSaToWXLlkZtdTodSpcubaR8cRxnlRIhlaE6e8LNfomvWbMGDMNAo9FAo9Gj/OnQAAAgAElEQVTYfVX7IZOUlIQWLVro0yBQFIU+ffrYPUGlrVi5ciW8vLzAMAxYlsXIkSOdGsSSG2fPnoWnp6f+/mZZFhs3bhRtu3btWklrS79+/Rws+X91LsuUKWOQOoPneVy5ckXUh02pVNo9Y3hKSoqo9ZxlWSxatMimY/3666+SW3vv+oZ9aPUwxXArUm7yJWFhYQY1ppRKJXiex61bt0TbP3v2DA0aNNAnEixevDhOnTpllQw51YqiKApv377Vt01MTERwcDAOHTr0Qa/s7E3fvn2NfFtYlsXs2bPtPnZqairCwsJw+fJlkxKOXrt2DTNmzMCCBQvw7Nkz7N692+jFxrIsRo0aZXfZLWHLli2Si4jw8HAAQHR0NB48eABBEHDgwAFRa4tKpcLEiROdcg6pqanYsGEDBg0ahDlz5hhsU27YsAFarRY8z4OmaTRt2tQhuYs2btwIlmUNCvdWq1bN5hbs5ORkVKlSRX/PeXh4gGVZzJ8/H8OHD0fFihXRvHnzfBmsZC5uRcpNviU8PBx9+/ZFYGAghg8fjsePH+d6TExMDJ48eWKTzNr9+/cX3WL08PCwyvfKjWVkZGSIOggTQuDv72/XsXfs2KF3Gler1ShWrJhkUlBBEDB8+HD9y/LdLOFS29Wupnw/fvxYdFuMkP+c/QcNGoT69euDpmmwLIuiRYvi6NGj8PPzM9oyY1nWpGfXGaSnp+PmzZsOz6f0999/4+uvv8aXX36JNWvW2M1NIyUlBStWrMBnn32Gfv364fLly3YZJ6+TkyIl++/7vEOdOnVw5coVZ4vhxg0hhJDExETSqFEjcv/+fZKRkUEIIUQmk5EWLVqQ4OBgwnGcXcYNDw8n27dvJ1lZWaRjx46kdu3aou0AkJs3b5KXL1+S2rVrE29vb7vI4yokJyeTAgUKkKysLKPv1Go1efv2rV3GjYiIIDVr1iQpKSkGn/v4+JCoqCiiVCoNPj958iRp06YNSU5ONql/mqbJ48ePSaFChWwms7XMmDGDTJs2jeh0OtHv1Wo1SU1NNfie4ziyd+9eMnToUBIVFUXkcjlRKpVk06ZN5LPPPnOU6G7yAC9fviRxcXGkbNmyhKZpZ4tDZDLZVQB1xL7zcLQwbpzHtWvXSFBQENFqtaRcuXJk/fr1JK8p0q6Gp6cnuXnzJtm/fz+ZNWsW+eWXX8jTp0/J4cOH7aZEzZ8/nwQGBpKffvqJzJkzhzRu3Jh8//33Ru1evnxJatasSRo0aEC6dOlCihUrRiZNmpSvf3OO40i5cuWMPpfJZKRZs2Z2G3fVqlV6Rfpd0tPTybFjx4w+37p1q5HSRQghcrlctH+1Wk18fHysF/QdUlJSyMaNG8nMmTNJSEgIEQTBrOMTEhIklSilUkmysrKMvs/MzCShoaHk3r175PLly+TEiRMkJibGrUS50fPmzRvSunVrUqJECdKgQQPi6+tLVqxY4WyxckbKVOWqf/llay8iIgKXLl1ymLn+xo0bRv48LMvip59+Em2flpaGp0+f5tuov7zKkydPJBMiXr9+3aBt/fr1RWui7dq1y0nSO4YzZ86A4zj9uatUKhQoUAARERF2G7NXr16iW1xqtRp//PGHUfshQ4aIRoSxLCtavmf16tU2lffevXvw8fHRp0JQq9WoXbu2gU9fbhw9elTSR7BUqVKS37Vr186m5+Imf/HZZ5+J+jg6u6YpcftIuQ5Pnz5FjRo19PluNBoNNm/ebPdxpUJ51Wq1gbIkCAJmzJgBtVoNlmXBcRwmTpwInU5ndxnd5M7ixYtFFSkPDw9MnjxZ3+7p06eSebbyagZzc4iIiMDQoUPRqFEjfP/993bzb3n9+jVmzJiBUqVKifrK0TSNp0+fGh13+vRp0WgplmVx8uRJtGjRAt7e3qhZs6ZdaooFBgYazQc0TWP8+PEm9yEIAtq0aWOgMHl4eKB58+a4deuW5P2nVqtFr4mbvElMTAw2b96M4OBgq53hX7x4IenjGBQUZCOJLcOtSLkIgiCgfPnyRhMuy7IWZzM2lWLFiklOau+u1BcvXiwaNSRluXIEKSkpbsvY/1ixYoXoC1ihUGD69On6djdu3JCsiVahQgUnnkH+4c2bNyhZsqSkwsBxHEaPHi15/OjRo8EwDJRKJRiGMUjiak/i4+MlncSLFi1qVl9ZWVnYtm0bvvjiC3Tq1AkhISH6II6ePXuKLt7kcjl69uxpj1Nz42CWLFkCmqahVqvB8zzUajVCQ0Mt7i+neat8+fI2lNx83IqUi3Dp0iXR/CAeHh52z6HStGlT0ZuTpmmD0g5SmX49PT1tIsfbt2+xevVqjB07Ftu2bcuxpMW9e/fQsGFDKBQKKJVKtGrVyimVyF2Jly9fiuauomka9+7d07fLyMiAp6enUTuKojBu3DgnnkH+Yc6cOaK/hUwmQ/PmzbFv375cI0PDw8Mxd+5cLF261GGZ2F+9emUzRSonXr58KZrRnxACb29vm43jxjncvHlT9P5Xq9U5JmXNidTUVNF3pEKhwDfffGPjMzAPtyLlIkjlUCGEoEWLFnYdW6wOH8uy+Prrrw3aSU18hBCrt/fu378Pb29v/VaAWq1GmTJl8OrVK6O2CQkJRisThUKBkiVLunRyQkewadMmfRmgbItG3bp1MXXqVIMiyNu3bwfLsvraagzDoFixYqLX2435SGWF1mq1Vq3KzSEzMxNr165Fw4YN0bBhQ6xdu9akxKN16tSxemsvN5KSkiQVtlKlStlsHDfOYdSoUaLb2TzPY/v27Rb3u3TpUoN3lUKhgJeXl8MLvL+PW5FyEaQKxrIsi19//dXu4+/atQv+/v5QqVT6jMnv17eqUaOG6MRXtmxZq8dv2LChUcFUpVKJQYMGGbR79uwZChYsKCoHz/PYv3+/1bLkdWJiYrBo0SL4+fnpV4UURYHjOISFhenbXb16Fb1790aTJk3w888/IzEx0YlS5y+kygNxHOeQmmRiPkocx+GLL77I1RJ27949eHt7Gzib16pVyyxnc1Po0KGDqPP8woULbTqOG9PJzMzE5MmT4enpCblcjo8//hhXr1416dgnT57g5MmTiImJkSzGrlarsW7dOqtkDAkJQdOmTVGuXDkMGzbM6UoU4FakLCY1NRVbtmzBjBkzsH//fpuUmJg8ebLBxEfTNMqUKWPVBBYdHY1ff/0V06dPx6VLl3JsKwgCEhMTJQuE/vXXX6KWq4MHD1osH/Cfn5OUtev9bcNGjRpJ1q+jKMrmZRLyKpMmTRJ1zCxWrJhNko26yRmxEiJyuRxVqlRxyPU/ffq0aGQcx3E4c+ZMrscnJydjw4YNmD59Og4dOmSXgJLExEQ0aNAALMtCo9GAoij069fPHbxiJ1JTU3H8+HGEhYVJWu779OljtCX3vq/s+yQlJaF169agaRparRY0TeOLL74Q9dekaRrR0dH2OkWn4VakLODx48coVKgQ1Go1PDw8wPM8qlSpgtevX1vd9969exEUFISaNWtixowZVvW5d+9eMAwDmqb16f379u1r1UR+7tw5BAUFwc/PD40bN8bJkyct7iub1NRUSUWqYMGC+nY5OcJmP/AnTpywWp78QJkyZUSvEcuydi2q6ub/s3LlSnAcp68xV716dYetnmfMmGFk4c1W5mbNmuUQGUzl1q1bOHjwoEtYFvIr+/bt00eC8zwPb29vnD171qCNVFScQqHAwIEDJfvu06eP0W4Ky7KoUaOGXpn38PAAwzCYN2+evU/VKbgVKQv45JNPjCYpiqLwf//3fw4Z3xSSk5MlV6QHDhxwtnhGNG/e3GhPnaIofPvtt/o2L1++lAx/JYQgMDDQbW35H1WrVhW9RjRNu19YDiQ5ORlnz57FnTt3LO7j7t276N+/P2rVqoUBAwYYBA5IIRXByXEcVq5cabEsbvIekZGRovcCz/MGux2nTp2CVqsVnTek3q1paWmSc3Lx4sUREhKC/v37Y/jw4bhy5YqjTtnhuBUpM0lOTs4T0SY5Oa936dLF2eIZ8fz5cwQEBIDneahUKr1fxrtRgwBQsWJF0XOqUaOGzX04XBFBEJCSkpKrwrhs2TKjydPDw0NyQnTjmly6dMmg+LZcLgfHcbnWPBMLyMh+ebp94T4sZs2aJarsqNVqbNy4Ud8uOjpatJ1cLseAAQNE+379+jWUSqXonKzVah11ik4nJ0XKXSJGhP+umWsAgERHR5O4uDij72QymeRxOX3nLIoUKUIePHhANm7cSH766SeyZ88ecvnyZcLzvEG7jRs3Ep7n9fWVOI4jpUuXJqGhoUStVjtDdIexfPly4uvrS3ieJ35+fuT333+XbDt48GDStm1bwjAM4TiO8DxPihQpQnbt2uVAid1Yy/Dhw0lycrK+nIpOpyPJyclk+PDhOR7n6elJQkJCiJ+fH+F5nvA8TwoVKkQOHz5MChQoQAghJC4ujkRGRrrUnObG9iQmJpL09HSjz7OyskhiYqL+/4ULFyYdO3YkDMMYtKNpmowdO1a0b41GQwICAow+l8lkpEmTJlbJnZKSQvbs2UN27NhBEhISrOrLqUhpWK7656jVduPGjY229lQqFYYPH57jcYIg4OXLlxbn0XiXy5cvo3z58qBpGhRFoX79+njy5In++5SUFNGcGxzHISQkxOrxnUlMTAzmzJmDgQMHYsOGDR9EQs7ff/9d1NE/twiY8PBwrF27FocPH7ZJQIQbxyLm50T+ZyUwhaysLFy+fBlXrlzRO3FHRUWhUaNGoCgKDMMgICDAJr6OblyLO3fuYNKkSejUqZNoRDjDMLh9+7bBMRkZGfj+++/B8zxkMhnq1KmDixcv5jhOaGgoWJbVW01VKhW0Wq1JW9BSHDt2DGq1Wu/TRdO0zUsh2RLi3tozn0ePHsHPz88gPLhy5co5OoYfOXIEAQEBoCgKFEWhc+fOePPmjUXjx8bGGpnt5XI5ihUrZhCNcejQIbAsC4ZhoFAowLIshgwZ4vYjyoMULlxY9IVarFgxZ4vmxo5I+awUKFBA8hhBEHDixAmsWLECp0+fNnjepSoocBxnsBBzk7dZunSpft6XyWSQy+UGLikcx2HIkCE59mHOe+Kff/5Bnz598NFHH+G7775DZGSkxbK/efNG1L+XYRjcvXvX4n7tiVuRspDU1FRs2rQJ06dPx759+3Jc7f/zzz9G1gSKoiyuDzRv3jzRrLE8zxulIoiLi8PkyZPRsmVLjBgxAg8fPrRozA8dQRBw6dIlhISEONzHRBAEyZQPHh4eDpXFjWMZP3680bPOMAx++OEH0fYJCQmoWrUq1Go1GIYBx3EIDAzU+xqeOnVK1FKtUqlsmnAzP5GUlITVq1dj2LBhWLp0qcULYEfx4sULUQsURVGoW7cuvvjiC+zdu9dlF9SbNm2SzGA+ceJEZ4sniluRcgB9+vQRzfLKMAwePHhg0DYjIyPXraqvv/5a9KXKMAyWL19u0HbSpElgGAZyuRxKpRI0TWPZsmUmyZ2eno4//vgD7dq1Q79+/XDhwgXzTjyf8PDhQ5QpU0ZvaqZpGvPnzxdtm5GRgc2bN6NTp04YPHiwzSJVSpQoIfqb2yIZqhvXJSMjA7169QJFUdBqtaAoCr1795bM9da9e3ejFCEURemrFGzevFmyXlnnzp0deWp5gqioKPj7++stJBzHwdvb26VTiKxbt07UoiOTyXJ1P3EFxNwYsuV/N4rblXArUg6gfv36klEN2eUi4uPj0alTJyiVSsjlctSrVw+3bt0S7U9KY2dZ1uDF/ffff0vWXnv+/HmOMqenp+Pjjz82yAPCsuwHl/BSEASUK1fOyFeFZVmjnFUZGRlo2LCh0TUTU1ylLJh3797FtGnTMHHiRIPfcseOHUaTC8Mw+PPPP216vm5ckxcvXuD06dN48eKFZBtBECTzrPE8D+C/Ukxi1gqO40xeYH1IfPXVV0aLYA8PDzRt2tTZokki9X7w8PDAmDFjnC1erjx9+lTyHnVUeSVzcStSDmDcuHGiExxN04iJiYEgCKhevbpBGKlMJoNWq0VsbKxRf2lpaShfvrxBqCrDMGjVqpVBu0mTJklawt63XL3Phg0bRFc1NE0jISHBptfHlbl27ZropEQIQfv27Q3a/vHHH5J7+9n+c2vXrtUXfy5cuLCBA2V2tXSFQqFXwkaOHKn//s8//0SlSpVA0zQqV66Mffv2OeYiuMkT6HQ60ec92yqVTc+ePQ2UcpVKheLFi38Q6UPMRex5JuQ/n1RXreuZmJgoatFhGAbXr193tngmMW3aNLAsq3dp4DgOXbt2ddntSLci5QBevHgBLy8vA6sGy7L6BJ6nT58WfVkzDIOff/5ZtM/ExESMGTMGxYoVQ+nSpTFnzhwkJCRg165d2LJlC169eoXJkyeLTqwsy2LFihU5yty2bVvRCUSj0WDv3r02uzYPHjzA6dOnXdbvIDQ0VDIfV8OGDQ3afvHFF5LXbN++fdiwYYNo5N3atWsRFRUlWWsxt9I+75OZmYnQ0FDs37/fZa+rG/vw6aefGllP5XK5gdKflZWFJUuWoGLFiggICMB3332Xr4tVZ2VlYceOHejQoQN69OiBv/76y+RjpZ59hULh0qVssqtaqNVqsCwLmqYl3yW2RhAEpKenW630nD9/HkOGDEHv3r1x6NAhl1WiALci5TAeP36M7t27w8fHB2XLlsWyZcv0N8a6deskrR69evUyqf/Dhw+D4zjwPK8PF506dark1l5OWwQA0LdvX1EHZ57nbVKGJT4+Ho0aNQLDMPr6TDNmzLC6X1vz9u1bydXd+8Wke/XqleM1CwgIEP2NixYtKukX4OHhgbFjx5os76VLl+Dt7a0vB8EwDNasWWPry+LGRXnw4AG8vb319xLHcfDz87Mqigr4L1J48ODB8PHxQZEiRTBlyhSkpaXZSGr7odPp0Lp1a6PizaY6LQ8dOtQoSaVSqUSnTp3sLLn1JCQkYN26dVi+fLlVv396erpJv7UgCFi8eDG8vb0hk8ng7++PDRs2WDxuXsKtSLkAV65cEX2JsiyLxYsXix7z9u1bLF68GK1bt8aAAQMk84SMHDkSNE1DpVKBpmnQNG1S9e3z58+LyuTn52eTfETNmzc3yojLcRyCg4Ot7tvWLF++3MDMzLIsKlasaJQP7MyZMzleM6mcQDKZDKtXrxbdRpDL5ZIRWu+TlpYGT09P0fvgn3/+scelceOCvH79GosXL8bgwYOxfPlyo+oA5pKcnIzixYsbPK8Mw6B58+Y2kth+HDp0SHSRStO0Seke/v33XwQGBuqjINVqNSpWrIi4uDgHSO9cIiMj0aJFCygUCigUCgQFBeV4zRYvXixqcd++fbsDpXYObkXKRWjatKmBMiSXy+Hn5ye6NZOYmIjSpUvrb1qpF7RCocCkSZPw4MEDLFiwAL/99luuTubvsnDhQtA0rU+K5ufnhxs3blh9rlLFMQkhqF+/vtX924Nz586he/fuCAoKwuLFiyWTqs6dOxc0Testgz4+Pnq/hFKlSomec/HixREXFydqPTRHCdq3b5/oVoRcLseIESNsdi3cfFisWrVKVMlnWRZXr151tng5MnToUNFnjuM4kxM8CoKAsLAwLF26FMeOHXPpLT1bkZaWhiJFihi4hsjlchQqVEg0qlwQBHh7e4te63LlytlMruDgYFSsWBEsy6JWrVo4duyYzfq2Brci5SKkpKRg7Nix+m2Zrl27Sio9kyZNyrF477uWjnedlS0hPj4ee/bswV9//WWzzNjh4eGSW5mlS5e2yRjOJDY2Frt27cLRo0cNHFLFIu9YlsXWrVsBAFu3bgXDMHqfBpqmMWfOHJPHlYrWIcS0LeKEhAQsWrQIgwcPxsqVK22Sgd9N3qdfv36i9xTLsi6dbRr4Lw+XWC04nuexY8cOZ4vnsmzdulWyPt+mTZuM2qelpVmdhT83/vjjD9HI5aNHj9qkf2twK1J5kEqVKuWqRGWvulyx9ENGRoboFpRSqcwTeU6sITg4GGXLloVSqUSZMmWMJvOYmBisXLkSS5YsMTvTdFRUlOjkx3Ecdu/eneOxd+/ehZeXl4Fvjb+/P6Kiosw+Rze2JzIyEnPnzsWUKVNw4cIFhzrezpkzR9R1gOd5HD9+3GFyWMLdu3dFLb0ajQbJycnOFs9lCQwMlHyvTJ061ai9IAiS1RdkMplRomhzyan/GjVqWNW3LXArUnkQqbxU2Tdt9ouwZ8+eLhvpsGnTJgO/I5VKBV9fX0RHRztbNIvR6XTYu3cvevXqhW+++cYp2x7Tp083ChsOCgrK1ZrYuHFjI0d5hUKBbt26OUhyN1Ls2LEDDMNApVJBJpOB4zj07dvXYc92bGys0ZaxQqFA2bJlHbLNdevWLSxYsAC///474uPjzT7+jz/+AMMw0Gg00Gg08PT0xJkzZ+wgaf7gxYsXBuVk3l/sSi3Kfv31V8n3UpMmTaySKSUlRTK1B03TVvVtC9yKVB5k69atRj4LcrkcFStWxLBhw9C/f38cPXrUZZWobM6dO4eOHTuiTp06GD9+PGJiYpwtksXodDq0adPGKBnnwoULHS5LWFgYevbsibZt22Lz5s255rtJT0+XnKTUarWDpHYjxps3b0QDGBxdfPz69ev6XHdKpRItW7bMNfLXWgRBwPDhw/VKJMuyYFkWR44cMbuvf//9F/v27cPRo0eRnp5uB2nzDzmlfKFpWnI+uXHjhqTLSfny5XMdNz09XbJvQRBEdzEIcY3qDm5FKg8iCAJGjhwJiqKg0WigVqtRrlw5PHv2zNmifbDs2bNHMoGpWFJVVyIzM1PUj4QQAk9PT2eL90Gze/duyZdaz549HS5PQkKCwxJ3HjlyRPSZ4nkeKSkpBm0FQcC5c+cwceJE/PTTT+4CzFbw6NEj0a3c3O65tLQ00fJDSqUyx9Iu9+7dw8cffwwPDw8olUq0b99edFE9b968HH1MnYlbkcrDREVFYffu3Th//rzLW5/yO7169RKdeHiex5YtW5wtXq506NDBSJmiKCpfRfvdvn0bq1evxoEDB1w2K/X77NmzR1KR6tu3r7PFy5W1a9ciICAAcrkcFSpUMCsbf/fu3UXPW6PR4MCBA/p2giCgb9++4DgOMpkMKpUKDMNg8+bN9jilD4LPPvvMSJliWRa3b9/O8bhVq1YZZc338fGRdNlYtWqVkUuBXC5H+fLljbaNBUHA3LlzUaBAASgUCvj6+rpMjjy3IuXGjQ0YNmyYaNSKrTPB24u4uDhUqlRJny+H4zjUr18/X0Tu6XQ69OjRQx8RyfM8ChcujIiICGeLlitJSUmiVhlr646lpaXh5MmTOHv2rM2icd8nO//au3KrVCrUrVsXbdq0wc6dO3P0serSpYukIpWtkEVFRaFLly6SpbCkMvvfu3cPwcHBuHnzpl3O3Rm8ePECgwcPRqFChVCmTBksXLjQ4t82KSkJffr0AUVRUCgUKFeunMmBSydOnMDnn3+OqlWrYvTo0ZJbwPv27ZO0hPM8LxmNp9Pp8PbtW5cyHrgVKTdubIBUUlWtViuad8UV0el0CA0NxYoVK3D27FmnTVSXLl1C8+bNUbBgQdSuXRv79++3qj+xZKcymQxVqlSxkcT25dChQ3r/oGxry3fffWfx77N//3694zXP8/D19cXFixdtKnNOeYXeVQa7desmeR779++XzF+VlJSE8PBwaLVaybB7jUaDXbt2GfSZlpaGtm3b6p3PWZZF48aNrU5a6mxev34Nf39/AydxlmXRo0cPq/pNT0+3W5mp6tWrS94bFEVh6dKldhnXHrgVKTd25+HDhxg4cCAqV66M9u3bm107Lq+wcOFCUBSlL8+i1Wrd0UFmcvHiRVE/CGtKTdSpU0d0smYYBg8fPrSh9Pbj1atX+P3337FgwYJct1dy4unTp5IKvy3TASQlJUlGfr2vTEkpcYIgoFevXvotO4qiwDCMvvpBs2bNREsyvWvV+PPPPw36nDBhglE6BIqi0KdPH5uduzNYsGCBZDmwBw8eOFs8UbRabY73xalTp5wtosm4FSk3diU8PBw8z+tN7zKZDCzLWp1XxFWJjY3Fli1bsHfv3jxjiXIlmjRpIjqx+vr6WhxqX7lyZcnJOjw83MZn4NrMnDkTKpXK6Fqo1WqbOu0KggAvL69cFSkPD48ca2wKgoDz589j8uTJmD9/vkGSYqltoXd/3/e3pgsWLChpAbHXFqcjaNeunaQy6aqJRxs0aCD52wUGBrrU1l1u5KRIeRA3bqxk3LhxJCkpieh0OkLIf8p5SkoKGTp06H/aej7Dx8eHdOvWjbRt25bQNO1scfIc169fF/389evXJDEx0aI+u3btKvpb8DxPKlSoYFGfeZVXr16RjIwMo891Oh1JSEiw2TgymYz8+OOPhGXZHNtRFEU8PT1z7KdevXpk+vTpZPTo0aRIkSL673Lqm2VZsnPnTsJxHElOTibLly8n7dq1I2/evBFtn5mZqZ+jrCEmJoYsWrSITJ8+nVy4cMFhc1y5cuWIUqk0+lwQBFK8eHGHyGAuP//8M2EYxujzJk2akL/++ovIZDInSGUHpDQsV/1zW6RcjwIFCoiuOJRKpUXJ9VyZ9PR0TJkyBYUKFYJWq0W3bt3cKSnMRCprP8uyyMjIsKjPpKQkVKtWTV8+h6IosCyLv/76y8bSuz4hISGSRXw3b96MyMjIHI/Pysoy2VIgCAKWLVuGQoUK6a3RYr+rpelBRo8ebRRZplAo0LRpU/3c8ubNG5QtW1Z0O5O8ZwGxloMHD+rLO3l4eIDjOHTv3t0hSUsfPXpk5E+mUChQrVo1l7bshIWF4aOPPgLHcShfvrxLpDKwBOLe2nNjT8qUKSM6cdE0jbS0NGeLZ1PatGlj4Kcgl8vh6+uLxMREZ4uWZ9i+fbuoj9T3339vVb/p6enYunUrBgwYgGnTpn2wCq5Op0OLFi0MXvYAyAoAACAASURBVLoKhQJyuRxarRY0TePzzz83yhV16tQpVK1aFTKZDGq1Gt9//71Ziq1Op8OxY8eg1Wr1ju5ardai5JrZvOs4rtVqwTAMWrVqZZBjatq0aZI5kQj5L4pQrVbj2rVrFssBAKmpqaI5lDiOM/LTshenTp1CqVKlQFEUVCoVWrZs6fI57PILbkXKjSTh4eGYOHEixo4di/Pnz1vUh1gINE3TGDRokI2ldS7h4eGizp4sy2LBggUGbd++fYtly5ahd+/emD17dp7O6G4Pli1bBk9PT326gjFjxuRp/xVXIzMzExs2bMCnn36KqlWrGmWjpigKXbt21be/ceOGaLFYS/JYpaen46+//kJoaKjNMozfv38fe/fuxb1794y+q1atmqQC1ahRI4wfP94mSvWRI0ck8321b9/e6v5NRRAEREdH4/Xr1w4b041bkXIjwaJFi8AwDBQKhb6+17Bhw8zuRxAEjBs3DjRN61e8nTt3zneO2Fu2bBFdkRJC0LlzZ327ly9fomjRonqLAE3T0Gg0uH79uhOl///cunULQ4cOxeeff47ffvvNYVms3yczMxPR0dH5zmophSAIiIuLc3gh3YoVK0o6X2f/9l27dhVNMZAXsvY3atRI9PwYhrE6mi0zMxNnz57F2bNnERISIqlIdejQwUZn48ZVcStS+Yhr165hwoQJmDx5Mm7dumVxP1FRUaLmcJZlce7cOYv6fP36NS5fvoyXL19aLJcrc/HiRdGcNxRFYcqUKfp2/fr1Ew0Ld4UK5nv27AHLsvoIS5ZlUapUKffWpJ05fvw4SpYsCZVKBYqi0KVLF4flNfL19ZXces/ORi0V9ajRaFw+lcmOHTuMnksPDw9Ur17dqn5PnjyJggULgud58DwPLy8vycSp5mRzd5M3cStS+YQJEyaAZVl4eHhALpeDYRjMmTPHor5WrVolOinIZDKMGjXKxpJbTmxsLJ48eeISzpSCIKBWrVpGIdk8zyMqKkrfTiokXKlUiprjMzMzsX37dnTu3Bn9+/cX3WLV6XSYP38+ChcuDIqi0KBBA7NfcJmZmaKyURSFSZMmmX9B3JhEeHi40bYZRVEICgpyyPhS1iZ/f3/9c9W7d2/RzOE0Tbt8wIggCBg1apTe8svzPEqXLm1VLb5Xr15JOuxnJ05VKpVgWRYDBgxwifnJjX1xK1L5gBs3bkgmY3v06JHZ/a1fv150opDL5Rg/frwdzsA8oqKi0KhRI32CvuLFiyMsLMzhcmQ7MA8ZMgSzZ89GeHg4OnbsCKVSCYVCgZo1a+Lq1asGxxQuXFhSkXp/WycrKwvNmzfXK7XZObjmz59v0G7UqFGiDtr//POPyedy8+ZN0d+cEIJKlSpZfpHc5MiAAQMky5vcv3/f7uM/fPgQBQoU0C8Asu+xd60od+7cMVpYsSxr0Va/s4iKikJwcDDOnDkjqdg8fPgQY8aMQYcOHbB06VLJbe1ly5aJRgFm+0OuWLECc+bMcdp2fVpaGhYvXoy6deuicePG2Lp1q1uZszNuRSofMHXqVMkV46JFi8zuLz4+XlQxYxjG6bWpBEFAuXLljM6X4ziHVnx/+/Ytqlatqlc+aJoGx3E4ffo00tLSJCfhKVOmGG2bKpVKtG7d2qjtrl27JFe+2b4pb968Ed2G9fDwQJcuXUw+nydPnoj+5oQQ1K9f37KL5CZXpJISarVaHD9+3CEyREZG4ttvv0XNmjXx1Vdf4fLly0ZtLl++jAYNGkCpVMLX1xezZs3KVwEAx48f11uSspWikiVLilrcZsyYIWrFk8vlmDVrlkHb+Ph4XLlyBa9evXLIeWRmZqJevXoGih7Hcejfv79Dxv9QcStS+YCZM2eK+t0wDGNxvaLg4GAwDAO1Wq3PjfK+JcQZnDp1SlS5UKlUDrWWTZ06VVSBKVasWI6rv7S0NLRo0QIsy4LjOKjValSsWFE0cq979+6iL1me57Ft2zZkZGRg/vz5RlFX2X/lypUz65zq1KkjqqBu27bN7OvjxjTGjx8v+vtRFCVZ7NWNbdHpdPDz8xOdU8aMGWPU/uzZs5L+UNlb71lZWRg6dCgoioJGowFFURg4cCAyMzPtei7BwcGi8yPDMLhz545dx3YkiYmJOHnypGikpjNwK1L5gIiICMmtvWyHUUuIj4/H2rVrsWLFCpfJu7N582bJLaivvvrKYXKUK1dOVAaWZREREZHr8deuXcO6detw8uRJScVr6NChoitfnuexYcMGFC9eXPJayGQys8Ounz17hvLly0OtVusn/5EjR+bZbYH09HT8+eefWLlypVX16exJdHQ0PD09DX5nlmUxdOhQZ4v2QfDgwQNUrVpV9BkihKBUqVJGxwiCgA4dOhgoUxzHoVOnTvpnZfr06aLb7fb2NxwyZIjkvLRy5Uq7ju0IBEHQL2Kzc4d9/PHHDrP4SeFWpPIJS5YsMXB2pGkaf/zxh7PFsjkRERGSEYXLli1zmBxSk69CoUD16tXRvHlz7Nu3zyol5OrVq5IZmWUyWY4FW1mWxZUrV8weUxAEXLhwAX/++adVSrizuXXrFnx8fMDzPBiGAcMw6NOnj0OyTJvLo0eP0KVLFxQsWBClSpXCb7/9ZrKccXFxWLduHdasWZNnI2KPHTuGypUrw8PDAz4+PpgzZw7OnDmDCxcu2HX7MD09HYUKFcrxOapWrZrosVlZWdi0aROCgoLw6aefYvPmzQa/mVRNP61Wa7fzAf6zlIvVUuR5Hrt377br2I5g586dRtZApVLpsOAMKdyKVD7i+fPnWLZsGVauXJmvkzz26NHDQMFQqVQoUaKEQ3MeLVmyRFTJeXdS5jgOP/zwg9Xj0DQNnudznPDfV+Y6duxo04gqQRBw+fJlbN++3WXM6VIIgoDSpUuLbr1s3LjR2eLZjM2bN+t98ziOA03TWLVqlbPFMouzZ8+KWtNVKhV4noevr6/FKVdyIzg4WDL3m7VWHDGf1ew/uVyOoKAg3L1718ZnBDx9+lR0XvL29nbpnGxZWVmYNm0avLy8IJfLERgYKBqhXK9ePdFr6uytcLci5SbPkZWVhSVLlqBSpUoICAjAyJEjHW7azcrKQseOHQ0sgGIPOE3T2Lt3Lzp06ICPPvoIU6ZMMVvW+Ph4jBw5UtIZXOxPpVKhVKlSBuUyLCU+Ph516tQBx3F6C0/Hjh0trn1nb27duiXqw0IIQYMGDZwtnk2Ijo6WDAixJFLXWQQFBeV6L2s0Grvk1fr1118l/Qvlcjn69etnsmVQEARcu3YNhw4dQmxsLOrWrZvjOclkMhQoUMAuC96QkBB4eXmB53mo1WqUKFHC6UFCufH111+LboW+nw9RquSYWq126va9W5Fy48YKbty4gRUrVkhOnDRNg6IovTWJoigUKVIEcXFxZo0zdepUk5Wody0wa9asMerr7du3ZpXnaN++vVF+LIZhjCKUXIWrV69KWhpq1arlbPFswpIlSyQtOZbmj3MGUulA3n9Jrlu3zuZjSzmNUxSFJUuWmNxPdHQ0qlatCo7j9NUbevfurc/rJ3VeNE1j5syZJo/z5s0bnD592qS0GJmZmbh48SJu3Ljh8j6O8fHxkpHH3bt3N2g7fPhwo7mIEAJPT0+nLuxyUqQ8iBs3bnKkWrVqZMiQIaRWrVpELpcbfZ+WlkbS09P/W5kQQtLT08mrV6/I/PnzzRqnUqVKRK1Wm3VMcnIyCQsL0///4sWLpGrVqsTT05PwPE+6d+9O/v333xz7SE1NJQcPHiSZmZlGny9fvtwseRxF9erVCU3TRp8zDEN69erlBIlsT0ZGBhEEwehznU5H0tLSnCCRZVSsWDHXNhkZGSQ+Pt7mY9evX5/Uq1fP4F6hKIqULVuWDB482OR+OnbsSO7cuUOSk5PJmzdvSFpaGgkODiYzZ84kXbt2JUWKFCEKhcLouLS0NHL16lWTxpg9ezYpVKgQadOmDalWrRpp0KBBjtdEoVCQunXrkmrVqhGZTGbyuTiDR48eEZVKZfS5IAjk77//Nvhs4sSJxMvLi1AURQghRCaTEZZlybJly4hSqXSIvGYjpWG56p/bIuXGWYgVds3JIbxKlSpm9Z+eno6SJUsapLlQKpXw8/NDz549RVd0FEVh+vTpAIDHjx8brb6zC7fmRGJiougKkBACLy8vi6+XvTl69ChYltVv3ajVatStWzff1HiUitRlWRZ///23s8UzmTNnzuS6Zc2yLK5du2ZSf69evcKBAwdw7ty5XC0xt27dQpkyZfTPqEKhwKBBg8zaRnz69Knktv7HH38MAPj7779F/ZZomsaMGTNyHWPPnj2iDtbNmjUzWU5botPpcObMGRw6dAhv3ryxur9Xr15JWqS6detm1D42NhaTJk3CRx99hK+++goXL160WgZrIe6tPTeuTlpaGpYvX44mTZqgTZs2OHjwoN3HfPbsGfr06QMfHx+UKlUKv/zyS64RRFu3bgXP89BoNOA4DqVLl5b0wbBkEnz58iW6desGmqbBMAx69OiBuLg46HQ6lCxZ0sjBVa1W68vTjB49WlQhMiUDeqVKlYyOk8vl6NWrl9nn4EgiIyMxffp0DBkyBLt27bJ7Dh9HM3XqVP32UXZGcrG8R67O0aNHUaVKFchkMiiVSoP7lOM49OjRw6R+Zs+ebVAKpmTJkpKFid++fSuq3LxbrNkUbty4IbmNXKFCBX27Jk2aGMwF5vhISSVtpWnaoPyUI7h16xaKFi2qn+cYhsHy5cut7nfQoEFWV2dwJm5Fyo1Lk5GRgY8++sgoU+/48eORmpqK7du3Y+HChTh//rzNfAHi4+Ph6+trYP1hWdYkxSEtLQ3nzp3DrVu3IAgCPv74YyMFhmVZmyuDz549Q8OGDUFRFGiaRunSpQ2inVq2bCk6GWs0GuzduzfHvi9evAi1Wq0Pq2YYBr6+vi6TWywvIQgCQkJC0L17d/Ts2RPHjh2zOkXGmDFjMGrUKJdYmVtLZmYm1q9fjyZNmuDTTz/F1q1bTXL4PnbsmKhFuGzZsqLXd9GiRZIWsHHjxpksb0ZGBjw9PUUVsncTBCclJWHo0KHgOE4ftWdqgkypnHU8zztU0cjKyhL1aWNZ1uri1ZmZmZg8eTIKFCgAmUyGWrVq4ezZszaS3P64FSk3Ls2WLVtEHUJVKpU+MkWlUoHjOLRq1comDoezZs0SNTXTNG12GZqYmBgEBgaCZVl9Ajl7OgPHxcXh+fPnRi+PadOmSZ7Tw4cPc+03MjIS48ePx5dffom5c+ciISHBXqeQr+nXr59RIsfhw4c7W6w8T7t27USVDY7jRGvedezYUVKRqlOnjllj79y508CxnGEYBAQE2CySeMSIEaLW5AIFCjjUwfrEiROi1jcPDw+blqBxded4MdyKlBuXplu3bqKTnVg0THbRUGtp1aqVpPVmz549FvV59+5dhIWF2cSnwBJiY2NRsGBBg+vGMIxDs8F/6Fy6dEl0O4lhmDyzheGqNGzYUNJqc/LkSaP2EyZMkFSk2rVrZ/b4169fR79+/dCsWTPMnTsXr1+/tsVpAfhvS9/Pz0+/NZi9jevohMt79uyBRqMRvWZt27Z1qCyuRk6KlDtqz4ncvn2bjBs3jgwbNowcOXJENELnQ8DPz080Gk7seqSkpJA1a9ZYPWaFChVEI0CysrJIiRIlLOqzfPnypHHjxkSj0VgpnWX4+PiQK1eukI4dOxKNRkP8/f3JxIkTyebNm50iz4fIoUOHRCPqdDodOXz4sBMkyj907NhRNFLz7du3xM/Pz+jzcePGEQ8P41ech4cHmTBhgtnj16hRg6xdu5aEhoaSsWPHEq1Wa3YfUvj5+ZF//vmHjB49mtSpU4e0b9+eHDt2zCYRqJmZmWTfvn1kxYoV5ObNmzm2bdiwIcnIyDD6nOM40qFDB6tlybdIaViu+pdfLFKrVq0CwzB6Hx2GYVCyZEl06dIFmzdvdtlEiPYgPDzcrESU5hbqFePBgweiUTKBgYE2OCM3HyoLFiwQDT5gWdYmDrsfMklJSfDy8hK1XDdp0kT0mF27dkGhUOija+Vyud1r4bkSERERKFSoEFiWhVKphEqlQrt27XIMqpk7dy5YltVHOnIch8DAQJfImp6amop79+45xepP3Ft7rkVCQoJkOG32jVuvXj2XuHEdxZYtW/SFdNVqNYoVK4aiRYuK+vtkh/tby6lTp1CmTBlQFAWVSoW2bdvatOSKmw+P58+fS2YjNzdBqxtjvL29RedMhUKBpKQk0WMSEhKwbt06LFu2DI8fP3aswE6mSpUqotdr4sSJOR536tQpdO3aFS1btsTq1aud/i4SBAE//fQT1Go11Go1aJrGkCFDHGpwcCtSLsauXbtyrP+UvYLNazW1rCUlJQUnTpzApUuXoNPpcPnyZfA8r/c5UavVqF27NpKTk202piAIiI2NdWgNPzf5m+DgYLAsC41Go18YmBLB+eDBA4wePRrt27fH4sWL7VIyJa9jiSL1ofLkyRPJ/HAqlSpPOXyvX79eNHXCiBEjHCZDToqU7L/v8w516tTBlStXHD7uixcvyPr168mzZ89I06ZNyZdffmlxltUDBw6Q7t27k7dv3+bYrlmzZiQ0NNSiMfILCQkJZMuWLSQyMpI0bNiQ1KtXj4SGhhKFQkFatWpFeJ53tohu3BiRlJREQkNDiUwmI59++ilhWTbH9qGhoaRt27YkMzOTZGZmEpZliY+PD7l69SopWLCgRTJkZGSQ8PBw4uXlRYoXL25RH67G8OHDyapVqwz8eDw8PEiDBg3IqVOnnCiZ6xEREUEqVKhAxN7xMpmMREREkDJlyjhBMvMpX748iYiIMPqcYRjy5s0bh2Q8l8lkVwHUEf1SSsNy1T9nWKTCwsL0ldfJ/ywjNWrUsHgFlJqaCq1Wm6sv0JdffmnjM8nbrFmzBjRNg+d5vaXqwIEDNh8nLi4OP/74I5o2bYrBgwebnAvGjRtLEAQBRYoUEbUajB492qI+N2zYoE9aSdM0GjRoYJfiuaYSGxuL48ePm1RDLicSExNRsWJFqNVq/Vzs6+srmZTzQ0YQBIM8eeQ9C15ERISzRTQZqfelSqVyWJoW4t7asxydTgd/f39RXx1zilG+T1hYmL5yt1iJEY7jcPToURueSd7m/v37kuUybPkgPXv2DD4+PnqlWS6Xg2VZHD9+3GZjuHHzLg8fPhRNmUAIQYkSJczu79y5c0b9KRQKs3Mn2QJBEDBixAhQFKXPsda0aVOrnIUzMzOxe/duTJkyBevXr7fpVr8j+Oeff7Bw4UKsW7fOpikUxBg2bJjkfZWXtvaCgoJEz8Pf399h5+FWpKzgzp07oskiCSGoVKmSVX0nJSVhx44dmD59Ory9vfWWFoqiMHnyZBudQf5g2rRpovv9HMdh7dq1Nhunb9++RmVYCCEoXrx4npp43OQdXr58KVlmqGrVqmb317lzZ9HFGcuyuH37th3OQJqVK1caKXUURaFjx44OlcMVEAQBQ4YMAcMwoCgKHMdBrVaL5sCyFWlpaahbt65+7lSpVOB5HleuXLHbmPbg2rVr4DjO4L5mWRY7d+50mAw5KVLuPFK5oFKpJPM7ZVenthSO40jnzp3J5MmTyYsXL8jOnTvJ77//Th49ekSmT59uVd/5jZSUFJKVlWX0uU6nIykpKTYbJyQkhOh0OqPPY2JiyMuXL202jhvX58mTJ6R///6kRIkS5KOPPiJ//vmnXcbx8/MjgYGBRKFQGHzOsiwZPny42f09f/78v1XyeyiVShITE2OxnJawcOFCo+czPT2d7N+/P1cf0fzGwYMHyaZNm0hqaipJT08nycnJJCkpibRv355kZmbaZUyKosj58+fJgQMHyI8//kh+++038uzZM1K7dm27jGcvatasSS5cuEA6dOhAAgICSNOmTcnBgwdJp06dnC3af0hpWK765wwfqUqVKhmt8FiWxcqVKx0uy4fK2bNnRS2DNE3j0aNHNhtHquaVSqVyWsZyN44nMjISnp6eBtZJlmUxb948u4wXFRWFChUqQK1W6/2a+vXrZ1INuvfJqVSQvbeS3sfPz0/0ebJXMd6kpCRER0e7pPW4ffv2otdCo9EgNDTU2eK5yQXitkiZR1paGlm/fj356quvyHfffUfmz59PfH19Cc/zhGEYwrIsadOmDRkwYICzRf1gqF+/PunSpQvhOI4Q8l+kDsuyZPz48aRkyZI2G+fbb781irBSqVSkVatWTstY7sbx/PTTT+Tt27cG1smUlBTy448/2tQCmo2/vz+5ffs2OXLkCFmzZg25ffs2Wbt2rWhm7twYPnw4KViwIFGpVPrPOI4jkydPtmk2blNo0aKFaNUCHx8fUrhwYZuNk5SURHr06EEKFixISpUqRYoVK0YOHDhgs/5tgZhFPRsxK7gtePjwIVmwYAFZuHAhefr0qV3GcEPcFqn3SUpKQrVq1fTWD4VCAZZlsWPHDuzZswfLly/HzZs37SrDh8Dhw4dRr149+Pr6onnz5iZVFhcEAaGhoRg0aBC++eYbXLhwweZy6XQ6DBkyRO8cy7IsPv74Y3cB3w+MihUrSloPrl275mzxciUuLg7jxo1D5cqV0aRJE+zbt89uY719+xbbtm3D2rVr8ezZM4Pvnjx5goIFC+p9wLKDN0JCQnLs89KlS2jdujUCAgLQsmXLXJ/1zz//3MjPjGVZXL582erzsxXbt28Xtaqr1WqkpqbafLy5c+fq/bEoigJN01i2bJnNx/lQIG5nc9OZN2+eaHSYVqtFenq6Xcf+UNi6datocrXz5887WzQ9UVFROHjwIG7duuVsUdxYSVJSktmZmaWKWtM0jejoaDtJmvc4ceKEfjsyO0XMrFmzDNq8ePEC48ePR/369dG7d2/cuHEjxz7DwsJE5wepyNnIyEjRrUyZTIbOnTvb7FytRafToUOHDnpliqIoMAxjFyX37t27ou8xmqYRGRlp8/E+BNyKlBkEBgZKrkTtYQH50BAEAYULFxa9xo0aNXK2eG7yETdu3ECdOnWgUCigVCrRoUMHvHr1yqRjT5w4IRpt1rp1aztLnXdISUmBRqMRjQ60Zq6sWbOm6PxQuXJl0fZnz56VzDNUo0YNi+WwB4IgICwsDBMmTMDcuXPx/Plzu4wze/Zs0RxSNE1j0aJFdhkzv5OTIuX2kXoPqUzZOp2OqNVqi/tNSkoicXFx/2mvEkRGRpJDhw6Re/fuWTyOq/Pvv/+SV69eiX53/fp1B0vjxlxevXpFLly4QGJjY0lycjKZPn06KVeuHKlUqRL59ddf7RZ9ZC4xMTGkUaNG5MqVKyQrK4tkZmaS/fv3k6CgoByfwWyaNGlCli9fTjw9PQnHcYSiKPL555+TrVu3OkD6vMHRo0dFP09LSyPr1q2zuN+bN2+Kfn779m3R365SpUokPT3d6HOlUkkaN25ssRz2QCaTkcaNG5PZs2eTsWPHkiJFithlHKlIc0KISfe/GzOR0rBc9c/eFqng4GCjfWyZTIZy5cpZFAny6tUrtGnTBiqVCiqVCuXKlcPZs2cN2mRmZqJHjx6gaVqftK5Zs2b5sv5bZmamZF6u8uXLO1s8NxJkZWVh0KBB+nuUoih4enoa+KWwLOsyFpuZM2eKbveo1WqcOXPG5H4yMjIQERHhLmYtwvbt2yVrhvbq1cusvuLi4rB3716cOnUKvr6+on16eXlJHv/99/+PvTMPj+n84viZzHqXmYhIBAlJbCVILbW1lBbVatNSSxuqpVrV0lKqqB+tpbaqfWuppaUoWtSulJRSqsQS+xpbSSIii0nmfn9/3GaYzL2TyeyJ+TzPfcjMe9/33Jk77z3vOec9Z7CFBTEgIAClSpV6ZN1YSUlJsq69ixcvelu8Ygn5XXv2IwgCBgwYAK1Wa06QGR4e7lA6fUEQULduXatEkhzHWVQhHzt2rNVNr9Vq0b17dxdeme8wdOhQyRiIH374wduiPTIIgoB9+/bhf//7H8aPH49Lly7ZbD9q1CjZ7NsFv0d7Ng64m/j4eEn5eJ7HkiVLvC1eiSAlJUVSWeU4DuvXr7e7n/Hjx0On05lL2gQGBlr1y7KsVezVwwiCgPnz5+Oxxx5DSEgIOnfuXGjZmPXr16NWrVrQ6XSoWbMmfv75Z7tlLg58+eWXYBgGarUaGo3GI269O3fuYO7cuRg6dCjWrl2LvLw8t47nSfyKlANcvnwZP/74I7Zv3+7wzfDXX39JWl80Gg0GDx5sbicXM6TVamE0Gl11ST5DXl4eBg0aBJZlwbIsAgMDMXXqVG+L9cggCAJ69OgBlmWhUCig0WjAMAx+/PFH2XOCg4MLVaLyV7zTp0/34NVIM336dEnFj2VZHD582NviuZVLly7hzz//9Ejes7lz54JhGHM8DsdxePXVV+3Of7Vjxw7J78lgMIBhGPA8D4ZhMHDgQIdyasnxyy+/SC7mVqxY4bIxfIGTJ09i3LhxmDBhgtvrER45csS80zl/0VK3bl2Ha9L6Gn5FykusXLlSMhiTiBAXF2duJ2ceVyqVdt2EKSkpPpuEzhbZ2dlITk4ukcqiL7N582ZJBZ9hGNmHr1zx04KHXq/H6tWrPXxF1qSnpyMsLMwioaZOp0ObNm28LZokgiBg27ZtGDBgAEaNGuVQktk7d+6gdevWZverTqfD559/7vZ54dixYxg8eDD69OmDLVu2FGm8jh07yloOf//9d5w6dcotD2JbiXfnzZuH3Nxcl49Z0qlZs6bkwqqklDvzK1Je4syZM5Kmb4ZhLDIkv/LKKwgICLBqV1idreTkZDRv3txstq1WrZp/Z6GfQunevbvkQ8RgMGDVqlWS5zRp0qRQJUqhUCA0NNRn0oQkJycjPj4eBoMBoaGhGDZsWJHTIHiCvLw8xMXFmZXbfAthUeuIxcXFWeVS4jjOp60szzzzjOy9uG3bNreNK1VP82HL1Esv8HZT9wAAIABJREFUveRWBTQvL6/YLXxtkZycLPmsI3Ks8LYtdu/ejSeeeAJarRYRERGYM2eORz5LvyLlRV5//XULE7JKpUJYWBjS0tLMbc6cOWMRuKtWq8FxHPbu3Svbr8lkQnR0tNWEwPO8P8+NH5v06NFDsqitXq+XjRM5cOAAOI4z329KpRI6nQ7lypUDwzDQ6XSIjY3FqVOnPHw1xR+5RI0cxyEzM9OuPlJSUmQLH/vynDlr1ixJ1x7DMG7dbBMREWFzUVDY/Osof/zxB2JjY6FQKMBxHAYNGuQzCw9nOH78uGRReSJC5cqVXTbOvn37JF2ytuLnXIVfkfIiubm5mDhxIiIjIxESEoKePXtK1pi6fv06hg0bhpYtW6Jfv36F+rO3b98u6RLU6XQYPXq0uy7HTwlg586dsg9uW26UkydPokePHqhTpw7eeOMNHD9+HIIg4Ny5c4/s7ihXEBcXJ2uVKSwDeD5nz56V3Q0bERHh5itwnKysLDz++ONm2QMCAjxSx3ThwoU2N0+oVCqMHz/epWMeO3bMakyGYdCtWzeXjuNJTCYTPvjgA2i1WkmvCsMwLlVy2rRpI/l98TzvdmuzX5HyIjdv3nRLeZHvvvtOduJ88803XT6evdy5cwfbt2/H4cOHS5TpuqQxcOBAc/kIjuPAMAw2bNjg8nH++OMP9OzZE/Hx8fjll19cGjBcUujUqZOsIiWXzbsgeXl5KFOmjFUfSqUSPXv2dPMVOEd2djbmz5+Pdu3aoUePHrJlXQRBwJ49e7Bs2TKcPHnS6XHnzZsHnudlH8wLFy50eoyH6datm6RLUafT4caNGw73u2bNGtSrVw+hoaGIi4vD0aNHXSi1bSZNmiSpkCoUCvA8j+bNm7tUwQkLC5N1x7o7rYNfkXICQRBw5cqVIitDBw8eRI0aNaDVaqHRaPD000+7NIttYmKiZJ4QjuOwYMECl41TFCZNmmQOdOU4DjExMcXKUpGbm4sbN26UCFO7PSQlJeHrr7/GN998Y3fG76LwxRdfmHcG5t+br7zyCkwmE3777Td07twZbdu2xaJFix7pDQdywf9BQUFF+lyWL19u8XlrNBqULl260NQWxYGbN28iJibGXI6GYRh06tTJ6aDw27dvSypTgYGBuHv3roukF4mNjZVUAgIDAx12IxZ0jeYrMJ4qbVWhQgVZi97gwYMxd+5cq/qLztC8eXNZRSorK8tl40jhV6QcZNu2bYiIiDCv3Nu2bYtbt24Vet7Nmzet3G5KpRJRUVEuzavxyiuvWPyINBoNoqKi7I6rcCVbt261WpkolUrUqVPH47I4wrRp01CqVCnodDrwPI///e9/hVpPTp8+jZUrV+LgwYN+61sB5OqfcRyHbt26WbzHsiyaNWv2yO6UEgQB/fv3h06nM2/51+v1SEhIKHJfe/fuRfv27fH4449jwIABkmEEvs7JkyfRt29fvPjii5g6dSrS09PRpk0bqxgclmUtNu04yp49e1CuXDnwPA+O4xAREYGDBw+64Eos6dmzp6xF6t9//y1yf0ajUbI0jkKhQIcOHVwuvxS23KMcx4FlWeh0Onz11VcuGW/nzp1WBgSWZS3SCbkLvyLlACdPnrS6SdRqNRo0aFDoufkJ5greWHq9Hlu2bHGZjEajERMnTkTlypVRoUIFfPjhhx7PwHzs2DFMnjwZtWvXll0pnDhxwqMyFZXFixdLBjDKxZoZjUa8+uqrYBjGXKy1QYMG/uzXD7FgwQJZ17PUwTAMVq5c6W2xvcrp06cxa9YsLF26tERWNbCHTZs2gWVZc7oNlmUREREhG8gcHR3tknFNJhOOHDmCxMTEIi+KTCaTXS7rU6dOWVm/WJbFu+++65DM586dk/2NlS9f3qE+i0qrVq3s/n0nJia6ZMx169YhOjoaAQEBMBgM+OKLLzwSMuBXpBzg/fffl8ydw3FcoQn93n77bVml4ptvvvGI/O5GEAR88MEHYBgGGo1GMtCQSIzzKEpJDm9QuXJlWZO71A9UKhO9Wq1G+/btvSC9b2KrfIjc0bVrV4/KmJycjKFDh+K5557DsGHDiqX1piRhMplQtmxZq/tCrVbLzi9hYWFek/fGjRto3749VCoVlEolnn/++UJDGf7++280a9YMGo0GISEhGDNmjMNeirt378qmHGjSpIlDfRaVxMRE8DxfaJ45pVKJTz/91KVj379/36OeAL8i5QCtW7eWVQzWrVtn89yFCxdKrhRYlsWhQ4c8Ir+72bRpk10Wh6Js4fYWUrFm+T9+Kb97eHi4ZHuNRuN2P31x4d69e0VWpHr16uUx+Y4dOwaDwWBOGaDVamEwGCRjS1JSUjBlyhT07t0bixYt8n/HbuL06dOyc4qURUqtVuO9997ziqy5ubmIioqyUCCUSiXKlSvn0fvj7bfflnR1uWPjiBxnz55Fr169bObmUigUGDBggMdkcgd+RcoB8usUFbwhtFptocFzWVlZiI6OhkajsTBtPv/88x6R3ZVcvnwZw4cPR+fOnTFz5kyzy+G1114r9MGo0+ncvo3ZFTzxxBOS8oeHh0uueIKCgmQn+4fzgz1qnD17Fv369UPLli0xZMgQrF69GoGBgTAYDDAYDNDpdChdurTs/WLvVn9X8PTTT0tO9i1btrRol5iYaC4kTiTu5oqKirIrVtJP0bh27ZpsLqxq1aqB53nznMqyLMLDw3Hz5k2vyPrLL79ILhQ8Xcvx/v37ePfdd6HT6cCyLEqXLo3vvvvOY+Pnk5aWZvG8k1pQ+7pnojD8ipQDpKamIiwszGLFURR/dkpKCvr164dy5cohMjISY8eOLXa7wfbs2WM1eUVERODmzZuypR0KKp3uSGrnan7//XfJVd3y5csl23ft2lVy9RUTE+NhyX2Hffv2geM4s+VAq9UiMDAQiYmJ+PXXX7Fq1SqkpaXho48+knQDBAUFedRML7d6ViqVFu3q1asnqTA7GtfixzZPPvmk1f3BcRwWLlyIy5cv47PPPkPHjh0xffp0j9QSlGPChAmy7qxhw4Z5XJ7MzExcuXLFa0WC8/LyZC3QCoUC7733XrHfkONXpBzk2rVrePfdd1GhQgXUqFEDs2fPLnZ5cE6fPo1evXqhbt26ePPNN+0O/BYEAVWrVpV8iPTp0wdr1661y7XXrFkzN1+ha/jjjz/QrFkzBAUFoUGDBti4caNs2ytXriA0NNSsfGk0GvA8/0iX55Ha2q1QKPDiiy9atLt16xYqVqxoDu5XqVRgWdbufEmuQu7e1ev15jZ37tyRDXIuU6aMR+V9VLh27Rpq1qwJnufNrtc+ffr43EN4w4YNshapgsW/z507h379+qF58+YYNGhQsUoJUxRGjRpltWlHpVJh3Lhx3hbNJfgVqUeUv//+GzzPW5T1sLf0wfXr12XN7OXKlYPJZEJ8fHyhypTBYPDAlXqe1NRUTJw4ES+//DKGDBlSInL1OEp2drZsMDDLslbt7969i+nTp+Pll1/Gxx9/7Paq9FL069fPKlBXp9Phww8/NLfJyMiQVaTKlSvncZkfFQRBwP79+7FmzRqvKB1paWk4cuQI7ty5I9smLy8PNWrUsHBnqVQqREZGWiSgPHDgAHieN99HGo0GBoMBx48f98SleBSTyYQxY8bAYDCYS6EtXrzY22K5DL8i9Yjy1FNPST4E6tatW+i5tnze+bWTBEHA3r17MWzYMNm2NWvWdPdl+vEyJ0+elFWkQ0NDvS2eJFlZWWjbti0YhoHBYDDHMGZnZ1u0a926tZULR6fTYfjw4V6S3I+7yMvLw/vvvw+dTge9Xm9WrOW8ECkpKejRo4e5MsDrr79ulaG8fv36kpba1q1be+KSvILJZEJGRobPWRGdxWuKFBG1JaJTRHSWiIbItOlMRCeI6DgRLSusT78iZT9yq2mFQmGXi7JVq1ZWDxGWZSWTqw0bNkwyF5NU5fmcnByvxjcUV86cOYMlS5Zg27ZtXouFkGLgwIGSRZCJCG+//ba3xbPJyZMn8csvv8iWHLl69SoqV65szqbNcRxatGhhpXDZIikpCZMmTcL06dNx4MABxMXFQaPRgGEYvPXWW4/0BgVfYuTIkZJz2JdffulQf3l5ebK/C61W62Lp/bgbryhSRKQkonNEFE1EGiI6QkQ1C7SpSkT/EFHQf3+HFtavX5Gyn+DgYMkfMcdxdq0Wrl+/jho1aliUZejYsaNkBuq8vDwMHToUHMeZd2fNmTPHok1GRga6desGjUYDlUqF6tWrY/fu3S673pKKyWTCW2+9Zc66rtfrUbFiRZw/f97bogEA2rdvL3mfqVQqLFu2zNviOU1eXh42b96MOXPmYP/+/UVaaQ8bNsyca00q549Go0GdOnVK3Oq9OFKqVCmXxsMJgiCbWiU4ONjF0vtxN7YUKRW5j4ZEdBbAeSIihUKxnIheJtH6lM87RDQLQBoREYB/3SjPI8eHH35IEyZMoKysLPNrDMNQnz59SKFQFHp+WFgYHT9+nPbs2UOXLl2iBg0aUPXq1SXbKpVK+vLLL2nw4MH0/fff0/Xr1ykoKIiMRiNpNBoiImrfvj0lJCSQ0WgkIqJTp05R27Zt6Z9//qFq1aq54IpLJosWLaKVK1dSTk6O+bXMzEx69dVX6dChQ16UTOSZZ56hLVu2WNxnREQqlYqaNGniJalch1KppOeee67I5+3fv5+mTp1K2dnZsm2MRiOdP3+edu7cSc8884xjAubkEB06RHT+PNHVq9ZHVhYRzz849Hrx36pViZo1I3rqKaLSpR0bu4QAgNLT0yXfS0tLc6hPhUJBPXr0oO+++87it5s/B/spQchpWM4eRNSRiOY/9PcbRDSzQJtfiGgiEe0hon1E1Lawfv0WKfvJzc1Fz549zYWEdTod4uPjJdMwCIKAO3fuOFXv7OLFiyhbtqw5AJ3neURHR+PWrVs4ffq05OpMpVKhT58+zlxmiUcqzoL+i9Vxd8Vze8jIyEBkZKRFnBzHcejZs6e3RfMqH330kWwQfsHvcebMmfZ3fPs2sG4dMHgw0LQpoNGIzgVnjpgYoE8fYMMG4BG1jtWpU0fy+7GnLJgcWVlZaNeuncUc3KVLl0e6SHdxhbxkkZIyeaDA3yoS3XstiCiciBIUCkUtAHcsOlIo3iWid4mIKlas6HpJSygqlYoWLFhA48aNozNnzlDlypUpLCzMqt3y5cvp448/ptu3b5NWq6V+/frR6NGjSalUFmm8Xr160a1bt0gQBCIiunfvHt2/f58GDx5MXbp0IY1GY7U6z8vLoxMnTkh15+c/MjMzJV9XKpVWViBvwPM8HTx4kMaPH09r1qwhnuepb9++9Pbbb3tbNK+SP8kWhkqloscee0y+gSAQ7d1LtGIF0Y4dRAV/LwoFUa1aRDExRBUqWB88T5SZSXTvHlFGhvhvejrR4cNECQlE+/cTHT8uHnPmENWtSzR8ONErrxAFBDj5KRQfZsyYQc8//zxlZ2cTAFIoFMQwDE2bNs3hPhmGoV9//ZXOnz9PZ86coRo1avifYSUROQ3L2YOImhDRlof+HkpEQwu0mUtEbz30929E9IStfv0WKdeyefNmyQDLQYMGFakfo9Eom6BOr9cjOTlZMp2CVqvFkCFD3HR1JYMRI0ZIxteEhYX5dF4zQRCwY8cO9O3bF59++mmJ3PJtiz179lj9tgoeGo0GtWvXtv4eBQE4eBAYNAiIiLC0Hmm1QPPmwLBhwMaNgLPB6jk5QEIC8MUXQFjYg3Fq1QJ+/BF4SLbMzEx8//33GD16NDZt2uTT919RSUhIAMdxUKlUUCgUCAgI8FvL/ZghLwWbq4joPBFF0YNg85gCbdoS0eL//l+GiK4QUbCtfv2KlGtp1KiR5ATPsmyRdibZUqQCAwMBAG+99ZbFgyUgIABBQUG4du2auy6vRJCeno7HHnvM7DLVaDRgWRbbtm0DAPz777+YMWMGRo0ahT179vhE4LIgCBZ5xlQqFRiGwezZs70tmkf5+OOPwbIslEoltFottFotYmNjoVKpoNVq0a1bN6Smpj444cQJ4H//A6pWtVSeIiKATz4B9uwRFR93kZUFzJgBhIc/GDsuDkhLw+nTpxESEgKe5xEQEACe51G/fn3cu3fPffJ4iJycHAQGBkrOgwkJCd4Wr9iwefNm1KlTB1qtFlWqVMHSpUu9LZLL8IoiJY5LLxDRaRJ3733232ujiCjuv/8riOhrEgPQjxLRa4X16VekXEtISIisIpWcnFykvtq1a2dVekOj0aB3794AxN1PEydORHh4OAwGAzp06OCVZIzFkezsbCxcuBBdu3bFsGHDcOHCBQDAtm3bzHlsAgICwHEcOnXq5HVLwZYtWySTtep0Ovz7779elc3THDlyBGPGjMFXX31lTtxqoeyaTMD69UDLlpbKU9myQL9+ovLk6e8zJweYMwcoVUqUJToanWrXttrOX1Isyhs2bIDBYLC6XxUKBXr06OFt8YoFW7dulSy19e2333pbNJfgNUXKHYdfkXItrVu3lrUiFTUg8urVq6hUqRL0ej1UKhV4nketWrX8eXLspKiJ7IxGo+SWbY7jJPN3uYutW7eiffv2eOaZZzB37lzk5OSgV69ekvcVz/P44YcfPCabT5OZCcyeDVSr9kB50uuBXr2A7dsBJzZ+uIxz54C6dQEi3CLCExLfaXh4uLeldJrVq1dLKlJEhC5dunhbPJ/h2rVrmD17NqZPn25VzUGqLiURISQkxCes5M7iV6T8yPLXX39JxkhNnTrVof6MRiN+/vlnTJgwocTFULgLqdIK9lSQ//3332Un/+eee84DkgOff/65heWJZVk0bNgQffr0kdyxptfr8dNPP7lFlqNHj6J3795o27YtJk+e7LtJX69eFeObSpd+oEBVrAhMngzYKEviNTIzcb9NG4AId4lQvcB3WqFCBW9L6DRpaWmSu4o5jsOaNWu8LZ5PsGjRIuh0OjAMA51OB51Oh6+//tr8vlw8oEqlwt27d70ouWvwK1J+bPLnn3/iqaeeAs/zqFatmt9i4GGkin2yLIuff/7Z5nm7du2SVaSef/55t8t9/fp1ySB4juMkryn/PXfE1Kxdu9Yci0REYBgGlSpVwu3bt10+lsOcPQu8+SagVj9QoBo1Alau9A3rky2MRmwPCgKI8A8RtA+59j799FNvS+cSFixYAIZhzLGeHMchLi7OvxiEaImS+q0zDIOkpCQAQM2aNSXnoqCgILs+w1WrViE2NhZlypTBCy+8gCNHjrj7soqEX5Hy48dHyc3NlawiT0SoXbu2zXONRiNKly4tqawUZvU5cuQIVq1ahdOnTzss+4oVK2Rl79SpE8aNGwedTgeO46DX68FxHLZu3erweHLk5eWhTJkyVjL4zEM+ORno3RtQqcQpNyAA6NgRsKN4uC9x+u+/cT4gACDCtP/ctPXq1UNGRoa3RXMZJ06cwODBg9G7d+9ibVEXBAFbt25F//79MWrUKHNMpaPMnj1bNg/gqFGjAABr1qyRXBBOmjSp0P5nzpxpca5CoQDHcUhMTHRKblfiV6QeEc6ePYupU6di7ty5uHnzprfF8WMHqampsgWfDQZDoefv3LkTHMeBZVmoVCqwLIv4+HjZB0B6ejqefPJJsCxrLtbbvn17ySSthbF161ZJRUqpVOKDDz4AAFy5cgXz58/H0qVL3WbeP3HihGRgOxGhWrVqbhnTLlJSgIEDxXQF+QrUW2+JcUfFlOyEBJiUSoAIB0eOLLaKRkkmLy8PL774osUuX4ZhnHKpz5gxQ9IipVQqMWLECHO7H374AeXLl0dAQABKly6NyZMnFxofZTQaJXdMKhQKvPLKKw7L7Gr8itQjwOeff272W7Msa/cP59KlS9i3b1+JWlX6AoIgYPv27Rg7diwWLVok684ymUyS1hQiQuPGje0aKyUlBXPnzsW4cePw119/2WwbHx9vpbgxDIORI0cW9RKRm5uLsmXLWsnNsqxHzfJXrlyRnOSJCA0bNvSYHGays4GJEx/seCMCOnUC/nOBFHsmTRKvqUwZwD9v+BzLly+XXFhwHIfMzEyH+rx06ZKsa6/gb10QBOTk5NgdYH7hwgXZ+Kpy5co5JK878CtSJZwDBw5I3ogMw1jmqHmItLQ0PPvss9DpdGbLhKNVzv1Ykp2dbY45y8+3U7p0aRw7dkyy/bx58yRN4rt27XKpXEajUdb6VbZsWYf6PHr0KMLDw6HX62EwGMCyLBYtWuRSue2hSZMmVqk3OI7zbB4bQQCWLgUqVXqgQLVqBfz9t+dk8AQmkxjbRQTMmlXk03Nzc7F161YsW7YMV65ccYOAjzYvvfSSrIV78+bNDvc7ZcoUcwyZUqkEwzD47LPPnJY3IyNDdiFk72LSE/gVKRdw5coVfPbZZ3j11VcxZcoU3PGh3TUDBgyQ3CHF8zy+//57yXNeeOEFq4cqy7L+HSouYOzYsVbxBAqFAjExMbLnLF++HNWrVwfHcWjYsCF27tzpcrmysrKslI38Q6/XO9yvyWTCvn37sH37drsDyQVBwLFjx5CYmOgS99C1a9dQq1YtcBwHg8EArVaLAQMGeG7b9YkTYrbxfAWqdm1g06biX7fu8mVgxAige3dg4ULR2gYAK1aI11m9ut05rm7duoV58+ahTJky0Ov10Ov10Gq1GDRoUInYHu8rdOzYUVaR+u2335zq++TJkxg9ejRGjhzpUqtz7969JXNQbdy40WVjOItfkXKSffv2ged5s+LBsizKly/vMxm527ZtK/nD4Xle0jpw8+ZNyXItvrYCKK5UrVpV8rPV6XReX4E//vjjVnIFBATg1Vdf9ZgMf//9NypVqgSO48DzPMqXL489e/Y43a8gCDhw4ADWrVvnud9mVhYwfPiDnXghIcD8+UBenmfGdye//w5w3IOiyBwn5ry6cwcwGh9kP9+0yWY3giBg+PDh0Gg0kgs+juOwdu1aD11UyWfjxo2Srr3SpUv7bLHk+/fv4/333wfDMGAYBsHBwVi4cKG3xbLAr0g5SY0aNaxuSpVKhbffftvjshTk999/l1WK5LJIJyUlged5yXOio6O9cBUlC1uK1OXLl90+/u3btzF58mS88847mD9/vkVcxMGDBy0WBTqdDsHBwTZ39ZhMJpdNwBkZGZKBpTzPy6YqOHHiBBYtWoQdO3b4VnDz1q1A5coPrFC9eokB5iUBQbAsE5N/aLVAvjtn3DjxtbZtbXa1Zs0a2c0A+UebNm08cFGPBoIg4KOPPjLnfMq3/v3xxx/eFq1QsrKycO3aNeT54ELEr0g5we3bt2XjSsqUKeNRWaRo1aqV7OQ0bdo0yXPkMmKrVCpzORc/jjN69GjJrcI1a9Z0+9hHjx5FYGCgeXyO4xAREYEbN26Y21y+fBlDhgxBu3btMGbMGNy6dUuyr7t37+LNN9+EVqtFQEAAnnjiCfzzzz9Oybd48WJJJZ5lWcycOdOibW5uLjp16gSGYcDzPPR6PaKjo4tcusjlXL8OvP76A+WiVi2gGDykisSZMwDLWitSRECVKmKb27cBhhFfs7FAaN68uU0lym8Jdw+nT5/G7NmzsXTpUv9mIhfgV6ScICMjQ1aRUqvV2Ldvn0flKUhUVJSkbBzH4fjx47LnLVmyxCLAWaPRIDg42OuuJ2+TlJSEXr16oUmTJujfv79DFqSsrCw0btwYPM+b86EEBQV5JCdKgwYNJBVkR+qFNWvWzMraqdfrnVJkJk6cCLVaLXnPDh8+3KLtlClTrILwlUolnnrqKYfHdwqTCZg7FwgMFKdOhgHGjxfdXCWN5GRAp5NWpOrUedDuhRfE15Ytk+2qVq1aNpUolmVlF31+Hl1yc3Px008/oUePHvj000+dynnnCvyKlAMIgoBvv/0WMTEx0Ol0VsU6H1ZYTp065RGZpIiPj5eNO8jKyrJ5bkJCAuLi4hAbG4uPP/7YZ2K+vEVCQoJFdmy1Wg2DwYATJ04UuS+TyYQtW7bgiy++wIIFCzyyIszIyDBnZS54BAUF2d1Peno6vvnmG8mdNFqtFkOHDnVYxj///FPSzcPzvFWyzurVq0tei1ar9Xzh40uXgBYtHigTL7wAnD/vWRk8TYMGYu6rh5UolhWLGeczZoz4er9+st0MHz5cNvyA4zjUrVu30LnKz6NFTk4OmjZtarZeq9Vqp3NhOYtfkXKADz74oFC/fv5q/9133/WITFKcPHnSbPl4eHIaN26c12QqrsTExFh9vwqFAi+88IK3RbOLrKwsWWuPvekNZsyYAYZhZPO6EBFefPFFh2UUBAEvvfSSRf8sy6Jly5ZW8U8RERGS4zMM45FYMzNLlz6wQpUtC/z0U/HfjWcPFy+KqRz0ejHQXKcD4uMtA+l37BA/FxvzcmpqKiIjI83uZoVCAZVKhSZNmuD7779HTk6O+6/FjyQHDx5Ex44dERMTg549e+LMmTPeFgkAMHfuXMk5SK/XIzt/56iH8StSReTatWuyKyipwytJ/x7i2LFjeOmllxAcHIyYmBjZWnk5OTlYsmQJ3njjDQwbNkw2wHjZsmWIjIxEQEAAoqKisHz5cjdK7xvYSg3AcZy3xbObF154wcoqpdPpMGTIkELP3b17t00FKr+v0aNHOyVjbm4u5s2bh4YNG6J+/fqYOXOmZGb1/v37S7rVo6OjPbNdPjXVMhbq5ZcBT1vCvE1eHrBtG7BokXRC0YwMQKkUDxupL9LT0zFp0iQ8++yzePPNN3Ho0CGbwxqNRhw9etT78XAlmM2bN4NlWfMiXKlUQq/X4+jRo94WDU8//bTk/GMwGFyeX89e/IpUEdmwYYPkziI5i1SfPn1k+8rMzMS0adPQvHlzvPLKK9i+fbvb5ZciIyPDnGeHSIyJYlkWW7ZssWj3ww8/SCaHLOnKVG5urmxSuPLly3tbPLu5ceMGqlWrBr1eD5ZlwXEcnn76aZuuk9zcXHwtNvo9AAAgAElEQVTyySeyimT+kV/2wVNutZSUFERHR5vvWa1WC47jPLP7aMeOB7vWOE5MaeCI8paSAvzyi9ifD+5Ecgn16omfk4tyn/34448oVaoUeJ6HTqdDs2bN/CWvXIwgCIiOjpb8nT/33HPeFg8vvPCCpGx6vb7Q6g3uwq9IFZGjR4/KrswLPmx4nsc5mdpZWVlZqFWrlpUbwxtutzFjxkgqCqGhoRZbTStWrCh53VFRUR6X2dO88847Vp8Ry7LFLuO7yWTCtm3b8M0332D//v2FWm969+5t0xKlUCig0WgQFxeHs2fPeugqRDIzM/Htt9+ia9eu+Pzzz91vocjJAQYNAhQKcXps1EjcweYIX38tusMMBtE9VrYs4ENFWF3GO++In9WMGU53JVWlQa1Wo0GDBi4Q1E8+6enpsvGUziTndRXr1q2TDK0JDw/3WgoUvyLlAE888YRVvAnLsujTpw+Cg4OhVqvRvHlzHD58WLaPOXPmSD6gdDqdbM4cdyG3c4bnefNuMkEQZIPqAwICPCqvN8jMzMSLL74InU6HwMBAaLVa9OzZ0ydzmriKtLQ0WUtc/sEwDNLT090uS25urnczXB89Ku5IIxJdVZ9/DuTmOtbXnj3S6QPCwkqeZeqzz8RrGzXK6a7i4+Ml5yCWZW3uQvZTNIxGo+zvPjIy0tviQRAEDBgwADqdDhzHQa/Xo0yZMh6t4VkQW4pUAPmRZNOmTfTss8+SVqslhmGoQoUKtHr1apo9ezbdvn2bjEYj7dq1i2JjY2X7WLt2LWVlZVm9rtFo6M8//3Sn+FZwHCf5uslkIpZliYhIoVBQeHi4ZLuIiAi3yeYrsCxL69evp6SkJFqzZg1duHCBFixYQEql0tuiuY2rV6+SWq2WfZ9lWRo3bhwZDAa3ybBhwwaqUqUKaTQaKl26NI0ZM4YEQXDbeJIsWkT0xBNEiYlEVaoQ7dlDNHIkkUpl3/lr1xLVrk2k1xM1aCCem51t3S4zk+iPP1wqutcpXVr8NzXV6a4uX74srvALoFar6fr1607370dErVZTjx49iGEYi9dZlqVBgwZ5SaoHKBQK+vrrrykpKYlmzZpFS5cupatXr1KdOnW8LZo0chqWrx6eziOVkpKCixcvOrRSfvPNN2Vr4O3du9cN0sqzePFiK1NpQEAAatWqZdVOKkZKLoC9pJOdnY358+fj5ZdfRu/evW1aIIsjGRkZkslD6T8zursDO3ft2iV5v3366aduHddMTg7Qu/cDi1HPnmIAdVFYtsza+lQwbUD+YTAA69a551q8xcKF4rV17+50V6NGjZK0lOh0OqR4IGt8Xl4efv31V3zxxRdYvHixRVWAkkZOTg5ee+01aLVaBAYGQqfT+ese2oD8rj3v8Ndff1k9JBQKBSIjIz1+s5pMJvTs2RM6nc6cJbpChQqSMS+LFi1CREQEFAoFKlasiCVLlnhUVl8hMzMTsbGxZgVUqVSCZdkS93kMGzbM6j7lOM4ju3fkduewLOv+3EIXL4pZyYnE0ifz5zvWj1QpFaIHcVYPHzodkJbm2uvwNmvXitfmRFqMfFJSUlC+fHmL3Zocx2HkyJHOy1kId+/eRWxsrDmdDM/zCAkJ8XoiSHdz48YNHDhwAGkl7b50MX5Fyot88803YFkWBoMBPM+jSpUqXs3VcebMGSxatAhbtmwpNPbnUV+ZTJ06VdJaw/O80w/5kydP4vXXX0dkZCRatmzptd2cgPg9z5gxAxEREWAYBs2bN8eBAwc8Mna5cuUkFSmO42zW/3OaGTMeWI0UCjEQ3JHdQPfvSytM+f1y3AMLFcs6F5B96xYwcaJo+Zk1C7h71/G+XElCgniNTZu6pLt///0XAwcORPXq1dG0aVOsWrXKJf0WxqBBg6zS3igUCjRq1MjlY6WmpmL//v24fv261Xs5OTmYOXMmGjZsiGbNmuH777/3rRqTjyh+RcrL3Lt3Dzt27MDff/8NQRAgCALu3btXooOYSwJPPvmk5EPe2Vwmx48fB8/zFm7fR9V92rp1a9lNEG5J1GgyAf37Sys+BgNQ1KB6QQBKl5buLzoaWLJEzD/VowfgTDmpY8eAUqUe1LZjWaBcObGUi7dJTBRlcrCWZHZ2tk8oCnJKvVqtRmpqqkvGEAQBH3/8MXQ6HQwGA3Q6HTp37mxOMpmXl4ennnrKwkLMcRy6devmkvH9OI5fkfIh1q9fj0qVKkGlUoHjOAwaNAi5ju4M8uNW2rVrJ2stKSyhoC1efvllyZ1JISEhj5xyvW/fPkm34igX7ACzIi0NaNdOWukhEq1H335b9H4nT7aOkVKrgQULXCd748bWli+lUkwY6m3++kuUp4hz87Zt21C1alUEBASA4zgMGDAARi/WLbSlSLnK7TVjxgyr+51hGLz33nsAxG3/UkW9GYbxSK1OP/L4FSkfISEhwcpV9PCPyI9vsXHjRqsAfYVCgcqVKzvl9gwNDZWcsBmGwdWrV114BcWDXbt2oX79+tBoNAgPD8esWbNc71Y+ehSoXFleicp3xY0ZU/S+BQF4/HHLvjQaUflxhWKcnS0qTVIy+0DOH2zfLsrSsqXdpxw8eFBSoXjrrbeKPPy9e/ewfPlyzJ8/H5cuXSry+fkMHjzYyrUXEBCAxo0bO9xnQSpVqiT529fpdDAajfjwww9l3585c6bL5PBTdPyKlI/Qpk0b2R+JJ/L0+Ck6n3/+udkMr9frUbFiRaeLVNepU0f2PijJu4S8xubNosJBJMZCySlSGg3giMs2MfGBy+3hg+eBn392Xn6jUbRwSclcpozz/TvLmjWiLK+8Yvcp7du3l7TKFjXH3q5du6DX66HX68FxHHQ6ncOB6RkZGahXr57Z7c7zPEJDQ10a06rX6yV/+yqVCunp6Rg3bpxkeTK9Xo+VK1e6TA4/RceWIuXPI+VBTp8+Lfm6Wq2mq1evun18o9FImzZtolWrVlFKSorbxysJjBw5ki5evEgLFy6k9evX04ULF6hatWpO9fnZZ5+Zc3flwzAMde3a1ep1P04ybx5Ru3ZEGRlEnToRTZ5MxPPSbWvWJGrWrOhjJCRIv37vHtFvvxW9v4Ko1URxceK/D6PTEb31lvP9O8vdu+K/Rcg1lpSUJK7kC6DRaOjy5ct29XH//n2Ki4ujjIwMysjIoMzMTMrJyaFJkybRHw7k6uJ5ng4cOEA//fQTjRo1iubOnUsXL16kKlWqFLkvOZ588klSKBRWr1esWJH0ej11795dMm+dWq2ml156yWVy+HExchqWrx7F2SLVoUMH2ay97rZE/PnnnwgKCjJbVjxpKj59+jT27dvntardvshXX30FnufB8zy0Wi26d+/unuDqRxWTCRg48IHlZuhQ8bX798UgcJXK0rITEgI4uhNz1aoHFq+HD60WcFU5qNu3gdq1RSsXx4lHixaOy+xKpk8Xr7dvX8m3U1JS0LdvX4SGhqJ8+fIYPnw4XnvtNcnajjqdDnfu3LFr2A0bNsBgMFj1oVAoHHIReoJjx45Br9eby7MoFAqrmqfbtm1DcHAw9Ho9eJ5HpUqVSlz+uqJw+vRpHDp0yOuxxOR37fkGiYmJkskHhwwZgj179rhtu3dOTg5KlSolGZPjTNB0YSQnJ6Nu3brm9A96vR7fffed28YrbmRnZyMpKcmfv8XVZGYC7duL05tKZR30ffMm0LWr6I5jWeCNN8TUAo6SnQ0EB1srUiwLuDLmTRCA3bvF6zl40HX9OsuYMeL1Dhtm9VZOTg6qVKlikRdKp9Ohfv36knPhwIED7R52zZo1kooUEaFLly6uvEKXcvbsWbz99tuoXbs2OnXqhL///tuqTV5eHg4cOIAjR448smlozp07Z65Vq9frERQUhF9++cVr8vgVKR/iwIEDaNGiBTiOQ1RUFOLi4iy2wrZs2dLlD9Z169ZJTjhKpRJ9ZVaRziIIAmrVqmW16mRZFn/++adbxvTjB9euAQ0aiFNbYKAYCA2IcUa7d4s5j9yxss0PZuc40WoUGgr89pvrx/FF8i1/48dbvbV06VLJXWgcx+G7775DixYtwDAMwsPDMWXKlCKlQbhz545knjeO4/CzK2LT/HgNk8mESpUqWVUGYVkWSUlJXpHJliJlZyGpRwsAtHfvXtqyZQuVKlWKXnvtNSpfvrxL+m7QoAHt3LmTiIhWr15N3bt3p5ycHMrJySEioj179lB8fDxt3LjRJeMREd27d0/UmgtgMpkoPT3dZeM8zNGjR+nChQtkMpksXs/OzqZp06ZR48aN3TKun5JB/m9w165dFBISQp06daJSpUrZPunoUTEe6soVoshIoo0biWrUINq5k6hjR6K8PLGdWk20ejXR00+7TuBatYjOnCFKSiIyGsW6eyW4RqMF+bGf0dFWb+3fv5/u3btn9brJZKLMzEzzXGgP2dnZ9O+//1JYWBhptVoKDAyk2bNn0/vvv0+5ubmUl5dHHMdRq1atKC4uzuHL8eN9EhISKDU11armptFopLlz59LUqVO9JJkMchqWrx7utkiZTCZ06dIFHMdBoVBAq9WCYRisX79esn1mZibmz5+Pnj17Yvz48bh586bdYzVq1EjSLK3VavHvv/+66pJw48YNyfpVPM+7beW2bds2BAYGSl5f8+bN3TKmn5JBXl4e4uLiwHEclEqlufr7nj175E96eGde48ai+w4QXXb52cUL7qjzQO02n+TECeCTT4C33xbLuziboqFKFfEzlSgpNH36dCsXHv23C01uTi2IyWTC4MGDwbIsOI4Dz/MYO3as2eWVlJSEIUOGoE+fPtiyZYtPJPcsSFpaGo4dO4Z79+55WxSXk5SUhG3btrn0mbVixQrZHY4dOnRw2ThFgfyuPftZtWqVVe6gfKWjYFmQW7duITIy0txep9NBr9dL+ryliIqKkrxReJ7HyZMnZc8TBAE//vgjmjdvjoYNG2L69OmFBnJPmjQJLMuaTaUcx6Ft27ZuSwCZlpYmqbwxDIMJEya4ZUw/JYOFCxdK/gbDwsKkH5JLlz7Is9S5s2UA9qxZ0qkJWBaYO9dzF+UrLF4sfh75wfY8D7Ru7bi7MztbLH8TECAWgC5AamqqVXymUqlExYoV7Q4e/uKLLyTjqeYWg+/PaDSiV69e5mcDy7IYMWJEiYh7SklJQdOmTcEwjLno8cCBA11ybZcvX5ZMA8FxHL51JGmuC/ArUkXg5ZdfllRuDAYDNm/ebNH2vffeg1qttmpbq1Ytu8Z67733zLs3Hj6CgoJsTjK9evWyeNCwLIvGjRsXOjHt378f7777Ll577TWsWrXK7Vm0v/zySws5tVotoqKi7N6V46fksWvXLnTu3BnPPvssZs2aJVmz8KmnnpJdYBwsGGQ9e/aDjN+ffCLuzHuY0aMf1NR7+FAqgS+/dOOV+iB371pnYCcSLXbLljnW59GjYh9VqthochT16tWDRqOBWq1GixYtcOXKFbu6FwRB1rIdERHhmMweZMCAAVZxXCzLYs6cOd4WzWmef/55q+cfx3FYvHixS/r/6KOPLJ4fOp0ONWrUcH8xcxn8ilQR6NChg6witW3bNou2ZcuWlWyr0WjsSip37Ngx8DxvDsjO3wprq+bayZMnZQMsV69e7fT1u5qNGzfiueeeQ7169fDFF18gLS0NJpMJSUlJdk+mfkoGX331lYVlgWVZxMbGWk2McoqUXq9/UExZEERFKF8ZkAh0BgDs2SPt2mNZ52rfFUc2bBDrCRb8LIiAuDjH+ly5Ujz/pZcKbZqamlrkxMP379+XTBmTvzDzZXJzcyXdmkSEqKgob4vnFLdv35a0GBERYmNj7erj/v37WLVqFcaNG4f169dbLewFQcCKFSvQrFkzxMbGYuzYsbjrxULdfkWqCKxfv17SrRAYGGiV56dixYqSN5JSqSx0wti9ezd4njcrRQEBAShfvjx2795t87x58+ZJusyICG+//bbT1+9uNm/ejNDQUHMW4oYNG+Ly5cveFsuPm0lNTZW8b1mWxbx58yzaLliwQPI3WLZsWdG1Jwii9YlItEbZcvEIAtCxo6UyxXFAly7ie48Sv/0mr0jFxzvW5xdfiOcPHuxaWR9CLgSiQYMGbhvTFWRkZEh6HPKtq8WZ8+fPyyqJ9lgKr169iooVK0Kv10OpVEKv16NmzZouKw7tDmwpUv7M5gVo164dde3alRiGIY1GQxzHEcdxtGbNGtJqtRZte/XqRQEB1h8hADpw4IDsGHl5edShQwe6d+8eZWdnExGRIAiUnp5eaFbfkJAQun//vuR79mYEdgQAtHz5cnryySepdu3aNHr0aLqbn9HYTs6cOUMdOnSgf//915yF+O+//6ZnnnlG1Or9lFj27t1LGo3G6vWsrCz6+eefLV7r3r07tWjRgjiOo4CAAGJZlniep1WrVlEAQNS7N9GkSUQqFdGyZeLfcigURCtWEH37LVHr1kRt2hDNny+eJ5FhukTTvDmRxHdALEvUq5djfSYlif8+9pjjchXCtGnTiGEYi9dYlqWvv/7abWO6Ao7jKDw8XPK9J554wsPSuJZKlSqRXq+3el2lUtHzzz9f6PnvvPMOXb16lTIyMshkMlFGRgadPXuWPv30U3eI637kNCxfPTyVRyoxMRFfffUVvv32W9m8TpcvX7bKc5F/tG7dWrbvvXv3yu5IePbZZ23Kdfz4ccnziAjVqlVz6ppt8eGHH1r5q6tXr16kjOwDBgyQjCnjeR4JCQluk12OH3/8EVFRUVAqlahcuTJWrFjhcRkeFfbs2SN5zysUCrzxxhtW7QVBwO7duzF69GjMmTNHXKnevy8GkxMBOp3oqvJTNPbtA0qVEnc4cpz4OQ4f7nh/1aqJ38f+/a6TUYKdO3eiefPmKFu2LFq3bo19xcQt++uvv1qEYgQEBIDjOLs3JElhMpkwa9YsxMTEoFKlSujfv3+R6hO6inXr1llsYNJqtQgNDS208Hpubq6spU7vC0W4ZSC/a889HDlyRFYhql69uux5thSpZ555xuaYZ8+elXXt2RvkXlRs7aAoys4ZufgzvV7vViUmOzsbS5YswaBBg7Bw4UJkZmbihx9+kNwJtHz5crfJ4YsIgoDExETs27cP9+/ft3r/5MmT6N+/Pzp27Ij58+c7HOhpMplQsWJFq3gXuxO0ZmYCbduKU5bBICbX9OMY2dlioeFFiwBn3OrXrj1wlRqNrpOvhLF37160bdsWUVFR6Ny5M44dO+ZUf927d7eYuzQaDSpVqoSMjAwXSWw/hw8fxptvvomnnnoKI0aMwC07KgQYjUbJ8kB+ReoRVaSysrIkYzlUKhXee+892fNyc3MRHBwsqZh8//33NscUBAFVq1aVjDWZMmWKqy8RALBy5UpZxa99+/Z29zN79mxJv7pOp8PFixfdIvu1a9cQERFhzq7McRzCwsJQvnx5yeuJjo52ixxy5OXlYeXKlWjfvj1ee+01bM/PxO0BkpKSUKVKFXAcB4PBgFKlSlmUYFi7di1YljWvHjmOQ40aNRwO+Dx16hQiIyPB8zwMBgMYhsHs2bMLP/HOHeCpp8TpqkwZwInVvB8X8uOP4nfy3HPelsQpkpOT0b59e2g0Gmi1WnTt2tUrFh57kFtIsyzrsdqprqBNmzZWypRarUaPHj28LZosfkXKjUyZMsVCOVAqlShVqhQuXbpk87zff/8dHMeBZVlz4s+mTZvaVdj3yJEjCAoKAs/zUKlU4DgOrVq1krQouILdu3dLKlIqlQofffSR3f3cu3cP0dHRFtYtjuPw7rvvukVuAOjcubOVGVluNZRvevcUJpMJL730koUyznEcBrsxcDef3NxchIWFWVmIGIbB6dOnYTQaERQUJKn0jh071uFxBUHAvn37sGXLFvsUsvR0oFEjcaoKDwe8VB7CjwS9e4vfi6sKM3uBrKwsVKhQwWJOUKvVeOyxx9yeHsYRli9fLruoffXVV70tnt1cunQJ5cqVMy9weZ5H5cqV7bJoeQu/IuVm1q5di6ZNmyIyMhI9e/a0u/hwSkoK2rRpA5VKBYZhYDAYEBoaiqMSGYILcu/ePSxZsgTjx49HQkKCWxO8mUwmREVFuaTuUWpqKoYNG4aqVauifv36WLhwoVtll3ODyh2VKlVymywF2bx5s2QdMp1Oh3Pnzrl17E2bNklOyGq1Gp988gkOHTokO2E//vjjbpXNzN27QNOm4jQVGQm4qai3HwepXl38bopx7czFixdL/gb1ej02btxo89yUlBRcvHjRo8k1//jjD0l51Wq1RxZgriQrKwvff/89RowYgZ9++glGH3cP+xUpH2Xjxo2SrsGIiAifK3Nw4cIFxMbGgmEY6PV6BAcHY926dd4Wq1DktugqlUrJRHmFuVZdSd++fSVlk0oJ4GqWLFkiOSETEbp164ZTp07JfnbNmjVzq2wAgIyMB+68ihUfHSXq/n3gr78AG5UNfILr18XvppjHR33yySeS97hGo8HkyZMlz7l16xbatGkDjUYDhmFQoUIFbNmyxSPyCoKA6tWrSxaDP3/+vEdkeFSxpUgVmv5AoVD0VSgUQYW181N05syZQ5mZmVavp6Wl0cGDB70gkTyRkZF0+PBhOnr0KCUkJNCNGzfopZde8rZYhdKlSxerbfdqtZo6dOhAs2fPpgoVKhARUXh4OM2dO5e6devmMdmCgoJIrVZbva5UKslgMLh17GbNmlFefhHfh+A4jp5//nmqVq0aRUVFWaX34DiO+vbt61bZKDOT6MUXif74gyg8nGjHDrEIcUln1Sqi0FCiVq2I6tUTCyFfuOBtqaTZtUv898knxSLQxZRatWoRz/NWr2u1WqpRo4bkOW3btqWdO3eS0Wik7Oxsunr1KrVv355OnjzpbnFJoVDQjh07qGnTpqTVaolhGIqIiKBff/2VoqKi3D6+HxnkNKz8g4jGENFZIlpJRG2JSFHYOe48SpJFqkWLFpKrIYPBgB07dtg8VxAEZGZmloiaTe4kNTUVMTEx4HkeGo0Ger0eVatWtSiw6S3r35kzZySz1Ov1eo8UN+3Xr59VqaF69eqZY+3OnTuHSpUqQa/XQ6/XQ6vV4sMPP3TvPZeZCbRsKVo7ypcHTp9231i+xLFj1uVbAgJEl6aPWacBAO+9J8pYzMvsZGVloXz58lYxUtWrV5eMkTp8+LDsBqM+ffp4VPabN2/iwoUL/meAhyBnXXtEpCCi54ho+X9K1ZdEVNmec119lCRFau7cuZLuE6kCyQ+zYMEClC1bFkqlEkFBQZg8ebL/x2QDk8mEzZs3Y/LkydiwYUORgkj37t2Lli1bIjg4GA0aNMAGF+cuWrp0KViWhcFggMFgQFBQkMdyagmCgFWrVuHZZ59Fw4YNMXXqVKv7zmQyYefOnVi+fLn7M9BnZQGtWonTUliYtHvLZAImTADKlgXUaqBxY98u9ZKaKu4yTEmx3e799x8UXn744HnfS/UgCGJtPSKxBI8MKSkpmDJlCvr06YPFixfbtZHGGyQnJ+OVV16BWq2GVqtFfHy87K69devWwWAwSC6AbeUO9FP8cVqREvugWCKaSkQniWgOEf1DRBPtPd9VR0lSpHJyctCoUSPzCic/6HyZjQKiy5Ytk8x/NGXKFGRmZuLHH3/E9OnTceTIEafl8zXl7MSJE5g4cSKmT59eaNI3V5CQkCD5Wdv6fhwhIyMDv/76K7Zu3eq2nZe+QHp6OrZu3YoDBw5Y31vZ2Q/yRJUtC5w4Id3JgAHWlhuWFYvnFsadO8A774h5qHgeePNNoCi7hHJzxcMe8vKAvn3FhJcGg/hvr17y57/8srUSRSSeu2qV/TJ6gvxCxWXKiNcpQWJiIgIDA80WV57nERUV5bNpBQD75rvk5GTJDSwMw2BcMd696KdwnFKkiOhDIvqbiLYQUSciUv/3egARnSvsfFcfJUmRAsTkZMuWLUN8fDz69++PE3IPkP+oUqWK5GooMDAQpUqVgl6vh06nA8Mw6Nq1q0Nuq/nz56NChQpQKBSIiorCTz/95OjluYyhQ4eCYRio1WrodDrodDosXbrUrWM2btxY8rMuX768zymZvs6MGTPMO1PztzqfPXtWfDMnB2jXTpyOQkJEN5cUd+6ICklBZSMgQKydZwujUey74HnR0WKAd0EuXhSzqAcGiopd1aqASiUebdsWnsjyyy+lFb6hQ6Xbz51r3Z4I0GiA7t2BJk1ExcwXAopHjRJl69lTtkm9evWsfjdqtdpmfr3iQp8+fSwWWGq1GmFhYQ7ViUtLS8Pw4cNRo0YNNG7cGMuWLfPPLT6Ks4rUKCKqJPNejcLOd/VR0hSpoiJXcVvq4DgOP/zwQ5H6nzNnjqQV5uFEjZ5m//79ki5QhmGQUpjLxAmkYiHyLYfeyCJcXJGy7CkUClSuXBmC0Qi0by9ORcHBQGKifEf//CNfdLew8kgdO0qfp9MBBbPZ374tWlsCAqTPUSqBChVEBVCOgkrbwxYmKTIzgRo1LBVFnU50X6pU4t9qtWhJO3zY9rW6m3r1RHnWr5d8Oy0tTbIUFBEhJCTEw8K6HpPJhG+++QYxMTEIDw9Hnz59cP369SL3k5GRgcqVK1vl1evfv78bpPbjLC5x7fnK8agrUnXq1JGcoAomVsw/mjdvbnffgiAgJCREsp8aNWq48aps89FHH0nWNOR5HkuWLHHbuNWqVZP8LPR6vUeS9eXk5OD06dNIT09Heno6hg0bhipVqqBWrVqYOXOmTyYMlKJLly6S9yfPcfg336VVqlThCkJqKqDVWisnCgXQoYP8eTk5ohIipdgQAUOGWLb/8ktpy9fDB8+Lmb3lsDVehQqi0vTVV5bWsLt3gfHjgbp1xYD7/DikgkcRftMu5+LFB9cvE/OUkZEhq0iVL1/eaRFMJhMOHjyIhIQE5NhSZn2cGTNmyFZ6SE5O9rZ4fgpgS5EqNP2BH99iwoQJVpXQtVotaZpd94MAACAASURBVLVayfZGo9Huvu/fv08pKSmS713w0W3Y4v3t+j537NhB9erVs/pcWZaljz/+mJRKpcvHfZipU6dSSEgI1atXj0JDQ6lixYr01Vdf0dmzZ+nYsWM0ePBgio+Pd6sMruLWrVuS39OI3FwKWbuWSKcj+vVXothY2x0FBRG99RYRy1q+zjBEn30mf15KCpFCIf9+9eqWf+/dS5STY1uWzEyiM2fk369fX/69q1eJkpKIRowgiosT1SMiIr2e6NNPiQ4dIvrtN6Jz56TP37vXtmzuZOVK8d927cTvTQKe5+npp5+2+o3odDrq2bOnU8MnJiZSZGQktWjRgtq1a0ehoaG0du1ap/r0Flu2bKGsrCyr1zUaDe3fv9+hPjdu3EixsbHEcRzVrl2b1q9f76yYfuxBTsPy1eNRt0gBYkbsxx9/HAzD4LHHHsOKFSska/exLGtfLbP/EAQBoaGhkivJmjVruvGKbPPnn3/KrtxcHbx67949NGzYEDzPm3fx5Jfw4TgOw4YNc3u6hBUrVsi6FR8+GIZxugCqJ5Baeff9z7oiKJWyLiJJcnOBYcMeuPhiYoBCUoUgN1eMdZKy7qjVolvtYQYPFmOTbFmk9Hrg55/lx9y/XzrmqeDBccDevdJ9cJz0OUFB9n9erqZ+fVGGNWtsNktOTkZUVBT0ej0YhgHHcWjRooVTO/fu37+PMmXKSM5z5ni7YsQHH3wgWa6K53nslbsnbLB27VrJJMOrfG2zQjGF/K69ks/27dvBsqzZ387zPJ5++uki7wKTSsnAsizWrl3rJsntY+DAgWAYBkqlElqtFgzDYPHixS4fZ/DgwVa7chQKBRo1amT1Webl5eHUqVO4ceOGS2WQc98WPDiOw/z58106tjvIzMxETEyM+b7qQgRTvlKwcKFjnQqC7I4xSaZNAxjGUiEJCJBWhi5dEl1XcsqPWi3GZBW2g2/9etHtaEuR0mgAmQza+Phja5kZRlQkvcGZMw+USDsUory8PGzatAmzZ8/Gvn37nA6iXrt2rWxZo2He+kyc4Pjx41ZzrVKpRLVq1Rz6rORCEaKiotwg/aOHX5F6RLh27RomTJiAAQMGYMOGDQ5bTr777jtEREQgICAAVapUwerVq10sqWMkJiZizJgxmDx5sttyGpUrV05yMlKr1UhPTze3W79+PUJCQsBxHLRaLZ5++mncvHnTJTLIxakVPPR6PTZt2uSSMd1NZmYmZsyYgUGxscjND+IeP96zQvzwg1gfjufFGn75q/6sLGDxYqBfP2DmTHF34P79QJ06YqC3Wg1ERYkKhF4v7lazZ5NDWpp8wPrDlq2Cwe755OSIQfI6nWhR0+mA+HjvlWQZM0aU+Y03vDL8d999J2up7VlgB+GpU6ewZMkSbN++3efKbT3MunXrEBwcDJ7nwTAMGjRogCtXrjjUl1wxdoVC4d8J6AL8ipSfYo3JZMKECRNQpkwZKBQK1KxZE1u3bnXLWGXLlpVVpNLS0gAAR48etVpJqtVqlxXzjYuLk908kH8EBAQgIiKi2AScAwAOHHhg6RkwQLQqeZubN8Xs4flysSxQuvSDZKB379renVcYrVvLK1EKhbi7rzDrzuXLwG+/AQ4+YF2CIIgpIIgAFyeltZdz585J5nDied7svjKZTOjWrRsYhgHP89Dr9YiMjMTFixe9IrM95ObmIjExUVLG7Oxs5NqZuywiIkJyrggLC7N5niAISEhIwKRJk7B06VJkFnR1O8nNmzfRv39/VK1aFU2aNMFPP/1ULBU7vyLlp1jz2WefWSkuDMNgj42syo7y4YcfQqPRWK3oGjZsaG7Tq1cvydUfx3E47IKt6UePHgXP8xY7FfPzZ2k0Gmi1WjRo0AAXilMh39OnH6QE6NbNd8qe9OjxIL3AwwpO06au6T87G6hVy1qJ0mjE15OSXDOOu9mxQ5S7QgX7k5K6gb59+1qVNWratKlZ2ZAKTQgICMATTzzhNZkd4dChQ6hfvz6USiU0Gg26du2KO3fu2Dxn/vz5kmEZtuJk79+/j9atW4PjOKjVavA8j+DgYJfFXt6+fRvlypWz2MXJcRxGjBjhkv49iV+R8uNWUlNT8fPPP2Pr1q0wutjtkJWVJRloTkR49tlnXToWANy5cwc1a9YEz/PmmIV8ReaNN95AamoqWrVqJSmPwWBwWQmZEydOoFOnTqhQoYI5AWm+AhkcHFy8Kr1fvSpafYjEZJbeck0VJDNTPk2BSmUdhO4M//wDfP45MG+e+P9Ll1zXtyfo0kX8XEaO9KoYgiDg559/xnPPPYdmzZph9uzZFikQYmNjJX+bxSmlQHJyslUsmEajQVM7lPvZs2ejTJkyUKlUKF26NKZNm2bT+jN58mTJHG+uSnczcuRIydyHOp3OoQSm3sSvSPlxG7NmzYJOp4PBYIBer0dwcDD++usvl/V//vx52biIcuXKuWych8nNzcUPP/wAlmUtXGwajQa1a9fG2LFjJV0MWq3WocR8tnjrrbescvIEBATgmWeecek4biMjA3j8cXGqadhQ/NtXiI+XVqKIRAXLR2vDFcrhw8CUKWLc1927zvd386b4eQQEFJ7R3ctUrVpVcq5gWRani0kB7M8++0xS+WBZFocOHSr0fEEQkJGRYVdsWExMjOTnxTCMSyzeTZs2lew/MDAQv/32m+Q5GRkZWLZsGb755hufcsnaUqT8eaT8OMyhQ4do0KBBlJOTQ3fv3qWMjAxKSUmhtm3bFil/lS3KlSsn+15MTIxLxiiISqWirKwsUigU4mrjP4xGI124cIE4jrN4nYiI4zjq06cPhYWFuVSWNWvWUG5ursVrgiDQ7t27XfYZuw2Tiej114kOHyaqWpVowwYinve2VCIZGUSrV8u/37q1bJ4kn0UQiLp3J2ralGjIEKIPPiAKDyfat8+5fhcvJsrNJXrhBaKICNfI6iY6deokmVMvKCiIKleu7AWJis6xY8fo/v37Vq8rlUo6e/ZsoecrFArieZ4CAgp/vJtMJtk+5N4rChUrViSFRA43o9FI5cuXt3r9999/p3LlylHv3r2pf//+9Nhjj9GIESOclsPtyGlYvnr4LVK+w/vvvy+ZcdyVLi4A+N///ifp+3ck14q9fPDBB5IrKY1GA41GY2GpUigU6NWrl1sCKEuVKiUph0qlcrkb1eX07y9ad0qXFmOkfIlLl+TzPCmVgIstix5hxQrp3FNlyxYtVcTDmEwPMqwXJd+Xl7hz5w6qVatmtmJrNBpwHIcdheUae4i9e/fivffeQ8+ePbF161aPB0Z/+eWXVvmg6D8rUZILYuqSk5MxZswY9O7dG/Hx8ZJjRUdHu+S6//rrL8mNOY0aNbJqm52dDYPBIGmJ2717t9OyOAv5XXuPLoIgYPny5WjUqBGqVauGTz75BLckKt5fvHgRx44dK9IusNf/z955h0dRfX18tk/ZSQJJSAg1mgBSQn/pUqUq0n50lCJNAlIUFFSagNKkSUcIvTfphCIdlN4RCBBCCS0ESN/5vn9cdpPNzmx2N7PZDezneeZRYObeM5PMzJlzz/meDh1EX/I8z2O1VEm3g+cwdepUBAQEQKlUokyZMoiMjDTbJzExEStWrMDYsWOxdevWbFezzZ8/X3RJUaVSiVbU+fr6OqWCrk+fPhbJ7yqVCk2bNpV9LlmZPTt9iezvv11tjSVpaaSfXmanQ6kE2rd3tXWO0aCBuGPI88CJE46NGRlJxihY0KVJ5vaQkJCARYsWoWPHjhgxYoRdy0PGjzbjPc5xHLp27ZqjztTTp0/h6+tr9pHKMAw+++yzbI+9b98+M71BjuPAsqwpJ5RlWXh5eeHff/+V4UwIq1evRp48eaDX60HTNGrXro3Y2FiL/bZt2ybqSCkUCnTr1k02exzF40i9x3z33XdmDoFWq0WhQoVMpfz37t1DpUqVQNM09Ho9/P39sWPHDpvGXrdunaizQdO0bJpKthAVFYXAwEDo9XooFAro9XqULl06yyoXa7x69crkuGW8dlJaLQzD4MGDBzKeFSEuLg5hYWHgeR4ajQY8z6NIkSKIiYmRfS7Z2L2bRHUoCliyxNXWSLNihXlUSq0miun//edqyxyjTh1xR8rLCzhyxLEx27YlY4waJa+tboiUvALHcTji6PVzkNu3b6NVq1bgOA7+/v4YPnx4tvsKpqWlicq70DSNbt26YcSIEZg9e7ZTksBTUlJw6dIlq8+tDRs2iDpSFEWhvRt83HgcqfeUx48fiz4YGIbBxIkTIQgCQkJCLJwDlmVx/fr1LMdPTU1F/fr1Tc6UQqEAy7KYOHFiDpxdOnXq1LFYYtRqtQgPD8/WuHfv3kXz5s2h0WjAMAy6du2KMmXKSDpSCQkJMp2ROQaDAbt27cLEiROxadMm2Zb0Xr9+jXv37tmsU2MTV6+mt28ZMUK+cZ3FwYOkkrB4caBHDyA3VUNmZvFi8aW9PHkcq5TMmGTuSg2rHGLWrFmiy1wKhQJDhw51tXnZ5vz586bIU+atbNmyLrXt9OnTmD9/vmiSPcdxLu+sAXgcKdkRBAErVqxAtWrVUKpUKYwcOdJM9dpd2LFjh6SHX79+fRw+fFi05YJarcbAgQNtmiM1NRWrV69G69at0b17d6fmLYnx5s0bqNVq0XP09fWVfb4NGzaIalp9/fXXss+VkZiYGJw7d06WbvdJSUn46quvQNM0WJZF3rx58eeff2bfyGfP0vNpWrd2H62o94XUVOIUGp0pmiYRN0fFa0ePJuPIsKSUG5BSTtdoNBg9erSrzcs2165dk5SSEctZygni4+NRo0YNcBwHnueh1WqhVCpNH/ccx6F169ZuoU7vcaRkJrMoHE3TCA0NlV0RNrucPXtWMs+nR48eWLt2raSj1bJlS1ebbxM57UgBRKvFx8cHLMuCYRj07dvXaYnfz58/R8OGDUHTNHieB8/zmDdvXrbG7N69u2hz02wVCKSkAPXrk0dKuXLA69fZstGDgwgCsHcv8P33wOTJjifNv34N+PqSn+eBA7Ka6K48f/5c1NFgGCZXNkXOjCAIKFasmEWOJ8dxWOxoz8ts0q1bN4solFqtRpkyZRAeHo7IyEi3UUH3OFIycvfuXcl19Llz57rUtswIgoCwsDALR4NlWZw7d07yXLJSw3U3ateu7ZSlPWukpKTgzp07eO1kh6F+/foWyeYsy1ok29tKfHy86M+coihUq1bNcUP79SOPk4CA3Cc26cGS6dPJz7NKFfdo5ZND7NixwxQd4XkeOp0OgwYNwv79++VdApcJQRBw5MgRjBgxApMmTcpSdPTKlSvIly8feJ43fQh27tzZJREfQRBEl/KMW6dOndyqBZbHkZKRtWvXii6HuWsU5+HDh6hRo4YpmdzX19esCXHfvn3NolY6nQ4hISFOdxDk5Pbt2wgICDBLNi9VqlS2ks3dgXv37kk6PY0aNXJozFu3bkkKnBYoUMAxQ+fOJY8SrTa9EbAHgiCQyrfffyfyARlfxsnJ7uGkCAJw6hSwYAHp6ZeUBBQuTH6mmza52roc59WrV1i/fj369esHhmHg5eUFLy8v+Pn54YSj1Y9OwGAwoF27duA4DgqFAjqdDgzDZJlPlJycjM2bN2Pu3Lm4fPlyDllricFgEJXPyfjBOGPGDJfZlxmPIyUjhw4dkswr+uabb1xqmzXu37+PS5cuWXxVCYKApUuXonLlyihevDh+/PFHU0VfbkJu+QNXkZCQgCVLlmDQoEH48ccfJZ32UqVKOTR+cnKy6HKuUqlE69at7R/w5EniQFEUUdL2kE58PFCxImmIrNMRGYLgYJIUXrQoSeL29gbGjHFdPllCAlC3LsmrYllia/785OdZosR7m+d27do10cRzHx8fpxWV2MvGjRtFP4r0er3b2JgVH3/8sdUG7aGhoa420YTHkZIRg8GADz74wMKTZlkW14wd4z3IQkJCAiIiIjBw4EDMnz8f8W/bXezbtw+ff/45qlWrhl9//dUtE/0d4cGDByhUqJCpskYqcqTVajFo0CCH5/njjz/MckGMUTy7v06fPEmPXDhxGTXXEh5OHCiKSt+USrJl/DuWBX74wfzYN2+ARYuAXr1INOvZM+fYOGwYSUrPaI9xk6MAIZcybNgw0dxLnufNIvqupGXLlqLPBy8vL5slbFzNlStXJPN0KYpCUFCQq0004XGkZObOnTsoX748GIaBXq+Hn58f/soFqr+5AWNi4cOHDy2cCn9/f4wYMcLMCWAYBiEhISYnKzfTvn17i4e3QqEwc9o1Gg38/Pwc0qx6/Pgxpk+fjlGjRmHChAmoUKECAgIC0KJFC1y6dAn//vsvGjVqBH9/f1SqVAnbtm2THiwtDWjYEKY8muTkbJz5O0qePOIOitjGsum9/R4/Jg6qsfqOZQEfH8AZyzD58knb9I58oEhx8uRJfPPNNwgPD7fQierVq5foi53jOHkqXGWgTZs2ko7U7t27XW2ezTx69Ah58uSxOA+NRuP0amh78DhSTuL27du4cOFCrl1GkpP4+HjMnz8f3333HVavXo1kO16sBoMBEyZMgK+vLxQKBUqWLIl69epl6VRkdKYmTZrkxLPLGaRKk5VKJerUqYPixYtjwIABDolx7t69GyzLgqZpKBQKcByH//3vf6Yk03/++Ue0DU+E1HLdyJHk8eHn5/aNbPHmDRAVlfPOnlFPy1ZHyngdu3Uj4qAZ/12hIE2f5cbHR9wepfKdrrz88ccfwbIslEql6X4YMGCA6d+3bt0qqrlE0zTuukkxxfbt20Wj1t7e3rLIpOQkhw4dAsdxpsIalmVRoECBHBV2zgqPI+XBqVy/fh1+fn6mm1qv1yMkJARPnz616fhhw4ZJOhG2brVq1XLyWTofqXwotVqdraqa5ORkeHt7i35dr1mzBgCpDhSb29/f33LuHTvIi12hIKX27kpqKjBgAMAwJLrD88CkSUQS4NUr58//5ZdE0NIWR4rn0x09KedGrZbf7i+/tHTaKAqoUEHeeVxIcnIyfvrpJwQEBIDneTRu3Fi0WoxlWZw+fRoA+bhr2LChmaPCcRx+yLwE60IEQUDfvn3BMIyppyDHcdi3b5+rTXOIqKgoDB06FC1btsS0adPcLmXD40h5cCrVq1e3SBjUaDTo3bt3lse+efNGNKnTnk2hUOB///tfDpypc+nVq5eF1IFGo0GrVq2yNe6BAwck8xCMPfvEQusURao4zfpiRUWRJsQUBfzyS7bscjrffWfZmFihII6DTkfanzhzSTg2liSV6/Vkbo4jyeWZc5JYFpgwIf04qeU2jSZ9+U8uHj4kffQyKqLrdMDFi/LO40KaN29u9oyRSm5WKpUYlaEVTmpqKlauXInPPvsM7dq1s5AcefXqFXbu3IkDBw64VBrh0qVLmDJlChYuXJgrC4VyCx5HKpeSmpqK6dOno1SpUggNDcXPP/+MVznxJW0Hr1+/lhTEzJs3b5bH37x5UzKpOvOmUqnA87xoS5vDhw/nwNk6l7i4OJQtWxZ6vR46nQ48zyM0NFS0wac9HDx4UNKRatasGQCgdOnSov/Osmz6Mm1iIqlCoyigWTP3ruhKTRVvl5Jx0+kAB2UkbCYpCVi+HBgyBJg/n0SU/v4bqFSJzF+4MDBvnrkMwtChls6WWg04q1H169fEPuM1saE9VG7h6tWrNn+oabVa/PbbbzaNu2zZMlODX57n4efnh1OnTjn5bOQnLS0NR48excGDB+1Kx3AVSUlJmD59OipXroyaNWti2bJlOaaB5XGkcimfffaZ2ZIXTdMICwtzmoq2IyQkJEg6Uv7+/jYdL7Ws5+XlZeFUnD59GqVKlQLHcfDy8sp14qFZYTAYEBkZiWnTpmHnzp2y5N+lpKSIRpw4jsP69esBEH00sRypIUOGpA/Uuzd5ZBQtCjihsamsvHhh27Iaw5AomzuRkAB8/DFxBBmGLPsVKwY8euSc+QQBqFaNXI93oBVKRpYuXSq5ZJ55o2kaUTb8LliTRkiUO2LoRE6cOGES5zRqZWWnu8GTJ08QGRmJGzduyGhlOqmpqahWrZrZc4rjOHzxxRdOmS8zHkcqF3L69GlRB0Ov12Pt2rWuNs+MTz75xCJKpNPpMHjwYJuOz1yJZ3yJHz9+HPv378f06dOxY8cOk1MhCAIuXryIv//+O1cJh7qCvXv3omnTpihevDg0Gg1YloVarQbLsujSpYtZ+wVj6xuGYcAwDAYNGpS+ZLFkSXrE4m0eiVsjCEBQUNaOlLc3iRC5G4IAHD9OxE737nVu9G/LFnIt/P2du9SZg8TFxaFt27aSH3kajQZqtRp6vR56vR40TWPJkiU2jf3dd99JSiNs3LjRbN+zZ8+ic+fOqFq1KoYOHYqHjrbskZnXr1+LRqlZls1SHT0zgiBg8ODBoGka3t7eYBgGtWrVkn2ZcdOmTaIFAAzD5IiwqMeRyoX88ccfkqrW/fv3d7V5ZkRHR6Nw4cKmppN6vR6VKlWyeRlSEARMmTIFAQEBUKlUKFu2LA68J/29nMmUKVPMHFSdTgdfX1+MGjXKlFSbmdTUVMTExJh/WV+9SiIjFAUsXJhD1svAmjWWOVKZN5p2nkZTbiAtDShVilyL6dNdbY1s1KxZ02r7EZ7ncfnyZSxfvhxLly61WhgTHR2N/v37IywsDC1btsRnn30mOmbmnnXbtm0zVQYalw59fX3doupv+fLlok6JTqfDr7/+atdYixYtskjP0Gq1aN68uaw2f/3116LXnWGYHFmV8DhSuZBNmzaJhqRpmsbkyZNdbZ4FKSkp2LRpE6ZOnYp9+/bJ3mjy1q1bOHLkiNtVcrgrL1++FF1+YBgGEzImNmdFcjJQvjx5VHTp4jyDncXevUDNmqQHoFpNks2NThTLktyg95mICHItihQh+VzvABcuXJBMF1AoFKhQoYLkh0RmoqKikCdPHmg0GtPxWq1W9COXpmnceythYTAYEBQUZLGPSqXCl19+6cSzt40ZM2ZIfqjbupJgRCq/UqfTyRqV+uWXX0Sd45wSSfU4UrmQ5ORkBAYGWlSY6PX6HNHWePbsGX7++WdUrFgRTZs2dbhJrhx21KpVCwzDmMLG48aNc4ktAOkQP2PGDAwYMAArV650W72W/fv3i0oeUBSF6tWr2z7Q0KHkMREcbLtA48uXJHL1yy/AoUPu0U8OAG7fBjp0IFVxJUqQ5G93sc0VJCURB4qi8GzqVERGRrpFtCS7bN68WbK4okGDBnaN1aVLF4u0BePSYGZphOHDh5uOi46OlkxyDwwMlPuU7ebSpUui9un1ervFPMUcRuNHm5y/T9HR0aIOsq+vb448hz2OVC7lxo0bKFu2LGiaBsuyKFq0KI4fP+70eZ89e4ZChQqZef8sy2LatGl2jyUIAk6cOIGff/4ZkydPtnv9vUGDBhaSACzLWuQiOINt27ahcePGqFq1KiZPnowTJ07A29vbdDPr9XqEhobiuRsmXl+8eFH0oaNQKNCmTRvbBtm3j0RwVCrbmxGfOkWEKDmOiDpyHKmMc6MCCQ9vmT4doChEe3mB1eng7e0NmqbRunVrl38gPHjwAH369EHBggVRpkwZLFq0yOYo9+3btyUjRmPGjLHLDikngaZpTJs2Dc2aNUPbtm2xN5OeWlxcnOTSYsmSJe2ywVl89dVXFs5g48aN7a6C6969u2jOWFBQkOwVdXv27IGfnx94ngfHcQgODsaFCxdknUMKjyMlM8+fP8fq1auxfv36HJEjuHfvHm7duiX7cpkUo0aNEn0QMQxj1/kKgoAvv/wSLMuadSe3NQz74MEDyYdRjRo1HD09m/jxxx/NHjIMw4heE61Wa6aI7E6EhYU5LhXx7BlQoAB5RGTQ1rGKIACFCsG0dJZxCe0dqqx8J4iPJ8nlFIX/ZfpQYRjG7uUdOXn69CkCAgLMXs6ZlcezokOHDmYRF6VSCV9fXzx58sQuW8qWLSu5bBUXF2f12JYtW1o8v1iWxaJFi+yywVkIgoANGzagSZMmaNCgASIiIhzSw4qOjoafn5/pXJVKJViWdUrbtOTkZJw8eRIbN27EhQsXcuydCHgcKVlZsmQJaJoGz/Mmrzi3NIi0lbCwMNGHh7e3t116TVItDFiWtana7tKlS6IJkRTl3K7gjx49kswfcNdQvRj3799HuXLlTHo3HMdh7ty5WR8oCEDr1uTxUL060WSyhYsXpbWbKlXK3sl4kJfRowGKwkmRZStjtNUagiBg8eLFKF++PEJCQjB06FA8kylpf8yYMZIRpUc2SkCkpqZi/PjxKFCgALy9vdG2bVubpA0ys2LFCovIrk6nsymqGxcXh7p165rSEnQ6HYYMGZKjL/+c4vHjxxgxYgRq1KiBL774AufOnZN9jrVr18Lb2xs8z4NlWYSFheHOnTuyzyOFx5GSiZs3b4quK9M07ZbLO44QHx9vsZSW8TyvXbtm81gdOnQQHcfLywtbtmzJ8viUlBT4+PhYHK/RaJxaubhx40arHckzbwULFnSaLXJw7do1HD16FG/evLHtgEWLyKOB50leka1Yc6Qy37cpKcD27UDduqRyzs+P9O9LTATWryeOXOfOwP79ts/vwTaio03VjPVEelcal4CtvfB79+5t9pGk1WoRHBxsd4Q+NjYWPXr0QN68eZEvXz4MHToUtWrVkvyQ27VrV3bP3i4EQcDPP/9sKu2naRpNmjSxaJL+8uVLyY/Dmzdv4sCBA3ZHwzykI1ZAoFQqERISkmOOqceRkokxY8aYqjfE1r1tflG5MXPnzpWMxtA0bdd6dOfOnSUdKVvDvkYFYWPSvVarRb58+fDgwQNHTzFLDh06ZJeI308//eQ0W+TCYDBgw4YN+Pzzz9GiRQts3rxZ/AF040a6M7RsmX2TCAJpN5LZiWJZ4I8/0vdbskS8oS/DkOXEjM4YywIZknidQlIS8NNPRHfK1xfo3h1wn+e7hwAAIABJREFUo2apstO+Pbm2rVpJOi1VqlSRPPzu3buizwiWZTFz5kybzUhMTERwcLDZM5WmaeTLl0+0OTnLsrh06ZIcV8BuXr58iRMnTiA6Otrs769cuYJKlSpBo9FAo9Ggfv36dueBesiaPn36iCb96/V6HLM1fzObeBwpmRg2bJhknyaFQoHu3bu7zDa5CA8Pt+o48Dxvczh1z549okt7NE1j9uzZOH/+vE3jHD16FC1btkTFihXx/fffO71q0WAwoEiRIhY/a4ZhEBgYCJ7nodPpwHEcPv74Y7dXMxYEAe3bt7dILO3atav5jikpQOXK5LHQoYNjFW0nT6YnmysU5L8NG6Ynmx84kLW2U+aNpp2rPv7JJ+k6WRRFFNELFSKtU941DhxIv6Z37uDcuXPQ6/UmZ8YoUvnPP/9IDrFu3TrJD43PP//cZlMiIiIkBRYz5xZpNBr83//9nwwXQD7i4uKQJ08es+eESqVCkSJFXNp7712kWbNmkh/lmzZtyhEbPI6UTBw5ciTLvnA5IU3gTMTE1TI/0AYOHGjTWIIgIDw83NSdnKZpKBQKMAwDlmXBMAxatGjhlg+d//77D8WKFTO1ouF5HsuXL0dqaiq2bt2KmTNn4ujRo7ki3+HYsWOiFXwsy+LMmTPpO44YQR4JhQuTFiuOEhdHpAXGjAEOHjR3yBo3ts+JMkal5s1z3B5r/PuvuGPHcc6b01WkpgJlypDzy9AKJioqCuHh4ahevTq+/vpr3Lx50+owR48eFXWA1Gq1zc8GAOjXr5/oM4amafTt2xf58+cHy7LQ6XRo3LixVdFMVzBr1izR+4rnebOIuyAIWL9+PWrWrInSpUvjp59+8jQXtpM//vhD9FrrdLocU4v3OFIyIQgCunbtatWRcmW1ixy8fv0a+fPnFw2tG7datWrZNealS5cwadIkBAcHi1aR/f777046m+whCAIuXLiAI0eOuH3UyRqjR48WjaRqNJr0Jq2nTxOZA4XCuS1TSpa035HieWDVKvlsiIoCdu0i/124UDpC1q1b9uZYsgTYupWImroDM2aQ8ypalPTzcxBBEFCsWDHRe9mePmszZ86UdER27NgBg8GA27dvu50DZeSbb74RfT7qdDrMmDHDtN/3339v9nGq0+kQHBxskWf1viIIQpY9RV+/fo3Q0FCzJWWO4zB06NAcstLjSMmKIAgoUaKEpJNRokQJl9onB/fv30fjxo0lI1KOlPs/evRIUsrgXbhm7sz06dMlc1rmzp1Llt3KliWPA7GIwqlTwGefAR98QJLAs1OREx5OFMbFHBedjmhPiTlSciyzJSUBrVqRZS1vb/LfmjUBvd5yToYB7GyVAYBE3wYOJGNzHLHdzw+wcRnbaTx+DPj4kHPbvDnbw92/fx/VqlUDTdPgOA4BAQHYuXOnXWO8ePHCYmlMrVbjgw8+kKVZt7NZsWKFaGSO4zgcOnQIgHQFMMMwDunyvUvEx8ejW7du0Ol0UCqVqFmzptUcuJcvX2Ls2LEoV64c6tSpgw0bNnjkDxzdXO1IAcCBAweyHa25evUqxo4dizFjxuRIw0VHaNGihUWVol6vx217KrnecvfuXUml3yJFishvvAcTjx49Ev3y92FZvFq0CKhThzwKgoMtHZbISBKxMbZWUSjInx1N8IyOBvLmtXSm1GqgTx9SMciyJM/Ky4u8/N++lLLNkCHmuVAURRyePHks7fHyAmJj7Z9jyxbxysWCBZ3beDgrevQgdjRqJKuae0xMDK5du+aw8OLly5fxf//3f1Cr1dBoNGjcuLFTC0nkJCkpCSEhIWZVzjRNo3r16qYX/NatWyUrgBs2bOjiM3At1atXN/u4VigU8Pb2dtv0GI8j5QSqVq1qsfzFcRw22/C1N3HiRDAMA7VaDbVaDYZhMHbs2Byw2j4SExMxcOBAcBwHhUKBqlWrWu1RtXPnTpQpUwYajQZFixZFRESE6d8EQcAHH3wgGga3JTyblpaG+Pj4XJGT5I7s2LEDXl5epi2E55EQGGi+rOXnRxydjHz0kaVTQFGAlaquLLl7F+jZkzhu1aoB69aZOxnx8cQh2bVL3mUxnhc/F70eaNKEJJlrNEC5co5H3Zo2lZ7DSgK3Uzl1ijjAGg1gh3xJTvLq1SskZGO50VU8ffoUffr0gZ+fHwIDAzFs2DCz6u1Tp06JRq1UKhW++uorF1ruWk6fPi1ZiOSO70LAhY4URVGNKYq6TlHUTYqivreyX5u3F7JSVmO6iyMVGxuLKlWqmMQOaZrGL7/8kuVxN2/elAz1Xr16NQcsd4ysHJg9e/ZYRJxYlsWcOXNM+xw7dgx6vd50/nq9HsWKFbOaeJmWlobhw4dDr9dDrVajYMGCWL9+vWzn9T6RlJSEvXv3IjIyEmnt2pGcqIwve5WKLOEZSU01b/KbcdNoXHMSb96QvKaePYEpUwB78mcyn69xUyrTx85CrTpLatcWn8PLS77Imj0YDMD//R+xIQfzSTwQjKkgYvlktlYt5yRRUVGYNGkSxo8f71SpiZUrV0pWfrZq1cpp82YHlzhSFEWpKIq6RVHUBxRFaSmKOk9RVEmR/XiKog5RFHUiNzlSRq5du4aDBw/aXIUxZcoU0VwhtVqN8ePHO9la51GhQgXRm8LPz88s7P/gwQOMGzcOPXr0QERERJZJ3IMHD7ZYlmJZ1mVNlN8ZMi9xZVxiMzrNgiCu90RRgCvU3B8/JhWFxqUzhiG5Thcv2nZ8jRri52Jn8YRV5swRT17neZKjldMsWEDmz5+fRPo85DjR0dGoWLEiGIYBz/PIkycP1q5d62qzLFiwYAFomoZWqzWtlIwYMcIpc50/f1403YBhGPzqSG5iDuAqR6oaRVG7M/z5B4qifhDZbxpFUZ9SFHUwNzpS9jJt2jTRiJRZBVUuRKqVi0ajwcuXLx0a882bN5J5VTVr1pT5DN4zaDprRwogQpWZHQOWBSZPzll7L18GKlQQT0a3tf3MuXPEodFoYIqq6fXZS57PTFISaatjTGDXaIjD54ooakwMcTQpSt6qx1zM3bt3MWjQINSqVQvh4eG4detWjs19+/ZtnD17Filu2MD74cOHkgUpZhIpMlK/fn2zOY39EN21StNVjlQbiqIWZvhzF4qiZmXapzxFURve/v974UhJqQLTNJ2lfos7U7p0aVGHx8fHx+FE1KioKNGvFoqS7m9n1HmaMmUK9uzZI3v38XcCQSARJTEnqmVL833T0oB+/YjjxfPEKfjuu5xNnB49WjqCZrTb1mjLnTvAoEHAxx+T6jpn9OpKTSV5X926Ad9/T9TirWEwAE+eyBuxEgSgeXNyfT79VNYE89zKxYsXwfO8SXxUo9FAr9fj33//dbVpLmf+/Pmiz1qFQoFhw4Y5Zc6EhAQMHDjQ1IewWbNmbv0OdJUj9T8RR2pmhj8r3zpPRZGFI0VRVC+Kov6lKOrfwoULO/Na5QjGNiwZt+nTp7varGyxZcsW0SW4SZMmOTxmcnKy5Dp6kyZNLPZ/+PAhgoODwfM8tFot9Ho9ypUr53BE7J1l4UJy66tUZJlMrSZOUnAwICVuFxcHXLqU88tDly5Zd6KMUZ9cmKgMAFi9mji1Oh05z6+/lifBftUqcm28vCwLCHIxiYmJePjwoUPyCHXr1hV9lribYrormDdvnmTXjtyujSgXbrm0R1GUN0VRTymKuvN2S6Io6kFWUancHpEyEh0djZkzZ2LGjBm4e/euq82RhVWrVqFw4cJQKBTw8/PDtGnTsl1lN3HiRFEH7Z9//sHx48fRu3dvdOvWDTt37kTDhg2hVqvN9tVqtejbt69MZ/gO8OhR+nLPsmVEMHLCBGDTpvQ2Lu7EmDHSulPGaFTTpq620jH277dcNmUYIlWQHZ48IRWYFPXOqLOnpKSYuiTQNA0/Pz8sWbLErjGkmrErFIr3PnK9fPly0WtDURRGjhzpavPcAlc5UmqKom5TFBVMpSebl7Ky/3uxtPc+kJKSIptMgSAIWLx4MUJCQsBxHGrWrInjx49j1KhRZs2MrSmx+/j4yGKLM4iPj8e0adPQrFkzhIeHO79ys2tXcts3aZI7lnvGjrUu4FmsGHEOcyN164qfF00D2YmiduxIxqlbN3f8jG2gb9++oh9UO3bssHmMPHnyiD4fWJbNNbIqBoPBKS21pk6davERatyGDBki+3yOIAgCzp8/jwMHDrhEFd4ljhSZl2pKUdQNilTvjXj7d2Moimousu977Ug9fvwY/fr1Q8GCBVGyZEnMmTMn130lxcTEYPHixVi9ejVevXrltHmioqJE88ykNp7nnWZLdnj69CmKFCliekGoVCqwLIvt27c7Z8Jjx8gtr9UC//3nnDnk5to18aU9jQZYuVK+XK0DB4jjUaAAySlyUoKtGYULiztSej1w/bpjY/71V3pky43zTezh9evXkvd71apVbR7nhx9+sCheoWka/fv3d6L18hAXF4dOnTpBq9VCqVSiRo0asgo57927V7RgSK/XY/ny5bLN4yh3795FyZIlTb1PGYbBzJkzc9QGlzlSztjeRUcqLi4OBQoUMCVBGr+Sunfv7mrTbGbSpEmmdhE8z4PjOOzdu9cpc82dO1cyCT3zptFo8OWXXzo817lz5zBo0CD07NkTu3btkvXL9dtvvxVdbsiXL5/8TnRaGlCxIrnlhw+Xd2xnM2kSidLodOS/NC3vktXmzeZLbEb19hMn5JtDjDZtxKsQ9XrAkd6OcXHEEaQoorH1jnDnzh3JRur58+e3eZzk5GS0bdsWNE3D29sbNE2jefPmbt9HUxAEVK5c2exZYVQBj3VEfV8Eg8GAcuXKmc2hVqtRpEgRl18fQRBQsmRJUS2uv53ZFzQTHkfKzZk8ebJomT9N07jjjKoimTl9+rSo/RzH4bUcPdIysXTpUkm5hcxOVHBwsMMtB6ZPnw6WZU03MMdxaNOmjWzO1IcffihqN8dxuCa3AvX8+eR2L1hQnr51Oc3t28DUqcD06cC9e/KNKwhAkSLikSE59aXEuHzZsp0MyzrW4w8AevUiY1SpQhznd4SUlBR4e3tb3CcKhQKfZRSQtZG7d+9i165dDrW6cgUnTpyQVAEfN26cbPO8fPkSffv2hbe3N/R6Pbp06eIW7VrOnz8v6Ui3bt06x+zwOFJuTsOGDUV/Sby8vLBx40bRY86ePYv69etDr9ejaNGimD17ttUX/OPHj3H48GHExMRYtcVgMGD//v2YP38+Tpw4YZPT0L9/f9EcJZ7nsW7duiyPt5e4uDjJGyujEzVgwAAkOVhS/vjxY9HlBI7j7MrLsIaUiClN01n+nOzi2TPA15fc7qtXyzfuu8Dr19I5WCyb9fFRUcDIkUDfviRx314H5tw5oHFj0u/vo48AR5dR9u8nNms0pNLxHWPWrFkWUWiO47JUB09JScHGjRsxefJkREZG5ppcqIxY+3Bs165dtsdPSEjAnDlz0LBhQ3Tq1AnHHO2j6ST2798v2a+wRo0aOWaHx5FycwIDA0V/SYzVaZm5cuWKhSPBsqyoCm1aWhq++uorUzhbp9Ohbdu2Zg6GwWDA7t27ER4ejoCAAHAcB5ZlTcndGXtHidGzZ09R+/V6PZYtW5b9CyTC7t27wXGcqEo8RVEoVqxYtoTvpDq7UxQl25JrRESExc9RpVLJ/3Do14/c6nXqvDPJx7KRlpYunpl5Cw62fuzmzSQXSasl++v1JM8qp6sf4+LSo2qjR+fs3DnIunXrEBYWBl9fXzRp0gRnz561uv+9e/dQsGBBk3aUXq9HpUqVnJq/6QzOnj0rmsrAsiymZHMJNyEhAWXLljWNr1AowLIsZs2aJZP12Sc+Pl50xYNhmGzJ69iLx5FyY86fPy+ZSOnr6yv6BdWxY0fRCBDDMBYPiXHjxlnchAzDYMCAAQCIgGXDhg0lnQaaprPUEdm1a5fo8TRNOzU0HB0dbZZXZtzUarVNfQ8zkpSUhD///BNNmjRBx44dMXbsWFENK5VKJVtyqiAI6NevH2iahpeXFziOQ8mSJeWNRp07R/JwVCrbW6m8b/zwg7h6+/z50sc8eSLeCobjgEWLcs52AOjUicxdsaK8TZ5zOfXq1bPIq9HpdG5ThWYP9erVs1AB9/f3x/Pnz7M17uzZsyVbtbiT/t6MGTPM7GQYBqGhoTlavedxpNyYLVu2SIYt69SpI3pMaGio6P5eXl64cOGC2b4BAQGS0S6DwYBFixZlmbjt6+tr9RwEQUD79u1N0RWVSpUjVRW7d++WvHZ169a1eZzk5GRUqVLFZL/xq0wsEZxlWZw+fVrW84iOjsamTZtw8uRJeZceBIHk+VAU8NZx9iBCWhq5PgxDHCG9Hhg3Tjp6N3cuSXwXi2JRFIlK5RTLl6c7fnLn1eVi3rx5I1nOzzAMunXrhs2bNzsk7JkT/Pvvv+jatSsaNmyIGTNmIDY2FoMHD0aePHnAMAxatGghS/5sgwYNJN8lu3fvluFM5OPgwYNo1aoVatSogYkTJ+a4BILHkXJj7ty5I9kyZuzYsaLHfPrpp6K//DqdDs+ePTPbVyrapVQqkZycjNq1a1t1oijKNvmA1NRU/P7772jWrBkGDBhg4dAZefz4MaZNm4Yffvgh2y1czpw5I5kr1bFjR5vHWbp0qeg4Wq3WVIWo1+tB0zQm53SPueywYgW5xf39ARubar/XvH5NJAOsVSmdPCkeicq45ZRAaFRUelNpa9Gz95Dbt29LKnUbN47j8MknnzhFlyk7LF26FCzLmlYdWJZFsWLFnBIhateuneh10uv1OOHsqtVchseRcnO6dOliFhVSqVTw8/PDkydPRPc/fvy46HJd165dLfatV6+e6EOkTJkyAEjjSGsPG7VanaVTcvr0aQQGBoLneXh5eYFlWdHcqAMHDoDjOJNzp9fr0aBBA4dzmQRBgL+/v6jd3333nc3jtGzZUvKrbOXKlVi3bh0iIiLwUKp9ijuSmEgq9Cgq55ea3mW+/JLII0g5URxHcqecSGpqKuKePoVQowaZs0ULT+5bBi5fvgxvb+8sHSmjM7Vy5UpXm2wiMTFRNKWApmlMmDBB9vkOHTpk8S5RKBQoWrRorkzMdyYeR8rNSUtLw+TJk1G0aFH4+fmhc+fOuJdFiff27dsRHBwMtVoNlmXxzTffIFkkP+L8+fPQ6/WmMLdR9PHw4cMASFsXqagOx3EICgrCgwcPJO1ITk5G3rx5RcPnV65cMTtHMaeHZVnMc1ATSBAEydyuggULSh738uVLDB06FIUKFcKHH36ISpUqSVYd7tu3zyHbXM6UKeT2DgvLWrRSEEikZfVqQCKS6OEtTZtKO1EaDUnsl+MFlJRE2uMUKUK0oQYPRurTp/j222/BcRxGvtWfSsiTh+RreTBRvXp1m5wo49a8eXNXm2zi+PHjkukKlStXdsqcU6dONeVp6vV6FClSBNcdFYR9h/E4Uu8ogiAgPj4+y9D0rVu30KdPH1SsWBFffPGFmSKuwWAwRcR0Op2pEq558+aYN29elhUuW7duFf2CUqvVZkmd//zzj2QD4urVqzt0/snJyZIPTJ1OJ3nMRx99ZFbtp9PpRB2pgIAAt82hsMrLl+lyB1mppK9bRwQujc6AWk3yqlxd2XTrFlEuP3BAPvVyOZg3z1L7yehE/fIL8PHHJOl70iQgi2pXSQSB5FllVHTX6RDu4wOWZVGFopD69u8/1elyr7PvBFJSUqy2ixLb7EkDcDZXrlyRzFlt1KiR0+Z98eIFtm/fjmPHjnkiURJ4HCkPWXLu3DlMmzYNy5Yts0tE05rGyRdffGHa78yZM5L71cqG8GFISIjomFId3VetWiVqh1arhU6ng5eXF3ieR1BQkGSel9vz88/k1q5Z03p05MgRcQ0lpRJwlaq+wUDmpmmA58kWHAy4S2PvxESgXDnzPCmWBapWNXewGAYoW9axKrpjxyyctVcUBZqioKco3Hz7d5Pf/u5+/PHHosMIgoD169ejRo0a+Oijj/D999/j6dOn2bwA7k1aWppoJa9xyUosIn7gwAFXm21G6dKlLZxBjuOc1zrKg014HCkPTiM6Olo0oV2v12PDhg2m/QwGA4KCgiz24zgOERERDs+/fft2M40RY8XdkSNHRPfv37+/6EOWpmlMmjQJ27dvx+HDh3Ndn0MTjx+nv4TfLt+KIgjEIcjsRGWIgLgk72bRIsuIj0oFOGlZwyESEoA//gDq1SNtXlasMI/qGTeOc0xgc8aMdG2qt9tNigJHUfjz7Z/PUhS0b393CxQoIDrMiBEjzJbtdTodChcujBfveOFBhw4dLCpuaZpGx44d4ePjY1Y8MnLkSFeba8GdO3cQGhoKvV4PLy8v0DSNUaNGyTpHTEwMIiIisGHDBiQkJMg69ruKx5Hy4FSGDx9u9sDmOA4ff/yxxZLjqVOnTO0HtFotWJZF27Zts+20HDp0CPXr10eBAgXQtGlTURFTI1OnThUVd+N5Hlu2bMmWHRlJTk7Gxo0bMWPGDJsV4mVhwAByW3/6qfX9eva0njStUACuqGaqUEHcHpoGoqPtH+/lS3KuHEecw5YtHRvHGkuXSot6du5s/3hbtlg0ak6iKHzx9v8TKAofZfhwEGuT8uTJE9EPHIZh8KujLWhyCS9evECFChXAcRz0ej1YlkXdunWRkJCApKQkbN68GREREbh//76rTZVEEAScPHkS27Ztkyw6cpRx48aBpmno9XpTgdBhax9dEjx//hxLlizB/PnzES33PeWGeBwpD05nz549aN26NRo1aoQlS5ZIVuK9evUKS5cuxZQpU/Dvv//msJXA06dPLZI5lUolChQokC0l9Iz8999/pipGY95Zw4YNRYsBZCUqiuTqKBSAtdYZV69avKgttipVnGurFMWKidvDcfbrJAkCccwyRndUKiAwUN4csF27yBJkZps1GmDYMPvHS0kRjXAlvf1v30xLU2IK37t27RLtT0dR9mms2cvWrVtRpUoVFCxYEO3atXNZ0rIgCDh27BgiIiJw5swZl9jgjhw7dkw0B8vb29uudlqbNm0CwzAmR5Wm6WyrrLs7HkfKg93ExMRg1apV2LVrl9vprGSXI0eOICAgAEqlEkqlEhUqVJC1gWnFihUtchwYhsHEiRNlm0OUL76ATVGQOXOsO1JaLVFEl5PUVGDbNmD2bMBKxBDDh4uLXQYG2p90fvCgeKSI40jSuFykpgL581tG+FiW6FI5Qr16oj+b20olQvLnB8/zqFOnDk6dOiV6+Llz50SrcZVKpVnuopxkVslWKpXgeR7Xr1+HwWDA2bNncf78+Syjs2/evMGkSZNQqVIl1K5dG2vWrPEkQMtEjx49RHPFvLy8bM7Bev78uWTLlovvcPcEjyPlwS5++ukn6HQ68DwPnueRL1++3Jt4nYnY2FgULlzY9JKhaRo8z5t9tT58+BATJkxAjx49EBERgURrAo2ZePDggdX+f07j4kXyIlerScWbNdauFY+gUBSJCMm95HH3LlC4MJmTYYiD0bChZSJ2XBxw/ToQGpqeJ6XRkP337LF/3tmzxXOXKIo0GZYiMZEcW7cu0KoVEBmZ9VzXrpFrx3HkPPPkAf76y3yfmBjiRNoSDVu9Wrw6kONIjlYWCIKAsLAwC3VvZyjzA2QpW6xsX6lUokGDBggMDIRer4der0ehQoUko9FJSUkoV66c2Yua4ziEh4fLbvP7SIcOHUSfTTzPY/369TaNERERIVqwo1KpMMyRCGwuweNIebAZYzPgzDdJwYIFc28CdgZ69eolWtUTFhYGADh58qQpEdWYNB8aGmpzgu69e/ck1eSDs2qCmx1atCC3c79+We+bmEhe9Jlf0iwLZKFf5hA1apAltYxzMQwwfjz59ydPgCZNSCRMpwOKFgW+/RZo2xYYOjRrx1CKffukI1KzZ4sfk5RE5AsyV+XZ0rtREIArV4izlDGK++oVyVmjaaJEzjBZj5eWBjRvbr4sqdPZJfb54MEDVKtWzfSx4OPjgzVr1th8fPppEZkVa/f/f//9J1mVKxYB8fb2FpVWWbZsmejzh6ZpREVF2W27B3M2btwoeX1t7du3YMEC0TEUCgUGDRrk5DNwHR5HyoPNSKl88zyP48ePu9q8bCEIgqT4qFarxbNnz0T7GOp0Onz77bc2z1GsWDHRMUaMGOGcE7t4kdzKNA3Yqr5+5gwRetTrycvdxydrzSlHePrUogLNtAUHE+ejfHkSecrs7GR3udVgAEqXNh9bqSQtc6TabSxeLB4J0umA2FjH7GjTxnK5kmVJ1MkaR4+my1O0b++wk3v37l2cO3fOoRzAhQsXIl++fFCr1fDx8cGECRNEl9levHghGYmVakGyZMkSi3E6duwoOoZer8fSpUsdOv83b95g7dq1+PPPP7MUOnYnYmNjcf78ebxxVI9MBIPBgM8++8zk9Br7os6dO9fmMWJiYkQ/Fq1VS78LeBwpDzYj1TLGy8sLkbYscbgxkydPFj03iqKg0Whw7do1yWhSoUKFbJ5n7dq1Fi8PnU7nvMoWY27U11/bd5zBQKInR4+SBGdn8PChdIPfAgXI/FIClxkEXR3m2TOgQwfizKlUZEnRWoTLGNnLvHl5ARnkPGwmLk76/MuXlz4uNpZcH4oCvvnG/nllYPXq1RaJyRzH4bfffhPdv1OnThb3j5Smk0ajEc0Z/O6770SP4Xkeu3btsvscDh8+bNKGM7anMkoJ3LhxA927d0fZsmXRuXNnXLp0ye7xnUFCQgL+97//mdIrWJaVtT2MwWDA9u3b0aNHDwwZMsShvKbSpUuLOlLO6AeYkUOHDqFu3brInz8/Pvnkkxz9uPc4UrkYg8GAEydOYO/evVmqjMvBvHnzRKs6WJaV9csopxEEAXny5JF0pBo1aoTHjx9LflWHhobaPFfFihVFI14DBw6U/8Tu3CFRC5Uq+xEcZ/F4MZXDAAAgAElEQVTRR5ZOhFYLDB4MrF+f3ng389asmXw2CIJtyeq9epGoVWZbeJ6orNtLVJR0k+NM+k937tzBnDlzsHTxYqTUrk32qV7dMVFPGShevLjoveDj4yO6zJeQkIAuXbqApmlwHAcfHx8MHDhQdMmP4zjRprg3btwQ7f0WFBRkd5eBpKQk+Pj4iD7L/vzzT+j1eqhUKlAUyeXiOM4hGQC5MV7DzDavWrXK1aYBAC5duiSZbD5r1ixZ53r58iXCw8ORJ08esCxr+nllnDOnBFU9jlQu5fLlyyhUqJBJmM34AHAmSUlJqFq1qmkJzBj6dTSs7i4kJiZKto5QKBSmhsTVq1e3uFlZlsXkyZNtmufZs2cWYoDGLX/+/PKfmFE3yo3aXFhw+nR6bhBFkeXE0FDgxQvi/IklhDMMabOS05w5Y+n4KBRAUBDJW7KXtDTAz8/y/JRKoEsX025jx44FTdNgWRa/vV2KTPL2lj/x3w7EXpYURdo/Wet+8PLlS9y6dQspKSkwGAyoX7++mXPEsiw+//xzyUq8rVu3Ik+ePKYoUmhoKK7ZK30BYMeOHaIJ8AqFAgEBAaLnZsyVdBWvXr2S/JgrW7asS20zYq2bRfv27WWbx2AwoFy5cpLXw7iVtxbZlRGPI5ULSUtLQ/78+UW9/nNyl6ZnIiUlBStXrkS7du3Qv39/2UtaXZG0LgiCqLJ65ofn3bt3UaRIEVNInWVZNG/e3Ob8khcvXkguZ0gpUDvMkyfpL31rulHuwJMnpJFy375E7TujZk2XLubOi1pN5ARcpcC9aBGxx8uLOH2FC5MkckdZtcr8/DQakpP2NoJ44sQJk6PR7O0+aRSFpjSdI1FoKcQiq8YPAnvkCJKTkzF79mxUrlwZVatWxcKFC7Fp0yaULl0aLMsiLCzMovQ+JSUFp06dwuXLlx2WPti4caNkA2CpHp0KhcKlci/R0dGSDmxAQAAA8vxcunQpatWqhWrVqmHOnDkO5b85+hw+fPiwqCOl0+lkVWDfs2ePpMOWcdNoNLLNaQ2PI5ULiYyMFG3yq1Kp0KdPH1eb5xCrVq1C4cKFQVEUAgMDMWfOnBzVh1m2bJnFsgHLsti9e7fZfmlpadi5cycWLFjgkNNao0YNi+gXTdMYPny4XKdCGDmS3MJNmsg77qtXwKxZRAV8yBDHtZBsJS0N+P13ICSE6EX17Ak8eODcObPi9Wtg717g5El5WuUcOUIq90qVIpWVGXoHfv3111AqlShGUXjx1pEaRpG8oHXr1mV/bgeJjIy0eKmzLGtzS6eUlBRERESgYcOGaNGiBXbs2GHq/yd2H8rZWQAgHzViTgnHcZJipRzHuVSzKjY2VlL/q02bNgCAdu3ame3Dsizq1atnk2NkMBgwYcIE5M2bFxRFJFl27Nhhl42CIKBUqVIW0ho8zyMmJsah8xZj8uTJktH9jFtQUJBsc1rD40jlQtatWyf5NdWqVStXm2c3GzZsEH14/vHHHzluR8mSJcGyLCpWrIi9e/fKPkdUVBSCgoLA8zy0Wi30ej2qVasmb47Zq1dA3rzkFh4yBChUiEQ6ypUD9u93fNxnz4j8gDGCYtRxcsJ18kD46quv4ENRuP7WidpAUVBQpFJtxYoVLrVt3759qFSpEjiOw0cffWTWP9MaaWlpqF+/vkXrqMGDByM4OFj0ueYMnbVFixaBYRjTS1+v1+Ozzz7DmDFjLJ5HDMNgiBwFDg5y4cIFeHt7W0S0VSoVvLy8cP36dZw5c0Y0h1Wv11t8EIoxYsQI0fP++++/7bI1NjYWTZo0gUajgVarRcmSJa225nKEzZs3iwYTMr9DZsyYIeu8UngcqVzIo0ePRCvIOI6TLV/p7NmzmD9/Pnbt2mV3Iqe9lChRQvRG8PPzeydVi5OTk7F+/XpMmTIFBw4ckP8cf/+d3L6FC1uqlLMsiYA4wrffissVKJUkZ+kd0BJzN/bu3Il9bxPcz1KkObExivn06VNXm+cQW7ZskVz+kXopqlQqp9hy5coVDB06FL169cLOnTthMBiQlpaG3r17g6ZpeHt7m5oaO72NkxXKly8vel1KlCiBm2+jwlOnTpW8hkOHDrU6fmJioqT8S+3atR2y+dWrV3j27FmW+/3333/4/fffMXv2bDx69MimsVNTU1G0aFGznFXjkizLsuA4DqNGjcqx94fHkcqljB071iKEW7ly5Wzf7CkpKfj0009NOUA8z6No0aJO1ViRkhVQKpV2KYd7AJEqKFSI3L5Syt0OPhjxwQfi4xnnGjxY1lPxAAj9+wMUhccUhSIUSeZmGAbz5893tWkO8+WXX0pGEKQi7fZIjMjFkydPcOzYMVOxiat4/vy5ZG6lv7+/ab9ly5aJOqi29Lq7c+eOaDSLotLzr5zBqFGjQNM0dDodWJYFwzBYnZWG2ltiYmLQpEkTqNVqqFQq1KlTB5cuXUJUVFSOvzc8jlQuJjIyEq1atUK9evUwd+5cWX55fvvtN4vcAZVKhZo1a8pgsTilSpWSvIHfxYiUU1mzhty6oaHSjpSfn2Njh4VJO1JGZ8pVSeDvIvPmARQFQavF2T/+wODBg/Hjjz86VKXmTnzwwQei9zvDMOjVq5foMv+iRYtcbbbLiI+Pl3SkMuYAvX79WjS/i+M4PH782OocSUlJksnbDRo0cMp5nT59WtR5YxjGpkiWkeTkZJd/cHscKQ9mSD3ktFqt05YS/vrrL9GH54IFC5wyn9zExcWhT58+8Pb2Bs/z6Nq1K2IdVbrOLsaGttOmiYtZUhTRH3KE+fOldY8oilSy/fsvcaaWLCGtVtxVv8rd2bs3Xbl88WJXWyMbjx49kkwSVqlUSEhIwMyZM+Hr6wu1Wg0/Pz/MlmrZ8x5Rv359UZ2kn376yWy/f/75BwUKFIBerwfP8/D398d+G/Mix4wZY7G8xzAMjh075oxTwpAhQ0RlZ/R6vc1FC+6Cx5HyYEbBggVFH3I6nQ4PnFgttWXLFhQvXhxqtRpFihTJNTeSwWBAWFiY2ctBoVDA29sbt3Paibhxg9y2DEOcmZ9+snR8WNa2RrtiGAxAjx7iopTGiNTq1WQOjiN20DQgY9lzriM+Hpgxg7SCGT7crCJPkitXAG9vck2zyG3JbVy6dEky8pFx+c5gMODVq1eeiPRb7t+/j+DgYPA8D4ZhwHEcateuLRqJMRgMOHv2LP755x+78lsFQcCMGTMQFBQEtVqNcuXK2eyEOcI333wj6Ug5WxNRbjyOlAczBg4cKPrFWKJECVeb5pbs2rVLsnqEZVlcyY7GkL18+y25bbt1I382GIAJE0gTYoWC5DjZ0dhWkr/+skw6Zxgi/CkWBWNZIGO7BoMBWLCANAAuXRoYN45ICrxrPHpEFMqNzqxWS67P0aPSx8TGkj6DFAW0avXOJfAnJyeLLj9pNBr0s6Wp9ntMWloaduzYgdmzZ+P48eMudTITExMxd+5cdOrUCSNGjHCoafSxY8dEl/Zoms5yKdLd8DhSHsx4/vw5QkJCTCFeY3f4U6dO2XR8SkoKnjx54vRKP3dh0qRJkvkLFEWhYcOGOWNIUlK6Snbm9hqCAMgtJBgZCRQvTqJTHAcMGkSiUTxv6UgpFEBGfbOOHc0jZTRNpBmc1dPPVfTubdlwmaKIJpbYSzAxkSy7UhRQqRKQi9suWWPx4sVmL1CtVgs/Pz8cOnQIEydOxO+//467tkTuPLiEpUuXmulEKZVKMAxjk8RCZgYOHAiWZaFUKqHRaMAwTK5J6ciIx5Fyc65cuYJp06Zh0aJFeJFDibyJiYlYsmQJvvrqK0yYMMGmklSDwYCRI0eC53nodDr4+vra1TU8t7J582arCrs6nS5nDFm1ityyYWHyiETaSmJietRk1SpxR4qigO7dgcuXifCkQmH573o9ccTeJQIDxa+FTkeiVRkxGIB27ci/FyzoetFRJ3Pw4EE0bdoUZcqUweDBg/Htt9+CpmloNBrodDrQNI2FCxe62kwPmdi/f7/VCkJHPqDPnDmDkSNHYvz48bhlrWm4G+NxpNwUQRAwYMAAMAwDnU4HjuPAcRwiHc1vcTKjR48WTRhfuXKlq02TDUEQLMLpqampKFKkiKQjlTdv3pwxrk4dcsvmsIipGc+eiVcKchzJE+I46fwqiiJNgd8lpOQitFogLi59P0EA3socQK8Hzp51nc0u4Pz585JLPK6WHvBgTt26dSWfdRzH4cKFC6420SVYc6SUlAeXsXfvXmrRokVUYmIilZycTL1584Z68+YN1apVKyo5OdnV5plhMBioyZMnUwkJCWZ/n5CQQI0ePdpFVsnHtWvXqHr16lFqtZriOI7q1asX9fr1a4qiKEqtVlPHjx+nChcubHEcwzBU7969nW/g9esUdfAgRbEsRXXq5Pz5pMibl6L++IOiGIaiNBqKUigoiuMoqlUrilq+nKLevKEoQRA/VqejqIIFc9ZeZ9O3L/mZZEStpqjatSnK2zv97yZMoKiZMylKq6WozZspqly5nLXTxaxZs0b0maZUKqmtW7e6wCIPUty6dUvy3wwGA8UwTA5akzvwOFIuZPHixdSbN29E/+3AgQM5bI11EhISqMTERNF/i4mJyWFr5CU2NpaqVq0adfDgQUoQBCoxMZFaunQp1bRpU9M++fPnp65evUo1atSIYhiG8vb2pmiappo0aUKNGjXK4bmvXLlC1atXj9JoNJSXlxf1zTffUElJSZY7LlhA/tu+vfkL2hV0705R589T1IgRFDVkCEXt2kVREREUdeaM9ePUanLsu8TAgRTVrBlxLHmeovR6iipenDiVRhYuJNdKoSB/X7++6+x1IeSj3va/9+AaKleuTCkUCtF/K1q0KBUSEpLDFuUCpEJV7rq9S0t7bdq0EQ2fenl54a+//nKpbampqVi9ejU6dOiA8PBwnD9/Hvnz5xe1t0qVKi61Nbv88ssvosrrLMvizJkzAGC23Hfjxg1s27YtS+kDg8GAffv2YebMmdi7d69FU9EHDx7A29vbrBM9TdNokrkJcWoq4O8P0SRzd8LXV3pJLzAwez0A3Z3r14GVK0m1Xsal4c2b05c6Xbkk62LOnTsn2kDYs7Tnfly8eNFCz4qiiOTLpUuXXG2ey6A8OVLuyebNm0V7H3Ech9cyl4rb0hncSHJyMmrWrGmyTaVSgWVZ9OzZU5aGl+5G69atRR1EnufRuXNn+Pv7Q6FQoESJEti5c6dNY7548QJhYWHQ6/WgaRp6vR6lSpUyU/MdMWKEaN8shmHMla337CG3arFiOZtkbi9jxlhqWtE08NVX71yJv00cOpSeT/bzz662xgJBEDBr1iwUKFAgRzSFRo4cCYZhoNFoTAnnubkNjsFgwIQJE+Dv7w+1Wo1KlSrhqDXZi1zChQsXRJ9LLMu6vIm2K/E4Um6KwWBAu3btwHEcFAoFtFotGIbB+vXrZZtj/vz5CAwMBEURMbzly5dneczixYtFHTyWZbFmzRqULVsW3t7eqFmzJg4fPiybrc7kyZMnuH37tqhDOX78eNEHh1qttohUMQyDgwcPZjlf165dLbS6tFotOnXqZNqncePGkhHJTZs2pQ/Wowe5VTMpHLsdaWlEDoCmidgkTZNKPrllGXIDFy6kC2726uWWDvAvv/xicZ+zLOtUZ+Cff/5B+fLloVKpoFarUaJECRw6dMhp8zmTQYMGiRbfnDt3ztWmZYv58+dL9uTr2bOnw+NGR0ejf//+KFu2LFq1aoWTJ0/KaLXz8ThSbowgCDh8+DB++OEH/Prrr7I2Dp43b57ojb5mzRqrx1l7wdsakXEXHj9+jPr160On04FhGAQFBWHXrl1m+0RFRZktr2W11apVK8t5xZYxKIpIJRiXCX/44QfJiNTVq1fJQMnJgI8PuVVzS1j96VPg1CngyRNXW+IaoqKA/PnJz6xVK+JguhnJycmSkh716tVz2rwNGza0+J1nWTbX9RZ8+fKlaDqAQqFA69atXW1etti2bZuoALFOp8O4ceMcGvP27dvw8fExySooFAqwLIsNGzbIbL3z8DhSbsT+/fvRpk0b1K9fX7YmxFIYI1GZt5CQEKvHtW3bVnKpKzd9PQqCgHLlylloorAsm+6oAJgzZ47oQ1Fqy9iNXQqpXmNqtdrkSMXExMDLy8vs32maRqNGjdIH2r6d3KalS8t+fZCcDPzwA5A3LynXb9CAtC7x4DixsWQJlqKIXIWLG61Kce/ePcmoQ758+Zwy53///Sf6gaFWq9GrVy/ExcXh5s2bSHFj0daEhARs2rQJEydOlHREs3q+ujupqakICgqyaO3CcZzDLcQ6deok2iomMDDQrrQTV+JxpNyEcePGmT28WJZFpUqVkJSUJPtcqampko6ARqOxeuz+/ftFH7KBgYG5Ss38zJkzokuUarUaX3/9tWm/Pn362OxE2RqR+vzzzy0SNlUqFZo2bWq238WLF1G7dm0olUpwHIfw8HAkJCSk79C9O7lNR4+W7bqYaN2atH2hKLIpFKQp8f378s/1PvD8OVChArmWZcua60i5GUlJSaL3hq2/346we/du0dYxxo8To5aet7c35s2b5xQbssO+ffvA8zy8vLwknSiFQoEWLVq42tRsc/PmTZQvXx40TYNlWRQqVChbaRxSH/UqlQpjx47Fzp07sWDBApe3xbGGx5FyA2JjY0WXcTiOc1rz3qCgINFf3uLFi2d57OjRo02tYziOg1arRdGiRdGhQwdcvHjRKfbKzdatWy0iPsYtY9Rn7ty5ol9Lxry1zNEsW5Lr7927h8DAQNPLiuM45MuXD3fu3BHdX/ThkZaW3hLGURG8K1eAOXOAdevMoyO3b4sLa2q1wLBhjs31PvPiBVC5MrmGH36YK1TLf/zxR9Gl/wMHDjhlvpiYGNHIr1KptPjoYFkWO3bscIodjhAfH2+1u0FGu0+fPu1qc2Xj3r17uHHjRradmzJlyli9bgqFAjRNg+M4VKtWDa9evZLpDOTD40i5ARs2bJB8qTvrC2bJkiWiVXabbWxq+/DhQ/z888/Q6XSmHCKlUgmWZXHCncvw33L//n3JHKSJEyea9tu1a5foz0WpVKJHjx4ICAiAUqlEqVKl7Oo19fr1ayxcuBDh4eGYP3++/Q+Hv/9OfzHb+yATBBLNYhiy8TxZwjMmwm7fTqJPmR0pigKcmCPzThAXB/z5JzB1KnDxIvDyJVClCrl2wcGAjHmOtiL1uxYTE4Mvv/wSvr6+KFSoEMaPH29aOjMYDPj111+RN29eUBSF0NBQbNu2zal2du/e3eyZJPYBY9xq1KjhVFvsYeXKlaJ5QwqFwvR8LFOmjNOc0NzO0qVLJZeSM286nc4tm1t7HCk3YP/+/aI3olKpRC8nts1YsWIFgoODoVarUaxYMWzcuNGu46W+JKpWrZrlscnJyVi7di3Gjh2LDRs2uCT3oW/fvmZLGBqNBkFBQWY9DSdNmmTWoDPj9v333+e4zSYGDiS36Lff2n/s6tWkXUtmJ6lwYeJk3bghHpHSaEhzYg/iHDxIWrxwHIne0TQQEECuXZEigETE0ZlER0eLRj/Pnz+PgIAAs99thmFEk6FtXbI3GAyIjIzE1KlT8ddffyHVzorMtLQ0TJw4EQULFoSXlxc++eQTyRds4cKF7RrbmSxcuFDSzn79+uWaPB9XIQgCfvzxR5tzUb28vFxtsgUeR8oNSEtLExW0dOdQsMFgkPxFV6vVVo998OABihQpAp7noVAooNfr8eGHHyI2NjaHrCcYDAYsWLAAZcqUQeHChdG/f3+LBs2rV68WdXJZlsWcOXNy1F4zSpQgt6gjuQl164pHm/R64K3IKJo0sXSm9HpSdebBkuRkIE8e8evq50eWS11Ay5YtRfPxSpQoIdnfzt4quYcPH2LBggUIDg42LfXzPI8PPvggW4KaycnJopF6lUqFjh07Ojyu3Ny7d0/UCXDn3qjuyPPnz0XFPsVWDdwNjyPlJly+fBmFChUyJSyyLOvW3c8FQZBcjjRW9ly9ehXff/89+vTpg6lTp2LChAn4888/0axZM4soj0ajQefOnV18VpYkJiYiX758FhII3t7eiHNVwvDDh+T2ZFnAkUhe9eriL3yeT1dHT0gAvv6aLP0pFGR5yk2derdg3z7p5dBPPnGZWVIVolKSHjzPY/Xq1TaP/9tvv4GmaYvqV+MH1aeffpot+2fPnm2x3MfzPG7cuJGtceVm7NixYFnWtBzJcRzatm3rtsnR7kq7du1Ef5cy/vxbtWrlajMt8DhSboTBYMDx48exe/dut0yoy8yIESNEE1LHjx+PxYsXg2EYsy8MY/QpN31pAMD169dRvnx56HQ60DSNkiVLOkVY7+XLl1i4cCHGjh2LyMhI6Yfw6tXk9mzY0PbBjx4FmjYFQkKASpXEl+7y5rUUyBQEt9Q6cjv27JF2pLLpTGQHqSUnlUol+sLiOM5mMcTjx49nmduiVquzvWz/119/oWrVqihYsCA6dOjgdk6UkePHj6N3797o0qULtm3b5lnSc4Bnz56Zuj4Y5TCMzinLssiXL5+seopy4XGkPAAAnj59igsXLtjVfiY1NRW9evWCTqeDl5cXaJpG//798fz5c0nRydwWss3IgwcPcN9J5f9nz56Ft7e3Scler9fj448/Fpe/6NuX3J62CuBt3WrenkWhID3ejPIGOh35dzkEVe/fB7p0IctcQUHAyJFk2etdJzGRLH1mdqI4Dli71mVmdevWzSIqpdFo8Pnnn1t81Gg0GpQvX97mKErPnj2tJoQbHbbk9+Hn70E2BEHAoUOHsHDhQuzZswdTp05Ft27dMGvWLMTHx7vaPFE8jtR7TlJSEjp16gSdTgee58GyLEaPHm1XSPrZs2c4c+aMKUl706ZNkst+UptGozFrkZIdzp49i4EDB6JXr17YvXu324fXBUFASEiIqGM5adIkywM++ojcnra06xAEkkQuFikpXx7o1w8YO1aearK4ONKAWK1On4NhXBqRyTHevEnXicroRLVq5dJegi9evEDZsmVF+zqeOHECJUuWhFarhVarRfPmzfH06VObx27fvr3Ve1qpVKJu3bpOPDsPHtwDjyP1ntO7d2+L6BHLsli8eLHDY+7YsSNLR0qhUIBhGCgUClNiqhzJ5lOnTgXDMGa5Cu3atXNrZ+rmzZuSSyQlS5Y03/nRI3JrsqxtkZ4XL0i1nZgjJXf1y++/WzYmNjpTuaWFjSPExQG1asG0PPrtt8Dw4USiwg1+7wRBwL59+zBz5kzs3bvXYsnp+fPnDjVC37Bhg6RwJ8uy8Pf3x61bt+Q6Dbfh2LFjaNCgAfLnz4/69eu/E82IPWQPjyP1HpOUlCRZcpqVMGdCQgJmz56NBg0aoEOHDmbKtklJSZIqxcYtMDAQq1atwpgxY2STP3j48KFk9cyePXuyPb6zuHnzpuRSaKlSpcx3XrOG3Jq2JjCnpJgrlGfc5G5X0bat+Dw8D7yrneFjY/+fvfMOa+p64/jJvithyHAioIi7de9Z66jWPerWqlj9qXXWVVtH1da21r1aB65qxVVXtTjrVlTcq0pVRMUFIggk9/v7IyYacy8ESHID5vM892kNuee8N8k99z3vec/3fROJKlQIuHRJaouchl6vR7NmzcxLhAqFAmq1Gg0bNsSvv/6aK/I8s0pkZKSg/p7Q+KLX63Hp0iWXzOlxY1/cjtR7THx8vKAoJSEEXl5eouclJyfjgw8+MA8opiKTs2bNMr/n0KFD0Gq14DjOIo+CpmlwHIfDhw/b/XrCw8NFk9n79+9v9/7sRUZLez/99JPlmwcONN6aWSkQOmiQtTPFMMCSJfa9kG+/NeZbvetIcRxw7Jh9+3IF7tx5I0NRrNh7KQ1hMBjw559/olevXhgyZIhDNmHkFL1ej8uXL+Pu3bs5bqts2bI2RY63b98OX19f85JqtWrVHJZf6UZ63I7UewzP84KlYmQyGZo3by563sKFC0U1aN6WBHj58iX++OMP/Prrr/j999/xzTffYP78+Xjy5IlDrmf9+vWCmk8KhQLDhw93SJ85ITk5GStWrMDgwYMxbtw4c7K5XC4Hx3GoV6+edbL5Bx8Yb82s6EelpgI9exqdHJ3O6FR98439l51iY43Rp7edKJXKaLMLLHHZlevX3+SelStnlKTIYzx69Ai//fYbFi9enGudAHs7NGLJ9TKZzJw+cOXKFasIs0m7y5VTDNxkH7cj9Z6zceNGC6dIoVCA4zhczCCnpXHjxoKDiU6nk7QG1osXLwRzNmiadrmZclxcHIoUKWKOoLEsC29vb0yfPh3fffcd9u7dax50k5KSsHHjRvy+ejV4U8QnISHrnT55Yixb4sgll6goo+OkUhmP1q2BLCQw5wrOnXujWF6jhrEgcR5jzZo15vpmDMOAoijMmzdParOyxJUrV6wmfAqFAqGhodl2aPz8/ATHPh8fH/N7Bg0aJFgNgeM4HMuLkVk3bkfKDfDPP/+gWbNmCAkJQbdu3XDt2rUM39+lSxdBQT9XGCj+/vtvcBxnXlakKAq//PKLpDYJ0bVrV6vBVi6Xo169ehbve/t6yr1O5H7h6SmN0VkhMdGyEHJe4cgRwNMT5jy1bCRp20JMTAzatWsHlmWRL18+jB49GilO+jwfPHggmLNH03SmY4OrEB8fj+bNmwsqZXMch6NHj2ar3Z9++klQO+/t+pwtWrQQnWhu3LjRXpfoxoVwO1JussyRI0cEl/Y4jnN6mRchkpKS8Mcff2DlypVWJV9cBaElSNOM2aS7k5iYaBFha/56uSxSLsel9yip2WXYvfvNrsS2bQEhjS8Y1fCnTZuG0NBQhIaG4vvvvxfWAxPh6dOn8PX1tVhGoigKTZo0sdeVZMiiRYsE72+lUokpU6Y4xYacMHnyZFAUJVojMycODc/zmDBhAliWNR/jx4+3iHDNmTNHNPXBHnlablwPt1LiztgAACAASURBVCPlJlvMnj3bKiqlVCoRFBTktJlzbsbT01NwkFcqleZir+9WlR/52pGaJ5Nh9OjREl/Be8bvv7+Rkejd21oB/jUGgwG1atWyiOjQNI06derYvJw0Y8YMwYgQwzC4cOGCPa9KkLlz5wrufpXL5fj6668d3n9O2Llzp6gkg+nQaDQ5dmhSUlJw69YtJCcnW/3txYsXCAoKstjIw7IsBg0alKM+peLFixc4c+YMHj58KLUpLktGjpScuHEjQoUKFQjDMBav6fV6Eh8fTyIiIiSyKvfQrVs3otFoLF5TKBSkadOmRKlUEkIISU5OJjzPm/9e8vV/LwEkKSnJWaa+3wCETJ1KSOfOhKSnEzJsGCG//UbI6+/oXfbt20eio6NJSkqK+bWUlBRy9uxZsn//fpu6PHXqlMX5JhQKBTl//nz2riMLtGjRQvB1iqJI27ZtMzw3NTWVPHz40OJ360zmzp1LXr58Kfp3lmVJv379SOHChXPUD0VRJCgoiNA0bfU3juNIVFQUGT58OClRogSpUqUKWbRoEZkzZ06O+nQ2AMjkyZOJn58fqV+/PgkICCAdOnQgycnJUpuWq3A7Uhmg1+vJnj17yPr160lcXJzU5jidc+fOEYPBYPV6UlISOX36tAQWZc7Lly/JkydPjOFWiZk2bRopX748YVmWKBQKQgghPM+T/fv3k6lTpxIApEmTJhafcanX/42hKNKmTRsJrH7PSEsj5PPPCfn6a0JkMkJ++YWQn38mRC4+NB47dkzwQZ6cnEyOHTtmU7dly5YlFEVZvc7zPAkJCbHd/mwSGBhIJk2aRGiaJgqFgsjlcsIwDBk4cCCpUKGC4Dl6vZ4MGzaMeHt7k8DAQOLv709WrFjhcFvf5dmzZ4Kvy+VyUrJkSbJw4UKnODReXl5k2rRp5Nq1a+TkyZOkW7duRCaTObxfe7JmzRryww8/kJSUFJKYmEhSU1PJ9u3byYABA6Q2LXchFqpy1cNZS3vnz5+Hn58ftFottFotNBoNvv32W6f07Srs2LFDMM+HYRiX293z7NkztGvXzlwKo3jx4jh48KDUZoHneXTr1s2qeCzDMFi8eDEAYNq0acaq8jIZnr5e2uvfqpV7G7WjefoUaNDAuJTHMMCWLTadtnTpUsGlJY7jbK4WEBcXZ1UZQK1Wo0qVKk793i9cuIBx48Zh9OjROHXqVIbvHTx4sFVekFqtRq1atTBixAiHFxo+efIkhg4dipo1a1rVFjR9/kLLcG7EKVOmjOjSaHaU8PMyxJ0jlTUMBgMKFy5s9eNydfVse6PX6xEUFGSxK0Ymk8Hb29tCS8oVEBpcGYaRvIq8wWAQFRANDAw0v+/kyZMY1q8fQAj0ajV4d1V5x3LzJhAaahwCCxQATp+2+dTExETB/DcvL68sPXyio6NRrVo1s1p4586dzbUsXY3k5OQMi5SrVCowDOMwaZRvv/0WDMNAJpOZD1OiuVwuB8MwCA8Pt7m9xMRE7Nq1C//88w/0er1DbM4N+Pr6Cn6fFEUhNjZWavNcCrcjlUWOHTsmuuOqbdu2Du/flYiNjUWTJk2gVCqhVCpRrVo1XL58WWqzLLhw4YLoDiSpkz+Tk5MFt2ebHD0LYmONt2T+/NIYm1Nu3TJqSvn4GIsuR0Rk7fzbt4EZM4wFlqOjHWIiAODwYaONhADly2ermHN0dDRCQ0NB0zRomkbJkiVx/vz5DM/Zs2cPWrVqhbp162Lu3Lnm6MmrV6/Mmw9clbt374rWinz78PX1tckxefXqFX7//XdMmDABa9euzXDH440bNwQT49VqNWrWrInPP/8cUVFRNl/LL7/8YnFP0jRtUf7qfaJdu3aCAqT58+e3qtf4vuN2pLLI33//LVqQ96OPPnJ4/67Iy5cvXaauFs/ziI6ORlRUFPR6PbZt2yb6fX1sa706B9patGhRQdtq1qxp+eYrV4y3ZIkS0hibEy5fFi6cPHCgbecvWwZQFKBWAwqFUZl95Ej727l27ZsSN82aGbWwcsDt27cRExOT6fumTJlisRzIMAw++OCDXLP7NT09XXQX6rtR+8xkO+Li4lC0aFFzpJbjOBQpUkQ0AjJr1izBMldyuRzffPNNlq7j5MmTgvp4crkcKSkpOHv2LH744QcsXLgQ8fHxWWo7N3Lt2jXodDoLGQmGYbBhwwapTXM53I5UFklKShKcfbEsa85ryWukpKTg33//xcuXL6U2JUPOnDmDgIAAsCwLjuPg5+eH9evXC85YKYrCpEmTRNtKS0vD8+fPHZ6TsmXLFotlEVPdQith0xMnjLdk5coOtcch1Kpl7USZjsxKqzx8aHSi3j2PYYDjx+1jn8EATJ5s6eA5KQr06NEjQUeAZVn89ttvTrHBHixYsCDTqBRFUZk6lh07drTSf1IoFGjTpo3g+8XKValUKkybNi1L1yBWscEUTaNp2rxMyTAMdu/enaX2cyP//vsv+vTpg5IlS6JFixYOqZGaF3A7UtkgPDwcNE2bQ8AqlcocAv3www/zzI+N53lMmjTJLDxH0zRGjBjhknkDL1++FJwVsyyLjh07WpXB8fHxERQPTUlJQVhYGCiKgkqlQnBwMP766y+H2n7gwAE0aNAAhQoVQosWLYSXIv7+23hLNmzoUFscglAhY9Mxd27G5y5fDrCs9XkyGTB0aM5te/YMaNnyTZu//OLUuoCbN28WjZh++umnTrPDHkRERKB8+fLmepHvOkO2jM9iRdSVSqXgpObhw4eiKuy3bt3Kkv2lS5fONKr29qHT6XJN1NCNY3E7Utnk/PnzGDx4MAIDAwV3XWVUqy63MH/+fMFyCBMnTpTaNCtWr14tmLhNURR+/PFH/PzzzwgMDES+fPnQtWtX/Pfff4LtdOjQwWpgZhgGZ86ccfIVvcPGjcZbUmRm7tJ4eIg7UsuWGaM/Ys75ihUAx1mfJ5cDI0bkzK7z54HixY3teXoC27fnrL1scPDgQcGcS7lcjr59+zrdHnvA8zy++OILUBRl3tkcHBxs0zKnUPTYNFkViw5HRESApmlwHGcuC7V06dIs2z1w4MAsO1KOnmQBwM2bNzF37lxMnz4dCxcuxJ49e1xyMusKnDhxAo0aNYKPjw8qVaqE7U66p92OVA549OiRqAJw165dnWqLIxDanWgaQFxt+/3MmTMFtz0TQjBq1Cib2rh//77g9ymTydCxY0cHX0EmLF9uvCV79pTWjuwwbpywEyWXGyUGFApAqTQmo79b0ufxY/GlvSzsprNi9WpjrhUhxiLL//6bs2vMJgaDAUWKFLHKzXEJ5z2H3L59G+vWrcPBgwdtTk7u0qWL1cRUqVSiffv2GZ737NkzrF69GuHh4dnOX0pMTBQtKyM2Djq6SPu4ceNAUZRVAnyRIkXwr0S/WXtw9epVdOvWDSEhIfjkk09w5MiRHLd5/PhxwYn/qlWr7GBxxrgdqRxw/PhxeHh4CN5k5cqVc6otjkAszC6TyZCWlia1eRZERUWJ1v/btWuXTW1k9H2WL1/ewVeQCUuWGG/Jzz+X1o7swPNAnTrWTpSHh/G/ptdUKqBYMevo1Jo1RqeHpo0J5xQFTJiQPVtSU4FBg9702bMnIHHu37Vr1xAcHAyO46DT6cCyrM2aU3mN+Ph4hISEQKvVQqlUmqNZzipP8u+//4pOyITGFkdqUx0+fFg070wmk0k/JmWT8+fPg+M4C+eQYRhssVGrTYx69eoJflb+/v4O32XodqRywOPHjwUjGAqFAj1zY+TgHapUqSL4wyxWrJhkNhkMBixatAhlypRBQEAAhgwZglu3buG3335DaGiohfPHMAzq169v80309OlTwe9TqVQiLCzMwVeWCRs2GG/J3Li0Z+L8eWDUKGDmTGDOHOHcJ61WeInt/n1jPtVPPwHXrtnc5YMHDzB06FCEhITg04oV8dikD6VSAYsWOTUfKiN4nsfp06exb98+l9/U4WjS09OxdetWTJ8+HVu2bHG6/ENkZKRRBPd1npdCoYBSqQRFUZDL5aAoCjRNY9u2bQ61IywsTHAX4duRqdwYlWrWrJngdRUuXDhHKx1iuYZqtRpPnjyx4xVY43akckj//v2tZg0sy+LKlStOt8Xe/PPPP2ahu7edE2etOwvx+eefW3zepkR/02sajQYURaFixYqYP38+UlNTs9T+8OHDLdqXyWTQarXSD1h79xpvyXr1pLXDXowcae1EEWKMOM2caZcu4uPjkT9/fqhUKtQjBA9e9/Fcp7Pfjj83eZJz586hU6dOKFeuHPr06YPr16/jxIkTmDx5MmbNmoW4zHab2oHevXtnGhFzRhFreyMmlZFTh6dUqVKC7bIs6/AVFLcjlUP0ej0mT54MHx8fKJVK1KhRI9NyCrmJU6dO4ZNPPkGhQoXQsGFDHDp0SDJbYmJiRJNR3z5UKlW2I0g8z2Pu3LkIDAyETqfDJ598kqn2jVM4e9Z4S+aBJWMAwKpVwknkHAfYqULAN998A0atxteEIP11+5GEoLBG47Iq4W7cmNi9e7dguSHT4efnJxht1+v1OHnyJE6cOOGSSenFixcXvB6KorI88X2bdevWCeZIjRkzxo7WC+N2pNzkGiIiIkTDt+8e3t7eUptrX/77z3hLFioktSX2ISXFeC0KhWU0qnx5o66THWhfoQKOvOWkTSMECkLg4eGB/fv326UPN67LkydP8P333+OTTz7BsGHDpI8qZxGe59GzZ08r50ChUIjqWB0+fNiiDqyvry+GDBmCli1bYujQoZKXxQKAX3/91cpBpGkaAwYMyHHb8+fPh6enJ2iaBsMwGDVqlFOcSbcj5SbXcPz4cdHadO8ePj4+UptrX168MN6S75aOyY28egV06mTUlzIpnqvVQL9+gFidRoPBmB9VsKAx2bxuXUCs9AfPA0uXIlmpBAjBPULw0TuD9tWrVx13fW6cyqtXr7B582YsWbIE117nz927dw9+fn5mKROVSgWWZSWNqGcHnudx+PBhjBgxAu3atUPLli0xbtw4QY2sp0+fZjg+msREd+/ejfT0dOzatQurV68WlYJx5DV98803oGkaOp0OFEWhe/fuGZYCygrp6em4f/++3dqzBbcj5URMSZSzZs3CwYMHXU5CwNXheR5lypTJdIuyRqPBl19+KbW59oXn3whbulhR6CwzcOAb6QHTwTBGMUwxhg0zvuftc1jWWH7mbeLjjQn5r98ToVDA652HSfXq1R17fW6cxvnz5+Hj4wOtVguGYUDTNPr164cePXoIjhMhISF5dtxdvHixzTUP/f39odVqzbpbw4cPd/rn8uLFC5w/fx6PHz92ar+OwO1IOYm7d+8iICAAWq0WGo0GHMehRo0a7/0OnawSFxeHevXqie5moWkalSpVcpnaf3alWjXjbWmnHCJJSE+3dqJMR5Eiwuc8eyasJaVQAN26vXnfX38ZizoTYtz9t3Il1qxeDS8vL/MDo0GDBnatk3b//n3069cPBQoUQIkSJTB37lx3QVcnIVarkmVZ0cLyKpVKsKJBXmDq1KmiRdDfPoTGTpZlcyw/8D7jdqScRIMGDax+5BRFYfTo0VKbJjmnTp1Cu3bt0LhxY0RERGT6IIqOjhadedWuXTtPzDifP3+OjRs3YuvWrW+c7WHDjLelCyrLW3H7trH0ikZjdGr+9z8gKcm4RPl6yc3qYFnhtqKiAJ1O+JxSpYDkZEttqNq1jf2/Ji0tDRcvXhQtfJtdnj59ivz581sVde3du7dd+3EjzLlz50SXsjLalPLVV19JbbpDOHLkSIbJ6ZkdTZo0kfoSci1uR8oJvHjxwkqt13QUKFBAavMkZdSoUVafScWKFTN0pvbv3y+adF6rVi0nWu8YVq9ebc4f0Ol04DjOmFhq0pJq3FhqEzPm2TPA19dSbFOjMTo4ABASIuwUiQ3k8fHC9fpkMmOuVIkSxn8rlcD06eLlZuzM999/L1jnjaIop+eduCJ79+7FBx98AKVSiYIFC2Lu3Ll2neQcP35cNPIUEBAgOtliGAYHDhywmx2uAs/zaNWqVYbOlEKhEI1a5YWxUyrcjpQTSEhIEHWkfH19pTZPMu7evSt6wy9cuFD0vMTERNFCpT/88IMTr8D+3Lp1S/DaGIbB88uXjbelTuc0ZyFbzJxpnc9kijidOgVERhr/bnK0lEpj1CojTZxevayXBN/e8VeqlHjyuYNo2rSp4G9Xp9Nh8+bNTrXF1Thy5IjgVvTvvvvO5jb0ej0OHz6MPXv2ICkpyervaWlp8PLyErxX5syZgwYNGgh+PzKZDN27d7fn5boMer0e4eHhqFu3LurUqYP69etDo9GY86FCQ0MFo3gMw2BuZgXE3YjidqScRNWqVa3WptVqNQYOHCi1aZIxfPhwUUeqTJkyGZ47Z84ci4GapmkUL14cCQkJTrLeMXz33XeCTjfHcVi2bBlQtKjx1jx3TmpT3xAVZYwm+fgAFSoYo0RCESeOM9YMBIy6WJ06GeUO+vYFbt7MuI+0NKOIJ8MYI1EmJ0yjASZPNu4EdDJDhgwRTGhmWdbl6+TFxsY6tOyKmBPDcZxNWkFnz55FgQIFoNVqodPpRGum7dixAwzDmMu6mHJPX716hS1btogu/WVWuy8vERMTg4iICBw7dgw8z5uLPJt+uxzHoXLlykhJSZHa1FyL25FyEpcvX4aXl5f54c9xHIoXL+5w6XoTPM+7XO7Q4MGDRR2pkiVLZnr+gQMH0LZtW9SsWRMzZsxAYmKiE6x2LKNHjxZMBqUoyjhj7N3beGuOHOlYQ/R6Y06T6TeTlGQs0dK4MdCjB3DypPH1M2eso09K5RtZg3cjUseOZd+mixeNy4Om9ho1AiTUxblx44bg8hHDMNi6datkdmVEVFQUSpYsCYqioNFoULVqVcGt9DnFz89P8L5mGAZ37tzJ8NzU1FT4+PgIRpyFxHFjYmIwceJE9O/fH5s2bTKXlElISBCM7rIsi40bN9r9mnMT165dw8iRI9G1a1esXbs2R0KYbtyOlFN5/vw5FixYgOHDh2Pt2rVO0bl4/vw5evbsCY1GA4VCgUaNGuHGjRsO79cWrl69KupI/fTTT1KbJwmHDh0SzHGgadoopnfypPHW9PQ0Ojf2Jj0dGDPG6PQolUBAgLFocGjoG4dJLjf+//LlxkiUUPRJJjMepn+r1UDlytmrbffyJTB27JskdT8/o00uMDHYt28fChUqJLq85Eo8fvzYKrdQLpejYMGCuHfvnl3Hozp16gje1yzLZtrP9u3bBXMglUolhg0bliU7wsPDLaIvLMuiZcuWku+svHDhAmbOnImlS5fieW6XM3ESL168wMKFC9G3b1/MmjULT58+ldokM25HKg/D8zwqVapkUc1cLpcjX758LvMj7NKli9WAWbx4cZcsbeAIbt68iX379pm3ZPM8j65du5qdKZlMBpZlLXZ3plSsCBCCr3Q6lC1bFuHh4faLNg4eLBxhUqutnSWOA/LlE3akNBqgZk2j06VWG6NYWX1g8Dzwxx9AUNCbdvv3B1zkt2uiY8eOgk6DVqu1i3OSkJCA8ePHo1ixYihdujRmz56drUK+v/zyi2CExuSkMAyD4cOH26VI8P79+wVzpL7++utMz129erXokly3t+UuMuDGjRtYsGABVq9ejTNnzmDs2LEYOHAgdu/e7TAn6uDBg+jatStatWqFtWvXCn6OPM8jLCwMNE1DrVaDZVlwHOcSSvupqanYuXMnNmzYgNu3b2P16tX49ddfcffuXalNw71791CgQAHzuMgwDLy9vc0CrFLjdqTyMIcPHxZNLPwlI/FDJ7Nt2zbUqFEDH3zwAebMmePwApOuQEJCAj766CPQNA0PDw9QFIWhQ4eal2B37tyJbt264fPPP8fBgwfN58XGxuJzlgUIwWVCIHv9fY4bNy7nRiUliWs8CR06nfgOPJo2loExGLIXOTp8GKhe/U175coBR4/m/BrtzM2bNyGXywUf+hzH4fK7gqFZJDU1FaVLl4ZGo7G4f1u3bp3ltoYMGSIaAX677aFDh+bIZhPbt29HSEgICDGWbPr+++9tcmLu3r0rKF/Asiz++OOPDM/leR4jRowARVGgadpcKsXRiuYTJ060KPDOsiwaNWpkNSH8888/BSPOnp6eki6vHT9+HF5eXtDpdGZnW61Wg2EYUBSF6dOnS2YbYJysvLvbUCaToZ6LFHF3O1J5mKVLl4puhe3Zs6fU5tmVmzdvYtCgQahbty5GjRrlErOojGjXrp1FpND0EFuyZEmG5w0bNgyMSoW7rx2MNuRNDlWOC/HevClcSFjsYFlg9mzrCBbDAEOGZM+Gy5ctlMnh5wcsXGhccnRBPvroI1GnRKPR5DgHcs2aNaKToXNZ3HCwbt06m0os0TRt18Tj7ESAxo8fbzF2sSyL2rVrZxotEyv060hH5d69e4KOH8dxViKXbdq0EfzMdTod9u7d6xD7MuPVq1eCux/f/b2dPn1aEvsAiD7HFAqFS0y83Y5ULuHu3bvYsGEDDh48aPPAdOzYMcEfIMMwmD17toMtzj4GgwE7d+7EkCFDMGXKlEw1eU6cOAGO48x5EGq1GjqdLsfRAEeRmJho5USZjsyS7CtWrAhCCIa8djQeEYL8xFiI9/DhwzkzLCVF3JF6W2qAEOOSXalSxmjTr78al/ho2ngMHZp1x+fWLaBnzze78RgGmDABcOENBHq9PkMl6U6dOuW4j/79+4s+2BYvXpyltoSiW2KOlL3FS7PDnj170LZtWzRu3BjLli2zyRHq1KmTqKOyx0EVAVauXCnqoPbq1cvivZ9++qnT7cuM7du3i+pxmQ65XI7BgwdLYh8AeHh4CNqlUqlcIg3E7Ui5ODzPY9iwYaAoyhymDgoKwu23lJszOrd69eoWA6dcLoevr6/LJjimp6fj448/Ng9MpvDytm3bRM/58MMPrW4wmUyGZs2aOdFy27l//76o8rK/v3+G53bo0AEymQwyQrDntVPzNyGgNRrExMTk3LipU4UjTAMHGsu06HRGZ6t4caPzY0KvB2Jjjc5YVrh929i2aZefUgl88YWxLRfHYDCI6sMplUq7lH+aPn264G9Fq9Vi+/btWW4vISEBo0ePRkBAgGi+lJeXl13ypKQgo4jPjh07HNLn1q1bBR0RhUKB4cOHW7z3jz/+EJzcarVayeQHevTokaETZTrCwsIksQ8ABg0aZDUBUKlU6NChg2Q2vY3bkXJxhG48uVyO8uXL23R+YmIi+vfvD47joFar0aJFC5ucMKlYvny54ECj0+kEE3dTU1NFc1RompbgCjKH53kULlxYcODt2rVrhueeOnXKnMSbnxA8fO3s/BYSYi/jjBGm4GDj0l2dOsDx48a/PX4M7NgBnDiR8x1zx44BHTq8iUDJZED37sC//+b8GpxIx44drZwptVqNL774wi7tx8XFWUU7ZDIZNBoNKleujMmTJ2d7STcqKkowITwjMVxXR8xRYRhGUNTTHrx69Qqenp6C48+Fd0RmDQYD2rdvb7ZRo9GApukMJ4pvc+fOHUyaNAn9+/fHhg0bRB3eixcv4pdffsGKFSsy1NbbtGmTqEP99sGyLP7++2/bPxQ7k5SUhBo1aoBlWTAMA47jUKZMGZcpeOx2pFyc2rVrC/6wGYZxGRkDe9KwYUPRGaVQWQeDwSC6VOHn5yfBFdjGzp07wTCM2QnUaDTw9va2Kaq0efNm5M+fHzRN49PXkgC8QgHktOgozxuTwx1FerpxF16NGm+iXUql0YG6eNFx/TqQx48fo0yZMuA4DjRNm8UN7alpdvToUQQGBoKmaSgUCouJA0VRKFq0aLadqVOnTqFRo0bw8vJC+fLlERERYTe7pUCv16Nly5YWEW2aprF+/XqH9nvixAnky5fPXNaJpmmjgK4APM/j0KFDGDduHH766Sebl1H37NkDhmHM4x3HcahSpQqSk5Mt2u7fvz9omoZGowHHceA4zmLDyttUqVLFJieqe/fuTtUh5Hkex44dw+zZs7Fp0yakpqaC53kcPXoUixcvxr59+1xKF9HtSLk45cuXF/xxa7Val1dPzg4ff/yx6PUeFdi1tXfvXsGwOk3TmOjixX2jo6PRo0cPVK9eHaNHj0ZcXJzN5xoMBty5c8c42xwzxni7yuXGaFJW0euBb78FPDyM7ZQubSzjYi8SEoxlY0yq7IQAXl5Gbah79+zXj0QYDAZERkZiwYIFOHTokEMGeJ7ncf78ecFlPoqiMGXKFLv3mVvheR6RkZH48ssvMWnSJIcIjgqRlpaGyMhIbNu2ze4VFvR6vaBIKcMwmDlzpvl9YrsCvby8BJOyhTTQTA5oWFgYhgwZgv379zvVaXn16hUaNWoElmXN5W0KFCiAf104Wu12pFycKVOmCA6euTmPQYytW7eKJmH7+/tbJRVevnxZUFlaJpOhS5cuLrGbwynwvNERMjkp//tf1kqmDBkinBd14kT2bUpNBf78E+jSxbhEaGq3eHFg/nzHiInmcQ4ePCharLt69epSm+fGgZw5c0Y0ob1ixYrm97Vq1Uo0oi+kVdW5c2fB1Agpny9CxcDlcjmqVKli8b7U1FRs3LgRM2fOdNgExlYkc6QIIU0JIdcIITcJIWME/j6cEHKZEHKeELKXEFI0szbzoiOVmJiI0NBQs8NgEs57d1ttbufBgweia/VarRYnTSVJ3iIsLEx011Tp0qWxZs0alwr/OpwlS94IZ37wAbB1qzmXSa/XC+96SkgwJpG/7UQRYsxZatEia/3r9cDffwN9+hiV199ur149oz0SK0rnZi5duiQ4cSCEZEtXyk3u4dKlS6ISALVq1TK/r3nz5qKOlFCO0/Xr16HT6SzGUYZhsNxUE1MCihcvLngNGo0GDx48AGAs7m6qxWgSNq1bt65kCfuSOFKEEAUh5F9CSDAhRE0IiSaElH7nPQ0IIczr/x9ACFmf2e/cCAAAIABJREFUWbt50ZECgJcvX2Lx4sVo3bo1hgwZ4rLb+nPCvHnzBB0ppVKJ77//XvCcunXrCt5wpuNdRfC8As/zWLFiBcqVK4dChQqhT58+b3SzTp60WELTlyuH2XXqQKNSQS6Xo1q1ajh//vybxi5dArRaa0eKECAoCHq9HkePHsW+ffuEB6n4eKODNGgQ4O9veX65csC0abkugdyV+fDDD60mDwzDCOYPusk78DyP4sWLW9XhZFnWopjzunXrsrwr8ObNm+jRoweCg4NRv359yWQYTBQtWlRwPKcoCvdepwLUqFHDKpJGUZRk6RxSOVI1CCG73/r3WELI2AzeX4EQciSzdvOqI/U+MGPGDMGt5HK5XDT/4+uvv85UE4eiKKfu7Lh06RLGjBnj0NyCESNGWAyWCoUC+fLlw8OHD41vePkSmDULKFjQ7NRcIgRTCUFTQlBYq32Tj/XihbCauUyGqHr1zLM+nU4HLcdh17x5wIoVQN++Rh2pd88rXtyo/5RLk8ddndjYWFSoUAEMw0Cn04FhGMyfP19qs+zO33//jQYNGqB48eLo3bu30/KcXJlLly7B19cXWq0WDMOApmn06NHDQldQr9ejVatWVrsC//zzTwktzxpjxowRHNdNGnuPHz8WTQEpWrSoJDZL5Ui1J4T89ta/uxNC5mXw/nmEkK8za9ftSOVeLly4IBiRYhgGUVFRguc8ePAA+fLlE5U/IMQoVBkZGYlXr15h3759OHjwoMNypxYsWGAukGqqkWfv3S7x8fGiGlR9+vSxeO+Zo0cxVK3Gf+84O3pCcD9/fmMUaepU4KOPrGrppalUmKzRYB4h2EwITpI3UgsWB0UZl+3GjwdOn3aJQsLvA1evXsXhw4cdtqVfSpYtW2axhKlQKODh4YGbN29KbZrkpKamYsuWLVi8eLHoygTP8zhw4ABGjx6NH374wRzFyS0kJiaibNmy5pwwmqah0+nMz4GHDx+KTqALFSokic1SOVIdBBypuSLv7UYIOU4I0Yj8PYwQcpoQcjogIMBxn5Qbh/Pll1+CZVmLelX9+/fP8JyYmBh06dJFdIZC0zQWL15s3pas0+ng7e1t99pbjx49Eq0PZk/9lcjISFEVYoVCYfFg/f3336HVaqEiBM0JwfeE4AghSBNyiGw8HhGCSyVKAD/+aNSCkrA+WG4nNTUVJ06cwOXLl9+vXL4MSEtLE9RkksvlNhcsdpP7SUtLw4YNGzBs2DDMnj3bqtSS0G52jUaDESNGSGJvRo6UzPh3+yOTyWoQQiYCaPL632MJIQTA9Hfe14gQMpcQUg/Ao8zarVy5Mk6fPu0Ai904AwDk4MGDZOXKlQQA6datG2nYsCGRyWSZnnv27FlSu3ZtkpycbH5NpVKR8uXLkytXrli8TgghHMeR2NhYotPp7GL76tWryYABA0hSUpLV38LCwsjixYvt0s/169dJ2bJlSXp6utXflEolWbp0KenRowchhJCLFy+SqlWrkpSUFIv3eVMUmd+jB/ksOJiQ588JSUoi5MUL43+TkghJTyc3X74kf545Q2LS00ksIeQ+IeTe68Oe1yPGmTNnyO+//054nicdO3Yk1apVc2h/zmbDhg2kb9++hBBC9Ho9CQwMJNu2bSPBwcESWyYNCQkJJCIigly9epXMmzePvHr1yuo9RYoUIXfu3JHAOjeuxoULF0jdunVJWloaSU5OJhzHkYCAAHL06FHi4eHhdHtkMlkUgMqCfxTzsHJ6EEKUhJBbhJAg8ibZvMw776lAjAnpIba2617ae7/ZtGkTfH19zfojjRs3xqRJkwTDwBzH2XVnyvr16wUjRY6oUVWkSBHBiJRSqcSMGTMs3tukSROLSJlcLoePj0+mxXT//fdfmwux2puJEyeaxUplMhkYhnH4TDM5Odnu2j9inD9/3mr3nVwuR2BgYLYK/OZ2jh07Bq1WC5ZlzfUyhY5q1apJbaqbt4iKikLNmjWhVCrh5eWFCRMmOFUy4fnz51iwYAFGjBiBDRs2SCp3QySUP/iEEHL9tbM0/vVrkwkhLV//fyQh5CEh5Nzr48/M2nQ7UkYePHiAvXv3urSAmaPQ6/W4fv06Hj16BAAYO3as4KCsVqvx888/263fFy9eiJamsHfV9IiICEHZB5ZlrURLU1JS8NVXXyFfvnxgGAZt2rSxOXF36NChFtfEsizq1avn0CKh169fF8yVo2kaZ8+etXt/8fHxaNmyJVQqFZRKJcqXL+/wKvcDBgwQ/P60Wq3dl5wzQ6/XY8eOHZg1axb27t3r9CVGg8GAAgUKiDpPb//28prkS27mxo0bVrpWNE2jZ8+eUpsmCZI5Uo443ndHymAwYMCAAaAoCh4eHqBpGo0bN8aLFy+kNk0yDhw4IOjg0DRtKQNgB/766y8wDGPeVUNRFKZPn27XPgDj91yvXj0Lh4NhGLRo0cKuD0Ke57Ft2za0aNECDRs2xLJlyxw+65s5c6ZgBFGhUJi3NkdFRWHatGmYO3euWVcmO/A8j/Lly1vtFtVqtbh//75NbZw9exbNmzeHv78/qlWrZlNh3JYtWwo6CzqdzqklWh48eIBixYpBq9Way4lUrFjRruVtMiMqKkpUaFImk0Gr1YLjOPzyyy9Os8lN5vTr109wMqDRaLJUoSGv4Hak8hCzZ8+2WjLQaDTo0qWL1KZJBs/zFtuBTbPb3r17O6S/hIQErFixAl999RW2bNnisOhNamoq5syZg4oVK6Jy5cpYtGhRnlC6nz9/vmBESq1WY/r06ejXrx8YhoFCoQBN02AYxuaCr+9y9OhRwYe4RqOxSY/mzJkzYBjGQtuHYRiEh4dneN6iRYsEhTU1Go3NDpw9aNmypdVSmkajwcCBA51mw+nTp0UdqapVq+LixYuSiSy6EadSpUqC35mHh4fTo6qugNuRykMEBwcL/rg1Gs17PRjp9XqsXbsWTZs2RYsWLbBp0yaHLWHs2bMHXl5eRt0lrRZ+fn6CNQLdCBMXFyfoSFEUheXLlwtGF1mWxcuXL7Pc1+rVq0V3QHbq1CnT8xs3bix4rq+vb4a5Ti9fvkSpUqUsctBYlsWYMWOyfA3ZJS0tTTQfydPT02l26PV6+Pv7C36nv/32m137unr1KsLDwxEZGfle5qLZk88//1wwIkVRlFMnA66C25HKQ3h5eQkOjGq1OtPkYmeQnp6O2bNno3Tp0ihWrBjGjx/vtARfZxAXFycYadDpdE5dLsntrF27FhRFgeM4sCwLiqKwZMkSdOnSRXRJbPv27Vnu5+LFi6LaZbNnz870fG9vb0F7KIp6I44qwosXL/D999+jUqVKaNiwITZv3uzU/KTU1FTR8kpardZpdgDAP//8A47jQNM0ZDIZOI5Ds2bN7BZh1ev16NKlC2iaBsdx0Gq1CAwMxH///WeX9t9Hrl69ajWpoWn6vV39cDtSEhMTE4OuXbvCz88PJUqUwIIFC7I9oLZv315QnDI4OBg8z+PevXvo3r07vL29UaRIEUybNs2pOx3atGlj4WhoNBqULl1auAacBBgMBuzfvx+rVq3CtWvXsnz+zz//LLrTbcWKFQ6wOO/y+PFjrFixAsuWLTM7JZ999pmoI5Xd5b1PP/3UwplSKpXInz+/TQ5+uXLlBO1hGAavslI0WiLq169vNV4olUp0797d6bY8efIE8+fPx8SJE3HgwAG7OpXz58+3muAoFApUrVrVbn28LxgMBqxatQp169ZF+fLlERAQYHa+R40ahVevXr2XmmhuR0pC4uLikC9fPquCkYMGDcpWezdv3oSnp6dZnFKhUIBhGERGRuLp06fw9/e36IumabRr1w67du3C//73P3z99de4ceOGna/SyLlz5wSjNRzHYc2aNQ7pMyvcu3cPxYsXB8dx4DgOFEWhc+fOWcpxymiH4MyZMx1o/fvBzp077bq0BxgjMxMnTkTBggXh7e2NHj16IDY21qZzN2zYYPWbZhgGX375ZbZscTY3b940y4WY7sWiRYvmKIHfWaSkpGDu3LmoVq0a6tevj3Xr1ok+wMuWLSua8vA+LkPlhM8++8ziHmQYBo0aNcLNmzfRpEkTKBQKqNVqdO7c2amluaTG7UhJiFhNIVuWBsSIjY3FyJEjUbNmTfTu3RsXX9c8mzFjhuAyhlwuNz8MVCoVaJp2iGOzePFi0cr1YWFhdu8vq9SuXdtqqYOiKMydO9fmNvbu3SsqgXDu3DkHWv9+wPM8+vbtC4ZhoFQqQdM0aJrOdjTKHsybNw+enp7m2meDBg2SVM/GxN27d9G/f38EBQWhevXq2LRpk+D7EhMTsWTJEgwbNgwrV67MFbmU6enpqF69usV4wrIs+vXrJ/j+YsWKiUYO3WVnbCcqKkpwDGdZFp6enhbRTZVKhTJlyrw3uWhuR0pCatWqJXiDe3h42KWsyMOHD9G/f3/kz59f1IkRG2DsLZmwfft2wcReiqIwbdo0u/aVVTKq3URRlM35ZTzP45NPPrHaISjFUkle5syZM5g6dWqO5Q/sRVpaGu7cuZPtqJi9iY2NRb58+SySyVmWdYgUhxRs3LhRcKcfTdOCS/KjR48WvL+LFCnyXi5DZZeZM2eKluIS2rjAcRwiIyOlNtspuB0pCendu7dgwidN07h+/XqO2k5MTEThwoWtNHJsObKbvJsR6enpKFSokFVOBsdxkuuOxMTECEbrTEebNm1sbis9PR0rVqxAw4YN0bhxY6xfv/69mZW5cQ2GDh0qeN/TNJ0nNOXCwsJEJ4C//vqr1fufPXuGkJAQ8wRHrVaDZVkcOHBAAutdg/T0dERHR+P27ds2n7Nq1SpBB1Zs0wJFUZg3b57jLsKFyMiRkhM3DmX48OFEo9FYvKbRaEj16tVJSEhIjtoODw8nT58+FazJZkIuF/+K37UrpyiVSvLPP/+QChUqEI1GQ2iaJoGBgWTPnj0kf/78du0rqwQEBBA/Pz/Rv+/YscOqXp0YSqWS9OzZk+zdu5fs3r2bdOzYMcPP2c37Dc/z5NKlS+T27dt2a3Pfvn2C971KpSKXL1+2Wz9SUaBAAaJWq61eVygUxMfHx+p1T09PEh0dTebMmUO6du1KvvrqK3LlyhVSr149h9uakJBgVedTajZt2kT8/PxI7dq1SenSpUmVKlXIvXv3Mj2vdevWRKFQWL2uUCgIwzBWryuVSlKmTBm72JyrEfOwXPXIbREpANi9ezcCAgJAURTUajXatWuH58+f57jdDh06CM4SZDKZOSGwZs2agkt+Xl5eDs3ziI2Nxa1bt1wqrH7w4EHRiJRKpcKzZ8+kNtHl0Ov1OHLkCA4cOJArdqm5Gnv27IG/v7956/8HH3xgl7JOLVq0EI0Q3Llzxw6WS0tMTIzguOXj4+Myv8OzZ8/iww8/hEqlgkqlQvPmzbOd92pPzp8/bxV9VygUKFmypE3j8alTp1CwYEGzjISPjw927NiBAgUKWESm1Go1PvzwQ/A8j9TUVIwfPx4+Pj6gaRrNmzfP8YqLq0HcS3vSw/M84uLi7Bp2b9u2reha9s6dO835HKNHjwZFUebSJjqdDocPH7abHbkJsc+sbNmyUpvmchw/fhx+fn7m30xOJAjeR27duiVYuLhIkSI5VsM/dOiQVdtqtRoff/yxnayXnp07d8LLy8tcQiYwMNDuJZ+yy4MHD6DT6azG3dKlS0s+eQwLCxNciuM4DidOnMj0/Pj4eMycORPdu3fHjz/+aHZc7969i7Zt20Kj0YBlWfTp08ccEGjbtq2F8yaTyeDp6Sl5Soc9cTtSeZTSpUuLRqTeTYq9desWlixZgvXr17tMwqwU3L17F35+fuabXq1WWwwwPM8jMjISQ4YMwYQJE/LcrMpWkpKS4OHhIZijkhciHs5g7NixovmLXbp0ybEztXLlSnh5eYHjOGg0GrRo0cIukW5XIi0tDcePH8e5c+eg1+vx66+/onz58ggKCsKIESMk234/depUUT05qfOymjVrJpoXm1lR6OPHj0Or1ZrHR47jULly5QyfGTdv3hT8LDQaDSZMmGDvy5MMtyOVR/Hx8REN7ztaO+Xly5dYvHgxOnXqhDFjxmQpoVFqnj59ihkzZqB169YYO3as2TEwGAxo166dOWHVJBWxcuVKiS22HxcvXkTDhg2hVqvh7e2NcePGCS7xrl27VnAHpkajwdSpU7Pd/6pVq1CiRAlwHIdatWrh2LFjObkcl6Zr166iS8lqtTrbWnJvk5aWhitXruDRo0d2sNi1CQsLs4jCqdVqFC1aVJKKAt26dRP8XlmWxfLly51uz9sI1WM13bsZRYh4nkfRokWtzqNpOsN7fuvWrVbROdPRuHFjR1yiJLgdqTxKixYtLIqpvp1H4KhCuoDRESlWrJjVDpl9+/Y5rE9nsGXLFtEt13mhzM2dO3esBjyaptGxY0er986bN090l+OwYcOy1f+sWbMExS1PnjyZ00tzScTqBr494ckLvytn8N9//wlGPRiGwZw5cxzW55w5czBv3jzcu3fP4m8LFixwWT25xMREBAUFWchBsCyLkSNHZnjejRs3RCV0QkJCsGbNGvzxxx9Wjuvly5dFi5Bn1mduwu1I5VGio6PBsqxVZXpHlyoR02xhGAZr1qxxeDkYg8HgEEcxo/Ikmzdvtnt/zmb48OGCGjEURVnVJBMbHDmOw19//ZXlvtPS0gSXCgkheSqv521SUlJQunRpwckOIcaSG5cvX5baTFFu3LiBVatWYe/evZLLe0RERIhGPVq2bGn3/mbNmgWKokBRFDQaDTQajYXswosXL1CoUCELbSWaptGkSRO725Idnj17hgkTJqBMmTKoWbMm1q9fn2nu1u3bt0UnTzKZDFqtFlqtFizLYseOHRbnNmzY0OqZwHFcnqp16Hak8hBpaWlYs2YNWrdujd69e2Pt2rVo27YtChYsiJo1a2LXrl0Ot0FMRdg0mFSqVAnJycl27zc+Ph7t27eHUqmEQqFAo0aNcOvWLbu136NHD8GHnk6nsxo4HE1qairCw8PRvHlzdOvWzS6bA+rUqSP4nXl4eAg6R2FhYVbCo02aNMnWQ/Xu3buis10/P78cX5uzuHXrFrZv325zncbExESULFlS9F5JSkpysMVZx2AwoFevXuai0lqtFkWLFsWNGzdw9+5dSZTRjx07JhgtViqVGDp0qF37unHjhmiFiLeT3ePi4tC7d294e3ujYMGC+Oabb1xmR2F2ycjxf3fS/PTpU/N5L168wOeffw6NRgO5XI7KlSvj9OnTEl6J/XE7UnmEtLQ01KlTx/xwk8lkYBjG6TXeypcvn+lNZu9wu8FgQGhoqEXyrlwuh6+vr912Qh44cEAwXK/T6Zw6QKalpaFmzZpW3/OPP/6Yo3YHDRokmPxMUZSgQ8rzPDZt2oRPPvkEjRo1Qnh4ONLT07PVd0pKiqgjFRoairCwMIwdO9Zlk/tTU1PRvn17UBQFDw8P0DSNxo0b27Rx4+zZs4JLmuPGjQNgfHCvXbsWhw4dknzHFwD89ttvVvbKZDLI5XLQNA2GYTBq1CiHpg+8C8/zKFWqlJW6NsMwdv/NTJ8+XVDFmxCC4sWL27UvV+Py5cvw9fWFVquFRqOBSqUSdKxYlsWyZcusztfr9S5ToN7euB2pPMLatWsFH/QURTl198qiRYsyzP0ghKB69ep27XP37t2Cyc8sy2Lx4sV262fcuHFmqQhTceP9+/fbrX1bWL16tUO+51u3blnN6imKwqeffmpH68UZOXKkoByAKffFlNy/bt06p9iTFcaPH28VpaAoSrT227scO3YM1atXh0ajQaFChTBr1iykp6eje/fuoCjKvMW/RIkSNhdUdhQVKlSwKSLx9ddfO9Wu2NhY1K5dGxqNBgzDoGDBgti9e7fd+/nuu+9Er1upVOap5SohUlJS8Mcff2DWrFno3r27oCNF0zTmz58vtalOxe1I5RHatWsneHNrtVps3LjRaXYYDAb06NFDtCYTIfbPe5kzZ45orbwhQ4bYta9bt25h0aJFWLNmjSTlNsS0rnQ6Xabf8+nTp9G7d280btwYc+bMsVo6OnXqFKpWrQqZTGYuwOuspRq9Xo9x48aB4zioVCp4enoKfqcsyzpMouP+/fvYtGkTjhw5kqXoT758+QS/E4qisp0/NG/ePCvHUqFQoE6dOtlqz16UKFEiU0fKNO5kNSp14cIFNGjQAEqlEp6enhg1alSWIxhxcXG4ceOGw/K2Ll26JLq8xXEcTp065ZB+XZHDhw+LTursmVaRG3A7UnmEvn37WtWxMw1oe/bscZodT548QVxcHK5duwZfX1/BB6FYJfrssm/fPsEcCVfYbmxv+vTpI/o9Z1QgdOXKlWAYxnwuwzAIDQ0V3B6u1+slW0bS6/V4/vx5hno3OYk07NixA02aNEHlypUxdepUJCQkgOd5jBw5EhqNBjqdDhzHoVixYoiJibGpTaEdY4QYl7yyWyFATAdOo9FIqpD99ddfi05a3o3OZEV64M6dO1ZRZZqm0aZNG/zwww/w9/eHSqVCtWrVcPz4cQdeYebUqFFD8JpZlnVI/qerwvM8evfubXam5HI5GIbBxIkTpTbN6bgdqTzCiRMnBPNMfH19s527khXu3buHunXrQq1WQ6PRoESJEli3bh38/f3NSxMUReHLL7+0+0Oa53lUqFDBIgqmVCpRqFChPCcweurUKcHv2c/PT/R7TklJEVz6pGka33//vZOvwDbEIm9arRYHDx7MVptTpkyxmEFTFIWQkBCsXLnSamYtl8vx4Ycf2tRu06ZNBaMUlStXzpadAAQ1e0zfmZS6bM+fP0doaKhFjp6QnYUKFcrSfT5y5EjBKLZCobBaNmUYRlIV8wcPHsDb29tiQsMwzHtToPdteJ7H3r170a9fP/zvf/+T3MmVCrcjlYeYM2cOKIoyl+zw9fXFmTNnHN6vwWBAcHCwVekBjuNw9+5d7Nq1C6tWrbJ5hp8dEhIS0L9/f7PybqdOnSTPJ3EU8+fPN3/PWq0W/v7+iI6OFn3/0aNHRbeHV6lSxYmW285ff/0luGyQ3YnB48ePRbWGgoODRZ2WGzduZNr21atX4eHhYY7UqFSqHC/zDB06VNCxCAgIwKtXrxAdHY27d+9mu30heJ5HQkJCpp9vcnIyli5dis6dO5vzuN79TLOay1a/fv1Mo1xvO7kdOnTIyaXmmAcPHmDkyJEoW7YsmjRp4tSof0bwPI9//vkHQ4YMwfDhwx22Oy4lJQWnTp2yS23IvIDbkcpjPHnyBJs3b0ZkZKRTIlEA8PfffwtGPCiKwnfffecUG943nj17hj///BMHDhzINBfl0qVLorvinKltYzAYsHXrVnTq1Andu3fPUKSV53mMGjUKFEWBZVlotVp4enraVA9MiB07dohqVQktC5uiX1FRUTa1HxsbizFjxuCjjz7CsGHDchw1evz4MQIDA62EbceNGwcPDw9otVpQFIU6derYrFx+8uRJdO7cGbVq1cKkSZPw5MkT89927tyJwMBAKJVKc36crflJJ06cQKNGjeDr64vq1atnS0ts2LBhoiVzxJbRLly4kOV+8jr/+9//wDCMeSclwzCYMmWKXftYunQpOI6DTqcDTdOoVq1anqqblx3cjpSbHLN06VLRnXo9e/aU2rwcYTAY8OTJE6c5pY6A53mUKVPGKrdKSDzPkTZ07NjRSntq1KhRGZ53+/Zt/Pbbb4iIiMhR4vvJkycFHSbTEp5QtMrLyyvbOU724MWLF1iwYAE6dOiA0aNHY+PGjVYOsUqlQtWqVTNt6/fffzc/YE2TnAIFCuDhw4c4fvy4Vbs0TaNHjx5OuEojMTExVt9PZppFbmfKErH0Dnsmfx8+fNiqD6VSiff92et2pNzkmOjoaMEbmGVZLF261On2HD16FE2bNkVQUBDatWuX7XyK5cuXw9fX11y8ePz48ZKrOGeX27dvo3jx4uaZpEajwaRJk5zW//79+0V3+NiyfJZTeJ5HiRIlrJxJhmGwf/9+hISEmH/DCoUCDMMgIiJCtL2XL1/i22+/RbFixRASEoKpU6c6fIdjhw4dBJ0LhmFw9epV0fPS0tLg6elpdZ5arcaIESPQsmVLwXadLZ1y9uxZ1KhRw2xLZo6UTCZziHK5vUhKSkJERARWr17tlA0C48aNE/0e586da5c+2rZtK/obvHLlil36yI24HSk3dqFly5YWSaFqtRpBQUFO38Wyc+dOC6fOJFiZ1ZptmzdvFhRKHD9+vIMsdzw8z+P48ePYvn074uPjndr3yJEjRTVnnJWk+99//6Fs2bJgGMacX2YqmZSUlIT58+ejRYsWGDBgQIaRDr1ej8qVK1tEsWiaRt26dcHzPHiex5EjR7B+/fpsRwLOnDmDOnXqQKVSwdvbGxMmTEDVqlUFHQoPDw8cOHBAtK2LFy+KLl+WKFECoaGhgn/T6XSS1Ibr1KmT4M5UocPf39/p9tlCZGSkWfndtNHGUXX/TEyePFlweZRlWYsSNjmhevXq2foN5nXcjpQbu5CWloYZM2agWLFiKFSoEIYMGWKRg+FoEhIScOTIERQpUkTwRs+q/o6YQjvLspIu9+RWJk+eLJg8zXEcwsPDnWrL5cuXcfTo0WxHkLZv3y7omHAch4iICJQsWdL8EKUoCr169cpSJPPmzZtW7dM0jfLlywsuQVIUhefPn4u2FxsbKypZULNmTXTr1s1qo4ipz6xIGNiLgIAAm5woQnK2M9JRvHjxQjD6StO0Q3cbXr9+XbB8DU3Tdps4TZo0SfA3mFeKt2cXtyNlZ54+fYpp06ahUaNG+OKLL97rcKct8DyP5OTkHEkiTJ06FTRNi+5MM93oWUFoKYQQo46PM5c7chsXL17E8uXLERkZaeE83Lp1S3CQZ1k21w3AEyZMEPxtKJVKBAYGWjklDMNg0aJFNrf/xRdfiJYhkclkFu2zLGu2kQtXAAAgAElEQVTTho66detaRStYlkVERASuXr1q5bixLIsxY8Zk2m5SUhJGjhwJX19feHl5oV+/fjl6aEdHR9vsSDEMg61bt2a7L0exfv16wc03CoUCI0aMcGjfixcvNtdB5DgONE3bVZD56dOnKFy4sIVjzjAMZsyYYbc+ciNuR8qOxMXFoUCBAuYHhinXwhGlCvICK1euRIECBaBQKODh4YEpU6ZkOQdp8+bNmZakIYSgSJEiWWq3bt26gu3ky5cv1+ZJOZL09HS0bdsWNE2bd9kFBwdbbNFfs2aNeVnNdOzdu1dCq7PHkiVLBH9zLMuKOkAajQZeXl6oX79+plo7lStXzvC3rFAooNVqUa9ePZsdiUePHqFKlSpgGAYeHh6gKArffvuteQJz7tw5fPzxx+A4DkFBQViwYEGmkxue51GtWjWLh6pKpUJQUFC26k+OGjUKNE0LLuvRNI2QkBBziSZPT0+7ln+yJytWrBBdSu3fv7/D+3/48CFWrFiB1atX49mzZ3Zv//Hjxxg/fjw++OADfPzxx9i5cycAoyzGihUrMHLkSCxfvjzPafhlhNuRsiNffPGF4Bp1VsXpcsqJEyfQqlUrlCpVCr169XK5Yq/p6en49NNPBWeY33zzTZbaqlmzpk0z16zm4Rw9elQwR2rJkiVZaud94eeffxYsaVK7dm2L9yUmJmLLli3YsWOH08rP2JuEhATBiKWteT0Mw+DYsWOi7fft21dwqe3tg6KobGn4XL58GXv37sXTp09z8hEAAA4ePCi6xLl69eostXXy5ElRiQ6NRoNevXohJSUFSUlJ+O+//1x6F+39+/cFl79YlnUZvSl7c+/ePRQqVMj8e+A4DgUKFLC71pmr4nak7EjhwoVFB05HilG+zY4dOyy2OZtmr/bcJqzX6/Hff/9lu9bc6NGjM6xXlZUcpGLFimX4wKJpGuPHj8+WI3vkyBHUrl0bOp0OZcqUyXAXly3Ex8fj7NmzktToczQhISGiD0FnJ7Y7g+joaJQqVQoURUGpVGa6w+zdo379+qJtX7t2LdMoq4eHh+TLWrNnzxbNvRo6dGiW2ho1apRoJMpeO86cyY8//mhRkollWXTq1Emy0kuOpk2bNlbOv0KhcOldlfbE7UjZkTJlyog+TByRV7Nnzx5Uq1YN3t7eqFmzJvbv3y9YWkImk6FZs2Z26TM8PBz58uUDwzDQaDSoUKECAgICUKBAAQwePDjTBHO9Xp/hQ4KiKDx48MBmewYNGiQYBfTw8MC5c+esCvNKQUpKCj777DNzLTeapjFx4sQ8NaiKJflTFJWnZ6U3b94UjaRkdHh5eWXY7vHjx1GpUqUMJwmXL1920lUKs337dsFcIJZlsWDBgkzPj4uLw8yZMzFu3Dh89tlngo4UwzCSSKjYg6ioKAwePBh9+/bFX3/95bD7PTY2Frt27ZI0H1esSL1SqcxT45wYbkfKjixZskRQMK9x48Z272vLli1Wybs0TYsuCeh0uhz3uWfPngwfGiqVCsHBwRku2SQlJYnmkRBC4OnpmaWw/f37981aTyankWEYrFq1KsfXay/69OljFepnWRbLli2T2rQs8+TJE3z11VcoUaIEqlatijVr1oDnedGSJsWKFcvTA+n169dF82EoihJ9wJQvX96m9m/dumXVvkajQcOGDR18ZZmTnp6OoKAgizFHJpPB29s70w0EprHEdF9QFCW6NPrzzz876YpyFwaDAWFhYaAoCh4eHmAYBnXr1s1wB6ejECvcrdFonG6LFLgdKTvC8zwGDBhgroPGsiwqVarkkKUNsSUtsSWGYsWK5bjPevXqZTrTZlnWrM0jBM/zorty5HI5Zs2alWW7Hjx4gK+++goVK1ZE69atcfjw4Zxcpl1JSUkRHWRCQ0OlNi9LJCQkoGjRohbOAcuyGD58OJ48eYLg4GBztFGj0YDjOBw9elRqsx1KQkKC6Pdbr149jBkzRjDXbtOmTTb3cerUKVSsWBFyuRwajQa9e/d2meXh2NhYNGnSBEqlEkqlEjVq1Mg0MpKWlgYvLy/B6IXQ5+ho2QB7cf78ebRr1w5BQUFo0qQJjhw54tD+5syZY/XbUqvVaNeunUP7FaJbt25WKwMqlQqdO3d2ui1S4HakHMC9e/ewbds2h4nZGQwGUUdGJpMJVktfuHBhjvsNDAzM1JEihKBv374ZtiMkdimTyfDtt9/m2EZX49GjR6J5JN7e3lKblyV+/vlnQQkDiqJw//59vHz5EkuXLkWPHj0wadKkXF80Ojo6GgMGDED79u2xcuVK0dpzffr0EbznIiMjodfrMWbMGLAsC41GAx8fn2yLI7569SrTuopSkZycbPMy+qFDh0SlSoSiUgqFIss5V87m1KlTFjlRpt+AI0swiU2m1Wq101Manjx5glKlSkGr1UKtVkOr1aJkyZJWKS1HjhzBkCFDMGzYsBwV9XY13I5ULsXHx0fwJipUqBC6dOlijorRNI2xY8faZXmlS5cume5MoigKP/zwQ6ZtHThwAA0bNkThwoXx6aef4uzZs+B5HidPnsS6desyLHmRm+B5HgULFhR0eHNbImbTpk0Fv3OdTid54rO9WbFiBRiGMS9bsSyLypUrCy5bp6amYuDAgaBpGhqNBn5+flizZo3Fe9LS0hAfH++WzoDxYSqUW2VymoRe79Wrl9RmZ4hYtD4wMNBhS9tizwCNRuOUkjTvYjAYsGvXLsycORM7d+60cvqHDh1qVVB54sSJTrfTEbgdqVyKaVfIu7Ngk7bKo0ePcObMGbuKHV67dg1arTZDZ0qr1QpWo4+Pj8eKFSsQHh4umJD+5MkTVKpUyaxBRNM02rRpkydUxDdt2mTxXZl2Ul66dElq07JE//79BR90LMvmqdllUlKS4IaIzIQ1U1JS8PDhQ7ezlAl6vR6+vr6CS3hCG0c4jnN5R10sd1ShUDgsOtS1a1fB+zE4ONjl8hKjoqJECyo7o9amo3E7UrkUnucxZcoUcxkKDw8P/Pjjjw6/ga5cuYL27dsjf/78KFu2LEqXLg21Wg2NRoPSpUvj9OnTVuesWLHCQm2XoiisXbvW4j1t2rSxGkRpmsaUKVMcej3O4siRI2jevDlCQ0PRq1evXDl4XLhwQVArqkyZMi43cOeEvXv3ii49NWjQQGrz8gSmqBTLslCr1WAYBt27d8d3331nId/CsiyaNm3qskuaJoR2S5vsd5TtMTExyJcvnzl1wCQA7Yoit99++63gBFyj0WDmzJlSm5dj3I5ULictLQ0PHjyQVKDu6dOnoqHkmJgY0dpM9+/fB2DMrxDb3VSoUCFnXoqbTNi6dSt8fHzMDnGNGjVyfS7Uu5w4cUJ0J17r1q2lNi/PkJCQgOXLl+Onn37C2bNnza8fOXIEvXv3Rvv27bFhwwaXd6IAYMGCBVZRTJqmMXLkSIf2+/DhQ0yYMAH16tVDWFiYy5YkmzZtmmC0kWEYm6QyXB23I+XGocyYMUPQSXpbaO/58+eCNxkhmevtuHE+er0ely5dyrP6UAaDAQEBAVY7YPOKMnVsbCxGjhyJKlWqoEuXLoiKipLapFwPz/P45ptvwDCMeZXgiy++cGkFdmfy77//ihZUzopuoKuSkSMlJ27c5JDU1FRiMBisXjcYDOTVq1eEEEI8PDxIaGio1XsUCgVp3ry5w210kzUUCgUpXbo0KVy4sNSmOAS5XE527dpF/P39iVarJTqdjlAURUaNGkU+/vhjqc3LETExMaRcuXJkzpw55NSpU2TdunWkTp06ZPv27VKblquRyWRk0qRJJD4+npw4cYI8ePCALFy4kCiVSqlNcwmCg4PJvHnzCEVRhOM4wnEcoWmahIeHE39/f6nNcygyo6OVe6hcuTJOnz4ttRmSkZaWRrZu3UquXLlCSpUqRVq1akXUarWkNp0/f55Ur16dpKSkWLxOURT5f3t3Ht5E2f0N/Nxpk0xmkhRaaqmWQlGqUkAQROCRRXFB4EFAUJRFQZBHQH8uFRFcUFZZBBHBBQqIslRQRBArQkEEAdmVfZFdoJWtdG/zff8ozduSSZukSSZtz+e6cl2QzHKS6cycudddu3bZE6g//viDHnjgAcrJyaGcnBwymUxksVho+/btFfaGXZFkZ2fTH3/8QbIsU6NGjUgIoXVIZZafn0/r1q2jixcvUsuWLal69epah1Rmffr0oQULFjg83Nx888106tQp0un4+Zn9fwBo586ddPbsWWrcuDFFRkaWaXspKSm0cuVK+0NyaGiolyLVlhBiO4Amqp9xIlV+nD9/npo1a0apqamUnp5OiqJQtWrVaPPmzW5l/IXH3Js3wvj4eJo5c6a9BEqSJHr11Vdp1KhRxZY7ffo0ffrpp7Rv3z5q0aIF9e/fn6pUqeK1OJhvLFmyhPr160dCCLLZbBQWFkYrV66kuLg4rUNjN4iMjKRz5845vG8ymejw4cN0yy23aBAVC0Tnzp2jRx55hI4ePUrBwcGUlZVFL7zwAn344YcV4kHJmziRqiC6d+9Oy5Yto7y8PPt7wcHB1KVLF0pMTCx1/fT0dHr11Vdp/vz5lJ2dTa1ataIZM2bQnXfe6ZX4Nm/eTIsWLSIhBPXs2ZOaNFH9m2PlzKFDh6hRo0aUkZFR7P2bbrqJTp8+TXq93qXtHD58mHbs2EExMTF0zz338IXaR+Li4mjfvn0O7xsMBkpJSSGr1apBVOXX5cuXKSEhgTZs2EB33HEHvfDCCxQdHa11WF7RsmVL2rx5c7F7iqIo9Omnn1KvXr00jCzwlJRIad543N1XZW5s7qzXm8FgcGn9Nm3aFBuBWwiBkJCQCtEQkPlOfHy86tQeVqsVq1atKnX93NxcdO/eHSaTyd4dvmHDhj6ZVqm8OX78OEaMGIFevXphzpw5Jc5h6arZs2c79C4zGo2aTCtS3p09exbVq1e3DwliMBigKEqFmBbpzJkzTqc+atKkidbhBRzixuZsz549tHXrVsrOzra/B4Cys7Pp888/1zAyFujOnTtX7Im1kM1mo9TU1FLXnzx5Mq1cuZIyMzMpLS2N0tPTae/evdS3b19fhFturFmzhuLi4mjixIn01Vdf0ZAhQ6hRo0Z09erVMm23b9++NGjQIJIkiUJCQkiSJGrVqhUlJCR4KfLKY8SIEZSammovjc3JyaH09HTq16+fxpGVXVpaGgUFBal+dvnyZT9HU75xIlWOPPbYYw49RIKDg6lz586lrnvgwAHVkyYrK4t27NjhtRhZxdO+fXtSFMXh/by8PGrVqlWp68+cOdOhWjA3N5d+/vlnunbtmtP1MjIyVBO4isBms1GvXr0oPT2dcnJyiKig6v3vv/+myZMnl2nbQgiaMGECnTlzhpYvX0779u2jn3/+mav0PPDDDz+o/g0eO3aM/v33Xw0i8p7bbruNTCaTw/sGg8Gle4o/HDlyhIYPH079+/enb7/9NmCvB5xIlSPTp0+nGjVqkMViIZ1ORxaLhWrUqEEff/xxqeveeeedqkMUSJJEjRs39kW4rILo1q0b1a1bl2RZtr+nKAoNGjTIpbYi6enpTj8rWkJa6LfffqO4uDiyWq1ksViof//+DomYN9lsNlqzZg19/vnntHXrVntnDF86dOgQpaWlObyfnZ1Nixcv9so+QkNDqVWrVhQTE+OV7ZVHOTk5dObMGdW/M1eoPUAUMhqNnoaluTlz5lCNGjXsJcqFPTlNJhNFRETQG2+8oWV4RES0dOlSatCgAU2aNIlmz55NzzzzDN1///32B4+A4qzOL1BflbmNFFAwyvmSJUswatQoLF261K156tq2bVusTlwIgSpVqmgy+aW/JSYmonbt2tDpdIiOjsa8efO0DqlcyczMxPTp0/Gf//wH7dq1w/fff+/ylDF9+/ZVbWN1xx13OCx74MABhylqJElC+/btvf2VAADnzp1DbGwszGYzZFmGoiho3bo1MjIyfLK/Qs5mAyAi3H333T7dd2Vgs9kwduxY+5yeiqLg7bffdnuao/HjxzsMMqnX69GxY0cfRe578+bNczoN1MSJE3H58mWv7SsnJwdr165FUlKSW+dUZmam6qTXiqLgiy++8Fp87iAe2ZwBQHp6Ol588UVYLBYEBwfj4YcfxsGDB7UOyy15eXmYP38+2rRpg9atW2POnDmljiy8dOlS1cmfExIS/BS1o7S0NFy9elWz/ftTYYPdwhuSwWCA2WxWbbD7/PPPq07SKkkSjh075vXY2rdv75DkSZKEYcOGeX1fN2rUqJHD3GSyLGPWrFk+33dFN336dNVz/oMPPnBrOzd2lJBlGXFxcTh9+rSPIve96Oho1QQ+KirKq/vZsGEDQkNDYbVaYbVaYTab8e2337q07rp16wJuLkxOpFiFYLPZ0K1bt2I9khRFQceOHUt80oyNjVU9ISMjI/0YfYETJ06gTZs20Ov10Ov1uPfee3HgwAG/x+Fvly5dwuTJk9GlSxcMGzYMJ06cUF2uRYsWqscqJCQEq1ev9mpMGRkZTqctioiI8Oq+1Bw7dgzR0dGwWCz2eQ379OmD/Px8n+870NlsNiQnJ2PSpElYsmQJsrOz3Vr/lltuUT2uoaGhHsVz6NAhPPfcc/YSLlmWER8fXy7mCLyR2sTChTUU3pqY/OrVq6olSiaTyem5X9TmzZtV1ycidOjQwSsxuosTKVYhbNmyxeEpszCZWr9+vdP1nN0siciv82Tl5OQgKiqqWImLEAJhYWGVpnSqNK+99prqMB+SJNknwPaWtLQ01SpHItfmfzx8+DDmzZuHn376yeO/o7y8PPz888+YN29euSsd9pX09HQ0b94cZrMZer0eFosFkZGRbpVIOjuuRORRorp48WLVEi5/lFx6W+3atVV/l1q1anltH/Pnz1edFNxgMGD06NGlrp+fn4+bb75Z9Vq/fPlyr8XpjpISKW5srpH8/HyaPXs2NW3alBo2bEiTJk1ymGKFFZecnKza0DAjI4OSk5OdrlezZk3V9yMjI/06T9aKFSvoypUrxRr9A6CsrCxatGiR3+IIZC+//DKZTKZig3XKskxPPfVUmaeuuJHZbKaGDRs6DAxaWk9YAPT8889T/fr1afDgwdS9e3eqWbMmHTlyxO0YgoKC6KGHHqI+ffpQbGys2+tXRGPHjqWdO3fStWvXKDc3l9LS0uj8+fPUu3dvl7fhbMT9iIgIevvtt2nRokVuNUB/7733HDo8ZGRk0Mcff0y5ubkubycQjB8/vljHEaKCc2zcuHFe28eVK1dUe9jl5OTQxYsXS11fp9PRypUrKTQ0lCwWCymKQpIk0YABA6hjx45ei9NrnGVYgfqqKCVSTzzxRLEqKpPJhKZNm/JM4iX44osvHAYaLPztpk+f7nS9xMRE1afJ2bNn+zF6YNKkSU5Lx4YOHerXWALZgQMH0KFDB5jNZtx8880YO3asz6pQ/vzzT1SpUsXefktRFNSoUaPEQWrnz5/v8HcohEDdunV9EmNlExUVpXqO6PV6XLp0yaVt/PLLL6ql14UN/M1mM2rVquVyRxtn7XUMBgNSU1PL8nU1sXTpUtSpUwd6vR633XYbEhMTvbr9/fv3OzTSL/z9a9eujaCgINx0002YOHFiidWJWVlZWLZsGRISEnzSRtIdxFV7gWXXrl2qJ7nZbMZ3332ndXgB6/Lly057cpR2MVu0aBFq1aoFIQSioqI0aWi+du1a1eJus9ns9QsZc11qaiomT56MAQMGYNasWUhPTy9x+ebNm6veVE0mEw4dOuSnqCuuyMhIp0nLv//+6/J2NmzYgDZt2iA8PBxVq1Z1aBsUHByMp59+2qVttWnTRjWmiIgIbtPmxJAhQ4o9cEiSpNq5YsSIEVqH6hJOpALM9OnTnXZ9fumll7QOL6Bt3LgRN910EywWCywWC8LCwrBu3TqX1/dWY0pP2Gw2NG3atNg0PQaDAbGxsW4NY8G01aBBA9Vz12w2Y9euXQ7L22w2zJgxA7fddhuqVq2KLl26eNwe6sCBA3jwwQcRHBwMRVHwwgsv4Nq1a2X9SgHllVdeKXaOFJb4eTosRH5+vmpP0MIbuZrMzEwkJiZi6tSp2LJlC37//XfVUu0vv/yyLF+1QrPZbFi5ciW6du2KDh064K677nJ6DEp7eAkEnEgFmCVLlqiWrEiShPHjx2sdXkArbJw7evRoLF++vNxVhV67dg3x8fGIiIhAeHg4Bg8ejIsXL2odFnPDuHHjVKstqlWrploF+dprrxW7Cet0OoSEhLjUe6moCxcuoEqVKhBC2LdlNBrRpk0bt7Zz+fJlLF68GImJibhy5Ypb6/rD5cuXUbduXXvpraIoqFq1Kvbu3evR9vLz8502PjebzQ7L79+/H+Hh4bBYLDAajVAUBR06dMCmTZvw4IMPolq1amjcuDF++OGHsn7VSsVZT0qz2YzDhw9rHV6pOJEKMFlZWahWrVqxC2LhBeOff/7ROryAdfDgQURFRdlLoyRJQnx8vKalTKzySUtLQ/369e3VFgaDAbIsq07g/O+//6qWPuv1egwZMsSt/Y4ePVp1W7Isq5aEqfnmm28gy7L9HJJlGUuWLHErjuzsbOzdu9enA/nm5ORg6dKlGDZsGD777LMyJ3ydO3d2SKYMBgP69u3rsGxcXJzDtVmWZUybNq1MMVR2Dz/8MJdIBcqrIiRSQEEj11tuuQV6vR4GgwE33XSTW1VUlY3NZkOdOnVUk89ly5ZpHZ6D48ePY/To0Xj99deRnJwcEMleZmYmjh075vNRuyuDrKwsfPnll+jduzfefPNNpw1hN27ciJCQENUbSKNGjdzaZ9euXVW3Y7FYsHDhwlLXP3PmjGpJmslkcnloiS+++MI+uKLRaESHDh28OhK2r/zzzz+IiYmxD0ZssVhQt25dh9Lgv//+W/U3IiLUq1dPo+grBmfVo2+88YbWobmEE6kAk5ubiw4dOkBRFAghIEkSzGZziWMhlUVmZiaOHz+OrKwsn2zfH/bs2aPaY4+I8NBDD2kdXjGJiYkwmUwwGAwQQkBRFDz++OOaNUq12Wx47733oCgKFEWxX7xKiyc9PR0vvfQSrFar/aZ55MgRP0VdMZw6dUq1FEmn0+HJJ590a1ujRo0qU4nU1KlTVdc3mUwulbasWbPG4UZoNBrRrl07t76HVnJzc7Fs2TJ88MEH+PHHH1WrYQ8fPqzaEYhIfUoj5p5ffvnFXuIXFhaG8ePHl5vG+pxIBZiEhATVpCA8PNyr3bzz8/MxYsQIyLJsn0ds5MiRAVE64q5NmzY57YLcqFGjgPlO165dUz22iqK4PD2Ct02bNk31SbC0gfHuv//+YjdenU6HsLCwctndW0v//e9/HRIYWZaxfft2t7Zz/vx51TZSrVu3dmn9sWPHqja6Dg4Oxrhx40pd/5FHHlE9/yRJwpkzZ9z6LoHEZrPh999/xzfffINjx46hVq1aqsnmmDFjtA61wgiU67U7OJEKMC1btnRaRL9lyxYAwJUrV7B58+Yyzek0fvx41Rvo1KlT7cscP34cK1asCPhpSrKyspwmUsHBwahduzY2bNigdZhYsWKF0zi7du2qSUxqIwQTlTx6986dO1WfzE0mk9vzlVV0+fn5WLVqFSZOnIhly5Y5dIBIT0/HM888A6PRCIPBgJo1a6q2p3LFgQMH0LZtWwQFBUFRFPzvf/9zudferl27nFbt7dmzp9T169atq/p3ZLVa3U4KA8U///yDuLg4mM1mWK1WSJKEjh072qeCISpoDN2kSZNy0Y6H+Q4nUgGmVatWqhcks9mMrVu3YuTIkTCZTPYTu0OHDkhLS3N7P2FhYar7qVKlCtLT0/Hkk09CkiSEhITAZDKhbdu2Hu3HXwqrzJzNFaUoits9obwtKSnJaSLVo0cPTWIqaYocZyWgX3/9tdO5rrp37+7nbxC4Ll26hPr16xebziQmJka100hmZiZSUlI0fRovHNtHCGGvdv6///s/l9dV+1tSFKXcJhmtW7d2aIQuyzImTZqEqVOnIj4+XjU5ZpUPJ1IBZt68earVP9WrV8f8+fNV2yF069bNrX3YbDanN8/Cp8gbqxuMRiOeffZZH31r79i7dy+6deum2p3ZYDBg+PDhmsaXlZWl2rhYURQkJSVpEpOz8VtiY2OdrrNt2zbVv1FJklyaK6uyeP755x3mBgwODsZ///tfrUNTZbPZsG7dOgwYMAADBgzA+vXrXU7sTp8+jdDQ0GLnnizLmDJlio+j9o3z5887jFdV+OKG5exGnEgFmLy8PHTt2hWyLNsH1rNYLNi0aZPTm57RaHS7d8ztt99eYjLlbD+B/vS1YMGCgC4tSU5OhtlshtlshiRJMJlMePnllzUpidi9e7fTMct+/PFHp+vZbDY0b9682I1GCIGQkBCfdnsvb0qqbvbleXT8+HF88MEHGDlypF+r1U6ePImBAwfi1ltvRcuWLcv1WErHjh1z2kMvOjpa6/BYgOFEKgAVNnAcP348Zs2aZU+SnLVnCQoKwu7du93ax6pVq5z2QHH2CgoKCvju8YcOHVK9AMqyXOKce/505coVzJs3Dx9//LHHo1iXlc1mQ0xMjMPvpNPpXOpyfPXqVfTt2xdGoxE6nQ6tW7fGvn37/BB5+aE25U/heeSr0ernzZsHSZJgMBig0+kgyzKGDBlSLhvwaslms6nO62cwGFyu7mTqVq9ejRYtWiAiIgIPP/wwtm7dqnVIZcaJVDnSs2dPp22AGjZs6PbF8tdff3U6qq+zfZQHTz31VLEkUa/Xo0aNGrh69WqJ62VmZpa6TEWxd+9ep0NGNGvWzOXt2Gw2r3RRvnz5Mvbu3Vtu29Oo6d27t0O7oaCgIJ8NyZGamqo6hIGiKPj11199sk932Wy2cpPUFU5uXHgMZVlGdHQ0UlJSVJe32WxYv349hg8fjg8++ACnTp3yS5w2mw2rV6/Giy++iOHDhwd056DCQUjFkHcAACAASURBVF9vfMjdtGmT1qGVCSdS5UhJxc2ejjU1cOBAh3YcQggEBQUVuwkEBwdj8ODBePrppzFq1CiPRlnPzMzErFmz0K5dO3Tr1g2//fab29twRV5eHqZMmYI6derg5ptvxpAhQ3DhwgWny6empqJLly4wGAwIDg5Gw4YNsWPHDp/EFih27drltMTE03nLPJGTk4P+/ftDkiT7aNrvvPNOubnZluTChQuIiYmx/85msxkRERH4+++/fbK/r776SvWYCiEwaNAgn+yzqL/++gsvvvgiunbtioSEBGRmZto/O3XqFDp27Ijg4GAYDAY88cQTThOSovLz87FhwwYsX77crUmJveXw4cN45ZVX0KlTJ3z00UdOR1HPz89Ht27d7A8nRqMRJpMJ33//vU/jy8/PR/fu3e37DQ4OhiRJ6NevH1566SV8+umnAfNw6KyUj4jQokULrcMrE06k/CglJQUjRozA3XffjY4dO3o0WnmPHj1U/xBlWcZnn33m9vb+/fdf1KlTp9jcVdWqVcPrr7/utLSq8KbnTvuLjIwMNGjQwGGbXbp0sZdqaHHztNlsaNiwoUMyabFYXB7RuTzKz89HRESE6t/RRx995Lc4Xn31VYeHA1mW8emnn/otBl/KysrCwoULMWzYMMyZM8enJW4TJkxQLbHW6XTFppzJycnB2rVrsXr16mLJTlkkJiZClmX7WFSKoqBBgwa4du0a0tPTERkZWWycKr1ej9jY2BLHxjtw4ABq1KgBi8Vi7wAzYcIEh+Xy8vKwYcMGJCUlaTZJ85IlS1RLeM1ms1eaQ6Snp+Ps2bMOpb/Lly93WrJceBzCw8MDYrDctLQ0p/cUZxNElxecSPlJSkoKIiMjizXQ9eSGMX36dKcnrKfF9zk5OUhMTMSwYcMwe/ZsXLhwwWlpRdFX/fr1Xd7Hxx9/7PQkio2NhU6ng8FgQM+ePXHp0iWPvocnNm3a5LQH2nvvvee3OLSwbt06KIpirw4ym81o0aKF30a5z83NddpOLyYmxi8xVBRpaWmoUqWK05vU5s2bARQc86pVq8JqtcJqtcJisZS5UXhWVpZqpwWTyYTJkydj7ty5qtcTi8WClStXqm4zPz8fNWvWVJ3XrugD6I4dO1C9enVYLBYoigKj0Yh3333X7w9ljz32mOpvb7Va8dNPP3m83YyMDDz77LMwGo2QJAkRERFITEy0f96rV69Sr9M6nQ5t27b1xtcsk7y8PKcdgW699VatwysTTqT85I033nAo9fDkieXKlSsIDw8v9uRpMBjQuHFjr108tm3b5rTHUdGXXq93OelxNj7WjS+DweDX0cidVYcQkdvTdJRH586dw6RJk/Dqq6/ihx9+8Oro+aUp6QnVbDb7LY6KYPbs2U5LJjp16gSgoB2a2t+6yWQq0+jjJc0s0LRpU7z++utOz/VJkyapbnPz5s1Oz8vC3rfZ2dkIDQ11+nDmStWht3Tr1s1pIrV69WqPt1s4nt+NyWThQ/Nzzz3nkGyqvYKCggKix3XhbBo3fp85c+ZoHVqZlJRI6Yh5zapVqygnJ8fhfZ1OR3/99ZfL27FarbR161Zq37496fV6kmWZevfuTWvXriUhhFdiDQ8PV41VjV6vd2k5q9Xq0nI5OTl0+PBh2rRpk0vLl9Vdd91F+fn5Du/LskwtWrTwSwxaioiIoNdee40mT55MHTt2pKCgIL/tW1EUioqKUv3snnvu8VscFcHJkycpPT3d4X2dTkfNmjUjIqJvv/224An5BjabjRYsWODxvs1ms+o5REQUEhJC9evXJ7PZ7PCZwWCguLg41fWuXr1KOp36LejixYtERJSUlES5ubmqyxw5coQ6d+5MDzzwAIWEhNCdd95JCxcudOXreOTZZ58lRVEc3hdCUKtWrTzaZmpqKn3//feUlZVV7P2MjAwaM2YMERH17duXTCZTqdsSQjj9Pf3pvffeo0GDBpEsyyTLMlksFnr//ffpmWee0To033GWYQXqK5BLpB566CHVJwVJknzW+LQsWrVqVeKo18HBwWjfvr3L21u9erVLT05EBfX6s2fP9uG3K65Dhw7F2ukEBQUhIiKiXMxc7y8pKSn49ttvsXbtWq+WWv3www/FfnudTgdFUcrttCJaWbFihWoJjtlstpeIfPjhh04HmXzzzTc93rfNZkNsbKzD+a0oCpYtW4aMjAxERUU5tJG68847nfb4vHr1qtNhTGbOnAkA+PLLL11qglB03aJTYHmTzWbD//73P5hMJhiNRvsk4GvXrvV4m87GeSMi1KlTx77cyJEjIUlSsR6GRV96vR6PP/64N76m12RkZODEiRPIzs7WOhSvIK7a84+kpCSHIk29Xh+wvRVSUlJw3333wWQywWKxQKfTQa/X2weTrFu3bok94dQ8/fTTLidShW06/CErKwvvvPMOIiMjUaVKFfTs2bNM8xhWNOPGjYPRaLS3qYmMjMRff/3lte1v3LgR7dq1Q0xMDLp37+7VbVcWeXl5uPvuu4tVA0mShGbNmtmryffs2aPaJk1RFI96/BZ16NAhe8Nwi8UCSZIwdOhQ+77PnDmDxx9/3N6brXfv3qX2wps5cyZkWbY3Y5BlGQ0bNrQ3hTh58qTqcA8lvaxWq8/G8AIKei5OmTIFCQkJZX4Qu3btmurxCgoKcphl4sSJE/j8888xa9YsNGzY0D7gr8ViQWxsrNvXauYeTqT8aMqUKZBlGVarFSaTCc2aNQv4kaCPHTuGzZs349q1a9i9ezfmzZuHX3/91eM2TMuWLUODBg1QvXp1dOrUCaGhocXaexmNRrRo0aJCdH+vCNatW6d6MY+KivLK+FHMe65du4YRI0agZs2aqFmzJt555x2HXoIDBgwo1pZKURR07drVK+dbXl4e1q5di8TERK89iGzZsgXPPPMM2rdvj1mzZjn0Mhw+fLhbY+HJsoyTJ096JTZ/GDNmTLHzTwgBi8WCw4cPO13HZrMhOTkZ06ZNw08//eTz8/TChQsYPXo0unbtilGjRgX8Pc0XOJHys2vXrmHjxo0B0R01EBw/fhydO3eGJEmwWq0YMmRIQE+OXNk88cQTqjekwmmLWPlis9nw/fff47HHHkPHjh2xePHicp8QL1y4EJIk2R/ICkfbV/u7NZlMAT87Q1E2mw1ff/016tWrh/DwcHTp0gX79+/XOiy7gwcPomrVqvaSQUmSUKVKlYCK0R9KSqREweflR5MmTbBt2zatw2Cswnj44Ydp9erVDu9brVZKTEykRx55RIOoyi4rK4v0er1fG9cz37ly5QrNnTuXNm7cSHfccQfFxsbSwIEDKSMjw76MLMs0YMAAmjp1qoaRViwPP/ww/fLLL1Q0VxBC0P33309r1qzRMDL/EkJsB9BE7TPtm/gzVoqMjAxavnw5ffvtt3T16lWtw6kQ8vLy6N1336XQ0FD65ZdfVHv75ObmlstejZs3b6a77rqLzGYzKYpC/fv3L3az9YfU1FTatWsXpaWl0alTp+iVV16hFi1a0IABA+jAgQN+jaWiCAkJoTZt2pDZbKbffvuNTp06RR999BFFRkaSwWAgWZZp0KBBNGnSJK1DLZPDhw9TfHw8Pfnkk5SQkODQo8/fkpOT6cYCFwC0fv16h/crLWdFVYH6Kg9Ve8x7kpKSYDab7Y2gTSYTvv76a63DKvf69+/vdKDMwolwPRlFX2tHjhxxGGtJkiS0a9fOL/vPyspCz5497dXYRqMRRqPR3tMqKCgIsixjw4YNfomnIlm6dGmxhumSJOGWW27B+fPncfHiRZ82MPeXFStWFOuZpygK6tatq+kUMM7GLivvI5W7i7iNFCuPLl26pHqzNxqNaNu2LWJjY9GzZ89KV1dfVikpKao9oYQQiIqKQv/+/bFt2zatw/TI4MGDVRsmm0ymEhvvessLL7zgdK7Moq+4uDifx1KR5ObmIiwszOF3NBgMeO2117QOzyucfUdJkjB69GjN4ho0aJDD9cJoNGLgwIGaxaSFkhIprtpjAeu7775THYA0Ozub1qxZQ4cOHaJFixbRPffcQ7t377Z/fvz4cRo0aBA1bNiQnnjiCdq+fbs/ww54R48eJaPR6PA+AKpatSp98cUX1LhxY6frnz9/nhISEmju3LmUmprqy1Dd9ueff1JeXp7D+waDgY4cOeLTfefk5NCcOXMoMzOz1GX3799P9957L5lMJoqOjqYZM2ZU+GqS9PR0mjZtGj3wwAPUo0cP2rhxo8vrHj58WLWKKycnh77//ntvhumygwcP0owZM2jhwoWqA6W666+//lIdJDkrK4sSExPLvH1PTZw4kZo3b24fXFOWZbr33ntp8uTJmsUUcJxlWIH64hKpymPatGkujyHz4IMPAiiYBNVqtdpLJYQQkGXZ6XxfldGFCxdUf9egoCD06tWrxHW/+OIL+zhBhXP4BVJV69ChQ1WnaZIkyedd4i9dulTiALclvRRFwciRI30an5bS0tJwxx132EuYC8/LTz75xKX1z5w54/Ra0LRpU4/junz5Mj777DO89dZbLk+fZLPZMHjwYJhMJvsYfFartcw9XA8dOuS0uv0///lPmbbtDbt27cLChQuxc+dOrUPRBHHVHiuPDh065HIiVThvW+fOnVVHV4+OjuZxq4ro16+fQxWULMslDpS5fv161d/WZDLhn3/+8WP0zp0+fRohISHF4jSZTKUmiN5gs9kQHR1d6t+qs277siyXq2777pg8ebJqlafJZHLa/sdms2H69OmoXr06hBCQJKnYyOmFCejChQs9imn37t2oUqWKvQ2Q2WxGkyZNcO3atRLXW758uWq7Ib1ej7Fjx+LKlSsexQMA9erVc/j7UBQFCxYs8HibzDs4kWLl1uuvv+60sWPRV0xMDACgatWqqp/r9Xrs27fPb3EnJSWhRYsWiIiIwKOPPhpwbY5yc3MxYsQIhISEQKfToXHjxiU+Uefl5SEkJET1t5UkCdOnT/dj9CU7cOAAOnToAFmWERERgffff99vk7kWNhYuTOR0Oh2Cg4NhMBgQEhICSZKcPhyYzWYcPHjQp/HZbDbMnTsXjRo1wq233orXXnsNqampPt0nALRs2VL1O1utVqxZs0Z1nUmTJjmU0AghYDQa7b9l0ZHV3XXnnXeq/i2XVjL42GOPOb0O6fV61KpVCxcvXvQopqNHjyI6OrrY6PGDBg0K6IfAo0ePYurUqZgxYwbOnTundTg+w4lUgMvPz8fKlSvRt29fDB48OOBuulpbvXp1iSMby7KMGTNmAABuu+02p8sZDAZ0797d50/9CxcuVJ39fMuWLT7dr6dcuUj/9NNPqlVmRAVVgpMnT/ZDpOXD5s2b0alTJ9xxxx3o06cPDh48iLNnz2LNmjX4+++/S5yT09cD1Q4aNKjY36bBYEB0dHSZSlFc0bVrV9XvrCgKduzYgcWLF6Nhw4aoXr06unXrhr179zpN3OvWrYtVq1aVaUqUU6dOOU1oa9euXeK67dq1K7XE8e233/Y4tvz8fKxZswYLFiwIyDlaixozZgwkSbJX95tMpgpbesaJVACz2Wzo2rWrfWLOwq7nEydO1Dq0gHHq1KkS254MHz7cngwUzt3lbFlJkvDMM8/4LFabzYbIyEjVfbdu3drpevn5+UhKSsKoUaMwZ84ce/VCcnIy7rrrLuh0OlSrVg3jxo3zeJTq3NxcbNq0Cb///rvbkxInJCQ4vfEEBQXh0KFDHsVUGW3YsEG1WvXFF1/06X6dJQ8mkwlTpkzx6b6Tk5MdzkudTofY2FhMmDCh2Gc6nQ5ms9npOW+1Wsscz5kzZ5xO7nzbbbeVuO78+fNLLSWPjo4uc4yBbvfu3arVtZIkISUlRevwvI4TqQC2atUq1dnNJUkKmHYnWtu+fbvTC1ajRo2KLWuz2fD6668Xm05C7be9cX4ybympwbGzG0BGRgaaN28Os9kMIQTMZjNCQ0OxaNEi1ZKt+Ph4t+NKTk5GWFiYfTyu8PBwt8Yy2rdvn9Nu/Z07d3Y7nm3btuHRRx9FREQEmjdvjqSkJLe3UZ6tXLkStWvXticNw4cPdzu5ddd3330Hq9Wqegw7dOjg030DwIcffghJkhASEgKz2Yw6depg3759qte/oKAgp+dRkyZNnO7DZrO5/DveddddDm3+TCYTxowZU+J6ubm5ePTRR0tsvxkSEuLWb1MeDRs2zKHNGlFBKePs2bO1Ds/rOJEKYAMGDFA9Ec1mM+bNm6d1eAHhvffeU23kTEQYMmSI6joXL15ElSpVnCZSZ8+e9Umsubm5Tp9Wb7/9dtV13n//fYckpXDiUmeNu0urAtq6dSumT5+OZcuW4ezZs6o3K7PZjEuXLrn83Xr06OFQclCrVi1kZWW59Rtt2bJFNUH0tNFweZaVleW39i9btmxR/dsMDg52eh552+XLl5GUlIRt27bBZrPhzz//hMViUT1fwsLCVP9Ofv75Z4ftZmRk2MfwEkKgadOm2L59O4CC5Gr9+vUYOHAgBg4ciPXr18Nms2H//v0IDw+HxWJBcHAwFEVBq1atXPp7zs/Px4wZM5wmUrVq1fL6bxdo4uPjVa9PiqLg888/1zo8r+NEKoC98sorqlm9xWLBN998o1lcKSkpuHz5smb7L2rUqFGqv5Fery+xkXPXrl1VT/Tq1av7dBLXoUOHqt4A5s+fjwsXLmDUqFF49NFHER8fj+PHj5fYrkvtZbFYnA5Cmp2djXbt2kGWZUiSZO+arfb07O4FLy8vDzNnzkSDBg1Qp04dvPXWWx61rWndurXq94qMjAzoRrVauXr1Ks6fP1/m38ZmsyEuLs6hvaEsy5oNapuamuq0ZKdt27aYMWMGIiMjodPpcPvtt2PFihWq21ErITKbzTh+/DhefvlleweAwmEXXn75ZQAFCdiCBQvwwQcfYN26dW79xnl5eQgNDVVNTMeNG+eV3yeQbd26VbUZRUWtTdEskSKidkR0kIiOENEwlc+NRLT4+udbiKhWadusaInUrl27VP8YzWazz6qfSrJjxw7Uq1cPBoMBBoMB999/P06fPu33OIrav3+/07r4M2fOOF3vwIEDsFgsxZIwWZZ9nqDm5ubilVdegclkgizLsFqt+PDDD3Hs2DGEhYXZL/gGgwFmsxlRUVGqNxKdTud2idTEiRNVS7fUtq/VBd9ZCYTBYHCrhKyiu3jxIjp16gSDwQCj0YjatWsjOTm5TNs8e/Ys7rvvPkiSBEVREBERofkYa08++aRDEiTLMtauXevS+s6GSdHr9ejdu7fTYRf27NlT5thXrVoFWZbtyaksy6hfv77POw0Eivj4eJhMJntVrCRJmDlzptZh+YQmiRQRBRHRUSKqTUQGItpNRHVvWGYQEX16/d89iGhxadutaIkUAHz88cf20oPCV1kvmJ64cOGCw00uKCgIMTExPm+/UZpJkybZu44XvmbNmlXqekeOHEG/fv1w++23o3379vjtt9/8EG2BjIwMnDx50j4H2OOPP67abisiIkI1+aldu7ZqyVZJU2LExsa6XLKlKIomPQlvv/12p/H4a5iC8qBZs2YOPSVlWfZKw/6zZ8/i4MGDPi2ZdVVGRgb69OkDo9EIWZZRrVo1fPXVVy6vv3LlSqdtv2rXrq3a49ebDxFHjx7FsGHD0LNnT8ybN8/tqu7ybufOnXj33XcxZswYv0zDpBWtEqnmRJRU5P9vEtGbNyyTRETNr/87mIhSiUiUtN2KmEgBBUnMggUL8N1332k2KN+ECRNUn94sFktANAY+duwYpkyZgmnTpmleSuYJZyUxwcHBuOeee4o1Nq9atSr++usvJCcno0GDBvZee2PHji3x5hcTE+O0dKvosVUUBd27d9ekKm3+/PmqCeLQoUP9Hkug2rNnj2pJtT/bM/lbWloaTpw44fZD27Fjx1RLpAwGA9q2bav6mSRJmDp1qo++CauISkqkgsl3biGiU0X+f5qI7nW2DIA8IcQVIgqjgoSqUgkPD6ennnpK0xgOHz6sOk9Yfn4+nThxQoOIiouJiaGXX35Z6zA8pigKpaWlObyv0+no119/pQ0bNtCWLVsoKiqKunfvToqiEBEVm0ewNE899RR9+OGHDvOS3XrrrfTWW2/R3LlzSQhBzz33HPXo0UN1LkNf69WrF6WmptK7775LeXl5BIAGDhxIY8eO9Xssger48eMUHOx4ec7Ly6ODBw9qEJHvmc1mMpvNbq8XExNDHTp0oB9//NF+/RJCkCRJNGHCBLrvvvsc1hFC0BNPPFHmmBkjIp+WSHUnollF/t+biD6+YZm9RBRV5P9HiShMZVvPE9E2ItpWGcbn0EpCQoJqrx5ZlnmQUC8YOXKkQ4mfwWDA008/7bV9XL16FfXq1bP30iucC+yPP/7w2j68JScnBydPnqyw06KUxcmTJ52WpIwePVrr8AJOdnY23nzzTYSGhsJgMOChhx6yz2SQmJhoPw8sFgtMJhMSExM1jpiVN1RCiZQo+Nz7hBDNiWgkgEeu///N64nbuCLLJF1f5nchRDARnSOicJQQVJMmTbBt2zafxFzZZWZmUlxcHJ05c8Y+C7nJZKKWLVtSUlKSxtGVf7m5ufT000/TihUryGAwUF5eHt199920cuVKslqtXt3Pd999Rxs3bqRatWpR7969qVq1al7bPvOPfv360eLFiykjI4OIiIKDg6lq1aq0f/9+CgsL0zi68uXKlSv0008/ERFRu3btKCQkROOIWHkjhNgOoInqZz5MpIKJ6BARtSWiM0T0BxE9DWBvkWUGE1F9AP8TQvQgoq4ASixv5UTKt/7991969913acmSJWQ0Gql///40dOhQMhqNWodWYRw9epT+/PNPuvXWW6l+/fpah8MCVH5+Pn3yySc0bdo0SktLo/bt29OoUaMoKipK69AYq3Q0SaSu77g9EU2lgh58CQDGCCHep4IisuVCCImI5hNRIyK6SEQ9ABwraZucSDHGGGPMn0pKpHzZ2JwA/EhEP97w3jtF/p1FBW2pGGOMMcbKHZ3WATDGGGOMlVecSDHGGGOMeYgTKcYYY4wxD3EixRhjjDHmIU6kGGOMMcY8xIkUY4wxxpiHOJFijDHGGPMQJ1KMMcYYYx7iRIoxxhhjzEOcSDHGGGOMeYgTKcYYY4wxD3EixRhjjDHmIU6kGGOMMcY8xIkUY4wxxpiHOJFijDHGGPMQJ1KMMcYYYx7iRIoxxhhjzEOcSDHGGGOMeYgTKcYYY4wxD3EixRhjjDHmIU6kGGOMMcY8xIkUY4wxxpiHBACtY3CLECKFiE74aXfViCjVT/tizvFxCAx8HAIDHwft8TEIDP48DjUBhKt9UO4SKX8SQmwD0ETrOCo7Pg6BgY9DYODjoD0+BoEhUI4DV+0xxhhjjHmIEynGGGOMMQ9xIlWyz7UOgBERH4dAwcchMPBx0B4fg8AQEMeB20gxxhhjjHmIS6QYY4wxxjzEiRQRCSHaCSEOCiGOCCGGqXxuFEIsvv75FiFELf9HWfG5cBxeFULsE0LsEUKsEULU1CLOiq6041BkuW5CCAghNO81U9G4cgyEEE9cPx/2CiEW+DvGysCFa1K0ECJZCLHz+nWpvRZxVnRCiAQhxAUhxF9OPhdCiGnXj9MeIcTd/oyv0idSQoggIvqEiB4lorpE9JQQou4Niz1HRJcA3EZEU4joA/9GWfG5eBx2ElETAA2IaAkRTfBvlBWfi8eBhBAWInqJiLb4N8KKz5VjIISoQ0RvEtF/AMQR0ct+D7SCc/FceIuIEgE0IqIeRDTDv1FWGnOJqF0Jnz9KRHWuv54nopl+iMmu0idSRNSUiI4AOAYgh4gWEdFjNyzzGBHNu/7vJUTUVggh/BhjZVDqcQCQDCDj+n83E1GUn2OsDFw5H4iIRlFBIpvlz+AqCVeOwQAi+gTAJSIiABf8HGNl4MpxABFZr/87hIjO+jG+SgPAr0R0sYRFHiOiL1FgMxFVEUJE+ic6TqSIiG4holNF/n/6+nuqywDII6IrRBTml+gqD1eOQ1HPEdEqn0ZUOZV6HIQQjYioBoAV/gysEnHlXIglolghxEYhxGYhRElP68wzrhyHkUTUSwhxmoh+JKIX/RMau4G79w+vCvbXjgKYWsnSjV0ZXVmGlY3Lv7EQohcRNSGi1j6NqHIq8TgIIXRUUL39rL8CqoRcOReCqaAaow0VlMxuEELUA3DZx7FVJq4ch6eIaC6AyUKI5kQ0//pxsPk+PFaEpvdoLpEqyFxrFPl/FDkWz9qXEUIEU0ERbknFjMx9rhwHEkI8SEQjiKgTgGw/xVaZlHYcLERUj4jWCSGOE1EzIlrODc69ytVr0vcAcgH8TUQHqSCxYt7jynF4jogSiYgA/E5EEhXM/8b8y6X7h69wIkX0BxHVEULECCEMVNBgcPkNyywnomeu/7sbEa0FD8DlbaUeh+tVSp9RQRLFbUJ8o8TjAOAKgGoAagGoRQVt1ToB2KZNuBWSK9ekZUR0PxGREKIaFVT1HfNrlBWfK8fhJBG1JSISQtxJBYlUil+jZEQFx6XP9d57zYjoCoB//LXzSl+1ByBPCDGEiJKIKIiIEgDsFUK8T0TbACwnotlUUGR7hApKonpoF3HF5OJxmEhEZiL65npb/5MAOmkWdAXk4nFgPuTiMUgiooeFEPuIKJ+IXgfwr3ZRVzwuHofXiOgLIcQrVFCV9Cw/ZHufEGIhFVRjV7veHu1dItITEQH4lArap7UnoiNElEFEff0aHx9zxhhjjDHPcNUeY4wxxpiHOJFijDHGGPMQJ1KMMcYYYx7iRIoxxhhjzEOcSDHGGGOMeYgTKcYYY4wxD3EixRhjjDHmIU6kGGMVmhDiHiHEHiGEJIRQhBB7hRD1tI6LMVYx8ICcjLEKTwgxmgqm7zAR0WkA4zQOiTFWQXAixRir8K7PlfYHEWURUQsA+RqHxBirILhqjzFWGYRSYky6cAAAAJlJREFUwTyNFioomWKMMa/gEinGWIUnhFhORIuIKIaIIgEM0TgkxlgFEax1AIwx5ktCiD5ElAdggRAiiIg2CSEeALBW69gYY+Ufl0gxxhhjjHmI20gxxhhjjHmIEynGGGOMMQ9xIsUYY4wx5iFOpBhjjDHGPMSJFGOMMcaYhziRYowxxhjzECdSjDHGGGMe4kSKMcYYY8xD/w8OP8WaAdufTwAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(10,10))\n", "ax.set_aspect('equal')\n", "ellipse1 = patches.Ellipse(ellipse_center, ellipse_width, ellipse_height, angle=rotation_angle, fill=False, \n", " edgecolor='red', linewidth=2)\n", "ax.add_patch(ellipse1)\n", "ax.scatter(x, y, c=colors_points)\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Finding the intersections of two arbitrarily rotated ellipses" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def ellipse_polyline(ellipses, n=1000):\n", " '''\n", " INPUT:\n", " ellipse parameters in the form:\n", " (center_x, center_y, semimajor_axis, semiminor_axis, rotation_angle(in degrees))\n", " '''\n", " t = np.linspace(0, 2*np.pi, n, endpoint=False)\n", " sin_t = np.sin(t)\n", " cos_t = np.cos(t)\n", " result = []\n", " for x0, y0, a, b, angle in ellipses:\n", " angle = np.deg2rad(angle)\n", " sin_a = np.sin(angle)\n", " cos_a = np.cos(angle)\n", " p = np.empty((n, 2))\n", " p[:, 0] = x0 + a*cos_a*cos_t - b*sin_a*sin_t\n", " p[:, 1] = y0 + a*sin_a*cos_t + b*cos_a*sin_t\n", " result.append(p)\n", " return result\n", "\n", "def num_intersections(a, b):\n", " ea = LinearRing(a)\n", " eb = LinearRing(b)\n", " mp = ea.intersection(eb)\n", " return len(mp)\n", "\n", "\n", "def intersections(a, b):\n", " ea = LinearRing(a)\n", " eb = LinearRing(b)\n", " mp = ea.intersection(eb)\n", " #print(mp)\n", " x = [p.x for p in mp]\n", " y = [p.y for p in mp]\n", " return x, y" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of intersections: 2\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ellipses = [(0, 0, 2, 1, 0), (2, 0.5, 5, 2, -30)]\n", "a, b = ellipse_polyline(ellipses)\n", "print('number of intersections: ', num_intersections(a, b))\n", "\n", "x, y = intersections(a, b)\n", "\n", "fig, ax = plt.subplots(figsize=(10,10))\n", "ax.plot(x, y, \"o\")\n", "ax.plot(a[:,0], a[:,1])\n", "ax.plot(b[:,0], b[:,1])\n", "ax.set_aspect('equal')\n", "ax.grid(':')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of intersections: 4\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ellipses = [(0, 0, 4, 1, 30), (2, 0.5, 5, 2, -30)]\n", "a, b = ellipse_polyline(ellipses)\n", "print('number of intersections: ', num_intersections(a, b))\n", "\n", "x, y = intersections(a, b)\n", "\n", "fig, ax = plt.subplots(figsize=(10,10))\n", "ax.plot(x, y, \"o\")\n", "ax.plot(a[:,0], a[:,1])\n", "ax.plot(b[:,0], b[:,1])\n", "ax.set_aspect('equal')\n", "ax.grid(':')" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of intersections: 0\n" ] }, { "data": { "image/png": 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+v/o7cUlxvFb7NRxsHFTHEaJYcLZzpkvlLnSp3IVDyYdYcGwBK06vYOHxhYT7hPNslWdpFdwKext71VGFECLfisVtawuOLsDRxpEulbuojiJEsVTNpxrvN3qf9U+vZ0S9EdzKusVbW98i6ucovtr7FVfSr6iOKIQQ+WL1RSo1K5UVp1fIWjdCWAA3eze6hXZjScclTGkxhTCfMKbsm0LUz1EM3TyUvZf3Yu4bYIQQoiBZ/V57a8+u5XbObTpX6qw6ihDiDpNmopF/Ixr5NyLhZgLzjs5j8fHFrDy9kmre1egW2o3Wwa3lsp8QwuJZ/YjUmrNr8Hf157GSj6mOIoS4h0D3QIbWHcr6p9czqv4obufcZuTWkbT8uSWT9kzicvpl1RGFEOK+rLpI3ci8QVxSHFFlo2S1ZSEsnLOdM89UeYb/dPgPU1tOpbpPdabtn0arha14a8tbHL12VHVEIYT4H1Z9aS8uKY6cvBwigyJVRxFCPCBN02hYpiENyzQk4VYCcw7PYdHxRSw9tZT6pevTq1ovGpdpLD8cCSEsglWPSG1P2o6LnQthPmGqowgh8iHQLZDh9YaztstaBtcazOnrp+m/rj9P/fIUi48vJis3S3VEIUQxZ9VFasfFHdTxrYOtyaoH3oSweh4OHvQJ78Oqzqv4+PGPMWkm3tn2DlE/RzFl3xSuZ1xXHVEIUUxZbcO4nH6ZszfPElM5RnUUIYSZ2NnY8WSFJ4kuH01cUhzf//49X+79kukHptOhYgcqZ1dWHVEIUcxYbZE6fPUwAOElwxUnEUKY2x/nUZ1IOcEPv//AouOLyMnLYXvsdvqG9yXUO1R1TCFEMWC1l/aOphh3+FT2lJ9QhbBmFT0r8kHjD1jTZQ0t3Fuw7cI2YpbF8K+1/2LnxZ2ywKcQokBZbZE6cu0IAa4BuNi5qI4ihCgEPk4+tPdsz5ouaxhUaxCHrx3mhdUv0GNlD2ITYsnT81RHFEJYIastUqeun6KSZyXVMYQQhczN3o2+4X1Z3Xk1I+uPJPl2Mq9ueJXOv3Rm6cml5OTlqI4ohLAiVlmkdF0nKS0Jf1d/1VGEEIo42jrStUpXlnZaysePfwzAW1vfInpxNPOPzCcjJ0NxQiGENbDKInUr+xbpOen4OvuqjiKEUMzOZNzpt7D9QiZGTMTbyZvR20fTemFrZh6cSXp2uuqIQogizCqL1MW0iwD4ufgpTiKEsBQmzUREUASz28zm21bfUsmzEuN3jafNojZ8e/BbKVRCiHyxyiJ1LeMaYEw+FUKIP9I0jbp+dZkWNY1ZbWYR6hXK57s+p9XCVkw/MJ3UrFTVEYUQRYhVFqn//mQpd+wJIf5OjVI1+KblN8xuO5twn3Am7J5Aq4WtmLJvCreybqmOJ4QoAqyzSOUYRcrJ1klxEiFEUfBYycf4usXXzGs3j1qlavHl3i9ptbAVk/dO5mbWTdXxhBAWzDqL1J0RKWc7Z8VJhBBFSZhPGJOaT+LH6B+p61uXr/d9TaufW/Hlni+lUAkh7skqi1R2XjZg3K0jhBAPq6p3VSZETuDnJ3+mYZmGTNk/hdYLWzN1/1TSstNUxxNCWBCrLFK2mrGFYK6eqziJEKIoC/EK4bNmn/Hzkz9T27c2k/ZMos3CNnx/6HtZh0oIAVhrkTLdKVJ5UqSEEI8uxCuESZGTmNt2LqHeoYyLH0fbRW2Zf2Q+2bnZquMJIRSyyiJlY7IBIEeXrSCEEOYTXjKcKS2n8F2r7wh0C2T09tFEL45m8fHFsvWMEMWUVRYpBxsHADJzMhUnEUJYozp+dZjZeibftPgGT0dP3tn2Dh2XdGTFqRWyObIQxYxVFikPBw8ArmdeV5xECGGtNE2jsX9j5rWbx4SICdjb2DNsyzA6/9KZ2IRYdF1XHVEIUQisskiVcCgBQEpmiuIkQghrp2kakUGR/Pzkz3za9FOy87J5dcOr9FrVi72X96qOJ4QoYFZZpDwdPAG4kXlDcRIhRHFh0ky0LteaxR0W83aDtzl78yw9VvZg8MbBnLpxSnU8IUQBscoiVcLRGJG6evuq4iRCiOLGzmRHTEgMK55awYAaA4hLiqPTkk68t+09LqVdUh1PCGFmVlmknGyd8HL0IjE1UXUUIUQx5WznzEuPvcSKp1bQrUo3lpxcQvTiaCbsniCrpAthRayySAEEuAVw/tZ51TGEEMWcl6MXw+oN45eOvxAZFMn0A9Npu6gt3x/6nsxcubNYiKLOeouUawDnU6VICSEsQ6BbIGObjmVB9AKqeVdjXPw4nlz8JMtPLZclE4Qowqy3SLkFkJSWRFZuluooQghxV6h3KFNaTmFqy6mUcCjB8C3D6b6iO3su71EdTQiRD1ZbpCqVqESenid3ywghLFLDMg2ZHz2fjxp/xKW0Szy/8nmGxA4h4VaC6mhCiIdgtUWqsldlAI5eO6o4iRBC3JtJM9GhYgeWdlrKy4+9zJbELXT4Twc+i/9MJqQLUURYbZEq61YWRxtHjlw7ojqKEEL8LWc7Z/rX6M/SjktpW64tMw/NJHpRNPOOzCM7TzZFFsKSWW2RsjHZUNmzMkdTZERKCFE0+Lr48tHjHzE/ej4VPSvy8faP6fxLZzaf3yxbzghhoay2SAFU9a7KoeRDsiu7EKJIqepdlRlRM5gYMZE8PY9X1r9Cv7X9OJFyQnU0IcRfWHWRquVbi/ScdI6lHFMdRQghHoqmaUQERbC4/WKG1xvO71d/p8vSLozZMUa2vxLCglh1kapZqiYAuy/tVpxECCHyx87GjudCn2NZp2V0rtSZuYfn8uTiJ/n52M/k5uWqjidEsWfVRcrPxQ9/V392X5YiJYQo2jwdPXm74dv8GP0j5TzK8f5v7/Ps8mfZe3mv6mhCFGtWXaQAavvWZtelXbJysBDCKoR6hzKz9UzGNhnL1Yyr9FjZgxFbRnA5/bLqaEIUS1ZfpBqUbsC1jGscvnZYdRQhhDALTdNoW74tSzsu5cXwF1l9ZjXRi6OZcWCG7OYgRCGz+iLV2L8xGhpbzm9RHUUIIczK2c6ZgbUGsqTDEhqUbsAXu7+g05JObD6/WXU0IYoNqy9SXo5ehPmEsSVRipQQwjoFugcyMXIi37T4BpNm4pX1rzBww0AupF5QHU0Iq2f1RQrgcf/HOXDlACkZKaqjCCFEgWns35hF7RfxWu3XiEuKo8N/OjD9wHSyc2V1dCEKSrEoUk8EPIGOTmxCrOooQghRoOxs7Hgh7AWWdFhCY//GTNg9gc5LO7MjaYfqaEJYpWJRpKp6V8Xf1Z81Z9eojiKEEIWitGtpvoj4gq+af0VWbhZ91vRh+JbhJN9OVh1NCKtSLIqUpmlElY0i7kKcrAgshChWmgY05T8d/sNL1V9izZk1PLn4SeYeniuLeQphJo9cpDRNC9Q0baOmaYc1TTukadogcwQzt6jgKHL0HDac26A6ihBCFCpHW0cG1BzAovaLCPMJ4987/s2zy5/lwJUDqqMJUeSZY0QqBxii63oo0AB4RdO0qmY4rllV866Gv6s/q8+sVh1FCCGUCPYIZmrLqXz6xKck307muRXP8VHcR9zKuqU6mhBF1iMXKV3Xk3Rd333n81vAYcD/UY9rbpqm0bZcW35L+k1WABZCFFuaptE6uDW/dPyF50Kf46djP9HhPx1Yd3ad6mhCFEmaruvmO5imBQObgTBd12/+5bl+QD8AX1/f2vPnzzfb+z6oy9mX+fDCh7Qv0Z6WHi3NcszU1FRcXV3NciyhjpxH6yDn8eGdyzzHvKvzOJ99nupO1eni1QVPW0+lmeQ8WgdrOo8RERG7dF2vc6/nzFakNE1zBTYBo3VdX/R3r61Tp44eHx9vlvd9WD1X9uRaxjV+6fgLmqY98vFiY2Np1qzZowcTSsl5tA5yHvMnJy+HWb/P4uu9X2NjsmFQrUE8E/IMJk3N/UhyHq2DNZ1HTdPuW6TM8qdE0zQ7YCEw559KlGodK3bkzM0z7LuyT3UUIYSwCLYmW3qH9WZRh0VU96nOx9s/5vmVz3M85bjqaEJYPHPctacBM4DDuq5/9uiRClZUcBROtk4sOm7RfU8IIQpdoFsgU1pO4d9N/s25m+eIWRrDxN0TyczNVB1NCItljhGpxkAPIFLTtL13Hm3NcNwC4WLnQrvy7VhxeoWsKSWEEH+haRrR5aNZ0nEJbcu3ZdqBaXT+pTM7L+5UHU0Ii2SOu/a26rqu6bpeXdf1GnceK8wRrqA8W+VZMnMzZVRKCCHuw9PRk9GPj2Zqy6nk5uXywuoXeG/be6RmpaqOJoRFKRYrm/9VZc/K1PGtw49Hf5TVfYUQ4m80LNOQRR0W0btabxafWEzHJR3ZmrhVdSwhLEaxLFJgjEolpiayJXGL6ihCCGHRnGydeL3O68xqMwtXO1f6r+vPqK2jZHqEEBTjIhURFIGvsy+zfp+lOooQQhQJ1UtWZ8GTC3gx/EWWnVpGpyWdiE2IVR1LCKWKbZGyM9nRo2oPdlzcwcHkg6rjCCFEkWBvY8/AWgOZ224uno6evLrhVYZtHsb1jOuqowmhRLEtUgBdKnfBzd6Nbw9+qzqKEEIUKVW9qzK/3Xxefuxl1pxZQ4clHVh7dq3qWEIUumJdpFzsXOga0pV1Z9dx5sYZ1XGEEKJIsbOxo3+N/syPno+vsy+vx77O67Gvc/X2VdXRhCg0xbpIAXQL7YadyY6Zh2aqjiKEEEVSiFcIc9rNYWDNgcQmxNJpSSfWn12vOpYQhaLYFykfJx86VerEkpNLSEpNUh1HCCGKJDuTHS9Wf5EF0Qvwc/FjcOxgRm4dyc2sm//8xUIUYcW+SAH0De+LhsbUA1NVRxFCiCKtomdF5rSdw0vVX2L5qeU8teQpfrvwm+pYQhQYKVKAn4sfXSp34T/H/0PCrQTVcYQQokizs7FjQM0BzGozCydbJ/qt7cfH2z/mds5t1dGEMDspUnf0De+LjcmGKfumqI4ihBBWIbxkOAueXED30O7MOzKPmKUx7L+yX3UsIcxKitQdpZxLERMSw9JTSzl786zqOEIIYRWcbJ0YVm8Y06Omk5mbSY+VPZi4eyLZudmqowlhFlKk/qBPWB8cbByYvG+y6ihCCGFV6peuz8L2C3my/JNMOzCNbiu6cTzluOpYQjwyKVJ/4O3kzbNVnmXFqRUcuXZEdRwhhLAqbvZufPT4R0yImMDl9Mt0XdaV2b/PRtd11dGEyDcpUn/RJ7wPHg4ejIsfJ3+4hRCiAEQGRbKo/SIalmnI2J1j6b++P8m3k1XHEiJfpEj9hbu9O/967F9sT9rOlsQtquMIIYRV8nbyZlLkJEbWH0n8xXg6/9KZTQmbVMcS4qFJkbqHmMoxlHUvy/j48eTk5aiOI4QQVknTNLpW6cr8dvPxcfJhwIYBjI4bTVZelupoQjwwKVL3YGdjx2u1X+PUjVMsPLZQdRwhhLBqFT0rMq/dPHpU7cH8o/P59OKnHL12VHUsIR6IFKn7iAyMpLZvbb7e9zWpWamq4wghhFWzt7FnaN2hTGkxhfS8dJ5d/iw/HPqBPD1PdTQh/pYUqfvQNI03677JtYxrfLPvG9VxhBCiWGjk34gRpUfQ2L8xn8Z/Sv91/bmSfkV1LCHuS4rU36jmXY3OlToz+/BsWe9ECCEKiauNKxMjJvJ2g7fZfWk3nX/pzNbErapjCXFPUqT+waBag3C1d2X09tGyHIIQQhQSTdOICYnhx+gf8XH2of+6/ny26zOy82RFdGFZpEj9A09HTwbVGsSuS7tYdmqZ6jhCCFGslC9Rnrlt5/J05af57uB39FrViwupF1THEuIuKVIPoHOlzoT7hDM+fjw3s26qjiOEEMWKo60j7zR8h0+bfsrJ6yfpsrQL68+tVx1LCECK1AMxaSZGNhjJtYxrfLXnK9VxhBCiWGpdrjU/Rf9EoFsggzcOZsyOMWTlyppTQi0pUg+omnc1YkJimH90PoeSD6mOI4QQxVKgeyCz2syie2h35hyeQ/cV3Tl385zqWKIYkyL1EAbWGoiPow9vb3ub7FyZ8CiEECrY29gzrN4wJkRMIDE1kZhlMaw8vVJ1LFFMSZF6CO727oxqMIrjKceZcXCG6jhCCFGsRQZF8vOTP1OpRCWGbh7K++U4Y4cAACAASURBVL+9T2ZupupYopiRIvWQIoIiaB3cmin7p3Dy+knVcYQQolgr7Vqab1t/ywthL/DzsZ95fuXzJKYmqo4lihEpUvkwvN5wXO1ceWfbO7J9gRBCKGZnMvZHnRgxkYSbCcQsjWHz+c2qY4liQopUPng7eTOs3jD2X9nPplubVMcRQgiBccXgx+gfKe1SmlfWv8KXe74kNy9XdSxh5aRI5VO7cu1o4t+EZdeXkXAzQXUcIYQQGHf1zW47m04VOzFl/xT6r+vPtYxrqmMJKyZFKp80TeOdhu9ggw0jto4gJy9HdSQhhBAYC3h+0PgD3m/0Prsu7SJmaQz7ruxTHUtYKSlSj8DPxY8Yb+MP6HcHv1MdRwghxB88VekpZredjZ3Jjl6rejHn8BzZM1WYnRSpR1TbuTatg1vz9d6vOXz1sOo4Qggh/iDUO5T50fN5vMzjjNkxhmGbh5Gena46lrAiUqQekaZpjGowCi9HL0ZsGSFrmAghhIXxcPBgQuQEBtUaxOqzq+m+sjsJt2RuqzAPKVJm4OHgwQeNP+DkjZNM2D1BdRwhhBB/YdJM9A3vy+Tmk7mUdomuy7qy7cI21bGEFZAiZSaN/RvzbJVnmfX7LOKS4lTHEUIIcQ+N/Bsxv918SjmXov+6/sw8OFPmTYlHIkXKjF6r/RrlPMrx1pa35HZbIYSwUIHugcxpO4fmQc0Zv2s8w7YM43bObdWxRBElRcqMnGyd+LTpp9zIvMHIrSNl1XMhhLBQznbOjH9iPINqDWLV6VWytYzINylSZhbiFcKbdd9ka+JWZv0+S3UcIYQQ96FpGn3D+/JV869IvJVI12VdZWqGeGi2qgNYo2dCnmF70na+2PUFtUrVIrxkuOpIQghhHroOWWmQngxpVyHtCmRch6xU4/cz73zMSoXcLNDzIC8X9Nw7H/PAxh5sHf780d4VnDzBqQReV8/DOSdw8QH3MmDnVKDfUpOAJsyLnsegDYN4ae1LDKk9hB5Ve6BpWoG+r7AOUqQKgKZpvNfoPWKWxvDm5jf56cmfcLN3Ux1LCCH+WcZNuH4ObpyHGwl//njzAqQlw9/OJ9KMUmTvbJQkzQSaDZhs7nxuMgpWThbkZkJOpvHrP6ztVB3gwB8O6eQFHv7g7g8egeBTGUqGGA9XXzBD4SnrXpY57eYwcutIPo3/lKMpR3m34bvY29g/8rGFdZMiVUA8HDwY23QsvVb14r1t7zHuiXHy040QwjLk5RnlKPk4XD0OyceMz5OPQeqlP7/WZAceAcajbGNwLQnOPsZokbMPuJQEpxLg4Ab2LmDnnL9ik5sDGTcg4zq7fl1H7dAKxmjXzTsF7kaiUebO/ApZt/7/6xw8oFQo+NeCMrWMj17l85XBxc6Fz5p9xjf7vmHyvsmcv3WezyM+x8vR6+G/H1FsSJEqQDVK1eDVmq/yxe4vmH90Ps9WeVZ1JCFEcZOTCZcPw8X9kLTf+HjxIGSn/f9rHEsYozwVW4JPRShRFkoEGeXJpRSYCmE6rY0tuHiDize33BOgUrN7v07X4dZFSD4KV44ZHy8ehPjvIOdr4zVOnhD8OJR7wnj4VHrgYmXSTLxc42XKe5Rn1K+j6La8G5MiJ1HJs5J5vk9hdaRIFbDeYb3ZfXk3n+z8hFCvUGqUqqE6khDCWum6MbJ0fgckbIfE3XDlCPx3U3V7V/ALh5rdwbeqUZ58KoOzt1kujxUKTQP30sajfLP///3cHLhy2PieE7bD6c1weKnxnLs/hLSFKu2MgmVj949v07pcawLcAhi4YSDdV3Tn0yc+pWlA0wL5lkTRJkWqgJk0Ex8//jFdl3VlyKYhLIhegLeTt+pYQghrkJUOifFGcUjYAed3wu0U4znHEuBfGypFQenq4FcdPMsVzuiSCja2Rkn0C4faPY1SmXIaTm2CE+tgz2zYOQ0cPSCkHdToZlyq/Jv/HmE+YcxtN5eBGwYyYP0AhtQZwvNVn5dpGuJPpEgVAg8HDz6P+JzuK7ozdPNQprScgq1J/tMLIR5SbjYk7jJGW05vNgpUbpbxXMkqUCUaAusbD++K1luaHoSmGXOlvMpDnd5G6Ty1EQ4vM0aq9s01LmHW6Aa1ehojXPfg5+LHzNYzGbl1JOPix3H6xmlG1h+J3QOMaoniwSz/mmua9i0QDVzWdT3MHMe0NlW8qvBOw3cYuXUkE/dM5PXar6uOJISwdLoOV47CibXGyMrZbXfmNmnGKFP9lyC4KQTWNeYFifuzdzYu7VVpB+3Gw5FlxihV7BjYPA7COkPDV4z/rn/hbOfM+Gbj+XLPl0w7MI2zN8/yebPPKeFYQsE3IiyNuYZFZgJfAj+Y6XhWqX2F9uy7vI/vDn5HdZ/qtCjbQnUkIYSlyc6AM1vh+Go4tspYigCMuUw1njUmTwc/Ds5yJ1m+2TtD9Rjjce0UbJ8Cu2fB/vlQoTlEjjLu/vsDk2ZiYK2BlC9Rnnd/fZduK7rxZfMvKe9RXtE3ISyFWYqUruubNU0LNsexrN2wesM4fO0wo34dRfkS5eUPoRACUq/A0eVwbDWcijXWVLJ1MiZTP/6aMc/JI0BxSCvlVR7ajIVmw2HXTPh1IkyLgNAnIfIdKFn5Ty+PLh9NgGsAgzYOoseKHkyMnEht39pqsguLoJlr1+s7RWrZ/S7taZrWD+gH4OvrW3v+/PlmeV/VUlNTcXV1faivSclJ4ZOkT3AyOfGG3xs42zgXUDrxoPJzHoXlKUrn0T4zBZ/k3yh5ZRslrh9CI4/bjqW45lWHq951uV4ijLxiuhikyvNok5NOwPlfCEz4D6a8LBICO3K27DPk2Tj86XXJ2clMvjyZaznX6O7TndouUqb+qij9efwnERERu3Rdr3Ov5wqtSP1RnTp19Pj4eLO8r2qxsbE0a9bsob9uz+U9vLD6Ber61uXrFl/L5HPF8nsehWWx+PN4MwkO/wK/LzHmO6Ebl+yqdoSq7cE3rOgsQ1CALOI8piXD2ndh72zwCILoz6BSyz+95EbmDQZuGMjuy7sZXGswL4S9IHf0/YFFnEcz0TTtvkWqGN/SoVbNUjV5p8E7/Jb0G+Pjx6uOI4QoKJmpsHce/NABPguFlUONJQqajYCXt8OAnRA50rhtX/4RthwuPtDxK+i1wphTNacLrBhqzGG7w8PBg6lRU2kT3IYvdn/Bh3EfkvPfNbtEsSHDIAp1qtSJYynHmH14NpU9K9OpUifVkYQQ5pCXa8x12jffuDssO9241f6JoRDW5X/m3QgLFtwY+m2Cde/B9snGjQBdZxtzqwAHGwfGNB1DGdcyzDg4g4tpFxn3xDic7WTKRnFhruUP5gHNAB9N084D7+q6PsMcx7Z2Q+oM4eT1k3wQ9wHBHsHULFVTdSQhRH5dPQm7fzAKVOpFY/HH6jHw2LPG2k4y4lQ02TlCmzFQsTksehGmRULMD1DOWOncpJkYXHswZVzLMHr7aHqt6sWXzb+klHMpxcFFYTDLpT1d15/Vdb20rut2uq4HSIl6cLYmWz594lPKuJRh8MbBJKUmqY4khHgYOVlwaLFx6W5SLdg2CcrUNP6hHXIMnpwAQQ2kRFmDSi3hxQ3G/oOzOsH+n/70dExIDJMiJ3Hm5hmeW/EcJ1JOKAoqCpPMkbIAHg4eTGo+iazcLAZsGEBqVqrqSEKIf3LtlDEZ+fOq8FMvYzQqYhS8dhC6zYeqHYyRDGFdvMpD33UQ1NAYndr95+UTmwY0ZWbrmeTk5fD8yueJv2gdN1aJ+5MiZSHKe5Rn/BPjOXn9JG9sfkMmLAphiXQdTm6AOU/DxJrG6FNgfXjuZxi0D554E9zLqE4pCpqjOzz3k3Gp75dXjUu5f1DVuypz2s7B28mbl9a+xIZzGxQFFYVBipQFaeTfiLcbvM2vib/y8faPMdfSFEKIR5R921is8euGxiWdC3uNu+5eOwRd5xiXfEw2qlOKwmTnBF3nGivNL3nF2Bj5D8q4luGHNj8Q4hXCa7Gvsej4IkVBRUGTImVhOlfuTJ+wPvx07CdmHpqpOo4QxdvNJFj/AXxWFZYOAhtb6PiNcfmu2fD7bnQriglbB3hmNpQMhQU9IfnPc6I8HT2ZHjWdhqUb8u62d5l+YLr8gGyFpEhZoIG1BtI6uDWf7fqMNWfWqI4jRPFz7ZRRnCZUhy2fQdlGxnpCL20x9ruzdfjnY4jiwdHdmBNnYw8Lnoes9D897WznzKTISbQt15YJuyfwyc5PyNPzFIUVBUHWkbJAJs3ER49/xMW0i7y19S18XXx5rORjqmMJYf0uHTKK06FFYLKDmj2g0avgVU51MmHJPAKg8zSY3QXWvgPtxv3paTsbO/7d5N94OXox+/BsrmZcZXTj0djZ2CkKLMxJRqQslIONAxMjJ1LKuRQDNwzk3M1zqiMJYb0SdsLcrjC5ERxbZZSnwQeMbUGkRIkHUbEF1P8X7JwO57b/z9MmzcTQukMZVGsQK0+vZMCGAaRnp9/jQKKokSJlwTwdPfm6+dfk6Xm8tPYlkm8nq44khHVJ3A2zO8OMFpAQBxEjjflPLT8AN1/V6URREznKGJ1aNthY3f4vNE2jb3hfPmj0AXFJcfRZ3YeUjBQFQYU5SZGycMEewXzV/CuuZlzl5XUvyxpTQpjDpUMw/zmYFmGUqRbvw+CDxhYuTp6q04miysEVoj6Ey7/D/gX3fVmnSp34otkXHEs5Ru9VvbmSfqUQQwpzkyJVBFQvWZ3xT4zneMpxBscOJis3S3UkIYqm5BPwcx+Y3BhObzZGoAbtg8cHG/8ICvGoQjuAX3WI/TfkZt/3ZRFBEUxuMZkLaRfouaonF1IvFGJIYU5SpIqIJgFNeL/x+2xP2s5bW9+Suz6EeBipl4278L6qC0dXQpPX7yygOdS460oIczGZjKUxrp+Foyv+9qX1StdjasupXM+4Ts9VPTlz40zhZBRmJUWqCGlfoT2v136d1WdWM3bHWFmPRIh/kn0bNo8zViHfMxvq9TMKVPN3wNlLdTphrSq3Bo9AWP/hP760RqkazGg1g8ycTHqt6sWxlGOFEFCYkxSpIqZXtV48X/V55h6Zy4yDsje0EPeUlwf7foRJdWDDh1C+Gby8HdqMBdeSqtMJa2eyMdYau3oczsX948tDvUOZ2XomNpoNL6x+gUPJhwohpDAXKVJFjKZpDKkzhHbl2zFh9wQWHL3/hEYhiqWEHTA9Ehb3Axcf6LXc2MbFp6LqZKI4eWqa8fHC3gd6efkS5ZnZZiaudq70WdOH3Zd2F2A4YU5SpIogk2biw0Yf0jSgKR/FfcTyU8tVRxJCvbRkQo5Mghkt4dYl6DQFXtwIwY+rTiaKI/9a4FMZjq184C8JdAtkZuuZlHQqyUtrX2LbhW0FGFCYixSpIsrOxo7xT4ynjl8dRm4dKbuLi+IrLw/iv4VJtfG9tBEaDYQBO+GxrsbEXyFUqdjCWJwzN+eBv8TPxY/vWn9HkHsQA9YPYFPCpgIMKMxB/pYpwhxtHZkUOYmq3lV5Y9Mb/HbhN9WRhChcF/bA9Oaw7DXwDSO+zhfGOj6ylIGwBP61Iec2XDn8UF/m4+TDt62+pbJnZQbHDiY2IbZg8gmzkCJVxLnYuTC5xWSCPYIZtHEQey8/2PV4IYq0rHRYPRKmRsCN88Z8lF7LSHcJUp1MiP9Xpqbx8QHnSf2Rh4MHU6OmEuIZwmuxr7Hx3EYzhxPmIkXKCng4eDC15VRKOZfi5XUvc+TaEdWRhCg4p7cYe+L99iXU6Q2vxkP1GNA01cmE+LMSZUEzGWtK5YO7vTtTo6ZSxbMKr296XcqUhZIiZSV8nHyY1nIaLvYuvLT2JU5dP6U6khDmlXHTuIT3fbTx657LIPpzcPRQm0uI+7GxBbcycD0h34dwt3dnStSUu2VK5sNaHilSVqS0a2mmR01HQ6PPmj6cvnFadSQhzOPEevi6IcR/Bw0HQP9tUK6J6lRC/DPXUpD+aBvO/7dMhXqFMmTTEClTFkaKlJUp616WGa1mkKfn0Wd1H87ezN+QshAWITsDVg6D2U+BvQv0WQutRoO9s+pkQjwYO2fj/+NH5G7vzpSWd8pU7BDWn1tvhnDCHKRIWaEKJSowPWo6OXk5vLD6BRJu5n9YWQhlLh2CaRGw/Ruo3x9e2gyBdVWnEuLh2DoYd+6ZgZu9G1NaTjHu1I59g/VnpUxZAilSVqqSZyWmRU0jKzeLF9a8QMItKVOiiMjLg7jJxh156Veh+0JoMwbsHFUnE+Lh5WaBjb3ZDudm78Y3Lb+5u+zN5vObzXZskT9SpKxYiFcI06KmkZ6dTp/VfUhMTVQdSYi/l3oF5nSBVcOhYnNjLlTFFqpTCZF/2enG5T0z+m+ZquxVmdc2vkZc0j/v5ycKjhQpK1fFqwrToqaRmp1Kn9V9SEpNUh1JiHs7FwdTmsDZX6HdZ9B1rrFXnhBFWcYNcHAz+2Hd7N2Y0mIKQe5BDNwwUPbmU0iKVDFQ1bsq01pO42bmTXqv7i0jU8Ky6Dps+xK+awt2TtB3HdTtI+tCiaJP1+FGIngEFMjhSziWYFrUNHydfXl5/cscSj5UIO8j/p4UqWKimk81pkZN5WbWTXqt6sW5m+dURxLC+Gn9x+6wZiRUaQv9YsEvXHUqIcwj/aox0dwjsMDewsfJh2lR0yjhUIJ+a/tx9NrRAnsvcW9SpIqRMJ8wZkTNICMng96renPqhizaKRRKPgHTmsPRlRA1GmJmyeKawrpcuVNqvCsU6Nv4ufgxLWoajraO9FvbT/5uL2RSpIqZUO9Qvm31LTl6Dr1X9eZ4ynHVkURxdHIDTI+E29eg51JoNEAu5Qnrk7TP+Fj6sQJ/q0C3QKZHTQfgxTUvyhSOQiRFqhiq5FmJ71p/h61mywurX+Dw1YfbmVyIfNN12D4VZncBd394cQMEN1adSoiCkbQX3Eobq5sXgnIe5ZjacioZORn0W9OPq7evFsr7FndSpIqp8h7lmdl6Jk62TvRZ04eDyQdVRxLWLjfH2Ctv5ZtQuRX0WQOewapTCVEwdN3YYDuwfqG+bYhXCF81/4rL6Zfpv64/qVmphfr+xZEUqWIs0D2Qma1n4mHvQd81fdl7ea/qSMJaZaXB/G6w6ztoPBiemVMgt4QLYTGuHIVbF6BCZKG/dY1SNfis2WccTznOwI0DyczNLPQMxYkUqWKujGsZvmv9HSWdStJvbT92XtypOpKwNmlX4fv2cGKtsT5Uy/fBJH/1CCt38s7GwhUilLx9k4AmfPj4h+y8uJOhm4aSk5ejJEdxIH+bCfxc/Pi21beUcSnDv9b+i43nNqqOJKxFyhn4NgouHTTuyqvbR3UiIQrH4V+gZCiUCFIWIbp8NMPrDWdDwgY+jPsQXdeVZbFmUqQEACWdSzKz9UxCvEJ4LfY1lp5cqjqSKOouH4EZUZCWDM8vgdBo1YmEKBzXz8G53yC8i+okPBf6HP2q92PR8UV8sfsL1XGskhQpcdd/V8mt41eHt7a+xZzDc1RHEkXVxYMwsx2gwQurIKiB6kRCFJ6DC42PFlCkAAbUGMDTlZ/m24Pfyt/rBUCKlPgTFzsXvm7+Nc2DmjNmxxi+3vu1DAeLh3NhD3wfDbYO0HsFlApVnUiIwpOXB7tnGXfrWchdqZqmMbL+SCIDIxm7Yyzrz65XHcmqSJES/8Pexp5xT4yjY8WOTN43mTE7xpCn56mOJYqC8/HwfQewdzNKVAGv6CyExTm5Hq6dhHr9VCf5ExuTDWOajiHcJ5xhW4bJXdpmJEVK3JOtyZYPGn1Az6o9mXtkLiO3jiQ7L1t1LGHJkvbBrE7g7GWUKAv5aVyIQhU3GVz9ILS96iT/w8nWiUnNJ1HKuRSvbniVszfPqo5kFaRIifvSNI0hdYYwqNYglp1axmsbXyMjJ0N1LGGJrhw1SpSjB/RaBiUKbpNWISzWpUPGiFTdvmBrrzrNPXk5ejG5xWQAXl73MtcyrilOVPRJkRJ/S9M0+ob35e0Gb7P5/GZeWvsSNzJvqI4lLEnKWfihI2g2xt15HgGqEwmhRuy/wcEd6vVVneRvlXUvy6TISVxKv8SrG17lds5t1ZGKNClS4oHEhMTwyROfcCD5AD1X9iQpNUl1JGEJbl2CHzpAdhr0WCxzokTxlbQfDi+FBi+Dk6fqNP+oRqkajGkyhgNXDjBiywiZB/sIpEiJB9Y6uDVTWk7hcvpluq/oztFrR1VHEiplpcO8rpB6CZ5bCH5hqhMJoc7Gj8HBAxr0V53kgbUo24I3677J+nPrmbh7ouo4RZYUKfFQ6vrV5fs234MGPVf1JC4pTnUkoUJeHizuZyx10Hk6BNZVnUgIdU5ugGMr4fHB4FRCdZqH0j20O09XfpoZB2fwy8lfVMcpkqRIiYdWybMSc9rOobRLafqv68/yU8tVRxKFbd27xmWMVh9DlXaq0wihTm42rBwOnuWg4Suq0zw0TdMYUX8E9f3q896299hzeY/qSEWOFCmRL34ufnzf5ntqlqrJ8C3D+fbgt7JwZ3GxexZsm2jcmVSELmMIUSB2TIPko8YPFbYOqtPki53JjvHNxlPapTSDNw4mMTVRdaQiRYqUyDd3e3e+afENrYNb8/muzxmzYwy5ebmqY4mCdGEvLB8C5ZtB67GgaaoTCaFOylnY8BFUbAEhbVSneSQeDh582fxLsnOzGbB+AGnZaaojFRlmKVKaprXWNO2opmknNE0bbo5jiqLB3saesU3H3l24841Nb8haU9bqdgos6AEuPtD5W7CxVZ1ICHV0HZYOMn6YiP7cKn6oKOdRjnHNxnH6xmmGbR4mPxg/oEcuUpqm2QBfAW2AqsCzmqZVfdTjiqLDpJl4o+4bDK07lPXn1tNndR+SbyerjiXMKS8PFv8LbibB09+Di7fqREKotWc2nNoILd6DEkGq05hNozKNGF5vOJvOb2LSnkmq4xQJ5hiRqgec0HX9lK7rWcB8oIMZjiuKmB5Ve/B5s885lnKM55Y/x4mUE6ojCXP57Us4tgpa/1vu0BPi2mlY/RaUbQx1+qhOY3Zdq3Slc6XOzDg4g7Vn16qOY/G0R50grGlaF6C1rut97/y6B1Bf1/UBf3ldP6AfgK+vb+358+c/0vtaitTUVFxdXVXHsCjnMs8x5coUsvKyeKHkC4Q6haqO9I/kPN6fS+oZau8awlXv2hyqNsKiL2HIebQOlnwetbxsau4ZgdPtC+yq/TkZTr6qIxWIbD2biRcnkpSdxBC/IZS2L/3Qx7Dk8/iwIiIidum6Xudez5mjSD0NtPpLkaqn6/qr9/uaOnXq6PHx8Y/0vpYiNjaWZs2aqY5hcS6mXeSV9a9w8vpJ3qr/FjEhMaoj/S05j/eRkwnTIiH1Mrz8mzE/yoLJebQOFn0e17xt3LUa8wNUte6LL5fSLvHMsmdwtXdlXrt5uNm7PdTXW/R5fEiapt23SJnj0t554I87lAYAF8xwXFGE+bn48UObH2hUphEfxn3IJzs/kYmLRVHsv+HSQejwpcWXKCEK3PG1Romq08fqSxSAr4sv45uNJ/FWomwj8zfMUaR2ApU0TSunaZo90BWQ5VEFLnYuTIycyHOhzzHr91kM3jiY9Ox01bHEg7p4EH6dCDW7Q+VWqtMIodbVk7CwL/iGQavRqtMUmtq+tXmj7htsOr+JKfumqI5jkR65SOm6ngMMAFYDh4EFuq4fetTjCutga7JleL3hjKg3gs2Jm+m5qicX0y6qjiX+SV4eLHvN2O6i5Yeq0wihVsYNmPcsaCboOgfsnFQnKlTdqnSjfYX2fL3vazaf36w6jsUxyzpSuq6v0HW9sq7rFXRdLz5VXTywbqHd+DLyS87dPMdzy5/jYPJB1ZHE39n9PZzfAVGjwdlLdRoh1MnLhYUvwrWTxrwoz2DViQqdpmm83eBtqnhV4a2tb5GUmqQ6kkWRlc1FoWkS0IRZbWdha7Kl16peLDu1THUkcS8ZN2HDh8at3Y91VZ1GCLXWvQvHV0ObT6BcE9VplHG0dWTcE+PIycvhjc1vkJ2XrTqSxZAiJQpVZc/KzIueR7hPOCO2jOCzXZ/JJHRL8+sESL9qzAOx4KUOhChwv30N2yZB3RehrvWtF/WwyrqX5b1G77H/yn4m7p6oOo7FkCIlCp2XoxdTo6byTMgzfHfwO17d8Cq3sm6pjiUAbl6A376CsC5QpqbqNEKoc+BnWD0CQttDm7Gq01iM1sGteSbkGWYemklsQqzqOBZBipRQws5kx6gGo3i7wdv8duE3ui3vxpkbZ1THEpvHQV4ORI5SnUQIdU5uMLZEKvs4PDUNTDaqE1mUN+u+SahXKCO3juRCqqx2JEVKKBUTEsO0qGncyLxBt+Xd2Jq4VXWk4iv1srF/WI1u4FVOdRoh1Di3HeZ3h5Ih8OxcsHNUncjiONg4MP6J8eTpeby56U2yc4v3fCkpUkK5On51mBc9j9KupXll/St8f+h7HnXFfZEPcZMhNwsaD1KdRAg1EnbA7M7g5gfdF4Kjh+pEFivQPdCYL5W8n6/2fqU6jlJSpIRF8Hf1Z1abWTQPas64+HGM3DqSjJwM1bGKj8xU2DkDqrYH7wqq0whR+M7Hw6ynwLUk9FpmlCnxt1oFt6Jzpc58e/Bbdl7cqTqOMlKkhMVwtnNm/BPjeaXGKyw9tZTnVz5PYmqi6ljFw6FFkHkDGryiOokQhS9xF8zqZGyD1HMZuJdRnajIGFp3KIFugby19S1uZN5QHUcJKVLComiaxr8e+xeTIidx/tZ5nln2DL8m/qo6lvXb9T2UrAKB9VQnEaJwndkK33cAJ09jJMrDX3WiIsXZzpmxTceSnJ7M6LjRxXJahhQpYZGaBTZjfvR8SjqVpP+6/kzdP1U2zCwol36HxHio9bysGyWKlyMrjMt5Hv7wwirwCFCdqEgK8wmjf43+rDyzslgutCxFSlisIPcg5rSdQ5tybZi0ZxKDYt7IdAAAIABJREFUNg7iZtZN1bGsz8GFxh5i1Z9RnUSIwrNvPvzYHfzCoPdKuZz3iPqE9aFWqVqM3j6a87fOq45TqKRICYvmbOfMmCZjGF5vOFvPb+XZZc9yPOW46ljW5egKYzsYFx/VSYQoeLpuLDq7+CUIbgzPL/m/9u47Lsty8eP452LvjSCgiIh7izP3RHGnlmVZtsvm6VeWzWN1LDt1smGWIyu13KPUTMtOQ3Ml5t4rEXCBCoLA/fvjMU+dY6WA3vDwfb9ez+tReMSv3gpfruu6r0vnSZYAVxdXXmrzEgbDyO9GlqsTK1SkpNQzxnBjrRuZ2G0i2fnZ3LjoRhbtWWR3LOdwbDekb4GayXYnEbnyCvJh0f/BF086diy/YSZ4+tudymlE+0UzotkI1qevZ/q26XbHuWpUpKTMaBzRmBk9Z1AzpCaPf/s4L69+WQdnFteu5Y7n6kn25hC50nJPwfTrYc370Op+GDhFm21eAb3je9M2pi1vrH+DjHMZdse5KlSkpEwJ9wlnYreJ3FjrRj7e+jG3fXEbR84csTtW2XVgJQREQ3AVu5OIXDmZv8CkJMfRLz3/BV1fABd9+bsSjDE80+IZ3F3cmXpsarm4SUj/kqTMcXdxZ0SzEYxuM5ptx7cxaOEgHS1TVAd/hErNdbeeOK/9K+H9DnBiP9w4ExJvtTuR04vwjeCxZo+xO3d3uZjiU5GSMiu5ajKf9PyEUO9Q7ll2D2PXjyW/MN/uWGVHVipk/eIoUiLOxrJg9fswpSd4+MLtX0K1TnanKjf6xPehtndt/rXuXxzIOmB3nCtKRUrKtKqBVZmWPI1+1frx/s/vc8fSO0jPTrc7VtlwdLvjuUIte3OIlLRzOTDvXlj0KFTrDHd8rX/nV5kxhsEhg3F3ceeZH55x6ik+FSkp87zdvPn7NX/nxdYvsvnYZgYuHMiq1FV2xyr9jp7fRiIswd4cIiXp+F6Y1A1SpkG7EXD9dPAOsjtVuRTkFsSjTR9lXdo65u+ab3ecK0ZFSpxG7/jeTE+eTpBnEHcuvZN3NrxTrvYyuWwn94OrJ/hXtDuJSMnYPBfGt4Xj+2DwJ9DhCS0qt1nfan1pXKEx/1z3T46fPW53nCtC/8LEqcQHxTM9eTq94nsxLmUcdy27i6M5R+2OVTplH3dswqmF5lLW5WXDwgdh5i0QXgPu/hZqdLc7lQAuxoWnWzzNmbwz/HPtP+2Oc0WoSInT8XH34YVrXuDvrf7OhvQNDFw4kB9Tf7Q7VumTfRy8taOzlHHp2+D9jrDuA7jmIcdxL8GxdqeS36gWXI1b6t7Cgt0LWHNkjd1xSpyKlDglYwz9EvoxLXka/h7+3LH0Dt5Y/4Y28Pyt/LPg7m13CpGiKSyEle/Ae+0g+ygMmQNdngdXd7uTyUXcWf9Oov2iGbVqFHkFeXbHKVEqUuLUqgdX55PkT+if0J8JP0/glsW3cPDUQbtjiUhxnNgPU3rBF09A1fZw9/fa2qCU83bzZmTzkezN3MvkTZPtjlOiVKTE6fm4+/Bcq+d4td2r7M3cy8CFA/l8z+d2x7KfcQHtuyVliWXBuikwrhWkpkDvtxyLyv0j7E4ml6BNTBu6xHZhws8TnOpEChUpKTe6VenGrN6zqB5cnRHfjmDkdyM5c+6M3bHs4x0MOSfsTiFyabIOw7RBsPABiGoE9/4AjW/SzRJlzKOJj2Jh8dq61+yOUmJUpKRcifKLYlK3Sdzd4G4+2/MZgxYOYvOxzXbHsodvOGQfszuFyJ8rLHDsUP5WM9j7LXR/BW5eAEGV7U4mRRDlF8XQOkNZvHcxG9I32B2nRKhISbnj5uLGfQ3vY2LXieQW5DJk0RCWZy136p13LyogCnKzNColpdeRTTCxq2OH8phExyhU87u0N1QZd1vd26jgXYHRq0c7xedd/WuUcisxMpHZvWfTLqYd807M495l95KRnWF3rKsnvKbjOX2bvTlE/otLQS58+azjjrwTe6H/+3DTXAipanc0KQE+7j481OQhNh/bzMLdC+2OU2wqUlKuBXoG8nr717ku5DrWpq2l/4L+LNu/zO5YV8evZ4+lbbI3h8ivLAu2LaLpmgfg+39B/eth+FqoP0hroZxMctVk6oXV4431b5T5taoqUlLuGWNo7d+aGb1mEOUXxcMrHuap757idN5pu6NdWYExEBAN+761O4kIZGyHj/vDJ4MpdHGDoQuh79vgo01jnZGLceHxZo+TkZPBh1s+tDtOsahIiZxXNbAqH/f4mDvr38nCPQsZsHAA69LW2R3ryjEG4to5FvAWlv11ClJG5ZyEJU84tjQ4tA6SRrM28Q2Ia2t3MrnCGoQ3oFPlTkzZPIUTZ8vuWk0VKZHfcHdx5/5G9zMlaQouxoVbl9zK6+ted7qdeC+o1glyjsP+7+1OIuVNQb7jWJc3m8CqcdBoCDywHlrcg+XiZnc6uUrub3Q/Ofk5TPx5ot1RikxFSuQiGlZoyKxes+if0J9JmyZxw+c3sOvELrtjlbwaPcDDDzZ+ancSKS8sC7Z+5hiBWvgghCXAXd9Arzcch2hLuRIfFE/Pqj2Zvm16md2kU0VK5A/8uiP62A5jycjJ4LrPruPDzR86xe26F3j4QK3esHkenM20O404u/0/OLYz+PRGsArhuo8dhwxXbGB3MrHRvQ3vpZBC3k151+4oRaIiJfIXOlTuwJzec2gV1Yoxa8dw59I7ST2danesktP8Lsg75ZhmEbkS0rbAtOtgcnfIPAi9xsK9q6BWL92NJ0T7RTOo+iDm7ZrH/qz9dse5bCpSIpcg1DuUsR3H8lzL59h4dCP9FvRjzs45WJZld7Tii2roWHS+8m3IK9u3IUspk7YFZt7imMbbvxI6PQv3r4cmQ8FV66DkP+6ofwcerh6MTxlvd5TLpiIlcomMMVxb/Vrm9J5D7dDaPPvDs9yz/J4yO6//Ox2ehNNp8P1Yu5OIM0jbDDNuhnEtYeeX0PoheHADtHnEMZ0s8l/CvMMYWH0gi/Yu4uCpg3bHuSwqUiKXKcY/hgldJ/BEsydYn7ae/vP7M2/XvLI9OlW5BdTpB9+/ASfK3tC6lBJHfoZPhzhGoHZ9BW0ehYd+hs7PaT8o+UtD6wzFxbgwedNku6NcFhUpkSJwMS7cUOsGZveaTUJwAk9//zTDvxpOena63dGKrssocHGD+fdpXym5dJYF+76DqYPg3daw5xto+xg8tBE6Pa0CJZesgk8F+lXrx7xd80g7k2Z3nEumIiVSDJUCKjE5aTKPN32c1amr6Tu/Lwt3Lyybo1NBlSDpH46dzle+ZXcaKe0K8mHzXHi/I3yQDL+shfZPOgpUx5EqUFIkw+oNo9Aq5IPNH9gd5ZKpSIkUk4txYUjtIczqPYtqQdV48rsneeDrBziac9TuaJev0RCo2ROWPQd7VtidRkqjvGxY/T682dixkPzsSUh+DR7eDO0fB+9guxNKGRbtF01y1WRm75xNZm7Z2JJFRUqkhMQGxDK522QeTXyUlYdX0mden7I3OmUM9B0HYdVhxlA46oSbkErRHN8LS5+C12rBokfBrwIM+shxqHDT28Dd2+6E4iRurn0zOfk5zN452+4ol0RFSqQEubq4MrTOUGb2mklcYBxPfvck9y6/l8OnD9sd7dJ5BcDgaY71Uh/21uLz8qywEHYshakDYWwjWPkOVG0Hty6B276E2r3BxdXulOJkaoTUoHlkc6Ztnca5wnN2x/lLKlIiV0BcYBxTkqYwotkI1qWto+/8vkzdOrXs7IoeUhVungd5p1WmyqMzxxxbYbzZCKYNhNQUaPcYPLwJBn0IsS21kaZcUTfVvom07DSW719ud5S/pCIlcoW4urhyY60bmdtnLo0rNGb06tHcvPhmdp/cbXe0SxNZD4bMhZwTMLGL49Z2cV4F+Y7Rpxk3wz9rwJdPg38UDJgED21y7DUWEGV3Sikn2sS0ITYglo+2fGR3lL+kIiVyhUX7RTOu8zheav0S+7L2MXDhQN5NeZdzBaV/yJqYJjDsC8c03+QesH2x3YmkpB3bDcueh3/VdYw+7fsOmt0J96yEYYuh7rXg5mF3SilnXIwLN9S8gY1HN7Ll2Ba74/wpFSmRq8AYQ6/4XszvM59OlTvx9oa3GfTZIH7OKAOjPBVqOdbDhFSF6dc7vugWFtidSorjzFFYMxEmJTnuvvv+XxBZ37F4/JFtkPQSRNS2O6WUcz3je+Ll6sXsHaV70XmxipQxZqAxZrMxptAYk1hSoUScVah3KGPajeHNjm+SlZfFkMVDeGXNK2Sfy7Y72p8LjHaMTDW+Gb57zfEF+OhOu1PJ5TibBRumw8fXwqvV4fNHIPuYY9fxh7fAjTMci8c1+iSlRIBHAF2rdOXzvZ+X6s+RxR2R2gT0B/5dAllEyo32ldozr888BiQM4KMtH9F/QX++PfSt3bH+nLsX9H4T+k+Aozscu1h/P9axtkZKp9xTjk0zPx0CY6rBvLshYwe0uh/u/g7uWw2tH4aAinYnFbmoAdUHcObcGZbsW2J3lD9UrOO3LcvaCo5pCxG5PP4e/jzd8mm6x3Xn+ZXPc+/ye+ka25XHmz1OBZ8Kdsf7Y/UHQlxb+Oxhx4LkDVOh24tQrbPdyQTgVBrsWAzbPncc11KQC74VoMktUG8AxDTVHXdSZjQMb0h8YDyzd8ymf0J/u+NclCmJzQKNMSuARy3LWvsnr7kTuBMgIiKiySeffFLs37c0OH36NH5+fnbHkGKy+zqes86xPHM5X2R+gZtxo2dQT9r4t8HFlOJljJZF2NFVxO/+AO+zRzgW0oS9cTdw2r+abZHsvo62sCx8sg8RemwNYUd/JCBrOwaLHK8IjoY152hYc7ICamGVof2eyuV1dEIldR2XZy1n3ol5PB31NBXc7fkms0OHDussy7roEqa/LFLGmGVA5EXeNdKyrPnnX7OCvyhSv5WYmGitXXtJLy31VqxYQfv27e2OIcVUWq7jgawDvLDqBVamrqROaB2eafkMtUNL+aLf/FxY/R78ewyczYRqXaDt/0Hl5lc9Smm5jldczgnHaNPu5bD7a8g86Hh7xQaOI35qJkOF2mV25KncXEcnV1LXMe1MGl1mdeGeBvdwT8N7ih+sCIwxf1ik/nJqz7IsjdeLXCWVAyozvst4luxbwsurX2bw54O5oeYNDG80HF93X7vjXZybp2PNTeObYc0EWPk2TOrqmEJKvA3q9NXxIcWVnwu/rHecf7h7OfyyDqxC8AyEqm2hzd8cU6tBlexOKlLiInwjaBrZlEV7F3F3g7tL3XKiYq2REpGSZ4yhe1x3rom+hrHrxzJ161SW7l/KiGYj6Fy5c6n7JHKBV6DjC3rzu2H9R45SNe9u+OIJaDDYsT4nqnGZHSW5qvLOwMHVsP8Hx+PQGsdaJwxEN4Y2j0K1ThCdCK76NC7Or0dcD55b+Rxbjm+hTmgdu+P8TrH+Bxpj+gFvAuHA58aYDZZldSuRZCLlXIBHAE+1eIre8b0ZtWoUj6x4hLYxbXmy+ZNE+0XbHe+PefhCi7uh+V2w99+wdiKsfh9WvQPBVRwbPNbqBZENwKUUrwG7WiwLju9xjDj9ss5RmlI3QGE+GBfHdF2zOyC2FVRuCT4hdicWueo6x3bmxR9fZPGexc5VpCzLmgvMLaEsInIR9cPrMz15OtO2TuOtDW/RZ14fbq93O7fWvRVPV0+74/0xYxwH3FZt51jTs/Uz2DQbvnsdvv2n406yap0hoTNUaQt+4XYnvvIKC+Hkfkjb5ChOh9fD4Z8ca8sA3LwhqiFc86CjOMU0cxwiLVLOBXoG0rxic746+BV/S/xbqRqZ15iwSBng5uLGzXVupmuVrry69lXe3vA283fNZ0SzEbSr1M7ueH/NOxga3+R4nM6AXctg15ewfRGkTHO8JiTeMeJSuQVENYKw6mV3c0jLglNHIGMrpG+F9C2QtgUytsGvGwsaV8fu4XX6OaY8oxtDeC1N1Yn8gQ6VOjBq1Sj2ZO4hPije7jgX6H+sSBkS6RvJq+1eZUD1Afzjx38w/KvhtI1py4imI6gUUEYWGvuFQ8PBjkdBvmNE5sAPcGCVo1ht+NjxOhd3CK8JEXUgsq6jaAVXgeBYx/Sh3XJPQVYqZB6A43vhxL7zz3sdz/k5/3mtbwXHUTuNhzqeK9R2/Jm0CF/kkrWLaccoRvH1wa9VpESkeFpUbMGsXrOYtm0a72x4h77z+3Jr3Vu5rd5teLuVoS/Orm5Qqanjcc2DjpGcozvhyEY48jOkbYa938DG/9p3zreCo1D5RYBvOPhVAN9wwtPTYXchuPs6ytavDzdPwDjWHJnzzwAFeY474vLP/uc5LxvOnnRMR+acPP/jk5B91DHKdCrV8Zx3+veZ3LwdRS8kDqp2cDyH13CUJt+wq/G3KeLUInwjqBNah68Pfs3t9W63O84FKlIiZZS7qztD6wyle1x3/rn2n4zfOJ4FuxfwWNPH6FS5U6laQ3DJjIHw6o5HvQH/eXv2ccdIz4l9/xn5Obkfju12jGRlHwMs6gBciYPiPQMc05MBURBZDxK6gn9FxyMwGoLjwD9SdySKXGHtYtoxLmUcJ8+eJMgryO44gIqUSJlXwacCL7d9mYHVB/LS6pd4eMXDtIpqxYhmI4gLjLM7XsnwCXE8optc/P0F+ZBznDUrFtG0fk3HaFHeGcfoUt5px2gTlmPEyyo8/+NCcPV0nCHo9uvD0zHd5hUM3kHgFeTY1kHrlkRKhRZRLXgn5R3Wpq2lc2zp2OZSnx1EnERiZCIzes7g0+2f8tZPb9F/QX9uqnUTd9S/A38Pf7vjXVmubuBXgTN+VRyL1UXEKdUNrYu3mzc/pv5YaoqUNnERcSJuLm7cWOtGFvZbSHJcMpM3T6bn3J7M2jGLgsICu+OJiBSLu6s7jSMas/rIarujXKAiJeKEwrzDeKH1C3yS/AmxAbE8v/J5rvvsOtYcWWN3NBGRYmke2Zw9mXs4mnPU7iiAipSIU6sTVocpSVMY03YMWXlZDPtiGA9//TAHTx20O5qISJE0qtAIgI0ZG21O4qAiJeLkjDEkxSWxoO8ChjcczveHv6fPvD68vu51Tv/3LfwiIqVcjZAauBpXNh3dZHcUQEVKpNzwcvPirgZ3sbDvQrrHdWfSpkn0nNuTOTvnaP2UiJQZ3m7eVAuqxuZjm+2OAqhIiZQ7Eb4RvNj6RaYnT6eSfyWe/eFZBn8+WOunRKTMqBtWl83HNmNZlt1RVKREyqu6YXX5sPuHvNL2FU7knmDYF8MYvnw4u07ssjuaiMifqh1am8zcTFLPpNodRUVKpDwzxtA9rjsL+y7k4SYPsz5tPdcuvJbnfniOjOwMu+OJiFzUr5sN78vcZ28QVKREBMf6qWF1h/F5/8+5oeYNzN89n+S5yby94W3OnDtjdzwRkd/5tUjtzdprcxIVKRH5jWCvYB5v9jgL+iygbUxb3k15l+Q5yczYPoP8wny744mIABDqFYq/uz97M1WkRKQUqhRQiVfbvcrUHlOJDYhl1KpR9Jvfj68OfFUqFneKSPlmjKFKYBX2Z+23O4qKlIj8sfrh9fkg6QPGdhiLMYYHv36QW5bcwob0DXZHE5FyLtI3kvTsdLtjqEiJyJ8zxtChcgfm9J7D0y2eZn/Wfm5afBP3L7+fHSd22B1PRMqpMO8wMnLsvylGRUpELombixuDagxiUf9FPNDoAdalrWPAggGM+HYEB7N05IyIXF3h3uGcyjvF2fyztuZQkRKRy+Lj7sMd9e9g8bWLGVZ3GMv3L6f3vN6MWjmqVAyzi0j5EO4TDmD7qJSKlIgUSaBnIA81eYhF/RdxbfVrmbNzDslzknlt3Wtk5mbaHU9EnJy/hz+A7WeGqkiJSLGE+4TzVIunWNBvAV1iu/DBpg9Imp3E+JTxZJ/LtjueiDgpb1dvAM4WaGpPRJxAJf9KvNTmJWb3nk3TyKa8teEtus/pzoebP7R9DYOIOB9vd0eRyjmXY2sOFSkRKVEJwQmM7TiWj3t8TEJQAmPWjqH7nO58vOVjFSoRKTHebueLVL6KlIg4oQbhDZjQbQKTu02mamBVXl7zMj3m9GDq1qnkFuTaHU9EyjiDAcDC3k2CVaRE5IpKjExkYreJTOo2icoBlRm9ejQ95vRg+rbp5BXk2R1PRMqoX4+tcnNxszWHipSIXBVNI5syudtkJnSdQIxfDC/9+BI95vTg022fqlCJyGU7V3gOUJESkXLEGEPzis35IOkD3uvyHhV9K/LCjy+QPNdxMPK5gnN2RxSRMkIjUiJSbhljaBnVkg+7f8j4LuOJ8Ilg1KpR9JjrWEOlReki8ldOn3PsH+Xv7m9rDhUpEbGNMYZWUa34qPtHjO88nijfKEavHk3S7CQmbZrEmXNn7I4oIqXU8bPHAQjxCrE1h4qUiNjOGEOr6FZM6T6Fyd0mUyOkBq+ve52us7oybsM47ZQuIv/j1yIV7BVsaw4VKREpVRIjExnfZTzTk6fTJKIJ76S8Q9dZXXlt3WsczTlqdzwRKSWO5RzDx80HLzcvW3OoSIlIqVQ3rC5jO45ldu/ZtKvUjimbp5A0O4mXfnyJ1NOpdscTEZsdPHWQaP9ou2OoSIlI6VY9uDqvtH2FBX0XkFw1mZk7ZtJjbg+e/v5p9pzcY3c8EbHJvqx9xAXE2R1DRUpEyobYgFieb/U8i/otYmD1gSzZu4Q+8/tw//L7WZ+2Hsuyd3djEbl68gryOHTqEHGBKlIiIpelol9Fnmz+JEsHLOXeBveSkpHC0CVDGbJ4CBuyN1BQWGB3RBG5wvZl7aPAKlCREhEpqmCvYO5peA9fDPiCkc1HcjznOBMzJtJnfh9m7pip8/xEnFhKRgoA9cLq2ZxERUpEyjhvN2+ur3k9n/X7jGFhw/Bz9+PvK/9O11ldeW/je9o6QcQJbUjfQIhXCJX8K9kdRUVKRJyDq4srjXwbMT15OpO6TaJ2aG3e/OlNuszqwujVozmYddDuiCJSQjakb6BheEOMMXZHwd4DakRESpgxhqaRTWka2ZQdJ3YwZfMUPt3+KdO2TqNdpXbcVOsmmkY2LRWfgEXk8h06dYgDpw4wqMYgu6MAGpESESdWPbg6L7Z+kaXXLuXO+neSkp7CbUtvY8DCAczdOVfrqETKoBUHVwDQoVIHe4OcpyIlIk4v3Cec4Y2G8+XAL/l7q79jYfHMD8/QdVZX3t7wtnZMFylDvj74NfGB8VQOqGx3FEBFSkTKEU9XT/ol9GN2r9lM6DqB+mH1GZ8yni6zujDyu5FsObbF7ogi8idOnD3BurR1dKhcOkajQGukRKQcMsbQvGJzmldszv6s/UzbOo25u+ayYPcCGldozOCag+lUuRPuru52RxWR3/hsz2cUWAX0iOthd5QLNCIlIuVabEAsTzR/guUDl/No4qOkZ6fzf//+P7rM6sKbP73JkTNH7I4oIoBlWczZOYd6YfVICE6wO84FKlIiIoC/hz9D6wzl8/6fM67zOOqF1eP9je/TbXY3HvzqQX44/AOFVqHdMUXKrfXp69l1chf9EvrZHeV3NLUnIvIbLsaF1tGtaR3dml9O/8LM7TOZs3MOXx38itiAWAZVH0Sfan0I9Ay0O6pIufLBpg8I9gymZ9Wedkf5nWKNSBljxhhjthljNhpj5hpjgkoqmIiI3aL9onmoyUMsG7iMf7T5B8GewYxZO4bOMzvz7A/PsvnYZrsjipQLu0/uZsWhFQyuORhvN2+74/xOcaf2vgTqWpZVH9gBPFH8SCIipYuHqwc9q/bkox4fMbPXTHrG92Tx3sVc/9n1DFo4iE+3fcqpvFN2xxRxWm/99Ba+7r5cX/N6u6P8j2IVKcuyllqWlX/+p6uAmOJHEhEpvWqG1OTZls+yfOBynmz+JIVWIS/8+AIdZ3Rk5HcjWZ+2Hsuy7I4p4jRSMlJYdmAZQ+sMJdgr2O44/6Mk10gNAz4twY8nIlJq+Xv4M7jmYK6vcT1bjm1h9s7ZLNq7iAW7FxAXGMe1CdfSK74XIV4hdkcVKbMsy2LIoiEADK091OY0F2f+6jsnY8wyIPIi7xppWdb8868ZCSQC/a0/+IDGmDuBOwEiIiKafPLJJ8XJXWqcPn0aPz8/u2NIMek6Oge7r2NuYS4/Zf/ED6d/YG/uXlxxpb5PfVr6taSGVw1cjG6UvhR2X0cpGSVxHVedXsXUY1Np4tOEW8JvKZlgRdChQ4d1lmUlXux9f1mk/ooxZihwN9DJsqzsS/k1iYmJ1tq1a4v1+5YWK1asoH379nbHkGLSdXQOpek67jqxizm75rBw90JO5p4kyjeKXvG96BXfi9iAWLvjlWql6TpK0RX3OqZnp9Nvfj/ig+L5IOkDW78RMcb8YZEq7l17ScDjQO9LLVEiIuVBteBqPNb0MZYPXM6YtmOIDYjlvY3v0XNuT25adBMzts8gKy/L7pgipZJlOc7DPFd4jlHXjCrVo7nFXSP1FuAJfGmMAVhlWdbdxU4lIuIkPFw9SIpLIikuibQzaXy+93MW7FrAqFWjeHn1y7Sv1J4+1frQKqoVbi7a2k8EYNq2aXz/y/eMbD6y1I/gFut/rWVZ1UoqiIiIs4vwjWBY3WHcWudWthzbwoLdC1i0dxFL9y8lxCuE5KrJ9I7vTc2QmnZHFbHNT+k/8eqaV2kf057ralxnd5y/pG9/RESuMmMMdcLqUCesDo8mPsq3v3zLwt0Lmb5tOh9t+YiE4AR6xPWge1x3ov2i7Y4rctWknUnjbyv+RpRfFC+2eZHzs12lmoqUiIiN3F3d6Vi5Ix0rd+Tk2ZMs2beEhXsW8sb6N3hj/Rs0CG9A97judKvSjTDvMLvjilwxmbmZ3L3sbrLzs3m3y7sEeATYHemSqEiJiJQSQV5BXF/zeq6veT2HTh1iyb4lLN67mNGrR/PKmldoGtGU7nHd6RzbWWf9iVPJLciVbvAUAAAMoElEQVTlga8eYF/WPsZ1Hkf14Op2R7pkKlIiIqVQjH8Mt9e7ndvr3c7uk7tZvHcxi/cu5rmVz/HCjy9wTdQ1dI/rTodKHfBx97E7rkiR5Rbk8rcVf2N9+npeafsKLSq2sDvSZVGREhEp5eKD4hneaDj3NbyPLce3sHjPYpbsW8I3h77B09WTa6KuoXNsZ9pValdmpkNEALLPZfPg1w+yKnUVT7d4mu5x3e2OdNlUpEREyghjDHVC61AntA6PJD7CT+k/8cW+L1h+YDlfHfwKNxc3mldsTufKnelQqQOh3qF2Rxb5Q1l5Wdy//H42ZGzghWteoE+1PnZHKhIVKRGRMsjFuNAkoglNIpowotkIfj76M8v3L+fL/V/y/MrnGbVqFI0rNKZzbGc6Ve5EpO/FTvoSscf+rP0MXz6cQ6cO8XLbl0mqkmR3pCJTkRIRKeNcjAsNwhvQILwBDzd5mB0ndrDswDKW7V/G6NWjGb16NPXC6tGxckfax7QnPii+TNxWLs5p5eGVPPrNo7gYF97r+h5NI5vaHalYVKRERJyIMYYaITWoEVKD+xrex97MvSw/4Bip+nVLhWi/aNrFtKNdTDsSIxPxcPWwO7aUAwWFBUzcNJF3NrxDXGAcb3Z8kxj/GLtjFZuKlIiIE4sLjLtw91/amTT+/cu/+ffBfzNn5xymbZuGj5sPraJa0TamLW1i2mivKrkiUk+n8sR3T7AubR3dq3Tn2VbP4uvua3esEqEiJSJSTkT4RjCw+kAGVh9ITn4Oa46s4ZuD3/DNoW9YdmAZBkO9sHq0jWlL65jW1AqpVaoPi5XSz7IsFuxewMtrXqagsIAXW79Ir6q9nGpqWUVKRKQc8nbzpm1MW9rGtOUp6ym2n9h+oVS9teEt3trwFkGeQbSo2IJWUa1oGdVSC9blshw5d4Tblt7GmiNraBjekJdav0SlgEp2xypxKlIiIuWcMYaaITWpGVKTuxrcxbGcY6xKXcUPh39g5eGVLNm3BICqgVUvlKrEiERtBCoXdTrvNJM2TWLS4Un4ePjwTMtnuDbhWqcd3VSREhGR3wn1DiW5ajLJVZOxLItdJ3ddKFUzd8zk460f4+biRuMKjWlRsQWJkYnUDa2Lu6u73dHFRnkFeczYPoPxG8dzMvckib6JjEke4/Tr7lSkRETkDxljSAhOICE4gaF1hpJbkMv6tPWsPLyS7w9/z9ifxgLg5epFgwoNSIxIpGlkU+qF1dPdgOVEbkEuC3cvZMLPE/jl9C80r9ich5s8TMbPGU5fokBFSkRELoOnqycto1rSMqolj/AIx88eZ33aetamrWXNkTW8veHtC6+rH16fphFNSYxMpH54fTxdPW1OLyXpVN4pZmyfwcdbP+ZozlHqhNbhmZbP0CqqFQArWGFvwKtERUpERIosxCuEzrGd6RzbGYDM3EzWpa1jzZE1rEtbx7iUcVgpFu4u7tQKrXVh49AG4Q20eL2M2n58OzN3zOSzPZ9x5twZWlZsyeg2o2kW2cyp7sa7VCpSIiJSYgI9A+lYuSMdK3cEHOep/ZT2E+vS1pGSkcKM7TP4aMtHAET4RNAgvAH1w+vTILwBtUNrazqwlDqVd4pl+5cxa8csNh7diIeLB92qdGNI7SHUDq1tdzxbqUiJiMgVE+ARQLtK7WhXqR0A5wrOsf3EdlIyUkhJTyElI4Wl+5cC4ObiRkJQAkF5QaRvT6d2aG0SghM0JWiT7HPZfHPoG5bsXcK3v3zLucJzVA2syuNNH6dXfC8CPQPtjlgqqEiJiMhV4+7qTt2wutQNq8uNtW4EICM7g5SMFDYd3cSWY1tIOZnCylUrAXAzblQLrkbt0NrUCqlFjZAaVAuqhr+Hv51/DKeVejqVb3/5lu9++Y5VqavIyc+hgncFrqtxHUlxSdQPq18up+/+jIqUiIjYKtwn/HfrrL7++muqN63OlmNbLjy+OvAVc3bOufBrIn0jSQhKoFpwNRKCEqgeXJ24wDhNDV6mzNxMfkr/ibVH1vL94e/ZdXIXAFG+UfSJ70O3Kt1oHNHYafeAKgkqUiIiUqoYY4j2iybaL5ousV0Ax1EjqWdS2XVyFztO7GDniZ3sOrmLlakryS/MB8DVuFLJvxKxAbEXHlUCqhAbEEsFnwrlfiSloLCAfVn7HKN+GSmsT1/PzhM7AXB3cadxhcb0TexLm+g2xAXGlfu/r0ulIiUiIqWeMYYovyii/KJoG9P2wtvPFZ7jQNYBdp7YyY4TO9iXtY/9Wfv5MfVHzhacvfA6bzdvKvtXppJ/pQsfp6JvxQvPAR4BTlMcLMsiPTudfVn72Je5j50nd7Lt+Da2H99+4e/Ex82HhhUaklQlicYVGlMvvJ7WohWRipSIiJRZ7i7uxAfFEx8UT1Jc0oW3F1qFF8rE/sz9jlKRtY9dJ3fx7S/fkluQ+7uP4+fuR0W/ikT4RBDmHUaYdxihXqGOZ+//PPu7+9teuM4VniMzN5OM7AxSz6SSeiaVI2eOkHomlUOnDrE3cy/Z+dkXXu/r7kvNkJoMqD7gwlqzKoFVcHNRBSgJ+lsUERGn42JciPSNJNI3khYVW/zufZZlcfzscVLPpHL49OELz4dPHyY9J50dJ3ZwPOc4+Vb+/3xcV+OKn4cf/u7+BHgG4O/hT4CH49nX3RdPV088XD3wcvXCw9UDT1dPPF09f398jgUW1oUshRSSV5BHTn4OuQW5nM0/y9n8s+Tk55Cdn01mbiYnck9w8uxJTuSe4FTeqf/J5eHiQUW/ikT5RtG3Wl+qBFYhLjCOuIA4TWteYSpSIiJSrhhjCPUOJdQ7lLphdS/6mkKrkMzcTI7lHOPo2aMczTnKsZxjZOZmcirvFKfOnSIrN4tTeafYk72HU3mnOH3uNHkFeRctYJfLy9ULLzcvvN28CfIMIsgziOiwaII9gwnyCiLYM5gw7zAq+lUk0ieSEK8QlSWbqEiJiIj8FxfjQrBXMMFewVSj2mX92vzCfPIK8sgryCO3IPfCM3Ch7BgMnO89BnOhOHm5eeHp6qm75MoQFSkREZES5ObihpuLGz7uPnZHkatAlVdERESkiFSkRERERIpIRUpERESkiFSkRERERIpIRUpERESkiFSkRERERIpIRUpERESkiFSkRERERIpIRUpERESkiFSkRERERIpIRUpERESkiFSkRERERIpIRUpERESkiFSkRERERIpIRUpERESkiIxlWVf/NzUmA9h/1X/jKyMMOGp3CCk2XUfnoOvoHHQdnYMzXcdYy7LCL/YOW4qUMzHGrLUsK9HuHFI8uo7OQdfROeg6Oofych01tSciIiJSRCpSIiIiIkWkIlV879kdQEqErqNz0HV0DrqOzqFcXEetkRIREREpIo1IiYiIiBSRilQxGWPGGGO2GWM2GmPmGmOC7M4kl84Yk2SM2W6M2WWMGWF3HikaY0wlY8zXxpitxpjNxpgH7c4kRWOMcTXG/GSM+czuLFJ0xpggY8ys818ftxpjWtqd6UpRkSq+L4G6lmXVB3YAT9icRy6RMcYVeBvoDtQGBhtjatubSoooH/ibZVm1gBbAfbqWZdaDwFa7Q0ixvQEssSyrJtAAJ76mKlLFZFnWUsuy8s//dBUQY2ceuSzNgF2WZe2xLCsP+AToY3MmKQLLslIty1p//sencHzSjrY3lVwuY0wMkAxMsDuLFJ0xJgBoC0wEsCwrz7Ksk/amunJUpErWMGCx3SHkkkUDB3/z80Poi2+ZZ4ypAjQCfrQ3iRTBv4DHgEK7g0ixVAUygMnnp2knGGN87Q51pahIXQJjzDJjzKaLPPr85jUjcUwvTLUvqVwmc5G36TbWMswY4wfMBh6yLCvL7jxy6YwxPYF0y7LW2Z1Fis0NaAyMsyyrEXAGcNo1qG52BygLLMvq/GfvN8YMBXoCnSztJ1GWHAIq/ebnMcBhm7JIMRlj3HGUqKmWZc2xO49ctmuA3saYHoAXEGCM+diyrCE255LLdwg4ZFnWr6PCs3DiIqURqWIyxiQBjwO9LcvKtjuPXJY1QIIxJs4Y4wFcDyywOZMUgTHG4FiPsdWyrNfsziOXz7KsJyzLirEsqwqO/4tfqUSVTZZlHQEOGmNqnH9TJ2CLjZGuKI1IFd9bgCfwpeNzOassy7rb3khyKSzLyjfGDAe+AFyBSZZlbbY5lhTNNcBNwM/GmA3n3/akZVmLbMwkUp7dD0w9/03qHuBWm/NcMdrZXERERKSINLUnIiIiUkQqUiIiIiJFpCIlIiIiUkQqUiIiIiJFpCIlIiIiUkQqUiIiIiJFpCIlIiIiUkQqUiIiIiJF9P+OERfeC0KnmgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ellipses = [(3, 0, 2, 1, 20), (2, 0.5, 5, 2, -30)]\n", "a, b = ellipse_polyline(ellipses)\n", "print('number of intersections: ', num_intersections(a, b))\n", "\n", "x, y = intersections(a, b)\n", "\n", "fig, ax = plt.subplots(figsize=(10,10))\n", "ax.plot(x, y, \"o\")\n", "ax.plot(a[:,0], a[:,1])\n", "ax.plot(b[:,0], b[:,1])\n", "ax.set_aspect('equal')\n", "ax.grid(':')" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of intersections: 0\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# It needs to be noted that this procedure is numerical in nature, e.g.:\n", "ellipses = [(-5, 0, 2, 1, 0), (2, 0, 5, 2, 0)]\n", "a, b = ellipse_polyline(ellipses)\n", "print('number of intersections: ', num_intersections(a, b))\n", "\n", "x, y = intersections(a, b)\n", "\n", "fig, ax = plt.subplots(figsize=(10,10))\n", "ax.plot(x, y, \"o\")\n", "ax.plot(a[:,0], a[:,1])\n", "ax.plot(b[:,0], b[:,1])\n", "ax.set_aspect('equal')\n", "ax.grid(':')" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of intersections: 3\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# or :\n", "ellipses = [(-1, 0, 2, 1, 0), (2, 0, 5, 2, 0)]\n", "a, b = ellipse_polyline(ellipses)\n", "print('number of intersections: ', num_intersections(a, b))\n", "\n", "x, y = intersections(a, b)\n", "\n", "fig, ax = plt.subplots(figsize=(10,10))\n", "ax.plot(x, y, \"o\")\n", "ax.plot(a[:,0], a[:,1])\n", "ax.plot(b[:,0], b[:,1])\n", "ax.set_aspect('equal')\n", "ax.grid(':')" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# however, this should not be a problem for our usecase" ] } ], "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }