(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 552181, 12949] NotebookOptionsPosition[ 412836, 10052] NotebookOutlinePosition[ 529286, 12233] CellTagsIndexPosition[ 529205, 12228] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[TextData[{ "\n", Cell[BoxData[ Graphics3DBox[{GraphicsComplex3DBox[CompressedData[" 1:eJyFnHl0T1fXx1PzXDU0ppKaGmOTojyoG0MVbYmhraltRFClhppaVWKOsaYS Q4mIeRZDqOaGEFNoQhBEJJKIRBIRLWp8rdX72fd5913W89dv5etrn3P23Wef ffY5+7ztO7zbgHwuLi61Crq45H/5G1GiwPU3rmUZ3xceHex7Kcu8dMPvbGb7 eNPPSAgYFZcr+NJrCV4DZ8SZ8D2bZ36RGHjbDMoZeOq8cUH4t+eNWJb/wh3B 4adOG/v0eJHb5vk3TbecReeFD76gUuEjT744a26o9emOb5ffk3aR495m/JMb 0XlG8oGGBRs1um82bN1hv3k1wbT+FtxncFDJaw0SRP6LY81CXsTmmqtCpmT7 Nr8qfPAylT/a/n33S8J/873x4b7Z90Q+OPKDvnNf8XXODZFDP0t1W+sydk2M 4KuTH1xyL3lX+t/y7wnhn51KNb7I9+PndVqkCL7ffeWoQUaK4OgZ/GzAmI9P N73p0DP8gIDfB+XLPSLtgudmBpxr226v8EMOZO1ufSbFdG9W/OCZjpHC7118 1L2BBdMFp90lLx74VLyWIN/l8Ioum1qWvC146TIPN+ZdOi78MgNSzpT2iRM5 8P1L5HbqE3fVgdNP9FazqFu/vwfY44KP/YAXWXjGv/jIU9J/7If+tGp4uaeX R7p8F74j7YJjJ/QfOdgJfHDsBH7hwf3CP6ufKfLBkT/mn+wNA4olme2C5swr //yOyOE7In9awpPZd0emCd5mkOf9ussyxN4STy3peql5iugB/NcnntkbM5NF Dvb8XsUa1+/kJgkfvGbD8Abd304U/uRT+0ZWPZAn8sHDD6c/Gz8wW8aFnOZF DlT19s4VvMOVtHdcBuSIfHDmKXbiUmRxhxv32sr3EvzUSLdxX05jPEb9bxNd Oz25Lnzk//D4Sbmkl3oBx57B/QOLnaoaGmKAx+14beLQ7ZeFT/8jMl9b9OlL e/L++mnq8Hf2CB/cvdn84keWRBjwBxb++/nb/4l19J92fb4fNcD774MGekMO 4wLPNWNe7Jh1XORgn8K3cOzHJSCp+OOrbWRcyAGnXfj+ixoGpl/bLXKwN/gV yox/nP52pIwLfNeRUx/v/umY4BHbL7ZKWb5I+Phh+gmOHsCbfVxw7lrfk6JP 5EfEeUUv7BgtfPCgYZu+/zQtVvgeRW+fCR4XLvK9POt59D1hCh8/ENjp4Wdr vogUHL/n4nVkUeta3sauOpm/Lavx8t+fv+hcs8xh4YMH7ayxKiprk/C93vu5 /u66+wzkgyM/cOV7t2/+YfuZEd1L+g2sGS39RP/YA/3he4Hjh+GjN/rDfGde aL8n88UaFzjyIwatGxlV5FfBH/Z6ntotJEnkoGfk0O7QQgvLvvbwhowX+2l+ uHrNIb43ZV7jH+g/+MPrXs/6p940fb47+3PNlATxe/gl8CV3vvLL+ydH5PSc 5Vdu/EcXxB/ir+CD46/gs37hZ+Czfgle3X3L530uSX90u8Qn4H13jRozeV6s rC/IgQ/OeoFd0U/0AA4f/4/eNqzJiy1e6Z6063N+z6FSbpvlu9Audogc9AkO H/3Qbnb/gd9XWZgkcvi+9FPrDfnEe8hnvYaPfNplfWSeIp9xIQf8cPBXbyVc ThV8/K3+FQ5+lebg871azdw96urudGkX/Meji7v7hqcJTvyJnG+WJCTWq3NN 1sdaowqe/ORl+3xH8Pyf/Lm42/oMwd9o2nD6iZR7Dj7t9oroUtItMcXcNWHi 5J6TTon9az54Qkhw/6pht6SftFu9c9mrS6bfERx+0OCIqUu33hacdRb5fC/4 6BMc+egNewNHb8wLe7371z/Qf/wJ8RjywYm74COHuAs+fhL5+BPk6Hbx/+DI kfXR8nt8X/FjVrwkfsbC2V8gP/xobOCLGZcdfOINHY+hN747cvCT+HPkyHpn +WHsmfEyv/i+4MT58IkT6A984hBw7BA54MhBb+gBOeDE84wLvfUNeuyT+OMl m2/FA3odYT31axS16Hi8zCvBcw+/dmGfeVnW9x96VPZ4PyXCCOxTNTOpns13 aVB6QdGLawQnbsytmFupYIMLRs0dLy6djRL7Fvyv6Rsn7Rl1XfCeO4v4xZU4 L3zahb93crX7DUKvGOwv6Cftsm6Cu7/bqlDrCjGCe5yJ639v4lkHH/n1H6Xs +SD6orRbotqdga1OJhhhnY6vqTvohvQTvPq3LiNKbkwW/q5v057t7h0v/Sfu Kldm1JXfPVOM3v65/a57yHwWPKRz96jik1MFv9U0N+Tvx0nCRz78xFlNNiye d9MgrqY/tMu4wD2OzPq6uf81wZETPvPe1123JwnuViZvwtNziSKHeAb9oDfm F3ombpQ42eITHwo++Y9lzxbsNXTcBZ84E3z03vy7Sm665mi3QMmHHpGNLgrO fpz+aPliD9a+ADz+9UenynqeED7y0Rv2Dx7V98XP69beFP2Ao0/sGfnIYX6x X4CPHPjg2DnfPWjJiEk9X6QbhTx9L50YnyZ2Al670YYqxfqkC3/VnLGplZqk iv0wX+q7Dqv1d3SWEVynX3z35zYfPKD8vvpRPW4LntTv8amEljZf9ncWv/PV 85+06pApeN1So2cfyJchfOwnMXpfWoezuYJjb+CZDyNbTumcYSi/LfLVftkY lvDmYn/3LOEHz2o65FHneyIfHPnoBznozWtou/1dZqYIzri+KTvy1tTRtwTv ceNpDa/h6aJP5p3M1/OxnU+fyTJUfsl4b23j0EeVcwQv9faoqnsr5AkfP0k/ tRzwHYeT+z5ufUfkgp8Lr7WuZfVswfl98t7mwWGF7X40y3tyoOV0Wz7jmmve Xnqm/13RG/MIPTBe7BMc/wMetmCkR4+YbOGzb0XP4HwXcPyn7Is/uJPbcGmm o134+GHxD4eyOy06meaYR4wbewafGPq4WPGsPBkvOPpkftEfxot/Jk7An5B/ AGf9wp8Q5+DfwFmvwckDgLOOwEc+fPb7wme/bOUrJA601mv2gxLnWOu13ifi r/CrxJn4JcEtOeCsm+CsX/DZX/AdwYlzkMO4iFvAWRfgI4f1HT7zFPnogXGx TtFPcOTAp13WL/aVomf0ae37+C7g9Aec/A84cQh8iRtZB1X8yXoHn7iR/mMn yJdxWesdOOs7fOTDx57BWe/gsw9F/8w7icOt+UJcAc66oPnIIT5hvjAf8QN8 F3D8Bjh+VfPpD+sy7eIPNZ/1jn6C00/iAeYLfgZ/gnz6yfqi9neyvvAdJX+v +gOO/8EOGRf95PvST+INcPjEFcgnTpB5bdkz/Uc+9oAc5js4fL4j7bK+aDn4 edqFjxz8vNp3y7qDHNZ9LR8+dnj6u5+edCsbY5LHYD8e+OG2LsVcIwVnv3+p kLHw3XcumORVJF9h8cHZV8Inf4V8/5+SLzb5bYVJ/kG3y7mDxuGT30A+OPkH cDmPsPIP6IH8P/Jjbrzr4Z4cZ7JPJN+SlLnx8ZWjCTIu8g/g8MlX0C77buTk rqid3n19ssl+FnzsoCLvtXk3ReSgZ3D46JN22e9rOeyjJe/0TqcOwYkHpf/g VyMDl5+fkCg4ekAOeTaNw0f/9Ie8peaj/+ke1TO9J2UJHzxiSIHT8XMyzUtd U/2e7bgi33FolbGtIi/afPKZ4MiHX7j8GK8uve4KH/x2Gc/HJX7MFj75NOTw vcjfggc8nDfvyewok3wUOHYIzrjAyX/Cx97gM15wzqd0f8jP3BracVf/Dbki H5zxwkd+p7+NYqe+zzHVfBc9MO8kP08expIv5z7kgS0cPvkT/Iacd1hy6A98 8qjg8MkLId/t5rD8jdvsdvQHPvk6cM5hJX9r4cwj8u18R8YFn/50+Gn78rmX zzhw+OS385X/8/Ubze+ZxCHqXN4k/iFPHplY5rZPdK7g9Ac+cpAPnzhZyyde Zf7CJ14F93+09ujgwrmiN/DJH49cmXU6S3Dy7eD0k3w78iUOt+xB2rXk4Jfo JzjrAvMRfdIu8xE7QT/wwemPzFPr+6Jn5Mi5odVP5ICTn5R2rbwfeoZPnlbb FfcT0Cf+in7Cv3/Bf3KrEqni35jXE64cHuj6LF1w5ik45wXwn0z8xfu51x3x t1oOOOvdow+b7C979bb4vau+o66ueukP4IPjT/ju9Gffk9abptexcdZf5IAj p0OXnhHVgu4JTn/wM8wXvhf9x37A8Z9i55adMC744Kw78FkHtXzWX/DnBzIy b2/MFjmsU/Sf/uCfwfEzmo89IJ/+oAf0TH/A8dvwaRd7AGc9Rf/IIY4Ch893 fOfG99d8y+YJH9w10TusdY174h/AtXy+b0/v8SleC/JEb6wvtIcewGcfmXyn akkbZx2EP9Xzad8ew/JEPrjYg7X+gsu6Za37/P2gxLXKdUbdcvCY1/xN/7F/ +ol+4IOjH/isy8gDJ25Eb8jhPAuc+Yh/wG8gBxw/Bo6/Yl1An6yPWg7nKeD4 H+Tgl5BDu8Sr4MwL4lvkg+PPiZPRC+PFf4LjH8A5f4RPPIz+tRxw/BJ2wnrN fMSuGBc4fHDiavqHn4cPLnGRtV/A3pin8NGPnNNZfHDOl+Ejh30ceQPsB5w8 DHjgPv+i+cbdFT7y5X6Klf9R9i/5GfjsB7Uc2iUfgj2Ak/cAJ0+IHNYp9r/k YZAPTp4HOeRF4dN/+F5frl+6ts9B4cv5m5UHI44lHyV5Hmu9Jm9D3g8cPnlF 9kG0q78LeQPkYJ/g6AecPImWQ/6N8cInzwBOvCr9J29m9Z9zH3DiEMYluBUv gaN/8NwGAa71SyU75BPvcf4LX/pz1fxPTbct0n/JQ1p5OcYLjhz2ofZ5k3Xf yWoXnHN2cM6h4Ev/rX5yHwl7K9Foav8BmzNlXKxf2A/fBT8p39fiE7dg/+D4 E8H//70+kY+e4YNjz/DLVDG/6FI9zyGf/JvkPy29YZ+SF7L0A858B2d+wZe8 hMXHb4DTLnzskP6TR4KPHiSfZrULTj5Q7WclzwYffyL5Ogvnu+APxf6tcw3J /1t5OfSq9+m0S54Tu0UP+BNw8YdW3pv1Dhz9sH4hHxw55F21/iU/b/lbcPLA jIv9NXxwtc5KvhE/yTzlXoTMCwvnXgR8/An7bvjk1cGJZ5jXzEf44Ho+kieH T7tybmLdP2R9lPNxq138CTh5APCe6xo3PHPmrKP/+BPyD/DByWNIHGXJJy9B P8HZP8r9eOu7oE/mLzh+DD7rAnqAz3cHJ56RcxZrXPDB1T18WUfgE+fb9vb/ 9T9x1/Q/Tl5LM9Q9eZkXfEfZT1k4/hx9YleMF5zzFC2f/qNn/DNy9HjB+V7I Aef7Sr7CWteQw3hZR3Re5djn5VOqTo4XnHgGOwHHTrhPC44fsM+V/h0v81TW Tet+Fzjtar7cJ7HmBTj9YV7jN8CxQ8m3WPkinZcjXwRO/CP3hy0cv0d/9PpL nkrblawvVjwg9/tZN634Ab6sv5Z+0LPgFj/3pxY/3ty8x/SZW8s/cfI6s/Qk z8oPSoYabuEtouruDxbcZajr9bzQLUbpyBnR5oM9pn/XfWndn002XXoF9S1z K1j45H/A4bskDLhT93awyPf55PzQtC7rTK8zJee69w11tAs+YvTp0KpH9thy uG9sxQnwBffK1+M1t0mGi9c0lxUL3O3+W+u+f8z5QmO/WWzjVj/h6/vM+l63 y8kWrx/7vq/w6afwr1xovmz5VBu35PubMasbFVpsuAVE7Sx052V70u6/8gWX /lvtLihe887CthK3uJ0fdGNi2LpX4l7rXVc3GrrQln/gz2/LXJxiuHVMXHe4 dKizXQv3//7m0uy6swzk0B+fpaHjvdO3GrnTY6eXqBcqON+r9NkqVzLGvZQb +X6nhcOniXzwiMuFKnfvavORvysivN27dfcIntQ2ttmxquukPw75arzoX/SG HrCHV/HRg/q+Imdy2cUtS00xtX5c6k4rGnpthil2qPWv7XDnh/+ZO3m86bBb S36RjV23eXhGinziEMYLvmvV6/l3uP8u+IgBvXO8dx0VPnYlcb6lN76Xvp+m 6x38bya3zvZdKOee/gPfvPfahcUiR+omRk68cjNyj+PcX+tBny/4X/hrUp3N c2xc8dEP84Xx8r30/QdHvUbZIe8XD17kbNeyZzlnsfwS4/Iodr7ab21DTV2f UiS40IaVuUelP/JdrH7CPzk3qv2EJ0cN/IncZ0ZvnL/c336k8+u2HMal63eK JG1tXznwuNwD0ffnwYM7Drnc46NrgveIr3U/Z36a8OceWGi2aWzfJ5Fz0gmn +t6+dU7O68H1Of6hZrV+rTss0cR+dLyEvel4NclnScteb+8UOcKfMbZAxzUL DB0vxUSeimsSfcq+36X6A9429tcunQ4kmV5P54W5+B0ROVJf2WdKu9ZH4+Uc n33Kgtw7vRqsvCjn8uD6Xke5Am0K7R6Soe/5G/Pbbvv+j2Z3TJdvm9/dH3VY +iPnGjk3Ck/rvkVwxus1o0q/VYvCRL7wJ9S7sGP6esHl3rVZz+3hwn3SrvAt fyh5J4uP35D7CUpvyG8eXvzE9WfJggeuGFunbBWb71Jn2pr04JnSf6ljsnA7 f/Uv7v7Ow+WPUo8LrusvJF+xe3zmkrC1pr435VMotJZ3tRBT3+uI8OgSub3b enNJnfZ/ueaLF77cT1j52D37T/ueD98xd+6og1crxQmu6x2QE1tjXMum3TIF d69SPatXZJbDHui/59bJrUa2SzH1fbO/XntuDpuTbur7ObPHF4qKmJYm/Imb d8wd9yRF+rOtz9lqsXUSRQ54h7Yr/f0+SxY59Effy83wPx84s9Ydwb8698eA WsFpjv7LvSOrn477Uc986311I8tsOdi9eohXrHxH+rNgY7qvt8s5sSvRv7oP g370PcmQ9wZ6LP46x9T3NjmviZlxuWHyuSRpl7z0edPz1Jkm9v1J4tr4Ogv/ 3DjYvqcPX9+fnFJl+WsNXPIED15QalXHd/+rnlvdj6pwNn3P9mp3hT8hOtm/ 5JfZIh99Rk9YW/7Ig2yHXcn9W2tc7otWxFWvkCP36ODre/58F3CfbeMK93WJ E37ImO9mbk+178/zfXU9Av5K37ev1GJWV/dom5/Q5sOTczbGG+ocTeRgV5JH i52RVHTjReHLvf3yU6+Mvmb3JzV/gYbfTMwW+0Rvun4BPev7/+gN/vmPI8yA uCSHHPjvtthWbtEDOe8S+ciR+23H2wxzH3PdUOd3Igd70HUEI0JHJod/lGjq Oo7VpQ6PKReSJPyYej3m9dxzztD11BViH1S5ueyUoeugg+r/9Ph1jyOGroMe Ufs/h/58dNjQdeVuq10O9e6+w9DvHgRVzl8ufPpmQ9cZuZz0XHq62HxD13v6 f9g4t8EHswxdj+/9dqthS78MNfS7AcR7mq/jNGlX4X6rPEvWikwz9L5e10H0 PHagRobbNXPFwgJV83e06y90fSj4nNsb/Vp42niRyxUund913KE3qWex/A94 qdLew//8KFnsdtXpr8Kyd6YJH/zbSK9h9Yumil0xH3VdSdqB+lmzR6aZus6C eQ0/YNH0RvEl40UO/KevB8xr4XXBYSfIYZ1iv4b96vpi/JjP9JnPvzm4Ud9H kjpl8QO1Mwp8VDtW+iN10zt/CNr27Lj0R/LsPy15FFLhnKHO74yI8pWmFugU 6fheYWPy5U8olehYL9Bb+91e64p0v2Dq++fYA/zbNXpuOlfRzk9KnaDVro5/ dD5T73d03Tf2r3HZB8U0yXZtdcY8FN9lZNKv9vrl2mqtb1B0rqMeoVaHcc0G rbXxEZc6lrrcMVv4D4zL+xdnpMn3Qo/6nn+LnMkfjl+d56gLMB9GzfJ4ck/4 7jX+qbJ1XY5DDvYctXVlpZhvchz1VvQTPudl9BO+V1rV6x4BKYJTR0M/dbus +1+WD/tx9Gv3HHUujEvehzm5clvjWfIuhRER3HHHG1EHDZ2f1PfJ/T5M6fQy djBLzzlU/lp0tOC6zhocvy33tF3fCXJzt/dB4Kx3Ot7WeTl9T97ljXK3W15a buo6iMf15t1dVd+2W59mM9odmrbO0PWqr8pL6Pv84Pq8UvfHP2n2/arLAh33 6iNmPRn8q99vst/U55jg+pxOx/P+Fd/PLVhxraMOwm3YsHpHJq0zvnHz/On6 7hzBdV2QWn8ddYXYOXjAhrc8XuTY9WZV3vO84jHEjjewz2Mefq2ubLoi45W6 eFVncb1Mu3zL/ex65x5n/N6pOP/Kf+1f/tWDPmcH1+eVjv3L0Q0DJ9xa77iX 7pbdpsDVihtF/1K3quSA+7jeWNv0003iB1b9etR3Ry1bj259mg7e3du2N12P 7JVRdtnqoEBD10FrewP3L/D7Byu+OuiQI/W51rxzW7Iw/6ojFw19PxN+fKXy f36QFu3A4TMf4x7N6b9/lb3+Uhf21Zjq2976OV3sR/tbcPwbOHkPXb/Gd2/e /q3fMt3vOupn8YfwT37m/mm3I0nSLvweV8rM+r3zdUd/6H+xx4WnHmto18fh Z2Qd/fbGd/ebrzD0+YWep16Hpn0Vum616RNxYtKdAvY+QtdLgi849NubYf0y DL2P0HWOLnW6/1V4X4JDP+wLwOW8M+3zJ6v8Lzpw2mW8et/RfG94iwEXswyd d6KuJKbJxKLFV9h5J11vAn9bv+udf2ie4qh/oT5O5x+Qo/MevZu23l2p8E3B 54ck7k8oYte56PyJlgPereYB9x2fpki9jK5P1Pvucj812rJ1yUs/qvJFnL/r vJCuo3HUMVnn7/p+gs4jCa7yRVLvpvJLtKvzLVJPlHH29aF/2ePSdUbw81Zt qz26T6bgo0PfrNT6dorwq4S9M9Y3v533APcfebJegzZ23gN703kecOS71Z79 Y41dThz56H/b8Sk/NKlk5zdoV+f9Gv88Ljd7dIbgETOKrpudki18nQ/RcsCZ Fy4rm8UdHjHX0PcKdJ5N5+31PSudd5Xvq/KrUueo8qLarpCzan/1R76N7Dop r6y/S075xq5jJQ/DfNf1sODMU73O9j61pkxQ71RHHfqIsF4xYybb9sP6i3y9 juv5VeDtXxpklktx9Cdk1vm3ht++Lt9F5y31OQX6eVp3weAQ/0RD77Mk/6/y 8Pp9A/bX8OXdKuv8S7+Xxf6d7yX19f9MWxZwZ73jXQjH/hr5Cpd4QrUr8YQV fzrezVByWJelTkG9MwC+a33Cvma9E0X/Sc/Div/T/7ijDpp9nK6/Jn+iv6Pc J7HsU+dhKh13nVF5hf1eBPkWLZ/8iX63gTyM/o7kYfR4sXPWHf1uyf7Rgy6n 3k92vFtSZE3+MW3esd/NYH+t399gPwuu8w/6PQFw3iUAH73hs85D0i871n36 z7yT/vR4sunWsTDHuygLbrY84ndsn+BxBxJWnF9pn6fgb/V5ivbDcu5gxV06 Xzqujl+tfFtzHXW7xA86r6Xf0yBPpXH29Xx3nWcmftP5ZPBX5J9Fn59c299l 0Eo7z+mRlz+m3HHHfsfU+9+tnoNiri3PM1+xr7HvTZY0y3zRIsUhZ0J4o2pD VtnvOE7ZUj3KdbOdf6A/4W9sKX7mqSPPYOo8A/0B96i48Jfk/ZJPMIv8p0AH 3y2O/b6ZsG7Fe2Nj7XiP7y7volQKexrYONkZZ1p5J/2OB/fKdHyLfep3WbFP /Z4q/pP9i/Z7+r1T5il1Unr+km/U/py4vfZHf7t8tsDep6B/nQ852/O3Apee 2vhXF5csHTsl3ZGX1vJ1PqFl1UeRbxr2uwdyv27PiiGJ31+W9THwg0NhdZ8d dbyTwP5O4+wTmUfMa/1ukt7H6fr6XW32FfALjHbUrcPHn+u8jeaDI1/nf0Ka dq7Wabk9Xr6vfteC/QvydT5H1neVP9T14HIusCWkYeM3zwge19Q9st/98w4+ cvhe7IMc70SpfBe43ifKOx6t5hfsOOKI6Xh/b/CvI8Z322nq92C5z6DfB9b1 45J3tfADW+6feBGb5qjLQz7nIy5/tAxp3WSe4Ngt9x/0u7tJV0Nz3u262dTv MLt8HDB86KAAwe198b95EnCdh6Fd8L/GTfy8+4Zzpn4/0L36tsX9Q46b+j1G XV/PfAcfeL9vvidf2HXcMeETzwXNOWXqdyB1vfw/H99cmbggyfTKaT7roxuH Tf1usK43p11dv0meBP603MUz3+x+wVEvn7csqFC/E1cc9ZKvqq8HJw8W9MZQ /65rL76ybhccOwE/vXvR1dSDF4W/Ov6NWwObX3DUv+t6UsZV98rGVTOKvrou HpxzSfA2n5d6tv/tROFjD/B13Qc45zL6HQA5r7mVb00vt1hTv8fYYfDDW173 jpv6/VL9HkJno+atZj+kC16z1+VxK2vniBxdP865rX4/gXOlkE5RlVoWiXe8 F6Hr+jknAo/+5ZMJlSukCn9Ysc7vL3h8wfH+w96M9J2BJc7JvVFw94yu//zw gX2PWI8XnO/CvU25r828tu49gksecnr9wjH714setB8AF39S7K0n9beGmfpd aL47uPYPUiet7qHBZ93X9f7MR6+29Q/N3LJPcPG31nj1+5P6/piuu4HPuYCu 9+e8Sdfvc59NcOverJY/Yt13n+fbHOrwn/q9a+q59PvA8PU729TF6HcyaTcw IXLo1B/tdyP1uwSMF7vS70zCj7nkOe7QcPudhDYZv0zLC7TfnSA+1+9RkL8F p24U/s/erqfXZ6XpulpD16Vy7qDrW+GfHjey0AcrMnRdraHrvjNK/NrzxpI8 Q9d9c/6l69OLNz4z98rDXOHvD1tbJ3hRhkP+2KLLSnSJkLpd49em/7y9cG6a XQdtxdvaf5KPAl9+st6IvoFpwr/rMXL+3b050h/Jd/dvtv3nhnadNbius0Zv 4NFLa2wf+ihN+IkjVi8r3idb+HwXXc/OdwSffrFm79ULUxzfnfuT2InUCc7I rFVoy0HB9fsD+v5/xL3Ypp3PLRec9Uu/16HfSeAcRL+HwDmgfg/B6/C1bZOH L3O8w8B6Cl4h0ON0wKXjjncSsq7Vj7xf7Owr39+gPx5nD/nWuBJt6vefsWPm HfcYdb0/6xH8b/w+qT753llHnS/v3oDfiim8+FnhnFfW+4OzzoJnzp36WtOy dr0/9qbruHW9MPfN6I/XiAVLfGtEOfibnsduS6puyxmw9+qHAXFZ//OdBO4p gfvW6Hp04KF44W9oMzKrzTDbnvW7Da96l6B8y6iWD64nOfir/55/oUuO3R/9 TgL3uBgXcRf8L4tGjz25Js3xfgV1l/+rnpr4Aby7y+dZLbsmO97B4DtyvxG8 9KiFDULd4kV+75iRCdebpTjeX9LvaXA/h/G6Lyr1RuAfp4T/YfXMqtdfOPy2 Y13Q7wPA556Y9s/kPaR+/EXDSdMv2O8hIOfknkkjdv9ovz/AuP7Xewj8av+v 2wUnPwD/lzOHo+NCUhzvigQfX1E2dU66Y7z6vZFXrFP2uwQ7/rMq/r/e9XiF /5df5f8d72yo+3hm32fHfjnWzslX64L85q7v/E3+gOuOca0Lj7y5aGua490P 7Jbx7vyiSblBi9Md72zod7Gwty+Wuba5H5vkeA8hs9MbD84Mvy7tvOq9hSVz +kaeXOV8PwG/MXpCviEDTsY73rOCPzZfxLVnN+x3t7YcHt/ljUsJjve42Jfp elv9vpDPzMRPmk4PcrxrwTkyfP/Pd3nOC5wj653Yf9alO+UaLTB1fVlSNd/U X6tskXUQvk/w17Pfy9wheJEpRQzjw2THOzz6fTD8mH4vgnvp+t0M9onwvS/V Xdit9EHHOxsejzaVDNhy2LHeoQe3hDcD8u4EO95T4l46fOrXdN2oS9yeObmn ZzjwpGcpg3ymbDBVvlHic623pKwhk0vFn3OsUz57t5V7a+w+6T9xnX7vSL9n Ql2G1OFmL8o5/tkRR/xAnEMeSe8jdL0zcZSup2Y91fXXos853cL6eyw19P7F q2mlnzedWmzo+Id8oI6vyO/peI92pU7Zeo9F8nvUe+Y/+6hieLTgi56vnrmh lr0ecc6i8y2cKyF/WAG/4M31bX7pYVGXbo638yS6Th+ccYHvP+7797jFF4Xf fker3+cH2PkZ5Os8Cf0B71a4wVvzX+5L4ev4Vn/HhK0j3v4r6IqDL/Fqk8iG V5+tMPzbzGzx8fuBdvxDvb/a58o5tcrvget8o+Q5A0PXprez94/yPr/Ky6Gf Uk2GtnxU1s4jif5nDH+9/Vw7vtXvGEicGdiu9NYK9jsJ5M30ew7I9/Yc3u5h iWuGjqvJq+v9LHldvZ9Fvs63cK5RbqPbyLPJl8VPgus8Eud0Oi/E+aP2t+zj VjTJd9815bqMC/k6X8S5IfjR5XuLphVIFX6FihfXB++0/Tby4Q8t4T74RLQT p13df3DuCeh1DTmp8X2PPFhrr5tavuSprH2iXn8XTW0bubf8XeOX4+2yfw+3 13f2j3o9knNGlffT3wWce1bglfobBQeUzRG+zhPKfSeVNwbX+Wo9T8GrZxzx WvFZjqHzdbqf4AObNtw8v/IdQ+fxtJ/R5/4SVyhc4gqFy/qocFkXFC7+51Xy WUese6o6zvFKbLTe+8waQ6/jSW3Pz+v/SbDhWPet+6iCq3bxM8xr7R/AOffR +XPut+h8Pnau88zMC3l/yXo3j+94dkDts71+tNd9/Jte97l3odd9zSdOY1yf N/DNmJ9sv8tHuzoPwD0o9B8X1L3K6Swnn30x8xT+7KJf59w8kWCqe4MiX92T lPVRy4GP3nRcyrh0HIgedDzJeaLY1aEd7cNHnJJ5oeM08LkLB/RsX9nOP6j7 G4Lz3dEP+RzNJ6+i9eld+XjFfWViHTj2wz0KnR/Aj+m8h2736sGqU5f2uy7+ EPnF2zc8bZ5OMtV9V4k3dB2e5BMsP6zjZ+IBHT+Dp0/3Nd/1t/drtKv3uTpP yP5Fy/f6za/VP53Xm+pek8S34Dr/wP1hvQ/S8uW7W/dIZVy1hzxdPTbMVPdn JJ6X98DVOanEaZ98U6NgtR2Ca/8DznwHZ1+s4x/ZZ1lxoz5nkfNldZ4i8bM6 n5X7hOocU+6vqvMR3R+5R2Ldg9LnL9yb0ue/6Efvx7EH4nmdn/d62GbPkBr2 +Tj9qZdvR/3C/9h+mPml81rEV+BPZ/Tr0P7xZQcfOcRROm+GH/vtZuF73kfs eQrOuZjkDVS8zbjkvq46R5N7pNb90pgC145lTDhi+JQP6D548k4jN6tk7ruu u4yIMt7Pe/jsNErv/2Hgd8P2G0Ejjk7puTrUcHHxKVgj8VYrF5cSV7f7PwwP Glh/bMO3Qk3B4+suTFjc3QxadrRyW2On6T9jXZBnwV1mRNycH8/77X/5/0/v LzegoOldO6/xk+4v5Xnkz/i9ZwvBK7Tw+ezRay/7F3ehTamTvc2YUVcen88f aep2Paq81cvf74AZcXHM6KKfLjJd2uePrth6u+E1ZfDgy6MXmhEDfyn7xz8v //2Ho7NLJG8zFrzT6W6+xruMpL9cP3+0fKfh9VVcFb+1+03a9aow+tb7H0ZK f3yqnN5y6dtIx3j9++bsdflslRHwNGdIzrhYY8T9OdO2DjcN7wtdXSe7RBgx p174tV5uGicHxfU89kOU4XJs6UcfuPYxXXKyvnvR/VvT5XC19BLLv5V2N1Xf OrZJlQsyXh/XSSGt60Y69Jn328Vbi9+64NBDkcNJfRovPmEGNSmV6tUi2Cx9 8mxk/U/+MPwLjoseNcs0c9v/NKNDjmm6Pfzy5oNRUUbE7V7Ri/5ca7rPaZrU /voJ079fgxq1q/xh/B8/z6Ik "], {{ {RGBColor[0.880722, 0.611041, 0.142051], Opacity[0.5], EdgeForm[None], Specularity[ GrayLevel[1], 3], StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData[" 1:eJxN1XmUj1Ucx/Hn/jJnxhjMGMOYMTIzZuz7FiJMJWsMWTqEIdthRkUSZS0t EtVJMWMpZStblrKVpRJC2UUoJ/ta1mzv77mfP/zxOvd+773P/d373O99fslZ OZnZoSAIfsFD2I+92I1oOgojAXHEsSiJey4IHG0piEQMIpBOXwrSNFeY6iXp S9Q8CcTxaIdGaIsGKIIY+02EMy4MBRCFsg/Ub/PbNxHFuIKICHw9ElVQGRVU t3XexR3cQCjk6/nosz2HozSVUtpLYeJCare9JGo9e3mmHP37Kdcijfpqyrr0 tUcNdEDmA/t6FB3RjXG90AXN0BJn8A2WYSnuMe4u/kdLtEIzTMFHFjOmEzqj IzLRHk+r3sb5MXcYe1vznMNZ3EIZ1ruH/lTK4uiq9bSmLwNNEUd7fp1jfeJ6 OpdaeAZVNSYWRdCEuDEew3Xmuup8e3XiahpfjDiL9viQn6em3lUJ4jzaZzlf t8OwMYeJ0ykPUFays8HDSLU9qP4cumKA2pNVP80zp/AvnifujE4YjBxk40f6 zmEjniXugu4YiH7oY/eAvh+wBcdwFH+iG31Z6IntxNuwFX/hBC7gCi5rDS8z bjhesfwnLo44XMJ5jbc1b8D36MG4YVqPPTsUQzASIzSPPfsfLuIl4l7al+XS Ou0rCQlas+VDC+VAfwzSHq3eW3uxfGuO3+wsKNvgDewm/t359jeJx2E0fibe qb1XJJ6IspZzxLd0N+0uJAX+W5HMebZTrtp3ICnk83A8fWP1W3YWr+m87K6t cf5+vUv8Nt7COxiDD/EBJquez9534N/hSqzSnbL5J2jNU/GU7pSd3Q6d73dY j304goPO595P2OT8fbff/VhrOG25joD2Jynq6O6E7HvofPsSLMYiNEEDDMZ8 vI4xeAQ1NGY8XrXz1JiFWIAZTJeHXHyG2ZiF1ViDdZjGuKmYixXES7EYM4h7 Wk45X5+N6ZYT9J3AQRQgLopYy2Hi44imvoxyCVbiK+KvtZ4v8QXmoDt6a35b 2+f6XRszT+v5lniV5hlIPMD5+z7OntF7mIlcrW2R/R4WWq4TD8NEOw/iHdgY +PoWy0HLC8sPjdlJ/CsO41O7exhq+Wt5jV2WM8TvYQom431M0pg9gf+/22b5 oflfpO8Fnd0oTMAI59c2XPPPZ9w8zLW9Y6bOaxo+0XlZ+xzt6w8c0vsfzfMj Necx4vU6U/vdIcqHDcQLNL+d3RHtcTM26Z00ZVwFNNTZNQz8N9nONxL5EY4I hKEWqqKy89/GvpbH1K9RFqO8QlmbsiaqO/89uRr49kr2Tuy+U5ZDeefrhRDl /PfN1tMCGRqTihQs57m1uIBqxP21Bvtfa4scdEBr5//jBqGf2s/zzKTA/59e xg3NY3vpo3VmI835vfxD3xmc1J09pbo9ewkXkc64ilrbSZzF3zqLo4F/V43Q WO82Hjf1rN3feqiL0khECee/86VUfwKP6z0URIzOoj6q6Nn7rgUhEw== "]], Polygon3DBox[CompressedData[" 1:eJwt1G1ojlEcx/HruvfkhWEeZii2MsWQ0siIrbYhIUzJ3KPNMjaEoliRscyw TdgDpXgnjxnbWEx70GJN5g0SG6NsXniap8L33/m9+HTOda5zznX+//O/77js 7Su3BTzPy0UohvqeNwgRGIK3jD3GI/RgAzKRg12ox018xHucRhGKUal17ejW +rOoRhVqEI7xiMYoLMcqzEYSPqEXfei3+ZzpBe1LRNK/T9uENrQgnbF9tIWY Sv847QntY+stLttjsOLbydgexbVL+7SiWfuF6oxhCEGANd9ov9o7+g88d4YO dCLGdzmMxgDPV3DJc/PsfTpSkYwU9dOUF8tHPqIwHKXKo8WwSPm0b//Sd2z/ q/rGXdzRutEo0foGXNY8e39LY42oxVjlfBnGIAGTsUY1sR/HNJ6rvFtNRPku /yd156dQgWlg2Iu1/GuvKRq35yzFmI2g7rbOc3Vk9WO1tU7zgqqLkRih+rC6 SMQc1YfV3g3FVat3s5Rny28Ih/F9d292X5abGMVt8Zah3HNxVOjsAd273Xci A5twDuexGEuwEGm2J5PDEIFwhCCAn7z7gUbU4zleoQpnUIZyqxOtyaEfxAIk Yz5SUIy9OIQDeIJOPEQbOvCXc/5DO/3bqMU9NOjbdRq35wGrT743DH98d04b +67zWlz2G0pVfBOY95S2CxPpxwXc2HjEIp/xFb4bt+chiA+4uC3e67iICyjy 3TntTpp8d16Lcx7mKt4uxfRM34vQnpHKr+0103f3YvdhcVhOfvsunkm2DtOR pL0TNG7PmchW3oPK60EUKr9HUYoSHMF6rVmLLLxBL96hBy34jC9oVduNfj1b /7XW2fwC1dxS+hmqhUrUoFp7j0MsPiiWeGzDDGz1Xc632F4aX43Nem/r4tCn 9fY/aP9xOzz3f2hz8zx3jgzFaTV2WPFarefpOwWqM4uxWfVm57Qa3a3z5mKj 8pSlXF7Tvdt9/wdPu78e "]], Polygon3DBox[CompressedData[" 1:eJw113f8T1Ucx/Fzvoifvbf4mYmiNFSkHUWKBqLQ0hJS0kBU2ktlNEQaopSi QjvtaKBNZSaKSmlIr3efd388H797z+/cMz7nc8893+KBF/UYXEgpvYtSWIUv sEtOqTRK4Rh0RhccicOxjTq/4Ff8hp/RAc9hLTbjZJSh7hb+voRvUrQ3CGej F07BRaiFmqiEiqiBsiifYywVUITd0QodcDA64gi09P8O8/hauvwotEYLt6U2 d0V993Gux6Hx7IM9sJFxbsfv+B7r0YzyJhor10OwH9ftsDfa+Nm9cAKOx3Ho ge5Y5PkrDlvxI/5w+9td9lOKZ7rhNq7vQFfHRLGpiwY54ryn+1Tf7bG/71Xe FG09j6upOw53405MwAGUH+T4Hehnt3idFPvaOcaicSkOz+BZj7mhY6cYlkM1 bKD8B6/5OseqlddCa7AbGqOe51DLsa+DKqiK6m6vyHVUdy2+wUrHU3E9Hxc6 Xy7FUIzAZbgEl/te5cNwcY5cVk5/jZX4HCMVY9yDyX52qNvshEMxBFdiFK7C aFyBhW5rlfP5RYyn/FpchzGup/XWur+ABa6nuCv+wz2+IW5f/YzFOK0Z3qfu GizBZ3gLj+EVvIxX8ajf2bexDB/jQyzHCnzksk/wuuu87fZew030c0uOWCh+ N+fo7wP38YbrqY7q3ogJuCNHO+r7Hbzn8S1zP4vxqftVnBSvJ7AUX+FxzMDD mOl5jPDaKX43eCy3eWzq/07cirsx0es2CXc5f5RHq2nnO1TmejZ/H8JUPIJZ mOR7lU/Hg7ifuvfhHFyAB3EI5dPwFOaik6+f9rvwPOan2DO0d5yEE3FyjrZn e83nYY7WTW06r6bgUd+rXPuq9ivtYdo3tX92dL/zvRZLnAsrHb/Ofk7PP4IZ joli87DL1Mc0TNeYMBX35tgv2rnsKTzpXJzj/LvG78xUx2syHsB9WkO/B8rX mXjcsVMMB+AB96GxKn+1Hl/6fTuT8lkek+r199imuXym836G80P58qTXTWuh NTkCU/5fN+fPDK+vxjfHc9H71d5ze9prN81rrvVQfxrPWcoTz+McygelWMvB Ofb2ztwfgy44Fken2K+1b+ubV6BOQi/+NEVv9MEpOA7HYzyuwbW+vlXvE67D GMWG57/EF/gKnyn/KR+bYu++EdfjFcpfxXvaG/T+KV+wEC/iGc3V9yp/Houw ALfz/IW4x+1N8PVAnI+b3MdAl6vuuRjgaz2v79EFODvFeD93Hy9gRY4Y/aN8 5foTfISu3N+V4tsz0fHriR6KM/bB3lhK3XocQJZ4bu/miKfi2hKt0RCve66a 43J8io/R031pjdTv39iG3/AX/sgR9/Fek4NTnEsUY8W6Fup4jTSGZTnm8Y7j rPslHmN9NEEV6hajMZqjcoqxaYxvYDFe0/tC+SiMxlnODZ0fhmIYLsZgnKF3 JEUeDnHZGp5fh1+xBT9iBOUjU7SrXDsdW50Xyo/v8UuOOiPcx5W4DKso35Dj 3KZzhL6rl3N9RYoz0tHYiE3YjLnOK81D5zw9t8F9vJzjOT1/CS51H+Oct2Od 92P8jPr+Fj97fBrvVsfqLa/5IM//TOefcq2v3yvlQxOcl2Keeh9KoKTHMtRx 1flM540WnsMm9/ud46c1q+K8P83tjXI8R3oewz0Grcmp6Od3YZ5jstnr8VOO sfV1vf5eD62Z1k7nl/VYneNsqTOvvjP75jgnKncapf+2kFQCzVLksnK6ITlW XIiz48Ac+6v22TqU1cZ5XGcd2gtRpu+WrgsogZqu15bi9mjn960NDseRKfbT o3AYDkjx3eng9+Mg7Ofn9Hw31yuizVIoibIoo3cB1VENNVym97saqmMv97vN 72aR61UtRB3V1Z5wIuor7jnaUpu10NtxV/yfxfwce11WeynOnzqjK5A/+F7l O/Cnr7PzZSfXf6U4Y+usrXOlfn/o293RcdgXh6b47mv/13dAe/Ymt6d9rov/ t8PtDfA6nYrTc3zf2jmGam//FHud9sOuXmf9NtD5vi/6+Nl+Oea7G3V2T7H/ tUKLFGurNda676TOjhz7mb413XGg160I5VAW5VFG41abPNcC5QuxJzbzvcq1 n+pb0SDFb8BdUMProfO+zv3FaJTj3F5R5a5XEqXRgHZ2LUTuNvU+qXuV/5Nj zI0LkfPK/WK/0w091oLfhT2wp+evOFTwPFSm3FP+KI80j3Iev+b3Id7M8V1o TlkFVMTXOb6rtXm+Xoo5KtdOSJFnyje9M7/nyEnlYk/HtK7rlfJzer6539Xs 91C/SRoVYm6aZ6VCfHu2e4303Vjq8VXmuq7j3szjK+15FBwHrV0lx1T9adz6 RlVN8Z2p5H4a+Huk9rTv6fepfvs1z/F7619pE9tP "]]}], Lighting->{{"Ambient", RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, { "Directional", RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], ImageScaled[{0, 2, 2}]}, {"Directional", RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], ImageScaled[{2, 2, 2}]}, {"Directional", RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], ImageScaled[{2, 0, 2}]}}]}, {RGBColor[0.368417, 0.506779, 0.709798], Opacity[0.5], EdgeForm[None], Specularity[ GrayLevel[1], 3], StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData[" 1:eJxNl2eMVkUUhj/uvUuzANJBWIpY6E1A6U2WDrv0ZaVZgiIa/WEQiJVepStI L1KVokQTNDZ6E5AmvVswioogJvq8mdfojydzZubMzJlzz5yZW37gs5lDo1Qq VTpXKhVTjkpSqddgLxRLS6Wy6WwHJZFrUFaHP+l7B+Ykob1+FPok14tCXWMz KPvACBgJr8BZxvwGpz1W8w2A4sh9KWt6rMZp7Q8w6kPYGId1b0Ju+ovAA/RX g6LITSizLGd5Xc2p+dq7XW0Znr+dZen0isLaj8MT8Jj3MigK+3mTNcfCGKhK vTLUkW3UN8HGJNgjW3rDaOuPh5bUm0Iz6AKdoRM0cnsDz7MEFsFd8BEsg3dh NSyHClARhsFg2/mc96V9aP/SXwGLbY98Kx+tcrvmnAdzYaH8CHlhPRREvzG6 reA25Gtq8zfS95Ev5sJ8mAPT+B7TYQaMQ2+X/TMF1sBb8DIsgO3wPHpPweA4 zDNPfkWeQjkVttvPO2ESDKfvJRgGP1G/A65Ca+qvQyv1S88+UXszaAlXqBeF 4lCaeim3z/KcM6Et1IOmcAm9M47JEo4ZxcNs73dqHPw2H2bDeTgIB5Lgq/xw e1oYq3E5kM/teeAweheT/3RyHLeKPcWm4m8P/buToH8f61WxnSUcV1XgbuQe lDeisJdLlCXiMLaQ42SifAoT4Cz9F2AM8iH6jtlmzVnFZ20/9X0+72upj0d3 teyh3AfNFZPod6OtRRTk5pSt4RSchBNQKi2UJy0/TNnWcrZ1ZP/7zNk9Crad gdOwCw7DDlgGB2ARbITN8Jnn0dw9LPewDeV8rm9azvbZl476G1pWKZsq+Bv1 svxqEuoVnAe2JEFWqT7N+btz0RE4Bt9Cadpved1pMBZGwU6dZ/hCfnf7ZPgF foWfYbnOJCy1zkR4A9bACrcvhiX2w+fwlf0wy+dFc16FHyFXHOzRvrNs2037 obTzoWzdC7vt562w7d9zBwtgNLwH66IQAwnzxhBBefunZxRklTfdrnKL40Tf RbEykfpkeFuxmRbyYDN/I9kmn1b0WejruFJ8NXe72uR/yQOjoFfQe1GuK2wb ZJNynfKu8p1y3QZYmQSdjrZ5iu2ZZDtbO5YK+wx2tKz52tv+Cc7hBX2/NLYN Xe3nio6fkd6j9qc93IPcLwp2F/K+OltWfm1pH8pnWu8inIfvPfbRKIxX3OoM tbPcznFYCbl/FPQkz2Cev+IgK1f39zw7kqAjO2XjQNsvG7SHXoxZBd3ioK9+ jalkG2ZYVu4fYPu1j1ZeV2uqrw/lOugN4x3Pk6Jwd2+CzZAFOdAVcjFvDGWh C7RV/k6CTib0016op+Bv5D/iIEdwCPkbOAjH4Dgchb3aQxLav2Pty5CGfMT6 9+ruhmpQRXmQtv3wNSyHpbazjL9vJtyPXmXrl00Le1H7eu93bRzadZ8rp2VT 7+k7awt8Ats8p8ZtkB0wQra6PcvfYrb2/L926erMNmXtF5OQh8s452jMFfgB SsYht1yD3HG478rF4V54hjE1oTrUg07wILSBDOgKM6PwNhsO4zzPk/CCc8L0 KPi5N7oN4Tr144oj2jpQz9R3gwJxuGvOQR7kvHGwpzt99b2u7vrDjg35Te8h +e5oFHJjUfT7K05hgO5k3WFwGQroroX8SYjbHo63bO+3BXxqn38MRaBwHOwc 4jkH6U1AvVgc1upIvTNkwwndp46lRxyTObobkrD3pwV9Q+PwhpH9+uaKibLO k4q3krpf/fbIl4T3VR6oTV8tqBkHuS7UgfOwA7ZCOnN2YM66cKfeC8phUMzv mSJ6R9jOCxpPva7mTsLd2t25V++6NEjc3s25brXP+8o4xPAayyd9jhqhn643 k89mus/+de9XMaxvlu68KlsfQq+BbUh3TlafzmnsM7sIeTEsjMP7Vm8VvS23 e++Hobn87u/4JeP3ROEO1Zy1o/AOlyzf1LYsu27FIf9Uh6pww23qq8EatRz/ QxSLcch15xxXp+xz6cvuxug1S+wH/8to/7JNb8smcfCn3l96x+gNmQFtZDdj mviM/ANgMW9o "]], Polygon3DBox[CompressedData[" 1:eJw1l3mYV1UZx3/ceylNsifrqXDJ0FBAUMwaFgEzFQgUzCe1FNmHYRuGkUWS GQbZyqUeQmNTBEFEik0wRHaHNVEBN1Q2Aw2EYZMdgenzfd4vf3yec++555x3 Oed9z3trdC66r0+Sy+WaV8nlMtofprlcOR3L4Ac8P0x7HI7BNqhJXx2oDbXc XgVX+n0HY07ASdgOB+EQbIGtsBxWwGWM/T6sSUKe5P4IevKc7zmaK+X+Dk9D 9yTmaO4py/jM8iT3U/gx31Ynsa7Wuw3y4CZoloZdy72O7GsJraEVtIBfQSN4 BOpBe7gUqkG7NGRK9gO2bzq8Ch/C+0nMvRkaQoM0+j+CD/z9HvougRzcDZVJ PJ+nPZfEvKbQBG6Ff9L3CrwH65JYs6G/NYb6ltfIuv+PMXvgK9jreZo/Dd5x OxXe9rv25RP7Uf5ryxr3Wrc29lue165nvzSybb9LQ04F7Le8Wj4LN8D1cKPX 0Ny6cDYJm2XrmSR8Ws0+kW++SWKMvp1OQo+c/SR9HqMtgSIYkIQfmnif2lmn BvaN7OgEXaAzdHRfY8vS2t2hm8fl+7nAcy70dfLcrp57q2VpjQ5wH8yF2TpD 0ln7DK2TsEv2fQcuhpX0jaAdmUYc/I12Pu1c+CvPf4Fh8AT8OY2z8yLtpDTO 0Aza6fAyvOJ1RqXR/6r1lK3FachZmoTekrvE51BrvU67EDrCH6EDtIexMA5G M2aKx2n8BFjE8yDa8TBOe2G9pN9Ej1H7Ajzvd+nWxzrPcP9k67UYbrR86dEp iW/59vVS+6rY68jWUhgARdDPfpK/hkKZbVf/o5433GP07U7rrvxV0zZcZr/N SyOutScj3Xfh2wz7ep7PxhDr0cVylT9aWkaR9ZNv+npMqXXq7LkDPabUY0qg PxS6X98HeY3p9l8v+Jf90tF7qz0t9Nz7obflSIee9sG3YQPj3oWLeJ6WxpnP 9z5M8J5oL7S/deFmqA83wE1QB2p7r34BtygPQZ7ztPJ1VzjsHK1c/SQUKB9C M2gJzZO4R65JI7frPrhW+0Pby/1NPV7zGlpWHeshmYol5ePvphFTyg2KMcWW cuhz0B/6wbNJ3F2SobUleyd8DpfzXj0NvVrBb62f8thuj6vuedJN95J0HgJl igMYaD/JXy0c73fB7dBEuSkJ24Zpn2zjQM99zPlLz4/Dn9ynscMtp9AM8bze znvKf0OTuBtf8J5O9j4O8Jge0Bdeou8ZeAqmup1N/9ok3pWrdX9fDT/1uSny udTZ6md/PgrFXrfIsrvbpkLr1tPnTPev7mGdt97WfYD1UV4Zk4Zeyi91KTpu g19DPXgziTylO1p39WHtddVc7ntwhOc8xvwG2kIbeBjawb1wF5yA43AYjsBn sBmOwiHoDlfC5dATGsD98Hv4A1yMnIvgU54/hJTn87Rns9CjBe09lit5z8N/ YD1MgQ7QETpBV8iHbpZbADtgI2yD7bAVNllH6boUG99SbMMSo+dVUO7nNbDa fWthhWIc3oaPWOMD2AKfWGZ329oDHrF+0rO9bZJtl9rHslv277B+VXhOYKF0 y+L5G9o3sug7Caey8NEFX1XCOftsNIyBVd6DuTAPXoOM8d+C01msqXknlDPZ 97O0x5UDfT50Tu6AgTAAimAQ9IP+7hvovd9qX+oMvJlGPaG6Yn4ae/EznwH5 pTU0t1/kj1/CLfAQNLYNsiVXNXwkv8tO+U1ncwnfXoc5MNu+kE2V9slWxvzD flrj57Eed9J2y/5F9ulDlt/A53G7z8ox+C8sYI1Fadgle3RuRtjP8u84eBEm Wc5JxpxKw6/y5yE4APuVD3136P65DgbDaXhQ/qI94zMmm2XrQTgKX3udYz6T q/ztgL/pLL7jMTvdp3lfeZzWUixX+Mxu8JidnlfutTT/C9gNn8MeWJhGrSUf yBeb4H3YDhvT0Fv2VslCf41VfdbWc3ZYjnTZ6z59a2OfHrCOFfbRPtjleRrf w7E0GPpmoddux6FsqfSeKk50bt6l7z3rKf320vcF7IM9WeSk1TobUJGFLxTP i+2Lg/R9DT+B6lBNMZtFv96Vl6fAJOdnnRXll02Og8XOIeVeb6XmQDGsyyJv TYans8hfVRUzcEDxCZuZswXWw8dp6P4lfJxFrjnq2F5tW7Z5PzZ7/D7bq7HK R/KzannFpPxdYdvXwv4scp9iRrGiXKc8pny2G3ZZL9l/ifU74jiv8PzDjv1D 7jvm+Nnq3KB1FXepY/mc90p5TjGuXDVUekC52xpZ5Ixyo2flkRW2e5Wfl/t5 jMet8FjNvyqLnKPcuoH2ySxyrO461XErfOepBlMtpnvwDT8v9Z2oPv0n6H/h NZiThMx87+lKy+zmPn1TjbTJNYVqJDHcdYbqpTqMqQXXQ21YlkUOqGHb5Ysn 3K/3856rukb/cMWWrRysXHzO31Rz6R/ujJ9Vh+l/TnXb5iR0km76B9E/xgL4 N1zDGlfDz+HaLGpJ/f+PghFwZxb5Wnm7FTSCptAMGmZRRzR1v+qJSY6PiTAe Zibxv67/9hlJ2C37lfeV74sdS2NgZBJ1hu77u7OoNxZY30XeH8lVPZJn+aqr VF/pv13/67JD8a88IHuG2/Yy13VX2F7ZrZpE+zoPZnl/9Z+u//WF9s8sf59p /bWW/LnRay5DTk3WqUyjlijzN9WYqjXX+Mwu93nRnaC79rxiIY06SPXQg/CA 43KNxypfDIEyKIWSLOY9m8W9prgt9XkZ6u+jZDMMg5EwE+ZnUQPMcf9wr6t7 THWc6rle0CWLHNsHCrO48wv9rlqgPvSGL31P6H5YkMV9rHt5sdeebJ0lYwLM gpezuHNVp+1ynu/qtR/Pou64w2M0dloW93Mvy+tt/RTTiu0rvH+qQ3pY7yLH hmKxwDEiXz+Xhc/kuxL7SjljtH0i36hOmu1xutPH2scjbEeJx1+XxX5r39el 8Q+velR1qeSc895qb5RbVbMtsG9Uzw22vX2s8zTbOxVess4Ftkm2qa5QfTER xmeRJ5QvdNfKD+t9X0gv6VPpc/WWz+P/AXrI5JE= "]], Polygon3DBox[CompressedData[" 1:eJwt1WeMVUUUAODne28XAWvUaFAxGBvs0tFgQYRFUaNSRBENIcFKBzVBBIJK 3ZUS6oKAZBFQikjHhon+0sUKiKBUQbBGRZomRr/JPT++3Pvmnpk7c97MuY36 Duk+OJ/L5R6lhCbFXK4FFZRTxreFXG4v29jDLprTjDvowK1cwPmcMuBJznPf kla0ph1tuYG76EwLro/7u2kT8al9pzG2Usd9lesU1rhfxmY28IC2K1wbkadA Q5awik1sjPj+DGIgA+jHIv2nk5LwAjNpbs3NIg8pH425Wux1XMs1XMUHbOF9 3uNduou9h3vpTDfeinmk+azlTS7Vfjn/uD/DtSEPRj5TXh+mF0fNp8z1slhX ScSk2J48QseUh/id2h+iB9OYTA0zmJXmx/10oytdKKcpveNZn/S/mc9zDGFQ 5OMA33OIg+znMfN7gn48xZOs1X4mdSmxqYqscb8u/aa0mMWkfo/Tn4EMZbn2 1WxgIzXkOGVOJ/iX/xgtdhTDGcFIjsScjnOCk8zjbf5OuWYuc1gYv0vN7bTr GD7mE/oaa7TrD1zCMeqLO4tDnv3Cr/zGz3zq+da0Zs/rUqckG6MPvWhKb3YW szHqRdwOvydpn0E1c5jKEu2rWMkbLA6vs6KY5agm+k5kHBMYTxe60p1udKJS 7MQUzwTGc7P2W2jLjdzEK9qnMi3ylnI1i/ksoJqZTM5n57GSl+P9G+KcrWdd IXv/AuYzN43NvBSv/yLGxlyqaKO9JeW0phXvxF5ZF2teSnvtFbGmdjH327zr djrRPupQB+0d07N81ietc7P+r8WeWs+mYva/NKZJvLssxaV3s4WP+JBjsdaq qEWlfKn/57zEOL6iRz6rR/fF/5DmcJhzxVcyiYn8JPZCLuJHjsaZ2sZu9sb5 6hnn+llGMoLdxtvHHo7zHdvYziYWU8NBsQeoZT/7CtleTnv6cLz3YoZrr456 NoqhNEh9jTE2clsR+R3DnVG7U65XR50qj5qR6tpIY/anAVcyIs5GOiO1TI+9 WBv7e1XstynFrK6m+jqb52PNLxayeaT5HMxn+asv9ux0ljiHejFWbbznM5bx apyrdL4Wxj7crv3rYnYWd0TOC8WsBp8uZHUmX8zOU/o2PMOwOFvp+5Dqzmxm xbci7Y0/+SOf1cJU//5iF9/wezwri1p+JJ3zWOMwno7v0GAmxDcifbuWspLl fGE++4rZOR4f+25AfMdSnV8Rsf8Df7T9iA== "]], Polygon3DBox[CompressedData[" 1:eJwt01lvTVEUAODr3ttqkJhVSQwxRIgHsxrbGqqJIESQklCPhEdp/wDppCXp A9KYWhQVEQ9eiJhatIipGiJaY4IEf8C3c/bDl7PO3meftYe1J1cc3HwgnUql ZpLLomwqNY+5LGYhC5iUSaXGs4oiiilhhb7lLKPX+zuWiqcykQlkeKX9JY8k 66aTNxylg3W+KWUNZaxlNe36rnCeNq5ymfn6ZjCL2RTGOV/Q18IZztEax/bz hT4+84mP3OQGd3nAfe7xlMcx7uJJnHORHCsp5pn1fMgkax/MUAaSRy5ZXmeS tafFKaYxnU5tHWE/uM0dHpJHPqP5J98fcsXHOUYDzdpO0ij+6vmdAvG4eEZj qeNa3KtqcS01/JX7N7+4xQiGcTbkj2fRQBOntbWxnR20c51LIS/veZNJ1tLP Z6poinMINVNOJc/pjjUQ9uQtL8I65R7DSIZQQH6sgU3spYLd7GIjJdmkxnaw k3LWm28payljSaiRdDJ2P9/k+kQfe+LYUKs9cS1f2JdNxhXG/4T/zYn/GR73 qiXUGBdpDXM3bhTD6PVdTzo5uxp9tZygmVOcDndBX5YB/PTtD3LER/Q1Ukd9 HFvNoBy1lZOcUZhDV6gx74c8q6hkSmjPJDW5ja3xzm4I+8KWbHKm4a7VUcth 6vkPdHR7gg== "]]}], Lighting->{{"Ambient", RGBColor[ 0.19699838300000003`, 0.252204821, 0.33320940200000004`]}, { "Directional", RGBColor[ 0.15473514000000002`, 0.21284718000000002`, 0.29811516000000005`], ImageScaled[{0, 2, 2}]}, {"Directional", RGBColor[ 0.15473514000000002`, 0.21284718000000002`, 0.29811516000000005`], ImageScaled[{2, 2, 2}]}, {"Directional", RGBColor[ 0.15473514000000002`, 0.21284718000000002`, 0.29811516000000005`], ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}, {}}, { {GrayLevel[0], Line3DBox[CompressedData[" 1:eJwt0L0rxHEABvAvSZzO6y+2u27BeDa7FMlivHSDsp7lLIqbdLok56VId5Mr io1VllNucoNTziJlYLD4A3wGw2d7nuF5UitrS7mOEEKWPnrpIc4kE+xSYIs8 62zwpbjAPHOcU+OYI07YZ48DyhxSYodtihTY5JorVsmSYZmxzhAihojRRTdx xnmTeaVNiztuuOWHXz754JsUSUaIGGaQd5seafBEkxbPvFDngXsuuKRGhSqn nDHLDItMk2aKiFES9DPw//kf9f8tmA== "]]}, {GrayLevel[0], Line3DBox[{626, 628, 660, 661, 635, 633, 634, 719, 721, 781, 782, 862, 828, 829, 819, 820, 842, 843, 896, 898, 904, 905, 783, 738, 741, 746, 749, 769, 772, 770, 801, 799, 797, 809, 810, 920, 888, 886, 894, 871, 870, 872, 931, 924, 922, 926, 725, 724, 680, 681, 688, 689, 690, 910, 909, 907, 911, 916, 915, 913, 668, 665, 666, 672, 626}], Line3DBox[{1000, 1001, 1011, 1012, 1003, 1004, 1009, 1295, 1294, 1280, 1281, 1212, 1210, 1211, 1197, 1199, 1284, 1285, 1033, 1031, 1039, 1034, 1038, 1043, 1046, 1044, 1257, 1255, 1258, 1240, 1239, 1250, 1248, 1254, 1270, 1265, 1259, 1222, 1223, 1137, 1139, 1142, 1144, 1073, 1071, 1065, 1063, 1082, 1114, 1112, 1108, 1110, 1111, 1107, 1106, 1105, 1096, 1092, 1098, 1099, 1118, 1119, 1124, 1002, 1000}]}}}, VertexNormals->CompressedData[" 1:eJzcunk4lV/7Np5EklKJVDKUMRkalDJcQipzMmWIEiVEGTJEVGTIUIYUpUyh lFJSdq4yZsgQO202tr3tbbYrITT87o7j9/7zHsdzPM/3+zyf4Xn/uo+9LGtd 6xrO6zzXfUsc9TRznj9v3jwprnnzOImnd7Pa0P3KdlR8TukOk+pFs8poRsrX IfD5g8ZN///xf7Tvn23PX73v/xlX+r/880ef698d/2dx/KPP9c/W/5+O/93s /3fX+U/l8/+2Tv8u5/qz6vpfPe//1p4/Og//bL/9v4q3vv9h/Pmf4u3f3Z9/ Vv3+Ufjzj+LyP43j/3TfM38RTv7d/P9X80OFv4i3/Lfw4T+LX/1d++w/w/// lrj8t+D8H4Vjf9c++5+y/6/Cmb9Kf/2rePt3i/t/Oo5/9Hn/2/Pq3+3L/6/r pr9Lf/l/pR7/W/nhf1s+/Lf47c+2/8/C/3/X/v807/274Pn/q+N/NJ//q+ro H+m7/5Sd/2d95f/h+n9Wff1V9zl/FW7/Ufd7/+o6fxT+/Fn3z3+3+4p/9B7z PxXHfzdef9S+f7XO/U+d6696//VnvVf9n87/Z/fS/yju//f8v0td/7vx/Z/e z/+790L/qfG/S939q3H5s95j/rP5/+i92L96D//fdh/4364r/7c89q/Sj392 f/ln73n/1br4q/rmH52ff7Ze+Hdx4D/dX/4u36H9Xe7T/uj3I3/W/D/6vvfv ss4/y+e/2/eif7c++3fjJ3+VPX/3+9t/dI/3n8qH/+13Jn80j/pX9eYfrYv/ Lvn/d+Wrf7Xf/qj6+qPv9/4q3fSP5jNr9rpMz5LBdY1q2Y2FTPB8Ya5v788E K9Yr5QYPGlisPJMTcKkXfDgeHFUIZsHJ51IcdxeUQW10RvquoFFobKSfUTxK hZ47FsoXxMmg65RSe0eLCdShoNxFZ5lwyj181SY1Mtx6p9IVY8CEzQqZ99Kd meB4vey9djATxnUmTud6kmHx0oF7ftJM6HPefie1hAntQk7XPb63g+eCLOsS HiYkXCtXCI48D67PZk3YJWywCTt5y23hG9iZLVQscTUeOsf2Z4YdZMNndMzp WlIPBwbbBbp+smER6s3tlPKBpzcTyHttE7BkboiSm02sHxq5xS+SDHMbHaoa pvvBL0jQdtKbCbbWizZ8/tIAlENnI/Ues1B3dej9ky9agaujTjHDpge7+Tic GK+GIX8oLevZLzaseMejNd/oGCx7tPhJUlAoKjD3jr66NgrfVDOrToyRAD1G Lvj2d0Fni0W6izkTux61HeP1JmN9w8WbLcZMYO+Q2W1hwUYu0wViVa9u4hEz 4aUJNXWQ9GA//bp5NwqZv11SvGUQk80/7Dve342irBPKrhiPO559U/v5g40X WTdsoxQSMIR2P87gTBuW78ipGp3PwnL8Or5UmAnNn+WNPc6Pojar1lxTmoRP 7Jfa3AMqHCjWk+O8xkZx2xpDbVI0ZpOWb3D/UAX0k1/fLprXi0f0JtLtZWnI emVa9pTKgu3TmmfWS5Jxq72d7kM3Jlq3PG/ZRMSTP6JMLHt+Od5M4eaeTBlF w+Zu7brXXWB1cLmirnM79mikvthTyMSHX4JljHYwwbni1YBLYT9O2zu9bjrz AWHWx/pRERNObtnvPk34Z+W+/bP5x8h4VNvbjXqACeLLqn+JCIbiwtzVm879 YuNpLvs7006h2NkydOXtTzZqb9vN21ztA/qNHkb53Ql42ME1/tXLBHx1PexQ 9Q82CEXr61XxXcXblAqzYuL/pTaebTW5dQwc7qcxa0mhaBah8zVzHRvtgo6d UYu7iVeoRS7BT95h5dNjD9uz2bja7QDXlsZorGDwC235VoFPN3LqZ10IxYSr t5b5EvEXs1MZS2kLxbaX23ZdxniI851NvhLGhuM/ThzKM63B4Zfhgq3Xz0N1 lG3DoRo2KCis+lqpVY5Lv1uOvlYnI92lwHXAkYm31FTnaCZMeJ64aNn+573I apnb6reZhlvDb31acJ0FL2SN21dwMnHatqkpiEHGbK81zW8vMGG4abtxvv8o iolXJXwyJKGPnfmDIGsqnJM9GalpwcS6fT3acfZklNWSO2l/kAmN+ursiw1s NKk+9s7jfSBesb3OlKOToFpava181ys012289v7SKB7If8DaLkyF+UFabhnd 7VjfWn+GGcbE4QfqDRv1mCArprleVtkL5xS403sIv6Y5PLC9fN4LZ7+N/Nob 6AnuPB1RsT1suEhZuuqV0HOcu/8odMTFCyk6t0q7Cb9lC11St3ruhSGrd4nk S9GA1KBhJZfZC6tLV8RRclng3aU0O0qsu3i7dKlUlDl0SvHkn3jghbY7NOra K9loXPrN/EtDIMoFaM+0jpbjldvOzWPnPWGPx6jlnn42lAnRZiu5noErr66X KKkMFkgp573wGwWVt85blF2psG/WfeqUKxMYnjIcok5k4B270PVYgwnMCzMG t++R4fwGNcYBJSYEl24S83Nhwo1+ce6f4UyYf7CQSZUjQ9+GvZzSxN9VBBdv 8L4wSuDlEckLRSQIbpMvfbmRClc1etu095Eh/kqICtOUCeThSrWF9kx42qmv O0ac/wynVtxPR3OgaFu/borxwhK77ptfvg7iq1U2PVUCjZgevzVApYKOqZvS YzRihzBgFfleIdbhQAF1o5wsHVdeef2ELDmMD+48edjpU4tN7/cUfgvpw7xl g/URpkxMlEmXtjhIxvF54k8ybZjIvOQvLqA6iCfzD3lNKjUj0m+WGJxgYOrh RJ0L2cN4WVC/3z2gGqk7T+/16Kfhk9BLjGqPUWze77ar14mEFtYXZbIvULEp MunbZS42xmkdrd6EtzH07tFQt03NOD/0+coPt8bw5uCmgWKVYhRfZl36+E0H 4oDPsnv2bHzE3Xal+0UydjT05n5SqcMHmf1xtXLDuMvfS/yUZy3WCSUfWujf hxw/zPbHOY2gtC6fw+CxCsyWKxJc1tCLLluVdMtWj2DXsSaBR1mVWMgl4jSp T0M564Bdlk4DaE9jKzupteLz6B0Z+cv7kRx794Dv9CCmf5F03rCqEc+Ic2yM LafjCbMXHA9pg2ijapv8OKYRs2GNaEMrHUvP1Z3MShxCdvlKa9/COrz+Idaz QpyOmTYrouQ8R1Eqo+7erxMkbOrvU6o9R0VZCsVXy3gcu+YOyz8rvo+LvaYl rHa348Y9xh2SRmPYIJy3eovHM7zruyjshywFrXK3vrr0ahx1K+TvKRVl4bfH kumDaa1Ij9zou69/DJfEjkw+qivCqNN51gt9P+DpUokLD7jZqJCv90i1/zZG ryrYfnd1M77aNqjSRdgjath3J96NhHG0+aSPAVREsdzilO8juOsL49jo2tfI jti6YGy6G5/vVZ7JOD6KypKpSza8JmFg2JPCQ8lU3MJeot4fx8aYyY7a3awo fG7F7XRtfTWKHMmX9X1A9JVUcqPN3giML/8ioqhYgcXX9cRFQ0eQ/dJp09Tw G6S2liifDujF1sLc8KNf2FhfFDZn12uDYx0Hmu+FFGKfKMpWfWWjTXDuuUWh FjhHZT562VCAW9R+ymlMs1H/ySH98yMHcJ7mUsnkgnu4u/draMQBJjrO1XlM E3k7f2cGPfAQE+NkA78omzFR2eNOspM5GVvcpO49s2aiTXPcC5+yAVxu+aR3 zdUWXLtt3D39HQNvz1/T/HSWgU+k5dcO8H1ErfDVz78NMTHjC42Sa8jEtt6s +M1Ef3mYdkNsP1EXHCopK933MzFEV2J91BEyfh14kSZ/mImf+TjnlWrTcWdC johHUBc+b96br+nCwgiMFbZsY2FWgoGoj+V7XPY0uLfsbD9u1BmxsbpGx/zT H6wEKZ34wz03e9aChUwhBmXbeB+efVlT5qJARd1nUpo7vVm4VUfy5pJkOt6Z /uoo9rETk1yCl3Cas/CWx5LwhbO96H+08YMLDw1jjHd+rE1noR9di/H6Ew2T xdwWzJPqQad+/6lTSSw0/uZclTg3gAkPrxlTlrSgTPj3LRvSGHi3r5/fx4iJ T9rXtlEJ/A//KrlyhS0Tj8j1qucEDuHId56MRLl6dCl1/dKoSscLApdy9lQO Y9VzXrmmgSo883zfhSVIwz0334xZuo8it91h6fE7JPy5PrIo+hIV/TWVZVwq +3CRzRmdhyFUfPPkbMGNIBbmoIOPrCIDJZwNhH5mUlBK9KWwugILNadOFRYQ cdQ3HH1fRMRx2fqsClkijpt2X5nmOsjEpM7O8mFifGQoXBCtmKilVsvxXmIA Tx73OsPzvBX1HeMivLX78ZnAh2s6lv0otU+HQ9SwAx8Gax5+UcdE7Rqvmh5j Jlp9VNWtdiRj2YwAdYxYX0PptuuQEwtX7UgPc4E2lHh5b6CP1I/KPlUbFA8y 0G5ndWWpBQVPGtxatX8DC+/msuT2bx9EEwUDnQ2yzZjoOthv4sbAZNP6jtbd A7isorZeMKQVH3DpbZfY2I/2yc4XJUeb8PFWs+QynUEsHs6PuODIQEbiT4XU oWaszu2Nfjt/EHPTjWs8rjMQvjVy7/NvQbHMj/1VFQNYGR5suqCegdxTa1fH 7CXsttB7k2DHxBUa0/VRRD24zPbLrXdoRE6fcrEE1iDeaBtfvLOJiJdxWADF iIxyLXIVb4m4ziRFCCCB+y4WI9y7pFsxeuUkvHMdQO56duG9pf3o4Nd8dkdM HbKd/cH89hDu3b+Fdn8lHb/+3PLooFgjcm9aWhMyO4gMi7fGpBd0DPUp7zG3 IqOl+7GCxUQ8bvycHhQl4hQZMO7Gr07Ba2I3IjWcGHjCYMfSqyIs7FU97CYo 34YyxScv559k4cQqLgWDl/3Io6p1XTmeghrRpdG22xlI4tSZpsizUEU9s5Cb WH9H5oXaEUsmliQeOWJGrC96s88kBDrwo9aDl45H+5E7r4dZ9YaJR115zl5y a0X+0JxdKXsJvy3llQiR6ce7S5RWj7xoxYt6/m+NpQbwbdmLVrJGP/Y1bfZ7 ZEJG7fk1lUeIOjdptdd7TPjzyULVNEWtauQq5bdMeTqMq22Fll5spqFJPu3w 4q0VWPvwNdPZawQXX8qt6crpRUs5qumbiSbMtcy7d06L8E9uAncLce4X2fLy XTtr8fGXNe71SsOY8uBZbbB3H5Z5hLmZH63EbkHdhXziI3hiWZKq5R4axod9 MWiIIyG3L+gGnh5FuSIJfbnTVPQ0Wflg/sMnCCeX3nK4O4ZnN/gPvyvpQFGT +P5fzQU47hBwx9d0HMVdQGVQtR2tL+mvOXU9Efnvb7V7fJiNApJ2j7bL1iH9 xHaXpJsxaEWbddoZz8bLL512+ApXo+DsIrunt0goFdt6bA2xrwpNYN4LYt/u 6RVBAV8z0PNS3/AVos+0nrqx2GhVM47Fux5P0TXFU/EB/T8I/vUi8Ni7Q0mm +LQtri5ikT76bA7M/UmMa325HqMcpY+svBk9vxW16Fd5p2eB+jAqibcl2x/r w+dvxN1EguswqDDaQTpzCO/yX0o9v4yO1/Nmr73UIqM0PfDNawcmPrBJHeIl 8tagd/kBBX0y7g84FJhC4O/L3X3+nUQ9P8uPfSAj3YixPF2fLxH5Oa1RM8RP 5GdJ8mEpe1cCh8I+e3C860M/vRvrMZCFo8xH7dFvOlH1w2l22W06NoqmfCo1 Y2F2FZfxl6U9eNdi7UPFORrGDl7dMJHIwtpZDZc95Z0or2wY03qLju2R/Wpn CRz+4UZfekvrPcZ3/pAv7Wehe+SSXwqu/Ti84EWUvGMXLozt3pJuTMfNfvbv +46xcCWDy6iCyGfpu/z6qkS9xA0o9n4g8O7xbn17F2syvlnPpRxEjJfrd3Wd JMZXZS0s0fjagSX8U9cdF/Rj53AgN2uAids4z1ZNIBvDPmo87Fx/Hp+XFUZ+ YCDO2zPsx/ONjUFVP90OlhrjmHuJ1+jVXFynvveQ7gwbf009HKX06WNrV9WX WcxGW461Warf63AFp2S+eugQfrx3KpFHhY5iTe0LRWfeIHvLD5FrF0bwB9g9 6jjViy0n/ONff6nCC6FWEaTqYRxo2hK9+yUNT78s4bS4TEJSqYhKAZE/C0Ia zfu8qCjUiTfrVlBxTP6xK/9sH56q5zZceYaFl95SnlhoMLFvC+V+uDsZTzXM XfE6zkTYb7sraKIXw1Ou73rLT0PLxOBtXTdYWBoZ+Y26i4mXWFuvXz1Pxup6 pZF1zkSfPpm15YYtGYcVj86vI3A8eYPGdRMiTxQ+c7teNmDi4Rfqk7KmxPph sctcCf3U1vU4/NJuJs5eykpo3E9GjbXuh78QOlXtilrgNNHXBfv2mx0hcJL+ 4QD3OsPf/HhJPbW5F91cjIQ2CRD2ZCSk/spi4UbtO+4WixkofyNesIlFwZlJ l8aoHSx4WtHSPazMQAWpV/sf5lJwZHwrqVaOBeNyUmv7jBhYen0wz8GBgoZO yRFSUiy445lqwmFP8BCtvQblWhTc7R229bE4C7pMuwu4PPvw4CKPaHXRbvyU W9l0KZoF2hKP9WjW/Ri/dDOfiEkHFj1cMRNUwwRzSZf+N6N9WHVVOMFQkorL W/ya1c6yIP8hR/1qZyoqUdzyLOr78I7r64FtISyQ3PchqPsaBV8ZttSJ7mRg e7qAu7MsC465rKx8fK0XY5485qjZSsPzdm/NN2ayINB2T7d8GwU/2dxWihRg oNHMp9kd21mw3EA6xOAzDXcMnTcvXduDRUvf7BIjdKh99wvjgC+9aGX8tDJo Pg1Dul6WZ2URfjjW/DaPrxvFdANS1p7tw+uRrsyxKBaEMC8fqOPtwV0CGd4m MzTEV3mPXqWwQFFgvVOM9DCmefb9qDtZi+KPHmzTDu7Dd83B/LazA1ias2+/ yLoWvCbcczD0BgMfCoudoxJ48H7V5at6ZmTUTyhJjyf6JOnl8RyJTQys5jE1 Un9EQUeDIz9PE/1lw/FW8e37CFzZcmFykRsZnYtuq/wi5gfHSNEDCB51Q8s5 5+DGHrS5TWdRr7HwoezVxFTXUaRQg1YHmpNQwDUjRi2JwBcBmtYyBhvTH85l LaecxHe6NpYmQc/wswfNUQbIOBGgGvzDhYlDxWvmyxM8MpESlXawnoSsRAvK LMHTl9XnBbt4E3Vi+tmhUsMRG+KnUqcJ/NQ+ym/qHOuID3Gbzhzx2/vEyE6h 87owvSQ3ViPbEVM07jN/46+m3DvBXBM1cNmyOfXxJkuMVis+Uc0k9NcuXu1D XSdRed2+K6XeT8GLvNXKms3GTPUnXBzDR9CbeuzxceMicOo40vobr2mJIwz+ wG2g3ScjJXfHFEPWuGj+IsaffaCnfHRUBu+CS4djU/Uxdf3HTLMJNm4+oTgp TbNB1w+euqO+D2C0XmSt9yQbjx7n3Hye4POiKebCzdP5oDijHr5KgIpL9/h+ 9f7ahw/uUc76+7FAP/BDnBQRJ4rWIY6LBO7N3qhymjjIBPYWOa4y9Q6M6VyR 8NWhH4+vPR5SU8WEvZfNp5drUxCUVK2DjzAwV6+64agIC+6e7mgr3EPBWK3G 7lminuru/OQ7JcqCtxEDY+5DNMw8U+3tKdODlyylb4kQeLK5/byB2ade/Czz ul5wIQ27LXhOS95l4VLfQW7BhT34pNvRrOQbDQXnxlluqSykNacE/PaD6/UM YSUDeRiSrry2XE4PxZx1b/0eV7pCpp09JgMrdd+WK/3Uxo9KnJYVU2zcPvz1 1C5CvygfSmjWNc6DuHYK9xkCn1kuQC0l8Jl+8I2l62wOPOR0e/p7He7NNIHY s5IwKFixS+y2Fi4qXWJ1g8DtLMeqIxJ0fZwWDXluq5YNN9M+Vx4l8K3WUdrs 53Eynmwzzkm1YQJp/VSL2SYy9qWufrvXlYksvolVcb9xcFefkPDHfPR1IB0K IXjC+KPztuUa7bhJbMMVLLRAVfv+3d+J/asoNZd5hS3RQepcXQBHLQoJNgyt 3TKMhYt1Rgp9+lBzcq3A1o/N+ML2bcl2nkGcN+0bHnWNgUfKZ6RLfnXj1SUZ 5tcW9GFewazAl6ssDCcfTT57iIwLXKjJw0R8Vezjv5YQ/CqB0aawKIqCWpV1 mm1qDFTsDV1Al2Xhr2UqY5kEjtCUvXHvBA1zrFfw5iezoDFYgR6wkYbp21Az hOBbEnsdvgGBS045zNtlr/twXZjy0eOBVNTYlW3Cf54FCRf3WbcN0nAEblg/ 29yD4raNPhIEnhg/lTr5RLYNF+DUbM9xFv5MOlpIfdUPUzGX9qV4tKKD9Hsd G/0BjBER1KVs6AcLXscPsrpkdOS8mORF4EL+bIrIBTMmhLd5UHJzW1F5+rDZ 4Y0DaFCgo7VbvR82TEbOpn7txVXP7TILuWh4yOi72N07LHi/+Lqwvh4Zjzaa r88j+kvzaa/RCmKdqsvyBmA4jiYxG0Ji0+8jb/mTqBajdpRjWT4aHCP6dVTu 2y1DRzCTa1K38GcRbq8eUFb73oT5C+4uJBM88/FCdkfkUQbU7xHcOXu0ES9P Kjawhwbxc8NEiVMdHewnIrcwA1twx3MBw+iaAZw8fLDnUxUDMreLvTiwm4xP FSIbg+yZOPzpzV15wp6LRezUONlWjOmGF3PuAygyb0uhF28/cPVpZa+baECD JPlvKb8GsUY/rWXFczo432jiOh1ZhxpXmS9i0oZQbyu3X5cwHaby5A63Ejzt op7i/XKiL9vl0pZcMWfC7kJxE28LJvYk1ZpqE3zn0vtTi88R40nfg5p1iPNE Qc26dkIn6VzxHK89xoCKPVESlgSe9/covfZ3IeOktFU2jzUT9PsfKhV0sPDF +nyr8UPvUXYPv5fYmX5I/mpES7g4gi92nDyoMvYGH+/d83mpRy98pXm2eM6M oNm6sIm1a17jl5xSv3HOHigPddsacmwUR0Q+mcxQSLi+7Yiv3B0qzJRF7K85 M4qtZnk6gadIeKvXmvbTgwo1MbOzdwn8P+94ZvO22yTM/s7hFxJPhX2+L7d5 KA+jxuqt6sFKtai9WGe5i3cfjIe3Ji3+NoC1m1m85xa3oP+2EeVPGQxYKDbV s8R7FPP8nkox3EkYFzpTPeNOBadbq1L2mI6h9TgpO8jzGT6rqhTYu4YC+cVC GinHR7AwYZP7reMVeN90YWolqZfAiVdLT5iNo6OEWEKTdwEujiGdElVqh8JL O3nHcBx5M745vHychbs2FpxaFNMKdTeLL1/lYWPBK+2ba1m38cupWAnDuSYi T85tbGON4YRsiuu6hiIkW5MWux7/AIs/Rzf7EfE6ZU9WGiR4q3AXVSieiBe5 9l6eDqFLy5R4NGT8WvDkzdaaZQ0MoLjmb3GbZuDnWgmOLzwfsVxaf++ScSbI 7bt+Sy2ajpKP3kTuGujEzsDoe77WLGjN3jFiNNWHrykMdzkhKj7s02lc6MOC pbYyEc1pdJQTOb5BsKoTKTbxfC7mLLi8oEsygLDHT+CW6APCHtduzrdphD3e fFTjX3uZ2MsLKmQPMi4+cfT8BTsmXM9Nu6sCdNSVObpCyq8Lq2S1ekpPsqDk Md9FL4LvHu5QuL95sg7nLn8zd1ShQ2NzTHRs9yAWPjoqvDayEWOuHgjX+UCH Te5Lna22DiJfzcmv9qrN2Lw3/6CNBwMS+FrFTWuGsTo9QkdxuArn79ZlzXtJ A9MwbsWclCG0vndcMrCoDptTFDaACB2UPoSuz3Fk47mAoqdD16/hHYVt8soL 6mBjOom/IIGNm1x2qpUMROG0YsZR3m9VoGLf2Gu2iI1Xv9xawa64jeIbQqXL 2E2QfOjqqltE/oyFvXR+6krCRQGZO9knqXD7yW5V/swxDCsukTqtWoxpkrvm +TzogKAUC74U0RGU2R31dOu9SpQ/JhOYpk0DieF9O3YnDqGDLG55VV2HJfs+ pUuJ0eE99cW9+2uG8eLW7W+rk2txbg/Z2z6mD2qD+6xWE3pZ3rblM4Woa5m7 CSIORL+2obaHZu4h40t1Y5OFhI42Ex0WiiPi8v1jYPX6b72EnyMeciwmeKK+ nMrNNBZkbtFvoTh3IanC5sUJMzp6XbM2XeTIgsSkbekUQn99916js+YHDd2D boVFXWNBvEmT4rsxGu7p6u5TV+rBL74qzrsSWaAWNKqyjeDz9fsypCMCyMix Q1rT0pEJG9mHp4LmupB3QKNFdj6RR8u8YqlnCP5ZlLSxppCN25IDP+7dF4Ho 2vjWfFEFxA4cEph3Zxhv8cXeqPetRoMLL6xaR2hgdj/35vRrol4evQmhbDiP dVEPJpmZCDkTH9VohM50Cm4ArzWNeP+i+otHL+iwfGEYTSw9BjUXWEf/IOJ5 qDvk9LzxKjhx4VrYkNpF3MzK4dz4kI1Lvl926OWoABHD2U9V7wuQmRy29/rB cVQM3EvlkW6Hup07lrO4s/GDp756yetxVJN5ncV5qRVm51SXvS/eg8G9X/h/ 84UewZbWXaJ62NRupEu7qY2V95JMfo+fPBO3fvWUNk7Ub7f42ROKr7IvCYi8 YePhJYKVy68jXJzymTh/PgPT6+64rCPya5mK/3nRT01gHT2hy7FPCxufMf1/ rxN67Jw7+boWrpGVsCndUotByiGX1xF84IWvj1aqVx8wuzbZ3lSvRo9CU5ZQ 0TCmO7Psxj/QYOvKsciydw14Y2LU/MmCIdwzpHr2ZTGRV5stWQ47yHj5stfD 9UcIvXYn2vG7KRMCtkYo5s40YUohs3/NnkEUlTwkfdqeAfMLbDcmna3D9pny lSnpQ5j/TORZD9FfyGIf6c9UKtCqzGfkpM8Inqp5nn/pei84vIhb46VRi3tW dGm0bx3GmCnnKHGPPpg9JipeUPQE9fWkjybnjOGqZdc/ptztAJb4lc/1zpVo Y2eU0i85goKpyUo/1Gmw+eXqmqJrJBxWcC+39R3Frbv0ZByOUOFFbZLWSY33 uB4XyT+jsZDrYstHp1P9wCmTcepXF2LWh872ac5RLDpXPedN74atMt7zGYRO iNl3cGil/yjGBlvWmtpQockk08t+7g1yDnz6OD9iBO9uNZz0O9oL/j+E8rSi iX3t8+8m+oxiRebHw4ucqXAv5Z1OYWUnGmZx9yXdpePJHMXqpyYsyDZqfhfy rQMPnDErGl/Yj/oLVpCDGEyQHxtMsNIgY10I+f3nw0zkGZn2fHKACe3LzQ/m jzfjKwO+i6ncg5gVExKifo0BV2+7ph9IfIZnnltc6TowhukaK4s+L6OAo5t9 5c3RIgTOvF2TA2MY7naeVuvwAY5cvr1A2nWA0P1lAkzJVkwZ1HxRzN8PdMqN ajeiLi6vOVjuT9TFa4VNevov6fA2TXq+2BEWzq9NdZin0YaMtL5t3q/7oXGU j18bBrBI40qs7LlW5I7NWhGq0A9CT1lyZYSOJ13y95YmdLn/4dCPM5ZMyEuP MP+RmogFZhtuKh8heLRPltmmqbcgruVibPctAzMuSDSb8bLx/s4lT193NgFd oeRUXBYJL5GvWo/4jWLkXRW1xYT/VxXaNQcSfaRth8rOsN99zWvfx2wCr3bu 82m4KjmA75IuuG140YqaCpWpFM1+EIyT4z9HzP/q7r70CDH/qoxi9n1i/mOV hdPP+ykovlrD+fUSBppuLShasZ2FBdfGk2YWUbFMg6lCmenDFfEpofN8Weic bbxTfVk3HuEXn9kd0IfFMtcERS6z8M2LPd6fNCmopiFgIeTAQKRyHz0qxsKx dVxcjZZkAgezu9osmbhpfekP/4NMPO7H4Rgq3IMnS27kGX2lIYO6vJudzMLb 9ufkYrkYmJhC6zX7RsGAxWv4juxgYVBOd/CkFQPXNwsv2W9KQantyuEF4iw0 WB8gL3+6D0NFes3fS3Tju+rNy4sJewTOSQ9t/NKHhdwyu+TXUtGbeTummrD/ mbC9uv4oDWfO2MaekOvBeVUzE8YpLAy8MpUgcYCM8eWmhpMEz49tLf3+hugL CbeVuP0KO9GeteNacA4dtUDVdtVBFrTM1aiX/KrDN8el0vIvDhH/fy9uRIng qyd8MrnfVOH9/oMVqfXDaNamQ7IuocHrrtVfua4+w/0D8ydJxmN4ZUdTZrYY BTtv+Z2WHynCrx5uMu7MMbzMZ/LhqMcHbGixGrfgysblfg6NJuXjKGwvtLE7 qRWF7k0vSQ7OwNOBG0t2LmTjldG+eSeXNuMF96PK13oR22XaVEUWjqLtTHq6 24du9Ju9kPDjAAmD7xzskSdwQChh27FNLlQ8aoZX1hF4rt7CvbLzARtdruoI FUhX4CmNquaPkjTcHrN5gfnTXiS5etYJELpS9ZqeT+tUL9YUHBbOX0DEy3Nb Z8IdFp7dKdKfcLcXDRm8DRsUadioYSfIQcw/KZXz0IfA7Tx3w5/CRP/ZRWlt Ge5AZL5b17Z6OxmjlitM9RC83dWWTyqRyMMFxVcWGtGb0SRLYvcH/kGsOLXj k0QkAyRr8zvCVhN86NTOMgF3Ji6w6dVwNWKC5tGizVd5alE94MBipV3D+Ln0 YN7E8T5YclHzvXt3PtpLp0ii5TjKGptbcgu3wzbZadaK1T044jxg2Ejkm5F4 3jcHQpeFFznXalygYH24ivCz7Qws2UAK1lNiQaVhVLa7AhnJ/Lum3x5j4koX +V2NJkz4sSAeMgd7McwjZLc5L6GvlRrXxN1lQci1obMeRH09vF948yOhC8JA Yb8dca6voztCuGUYWEglyTrnUfCrhnEHeTMLdBPdFhhMDOBF/hoNe+EW7Kg1 UF+TxYCZd6ferfhAwtf6jorJQaMo1bcvUUCXCmGZsadu0Gh4L/ydaqVODzbX RgtrEnrQP9dCyeA3vl+04ZR0JOGT4asfGo9RIWgtZ/URwh6B0QpfLhsyLrpw u1iEsOcUZF/bPtCLh3jnl34TpeEXvsyxwwQPIY+9NXm8iYnqiTV6T9LJuP59 4/NWNyZUdkRvkiZ46e2znhNufmTMuVrJ2mLLBPZS1zc/95FxpVjX4UhCD5pL WI+oEPrrV8kGVqbiMMpxsGZ4ztTiK/K2uQiizw6LnZSLInh+9v7BjH2Z93GT 9GElDtl2yNWYcd8vMgL2uhbzHt2vBMmGO1Or9WhocuD5fI2MMeha3z97yKgY PMRCks+/6EBlz7AP2l6jwFb6kFpxjgRGS+YeypylouD6der1d4aAaUUyvOdV B9810nUjBOioukQq8JT2MHxRndLUm6mBRzoBPyvt+jAsQcM/oXgYaHdXXTys Ug2WZ78f/NFKw2cie1pjDrPh3GH3uQz+REgQ5kqv2lSH3pkLfxpys6EkaJXj EZMM+Jks3jW4rhmfP++aETMdB0tDx5iW9AKIcRn7Oa3WjtMHm8ok4tnwavuH iCXPoqEuUfz++7XVOJ01/vseBsq5PZq1teUB1FIH3kvoIUfvj9/3VBDFcXjA zUYZ9E8k5YjG6WNJRLmQOAzCRMtHw6yRJmB3dP0yc2FgiJbCCv6ZQUi9dE3g 2ppG4CAv/ChMIvpqTb3ME0I3nL//6GWYHhkK9KhRBQeYGEIWCstyZcIJu8kf GVvJELM8t81xPxOtT22yb1QchqzeecsyNtdCqD9JsMC3D+9PhhwxPzsC2maM 4zmKFUC9Pk49HteLnyvTilsJ/3d1Ce69HkCC6ZhlrmK+VGRc/BxQfYwMl6x2 VxkReeAsHKJ+3pyJCiaadn55FEg76xe9WJ4BqxKU1a0VWbiwm1Nl8gwZQhPT gpUNmOAoaBXES/BxRrZrPV23B7Ze4B69T6dBQkq08oEkFmYJyGeHfqIBj5Xq tssyPbCXFLKuNpGFA6cCJ84toAEp0vvG0vFeSJWMjKrNIua32NgbbegBrwMH 00njNChd9UPuIoHz2iRhO20+GkxHgoINuxfMjzvOa73FwqJOO3Tk6INU7gNS qXPd8M35oUQp0Y9WumippVgwYe4i5+VyczJccOVav4uoq9mppd4WOxlQvDE5 d3k4BbyMXxcqbWKhU5fZ5OR0HwzM9hk9X0YFcvDrAyd8WPjjabzIHm4aTIan rnn6rRceRD9NrLjNQs4YOSUvWSrEXZyXFjvWBysmv2saEX1KRSf6/U8iH2wK Opdze22D2kXvs+enmuK3J1PXww3psHR7FMdX+y4okb68RPc4C9XiCxUt/bqA USFotlybDm+YTLbFCRaaeo6A5vkhaODJWMc5VQcDGV3Bs9vp+PDV8cj2sBEI brjBu/rzG1jzq84s6UwvRgVtnOrjGQSazKjuxrFmaLG7FJUUz8Dug2mK6/YP gr6Woj0SvGSbffvz87YM3GeAZaHMQUgXEd/ucagRWs+d+ybXQsd7n66zVRgE voa8dtHUeA/HmfUNGW79+HhJFl4j/HlgSM9W2IIMb/lHZGUIf/6yVp3Imt8P 0QsPvhX90gG5In6xy4aZqOspOHz9Hh0G/DqEjhV3wsqdfbfiTViYuDD3UMib ARB35lpr6NsCy62rxOUbGRg1vf/tRNUw7LupQIkerQL+J89X/CqjobznArnV p0fBtf+CHYc/CbiMo9es9aFi1vRckeutIcjXDFRkh9dBvOs9P08hOj7zzkhZ upAN9vHbX5lvygDVAq/ZoyuakZRW2rTkNRtubKhZN6UUCrEXO2+L/v4sZdna 3SvLx4FcsihvtCMLhDoLXQyut+KtjT9k0h6w4VbycQOYjYDFm3iS5OUqcKhl uEXHeAy4YzuqTgQ/g8wXRUms9RTc9jTo930s8EZcvTNkLwNLunMkur9po9zy hN/3q6Ahc29j5BlJkCvxnF18Uws/7n0RdJp7FErsttNimhDUt71L4O/sxlez n0TTfEYh9GyfWYY2CQoFIg44uxJ16urCuYI5BjEjEvvWUYpgn4Z6jYjXB+w2 6HqQcmoUOFRrfLQiSCDT+umtRjAV9co+7awn4iUmKbTsvAkZ9vDl11oQPC4j 8M7mHieiv5WVsYO3k2Gn53SRnzETTfMTJruJ+qI+XuAhUNMLA28bB1j3WbiU y7G//rQDlBgm7qd/YsO6gTXDH1c8wkOj16l7F5Ogh5458frEKIy5vpsSSif2 dfle+KWBDKSXjl3rNhI81eawrtNRJoaJ+hvOEX54MvA+db6bLqhcOB3/KdER I8zMRqeMxkGHwpOgM3Eftq6YmHm8ux0delwHfxDzHUXTLr3TUINlz9u1t4la 4g13+9VO8sNQk3kNVvnVQozjYBo/gXuKNd+qEoKZcL3sihZrGRnsZF+4D2gw sWXR7SoHHzKEfL7d6WbMBF545OZL4JvtiN2te4R/RJqW9v0wI8OPXSJ9qb/v B8m3tR8kkCG/JPaskhYTXm7q9gkn+uRSRptiz1IGFKpI6m0ZoICA3bmoY9sI Xf9R0zx8BwNkA62cr1+lQMSh/JvSG1nweVOO6XE7BvzSTaGf0KXAq1vnV24S Z0FkgbMEtyMDTvOLtq7fTQH1hby97HUs8NSaWRV1uB/mPj61CFXrAE09/thT NUzwVB4NVyf0R21/hM+0KRl0e9WDwgm7SzTzL5G/0uCtcMhY1doeYJ4rE/RO YkEb9bPlWADRt31NUiwFuuHwfJGPKeEsKB5mecav6YbJWfK5tlN9YJKww6Mr hgXKl01LZLlocOU9Z275bC+QE67att1mgabwcQk54R4QPHhOavVnGhiZawf7 pLLgYX5uafxsHwxePZb1jo8KH7NfGl7xZsFPtWsavgo9MNiVKnZgkAZqLTzu 49cJnnN7rD6GkwaK1IgPuhO90LL7ZHhaJguuXvjaakysm0G7t8F0TQ+MJzWU JRHzzbMP7hRZS4XWwwOHDn7tA5WGnfnLfFig8EGi9bQDGapirIftCD0ZGMJ5 q5rwS1p+oqCcQQdc6EmWa7Um9PD22UuptUy4+3RM76EJBcSMf100tGFA6ss9 o/WiLNi779SAugUFvnm2hL22YEDo49IEBQkWnL9jXpucSYHZT1r3XiozYI6v 4oW4PAs2Hbu8rJxOAeefvYWSixkQzM2ZSFdlgY5l/JSsJgnu3t+nHeYxCsJL 53/ji6CipOlScwGLWgjz3/K9W2oYtLiyrwqG9uGpRe8fDAvchtnezelnuNgw JyFSYKvcjE93Hk8RULoP0Rv1znIZjsO6gGu6/gfa8UmtZq/VETIUb9q0uM2U CWf7ZG6Rifp9rMO7445ACwgWMEwuzAwAx3RCWVA6A33UTGf03U0gqEdI/fU3 NljMi9984nIOWhrWH7wxYQ6eC9ZxHJtkw9HB5kVBvAXo3ZPAJ1NWB8tOSj89 njoExwKnHjULE7zr/EfSZqdGyDYTMN/yaRAUYkWOLX1DxxyZZTY95wj/J2Qu i9jLhCJ7ycPbDjFxymu6WZd7EPIc+xxT65qh4HSv2okUBqFXhXnSiTytKauj yxL9VyfjIekQUV+LI4Uc3LLroLOIBPmJQ/BC3nkgQoKOp8jZcmNhjXBope1I Jm0QJGpq79a8p2OIY4iffU8VTKyx89WvHIbJZd82VyANj5+un40Tq4fzoren bwYOAYskoPVmJx0nbJ4IW61ohq7dzb/q1QeBvdy6xMGZgez1ZkdieVpAk3fD D4+5AYjrJ1e4EH4zzDNP7Y1pAb/brgbGZQNglClzmN7EQM278yuPJ5Pg88op rvtEfGX8BYymz1NRaYnnl/ErJBCvjb1q4z4Kvmkdg6RwKvrcij5Uvq4C9pw4 dUIpZARE5q2PGvPvxRkZvtFYKxLMBR6/3uM5Cu7r7mjyBlFxngvowiEyBD5o DXci+H2M/NsrhoR/YE+VJ49aG2iJ+rO6nFiwkX757cSrfsy4fHtDy/ZW6J3m dN3vNACbg3Nqi1f0o30DV+gNAwr07+BJ5rFlAKwOkzpA6HeLqtnnzNsUqA4d GJ9WYMDiHzWDSQR/mxC7yq3iQobE2GgFFqGL7Kxb5KOJvLqyxiaN15UMCwfr zTsJnPSJiSruJcZ/XLp1KJGou8xtrcaphK7eeUxF5gKBn189Jxo+ajSCf8HU pOXkIJw+b/GW9IqOic6jMq/FeyBJ2nQACN6nnpmeuYvgbw70a3oWDZ1w2OHe 2sRbdOjU7Gp/bcrCBVOLKAt5PsKT0MRM61kGKEw/rswcIfhkfovu/bZOePf+ 8XBhEh1WHWpRyrdgIZ94yWiR6XuQ+mJzlquNBas47D45BPTjxMx91fkeZBCt GdNxInSm2MQGMysrJoY7iTL32JLBsnvJvvOE/Tz6b78+JPzc8V2EfDaQCg78 rdu5KvtAWXNeo1owC0+EbFcpdqqFhvfFXflyw3DvEcVcKaAPWzYKuM4SOLKm bivtvikFJkNKtw2vY2HCrICoFB8DGOLnPoYwKOCRScto2sHCMcUG30nHfvhM KWXpaHbAd+tWUY9KJlZ9lWi+ebYPDpwG3wD+brin7caZFclC/j1aiz7/6oOx RznVjzmpoP7p5pXf36tsXNVbV3CEAYL1yo/rd1Gg7+bFYmNRFqZV7QiPJepr t+QtuQyCjx096fOIlzgXub0za+0hJiiTG+PCjMmwa8MBHZ2DTHxad36rlGg3 FHBeU50hdJ35nDxlURQLv3PEPWyaTwPNFaRevqleENFifpfKZKHABa6bul8p oHJGJcmOizi31nH2C1UW7lj/ziWxqBd6qLvO+knSIGvyjl4BMb9MYQ3tzTYG OLaT1gzHUgitXTh8U4GF9o5PnbK/0MD8jHECbRXRH8aZO49dZ2FTQFxlp1QP GDzk/75qlAZOHV3bs4nxJ5x48dIqKlw9fqh94Zc+oHFtYnCdZaFP5rLIWTsy nLwc6alB1Itr0rWYi0QeLtjo2jxu1AExh2PWatgS/dMrbNv1KiaO711ZuZLQ NWoevDyPCPycb/96Zj+RzxriW49FG1Igr9i1l2nFgJHFmzXqJVi4wjx/pcHb VnhG/VpzWWwAUop7J/ft7id49eJ5O2Zo8LKppjpjSQ8sXvDet4fQFyt8szon A1qhy8RenbJ7ABwe3kj4sbEfudN/6i2Vo8H1PZ+l9J72grKy8pFVhF5I8xji Umjog2TrGxFLTlBBdP4IO+0cC0nOvyrjiDh6JEjwnyfi6Pva5+xyIo7HI6Te yUoOgMnPC/WbSlthBS/76mXoxzoZnpRagwHIXvFjZ4lHK9BXP6+SX9+PdwJ0 aA6uRP+8u2qPklwb5D9q/yRG6se40NAj35wHwMUlPqFKvRVeZpbeM1jaj3Kq aauFbJlgYcR8F7mHDHHPVY+GE3lSFjXunkDY8+hKh7Y5YU/O7dKwNYQ9djlN yhcJ3SqguSUvitCtIgHB5JAyOrrb6WXu/KwLET+WuZFm2dDrEz1udCgTRXh7 zvRL7Iclt1WogTNsSHN1OXDGLRutTKrnN2vGwS8LelhqHMEHf6i+6d5QjedD JjRdFZPhxrEPj+/Ys2Fl3SNufdU6rFhXEtYSdB+mZYqUdxiPw5pjweKo3Y5h Z+S1nQWL4b63tnHZrTGIpfVgR2UHHhfbpDCeTgfJKa4rX7ATfmWX6zw1J/Dw xBaKkQ0TaDxcazoMyOD3SE2kzIyJV+8q76Qsew3xj3Uw/vsIdLClT1+c6UYS S6S61L4CoufOG+50G4FIzqVvMx73ov4zM/P5Xc/A7+KJkTaDMXDu6k/bIUdB nxz7hlUmJDg/Xc0lSOD8ewzNfRZCxfvr3or/PAHwmtt6dt13NlwMOm6vE56B y7OfcglM7AZF8upFsXNsmDx72u9uzx08w/ElwwmDYXm16tsJZAO1XYQpy0SU Kvd6N3EuHHbkHmP6ELrE5elKXjmlChR33pfKkZoNvxaQN30kjUPFNH3UP70V V5X6y+2NvQ0DMqnGhdxsSLUfmR1Z04y7n+zIj9zQDHR7t8UNOwbh1Lb+ln5X BhbbzSx+9rQI9EWivfT7x+BHw+jqad8PuN94vPatcy20RsGVy5LDcICraGcR wWe+mFvsOuxWDYFcwjcNsodBzWr0O41Jw37uqNMmyZUgV23qErl6BM6nJbw+ bEjD3qElPC+33YcjtYviDpiNww+hgVtZ8u0Q1N7A0SlEAi8lZn4AoXsSZ5l5 d92pYKBH5JFdLYTM6Q5OKwyDkMMjHhvvPlgnXDdZTuBa8LuvP6MJPM+fCsqr smbCdyH7PQe+moPhsGvyuSk2SE17XCjLy4OyoeWCLE8HqF759v3kOBumGqgW oyFFUHdk0+Yrzwj+E+Rysv3aEMxUqixUkqDDZL5tBH1pCxyOsHLw+jIArb4a VoK5DJgd2lozrUOC7hTrpkPeo6B5S/2m5SkqLBB486uatxGuJqs9dZsdhJmJ nuaKMjqoXddYwyL4elKozrAbgVfJR1XNbayYsP/NOp0Sos9ui1+kFG3IhE/2 Px5xEnhdPpKT0vmIAkHNTdJXCf4Z5b/KxkOGBZmx93bPHCCDtH+hEpVY5/wp A6ccgvfaLRSbLlPvgdVazsodPTQwnTh4c/AGC+jxKoXvuGmgS9vdFNLfC778 QXEXclgw66CDyQTf/t6Q0Duxsgdao8dPyxLzuT8rr780S4NVOkNXxPl6QM+2 +7JTMgvOrfsg3KPJgOOJ3+DkFQrcM52/S1eKBbLh8kZfif3XZyl+difqiH+b TLMS8XtUXfpb6qrb8LnGyk9zERuaeVxuZk80wYIxq9Opcj2wSc/z/QMC59f1 OwhPEuv36l3NyHYzgXXnqmeFCL5amfpln25wLtSWrpPcaTkO84rvtR73yYeX Ky/Z7l3XDvb7DgWrBo7CtraMiZGrJIhMMw2lG1Ghx+ua70peNrRURpVvPpgB C7+0ahzoa4I9zLIOQb9RqJ93RC71AgkyTqukn3WggjBvQ2226jDkmT/YtW+q Bpau2FtX69YH6W2Uppmfg6AsLFO6S6IRtvnMzVwrpoPEoPlmTQcivw66ry/a SoZeyfK3jUTeuWtp8wUdZUKPQoL7MlkyfM5e9NSLGL/3Tn3RKw9Cf3At6Nir RYbGKNvqVdoEnkqyY+d7EX67WXfRWYEMTnl2rhd1mXDZcr7eu9wh2H2XtTjD rw6qXUei/Xjp4BKQ9oa1ZBAEA32ePG5rBjU+Ez6OKwxwkb/fudmNDEpzdxSM 9zCBm+/hZwphn0pOzb1zxHO8df/jVqJPXsreXLNvPxM4ZBQddKsHoGHhKoeh sy1wjS3VsqqWAcc4xnIN7ZmwMszEKm8XGVIF8xI4ifySaKULH+IahPChKAP/ wWbg97vK5ZLEgPSgJPUtvYR+8njrtnjXe1jX9NCV7NUPLQoB48vu0EF3XE7N p6oTPk09niWZsuDbgckL/PPoMLXn3BLnmS5wPdXEvcWXBdXHKry2cPdDaMtu K8epDsiN1X+cy2TCU2nDyPgMOii37asIeNMJlgoZkUvMWHAsWKp7nh0TtjUU GxkBoT+er+6XIeyUKabVBBB5F7b5K1nUhAxMT6ZWOdG34udXhJiZ0sHZTo8n y6kLvI2rF7gfZUHeiUPK6wmcCOQ9FTq1mwz39ehP7Yl65N1YPOL/fRBCZOTM etY1gqDihmG153Swc8+IqHUbgKyF2Rb60q0QM89oxpyPsLs1F3bsH4BVXxK3 NLi1Qt7Jg7+uSPVDmWUJ2cmdBRkxItqV8m0w52x8Vre0H5q2hrQJEH1WKEHB 9LY2GXqGNpbvJuxXunX0uA6xf5LQhedN+8gw0u1Fu0yc51m4bsP9C0Og5Fx8 J3SmDmgvvp/p3kyHX7bUr7TBQcDBBP099o3w/pR7gXkDHY4u2RmmpjcITkmy t+qGm2DZWKjzRXsGLBHW+LknfAQUP9rPWU28gbNSUvxbXXpB5qT/oo4tw6Bo mnp7q0otiCvzlxp69oHoO3Vd1BmERusPUpGfm4BPf9furw4M8Gby1/I39UG3 YAErj8Dl9m1P9vf4s4DzmaT1j9phmE/fkTE8XgX58RsffymhwfnsWgO3O0PA 9alz4XhkHdQtthAbWk6H6APjSpwEvnNmpAqPBpJg+bp7vtoED2q0MhWSOuSI Rveizk3/YsPl2Kq9RvmOuMozP+QH7sEtdsylv+/PJBiXR+5u1MO2wnXzl6zV x8iAvOzf96wiMrFFfGn6KOX1WqY1Sxs7xoeNf89nReRRVX5pI9nB5IRQjQXK 7fbf+Z0YX2oW8vKjsiV+fhmss9fMFBd8HaH9vmdqWiFbb5RpioM5QTTD9fth jwjj+S+CtxiZ/soRup4FD1avZgQSPKf84Vt+caJfj4WXLjLKuwvF8lqvBr/s hvqsmce7ifGCqiNKCm53IWVq6Okbou9ffOrnTSPGny2MFMzQuANvt64pphhr oft8n9/fOUCV6dzJ5tta6DxM36ofQoYvIn7nOgm8mDvnePU8UZ9LdB7veihM g1+c3538unuBFMe/2DCNBQKsd6KuPDQ4+CzYmjbZCy9ev/uicZsFb3blXtvi SNT/xtLmckIHHVu+f2IzwXtufPdu5T3XBUvG+l2pe+jQJHl/XQihL0f5OMSU llOhM2pzUO5kHwgFq3OI+LGAEbGeL82/FoJ+ljluWj9M5N3dwrsX+kAj7q7i Ps9quA0cFLl8Qh/JMMTo3TRYHjey5n1qJSjFfP3uJDoCqyKLMxbo0uBtXZCT qHAxSL0t2zx5dwx2+50oTX3YAQcvmj/5pkDg2kOVLNWthH7cLvgy5hQDMvnU L1uFNMKgMd/6C92D0MrnwwUddDB02Z8y5NUClRLxlSIVAxCTp7LNspEBBueS BmV2tkKN3/F9/i4DIPmdzR28tB/4In5J8B0kg/bcL3NCV0NczpnUT8ST16XK zvNeHTgbMXTvpwxBDde+VM51dFB4nt2ZubwRJGJtZM4QfXzRd9IbQaKPZ47r Hl2zmNi36ssLzV8DEL9AqVzlOgN4BVevKAi5Dy94gvNtD4zDwlHynY9K7SAl p6T7zYwEvTuFaDNnRsH/u9/jAYIndP/4EqxqWwGSIs/cg4+PQM7rzoz+8l7Y ba+z/9WGWiiMb3ttrDwMP8wKtGN9+mBYueVQoFwzmIXlR5xUH4RBvUztCCcG 8DyWns/ziAQdRd5WiSdHwZbf3vdRNMFD+Pf/7I4nQVnvYV09gn+q5hv7sQKo YPwkb86c/gaed7m1RF4cgQWc5qTnp3ph70jyYxKtCr6W0LZY1AzD1mVhkc9e 0uBjjCJZbqQOTudYP3EOHYLQhncrzLfTQXTzhxuZqm3gSOPasfwIC/hCYueF v+mHjKvvci4T/eamPb9pHKGzkpTrXhoTOLvx3QP0syFBiSTPcB3hhyTxM+uV PQk/CG8I5nnWCvImv3RuEPpm01Ixdgn0w9UtW2/bEPEiP6s55E7E6SizcppE PJ1WxJ5NJsZrI7JtLxG/7Q30d/9+r1MXLijCe64V1Kvrr9zSHYASszssa5l+ 0FuYIGP1OhiWMSeKp1+zQd3rSolKNkLcfOXIj8HhEKx0b3FNIRuU2nibjHgr IOjoBD5SpAF1iqfodE7v/1exuUdDncUBvBKm9Zg0dlucWEZsSB6ldqkvFdpe Eskjr6lklzgVI2+JFFY2q0Rm1nMz5ZFialN3MHlkdwgz3uaHMTJmTHYibKb9 +fd7zr33nO/9nu/n8z3nXqCbV4gc6EIIc50xcq7jg4+sp3TICINPRxfMXPA4 b77CJNk+C84Uim/6ZUsh69DcYbclNvz4MOdRXVIJtLUpLE2jWeip+Wl+KeMd hC/KxYa3aTD6JS3uDkEKx19RO3I/c8DOf2DBgjoMy8OfvbxZ+Jw7M2X9JEkI RT0EZR2LXCB8OqlKDpCCsQ7DzkCpHSyi1HkbiCxozD6XFrw0A10OHSapiqOg G/Bl2tqzDnrHHA/Zn5BA00XWrkKdAdio7Mz9rr4GQjtPneEKJZCdcPycZzAP iIVDMpVAKbw4SJAZauSAy0Ta+yfLbeAclX6SVCYBm9ki7fScWohO7Sm4U9YH /r4xY8RqESxXCZU7LN/AhHKeIHgAg+P8UWo+7lGXoxt+8dZqBdDk7Z8LHoNe tWP9+VdmwFl8fbu5WRN8dVZpqL6AD6eNKR6xrFlQ+aReGT1QAl7qAnH4jXdQ s++ByVlXCcxGVc/WJtZBe4hniJXmAGQaytP3u83CvOw6+Tc6A46Yrg39Zlsv NBb9bfoM54hunHwuJr4BGCrlxu7nh2Fmz/vHBVMS0E8jhGQM1kBnmC09icKD nmce7JQoMTwZSh687tgA0aOd62/5DoNvd13QUQUxxLqf/375LQLmvqC73wpH QOPajktC/F6Vc0aKM+vTYYlxMPH0HBtuSns3vTeagq5x9mHnv96BFiEjSmIr gGw9jiIF768/a+lLtfE5OtCJonkK5/tE2J9SKXkG9OceVod7N8OE1evXYYBB pbG+a8TAIGT8Uxp8LXccAtItzezchHB1PanQxL0bYm5qWnr3CWG+S7Wy+YoA 7OvNd9NOckF2TjdeD697E23FyT24Jzx9Kpg+ptoPjp27twlXJkA1K2HrD1OT QIpjV1j0DwKyGcvsvDcOBO02tVpXIWxq98saoXBB0cKf2egyCXLrzf+l4P5B 0uL2aVVJwb2qUsEsMhlsMfNA6vomOKDkxPoXr9f82EQzW3M63DeI1tT8yIFy 4hdjjUYpJDt6nY6xSIJirwCnvQUIaNm19klqEjQptWMiOhOt0HiCW6aDMLLo UreRzkejRTtafHZjiLc9jumE88sjK2CDf7kBOuCSP7H63m+b0uWFWRNrFLIo Kn1DJqPiX8cjZXIpiFS43RxKNqoNanuQaInB3V6ZW2UuH1Kiha2sYiEwdHcy +Pj6l0d6MHGdA5B8PIN3llBBM6URS8LjER/sG/XXWUHwnV5XbvoNRDMiWEj2 kpCy76XFVf4y7o351LaQkV+/VV7vBzaUfxRtP8EWwUEZXVrVgMEa/47Otq9n QK998WX482bwVI3gyFww8FVdF0/L4yMD5z0FrtYYytMqvhT6hxCVh+mMrv6f KX0QWZbZbAkTrPiLtGdBsCuz8E1f3yYkZLJWz0Xafl0erb5k5LCF4qJElKBc 8qOEh9lMVLhiU0bbOggJESWHqRw+anFdJ7isgyEvDcO1BTjfR2oCX68xnQSo +j12uZULHXrVmamUSeTOeZyF4fuKV2ixhdP6YNoyPWQYSkUV/Pv2OzaTkIk8 1ubVqv8I9xIJnkmofdeF2jWGCkg9RF++mgf34sR8tcck5ENQc+C/YoN8Q9mi abcImG0Nj0IZGPC7eC+24B4iFnCu3n3Lhwupy7c98PxjjjHEpmURPL+nYNps wIbIhU5ragQG/wPUkcbK "]], { {RGBColor[0, 1, 0], Opacity[0.5], SphereBox[{0, 0, 0}]}, {RGBColor[1, 0, 0], PointSize[Large], Point3DBox[ NCache[{{Rational[-2, 3], Rational[-1, 3], Rational[-2, 3]}, { Rational[-8, 17], Rational[-9, 17], Rational[-12, 17]}, { Rational[1, 51] (27 - 5 21^Rational[1, 2]), Rational[1, 9] (3 + Rational[19, 51] (27 - 5 21^Rational[1, 2])) + Rational[ 5, 9] (Rational[2, 17] (27 - 5 21^Rational[1, 2]) + Rational[13, 2601] (27 - 5 21^Rational[1, 2])^2)^Rational[1, 2], Rational[1, 5] (-1 + Rational[2, 51] (27 - 5 21^Rational[1, 2]) + 3 (Rational[1, 9] (3 + Rational[19, 51] (27 - 5 21^Rational[1, 2])) + Rational[ 5, 9] (Rational[2, 17] (27 - 5 21^Rational[1, 2]) + Rational[13, 2601] (27 - 5 21^Rational[1, 2])^2)^ Rational[1, 2]))}, { Rational[1, 51] (27 + 5 21^Rational[1, 2]), Rational[1, 9] (3 + Rational[19, 51] (27 + 5 21^Rational[1, 2])) + Rational[-5, 9] (Rational[2, 17] (27 + 5 21^Rational[1, 2]) + Rational[13, 2601] (27 + 5 21^Rational[1, 2])^2)^Rational[1, 2], Rational[1, 5] (-1 + Rational[2, 51] (27 + 5 21^Rational[1, 2]) + 3 (Rational[1, 9] (3 + Rational[19, 51] (27 + 5 21^Rational[1, 2])) + Rational[-5, 9] (Rational[2, 17] (27 + 5 21^Rational[1, 2]) + Rational[13, 2601] (27 + 5 21^Rational[1, 2])^2)^ Rational[ 1, 2]))}}, {{-0.6666666666666666, -0.3333333333333333, \ -0.6666666666666666}, {-0.47058823529411764`, -0.5294117647058824, \ -0.7058823529411765}, {0.08013963774942748, 0.9198603622505728, 0.3839720724501147}, {0.9786838916623372, 0.02131610833766251, 0.20426322166753239`}}]]}}}, Axes->True, BoxRatios->{1, 1, 1}, DisplayFunction->Identity, FaceGridsStyle->Automatic, ImageSize->{77., Automatic}, Method->{"DefaultBoundaryStyle" -> Directive[ GrayLevel[0.3]]}, PlotRange->{{-1.2, 1.2}, {-1.2, 1.2}, {-1.2, 1.2}}, PlotRangePadding->{ Scaled[0.02], Scaled[0.02], Scaled[0.02]}, Ticks->None, ViewPoint->{1.3000000000000003`, -2.4, 2.}, ViewVertical->{-0.007083333965668549, -0.0038639328383631797`, 0.9999674476716487}]], ImageSize->{225, 258}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, Graphics3DBoxOptions->{ImageSize->225}], "\n\n", StyleBox[" \[Integral] \[Sum] ", FontColor->RGBColor[0, 0, 1], Background->RGBColor[1, 1, 0.85]], StyleBox["\[Del]", FontSize->56, FontColor->RGBColor[0, 0, 1], Background->RGBColor[1, 1, 0.85]], StyleBox[" \[Gamma] ", FontColor->RGBColor[0, 0, 1], Background->RGBColor[1, 1, 0.85]], "\n\nSymbolic Computation with ", StyleBox["Mathematica", FontSlant->"Italic"], " " }], "Title", CellChangeTimes->{{3.448190122176695*^9, 3.44819012385317*^9}, { 3.485609127497636*^9, 3.485609133015955*^9}, {3.514308355088097*^9, 3.514308374696691*^9}, 3.5146594348020153`*^9, 3.5146601881617107`*^9, { 3.6071801166601562`*^9, 3.607180117693161*^9}, 3.617726624923478*^9, { 3.6177267158104258`*^9, 3.617726719586279*^9}, {3.6177279925387697`*^9, 3.6177279963765173`*^9}, {3.6218713978894234`*^9, 3.6218713987006702`*^9}, {3.6218714909487915`*^9, 3.621871491994052*^9}, { 3.6223686888329096`*^9, 3.622368796276308*^9}, {3.6223688327200108`*^9, 3.6223688343893065`*^9}, {3.6223688978849697`*^9, 3.6223689206310816`*^9}, {3.6223689582604523`*^9, 3.6223689764199*^9}, { 3.6223690457971025`*^9, 3.622369086733864*^9}, {3.6223691493870783`*^9, 3.6223691855187626`*^9}, {3.6223856736383467`*^9, 3.622385708506358*^9}, { 3.6224827931314735`*^9, 3.622482794192321*^9}, {3.623153593458613*^9, 3.623153598897826*^9}}, TextAlignment->Center], Cell["\<\ Adam Strzebonski, Devendra Kapadia, Itai Seggev, Oleksandr Pavlyk\ \>", "Subtitle", CellChangeTimes->{{3.485609136120798*^9, 3.4856091511532907`*^9}, { 3.4856091945334663`*^9, 3.485609199379443*^9}, {3.4951031489375*^9, 3.49510314984375*^9}, {3.495106455296875*^9, 3.495106455453125*^9}, { 3.5143083846926413`*^9, 3.514308395249558*^9}, 3.5443793532699003`*^9, { 3.6177267239706383`*^9, 3.617726772588651*^9}, 3.621871494973824*^9, { 3.6223857160883956`*^9, 3.622385717430073*^9}}, TextAlignment->Center], Cell["Wolfram Research, Inc.", "Subsubtitle", CellChangeTimes->{ 3.483202458953512*^9, {3.495105345328125*^9, 3.495105347890625*^9}, { 3.49510644571875*^9, 3.495106448390625*^9}, {3.5143083980990458`*^9, 3.514308409442589*^9}, {3.617726777331872*^9, 3.617726796740467*^9}}, TextAlignment->Center] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Plan for the Workshop", "Section", CellChangeTimes->{{3.6218713445187445`*^9, 3.6218713508839116`*^9}}], Cell[CellGroupData[{ Cell[TextData[{ "The following is a ", StyleBox["broad plan", FontColor->RGBColor[0, 0, 1]], " for topics to be discussed in this workshop:" }], "Subsection", CellChangeTimes->{{3.621871353582867*^9, 3.6218713810248504`*^9}, 3.6218720602713985`*^9, 3.62229337078496*^9, 3.62315357411292*^9}], Cell["Algebra and Optimization", "Subsubsection", CellDingbat->"\[FilledCircle]", CellChangeTimes->{{3.6218715416673174`*^9, 3.6218715816524243`*^9}, 3.6222933597542977`*^9, {3.6223692883598957`*^9, 3.622369297658032*^9}, { 3.623070938865882*^9, 3.6230709522466846`*^9}, {3.623153125329818*^9, 3.623153131817843*^9}, 3.6231555218064203`*^9}], Cell["Calculus Operations", "Subsubsection", CellDingbat->"\[FilledCircle]", CellChangeTimes->{{3.621871599983482*^9, 3.621871615319166*^9}, { 3.6218719578826914`*^9, 3.621871998055009*^9}, 3.622293361824422*^9, { 3.6223693064257383`*^9, 3.6223693317459984`*^9}, {3.6231554681608267`*^9, 3.6231554698782387`*^9}, 3.623155520406445*^9}], Cell["Vector Calculus and Special Functions", "Subsubsection", CellDingbat->"\[FilledCircle]", CellChangeTimes->{{3.621871625724967*^9, 3.6218716326205645`*^9}, 3.6222933637045345`*^9, {3.623150378320981*^9, 3.6231503821119995`*^9}, 3.6231555190623302`*^9}], Cell["Problems from Calculus", "Subsubsection", CellDingbat->"\[FilledCircle]", CellChangeTimes->{{3.621872006105074*^9, 3.621872018164569*^9}, 3.6222933683048105`*^9, {3.6223693387196007`*^9, 3.622369341231346*^9}, { 3.6231503861214314`*^9, 3.6231503903960776`*^9}, 3.62315551686229*^9}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Formulation of problems for algebraic solvers", "Section", CellChangeTimes->{{3.622420676284381*^9, 3.622420679235756*^9}, { 3.622593866807856*^9, 3.622593887520486*^9}, {3.622809799082014*^9, 3.6228098009777546`*^9}}], Cell[CellGroupData[{ Cell["Main classes of problems that are solvable algorithmically", \ "Subsection", CellChangeTimes->{{3.6224206837068233`*^9, 3.6224207140916815`*^9}, { 3.622421167595769*^9, 3.6224211714997654`*^9}, {3.6225941260802794`*^9, 3.6225942610324163`*^9}}], Cell["\<\ \[Bullet] Systems of linear equations (linear algebra) \[Bullet] Systems of polynomial equations and inequations in complex \ variables (Groebner bases) \[Bullet] Systems of polynomial equations and inequalities in real variables \ (cylindrical algebraic decomposition) \[Bullet] Real univariate equations and inequalities involving tame \ elementary functions (real root isolation)\ \>", "Text", CellChangeTimes->{{3.590495719669221*^9, 3.5904957664958572`*^9}, { 3.5904958952316313`*^9, 3.590496000166148*^9}, {3.5904960460377064`*^9, 3.5904961976548166`*^9}, {3.5904962300991354`*^9, 3.5904962304990377`*^9}, 3.590496269178705*^9, {3.5905001446396117`*^9, 3.5905002032308903`*^9}, { 3.590500236367592*^9, 3.590500254614165*^9}, {3.6223845824010396`*^9, 3.6223845945605836`*^9}, {3.6224207306362824`*^9, 3.6224207316759143`*^9}, {3.6225944439851484`*^9, 3.6225945973211193`*^9}, {3.622594635480465*^9, 3.6225947772169633`*^9}}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " solvers also implement several algorithms for solving certain classes of \ Diophantine problems (linear, binary quadratic equations, Thue equations, \ etc.). For other systems ", StyleBox["Mathematica", FontSlant->"Italic"], " tries various heuristics in order to reduce the problem to a combination \ of solving polynomial systems and using known solutions to simple \ transcendental problems." }], "Text", CellChangeTimes->{{3.6224213137163243`*^9, 3.6224213485807514`*^9}, { 3.62259427405657*^9, 3.62259428956804*^9}, {3.6225944196725607`*^9, 3.6225944211982546`*^9}, {3.62259485121686*^9, 3.6225949735618963`*^9}, { 3.622595008762366*^9, 3.62259516834663*^9}, {3.6225953033887787`*^9, 3.62259535136137*^9}, {3.6225953815051985`*^9, 3.622595396177061*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Example from StackExchange", "Subsection", CellChangeTimes->{{3.6224206837068233`*^9, 3.6224207140916815`*^9}, { 3.622421167595769*^9, 3.6224211714997654`*^9}, {3.622595508521827*^9, 3.6225955176249833`*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"f", "=", RowBox[{"y", " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{"x", "-", "z"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"g", "=", RowBox[{ RowBox[{"9", " ", RowBox[{"x", "^", "2"}]}], "+", RowBox[{"4", " ", RowBox[{"y", "^", "2"}]}], "+", RowBox[{"36", " ", RowBox[{"z", "^", "2"}]}], "-", "36"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"h", "=", RowBox[{ RowBox[{"x", " ", "y"}], "+", RowBox[{"y", " ", "z"}], "-", "1"}]}], ";"}]}], "Input", CellChangeTimes->{{3.6225955776020994`*^9, 3.622595641778249*^9}}], Cell[TextData[{ "Find the stationary points of ", Cell[BoxData[ FormBox["f", TraditionalForm]]], " over the constraints ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"g", "\[Equal]", "0"}], " ", "\[And]", RowBox[{"h", "\[Equal]", "0"}]}], TraditionalForm]]], "." }], "Text", CellChangeTimes->{{3.590495719669221*^9, 3.5904957664958572`*^9}, { 3.5904958952316313`*^9, 3.590496000166148*^9}, {3.5904960460377064`*^9, 3.5904961976548166`*^9}, {3.5904962300991354`*^9, 3.5904962304990377`*^9}, 3.590496269178705*^9, {3.5905001446396117`*^9, 3.5905002032308903`*^9}, { 3.590500236367592*^9, 3.590500254614165*^9}, {3.6223845824010396`*^9, 3.6223845945605836`*^9}, {3.6224211783006287`*^9, 3.6224211826201773`*^9}, {3.6225956468413916`*^9, 3.6225957206572647`*^9}}], Cell[CellGroupData[{ Cell["Direct solution (unsuccessful)", "Subsubsection", CellChangeTimes->{{3.6225957589276247`*^9, 3.622595787690277*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"gradf", "=", RowBox[{"Grad", "[", RowBox[{"f", ",", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"gradg", "=", RowBox[{"Grad", "[", RowBox[{"g", ",", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"gradh", "=", RowBox[{"Grad", "[", RowBox[{"h", ",", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}]}], ";"}], "\n", RowBox[{"TimeConstrained", "[", RowBox[{ RowBox[{"sol", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"gradf", "\[Equal]", RowBox[{ RowBox[{"L", " ", "gradg"}], "+", RowBox[{"M", " ", "gradh"}]}]}], " ", "&&", " ", RowBox[{"g", "\[Equal]", "0"}], " ", "&&", " ", RowBox[{"h", "\[Equal]", "0"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z", ",", "L", ",", "M"}], "}"}], ",", "Reals"}], "]"}]}], ",", "300"}], "]"}]}], "Input", Evaluatable->False, CellChangeTimes->{{3.6225955818696413`*^9, 3.6225955818711414`*^9}, { 3.622595794588653*^9, 3.622595859786932*^9}, {3.6225959318115783`*^9, 3.622595966651002*^9}}], Cell[BoxData["$Aborted"], "Output", CellChangeTimes->{{3.6225959592885675`*^9, 3.6225959680761833`*^9}, 3.622596279571238*^9}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Two-step solution (successful)", "Subsubsection", CellChangeTimes->{{3.6225957589276247`*^9, 3.622595787690277*^9}, { 3.6225960544976573`*^9, 3.622596060969479*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"eq1", "=", RowBox[{"Eliminate", "[", RowBox[{ RowBox[{ RowBox[{"gradf", "\[Equal]", RowBox[{ RowBox[{"L", " ", "gradg"}], "+", RowBox[{"M", " ", "gradh"}]}]}], " ", "&&", " ", RowBox[{"g", "\[Equal]", "0"}], " ", "&&", " ", RowBox[{"h", "\[Equal]", "0"}]}], ",", RowBox[{"{", RowBox[{"L", ",", "M"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6225955818696413`*^9, 3.6225955818711414`*^9}, { 3.622595794588653*^9, 3.622595859786932*^9}, {3.6225959318115783`*^9, 3.622595966651002*^9}, {3.622596102015191*^9, 3.6225961830024757`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"93960", " ", SuperscriptBox["\[ExponentialE]", "x"], " ", "x"}], "\[Equal]", RowBox[{ SuperscriptBox["\[ExponentialE]", "x"], " ", RowBox[{"(", RowBox[{"93231", "+", RowBox[{"173799", " ", "y"}], "-", RowBox[{"516555", " ", SuperscriptBox["y", "2"]}], "+", RowBox[{"210717", " ", SuperscriptBox["y", "3"]}], "+", RowBox[{"58995", " ", SuperscriptBox["y", "4"]}], "-", RowBox[{"16725", " ", SuperscriptBox["y", "5"]}], "+", RowBox[{"10000", " ", SuperscriptBox["y", "6"]}], "-", RowBox[{"8080", " ", SuperscriptBox["y", "7"]}]}], ")"}]}]}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "72"}], " ", "x", " ", "y"}], "+", RowBox[{"45", " ", SuperscriptBox["x", "2"], " ", SuperscriptBox["y", "2"]}]}], "\[Equal]", RowBox[{ RowBox[{"-", "36"}], "+", RowBox[{"36", " ", SuperscriptBox["y", "2"]}], "-", RowBox[{"4", " ", SuperscriptBox["y", "4"]}]}]}], "&&", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "486"}], " ", SuperscriptBox["\[ExponentialE]", "x"], " ", "y"}], "-", RowBox[{"324", " ", SuperscriptBox["\[ExponentialE]", "x"], " ", SuperscriptBox["y", "2"]}], "+", RowBox[{"2430", " ", SuperscriptBox["\[ExponentialE]", "x"], " ", SuperscriptBox["y", "3"]}], "-", RowBox[{"2232", " ", SuperscriptBox["\[ExponentialE]", "x"], " ", SuperscriptBox["y", "4"]}], "-", RowBox[{"270", " ", SuperscriptBox["\[ExponentialE]", "x"], " ", SuperscriptBox["y", "5"]}], "+", RowBox[{"225", " ", SuperscriptBox["\[ExponentialE]", "x"], " ", SuperscriptBox["y", "6"]}], "+", RowBox[{"80", " ", SuperscriptBox["\[ExponentialE]", "x"], " ", SuperscriptBox["y", "8"]}]}], "\[Equal]", RowBox[{ RowBox[{"-", "405"}], " ", SuperscriptBox["\[ExponentialE]", "x"]}]}], "&&", RowBox[{ RowBox[{"36", " ", "z"}], "\[Equal]", RowBox[{ RowBox[{"36", " ", "x"}], "+", RowBox[{"36", " ", "y"}], "-", RowBox[{"45", " ", SuperscriptBox["x", "2"], " ", "y"}], "-", RowBox[{"4", " ", SuperscriptBox["y", "3"]}]}]}]}]], "Output", CellChangeTimes->{3.6225964602096763`*^9}] }, Closed]], Cell[BoxData[ RowBox[{ RowBox[{"sol1", "=", RowBox[{"Solve", "[", RowBox[{"eq1", ",", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", "Reals"}], "]"}]}], ";"}]], "Input", CellChangeTimes->{3.6225961649541836`*^9, 3.6225964717556424`*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"y", " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{"x", "-", "z"}], ")"}]}]}], "/.", "sol1"}], "//", "N"}]], "Input", CellChangeTimes->{ 3.622596174721924*^9, {3.622596291107703*^9, 3.6225962917877893`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "0.06875035273701703`"}], ",", "0.4084486047082607`", ",", RowBox[{"-", "5.350645004045127`"}], ",", "9.793800629269787`"}], "}"}]], "Output", CellChangeTimes->{{3.6225964607082396`*^9, 3.622596478753531*^9}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Polynomial formulation", "Subsubsection", CellChangeTimes->{{3.6225957589276247`*^9, 3.622595787690277*^9}, { 3.6225960544976573`*^9, 3.622596060969479*^9}, {3.622596218025923*^9, 3.622596224729774*^9}}], Cell[CellGroupData[{ Cell[BoxData["gradf"], "Input", CellChangeTimes->{{3.6225955818696413`*^9, 3.6225955818711414`*^9}, { 3.622595794588653*^9, 3.622595859786932*^9}, {3.6225959318115783`*^9, 3.622595966651002*^9}, {3.622596102015191*^9, 3.6225961830024757`*^9}, { 3.622596237681919*^9, 3.622596249450413*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{"x", "-", "z"}]], " ", "y"}], ",", SuperscriptBox["\[ExponentialE]", RowBox[{"x", "-", "z"}]], ",", RowBox[{ RowBox[{"-", SuperscriptBox["\[ExponentialE]", RowBox[{"x", "-", "z"}]]}], " ", "y"}]}], "}"}]], "Output", CellChangeTimes->{3.622596489911948*^9}] }, Closed]], Cell["\<\ Since stationary point conditions depend only on directions of gradients and \ not on their magnitudes, one can divide gradients by nonzero functions.\ \>", "Text", CellChangeTimes->{{3.590495719669221*^9, 3.5904957664958572`*^9}, { 3.5904958952316313`*^9, 3.590496000166148*^9}, {3.5904960460377064`*^9, 3.5904961976548166`*^9}, {3.5904962300991354`*^9, 3.5904962304990377`*^9}, 3.590496269178705*^9, {3.5905001446396117`*^9, 3.5905002032308903`*^9}, { 3.590500236367592*^9, 3.590500254614165*^9}, {3.6223845824010396`*^9, 3.6223845945605836`*^9}, {3.6224211783006287`*^9, 3.6224211826201773`*^9}, {3.6225956468413916`*^9, 3.6225957206572647`*^9}, 3.6225964415118017`*^9}], Cell[BoxData[ RowBox[{ RowBox[{"sol2", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"gradf", "/", RowBox[{"E", "^", RowBox[{"(", RowBox[{"x", "-", "z"}], ")"}]}]}], "\[Equal]", RowBox[{ RowBox[{"L", " ", "gradg"}], "+", RowBox[{"M", " ", "gradh"}]}]}], " ", "&&", " ", RowBox[{"g", "\[Equal]", "0"}], " ", "&&", " ", RowBox[{"h", "\[Equal]", "0"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z", ",", "L", ",", "M"}], "}"}], ",", "Reals"}], "]"}]}], ";"}]], "Input", CellChangeTimes->{ 3.6225961649541836`*^9, 3.622596286506119*^9, {3.6225963302586746`*^9, 3.622596364595535*^9}, 3.6225963948513765`*^9, 3.622596517779987*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"y", " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{"x", "-", "z"}], ")"}]}]}], "/.", "sol2"}], "//", "N"}]], "Input", CellChangeTimes->{ 3.622596174721924*^9, {3.6225963137235746`*^9, 3.622596315506301*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "5.35064500404513`"}], ",", "0.408448604708261`", ",", RowBox[{"-", "0.06875035273701703`"}], ",", "9.793800629269802`"}], "}"}]], "Output", CellChangeTimes->{3.6225965228811345`*^9}] }, Closed]] }, Closed]] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Formulation of problems for exact optimization", "Section", CellChangeTimes->{{3.622420676284381*^9, 3.622420679235756*^9}, { 3.622593866807856*^9, 3.622593887520486*^9}, {3.6228098125942297`*^9, 3.6228098161301785`*^9}}], Cell[CellGroupData[{ Cell["\<\ Main classes of optimization problems that are solvable algorithmically\ \>", "Subsection", CellChangeTimes->{{3.6224206837068233`*^9, 3.6224207140916815`*^9}, { 3.622421167595769*^9, 3.6224211714997654`*^9}, {3.6225941260802794`*^9, 3.6225942610324163`*^9}, {3.622809823882163*^9, 3.6228098266260114`*^9}}], Cell["\<\ \[Bullet] Linear objective functions and constraints (linear programming) \[Bullet] Polynomial objective functions and constraints (cylindrical \ algebraic decomposition) \[Bullet] Real univariate objective functions and constraints involving tame \ or periodic elementary functions (differentiation/limits/real root isolation) \[Bullet] Some analytic objective functions and analytic equation constraints \ in a bounded box (Lagrange multipliers/equation solving)\ \>", "Text", CellChangeTimes->{{3.590495719669221*^9, 3.5904957664958572`*^9}, { 3.5904958952316313`*^9, 3.590496000166148*^9}, {3.5904960460377064`*^9, 3.5904961976548166`*^9}, {3.5904962300991354`*^9, 3.5904962304990377`*^9}, 3.590496269178705*^9, {3.5905001446396117`*^9, 3.5905002032308903`*^9}, { 3.590500236367592*^9, 3.590500254614165*^9}, {3.6223845824010396`*^9, 3.6223845945605836`*^9}, {3.6224207306362824`*^9, 3.6224207316759143`*^9}, {3.6225944439851484`*^9, 3.6225945973211193`*^9}, {3.622594635480465*^9, 3.6225947772169633`*^9}, { 3.622809847498662*^9, 3.622809966042715*^9}, {3.622809998266807*^9, 3.6228101185065756`*^9}, {3.6228102225552883`*^9, 3.6228103415233955`*^9}, 3.6228139176855097`*^9}], Cell[TextData[{ "For other systems ", StyleBox["Mathematica", FontSlant->"Italic"], " tries various heuristics in order to reduce the problem to a solvable form." }], "Text", CellChangeTimes->{{3.6224213137163243`*^9, 3.6224213485807514`*^9}, { 3.62259427405657*^9, 3.62259428956804*^9}, {3.6225944196725607`*^9, 3.6225944211982546`*^9}, {3.62259485121686*^9, 3.6225949735618963`*^9}, { 3.622595008762366*^9, 3.62259516834663*^9}, {3.6225953033887787`*^9, 3.62259535136137*^9}, {3.6225953815051985`*^9, 3.622595396177061*^9}, { 3.622810378466586*^9, 3.6228103845623603`*^9}, {3.622810458795287*^9, 3.6228104946028337`*^9}, {3.622811925883583*^9, 3.6228119658761616`*^9}, 3.622812016572099*^9}] }, Closed]], Cell[CellGroupData[{ Cell["Example", "Subsection", CellChangeTimes->{{3.6228262189982834`*^9, 3.6228262321780367`*^9}}], Cell[TextData[{ "Find the distance from the point ", Cell[BoxData[ FormBox[ RowBox[{"p", "=", RowBox[{"{", RowBox[{"3", ",", "3", ",", "3"}], "}"}]}], TraditionalForm]]], " to the torus given by the parametrization" }], "Text", CellChangeTimes->{{3.590495719669221*^9, 3.5904957664958572`*^9}, { 3.5904958952316313`*^9, 3.590496000166148*^9}, {3.5904960460377064`*^9, 3.5904961976548166`*^9}, {3.5904962300991354`*^9, 3.5904962304990377`*^9}, 3.590496269178705*^9, {3.5905001446396117`*^9, 3.5905002032308903`*^9}, { 3.590500236367592*^9, 3.590500254614165*^9}, {3.6223845824010396`*^9, 3.6223845945605836`*^9}, {3.6224211783006287`*^9, 3.6224211826201773`*^9}, {3.6225956468413916`*^9, 3.6225957206572647`*^9}, {3.622812109083847*^9, 3.6228121456919956`*^9}, { 3.622812204419953*^9, 3.622812204908015*^9}, {3.6228122856857724`*^9, 3.622812285893799*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"p", "=", RowBox[{"{", RowBox[{"3", ",", "3", ",", "3"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"par", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Cos", "[", "a", "]"}], RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", "b", "]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"Sin", "[", "a", "]"}], RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", "b", "]"}]}], ")"}]}], ",", RowBox[{"Sin", "[", "b", "]"}]}], "}"}]}], ";"}]}], "Input", CellChangeTimes->{{3.6225955776020994`*^9, 3.622595641778249*^9}, { 3.6228121525843706`*^9, 3.622812164837927*^9}, 3.622812219941424*^9, { 3.622812271981532*^9, 3.6228122790694323`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ParametricPlot3D", "[", RowBox[{ RowBox[{"Evaluate", "[", "par", "]"}], ",", RowBox[{"{", RowBox[{"a", ",", "0", ",", RowBox[{"2", "Pi"}]}], "}"}], ",", RowBox[{"{", RowBox[{"b", ",", "0", ",", RowBox[{"2", "Pi"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.6228077414397264`*^9, 3.6228078074811125`*^9}, { 3.622807846009005*^9, 3.622807891777817*^9}, {3.622812225670151*^9, 3.622812229413127*^9}}], Cell[BoxData[ Graphics3DBox[GraphicsComplex3DBox[CompressedData[" 1:eJyFnXVcVc/z/wERAwu7u7sTOdfC7sRObMXu7sAOVEQM7O7kXLsxUMIClFRp DCT8neO+Zrx3v29/n/c/9+HzPczOztmzOzO7e2+poRO7jbCysLBIyWxhkUH7 nJb6W/svkyFLoQnpV7dddKj0dNPhTsU9HHJfKmPvuiejIfeCWl03+iYpxGfG pKxyiU5TNhVSIjfdtjIQd1qwvsCx/mFKbIG0wt9GZGLezal1wIn+Yer99/cS kkx4rw+uByZFp6kvu2yeYarnTsqa1Vq7RtfVG2w3mLRb7PcfO425Vnl0aDTr qj3xu5BfLeRV4r2h/7nQbyQ+HPbcE/YwbwL744X9zEeiv26iv8yzwT9VhH+4 XfLn/bgk3Z/exIeF2eatUS+TocDwl1n9/S84lOi5/ebNO2+VXp1ti76MtDZU bzcxfWOZJIV4v2Z57FfGpSpjfnefa1nOykA8Q8Gc1codDlV6DXNKaORpw3z3 ziV+FQ6Hqh1/TX9syku17dpxVVyqmtZvcE5TPeEp70Zq7RoPFVt3e4NJu98i /thp9FhQpv6iHVfsiUdA/oCQV4mXhv5Uod9I/BTs6SDsYR5eQNjfW9jPvD36 6yL6y7wr/OMo/MPtkj+7Pehhq/nTm3irLr/zR6ZaG+6equz4y3jOwbpMj+Db 1lGK8+PSBV9GWhlanmj5bWL9BIX4RJvI5PAqv5QcVZuPvDDKwkA88mom/x4n PyoOZ11G155uzXzTnY5K75Mf1VoTHB1N+YYOGeIjqvxSSwy9am2qp//Xc/21 do3+zxYFTDBp163bHzuNqbEZ3Q+Xv2Qvy78S8irxjdBfXOg3Et8He2oKe5j7 wH5F2M98CPqbV/T3L4d/+gr/cLvkz8q7PHV/ehO/2Gbv18v3LQ0FPp/pnPf6 aQe7Uqll3GvHKhssCu38Zm1h6Prh888Tb2MU4iXTUvJGVPmu9HQduKb/0xTm odbPDr84GKQMzfTyx46elgbiy3ySr78+GKReOpjpjSk/6d8tXNOjfmw9PrSf iZ5tfWq80to1Wm9yyX/cpN2T7f7YaSwaUDS7v/s5e+LbIf974x95lfgp6A8W +pl7wp6Lwh4j8Suwf5iwn3le9HeQ6C/rWQP/TBf+YU7+PP8sXxfNn97EX49v e8bVJVU55FOvxdQ7Rx1qzh8Ys0vj6+P6WrnuSVZu3+5d9vWJSIV46eW3nZyu xSv1PKcFVrb/znx2j2eL23cJVOoUeBmW4WoK818FQu926hKort1c5aIpz+JQ w7LvtXj1ebmE7qZ6lrdvOUhrVw2vO3ufr0m7KS5/7FR/vFlZ8/PAU/bEV0D+ o5BXiWeF/mdCP/OcBYU9a4Q9zPvA/rrCfuYF0d+mor/MV8A/wcI/zMmfudxe 6/70Jp7v3PMpNWy+K6fHVBp3+OoBB+tbhdrp4/zIF/sir/wTlZQSUY77i35S iK8rd8bm3PQvSoXwBYeLNoxnnrKnxaYpO32Vr3ebF/Kd+Y355KI/Ck7f6at+ zNw/6aUJb63+znJ++hfVeKVwM1M9OS7UHKa1q7qk5y+6z6TdZRf+2Kkm3BtU tXX7w/bEc0J+vJBXibeFfm+hn/kS2BMi7GEeDPtjhP3MF6C/1UR/me+Hf3KX /OMf5uTP1RW9dH96E89wbN/+vVvjNf91yhq71tNh/PCxOY3avN3UffDkw6di lR92kWe8l35QiC+o4XnRJTpMaTi4pUOWBV+YW6VlLnCw4zPlzszONe+UjWfu U+RiiaMdn6ljMwbmNuXvWh9ZNik6TH09ttKOzCZ6zlg6hmntqn42N15dN2n3 2/E/dqob7w8pv23EfnviZyH/QsirxN9Dv6/QzzwS9owR9jAPSBX23xX2M5+C /jYX/WVeF/4pkvuPf5iTP6/Hn9b96U1cxCGxHD9l6p+3TvmDe+1f7anR5fqr r7zeEx/aLq2fZ+InXp+IBx7N+2jdnCc8nxIvP/P8tE1znvB7Rfz7loEF9yb+ HQfE8x+8ellrl+0mbvHnvziV/k2fBSA/Wsjz//8B/VZCP3MH2FND2MP8LOzP I+xn3hv9zS76y/wJ/GMQ/mFO/py73fGI5k9v4lbwvyvGM9nbBM/rG8Yz8fl4 vvUxnolbYjzfxngm/sR8/DB/az7emJ/G+HyF8Uw8CeN5A8YzcRr/zzCeidP7 8gLjmXg47BmN8UzcL9XsfWQ+Cf01YDwTrw3/FMJ4Jk7+vIbxTDwv5pNTmJ/p +R/G/PML8zNxV8xX5TE/E/+F+e0L5mfik8znQ+aOmD9VzM/Es2O+nYj5mfhS zM/xmJ+J03w+DvMzcZr/b2B+Jr4Y9gRjfiYeBPujMT8Tny/Nz8RpfrbD/Eyc /LkK8zPxl1gfDyDeoPdpLdbTm4g3iJfE+lsH8QbxmVivayLeIP4D8cYqxBv8 viIe8EG8QXwJ4odPiDeI/0S8kYR4g/hSyAcj3iCeGfqfIN4gnh3xxkrEG8R7 wv5aiDeI50d/myDeIL4M/vmAeIM4+TM74g3i5xDv5UX8TPOTK+LDDoifiRdD PNkV8TPxIMSfgxA/E1+IePU84mfiRxHfvkf8THyLeTzM/Bji50KIn2X5X4if WR763yJ+Jr4L9pxD/Ez8HOwfjPiZeC70tx/iZ+Kr4J9JiJ9ZD/x5BvEz8RbI X24jH6T5fjjynebIB4mPR36UHfkg8XDkU/bIB4lvRP5VA/kg8XXm+Rrzvsjv XiMfJL4N+WAy8kHi/SD/Evkg8fXQXxT5IHFPc3uYP4H9TZEPEh+I/uZBPkh8 EPzTB/kgcfJnReSDxIcgH8+H+gatnz2Rv1dFfYO4E/L9UahvELdEfaMH6hvE 3VFPaI/6BvES5vUH5qGoV3ihvkE8EfUNd9Q3iIdBfh/qG8RLQv8v1DeIn4A9 7VDfYD2ob/REfYN4W/R3IuobxDvDPy1R3yBO/uyC+gZxuV5H8YhcryMu1+uI y/U64nK9jrhcryMu1+uIy/U64nK9jrhcryMu1+uIy/U64nK9jrhcryMu1+uI zx553TmsTiZD+fSzVinVw5Sp/Ze236LFkRFFVmUdv8vKcKdlyW1jTqQxb3Hk 5VSnsxkNA7ZUH5Dq80lxa7h+uhanKhERn5IOPslk6PSi60dn54sOJP9xTFNF 9+NDX79akzV7KU7ffKjSZotDSUr7Jd/HtJuU0UDyk2MmBTR1tjS8PfRtbRtj Cutfl8M4ar3m965FjWf0/pGe51sqae0d9A6JEu2TnmmFW4583TlRaRq6LiYt m7WB9Fxf1krr/0HvKenCH6SnaZydn+WhJHWyZf1ipvb0XDh1Wa2EA94OZVS1 ZjMb1jMi45CT+nO1ftN7mKk9B/xbzNb8ZjwT/nneaBO/3Xpef6tf50R1YZ83 Xqb2XKgXdUp/fkpEywKTTPzzYJf7Ou25GB98+tD6p8lzWVD8q8HB2dJYq1/c 8tYm/lmUEmKjj4/P477MOK6NF1nPTaFHJT3LWxXdqT1H44BlF58lmzxH0hMq 9HC91wv9Oin69X/09BJ6VNJzEf2yF/1iPQb4eZLws5H0LES/qot+sZ5R8HMG 4WeuSydXP/3J5Lmznrvw8wLhZyPp2Tvm2W+T5856lmAcdhbjkPXkMYYsN3nu rGc+xmFPMQ5ZTxDeF3/xvrB/nDEOm4lxyHre4L14J94L9s9MvI9txfvIesbi vYgW7wX7x9v72Ad9/jrdcn/DUybPi95H15X++vvoTXqa4f2dL95f1vMj18JF +rhsX7lmVX/NXuLjOt0f4ZFiZbhRZfGJiz1ClJflLaL1vHFEKfE+NC25U3s/ zjuQ/Mqz0Rn0cZmvXqVp2vPkcW75Ld/jhpPTlTKWL4eebv2T9TSd+2vlT238 vbG7eVy3i+QLe/8qNyMsTglIT3nyfbWlgeRHu07On6LZnT5jxgpT+W4VK3df 0H2f98njj8K3z8zA8m2sErPo/vpmcyqbqT0HM1eqPjMsTp05Z5Crqf6vHnUf 6c+p3PSm6a9N/HBgc8SiRpPT1bJem+adMrH/HcbHVKfBrQesvWxP8h+/Oy/X /Gas1ObepPMmfouG/tJCvyrLlxHyKsm3g/2Jwn4eP4dgT2lhD8vPMvcPyx9B f2eI/hpJvjT8/1b4n+VvXB7dw8SfLD8Lz7eoeL4snw3P6614XiyfgHE1VIwr 7u+3JDEe6ojxoMrjalelAtr7d96b5MdgHL4R45DlL5947bar9m/l6NnwfFvm vFPEehyr5DomxsGcPO21cXHWgeTDmoY+u2WdrHzzsOi6NzGR5V9F5bRS73xR fhy6evH6q1Tm2X2PTtTXySdDbt/WAPNxb5qcN975oh71qtHJVH6dZ3Hn29bJ amrvPVs8TfQf6T7FR7NTHRHrOGaDiZ3E+wuuEt8APb+EHuYuaPeIaJd5Y+vL k0zsZO6NfqWJfjF/Cz9Y7fnjB1X2W6VZl3W/eZPfLsDPgcLPLH92lPekX+N/ Km+2jXx7taOfcrPMtKW6fNlBwl8PvwZr/jvpQPJTx9t86LA9UZmbXXEtq8Sy vPXFpbfWe4cpFoWafliz+TvzHylNWnps3e795VDQ3Wc5kpnfsFqYf6N3mGpR ZPBaU/l+W45077g9Uc1ypKFzGRP9N4Zd3aXZqRb225NyycRO4nkEV4kPgJ6M Qg9zI9r9XfhPu8znNfVvZWIn88QLol8ZRb+Yj4MfNgg/qLLfCl/a4qL5zZv8 dhp+/i38zPK5YxymLrVIVBrGPdtRw+mFYh9X7ape7/P3Ev4q6uSs+e+QA8m3 XXOxbN7ZMYpN+UNDkzpGsnxQxaT+vlHByn73elfmrY9nPvZTsd+N+mzyfrds eD2PeYnM3+1xHvEqKliNO7lylqn8sN6X3mr61UF7q85LNNF/zTJii2anOmfx wgHVTOwkPk1wlbgz9PQXepgHod1Y0S7zjvcGWDT+ayfzl+jXQdEv5k3hh/zC D6rstxGlE3W/eZPf7ODnnsLPLL+3/lknvf/xgXuiNLu4X1WWZ1oQ+CtWUWat TRxe+6niuCl0zwZt/XVYKvyYx99B8+s+B5K3HDAxq+6vr1cbNMin2UX89pGP h3p7RSnOq9etPT0llPXUeNRHqar5MSVLEy/dLpKfOLDiwF/T3yk7qgT4P3SN ZvlXjQ7Pqa7ZPf7npqWm8l/De4Z7BK3z7th7dMoZ5ziWHxAaFav7vWZC/YV5 TewpkLlBkdTp79RRFU6OM9XvWH7QDt2/r4dXC/E18UNIm5BmfbyiVKfyUx+f MrHfebl4Tj8vXPj8foGXPcnHdUy7oPlNLWscUHOIid9Iv6/Qr8ryRYS8SvID YX91YT/Lf4I9vYQ9LP/R3D8sXwT9HSn6y/IF4f9U4X+Wz9LCJdLEnyyf1F88 3x/i+bK8E56Xp3heLO+OcZXxzZ9xxfJXMB6miPGgyuMqpc9xfVx5k3xFjMOJ Yhyy/LvShRroz29VX+9krX/sZ3ncNhVcjespxkd4P1dtvHg4kPyuhPAx+nPt ti14neZX1iOPW9JTa8i9ToM0vZVrzHyht0Py8rgl+YXFvtkN0+yOG7N4p6m8 PG5JPraPZVXdL1l/hST1NrFHHrck371yi32637OdP2WfYuIHedyS/E081/ZN E6+ML7DPnuTlcUvyPaA/s9CvyvI0btnPsD+TsJ/l5XFL8m7wT6zwD8vL45bk s8D/VYX/WV4etyS/Ac+3v3i+LC+PW5J/hXF1TIwrlpfHrTyuah9uFaGNK2+S l8ctycvjlri8DjYW4///jFuSl8ctcXl9JD3yuCV5ed0keXnckry8npK8PG65 v9I6S/LyuCV5ef0leXnckry8LpO8PG5leVqv2c/SuCV5eR0neXncsj+l9Z3k 5XFL8vK6T/LyuCV5OR4geXnckrwcJ8jjisYtyctxAsnLcQLxM4jrAhE/G0W8 ocpxAsnLcQLxKYgn5yCuJj1ynEDyGRBv/y4o4m2Sl+MEkv+OOPwz4nCSl+ME kr9uHiezvBwnkHxfxNuZELeTvBwnsH7E7YUQz8v6KU6Q5XMjzid5OU4g+f6w xxrxP8nLcQLJq+hvOvICkpfjBJKfi3wB/mR5OU4g+QTkEdbII0hejhNIfizG w3rkF/K4ojiB5E9hHKYjvyD588j7Dprn16of4uQiyC9IPgR5ZaJ5fq2+QB6a aJ5fq1mQXz8wz6/VUchzD5nn1+oa5MXJ5vm16oU8eoh5fs28j3l+rbpCzw/z /FqlvP6geX6t1kd+/cA8v1avoV/J5vm16g8/WJjn1+y34cgvyG9n4OfX5vm1 SnWPa6i/BYh8XC2JPPGueX6tpqOuUgp1NpIviPqMH+ppxLugbnYcdTPiB1Av mo76GPG95nUn1h+M+lUF1LtkXgp1LdYPPSVQvyJ+yLxdI/FrqEfBTua26Fcg 6k7EE+CHWqgvyX7Lb55fq6Pg5wDUl0jegHppX+x3eIl6lJoDdZJZqC+R/ETU af2xf0HyU1AHboz9COLdsL/QBPsLxI2oY8/DfgHxuaiTV0P9n/gS1OH7op4v 8x6ozxOfDz2VUW8nTvsUc1E/J54L9XDYyXw4+uWA+jbxUfBDFOrVst8qoL5E fnOAn+egLk3y31A/bIu6NPFZqJOXw77VflHfVoeiftgYdWmSX4a6ZR7UpYmH o25/G/tcpKcx6qL+qEuTPO1btcO+Fck7o+6agro0yT/D/lQw9qdIvhXqugmo S5O8vfn+CMt/Nq8bsx/2Y1/mFPabSD4Qz2kS6tIkfx/7QfexryTrL4G6tCxv xP4RyTvC/njUpUme9omOY5+I5GeY+4flFfTXBftBJF8C/g9AXZrkf2LfB/5k +Wl4voVQlyb5xXhenbC/Q/KxGFeDUZcm+Q8YD37Yx5HHlRvq0iQ/A+OwDfZr SP6Gd8/vbbXn55d7+QwrrX3iN7Ff4yr2a3gfORz7NR2xf0ryleo9jx+lPdfk OqXO6nYRl/dVSc+7V1M/f9eeq+X5tft0u0he3j8l+TXxbbySNbtbLj4+21Re 3icl+VXbMmbV/dJutnNzU3vk/VCS/9Y8f0vd77Oe7K5raeIHed+T9X8Wz7Vr ZufZWw1X7Ule3t8k+e/QP13oV2V52sfk/sL+NsJ+Hg/yfiXJ7zb3D8vL+5Ik r8L/VsL/LC/vP5J8ITzf3+L5sry8z0jylzCuYsW44v7K+4nyuFqLfUCSl/cN SV4en7Sf6I12/TGeaT8x8nbGy/o5lQZvmlapdDiUz9tWlsYt78+uDA+wKGdl 2N0u7vWquFSWf2fuN5a/uKxYef1cy6Tnd1318yMkvxbPpRXGLcmfqHAsq7+/ l3cXcf6F5VdL45bk55xPH6yfR6ldPqmZqX4aV7Mxbkm+TvU3rfRzLTkdz95Z aWL/aozbbhi3fJ6hRuQH/XxMsNPDReVN/PMD+mdg3MrygUKe7wGthf1tMW5J vi7sySbsYXkPc/+w/Hz0t5boL98/onGbAeOWz4HYVsxm4k+WL4zna1FXjFuS P4jnNU08L5a/jPETh3FL8jcwHk6L8cD2h2FcOYlxxXxmuzN19fNnH+67TOlz 8iOf4340Z7rv+VEWhmnRG8ZFVvnF3H1QyXb6+bNWc1Ln6+e8iBetm8nxl3G/ dwZxHo15LuWTs34ObGT/sY1N5Ve3Tq+nnxtrenTatAgT/Q83vO2tnzNTjJVt e5nYQ7yR4HzPaA30NBZ6mOdBu86iXb6v5HlkUGsTO5m7ol9tRb+Y34Eflgs/ sP7p8Fua8BvzuKmlH+vnJq/VzHnf/2AQn38P2Je0QT83WbxFeqfIKt+Ztx9d p9yxtzFKqyWN4/XzicRvvdncOe91T++a4hwl88xXTmTSzy9mrFb2kqn8wC9h DfTzjpnGHpoXYaJ/hf/XSP185MYxoWd9TewhvkJwvk80GHoyCj3Ms6Fda9Eu 31d6ePRSFxM7mddBv9qIfjF/Cj9UFX5g/bHwW6zwG/Oxnft46Od9D8yYMLKL fi4Y9wbuONe008/7LikY1qPvtXjmo8euCXl5IlIJ+X7ZVT9XSzzwSsYWU+/s 9K4lzv8yz5g2atirE5Gq0eNZTVN5j0/ntunndLcOnXXCyUR/Wb/0p/q53i8X ncp2NLGH+CfB+X6DJ/RsEXqYZ0G7qmiXebm5AS1N7GTeC/0KF/1ifg1+WC/8 wHwU/OYj/MZ8y+HIEP2ceq7ALv1n7PTl+0HFSo/Krp9Tf5fl0Jrz078wz/31 xPK9RT8pRdwqr9DPgxNfXd163OGrW7yjzovz4MS9cy48o59Tj3xeXzGVH9fl 6VT9fHmtKX1WnjPR/3vkMxv9PLo6cPfrqSb2EL8iON8LGQ891YUe5jfRboRo l3mQ1/jxJnYyz4B+lRD9Yp4ffogRfmC+EX6rJfzGvNujYtb6/QrPw9nKHu/4 jO8BOcXuctTvVzR6WS16UnQY86vzK4RfW/pBeXTmcvEjp2KZR42pmTV27Qbv meK+BfNmrt1u31j6QfXv7HvssIn8/fCLX/T7FR2uly1uqn+jsqWUfo+iueug IodN7CHeUHC+T/MQetoJPcxboV0/0S7z19ZdbU3sZL4P/Xou+sW8E/zQWviB eRf4zVf4jXnFo+t99XFK6xndl5m4PjX9ln7/FedXiN8Z3bO+qv0dnasgPv5c fy3OWsf7/cRdByyK1O+F0D408TqJ9bfq55Fpn4/4/C7VsujnwWkfReZUpyZe D3qoDkh8I9ql+hRxj9DRR03sZH4S/aJ8nvgI+IHyJeLl4DeKR4l3hZ89MD7p XkwfPJeGGJ/Er+A5PsD4JB6J8TkD45O4gnHyGuOT+F2Mq/YYn8Q3YBwaMD5l 3gDjkziN8zYYn8Rbot1XGJ/EX2F8wk7me9GvZxifxDvCD44Yn8Q7w28vMD6J b8Y8kBPzJ91/KYp54y3mT+I0fxbG/El8FebPSMyfxG+Yz2PMx2Leq4n5k3g6 5klvzJ8yv4z5kzjNw9UwfxI3ot1wzJ/EP2D+hJ3MrdCv4pg/ieeDH6IxfxLf AL/VxPxJnNapfVjf6Z7LLaxri7G+Ex+JdfAD1nfifljfq2N9J54B6+wNrO/E 3c3XZealsI5HYn2XeTDWd+IUJ2zC+k7cBu1ex/pOvAzWd9jJvDv6FYr1nfgV +MEV6zvxEfDbY6zvxKMRR11A/En3WXwRdxVG/EncEXFac8SfxFXEn9UQfxK3 QhxohfiTuBPixgyIP4kvQ5y5FvGnzBcj/iTeH3osEX/y/Uu0a4n4k/g9xJ+w k3l19MsR8SfxB/BDRcSfxL/Cb58RfxKnOP8d8iO6t/IQecFk5EfEdyKPaIH8 iHgR5EeWyI+I50CeMgL5EfGV5nkN67+PPKgp8iOZN0B+RHwV9DRAfkTcDu0O R35E3AP5Eexkvhb9ao38iPgt+GEJ8iPiU+G3FORHfB8KeWg91Dfofspt5K07 Uccgfh7570TUK4gfQ12iE+oSxGchH6+J+gPxWsjrs6POQNwF9YEPqCfIPAB1 A+K1oScr6gPE56LdGqgD8L0e5Puwk/kB9Gsq8nri1+GHE8jfiX+C3/ogfyf+ ck5M1U1PMhlqvAg7e3vKa6X+pkZjrh25rjwHnyO4SlyWdxdcleWJTyni1r9E YiZDconU2u6rLzqQnnFOD/INDMxkqFzt2PoOC17zOfnx4O+r/uFcVyQ9A04t rqPp8Sb9sjzpkeWpXdke0iPbQ+3WuLcrMdYlo6FnWNKqmrfjuV40a/6Ep9lG WximvLq3PLv2STzzOE+v6prc/b2fe8dpf0f8+rKwtP+651K9VePZYwYmqAbb GTe7VLVhXsHlxdfpPy2MOUdFH9c+me9+nzVUkzPuC2/lO3pgAvfXxXpOfa09 493Pdq1r3I7n+sz5y+ltNPuMtu71bfVP4htHLYnU5cJH2ObT/454yvKuVXW9 d0562HTV2iH9qQOzjNftcJpxoeoMzS7i+xp88tDt9t9XvdRYrR/cryUhUZ+H ZTA0X+C7T8kVx3WYiw19ukw8maa0/5XF00X7JH5068uvTTU596puLb9of8f1 mXb9ymv/No4KfTnfIVcc10nyOrevqf292uD5WqOmj3mH2r65tPbUESOLZ9b/ jvi65ldyOYy3MGQuEew4p8EXrmNkrnP3e+FyycrtiXdyF9U+ibcZfXPwTE3u 6+5NA/S/4+9LeZ3UQvu38XRqyT6zGnzhOsPWTIXPFymXrFp4TOypfxI/uG5h 59ma3LZsvSvrf0f8ycfcE/s6/lIO1bp0qcOdMK4DOH7YtaRk0STl6IfrzqW0 T+LzU2s7t9Pk0q+nR+l/R/zKtIw3tX+rua9mqdr+Thjn6al1MxXR/l6tsbrr M00f8/nTg+N1uZSq2dz0v+PvbxlmeGnhlKR07+X9qM3bYM6j7Z7YTnUrF6vs vPPKd4f2SfyCfbHfjprcjr2Tallqf0c80vWinfZv1S+um1vrt8Gc5754sHGg 9vdqx8edojR9zHMfWFlLa0/NOyslXmufuUWZ5WHfHeKUQTtLNfL5/Ibz0G2D 6hdp+SFS+b0sX91W2ifxUnuq9XusyfmlLa/1Q/s74tMH1yqo/Vs91fZV5yef 3/z9foxn0/w0PerEgn4z9U/izxJmt3yqyVW79TZda595x/ZL54/dEK00quFQ NXReAOdxtSpfCt/tGa5sa9c63EP7JJ5yftyGEE3u5hbfzOO0vyO+peKVN5oe 1S4o08SP8wI4z7JtVmCj9veqQ/2IJvon8beZ9nf8pMkZr3oc1/+O+O/Swj8D 4R/KL7bCP+nwD/GS8M9r+If4NPjnBPxDPAL+mQD/EPeBf6rCP8Tl8UPxeS6M HzeMH+LnMX7cMH6IR2D8vMb4If4c46cDxg9xO4yfPBg/xB/i/fLC+0XxbQu8 X4fxfhGfi/crFe8X8Yt4v3Li/SL+C+9XNbxfrAfv10+8X/w9Bph/rDH/UHxo jflHxfxDvCXmnyjMP3zfHPPPMcw/xDdg/kndLeYf4vsw/2zG/EO8KuZnA+Zn iq/OYX5ug/mZ+GHMzzsxP3N8iPnZGfMzx4eYn+tifibeHvPzMMzPxKthne2O dZbik5lYZydjnSVug3X2HtZZ4hOwDt7GOkj8LNbBLFgHia/HOhiKdZD4Yaxr N8S6xnGI9SCxDnYR6yDvq+ZcIdZNVaybzGm93iPWa44rKmJ9zyHWd95PbIB4 wEHEA8wnZXrq3NY9o6FgTJtfhSLieR4KXHhhaO1DFgYr4+PidbTP+T4rBnco 81ppd/RX9/KlEpQtLUeWHfgxo6HorHNxJy69UErMqnNU02N8XzbwfMGIeLUJ 9IQcKxSs6TH6bhu5V/9cCD2eT1btrlAqQX3XonzwgI8ZjaWgZ/Wnzq8tL2Qw lOvWPHJc9zhl9fZ9Yzq+i1AaOvRfu9szXdneRp8P03leLD06vOPFZ3HK1Sob u9q2tzacnvLD7WK3MKXU5nu5rS5kMB7bNFcd2z1OJT0L439O1v5ePe929Lem T90OPa+3LFhw6VmcusfVMbemx3gWelpUPBlm9crCcOTnvkY3Q74owb7t/V6r MUrXyhtu1h3wS3Ef3uNLPe2zaIOTFu3rxihrbM8kbKwWraSd2Hmxrbulgebp HM0qF87wysLotfOJgxryRSU9ndJyr9T+Xl295UVZ/ZP0bBpRIOOWatHqgm8n Fmh6jLegp3yjeKfV+VOUE1Ef195xCVf6xPh0arY2VskzJ6FUz/7flASrunl6 aZ9Vd75fMO9JrKK+dO1T2CdCaeVuKNX0eqqSEtH4TtHEWOVa4fEnNT3qjC7f k265hKukx8/vwS1Nj7rmyIDJ+mcV6Lnv1yZLUZ8ItfeKvfftr6eqpKd6/zf5 dll9Ux48KHDu4cgQJZtf9fjchT4rVy4MSj+1K06p8CPxymnt832GwBoDCn5R mt0eO2zKxo/K6d4pfaNHa/l4ruojXll+VTbOH9Jb06NW7Xx2+oORISrp2dFg /Bzt79XiM8Lt9U/Sk9Q56fzUjR/VuWvz5NP0qHbQM/faxLRhnnHKlLqbbBqv fauEluv/RPn2QUmKGpZ1bsHPSsHkErXmaZ+jB55LG2kToty0Xe7Tzuq9YlHU 503lxfHKxxvRS2Yt/ag8ftWu1nDPOLXKJh+7hmvfqqTnVbsQH02PWnTXvnH6 J+lxPh34voPVe/XTm9oHND0q6emZ1mZDd/doZf+Tca1vrghQziZuvtHiwnFl 1sj4ElnvhisDI4qWstU+nU7fiTmn5RGzwvb5zfALUI7aHajQLyVaWdJma4C/ y12lRNq+r5oe1arGklXqigCV9Fh4D3us6VEHbD46Tf8kPevWl9k5yy9Ay/9K PeqbEq1OgR7HDCeyrHweq2z3aL6oYr83CsULNpVv+p8Ii1DmHj8cdlL7fHbl xI52ZV6r0f5Xvb9ODlQeV7Hr0eByjOKWvr/U8Usv1L2nw8dpetTQFRX3le/3 huOOw/6n12h/ry60vFJL/yQ907b1do2ZHKiOvt8sqf7lGJX0FHgy5vfLi4lK ztj6LWJ6BCsnz+V91OFdhDoj8WgW+2bRSmrffD2aap8Uv8yr2mD98csflK4N +pa9uTpB6TymU9iFbmHq9PIR9r4XE9WtL3sWju4RrJKeO6HxYZoeNXqczwz9 k/TMNh67cfLyB3Wccdln4+oEtRv0bO54+d7zmcnK+5zKPZvCYcrI2O2btfdU HfZ12jWb0ASld+yLDZm0z2qPC51pVzdGbdH7Z0BNn09KUKXdTVtG/lAonrJ/ XSn/i5nJ6nvfw44ZC4eppOdGy3Nttb9X8+/YYqV/kp4493RDbZ9PasHIbIkt In9wXBZT42Th8hktDLMKnHXJsOazkq1klRnae6rWiXvVKzz0hzLU69zwCO1z dID/Tu09VX99bDLucLUope7jVot2Dk9X0mbceKG9p6paxKuDpsfom7/2Oss1 n1XSc1D1zqr9vbo14OFpTZ9KeirMj653tFqUOqvanNKaHpX0eKTVuVcsZwbD 8oG1+qZvjlXKnnOfm6fQZ7Vv4+jla7xSlRX1Zz1aq30eyZH1tPaeqgvKXh3X eUyMsv6BZ+Vp/awMozJdC9TeU7VcWy/L4jkzGCs1rVw0dXOsSnpyhu4ZqP29 +nv9vQRNn0p6njfw2Np1TIyqvhoUP7WflZH09EoNHt7IkNFwaWOHLa93xivB FiUnN/v2QQ0Om/p0fmFtHbXstWSB9hk+/NLDUTYhatZZxW51ahqvXO7ScE6v Z9YGw6qJbWYv/aju7VDxkKbHeLFK6x6vdsarpCdg/wVH7e+NnVrly6p/kp53 wfNTOjeNV48U6NpY02MkPR0adt/eq5KN4Wn9p/6J/RKUsCNH73W7cFz9kvDN qV+shaFUnSaF+mufVB+YaWG7uUWbBGVeabd6W+1sDFntbq5763JX3b510jtN j9G+k93qhH4JKumxmDorUNNjjD53aYf+SXpaVxwS1LKNJhd0O26LnY2R9Mj2 bBR6FNkeB9QxnODPK/CnUfhBkeMT/h4Dyf5Puf60q3yE/+fD/wHCb4ocz5Ce ukMfhZh+v8c4Ovci8bng2fAcr+A51hP+Vxzgh3DhB4MP7NmOeOO9iDcMFRBv bJpTxOx7P7ZjH0/mO8F/TxH+jxX+NzSA34IR57wScY6B4hw/jJOTYpwYasLO J+bxhuEC4o1teO6KeO7KIjyv4oivgkV8pVB8FYjx2VWMT/bzfMQ5l0Sco1Cc I48r0r8f4/+aGP/83Esijjop4iiOx+T4k56jPD6pPnYA+i/j/SL9crxKeuTx HIjn+Ab97YL3kforx7ek5wP8fwzvaR34fwTG7WIxbll/A8S3O0R8ayyNcfIJ 70tl8b4Y6bm/QJxsK+Jkjm9/zRTj01uMT243F+JVbxGvcpzpiPc0Qryn6iQ8 l7GIz2uJ+Fxtiuf+Bu/XCvF+sR8qIU4+JOJkjm+7471+Kd5r9Qb8vwzxtr2I t9U1eL5W94u0X7re2hC5dW7YpMzxvL/tifl/Deb/omLeVtotubo+66zfyu/E Wom22ifJD8C6sBrrwn4xnytWBbLlc9H0tsje4Zjejts/3jvii7GObMQ6MkzM /8qqccfbafapG4OqjDXVk9TqXTf9HsEp3Hd4gX34RHD6/hBf8CrPz8/V7FZ3 H21gY2r/Paw7t8W6YxiMdhcjPl8o4nPDbcTnqd+brNHsMBqavzvlYuK33FjX bDb8WdeUffBDR8T/riL+5zyiItbH2mJ9ZD9THnFE5BGcj1C7TUW7/P0bpKca 1lnSUw393Sn6y/J5YGcGYadKdm6EnzcIP/P3gfjCPzexLg+Ff+Lyi+fbWjxf lm+CcZIr6c844XaH4vluEc+X9YxDPmVx8k8+xXlQ2j0xPi23/RmfrKcrxttO Md7Y/pbI146KfI3zLHeM5ytiPKuF4Z+myPuei7xPDYGf4xCPzUM8ZiviKKU+ 4rER5vGYkoZ4rCHisVQRRyk5fSv/uQ/1VPq+kezgjyVeEvHYIhGPsZ6r5nkZ 53dHENe5i7hOGQV7XiO/cxX5nUL53U3Eh+9EfMj9uoo8cY7IEznfJPkAxJMk fxTt7kQ8Se1Whv3zEE+S/Z/gHwfhH+ZeyFvbibyV882q8PMU4WfWnxn5b6rI fzlv/YrntV88LzUr7CyGPPqpyKM5/92G+D8Y8f9oEbcrcvxfXcTtSkvE/8Hm 8b9y2ejf4r++z+RfPArxfzER/yu3oCfKPM9VciLPpTyikMgjlBqwxw35ckmR L3Pe7YB85KPIR7hflHfXEHk35+8K5IOQv5C8N9otgPyF2o2H/YWQv9yE/TXg n1DhH+ZVUQc4J+oAnL/3h5+HCj+z/tOoJ9QU9QSuA6zH80oXz4vtrIS6RIio S3A9oSDyzVzIN0+LPFGZhXwzDfmmQeSJipxvdhV5opLw9Vn6f31fyr+4C/JN F5FvKr2hpw/qBmGibqAEoW5AeWu8yFvZnpeoP5QQ9QeuY1D+6ybyX+4X1TFq iDoG10NmSPkyyd9DuzHIl6ndubB/PPLlHrB/EPzTS/iH+T7UVaxFXYXrIWPh 52z9/viZ9UegPlNO1Ge4rpIHz6uCeF5s5wzUeXaKOg/XZ05uHlvKxzJBqbzd 9vCD1+/Z/3LdI5+oVygDplazG7rhi+KXc0GbYdonycv1EF9Rx1CyXVwx+66m 97nbkWl6O//rucv1k92i7qHk2x/kdv/1ezVHs4VNTfX0P/My7L++p+VfPKj2 lWDNfnV4j8SZQ03sH4N6y3hRb1EOoN2F5nUhZRjqQhOitzhpdqgjT5xbdc/E b4dQz1ks6jnsh983RN1pkKg7cf3KE3WhKFEXYj8XR/3KRtSvuA42Ee0OFe3+ /b4dqb5EeoLR3yGivywv153IzrLwc3bhZ5aX61H0XL5eEM/XVzxflu+CcRIm xsnf7x3C830pni/rGYg63mlRx+P62xGMzx5ifLKelEpivK0U443tn4A64VhR J+T6ngPG83Uxntk/HVFvvCfqjVwnnNc4NUu1TjFKlo39qxYoEsjjR65Prhfy 6tDRF1YF1opQXN6eWP9G+yR5uW7ZRtijel19siCvpjdWub1db+d/jVu5zjlb +Ed19KzaJn+RQLXrZodG/z89dL71XzxLtn4NNbvV/k0yhwSa2C+P/35oV35f PFGfnPF54SjNDrXyydRh+Uz8Jo9/8oP8vlD9Ux7/5Gf5faE66ky0W160y+d8 5Tow6cmK/vYV/WV5uT5MdnaDnzsLP7O8XDceA/+swfP9Jp4vy/fGOJkrxsnf 72WSxj/pkd8XqgNPxfisJsYn65HHP9kvvy/kZ3n8k3/k94X8LL8XNH7kfYRg sb78n/eC5BOxfuXH/sJIsX79n/fif41beT8iWKyb/+e9IHl53eHvkfgHl98L 0tPTfP9CeY92x2Pdn4C4pSfq5PJ7QXpeID4phviE/HAbcUUs4hmqw8vxCfl5 GuKT7YhnqJ4vvxfUrrxfQ3rk94K/HwZ2FsE+Dtkpvxf8/TbS/g49F/m9IHn5 vSAux0WkZyDiqJ6Io2g/Qn4vSE84xltZxEtk/2jEV7aIr8jPcrxE/smN+Ko8 4ivysxxH0fiphrj6Pvb7bEVcrcpxFMnL+4DvRNyuynHU/xq3CvKFE9g3zCXy BVWOo0j+EvIs+Xts/sXlOIr0fEb+NQ/5F7UbjnynMPI12q+R4yj+HiQpLyM/ XDfPp3hfaQPysurIy8jPTZCXBSOPo30lOY6iduV9VdIjx1EkL++3kp1yHEXy ifDPHOzDkn/kOIrk5TiKeBU837PIB0lPdSl/JD/LcRTpkfNEsr8v8sohyCvJ zxUxnoORJ5J/1iKvTEFeSX4ug7rBMey/9xZ1AzUX6g+x2H9H/UG9hjqGwXz/ Xc2KOo/8fTj/4pdR5+lpXudRi6CuMgd1Idqn8zXfx2d7vFCfcUNdiPb7LqPO Mwt1HuqXt3mdh/cfr0B+Gs4PkPwrtLvK/PyAegf2dzc/P6DuhX8czes8ahDq Qo1RF6J+2cDPv8zrPGoF1IUmoi5E/SqC5/UYdR6yMwp1oT2oC1G/DKj7eeG8 xydR91M7oX64A+c9Sor6oboC9clfOO9xX9Qn1XjUmeXv2/kXX4B68nzUk0nP TdRXjag/075nO/NzI2xPdtRvrVBnpv1TW/PzJ9wv2oetjjoz7cOSvCfOq5B8 B7S7AudVqF1X2D8P51XI/lHwT7rwD/OBqPduQr2X+tUMfj6EOi3p74C67jbU dalfTfC8nqJOS3a6oa57DnVd6tdK7HeUwfmiLWK/Q62HfZMtOF+0T+ybqCWx X3MJ54u8xX6Nuh77FPL3+fyLP8J+nwf2+0jPK/P9Kd6PnmN+Tont8cf+V2fs 99F+dDHs0x3HPh31i/a1r2Bfj/a1i0P+CM5Hkfw8tHsG56Oo3Zew3x3no8j+ HPDPNexnEf+J/a/r2P+ifpWHn72wP0X6A7CftQz7WdSvxXhejbE/RXZ2wX7W c+xnUb8ssG8Vjn0r8v9E7KPlxzm3/mIfTXXEfkQK9q1IPgD7epY4/7ZV7Oup v7GvYcC+1f967m2xn7gZ5+UaiP1EdQX2U9Zh34rkab9b/h6hf/EK2Mdxw74V 6dlqfr7O0Brtyvvjn8W+p5psvn/EeoLMz+/99YO0D07nEIpin/oD9qnJz/K+ Np1n+IV2m2DfitotBj1vcZ6Q9FREf7di30q28wXOGZKd6+FnV+xbkfwe+Oct zh/Sc4nG822JfSuSr49xkg37VszxfN2wX0x65P1lOo/xC/tW6WJ8sp7nGG9Z sI9M9sv7zuTn0RjPNbEvzONZ2kcmP7vb7K8RnJrR4GAM7VW8QQLfx83u8mx2 BW3+XDolpGFF7ZP4GfsGzkU1uVnrFm7T/+5/jcOhW3ueKdYgQX0Q9LWrqbx8 P4W/L6jY8mStXePs+5WvVjBpV763QvLXL9Wfquk1rh19z7aYif3yfRb5fCzd ZyF+A3pWCT38vTrfYc9MYQ9/P89Y9Ou+6Bfz3fDPPOEf5hnhT1fhT+by/Rey ZxueSx/xXNge+V4Mycv3YojL54rp/AM9dwXPne6v55CeO/Gz6NdsPPep/ziH Q3wY/PMQz514fLdO//n9POTnOXjuJL8S56UjxXlplqfn5YrnTvLncO46mzh3 zfITcU77gTinzfeqvKFnNZ476SF7ZuG5Ex9nPp6Ze8A/8/HcidtIz534t7Hi PPkTcZ6c70Ntx3NxwnMn+Uk4lz5XnEtn+Uo4xz5BnGPne1hzDeda/df327TE eXhncR6eeR6cn28kzs/zPanVOG8/Vpy3Z74D5/P3iPP5fO/pEM7z9xPn+fme VCWc/3cS5/+Zf7jW4T+/N2YH7hFsF/cImG/BvQMrce9Jke9JnRf3FJhXwb2G WHGvge9DpdYW9yBeiHsQfH9qNe5N1BD3Jpjv+7G5+X99H8sU3L9IE/cv/v5O NO5r1BL3NZhfxv2OfOJ+B/ORuA9ifePPfRC+J2WP+yMXxP0R5ndx3+SeuG/C /Em+42P/63tOsuLeSn5xb4U53XPpIu65MKd7MQHiXgzz/bhHs1vco+H7U1a4 d3NU3LthXgz3dMaKezrMh+b9nOW/vj/kFu77VBf3fZjT/aBJ4n4Qc7pPdE7c J2KeEfePAsX9I75XtRr3lbIt/3NfiXkq7jctF/ebmI8/9+7Qf30vxzPck6L9 eOJZca+K9i+Jb8Y9LNqPIR6Ce1uU//DvDuOeF8XBxFvhXhit6/y7xvCn/H0X RvP7ZczD4U8X+JP4VPjzDPxJPIPkT+Kr4E9b+JN4Cvy5FP4k/hjjU/4eiSwY n/kwPon7YHx2xviU723R+OTfgcX4dMf4JG6J8XkE45O/B0Man8T34H2Xv59h Et73X3jfiSfjfa+O9534BbzvefC+8/ch4H23xPtOvDHe93N43/n7JfC+38H7 Tvwt5k/5ew+2YP7cgvmT+HrMn+ni3pYi3/PCPVPmFczvpfJ9rp+YP59g/iS+ AvNnZcyfxGdjPZK/T6AF1qPhWI+I5zK/b8v3wlZiPRqN9Yj4dqxHHliPiB/A etQH6xHxCliPemM9Ih6L+ES+p7/C/P6yQb7nhfvO/+de2D3EG/y7nFj3H2Hd 5/v7WN/nYH0nXhHr+3is78Ttc+0NKjw8k2FlxjyrLawvOtD9rPIPTsyqcDij 4cJQ208Vhp53oPtQpwKe5J9X1dJQr2z5rbNXx/E90SVbste+njOD4dekkll9 4s44EF+3bMfC6Ds/lFcRrfu08Elj+StZBtUb+CNY2dXwdOSwrVZ8j2l9Up4R g38Eq6eaGx+Y8oJdbYbE3Pmhhvl18mpuomfEk9w9NXuMbdcv3zTLxJ492/7Y Y8xdLPbSYZsL9sSdId9ayKvEC0P/R6GfuQfsOSnsMRLfB/vdhf3MF6G/H0R/ Wc9R+K2t8BvzUqU/F9K/l9z5eVfXm3e+/P0dsbMT6uvfS/7yWZMzt62TmY+3 nbFl3Zx3StayzaP07/km/uJFfsOmOe/UdYsOnDPlGVOfJejfSx490bKIqR6P CtMW698zHvax3FvVpN3TQ8X3khd1fmtX/uAZe+J7IB8i5Pl3u2yg/4vQzzwK 9rgKe5g7wv5swn7mD9Hft6K/zAvBPyuEf5iXw/dvF5F+36rOtXk55nf5oSjr O/x0nRrO59wyuqfEdysdp2Sq0c+uZZMk5o67ne4NzuyvrPXMm9WlcTLziT1r eA/L7K8OaH3lw0QTnmdY19XdS8epFguDtrcw0RP0IdMwrV3V7X2dHWtN2s3m sL3qiuBktWfy8RDHNcftiQdDfquQ5/U/L/SnL/ijn/kS2NNf2MO8AuxfJ+xn nrpL9DeH6C/zavCPk/AP8xpN/tip1Eo698qi32Fv4jMntu1s2J+gnC31bdqE xBA+J3am3aZZux9HKZGxWb16VY1jfmFDFoedo18qoTZuXp8rJzH/3HrqbvfR L9WY0rGLTflhl5LjPR5HqSMPRrcw1WPR8cMmrV21fXTbAeNN2p0zaOql06eS 1JE2R2LnvDhoL8u3FfIcNx2Bfmehn3myuT3M3WF/mLCf+X70N0b0l/kU+Oe+ 8A/zWgP+2Kl07dmzSceZ+72J51wQNme9TaxSZFSpr8Eh7/n8knrtt+/YmWFK RL9fMzt8/cz8h4NXZbeDPsr5hqXiHR/GMZ/i9LiY+0Ef9ahFm1emfEvSJY9x M8PUN4u7+Lc30RN3bcRXrV015nVkwSCTdi+O3Z/7UYN4Nc+xe3typ++zJx4P +c9CnuPNrdAfIPQzXwt7jgh7mD+F/ReE/czPob/xor9/41n4RxH+Ye4z+o+d Sv83KXbudT29ZT6+2C6dO9C5i5rw/80iIY01/zvQPnVNjH97zA+031cV499j Q2l9/DsQz4B5wxrzBvGWeO9WY94gPg7vaV/MG8TtzN9r5u8wD2zDvEE8C+aN bpg3iL+H/CbMG8RzQ38q5g3iC2GPE+YN4mVh/xrMG8R/Yd6wxbxBvDL81hvz BvGimJ+Hmq9f6gvM5z7m65c6GvO/jfn6pT7FerHafP1SrbC+RJmvX+oO8/WI +TGsX4XN1y91J+Tfm69fagbojzBfv9Qw2LPKfP1Sm8P+zObrl3oP/fU3X7/U vPDPEvP1Sz2OeKA24ijK29YgfniGeIn4RcQbboiXiLsiPjmOeIl4PsQzwYiX iA9D/OOIeIm4O+KlHIiXZPmWiJeI54f+D4iXiO+CPccQLxHfA/t3IF4iPg/9 fYN4ifgh+McR8RLxhYgzF61eo8eZ3sTbXqlsVXRJBsPonQeHZH2cwPluaJ+8 9yZZpigf1i0a5xZjYSBeYGT5ZTcdPykXZx85VL5YRuYRvrks7zh+Ugu0G7zE lBcNzHl3smWKOtL3tY2pHvsuX9po7RqrOj5vksWk3dWP/sTPxjeD+ijrPl2y J94U8pWEPO9PFYP+EUK/kfhPc3uYpzkL+y8L+5n7ob+hor/MW8A/C4R/uN2y iPOb5lqmx/nexCe5TOpfME9Gw6cC6ya37ZDEdQKXjPZnslZJU3I9ynn6dFsr A/EsD8OPRr4IVdKaJWz5+dSGee7sN5y+vAhV2zS5Od6UF5+3745tlTRVDVKa m+qpMfLdYa1d47cONeu1MWn3Re4/eYpxyw//1OZPr9gTrwn5BCHP+xQloN9b 6DcSLwt7Wgt7mH99IOxPF/YzH4z+5hf9ZT4W/kkR/uF2GyOfGjJpm55PeRP3 GrT1Useqv5XtPbuUTHWxNFCe1bPdE9+g8Cjl6dqMlnlm2zB/O+1Hq4F9gtSe rSpeW5AzE/PKmwM6tcudop4M7PDpSJ4MzCuua5krZqa1MWnH+2bF937n79kw pp8wnOqbyThnYaBSIPUO8+cT7L07Vf2tbi6QdDTFxdLI7V66PfNjuBaPbWvx PPdsG+abzwcF9OkTpOR8fDhAs4f5+uUbarTNnaJYpTVoezRPBuYX9+S+Fj3T 2uB2t9L0Enu/q8Q7hzytr9lj+PBmTNPSqXeYZzyZMHaG+1eleL7H1lkmWRso 35zTsVtU+ghf9c6OLxXbL8vIfINftg69bH+ot2f0nTewlxXznYOuHdb+bYwo +etmT9sf/D0end2y1db+3ujWvMKQ1BG+zJ0Nu31nuX9VIxbG+mSeZG0kPrZ+ akCyJndsa7Um+t8RDxkd0UDXO82x6Cu9HebrkrvqdmRZU8JPt4u4zc5HJXS7 9/WeN8nS2Zf56pprFt4qdFPtMLxZXI7MGTjPjVtcwtnfJUG16lvr5NuTFsz9 3We3n1Tgt9poaYGOy3N+5zx3e4+7hR89sjJ+67uiQ/41gcwjrW6uuVLopjJt Xcefmn7OTw+9/DTGzyVBGdrfI1HTz/xthkFeLgV+K7fDazdYkfM756fjrl+1 0vQbDI8WXS68JpD5wCftFzVOCFcUh5WhLU9E8bni44UeZ4/O5atsGa7MX7Ym jvmVL9+sj+a+rxb1CkxenPyX50k6cbdb9Cf16Y0eX/fn+8p84qRsX3eUiVHf JQ+NbH44mHng8i3hb2rGq1ma1jpwJvQk859v9jZvkhCuHj18s4FmD5+/nVSl sEVsLl/16cp+fTV7mA/sON3mYO77in/qhpxLkv9y38D6CV2jPykd9g9afCDf V+bXm3tO0OxRqvbq9rjF4WDmV3d2DtLsUZIWOr68GXryb7tjNm1o0OOtsiLD wENLlifyedRxz20bT1pxS+2Xr6nT8HVJzNufye+eZBWuTj37tmjaknjm/WPa OWr/Vi1y1S2o/X/mJft8G6L9vXo3W7TPhBW3mPdx83rXqMdb9UuPr1O0dvl8 5tfWPsPGaXI3d5wYo/8d8VHju25J1PR2r3R1ot4Ocddp4xJTNTumdE0u8c3q 7/d7TXmxtItud4fNlb2maP0gfvFexxJ2DS6phR1fNizi9zfubdN/vc3LzFHq i6rrs8V7fWc+48Tq++cLf1PHFr6UFJAQzdxm1PnSMYuT1ZI+OQvv6PXib1z9 6fx36waXlN12agtNP8efARkXnHmeOUopl+/ZGE0/88ErH/XS9Csz562o/SYh mvmy6nZWmn4l06dxhd17vWBO89JeMS/xPHkD89giMY/9/R41vNdDxXvN88le zIepqX/mQ56fIzA/fF/9Z35g+RjMJ5PEfMLzmHwfn/TI9+5Jnub5IWKe53l1 a/v3Ufq8lvjj/p6Z2vxK8pWwXsSL9YLlu2CedBXzJM9X1bDunBDrDs/zuzDf hor5luXTsX71EOsXy2/CvH1LzNs8fx4yn+f/zsPS/XTSI99DJ3mqZw7D+kvy BS9Yntf8YGi+YnKmOdp8T/LtEReNRdxIfDzmvdxi3uN5NQLxVTDiSZIPx/x5 UcyfLF9opFmcxvJnMQ8PEvMwz/NRiPcKIf7k8YD4cBTiT+Ibzb/HifU4IM6s jriU5L3q3fHOPT5VnZUwxKnmyGS2cy3i1XeIV0l+4e3rBzN2tTJ2DgxLX1kk TJH1V0EcS/JuWI8+i/WI14sS5vEzP99ArGv1xbrG8snmfmD5H1gfLcT6yOvX b8TDVxEPk/wX83WW5QPwHMMRJ5O8fB+c5FthnCxC/EzyA33m/bYbn6r0HjC2 Rq2RyWw/1c8VxNUkX6ec5QLNn4ZMnuvLrykSxvJX8LuN+81/H1O5DH5O4uH4 Xchv5r+PqYSC/5R4AH5f8of572YqL8x/d9L0nrjLf90fH4/ftTxm/nua/+Tr 8fuYqea/s/lPfhS/s+ls/vub/5MPMP9dzn/yjWj3l/nvdf6TT0K/jpr/juc/ eRP8vudT89/3/CdX4f9089/9/Cd/i+ebwfz3QP/JaV9mKfJlGm8XMa7emP9O 6D/5aqybAR//rJtc3449s2zOnvc/lf7TJvzyPPSOOdXnH5r/rqgyHuvyELEu s3zwyRJ7l7dPVNxj+lxu4hDPPB7reymxvjOPRrxRDPEG8S6IN14i3iA+Lfe3 0ivaa35pm6uCqf45iENGIw4hXqvl9DNav9QS5ZZm9zDpV1bEJ/kQn8g8h+Cq rKeg0MN8Htp1Fu0ynwE7iwg7mXdCv3xFv5iXuW/mB+YTES95Il4i/gb+rIh4 iXgg/L9f+J/5MDyvOYijiH/Bc98gnjvzVRgnsWKcMJ+GuDGbiBu5nm85t05f PT7+XvWUVRMtXiZO+xGeqMeSns2IS4eKuJTlZyGO7SziWObjEW/3R7xNvAPi 7WmIt4kPQLxtiXib+N2qXq56PF3Ryv1iQxM7SyEOv4c4XObXBFdlPaWFHuYD 0e7vnH/aZd7JPC9g7mreL+bRiPNvIc4nPhr+6YE4n/g6+HMq4nziaXPEcylX 7c9zYT4Vz7Ej4n/ilAetFHkQ7y/QPsgt1OFJ/h7yqSIin2L5YORfLUT+xVzO H4nL+SNxOX8kLuePMv9k/4fzvoML9LwRepjnQ7tPRLvMfc3tZC7nmywv5ZvE 5XyTuJxvypz8T3movD9C8rL/SV72v5x3k3+Iy/4hLvuH82vJP8TlfTHiNN6y Yt6gfFPeLyN5mh+GYH4geXkfje9BS/MG57nS/hrJy/trxOX9NeLy/hrxO5gH KmA+oXblfTeSp3z/KuYTkpf340ie5rF0zCckL+/TkXxHzDNTMM+QvLx/R/Jr zesYLC/v6/H3hUv7evL4pH094qmYf8pi/uF7pthvPYP9aOIrsO4EIT6hvP40 9m0jsE9N8qOxrg1DHELy57H/+wn71yQfhXWzJOIQko/CPnI09rVJ/pD5vjPz 3x3EPnU77GsTp/ikEOIT0j8b+93O2O8m+RqIK3IhPiF50t8G++AkT3WVgohP SJ7230dgf5zkZyI+GYX4hOR/mveX5dsjPnmO+ITkd5mfB2D5kvfN6kUsvxfP Kxr77CQ/Gc/9HvbZifsjbtmLuIX00P5vF+y/k/xnxC2TEbfI+7/Vcf6B+BjU AaxQB6D9ptrI477s+ZPHMf+IOsBp1AGIj0Ce2ErkiczPoA7QH3UA3kdD3toW 9WHiCch/051EfZj375DXz0ReT9wX+XU91I153w15fQfk9cS3In//gHqyzH2R 18t6HIUe5q/Qbh3k9bwPCDunCzuZJ6FfaaJfvD8YZe4H5uGob09GfZv4Afhz MOrbxJ3g/+7I04n74XmpqHsTr4Xna408nfhojAd71MOJZ0Q9sD/qgbSPVgh1 pzKi7sSc9jF/4Lwc6QlDnTAJdUKSj0WdcALqhMSXom52C/sjxNehznYT+yPE d6BeF4b9EeKbUCdMQZ2QeEfUA7dh34R4J/A1qBMS3ww9SUKPKrf7EXVC4uth pxH1QOJe5v1iPgb7MkewL0M8CP6Zgn0Z5vBnJuzLEM+H59ID9UDi1niOntiv YT+gPrwS9WHeT0Sd5xzOSZL8NdSN56FuTPKeqA8noz5MPBT10u7Y7+P7aKi7 Hsd+H/EKqN8mYL+PuDfqwLOw3yfzwagPy3piUQcmXgXtHkO9l3gK7OyGui7x DdgfzI79QeKu6K8F9geJn4d/tmF/kDj5+T32B+V91eU4p0p8CvZhw7BPTfXe rBcr9tX3m4dWq3jm64tQ5pOxn2uH/WvieaJ62+r/XnOxZ6ds2v8nbot97d/Y 1yb+bMSiba219p4H2z3T2yeeF/vLbbHfTfzxrC+rLKwPelcT+9jMS2Kf+ib2 wYn/rh3kq+9nj/x6cLGp/lrY7/6B/XHio19XmKXvTxdtHtvY1sR+X+ybb8O+ OXFH1WmRvs/t+aWr1WcT/9SG/iTsp8vyO4U889Lm+/hc5x8DewoJe1i+nLl/ WN6qjuivs+gv8xjsy1s0F/vyxAsNHrvGxJ/Mh+L5FsR+PXEVz+u1eF7Mx2P8 pGEfn3g2jAcPMR6YZ8a4WirGFfMsp5tM0uv11zLbKHcdP3G9vWXSb9/tMRaG 1G2uLadYpjBfUDjscObHCUrBne3H6XVl4ivuhn+sMPSAd8JDMa8Q93W55qPX 2TtlXFPOVH7nmWON9Pr13UKbWk020f/749Kteh08s0eR27dM7CFuKTjXsd2h 57bQw9zPvF2uk++s1y7UxE7mLuhXUdEv5k3hh+zb//iB9WeC394KvzGv7vjg sn6eaeuomLlDfgQrcp38mFQPT2j/sr1+zin0vP2LmDs/WD4MddHvUj18yu36 dvr5J9879abq54xI/jXqrj+lenjBhhbaOr3Xu6A4J/X3dzd8j/7n96zW7+uX Rz+3ZO0bW89U/7/q5NUGP07Xz1H9/vIsLtrE/n/VySs5XA7Qz1HtXNCo4yAT //yrTk7yW4W8KsvLdfIasCdN2MPy/6qTN0R/M4j+8r7Jv+rkrjkb2Zr4k+X/ VScfgeflL54Xy/+rTh6O8ZAkxgPb/686eVWMtzNivKn/q05+3M32oX6+06NG 4cYjMvtzHdjnYKl++vnOlq3m+nUvHcc8fPGhqDVTw5W7MR1c9XOUXMd+/t3X op+bd4+mIv/gc+MNjG30c5Ynn95qaCpv12f3K/18p8XC8g6m+g8nOSfp5ztT ZrVsPtTEHuJJgnM9Njf0/F7wRw/zXGj3hGiX+cCle16b2Mn8Nfr1SPSL+T34 oZPwA/Oj8Nsd4TfmrU/tnKTnzxb7Kj3dreWLXP+0GJRHz58XLIoI1/JU5ju6 Jj0fp+XPDa4ePq/nhcS9Sns37jhzs3fkQJH/Ef+9Yk+Ung8bP+SZZCq/o/3c qXqeOXKgU+JuE/0zt7bYouerz796j99lYg/xR4Jz/XMn9AwXephbrRTtqqJd 5u8P2Nmb2Ml8DfrVRPSLeRv4YYPwA/NW8Ftx4TfmhmFv7+p1q8rDBxbwOOjD dU5tEC/X61YNcua1Hj8zjHm/1R1qfAh5rzzx9yq7wSb2bx3Vcr6de90N3vai jsX8bYllVnodp59HufPrTeSLuZSrqNd97gb0azTORH/53ec/6vWjrB0blt1p Yg9xS8G5nlkCem4JPcyD0G5f0S7zOtvdcpvYybwF+uUr+sXcFn5oJfzA3AF+ GyD8xlz2J9c5JX8Sl/3J55okfxKX/Ulc9idx2Z8yJ38Sl/1JXPYncdmfxGV/ Epf9SVz2J3FHjNvfe8X7TvWZjhjn8/G+E6f3vT7ed+IH8L5H4H0nnr7C7L1j 7ob3dATed64r4r1+hvdd5g/xvrM90DMM7ztxS7zv3njfib/D+w47ma9Gvxrj fSfeGn5Yj/edeEv4rRjed+JHMK/uwnpE9avHmIebYz0iHop5+xbWI+KfsR51 xXpEPCvWhWNYj4jnwDqSLtYR5l5Yd5KxHsk8HusR8VzQk4b1iHh2tHsU6xHx fliPYCfzl+jXfaxHxG/DDx2wHhE/BL/dxHpEvArigU2IP6k+E4O4IgRxJnEX xCcvEE/yOXzEjfkQNxKvg3jJEvEh8YqIu1IQBxIvj/jNDfGezDchriNeGXqS Eb8Rr4d2LRCnEV+NeAx2Mh+Gfr1C3MV1TvghDvEV8Urw20nEUXwfHXH+FeRH VCdpjrwgGfkR8XnIIwogPyK+HPlRHPIj4i+Qp3RAfsR1J/O8hvWnIQ+yQX4k cwvkR8QpzzIiPyL+yrxdrju5IT+CncwnoF9FkB8RbwI/2CI/Ip4RfgtEfkSc 8tDBqG9QPcQOeesq1DGIP0X+64N6BfGHqEtUQV2CeDrqDyNQfyA+0jyvZ/0t UR/Yg3qCzN1QNyBO9Yr8qA8Qt0QdYDjqAMQLIN+HncxvoF++yOuJZ4Uf3JG/ E7eB3xYjf+f7AtLvS1JeXwR1wtKo31J+Sucqo1Hn5PNy0u8/Eq+PenIE9gv4 fDXq0q2xL0Cczt21RV2d+EHUz2egfk5c/j1H4hY4X/EN5ytovaD9x5I4h0A8 GvsjnXGeh+bDIOyzbMf5HOK0D5UZ51v4fC/2swrgHAvxp6gT5hB1Qq5r+eDe wShx74D5dvNz+Fz38MH9ha3i/gLLD8Z5/khxnp/lG+KexTNxz4LrP1txL8ND 3MtgHn5C3EcoJe4jcB2jTAazc/Wc1zfF94h+wu908P3cUHEOZ484h/M3H8T3 uxbH71kQLws9Ufg+UuJTcJ58Jc6T8zmTNmbnPZh3xjnwaHEOnHlf8K84H84c +tcI/X/PpUjn/Ckels/5E1+Fcw5+4pwD8+E4h+8jzuH/vd+Kc/vHxbl95vJ5 fuLyeX7i22HPNmEP8+6wv42wX/2XnRSXynYSl+0kLrdLXG6X9/HbmJ3D5/ex k/lzYe6E57Iaz4V4HM53uWNc0fvVOoPZvhjHFRlwv6Yo7tfQOuKJ9+sw3i/i 3c3vxTAfBh6G+zLEP+F9KYH3hbiHdO+J6/x4Hx/j3hNxP8wPtpgfiD8wv5fE /L40D/C6Br4F95uIB0LPCNxvIl7f/B4W81Ww3xPzA98Li3L9z3r+jywbe+vn 1EMMC1fq59aJe1dxiWy82sLYtXyVo9on8wsOpXLr5/urnQ5/rK8/XPcuET5W l2tf80L5JtrfEf9cdsN/1oeN+wLaddkcp3btaNG7lNXfeS9q1qpinTfHKe5L Rm7VOM9jFZLPZfmvembr0o3+Mz/9tvnCxgr93qiv37Rton/PPXG/KqOHrHOK VPsUuJFR+2TuOHvX2XL93iinli7x0H9/gO/FWNodddXksir5buh/Rzxk2Nj/ zONWNru9sv3RIPVU4Mr+W4r+fS/G7yvftu3RIKVaybJuGv97XqXT+v/MXxwx r4ZI83MC5uEi0jy8AforC/1/60Ww56Swh+fJeehXmsOffvE8NhR+OCz8wNwf fusl/MbzkuUW4Wdf4WfmyXiO28Rz5PfxHp57J/Hc+b1LwvhpJsYPvxf3MN4q iPHG/AbGZycxPnmcp2M8fxDjmfnS008a6HY8qLcwpItuF8bVv+KoDFF1puv2 vcxR67zWj/8ZLz3e3mC4fp+h+IZ2ObZWi+a46GTbrPapSb+UZncXjkvTPon/ 617MUsRFi6T7EVaw55Wwh+U/JWTIpOlVs5ZYsTfVRL99t7K79LjKqVFoyiYT e4j3EJzjsVDoySz0/M847V/3Wf51H2E+/B8k/M/ye+GfzsI/3O59+LON8Cdz z0XvHcduSFMSvcukf5oXyfsF18uVuL7b87tiaHnqmof2yd8b07bb0BBNLuej qi/0v+P6+Y6VJbS/V73jfkw15T2aLHDW/l6tXKuznamehgNz79fk1HyTow0f TdptBG4nONfbe0JPRaHn774D2r0u2mW+FHbmE3YyP4N+dRD9Yu4GP+RX//iB edO7d57q379f1NvymzZP8LzRx/Z0c6VDgpL/qZOdQfskvsx1+hONqwkdNq9Q TPiRLD0L6vGc1+yUtbVM9BDfJ7gq64kTeph3RrslRbvMG8DOhsJO5lPn9Zqt z1NxCUmj2mnzGc1XfnWvOejz2u51Gw930OYz4m/BXQRn+WnQ80XoYfk3kJ8A eZqHqd0oyBNvAjsLw580P/dCv/LCn8SnQE8s7Cc9i839w/IH4c/98DPXecA9 4WfiS6AnBn4m/hr9cod/uD4JO4vD/yRfF/2qD//z+TeMqzjz90u9jHFob/5+ qbswbm3N3y+1Esb5FfP3S+2C96KC+ful1sV7lNv8/VLrgecwf7/UrtBTzvz9 Uuuh3Uvm75e6CHbamb9f6gn0q435+6Vuhh/ymL9f6kPMS4Uwz1O8ehTzWFPM 88SDMK/aYH4m3sh8Hv4/vAvmZ+LB0JMB8zPx3Wi3PeZP4ndgZwvMn8QtsI74 Yh2h9Xcu5ucPmJ+JLwa/h3WTuCX0PMf6SPw71vEWWMdpPX2AdbwS1nHi/7o3 SvFnZ6zvfM4E63sQ1nfi/7p3mYI4xA1xCK07DxCHdEEcQvw54jF5f7MW4rFw Kc/9iDhQ3r9bJcWBxCcgTquOOJC4HMdSHCXHscTlOJa4HMdyHirFscTlOJDi WzkOJC7HgcTlOJD4OvS3EuJSmpe2wz8nEJcSL4c4X64/RyKPkOuo3niOnZFH EI/Ec9+JPIL4QORBcv3wm/m4Yn7dfBwyP4fxXAV5EH8vB8Z/O+RBxP8fx9MV OA== "], {{ {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[2], EdgeForm[ None], Specularity[ GrayLevel[1], 3], StyleBox[GraphicsGroup3DBox[{Polygon3DBox[CompressedData[" 1:eJw1nHfgV9Mbxz/33HFuklDIlplKS/ZK0TBCRkZIZK+QEaVhlyQRmcnOqISE kqhkZGZHEiEZkezf+9X7/v443/N8zz333Pu595znPM/7eT+3ca9zup0darXa pUWtlqp+Rn92ymu1LyVPTWq1u1QGSH5d9QSVqyVPU32vykDJz6u+R+VyyXNV P65yleTeGu8njXOX5FuyWu1plft07ES1L1P7HWrvJfkHybfTX8evVLlUfU5V fbVKf8ZS/YDKrZKnqNyh0l/9T9a5v+rceyWfJPlHyXdKvlV9p3CO+o1RPVXl IcmzVB5RuUJ9Ope12pvqf7Dkrmo7QeV4yV9pnFdjrXac/t9Zz2GYygVq76L/ j1Q5WvKBOneJSheN+476v65xuqp9B/W9VuUsyZ10/A21HyR5js57VOVKyb/p nLpq/5XnIHmIysWS6+oFrFD9mvq01RjXqJwpebHGn6v76cm1JS+Jfh9fa4yf 9f9p9JH8k+RTJd/Oe1A5W3J9te2h/pMkryF5d8kTJa8juZPkZyWvKXkvyU9K Xkvy3pInS15XcmfJUyWvJ7mL5OckN5K8v+TnJW8i+VDJL0neSPIhkl+U/Kd+ 03q6p5W6j2WSU+5P8sbq0019ZqhPUNvmKv+pfVO1H672mWqvJ/lrnTOB96hn 0j3x7/pRbTm/mf/VZ4Xk+9Q+lueq0kfy3aqHqJwr+U7Vg1TO4Z2q74865xTJ iyQvk3yy5Md0/EaViyQ/ofomlYslX8E8VblZ/1/L3FEZI/kUnfebzh+nPhep bbTKtWr/VOUNlVvU3pfzmLv6/xLVt6kMlTxe5QaVC9XnYdXXq/SVfJt+41GJ 3+PJGnsv9T9K8pu61iKVAySPVJ9D1KeX5I/V9pKe1aH6v5XmyBUqJ6q9teor VU6S/LT6vMW7l/yh6hnq34370ziHJ/7t26nvIJUekocGz2/m9svqP1n9O/As 1d5OdTe1f6r2l6PP78G70312UPtLan9S7e3V3lTjDVA5jGeoc/dW26GSB0ve S/Ihktvo+FUqvSWfqHF2zDz+Uo3ztsY5O/E1zqnuc5DO3TPxOj209LvkPZ6n tuHV82Qtf63SRmPdELyej6/W4GKVVmpvqWsOUTlO7Teqz8GsefSPxmub+d4+ 0T3M1D0cpmMt1HewyrFqH6H+B6mtZ83r/Xn1OVD/vy35OckHSP5DY6yjsX6X fIzqzfR/e/WfpT5Pqc8+iZ/hezp2hNp30thDVc6v3uk7uZ/bPbrWqdV85h57 V/fZVb/jW5UDNO73vF+NeWbie35X5x6uPt9Jnqf209W+vca+WuUMtX+p9jlq PwZdrvFPqtYF9/+azj2w5t93YvUbd9R516mcxzpS/16VPmmmtstTX+t0nXdI 5nu7W31OrtYd83aqrrUf70B9mqnPfmrfRf93Vtlf8nXq3ynxPG+u8QamfibH qf+26t9F8r68a5VtWGPq3xH9q/bZGv9pjb9v4jVxSrUumOdv555vB+m871QO 0rm91bZH5nP3U9s3Krvp/2uCx+iu9tGSj0g8r1bTODto/Mck/61z30u8p/wj +f3Ee9lInf945j3vBtXjM+vkYaofzrw/1dEYf2isIeofJa+UPFjyXTr+fOb9 YKzqFzLvl7n6/K4+g9SnseTVVUZK7qPj12fWa6naVhTecxtI/k/ydbx33dva +n+05E1Vr6Zyo+SNVZcqIyRvqLpQuUFyN413TuZ51l/17Zl102DVd2fWg7M0 5j56Vp3Uf7rk9pLbST5Mxy/IPMeeUvsDPC+1T0YfS27LO5I8h/0D/SB5emFd MVPyDMn7SH5R8vPsN5KXSP5L8jXsQbrHfyRfK3kgzzKzjt5Sbcfo2Ktq/11t a+ic39Q+Q/ULhddalLylSqb3+bzqp9jzWEfqf2bmObqf6lMyz+ntNF6mPg+y v+j/Bfwm5n/0PGAOtJScS35I8rF6BoXkhyXvrPa6kh+XvCvvS/ITkneL3sPY v5Lg/WqW5F/QmTp2j+Sajn+UuM9StffQuGNoV/9lan9Z4nLdY6ljy/X/z5IL yb9I/jfxXvqK+hyo9tMyr+fvdXxdjX+b2o/HhuI9YTsl1hOs5YsS2zXohEsS 64PT0dWJ3yc6p19iWwPb45rE+hgddR3rO7Et9Df7oMqlks9gLWW2OXqo7pdZ N3/D/arPJerzreSGurdbJZ+g4wNULmRc1SMy799nq74u8579J3adSj/1P1z1 wuj5+ZzGmaT/d1P7s5Ifl7wL70LHtuV9ssZ5J7n7dOK95Z6fHXnPuefnvpIf kLy95A+ke/7E6NX5XXjnat+VPUXyo7nHf1/HV6r8I3kvvaPvVOtQbW/JP/h1 1rbU+YXKRpI7qP0n5qPKGzqvvTqvkLyBjv+uej3uQX2Wqy7Rw+rTQX3+kLw5 61xlQ8lbo0dUNmYsXaSVBnyEaSL548R2yJHYj5nf058a453EtvRfkt9NbGOX 6t9a546XXEfy9pIf5SdX8xD7mXn9Sea53URtq6tsIvlzjfNtYR27j+r79X8b yUfwDjPPraUqn6ncr/aUcRLbZpn6bqES9Funqp5Q+NlO0e/dWf8vkvye5H0k /y35U9VfF96750teUFhvvy/5s8K6eldds3vmPbql6n0z78Wfqc83hfevBZKX FN6bOrHuM8/p9qz7zPN+jvq8WniveVXya4X3qRbYNZn39Llqf6PwnvWB5M8L 71n7sOYyr6UP1b6wsO30nH7LLtwH+52OH57ZTpvHPlLYxmik/39VvS6Fta16 HZWGkpdRs3/peQX9X481Lvk/1aurvKPxVzBf0Z+ql6h8z1pQ/RVF8vOqv+aY 5LfYswrbV+yNHxTeH/F73i1sUz2J/1R4Lfyja9XVdUv2Vsm56jXUPkl97in8 3s+TfFlm2xX9MiKx/XxfsE2LfthK179EpaPkh3XeWM237XXsUvXZMfEzH6/2 cWpvq/+3Vt9+qfea7hp/nczz5DL13ynxe9kfO7PS58+yTnXu7jq2jc67NLUN g937qNp3VftjzFXJO0geI3mKSgveEfpB7XuovYnOuyy177al6otV9mVN6R7W y6xD+gWPwV6GfnhA526l/49QewPVjWt+7vUlr6l6Q41xjkrLmt/NmmpfGz2m /mtJ3kzyxjreR6U1+4XGvFJlC8kH4KekltFRt+pa6+mcg9T+r9qb8hwkL5W8 OWtQcoPMOmp39b9KZUvmDLo3tbwH+6rKVtX6vUVjroOe0vFzVVqpvX+wfcY8 v1By68R7dAf1vyFaFzCf6qleS/W2Oq9/at92C9UXpbYN7lL/m9V/O/XbPfgc +rdU+6dSdL3V79ua10da6YGpqeW6+jNNJavW0QuVfL7GaZHYTlhHbaelfobr qj499fNngL/VbzH6Ifh98C4e1HXv1v200fnd9EzKzM/8DrXfpPbmvD+d21dl z5rnyY1qb5p4vj0Sva8conNTnduc9yh5jcz7CM/n1sL7zsFqT9TerOY96CGd uw06h2de+Ny+urdWiW2hw9R/9czr7lDJq2VeXxeoT8vE9swaqpupbEr/4P+R N9f9Xqiyl+RWGvvs6D1pV+zNwnNjb9WjCt/Piep7ajSe85beQwvJH+t670ne RfJiye9K3knyV9h/kq/WuT/pvDdL6/YPsVslbwBWgN0qeSPJT0meU9o2npd5 /2EfYp96Ve3z9f9b+MSSr9WYyzXmrNJ702tqn13axn4j8xjY2dhdtGF/s0/R l/2M/ese9b9T4xTYrZJvlvyfxlyrNKaBjbR2aewC26lBaewCvKVhaewCu3Fz yccyt/VcG5XGLv5Q+/qlMYo/edaSj8ZuVp/NStufpeQ7JY/WdQP2suTbJeeS b5E8FNtI93OX5NskZ2rfoDRO8hfzTXIP7EuNs2Fp3OOfxPbJGMnrJ35m/1S4 2QfYfJLvZp6zJ3OPEruCIaVe1+wH2BbYFdg8d2icDRPbKxupbqS6h663KfpS 8qb4nWB8ko9T+xbYTzXbPPdF/48NspnKBmrfS+0jCvc5Rv03RmdL3gxsjL1c cjsdH1lYR+2JX1K4z7Hq3xhdK3lu6d/ztp7JJviXKjuqfQZ+HjhSZrsG+wbM 6m3JK3PbtG+UtivmZ66xM8CsXi99znuZbRlsGjAuZAyzsapeU58P9f87mev/ ctvhM8EA9f8ran9J8ra6h5exFyRvoXPnqM88yc3V/pHa38J+y23HvlL6/mar /eXSx2ZJXo4PEn3d3SXP1G9sULOd+KNvqXZ/sI0MdgG+dX5ijAus7+PcmMMB kn/QuMNT+y2DE/vX3dT2PXMxs8/aJ7Hf+oP6vxNto7MXU7NH3x6Mp/4fB1iO H4W+wk6L9it30TWuT21vPxC8r7Ong7csVTkuM0bVNzFONSYYs8R3OFf3e25m POEQ9Hy0PQ9egT2HLXe26tMz46JdsTmj/YWj1b5JZt3eQf0XoVMq32xAYszh QPVfpvYbUvs5AxNfCwz2k9x4Th/V52V+PmAg2KzYq/i3+Db4NQfxbKP9C/AB 7MWe7AXBGDP+zjlqOyvzdesFYzmv14wJf5QbK3sw2HcBJxwXjO2dXz3/L3Pj WhwfWfW5QG2DMj/P7uqzKNq/PhT9qvsYmfpdDave173BmCL+Wjf1+VF9bgQf YfxoX/h8jXl55vnD88TRAA8/TPIX0XYYWAd2MzYz2NrC3Ngg8wcM9GTJZ/EM Ms+9I9XnZ/SprnWU5G9ihbOrjK6ez8PBGDzzZHf1G5EarxgbjHfynMGmvsiN STKH/678RObLLdWc2Uvn3ZTax2+nelRqHONCnTc882/hfSXRcYe+ah+q9ssk PxKMxTLmQ8EYLT4mc3xUNc+ZM/8W7r/Kvoq2rTsH60r0JD7XuyqrSS5T75HY Ko3xC1U2QF+qbq3SSPJGqlvhY0teU3WT3Dq8hUpDlc90blOOqXwiubnqtVU+ lby2+jbNvdegJ4dF61ds/CyxnV9Px7fOvb+ssuWifYM2ks+L9iebYAOofIyO Vd/Zqf2FrsHjoatXU/tWufes+sEY/Bv0D7ZHsUVX13kzUvuw2A1La5Zb61rn RuuqFugHzYeTUtsVCyWfIbmeyiup9djXNftwxI6wv3YOtjE2CcZg3qdd7239 3PvpWsF77Jtq/5d9Mfee+C97SnAsYMNgf/G9mm9q49z7Y1tdcIHu4RT2LckD op9fA/3/cepn2A4/LrU/tb36XBDtY2MDXx3td+2tPm+m9r/qo1tT748831+8 lGprqO3V1DJ72TXRfvtfNfvodVQa6fiZqffTf2v2X5lLK2v29fHr8f3fSt1/ v+D9mGvtgI5Sh1N1bH2Vs1Lvj2ur/jC1r8d9/1aNkyT2AevWbNddH401dNJv +TQ1VrCz2gdG+2z/VecwDnv3lxrkbPVLUvt4q6Hz1d6/sI+/n8b5MjXOcAAv s7IxdmQNRY/XUMcXpPYH8dnnp74frhcTtzPmoGj/Ebt3eDR+0UXjf5EaGyFe Nz0z5vCz5M2ibRvihJtE2zzHo/eiMdJL1H5n5pjdpfiqmWOL6MM1ouV+7OeZ 42snoMei45ToqomVvnpGv+upxDqno+5lTGq7AnypXvS5+9KWen/viX6Oxmaf 1rmTEuOT6J7Jlf5BZ66jPkNr1kNPVrpoUnCccUil8+tHx0xfCbYTGL8ZMQGV ByS3V71GaezvAF3/ntR443fq/23imBq44mql//852M7FPumptt9UftHv/yXY 5gUj7a4xxqfGCRm/ezS2eaTaHk2NSe6v+u7U+Oe+Ol6/NLbYUfKapbHL41X/ Sjs2gPo+pjIbPQ8OljiWx341rtqzLta7uClzLJhn8HL1HHinW2ncUcw37OPU NtJx+L7siZJf1JizE+Pe0yW/khjHHqgxp2XuQwzuH3BgbCLsK3yLmmOC/6r9 NbUPUvuMzNciRvx39LjMjSbRcbqXg20/MPPT8CGiY3jHFsbfuYcekr+LjnOz J64neZjap+jcZxLvWe31O25JjbFj/4DRD5R8jORvo2METwTHvWlnnxxb7ZXs 78QGiAtgR9xf2RLcwy965rem3tPrRs//Dvp/dOpnMiE4vs3+20ltt6fGkNn7 H0yMw0wMjnsPrp7zsuh3gu1BfGJINc+3jn6Gw8GuMtvPP4BtJo7JfhZsY2OT Lwi2v7G9wcBLYir6/yu1L0ocLx4KdpfZB7xS8uuZccj5wb4cftwVap+bGat8 P9hvpP+HwX4gPuBV6OrM8ZfF+PWJY9AHMndSY5UfBPuK+IlD1H9O5ucwK9g+ Z42/FuxToVuGoYsy3wPvvWk0bnmIxrtf5ema58Xn1dwgRpDoN36h/7vp+AMq z/BMiEtorCnVWkZREz8gXhAkL0TXgLllxkI/D/ajia0fxvoG46g51hCJX+rY 9ejhzL/la/CMxHF24g7LsafBE1mvqa+7iP02cRz/BnDazO/ozWD/h/V1NVhf pW9/DfZ94RgcqzEmpt5nj9A9bFR6/0UPrF34OdzC3pt5jY+W/F/mWP9fwXvy O5L/DN7D3655vvxdzZkR6v995nnC715a/fY/gm2BtyQvxSZJPObyYB99ruRR OndF5nd9E35u5nn1afW7mJ+9dL8rVP4CqwXTKs2f6KrfdG/quMwbwf7ePZIP Utu41DGag1Xflzr+cg0YaWYs/fVg/5T96HDml8q0muM7deB86NgRantEZbra V1b2zDzJXdVn3dI+w9FcP7XvcAzXTG2D9eCaqe2fg6NxB84/CJyvtK32ue5l ZO532kV970x9/6zjl/6/ltU2KbV91ZtrqtTJrasbFp4bR2nMTUrbYcer75Ps 2WrfItg2/KDmvSIG7xfbBNuzH9U8R+CjME+2CrZJP6zZL16psnru/ScP3oN4 b3WC3922wXYuNirvBb4Ic/gUfqtKfZ17Bu9NZZPc+xd8FH7vCeq/dWl7uqfu d3JqW/o4MInSti/PbcPCz5/ntkHhd3S85C1L2989wWhL29+9WNOp7XOedYPg 93W6jv+psmHuuQR/hX2WublO8Py8XcfWyv27Wld2/oKa5/t6wXN++2Cf4PNq DqxfeF2foGs+ldr+3yHYh/ii5vvbrvIR7sL+yT3OkTp3s8L7dUhtE29U2cKb VvYw77Rx4b37P7XtFOynwNfaMbcdzvtuXNne+BTb5n7XvPPNq/fO+9yyeqes /ZOjY474DtvknifMq80L7/XMi62rucF7JBbLnEEHrB+sB/CJmuUek/e1deH5 wztoWflBvKNtCq8L3vW2hdcC77VZNWd4d00Krxeed6vqmfO+mhZ+d/hlbXM/ 8zT1s9ixeg9tqnfBubwz3jvzsUk1Pn5cm9xj8k7aVu8FH6157t/I/GxWeA5M 0/GZifd3fMMdcvcHQ+8ejNXPTe1X4FNg+xPbw27HZ7ko2pbGf+gY7HviQ3QK 9gvwG7oE+w7EGddM3R9/Dr8O2x5f5vzoc/Fh9gm+Fn5Q/2i7mthQ/cqXwV7f P9g+J765VmrfEHv+0ugx8UEuiW4Hnz8jGqdiHm5cet5drt80WfpoeM3cs0Zg CzVz9n6T/GxiO2f96D7w+lZIfk7t/XXuE5ntpcvAcTPbydjR8ypbeoDaJ2Ue E1sLjgL8BGylaZW9BIdwpdqnJ8aOwc3BzLF9Xqzsn85qvyO13n5B9z0j8Thw An/XuS9UNm2Dwns3MbI6qX1h/NzTouXPU/tC+EGLU8cbNqs5/nFosK/0e2rf D78PzJd4D7Ee/Jxuwefii10eLeMf7xK8Nr9JHbdoXHNc58jgGM3rqWM2yODa xGaIy4DhHh2Mo4ILHxWM936n4+ulxvnnpcaCaf9GZbfgeErMHGci3gGOT4yB +AJ4Qp/o+QO+0D7YXyaOcFY0nkBscbXU84HYIvgI2AgYSrvgPmAF50Sfiy96 cPA8XJg6FkLcgdjJCcHxkUWp4yjEQf6o/F583r+Ym6mxZXBn8GgwZGJsxweP QxylZ/C522hunhi91uEWdqvssYWZbQXshHaZsS1wLWK94JXgTuCS8KuwveHp wXPCZ4HvBwaKn7gnMe3cmCr8THhUYEq7Sz6jws2I+4Kr0g5vYmw1JrwasEhw SDiru6b2E8FY4UjRThwazBE8Db4rXE9kOCpgqWCbYJTwtJCJr4MJcp9wEXdL jWvBhwBHBgO8SOfdmBkrA9cN0f4X/gdcJXwQ4rBP58bb4WkQxwVvxF8AL0b+ P3aM7wB3Ef4rMngluCd4JvwNME3wTPDB8cF4Hbgk2DHtcCPht+HLwEUBr+Q+ 4SiAmdJObA7+ENwMsGB4ZuCu8H7h0YIV46vgS+P74IM9HqwT4I3gZ/Ib4RWD RaIH4PrumdqvATt4Mtivvz8z5ojv/2BmzBHfDb4TmAIYAjHCi4LjnnALbg7G S+ES75Ha7oKXCIcSjBdcYHLwuWANTwX7+PiQM4N9TPg5YMr8rkfAuVPrQHxR fF382VGZ9Sz6Ex33fLDu4p09Fvwb4ZY9Gvx+4S+Bp/N80GvPBZ/Le0afokuf yeyXsmehi6cGt+Mzzwj2i9Hdzwbr5+fUf5/UPu+4zH41/iD8NHzpVf0z+5/4 nvjYLwX3qZ+ZD9qh5pj7lNzxoP0Tx+Hhr96rtoGF4+9jJQ8urDPvk7x3aR01 TvIVhfUesaZ+hXXCZ7rm36l1zCeqO+bGnNi7Li68f7FXoxPYr7cqHF/DZmsu +aRo+2o4+11hndNQY2yX2+5opLplbjsF+6JXtI2xrtpa5LbXsGWIFWLPDGNP L6z/79HxMwvHZInR4TvgdxC7m1/5sMSLwHwerPTSsVUsBc77hMr/JR6Fn4Jv gt+J/wkuROwLHxYsiHgUsUjsbWJrfQvvC4PQw4X3lMtVn114z3pZz+rb1Dr7 rMRzt3el347OHHeao+Pfp94H4GM8kzsmuJ3k3tF23Smqzyis/49NzLUhPrWD xtg/M0d1e9WdM3NId1LdNTM384zEa4l11FptHTNzc4n1wClsVzMfY1ruWDa8 jhdyx+LRt0dVMa7xYEqF59VpiTk1J7Km0HuF75mY/hO559VuiWP48J/hJEzI Pa/uVn16YW4AvFE40b3Qh4n5qsTFXtLz2C03Bv6R5H1z48zYcRcWts36Sr6g sK2FXXZeYdtslvrvkRtLxqY4q7BdMV3tu+bG2uGjXV9Y78GdhhOJzoF3/XJu /snRiflHxJvgD7+Sm0sDJxZuZWfJD6u+obA+hxMLX7OT5EWZ/Wd853qZucjt JdfNHG/bGz0g+brc+Am++dvBGAixTzAL8Aq4YAdWGAvz8Z3gOUnMHnwHrIY5 /lHwPIc30LXyu1kHHwfLYL1gEPfWHN/F38bXJp4K/si6gH9wUOWbwyEABwED AWd6K/h+4AeA3YDbgCHNCcaUWFvvBo/DWnkveL0QZ0O/s3fBYRlQ2I4Dk76s sL1GDOLO3HqDWMNdlS9GDJM9BnsBHgexfmwQ+CDE9LFr4AHBPcBOgat5W+61 SX7HmNz+ERwL8Fzuhxgz+DLYL/F5eALYd8T84UVg38H3gXeBbVhUPuC7NesJ 8DJ0BfFm8D4wLvDiZcG+G7jtj8H+I7jtT8F+ItjckmCfFB7prbl9OvIvwIjp vzIzJkUfcKhvgn12OB/gOGA44FlfBttaYGELgzGipZmxoZdqjsGDIa7CDzNj avQBF/siGH8mfg9WBU4F5jc7+HeBrXwb7Mt/lxl7mlEzFjg3GLuDawImCB4I 5vdqsEzcHUwfrA9uCpgjc4N4P1jz2JpxI3Ax5iFY5rzgeQgXoUuFsYCtg7mD LSxR+825MQG4/YdXWBDjgEOBHaGzPwmet3BcOlc+CPkrB1f40paZuWWs6zx1 /KW+5Cx1zExDrFrr1wevd/Tr8GAdC7/t8mBu23aZuW7I7KsDgvdWOI3kcvSo dOwpuWPi6LNhwToN/Xxq7lg8evu03LFvdDU8/hNq5rLAvYN3h168KVg3omtH BetbuN/knCA3z5yvAh+yaWaePVxN+C7w5+DObZCZq4Rub5Q5HwAu37qZuf7w AOH/XRKs37bKzB1Ehi94cfBza8i+Wek9uHhw8tB1ddgjqn0Eztl5wdeC19Un eB9ZPzPHC5k94dzgfQHOEPw5uHNrZebEsI+snZnXwl6zZmaeCjp2cc3v60vV m6r9hNz8yY0l98zNhSPeeG7h2B1xMPLpiIWBTYBRgNUQh+xT2I+nLabGcYgx nl8YJwD3Ye2DxxKrY84wDvjg78HYCHHVO3LbKuBaYJFvVveIA8i8gicPhoUt hM0DLgn2Aka5IlgGM/0t2LZpnDkfBp5qrHCVhTVfn9gh85acCXInyNcg5+fK YE7pFpnzeeCawq0cGMyrhE8LzxK5ieSTcnMS4MeST0IuCbkxVwfLO2fOIyIX hmcAFvZu9azAehZW7ehHYsb8XtYSsWd4V/DzVnHzNOZVweNw/6w9uK3gi9h4 4EPEdrIqvkMO08zCv6lftdeDzVxc7fVgNnAlFld+5WWV/QnWAncGzjr+I/mL cHbgI5BXNK96nvB69i+9rs+sbAP8dTgU5H7gv1xY2RJgSOQFMu4qnk1lg4El wOPDhmEekh8JLwaOBrlZcKSx816J5k5jO82K5i1j78G1ebGyAV6M5gNjpz2t +/qo8LNvq/aidOwBXgZ5JvhKcG0OKK1b4FYcVtoPJc8AfhCcoa+jc1KIkZIH AEcJnhN5QgsqPQP3n+cIRwZODfoL3bWnzl29dDyA2OBf0fG/q7hm6fy/K1Qf XJp7fqXqQ0rz34eUvje43mNK7+/gEKNKrykwkgGlc1g2ZN2UtgfAJEaWXo9g MIdFc/LANeHn4p/gm9QrnRdJfGNw6fcIB3yg6o6leehwSydW/eGSYDdjM/Ob yK/kd5GHNL/Sk0+pfV5hvX615BNK500OVX1aab8EfuugyrYfpLYupfnv7aLv ifu5BjykNNf+OjgFpX2Xa+FulM6JmR3NUcfvmB7NCcduJweIdwNP6vvo/CCw t1+i84nA6pZG5xCBtxE/JC8Jv/yH6Dwj4hLkDA2qbK3l0bkexNr/jI7vg58S g4UXh+/7a3SuCjHU+3WPDxXWtQ9IfqSwPub9b17NgT+iuQHgeuQDwX0Cbxgf neMDdxmuN/kg7A8PRucawDXfXmM+U5pvNDqaxw6fmBgytik+8aTovCTyFZ+I zksi5/BBnfdo4T3h4ejcE/joE6JzjshpJGcFzhiYzcToXCdyJslXZv3AQfgn Nf8Bm5NcK/jz4DfvRuelskbIqSLnDjzpUV13auH9kxwL8gTBgZ4oraOwKV6L zpWAK/d6dO4D/DhyAVflHmjOTIvOO8AveyY634E8uhei+f/4YuTSkauFXp8S nQdBbt6z0bkP5IW+F51fzBrPSueSEOtFT5Arh654PzofmXVNjiNzlT1iPM+/ 8D4MP5HcW3AmcobgBIL9pKVzW4hlvhmdb8KcJK+F/Gtwo7x03gox4AmSXyls L7wRnesBR5I4Ldxm7FO4EuQ7Y9PdFp3jAK/6s9J7NJh9C8kjSvP14a62K409 wsffozS237e0riPPiZwV+FDoYfLjWefoYeKT8IyJg/2Qmp9PfIDYKdxf4kUX lMY6OE6OCFx49D9xrYYVFtFM8rDSHHf2DtYq6xQ9MCSaT9+/dL7YYzp+qeqj S+cgwvverTQm3E/1UaXzEYnnk/uNTU5MnjwifDd0EXsD+8LF6tu9dC7ghaoP L52PBc6MHiTPAU4ZMUbiSJeXzg3cWn0u4j2XzlMk9444IzEoclC47yXV/jg/ ei9D9zNXmCcESeDW4h/Af+kQ7dM0lXx9aW4W1x8VfQ+t1Da6NG+YeO+B0fYL vBWwYHygZak5YNhXcBPgt+MDoZ9Z/6x94u1w3fF1iNli32MTEePFdscXqVs6 dx6OC3v0Z9HcDfZQ1j9rn9ggPHLiS21U31aaDw2mMrvCVfD7yWvA9wcbgDsH PnCZ+h5TOh+U2Dv+GPYemM3MCrfZKzcPDXsSTALOHrgEOpt1whohBwheHty+ 1hrn1tLc7hHRmBs5A5ewT5bOpzy/9DwHVyPnDD4dts1X0TmY8Jj4reSZ8ns7 5+Z9YX+Cw31aYXEtNcaNpXNIFkfnbKLr4I+D1YDlfx6d9wq35efUvDvs2wXR ua7whuCrkicLDk0eGJw47K57o7GdxpUdwjUY/4Po3EDsK+Yz+mhRtdb4vsCM mmOqYH/48vtF8/6JaX9R2ib/vJqP5CcyJ1kjvG/e9eBoTO8r/LvoPEfsq4+q +YlfC9fm12r/+riah/jQzAfwR+xtklfg1IE53BON1Wxa2TZwxMeqy1ns56Ux pzOZq6WxIvLv0W/YsGejx0pjS1yXfFF8/3PUtmdpjIrfu21p/4JcRrh+OACs GzBV1s652CGlMdSR0Rgs+Uh9SusN8MLzSus9cEF0Gt+AIJ4CBgYvERwM/hE5 xuDA10VjofAah0bjq1z32mh8clWemsZbMxpXvisa+yJ/4LnStjf4d3PJw0vz KdFzYJjoDbBeuJ3gvduh50pzJeHPgg8TI70iGv9k/nNvSytb5fbofGTybeDj gGeBYdwZnbNMjhN21PzSPBXy47FFiRfBocDmhEdBzBDdAu7B9yrgzLBO4a4y 59Dt2I0flubHYG+wllhHTUrjz8SZyYOEs0FcFT4svBW4BnwnA04Ivh3fD4Ar gi4i3xfOHTwL8oDh98HXWPXtkMx7Dd/DgI8H3oP9/H5pDlCD3PwTdCPffsC2 x6fnOxxw/9CT0wrbK9gqSW6uILqXb0tgP+D3E3clx4e4BHoR3gu6EdyP3B54 Nm10/O3SnCqwRPKFPqj8iHdK85ngSsFdYn/n+wTgCNg5cF1Yw6zfsbqfe0vn QZHfyTciwI759gacdHwKYtSsEeKSvE94ULxT1vgHpTlDYIbkisDpAeeEDwbO BFZDHgi8H/gF2Mn40WCV5KXADQIXIp8EvhTkX/ZBYltgUOQ4wUWDv8B+je8M fwFbHb8b7JGcEHhpYFPkNcF7A6sk3wmuG1gluSLwO9uWtrmxt8FXyUWBi/lI pV/QLXBL2ceJGcE9ZK8nXrOT6mmlY97YAcTWied8UdjWx86fW9iew5aDX8le Q7wJm3daZffCxyTGQ3zn9cI2H/bei4VtYuxhYv7ElogfjVP7uNJ5a+RfYqOC UZFLR04WuAt6iNgBuohcwLsLYzNgmPABiEeRY0fOFHgM+ZrYh2BadSo/ij2a nFF8AXAgcvjwEYjRkTOKTQ5uRH4t3zxhrhLDQrfiL+yoe5hamuP7YmbOMDE6 vtUBHgHetkNpPwcfh+f5R+VfjC19z8TPdy7tw+C/wBFmD72yZj4m9tIVNX9b CJ4mfhDfdYCrTOwRbjL481U1jzO9NJeLe8NHwj/iG0XoLPTV/MI+Of4438/A N9yvus9nS/OSJ2bm1oJX8N0IOM/EIfkWBfFfYoZ8i4IcCmKG5E9gmxE35LsU 5FAQs2XuTSnNWyVWDNZNnPHQzN+TQVcsqWzH76q1iQ2N/Qz2hQ2E/UOeNN9I OaDSJ4+V/u4J+RPsScwBOLnkdhEzZI5NKv1NEHIp4F4Rx8feA/sA9yDfAl4Y OpNvG/C9E/yayditpfNy4SXh286u2e7CVsBO4Hs85MpgV8ARw6cGyyVXm+8p Ebcn1gcfjHgf32fCfwe7g3uFDQYezvecmCdgVnw3gu+I4F+QO843Vdgj4GHh d8+qObcGXOKkmjnjY6v3Aj+CvRuOBHsc+yJ7Ir8F3xW/FfyQnCf8Tew3bAXs BPjI5KMRTwazIN8WXA0bmH2UPXRiYb90p2p/ZD9mL76/8D7X+v99SudUs37Z F1tV8+3J0t/fYb0/XvqbPth12AfYBk+o/aHSOcarfKVoexJ+PXs6a2rvzN8R Yq5y3ftK58eC9fHtlo6VLppY+tsu+Ax87wXMj+8kYVtjZ8JLwp6Bm8R18eHx 34nBwqMjDsu3IsjzIi4Dz2hCpU/4Pgo5aPAs8KGw4bDfiEnyTSD8X/J14B7C ZYPngt0Fj4W8HOw2bHjiovhF+ETwCvELwPz5xgDfDgKbJ7eJ/evEmr8rwPe+ 4HSQ+wUe1bvm2DLcRXw6+EfkzBKr57sjfDOsV6WrJ5f+3hNxUb5RhD8Onws7 DS4N+UBwLeHrEQvluzVgesRd8Q/xDdl/8Y3xi/nWFPlk2Nv/A8W75Cs= "]], Polygon3DBox[CompressedData[" 1:eJwtnAf8V9Mfxu/93vs955KZka2sssreaWgRRXZFQxPJ3pQUIbKKEiIlEclI yYqo7CQrSRkNqYQIf//n7bmvV+f1O597zh3fe885n+fzfJ5Tna59211QSZLk 4TxJ9C9pUSRJf5U9syRpK3tiNUkelF1R4xGyh4YkGR2T5FyddIjse2WPVPu3 6r+37GGyH5D9P9m7p0nSVPXrVXaV3Vjtw9U+SvYS2fvIfqrq/v/KPlz2aapf QdHx62XX0vHlKlvoWqfpns/r+GNq31TPc4za5+l6r+p5BqjtJNnjZD8ou5fs g2V/Kvs12TfKbif7adljZZ9f8f1e1/V20rV2VjlR9iS1P672PhX/3ntkP1b2 P0z2ZPV/VPevof5NZM/Xs81T+Vv1/6l8ov6vqP8NFV9vuPovV98Vev6fdOzp 6PexvY411LEXZPeTvYfsZrJv1/kP6Vjv8vkny35CNh/pSNmzda9NVH5Tfa3K etU/U9lO9do6f7D636vrfcj717Ggc1eovKLzh8reWsd/VNlcfU/lGdV3oMr+ OtaN76nnXaJn+V7tP6j9Dx3/VGVbte2kY5uV9j+yj1P75uX9E7UdL/tm3f8e XW+VjtXSsW9lv6P736a29uq2nY7/pVJHbWfp2E1qv1v939Ox3dT+o+z31P9O tXWWvamOz1VZr3orHdtK9e95Bzr/FNm3qP8wnf8Lz6hjrVUfoFJf9lk65za1 D5f9q+zt1f6N7Ld1/Vt17plqXyh7puxbZJ8h+wHZD6v/Zeq/l/o/yHiXfTnj VfZ9wfMh1Tuqy/eT/aTO76vzj9L5z+r9FWrbIPd4f1r2Q+qf5/5+x6t+o0oD Xe9s2dvq758qO+taHXWN38vfu43adtCx33Tt69R/os6fKnsbta1T2VH1Dup/ tOoj1TZe9rOyl+l5PtA5d6veVddYKvt92XfJ7iJ7RPDzZDpnT76x7HfVPlTt ndT+iq73MmNE9WUqL+v5J6j/Nup/nOyP1Pa+yu+q/8F4V/1jfoPqf6k0Un2s +k7WtV/UNYfo/Pdlz5P9mex/dL/vdb8pfDv1f0jtico/av9Lxxrq/PvVf5zs SbJ/Vv+56j9c9R7q+qD6/k/tf6l9vY6Nkv237PWy/5R9up71SpWrdHwg65rO f4T1RNfdV32+ZC1RiapXVaap/pLKEvX9QaXQvX5SeVXXupPfpPO/i/4tg2Vv qPpKlddk3yX7DO6lcrXuN0j2d7rWVOaX6hszXnT8Jz3fStVX6pyFattSZUPZ hcoDal+n9t9U/1XtI2X/JvtX2WsZD7r/17rfM6r31zV/kT1f9njZV8neQNea rrJU9aN0bCO1/azyuup369iZPJvKtbrubbL31N+NGaNq311lb9U3U9lQ9boq HeiLD9Cxe3gf5e/5TvUj1L6PjtdU2Uj1PVVGqL5Wz7tWz/uL7H/1fD/o/i+p fqvOuV/ta9T+i9rXcA/upRJU31XlT/VfpP6TVb9R/dfJXhj97W9gjMn+Jnps D5B9u879UNf7VNf7XMc21LO9rrJCbUfL/lX9P1P/J1S/WsdOZe5SdN51sn9T ++dqn6D2a2SfwlynqP1a2dP09wnZW+sex8p+Q/0nq//l6t9M9pzo+dtS7Z31 DNOj/WUD2SfIfl/9pzJn1b8164+u967aPlHbfB37XM9aUyWXXVE5SvXhan8s 9Tc+UvYtskemfsa7dP7XshfLXsIzFKW/UL+Wuv7dav9G7UvU/p3aV+n+n+j+ 96neU+2Hq99AtQ9LPWYOk32V7Ntkj+Eb6fzZsufK/lT2c7LH6Pob61hTnX+Q 7J1VtsEfqRyq869Q2y3q/6jsqWobr/5b6lgr9T9E7ZepfrPaH+H59TyP6nnO 41y1H6D+O6hsLftArqn+vdT/OvUfJfsetX0r+zvZ3+OD1X6T7PtTf9Nhal8q e7nsFbJ/KMd/TV17Mx17RfebpPtdWvHzr5H9qewRsnvLbqy+j+v8F1KvQe31 7NeoXKfrDlH7wfpbR2U7nlflNZ3/rM6/rGK8sbQcb1uoXlPXmB3tb5rpmmfL vkPnzlP9S9W/1jlvggXUfoSOnaJjH0X729Nkny97lq7/oo5dXfH7u1Pnf662 r/FVOnaQ7tVd9jWsFbJnq/8U9b+m4vE5XfYzsi+pGI8cqP7nqP+V6j9Sx95V +0tqv7bi9Xu17Hmy75fdS/bHqg/S85yhcy7QOUN1//mqf6X6QjCe7Cm65mL1 PUx2x6qx1/6p58TXut5busZg1l7mi/oeqT6NKv8t68nhuvb5KkdV/c5Yf1uo 3lbtGzNn1daX+aRj28verxwfC6mrz/7l+PuGsSO7XrlefS57N9kv6npdVRqo XhNMV7X/Ass2lD1T9YY61kT1wBqpe12g0ljHtpLdS89+TuZ1jvXt3OBj1DdT +6scr/paXLOxzr1Epa2O7SW7j/qfH732MAafU/9O4Bv6cz21fVV4nWZ9pu+C wusW5xyheh+Vo3W9LXX+HuX6/Jnqu7CG6fpDdM7ZrLc6dpXs26KxUz3Z58se EI2Fdpb9KGNF578ge5K+0WVqvyUaK+yh9itk3xqNNeomXqvX6P5NMq/Z+OZ7 M88T5scF6n9jNFasDV7P7UumVoxHGuncC1WO5bsxRqr2p0DCI1mzwXe8Y9Ub 6NhA8KnsbrL3k91f9p2yu8quL/t5ndiZWEL2Jip7lf7mC94N71T3Wph7XWU9 bSL7UpV2svdXnxd0bhd8Pd9PZbSuf5+u3131AxKvDeD99lWvEeACYpOLK8YH D+bGDs/Jfkr2geV6sIi1kDWhnA8VxnbFOLGOyoUV40Xe/+sqc1S/KXEcxFjp VHE8xLdbXBgH8w3vUd9nVaarrV9inLmLykWVEm9G40l+H7/hLtWfVpmWOj4C 17ZRW/uK8e1otb2iMis1HgEXn6D2MyvGxx/IbiK7hex1am9aNZ7bQPWWOnaR 7ve1nm+Ojm2dGOeeqD6dK8a7vJ/pKm+nxlfNqo5/aqjemvGq878pHBcQDxxT NT7cUO3Hyr5S7QsLxxHED3foWk+qvJTaP4NLT9I5XSrGp4yVi8C7mcfMlfqe 1+pYm4pjHvxpc/U/Aewj+9Lge3BtMPQmJb6aA1bSscuDn5FnI6aZDA4Hf8uu cEztX+r5/uA9Jo63Gukax6hNpyW7l/hlvuq1dey84DnO3AbzbVvi0Q9V30LH nuU7q+yg+r/6PW9mXgsby/5ZfXbGVzP3dM4Mtb+TeS1oqvY1ar9M7bcX/k58 n+1K/PuR2raSvWOJnz/Wn1rYYC/1f5FxqOtdrOe7PDp2qsX8ZW6qfyr77cR4 tJXsk5hvzD+d10/2dHyfzp8s+3rWVNmvyL5G/euqXM/aJfsq1XdXuRJ/Lnsf 3a921fOG+XJ1ZqxyFb4ste/6Ts93VtU+7EriPjAF81PtQzJjFLAJ/mhA5lju dtnHp14f9mXtlf2Vnvda2fVU+sk+ijGUmbvoX3F8TazXUL+he9Ux3w2crzIE f8icY60BYzBWZd+SGZOARcB3xIY/6nm7VR0j9lfbPio3Vxyv438aqK0+vrBc f+rL3kf2gsRcwPc6v3PVnMDgzD4dXw5e6KNn60uMyLPJPhc/DOciu5/s3fU+ N696HWT9A9ut0PXOqxrjEbstld2z6hiO2HmZ7F5Vx9DEfstl9646Bhyoe++n co/q7VLHiifpnudWHTPepLYDVIZVjFcGZeYG7pV9suxa4OvC84r5hL/breq5 wJwAa3XW9fpUjbluzBzr3lExPma+7aq2nWR/qv4Xqu+Fsh+mb2ps8hOYoWqM cltmzAnWBC8xn3YBK8iep/NvzYw5wZrnqv3mzBgI7NOB8a/rX6T+o2UPYs1U 214qg2Q3Tc0d/aD7damaQ4IrOkjndK2aMyL2ujMzTgefE5usKhynEqNM0t9a 6ru56h8kXs+INZ6S/VDq9f1K2U/LfjT1+g23NRHfBObX+VuBqfhWiWPLX8CT mWPMn8r14ZjMMeknYGtioIoxZs8Sv+CX8Ee35Y5lnlR9VOrYaXVhnoAYCv9A rPq86k9z/9zYd5rsl1PHRj8XjkOIP/rqew+M5t7qgKnUdrHK8Tpn18Sx1srC OB18fqTqF6m0VvsuiWPV2zPHIcQf72bGXs1U/5X4Wu0P4QtU3mdM6HkGq/2j ijHoLNk3yn6n4hhlovpVZWey38H/6fwHdKylytuMf/UfRExTMecwR/ZA2bMq jsFukH2p7MfxvbK31u/7Vcdq6FjUsWtVv1j1saoPZX2QfYnscfheOAxiH9bb ijH6G7JvkD2D38Z8kn2T7DkVx6g76vr/5F63Wa9fzR1bv6H6bLU/rOdurTKX 8YN/UPsAtb/JeJCd6V2uLRynEZ+Nxq+qfKL6R8RY+HeVebI/lv206luAIXkX ej87Ee8W9hP4h5MK433mePfEscMS2WdWHUPwrb8tzLvyzTkOl1U/dTu4Ce6z QWr8NDwaf61kHKeuDy/xFpilo+p1CnMZ+OAerI3E1qk5QfwAseMhqf1Bh6pj z/1Sx1ysa/vLbpN6fWNdO1B229Tr25fR8f0FudfPxdF8TP/c34tv3YU5mfqb 8y07MQZSf9NzGMeym4BnZP8YzZcMyT1/vo3mk67LPR5YRw8GE6VeT7+I5g/O y71efxXNX1+Uez3Db9RTvUVq/4Ef2kt2y9T+iHWmjuzGqdebjoX5Psb8yMS/ hd/EfGXe8iw8E/gUnLp/NCYGCz+p/gPgAqLxP3HAJbIXRK8/rENbR88Z5soI YijV/1b5QPYjiZ+d38D6xDrFXOjInEg9Jw5UW7Uwl/cUMVr0GGVsTpB9dtXc yaGpY07WVbj1RqnXV/zgjrKPTu0PD9b5oTCXM1Hnd6qaazw8NYfCt+CbEG8Q dxB73R6Np8HVrDWDZJ9e8ZrD2nST7DMqXqMYG4wR1mPWZfzmUbr+aan9J76h nexeqX1Ec43jmbnn4luyW7Cu5J5rMyteZ97JPdd4hxdEx7ev6fhy/Fl0PDdD 9srE6/jL6j8z9XrOs/GMszLjO56d3/BWZjzIOj9V/d9Mvd63kv2R7Pmy3604 Tpsge0rqeO3YwvwCmOQ01mPN99ejx/LJcCK8D/h4nbMG/636zSrrZf+Ret2d q/rnqdffmvif6N9+H5hd7R+r/TO1v4fPlD1F9hupcwpbqu/a6Hdzfxkv11D5 KfH7uD46vv8iM9/VPzpe/Coz/8q35Jt+LTuAd1S/Db656nj+HLXXLcztgnl3 Yy2En6s6vgM7nKjn6ZEaQ4CdjsN/p8ZQYKsTZHdLjbHAFUfLPj01vgCnNJZ9 Zmq8Ag46lBgkNR7qpvvXK8w1g7F3VH2wSl51vNCrfJ4Omf03/MdGKqsSf/+L o/mGt3VstezusvcszHXPTcxPbKzyS+L2s9S+S2Eu+F3Zvcv30TEzvthJ9VtU YtX8Qlf134N4peKYY5don8q3HE2Movr66G/3MOer/mf0WHooMXf5H4dZMW6u r9/+cjSeBlfDdcJ5gt/AcT+ofQO+n+wTZX8lu1LY/+CH7pa9LDpeIG54UsdS Yhbmj+53CrFRNP4EhzYlVo3G4+ByuDQ4NfA+uP9w4qJofA5OBy/xrn+Xva70 d+1VfpP9e+p3S/xBXoF3DNcG5wZ+BceC13iX6yoe/3zbvwrnFfjGjLX1hfMK jDnmFhweeJ85Ble4NBovgZvwpXBo4GV8KtwsOT3iHeKeSXr+36PxBzikn+qL 1Ocbte2o97EoM3fSTu0bpMYh8P+zE+ORR9XeRuWLiteAxWAl9TlZ9kap8coD Kk/gLxNzNedmzvPB2fyUeV1kfcQ/k5djXWR9JD+Hb/6zcN4BH10t8e4wXXOM 2rco+aBxsp8Hb+jv6mi8A+4hV7AqGs+Aa/Bd5KzAa/gw8OgTKi+m5tdfU/2f aPwKjiUXSk4U/gUeBnxGLnqi+l+RGH+NgiOQfbnszdV3is55DN4k9VwhPiKP wpypzVwonJcgH8HcYw6CNxuX4/F01lrZP5d48kzmZsXr47bq/3thnhl+ub3O 3blw7mKW7n9OOf/PyBw/b1EYP8Jbw1dvVxjvkfcl39ta529ZOJc6Xf1r8n4K 8/bw9ZtzfmGeH37/Cb6bylKwiJ7nVJ2/feHc0Zs6/yTZ28heLvt12e2in5ln fSMxFgGTgP+JA7qV6wW/EbzcpVz/TyO+kD1ef09R+VH9f0i9NrNGMx4ZlxMy 910me6naT47+jfy2GTp/QWbu9sSK1+8mat+4MHf9vNrHqL2typcV+xB8AT6B /px3dumfTlaflxK/63VFmTeiT/Q74t1MTRzP3ckY4VnhO+XvRqhPD7CJ7MfQ H8juKfugxL4ZHw3fAu+Cb8ZHw6/AszyWletYxT6wVfQ34ttM0/nj1NZO5VvZ i8CQmZ91sexvZTdU/xqFuf7J6t9I9kaFufPnSr6FsbJK9mr1P0rtG6p9gexn 1d4heswyVpnzXOvH3HkErnls9BhjbL2s9rG61kkqi2Qv5H2qff9gXwPHXaj+ ceEcCs8/g9izMMZF/7CE/HAw99FR5Ve19yBHnzrf96r6HlrYv+Pnme+7R/OJ 8Irgg+XEn6lzvODHtVXnGrnGZJ37XjC+B+eTT4WTgosip0v+FM4LroucNf5o ddXaBO6JXuBz2Zel9sn4hy9kX6F6V9XfJfYK5oLap/Zva6rO1YKZyH/WAb+o PkFlL9V7B8dSC8Bger7DCvcFZ+Evf6k6lwtG+131XsGx3DAde1H2E8HcVnPZ v8nuGRy73ZtYL0LOkFwMMcwLxJbBXFazcn78DWeROr8BH42GpEnimGoSviqY e26UOJf2TPC1iIsY3+TkmiaOudC+jA3Ov5CHQc/wGbg4Naa5Q/bQwroN9BpD ZN9RWFeAnuB11feI5qfhqfF15xbGDvg89DHk9FrJPji1r8PnDc3NZ0xhDQ3m 8lok1qegESC3BOZHK/B8MH4Hx7+ktonB12qZWDvzSPBvIY5EfzEfHJ8aky9W faWOXUh8xG8E2wfH6s+kzuf9wHhLHdOR711PTiF1joz87t9w/qlzipvAXQTH gviUWrLPDI7t4JzJh33P+EkdE+JbDiycL8XHkG//Ue3DU+fUyEdHXWNs6hzq y+q7bTR/D4+/ijU3mCu9Q793V7WdHTwW4czBR9tE8/fw+CvVv2twLoX84/Zq 6xjMFb2qMk/tC2Sfqnqf1PHbiqpz68QA5Mvx2fhqcrJwvwcVzifDAZNf30Dt j4O1VSqsvcGxKWtoJvukYG7sEeYffiuYex2cGq8t0rGbeD+59Tlfy+6fGlOj N/lG9sDUMRR6kgX49dQYHNK8TXBs/EDqfOGnau+b+jelam8bHLs/mPpeK4K5 Pu6J/oFn5NnIKRPP8ht4dvwA775DMJfGN+Ddtg8eq7xj9E+8U94l7wQ9zELd Y0DqmAF8+QlxIc+Tey3qHsx9syb9LPucYG7s9tK/oEE7JjFHgd6MOc9cZ04y 95iD9WT3yawleoaYI3GuCK0bmjdyh+SG0OKgEUILR+7jPtlPVK2tuzizdunx qrVc5HrQHqHJQ2tHbmZ21Wsuay16phGqP1m1Vu3SzNol1hjWFnJLz4GHq/YF h4DpCq8fnNso9/xkfSJXtmFu7QyapsaJc2VDZPcLzgX2zqy9Gle1dotcE7kK chbkXnpkXntYg+rii2XfyfyvOhfYV/ZdssdUnQu8MLN2bGzV3CJYFe68ZWEt ItwBXNhZvKPEnBjPwjOhu0FvA3d6VrA/IvYGa3UujB3+w1yqNy+8vsE9gfW6 FsZSYD6wWKfCWARMBt4m8btHarwOV3ZM4fcBN8Z8w7/hf4ZnXj/AqGib7smc 620QnPsm50suuH5wrpicMLmwg4JzUeTEyJ0dHJzbIocGdweHB9b6Nzc3d0Qw twpHRy6xUXBumJwi2o0xwWMTHo2xMbtcn/fOrW3BX6Ft3Cq3PmB2+f3hpNAX zKpaCwdn9az6zwlug7d6U20zgrlz+AX43J+JN1Ln019R+9TgXMwJibHH68H8 GhjkI/QOwbmj1qyJ6v+O7Oap+YuZst8Ozq2cmvh5nw32LfBK5C/XqGyTOj+J /m46/iq1z3lL9beCczmnJNZXvFO1NoF7kF9bobJl6nw7+bhlmbUcfKMbguMn dCXoSdD/8Jv5rfwG4rV/VHZLne9+VW0vB+ea2iT2z6wPYM9Ncn8P/DfYdCPZ 4wr7UHwnubOxhTEG2IJc2OOFfSa+ktzZU4XvwbXJdeFf8bdoCWsRFxV+57xr cnPgB/w32tYtcn+/WSU+2TP395hRrl+75NaPoIFFqwonh37mjaq1tHB26F9m lOsFHOVEnie4Dm9JrHBY8NwgZphU+Bvy7citPVP4m/AtyL1w/hslnqmdO/fS qvD94Qrhk5ZVPX/Q6KAnIwYl9kQTtVb24uDczlWptcRoipmfSYkVvwvOrYEZ WU/3K6yXRDdJPoNvzLdFM8b606CwHhZdLPoI1iuwEhpX1ubjgnPfrNHPqd46 ODd9WGq97viqtRXc435da//Cek50neiHWY+Zn7um1kqjmWb8MI5Yy48N1gaw pr+o9rk61pv5lVs/wXrJesszviR7ZLDW4MjUfN/HYNLUnBV6kNGyN02t2UO/ wRrJ2rg08fpbv7B+Fh0t2ls0uMxf5jFrefNgboA1/Qa9+8Nl75SYc6gh+5Rg LAHnsLHsU4O5cWJ0tMdokJmfa8r165RofSc5iC9k1wzmg+CF0LPgL8GqaIj5 7V8G5xp5B7zblsHaBt4x37ppMFfCN7+fuR7MhdRL7d/mB7+LNrn1JviXOok1 5PiWZsFcCD4G39oiWBuBj0Uvcyvrb2rN8XtqnxucuzwrdXy7ORgztaYTX94q +Nvi09Hr3Bmsxc7AK+p/YLBWu3nF76ZhcO6Ld8S9jg7WYnDPu5lbwecSM6BH elj3+D6xBquPrrdfMLeKxgruEU4UPqxD6X/3KqzPRTOA/92n8G8hBoBLhGOF /+pY+vO9C48VfOggXfvIYC6aNRI9yAHB3CQaCMbKUcHc9dYl3tm38Fwh5kDP 8yj4JPUYu07nHxrM/aL5ukb2IbL/TazZABuNCta6gJHQ+y7RsSGpY4A/9Q23 LsyHnFryk3wTvsUxubHn8uDcLxi0X7kewS2jaWCuNQnmJphz1wWPZ7S3NVJz OXC6xOfE6eCnAwrr09Gpo1+cUDWe4xj7H8Bn4BnmeEX1HQrzSfBKW4JdCvOR 8JI/6xk3LcwfwCPAdcDJwx/AI8DFwMnDr8CzfMm3DtYeXJ16f8OHYNDUOS+4 HDhg+Co4HfY3gOe6p85Jsf/gA9ldUufMpqnvIYXXUnSP26v9RDjg1DnrHsRH 0dqUHSvWs/WO1m79mJj/2jVYi4ZmF/yC3mWJ2rpl5i92C9bioSmGHwKvkGtE ow1/tTPzq+I1gPdVOzh/Tx4fPc9V0dohxgR4CP0OevKeJR5Cr8P+il6ZuRzG P74bTge9D3gTbQznoO+5IlprxDnXl+MPXw3nBPfKGGFsoHvZU21d4Ogq1nBc W45PYnU0RuA3NHu8i+6Z+TZyuuRy0Zy/UJiTgItokjvfiWYDrQaa6qngucJc Cbp49O/gQ7hLNK31VO8SrNV7L3Vs3jk4N0+MTj6PGJbYFV4UffEc8FlqjgVu plOwVg2OBr36UrU/lzqGvbRcf9D+oPlqJnvvaO5oVer8yt7B2ko0uYzfusH6 GnQ25Cv2lX1IxZpY9E5oDtAaMAaIHxYFczVn5c5f7CG7XsUacfTI37EOpc4h kq/YK1jbyTsnv4JmCK0QGuPtVG8bzc2jibiw5LfAlnB2F5frEdgPTrcO947O hexU8oVbMf8r1pzDn6FZQauCpp7f1ik6d8RvPB0uMJoLRtRHPnLDYK6WPTBb qN4imhtGMwU/iGYAbh7NO/zuNrJrVKzhRxtzXHQdjQxtx0fnJuiDvqxNdO6C HD3rA/fg2lk5N86Izi0xR9CicQ59yevD7R0QrY+G42N95J3xrtCR8O7PjtZO 8g3I124QzB1yDvliOEK4QTTj5G9jcHyExhx+cpPgeGgZz4g/iK7DF9eQfVg0 N40+biPZR0Rzw6/KrsfaFZ27QwMFP7ppMDeNZhs9Gj4RX4iPgs/eIVgrx5qE 9hCfg69BdwdWaB7NnYIZPlX70dH7qdhXNZf4KfpbsW8pV/99o7naF3X9quwG 0VztlMRY6fNg7ROYiW99SDT3zTefT2wX7dvZtwGfu1lw/MU94Qq+CtZGwRmQ O+lZmLslhwL+w1+gdb8kM5fdvTD3Dqf9bYmXBiXO4S8t+Qq4BXJKS0q+6+bE OXy0uWh0wb7DMufC4a/gisiJLy75rZsSawSIj8nH8y0XlLkn+ItRiXNQx0Rj MLAXY35ZyZ/AVZGzW17yT3AfaACJp9EkwdXer/tvUni+vJCYg4Y/JGfG2rE9 cUj0mGWsMuZXlesTXCk5otXl+ga3Sg6JvSrwY3DP7FlZU66HwxNrYMglwY89 kDinFAt/L7QC5MQYf/N07Hv91mfK8fkJeIZYh5g5mv8dm1iz80c0v0PuE41O Ung9HJdYg4NI/N3COfFHEo+nD2V/IfvxxFoJ+PJHE2smGF8fqf1LtY/Xsf9F 88ePJdYwkeuCLx6TOOdFrpGcI2vdTnpHaeHxyrXR9KzTsTcLaxDIp5NrZX7x 28hRkDtgPk5KnENYF803PphY8/QH8W9hzQL6jv/Jnl1YQ0D+tyg8f3k35GT+ Vfucwjn+0YlzucwXfgs53T/VPrOw5gE9yk9V663QILCfiNwz/pPcNDlocgHo udA8wMGAXdDTtc6NYcjN9SicSyNHNyoa37PXkT2bY6L5ZeYPe0YejubTaWdP JFo2NG1wr3frPo9E8/PwZexJBYuBZ95KjMnQe+KX8c8dE2Mn/MXbiTEUesfT c3Or3RPvDYWvhj9jz+eE6HiPvX3s8RsfHQ8Sf7Mnc1x0/Aafwp5R9ooSDxxe ng82IyYhFgGjTYzmR8C6aLxHRscf8AXkrNBnEvcR+5yjY09F8yUNE2vMH6ta D82e2F0SY1f8xczEGBa9LLgYfMz+R2ID/B1aMGIEsCn+AW0BGHWrwv6JtY8c IFgb/8TaDuYmVmA9R9tAzAD3DKYES8JBE6uDccA2xOzkUsixkFshp0JuhpwS uSQ4MtZDcnxgyQ2qxr74e3wHGBi+jvzbf/vJco8X8mNgy42qXm/JWYOtNi35 O/KfYLG/cvN35Avx/atz50rBu/gucqZgb/w5vgAMzt4z4tmBSbkHTe+vuc7r lHp/Jtgd/4MvAcOTq4bvgU8lZ01sCYcAd0CMyXpHTvyh3JiMfNIM2W/lXhP2 jLbR+ZGT+lvtswrvaUNPtR7+q/CeMfRUf8GPFd5Dib4LPnq67Odyr+nkKNjf xV43MCV5evZLsbcNzoR8xCvg/9xrBPmrN2TPyL0mpfot7xXes0Q+MlS9Xw9/ hcYS/4u/WJn7HYAV2H/BnjMwwyXBMT+xPjFsRvxReA8T+U+wBPlM9myBKfCl +Fh8Kz61Ivv9wnuOyJ+CFfDx+HYww0XBHAXcBDHziNz71y5NnNO4L/d+tEsS 52QuDMYQYAdi7u2i3xc6dnIyO0S/D3TucPzkSNh/d0PiHCX5BHI69+b2iUXV +xtZr8CU8AVw8r9lnrNwWXBacGFwZnBtcG5wpXCoYC8wCtgEDAa+Jwc3JrcP nJZ7/+6NiXOW6C7YP3dx4pzONcExC7EKMSv8BRz56swc/fjc+wXRVqCxuD6Y E4MLgxOBz4GjX5uZg7w2mIOCe4JDYd8B+20HJM7J1o0eH+hayYHuE+3/yDsT Mxwa7V/RDYCZDo/2v+gWwISDcu9XOz9xDu7G3PvRzkuco7s+tx4TbQc5t/Nz 67f6Js4pXZNbn4nWg5jh6tz6Q7QtcALkIshJxNz7ffrm1u+hBSCn80Uwh8Ya CsZj3UXP1SXx+ts7tx7sgsQ5qva59WA9E+cg4SPI2VRz5yh65taT9eHdlTEO erFeiXOuZ+bWE/ZInNOC64NDgDuA85tQYkK4wHqJuQM4SbjIuon5Lp73sNwc KbkacjYhd04E7g/ODq6uNv40OObEp5HDnxnMucK1wnm3yq2PZS83HECL3PpZ 1jLWNPww+tXOif0x3Cwc7W65OWhiWa6/b25O+ebc+zP5/SPUf7Ny/JI7Jmat H41/0EmAufNy/pALJYf5ZvD14X7/09tXzWlvl3sNhbuGw942t0+E+4YDr5nb B48P5sjhxsmpTws+Hy6cHANcM79/99ycOlw6/TfLjQmmBF8fbpycA9w7HPzm uTHGU8H3g2snpz0huB1unpz/4Gh+bo/Ee6zYD0GeEOzfLbE2Db6Sb4dGjbU0 LfEhWn32cwzO/e54h6x1lRIPonVnrcxKvIi2nP0Qt+fOhTInwKJgUvAeWhXm IpiUtZg5ybsHg+LP+AZgOTAdeBHtDXo9Yjj8H1oefA0+B1+AVp21mDWZtXpF 7rWXNZi1eFlufV8IzoehfQFLginBj2jTyL2j72eeM7/Zz3Jr7lwvcwx+nz0W cFcH4BOi80fNEu/5IffOfhHWBdYDtHPkf/iWaOiej87nMDbZY8ReWfJFLRPv mWUvBnsyyH3flVm7iD6EsYuGkf0jl+fOZeMjyCeyJwdubD98THQ8SH6HPSFo IeF7ybegiWStI6YAD7HmsReIPUFoFY7MvV/pytxaBXwSWkHiQ/IfaAbZG0v+ ntwWe2RZK4lZwDusmexXQddCroI1kvie+Bxfvyj33orjg/05eyzgF2qV8fzv ubEWmGu07Acz6+vQ9Pyn5cm9luPz/4u/cu+tObnweocWlr1E7QqvX2ij2SvU tvD6gNadvURtCq8naO+JR88Ixv5okcHjJwf7L/aYgF3AMMRr7L3g+7QL9i8N y/d3XOF8HNp49pqcEOy/2HPCXqYTCq9XaP+nReuVjk+854z9WT1yr8XMJ2Il YibiJ/ZSoLdEU0F8zN4WYhdiGPLF7JUAS4GpwE7sFWE/VrfcXCs+C1+NzwaL Lc6NdcG8xFIjM+fK4bzwA6z/YF8wMLHaiMxaFvab4VfwJ2A9MCC+HswHFgYT E4uNyhyrEbONT7y3A20C+7Hwa/gzsAoYDiwCZgHLgAHhC8A07H9Cl4FWAsxA fps9duRu6+aON88rrJ1G43pHdP6EXBZ7OhkP7LlC+3J2bq08egz2lqKZZy8A ehH2prIngPw3e0bIFe6Qe28y+QpyH+xRRs8N304uC43+0Oj8zL6J93SyN4T8 C9iFPSLsTUB/0j/xHgXGI3vc4Ao75B4P7HFDS3Jsbu0wfH/XxBpixit73NBy tM09XtkDhzbleLBNdD4L7INGEK0u+hbWbjS7/N8i6I2I/fg/RtAKoz8h9kIz jPYZPp5YCg00+Xf2yJA7PC+zfp98CbkkNLZoL9G7sJcVDSZ6f/IluyXW3KJt Jj9JLIrG+Z7o/AdYgz3SaKH/y28m1kTfHJ0v2j3xHt67ovN/7JVmzzT5f/YU kzu7QM8zLFpPBnZgvyzrB3u00EbdkXm+sccLbdRQ2f8HZqW4Eg== "]], Polygon3DBox[CompressedData[" 1:eJwl1nf01mMYx/Fveup5kEglDdHeU7TUDw3tX9p7+7W0SEZDxo/KSkpaVkbz OJTQiaJFsmdZpcw41kHi4HWd7x/Xea7rfX2u676/93N/7/tbZdSUXpNPSpKk kBVjs4onyd3ZJBkB9gQOF02SVeLH8ZKZJOmLjZN7EGucS5Kr5Cuz8dgKbDVd Cbo+dGOx1jS3YGcWSZLv6HaxqeLptB3lL6Hbh92OPYAVYL2xn7EjfnupH6zf DexOPT7AumCtxQPZFKyvOFG7gr8Am8w+o8vH8/lXsrlyQ8Q/4HeQb8A2svHq Ghp7jPFayLU2/rVYM2ws1g7rjPVR+y+2TJ956iZm0udqxSbSfVs0fcbr1V6A jRO3V9tV7aNYU/XTsfPYRGwdzSP4BP65WCn97sBWZtP1jXX+HZ+PLc+maxlr +hv2id/u+nVWM5bNMu5Emka0V8i3lG9D/6nfHnTd4jnZHLoqdENjrem2Yruw Wti/7G0189S8gg9WVw3bI79N/CCrpq4AL0FTk1WlX0vzNF5Wvj8Wm6l6rB3d 6eLarDrWna4s9k08h7GP01eN+WIn09Rg58ldLv6Sv8C419EMYMvo1qmfIj9A LoP1pDvMn0c3Q9yPLaBpgE/SvzwbQr9U7ZpsOq+Y30nRT/wIfkom3Wux55aI n8An8fth/6l/UvwUXjqTssjNFN+E9+Z3wb6gq4SNMu7fdOWx0nJdxQf5N5jf GLw9q0s3Aa+INw6L/S9+LNbSnvxBrx9ZVv9etPfyl6p7XI+F4jw2GTsR+wib Jr6ddmCsrx778X76FcFWyd+ldhpbL95MWy6Trl+s48V0i7CqdP+o+4yVpRuA LeGvod0i96rf19ha8/tL7XK/ZWlGqP8Vz2HF9KsX7wFWWdyENcU6i9+PddOn P20r1hF7AxuOdRA3YlernWfsQWp6yL0V42MPZdNzJc6XM+hOjnXHF4mXiZ/U Y4N4dTZ9p+LdOhP/B+sW55i4ULyU7gyaX9hOupuNsRq/yFymYJdgbbA99Bnx 92wbdiO2OOYdewrLi/Ms3g+6o+Lz8fv4eWyL3DhxbePW5zekO4s9Q7cj1lmf IeIZcuPp6mAN+Y2ws2MNsaa0h+KcE38kVwbrgv2BLca+xlqKc7G3+PnG/Uqu IVYEew/rhh3ERsY+M0YprJzaE1h9ugR/N/Yn3QGsuLgZ/iX/LrqP5ZqLs/iB +D/iWeVmYHWxAvHprJPcbv0349fxa2A16J4X78Pr8IfpN0uuEnY8OP827Fm5 CuI/2WtYIbYJK6F/W+w7/j3Y53KnYRdjx7CF8b5hL4j3G6MeNhybjeXRzcbz +R2xT8xnTC49Y+JcqY5l4/ykuRBfLt+R7ZZrK56Jd+d3oDmAH4s7AL+ffyl7 UW6nXpvwa6MfVt34LXPp2RvnbSu12/Ff4w7Al/E7xJ0nN1pcRX1lfrU4w1i3 XHqWx/ldoNdlbIfaD+ku5I+Wu5W+DvYfe4c/H9sltyjOe/VT4/xho+UqivuE NvY83Y/YHL3uwUbG2Yodoe1Pdyq21rgraGez7XLt8Er8c1i+rbI39mOcO+KC uDf1aE+zh99Pfq5eNeUeijODdoz8OXF+YWWw4bQ/xx6jLyp31G9vbBg2k91t /FV092XT+cdzFMffpOsU7wO/U+zlIumZcRnWOM6QTHp+tBEXqi/DP6b2Vfaw Xk3wq4um92rcr3vVdsBqqasd95S5L4x7P95/mopsFN2luXQd4tlnB6fdqv9G 2mnyVbEK2FvYVmwOVgtrgJ0Qt1C/StyZ7Zf7C2uOrYz3hb0e95f4NHy9Oa+M 7xL2nH4bsKnyVeLuwlbE+Z9N5xXzK4a1E5dUfyj+y7grsKexl2KPx51t7tfI DcylZ3mc32vjPIn/gGYo/ml8G8V7mqTfM91jf8T3Vyb9thmWS/+7+L+K6fcT frNe9fDxcUewPnIHaF7GC/l149uJbhBNOex5fdbHO8zmi+vjV9KczQbT/w83 zTJU "]]}], Lighting->{{"Ambient", RGBColor[0.30100577, 0.22414668499999998`, 0.090484535]}, { "Directional", RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], ImageScaled[{0, 2, 2}]}, {"Directional", RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], ImageScaled[{2, 2, 2}]}, {"Directional", RGBColor[0.2642166, 0.18331229999999998`, 0.04261530000000001], ImageScaled[{2, 0, 2}]}}]}, {}, {}, {}, {}}, {{}, {}, {}, {GrayLevel[0.2], Line3DBox[{779, 958, 1338, 959, 2156, 1340, 963, 1001, 964, 2161, 1355, 1004, 1005, 2164, 1362, 1032, 1033, 1369, 2275, 1052, 1053, 1376, 2277, 1072, 1094, 1073, 1383, 2280, 1097, 1127, 1098, 1390, 1130, 1160, 1131, 2165, 1397, 1163, 1193, 1164, 2170, 1404, 1196, 1197, 2173, 1411, 1224, 1225, 1418, 2291, 1244, 1245, 1425, 2292, 1264, 1286, 1265, 1432, 2295, 1289, 1317, 1290, 1319}], Line3DBox[{780, 961, 1339, 962, 2157, 1342, 967, 1003, 968, 2162, 1356, 1007, 2195, 1008, 1363, 1034, 2210, 1035, 1370, 1054, 1055, 1377, 2278, 1074, 1096, 1075, 1384, 2281, 1100, 1129, 1101, 1391, 1133, 1162, 1134, 2166, 1398, 1166, 1195, 1167, 2171, 1405, 1199, 1200, 1412, 1226, 2246, 1227, 1419, 1246, 1247, 1426, 2293, 1266, 1288, 1267, 1433, 2296, 1292, 1318, 1293, 1321}], Line3DBox[{781, 965, 1341, 966, 2158, 1344, 971, 1006, 2194, 972, 1357, 1010, 2197, 1011, 1364, 1036, 2211, 1037, 1371, 1056, 2221, 1057, 1378, 1076, 1099, 1077, 1385, 2282, 1103, 1132, 1104, 1392, 1136, 1165, 1137, 2167, 1399, 1169, 1198, 1170, 1406, 1202, 2236, 1203, 1413, 1228, 2247, 1229, 1420, 1248, 2257, 1249, 1427, 1268, 1291, 1269, 1434, 2297, 1295, 1320, 1296, 1323}], Line3DBox[{782, 969, 1343, 2269, 970, 1345, 974, 1009, 2196, 975, 1358, 1012, 2198, 1013, 1365, 1038, 2212, 1039, 1372, 1058, 2222, 1059, 1379, 1078, 2227, 1102, 1079, 1386, 1105, 1135, 1106, 1393, 1138, 1168, 1139, 1400, 1171, 1201, 2235, 1172, 1407, 1204, 2237, 1205, 1414, 1230, 2248, 1231, 1421, 1250, 2258, 1251, 1428, 1270, 2263, 1294, 1271, 1435, 1297, 1322, 1298, 1324}], Line3DBox[{8, 581, 1907, 23, 282, 1674, 38, 1448, 53, 1461, 68, 1475, 83, 1489, 359, 98, 1503, 388, 113, 417, 1795, 128, 446, 1819, 143, 1520, 158, 1533, 173, 1546, 188, 1560, 523, 203, 1574, 552, 218}], Line3DBox[{257, 255, 1916, 590, 259, 1932, 606, 291, 1956, 620, 1957, 309, 634, 1974, 325, 648, 1988, 341, 662, 2002, 368, 676, 397, 2016, 690, 426, 2030, 704, 455, 2044, 718, 473, 732, 2058, 489, 746, 2072, 505, 760, 2086, 532, 561}], Line3DBox[{786, 984, 1349, 985, 2159, 1351, 988, 1020, 989, 2163, 1359, 1022, 2203, 1023, 1366, 1043, 2216, 1044, 1373, 2276, 1063, 1064, 1380, 2279, 1083, 1113, 1084, 1387, 2283, 1115, 1146, 1116, 1394, 1148, 1179, 1149, 2168, 1401, 1181, 1212, 1182, 2172, 1408, 1214, 1215, 1415, 1235, 2252, 1236, 1422, 1255, 1256, 1429, 2294, 1275, 1305, 1276, 1436, 2298, 1307, 1328, 1308, 1330}], Line3DBox[{787, 986, 1350, 987, 2160, 1353, 992, 1021, 2202, 993, 1360, 1025, 2205, 1026, 1367, 1045, 2217, 1046, 1374, 1065, 2225, 1066, 1381, 1085, 1114, 1086, 1388, 2284, 1118, 1147, 1119, 1395, 1151, 1180, 1152, 2169, 1402, 1184, 1213, 1185, 1409, 1217, 2241, 1218, 1416, 1237, 2253, 1238, 1423, 1257, 2261, 1258, 1430, 1277, 1306, 1278, 1437, 2299, 1310, 1329, 1311, 1332}], Line3DBox[{788, 990, 1352, 2272, 991, 1354, 994, 1024, 2204, 995, 1361, 1027, 2206, 1028, 1368, 1047, 2218, 1048, 1375, 1067, 2226, 1068, 1382, 1087, 2228, 1117, 1088, 1389, 1120, 1150, 1121, 1396, 1153, 1183, 1154, 1403, 1186, 1216, 2240, 1187, 1410, 1219, 2242, 1220, 1417, 1239, 2254, 1240, 1424, 1259, 2262, 1260, 1431, 1279, 2264, 1309, 1280, 1438, 1312, 1331, 1313, 1333}], Line3DBox[{861, 945, 1314, 1282, 855, 939, 1281, 2265, 1261, 849, 933, 2255, 1241, 843, 927, 2243, 1221, 837, 921, 2233, 1189, 831, 915, 2231, 1188, 1156, 825, 909, 1155, 1123, 819, 903, 1122, 1090, 813, 897, 1089, 2229, 1069, 807, 891, 2219, 1049, 801, 885, 2207, 1029, 795, 879, 2192, 997, 789, 873, 2188, 996, 953, 776, 867, 1335, 951, 1334}], Line3DBox[{862, 946, 1315, 1284, 2184, 856, 940, 1283, 1262, 850, 934, 2256, 1242, 844, 928, 2244, 1222, 838, 922, 2234, 1191, 832, 916, 1190, 1158, 826, 2285, 910, 1157, 1125, 820, 904, 1124, 1092, 2178, 814, 898, 1091, 1070, 808, 892, 2220, 1050, 802, 886, 2208, 1030, 796, 880, 2193, 999, 790, 874, 998, 956, 777, 2267, 868, 1336, 952, 954}], Line3DBox[{863, 947, 1316, 1287, 2185, 857, 941, 1285, 1263, 2182, 851, 935, 1243, 845, 929, 2245, 1223, 839, 923, 1194, 833, 2289, 917, 1192, 1161, 827, 2286, 911, 1159, 1128, 821, 905, 1126, 1095, 2179, 815, 899, 1093, 1071, 2176, 809, 893, 1051, 2174, 803, 887, 2209, 1031, 797, 881, 1002, 791, 2273, 875, 1000, 960, 778, 2268, 869, 1337, 955, 957}], Line3DBox[{864, 948, 1325, 1300, 858, 942, 1299, 2266, 1272, 852, 936, 2259, 1252, 846, 930, 2249, 1232, 840, 924, 2238, 1207, 834, 918, 2232, 1206, 1174, 828, 912, 1173, 1141, 822, 906, 1140, 1108, 816, 900, 1107, 2230, 1080, 810, 894, 2223, 1060, 804, 888, 2213, 1040, 798, 882, 2199, 1015, 792, 876, 2190, 1014, 978, 783, 870, 2189, 1346, 973, 976}], Line3DBox[{865, 949, 1326, 1302, 2186, 859, 943, 1301, 1273, 853, 937, 2260, 1253, 847, 931, 2250, 1233, 841, 925, 2239, 1209, 835, 919, 1208, 1176, 829, 2287, 913, 1175, 1143, 823, 907, 1142, 1110, 2180, 817, 901, 1109, 1081, 811, 895, 2224, 1061, 805, 889, 2214, 1041, 799, 883, 2200, 1017, 793, 877, 2191, 1016, 981, 784, 2270, 871, 1347, 977, 979}], Line3DBox[{866, 950, 1327, 1304, 2187, 860, 944, 1303, 1274, 2183, 854, 938, 1254, 848, 932, 2251, 1234, 842, 926, 1211, 836, 2290, 920, 1210, 1178, 830, 2288, 914, 1177, 1145, 824, 908, 1144, 1112, 2181, 818, 902, 1111, 1082, 2177, 812, 896, 1062, 2175, 806, 890, 2215, 1042, 800, 884, 2201, 1019, 794, 2274, 878, 1018, 983, 785, 2271, 872, 1348, 980, 982}]}, {GrayLevel[0.2], Line3DBox[{1439, 1642, 1896, 867, 1895, 1643, 1898, 2267, 1582, 1897, 1645, 1900, 2268, 1583, 1899, 2105, 2156, 1902, 1584, 1901, 2106, 2157, 1904, 1585, 1903, 2108, 2158, 1906, 1586, 1905, 2269, 1648, 1908, 1587, 1907, 1650, 1910, 2090, 2189, 1909, 1652, 1912, 2270, 1588, 1911, 1654, 1914, 2271, 1589, 1913, 1656, 1916, 1590, 1915, 2110, 2159, 1918, 1591, 1917, 2111, 2160, 1920, 1592, 1919, 2272, 1659, 1921, 1593, 1661}], Line3DBox[{1440, 1644, 1922, 2091, 2188, 1663, 1646, 1923, 874, 1665, 1647, 1924, 2273, 1594, 1667, 2107, 2161, 1925, 1595, 1669, 2109, 2162, 1926, 1596, 1670, 2194, 1649, 1927, 1597, 1672, 2196, 1651, 1928, 1598, 1674, 1653, 1929, 2092, 2190, 1676, 1655, 1930, 2093, 2191, 1678, 1657, 1931, 2274, 1599, 1680, 1658, 1932, 1600, 1682, 2112, 2163, 1933, 1601, 1684, 2202, 1660, 1934, 1602, 1686, 2204, 1662, 1935, 1603, 1688}], Line3DBox[{1442, 1664, 1936, 2094, 2192, 1441, 1666, 1938, 2095, 2193, 1443, 1668, 1940, 881, 1444, 2113, 2164, 1942, 1604, 1445, 2195, 1671, 1944, 1605, 1446, 2197, 1673, 1946, 1606, 1447, 2198, 1675, 1948, 1607, 1448, 1677, 1950, 2096, 2199, 1449, 1679, 1952, 2097, 2200, 1450, 1681, 1954, 2098, 2201, 1451, 1683, 1956, 1608, 1452, 2203, 1685, 1958, 1609, 1453, 2205, 1687, 1960, 1610, 1454, 2206, 1689, 1962, 1611, 1715}], Line3DBox[{1468, 1717, 1963, 1716, 2218, 1467, 1714, 1961, 1713, 2217, 1466, 1712, 1959, 1711, 2216, 1465, 1710, 1957, 1709, 1464, 2215, 1708, 1955, 1707, 1463, 2214, 1706, 1953, 1705, 1462, 2213, 1704, 1951, 1703, 1461, 1702, 1949, 1701, 2212, 1460, 1700, 1947, 1699, 2211, 1459, 1698, 1945, 1697, 2210, 1458, 1696, 1943, 1032, 1457, 2209, 1695, 1941, 1694, 1456, 2208, 1693, 1939, 1692, 1455, 2207, 1691, 1937, 1690, 1720}], Line3DBox[{1482, 1741, 1977, 1740, 2226, 1481, 1739, 1976, 1738, 2225, 1480, 1737, 1975, 2276, 2117, 1479, 1736, 1974, 1735, 1478, 2116, 2175, 1973, 1734, 1477, 2224, 1733, 1972, 1732, 1476, 2223, 1731, 1971, 1730, 1475, 1729, 1970, 1728, 2222, 1474, 1727, 1969, 1726, 2221, 1473, 1725, 1968, 1054, 1472, 1724, 1967, 2275, 2115, 1471, 2114, 2174, 1966, 1723, 1470, 2220, 1722, 1965, 1721, 1469, 2219, 1719, 1964, 1718, 1744}], Line3DBox[{1496, 1761, 1991, 1760, 2228, 1495, 1759, 1990, 1085, 1494, 1758, 1989, 2279, 2122, 1493, 1757, 1988, 1756, 1492, 2121, 2177, 1987, 1755, 1491, 1081, 1986, 1754, 1490, 2230, 1753, 1985, 1752, 1489, 1751, 1984, 1750, 2227, 1488, 1749, 1983, 1076, 1487, 1748, 1982, 2278, 2120, 1486, 1747, 1981, 2277, 2119, 1485, 2118, 2176, 1980, 1746, 1484, 1070, 1979, 1745, 1483, 2229, 1743, 1978, 1742, 1763}], Line3DBox[{106, 666, 819, 107, 667, 820, 108, 668, 821, 109, 1390, 669, 110, 1391, 670, 111, 1392, 671, 112, 1393, 672, 113, 673, 822, 114, 674, 823, 115, 675, 824, 116, 676, 117, 1394, 677, 118, 1395, 678, 119, 1396, 679, 120}], Line3DBox[{1510, 1777, 2005, 1120, 1509, 1776, 2004, 2284, 2131, 1508, 1775, 2003, 2283, 2130, 1507, 1774, 2002, 1773, 1506, 2129, 2181, 2001, 1772, 1505, 2128, 2180, 2000, 1771, 1504, 1108, 1999, 1770, 1503, 1769, 1998, 1105, 1502, 1768, 1997, 2282, 2127, 1501, 1767, 1996, 2281, 2126, 1500, 1766, 1995, 2280, 2125, 1499, 2124, 2179, 1994, 1765, 1498, 2123, 2178, 1993, 1764, 1497, 1090, 1992, 1762, 1779}], Line3DBox[{1511, 1778, 2006, 909, 1786, 1780, 2007, 2285, 1612, 1788, 1781, 2008, 2286, 1613, 1790, 2132, 2165, 2009, 1614, 1792, 2133, 2166, 2010, 1615, 1793, 2134, 2167, 2011, 1616, 1794, 1139, 2012, 1617, 1795, 1782, 2013, 912, 1797, 1783, 2014, 2287, 1618, 1799, 1784, 2015, 2288, 1619, 1801, 1785, 2016, 1620, 1803, 2135, 2168, 2017, 1621, 1805, 2136, 2169, 2018, 1622, 1806, 1154, 2019, 1623, 1807}], Line3DBox[{1512, 1787, 2020, 2099, 2231, 1809, 1789, 2021, 916, 1811, 1791, 2022, 2289, 1624, 1813, 2137, 2170, 2023, 1625, 1815, 2138, 2171, 2024, 1626, 1816, 1170, 2025, 1627, 1817, 2235, 1796, 2026, 1628, 1819, 1798, 2027, 2100, 2232, 1821, 1800, 2028, 919, 1823, 1802, 2029, 2290, 1629, 1825, 1804, 2030, 1630, 1827, 2139, 2172, 2031, 1631, 1829, 1185, 2032, 1632, 1830, 2240, 1808, 2033, 1633, 1832}], Line3DBox[{1514, 1810, 2034, 2101, 2233, 1513, 1812, 2035, 2102, 2234, 1515, 1814, 2036, 923, 1516, 2140, 2173, 2037, 1634, 1517, 1200, 2038, 1635, 1518, 2236, 1818, 2039, 1636, 1519, 2237, 1820, 2040, 1637, 1520, 1822, 2041, 2103, 2238, 1521, 1824, 2042, 2104, 2239, 1522, 1826, 2043, 926, 1523, 1828, 2044, 1638, 1524, 1215, 2045, 1639, 1525, 2241, 1831, 2046, 1640, 1526, 2242, 1833, 2047, 1641, 1834}], Line3DBox[{479, 462, 2243, 1527, 464, 2244, 1528, 465, 2245, 1529}], Line3DBox[{492, 477, 2254, 1539, 475, 2253, 1538, 474, 2252, 1537, 473, 1536, 2251, 472, 1535, 2250, 471, 1534, 2249, 470, 1533, 469, 2248, 1532, 468, 2247, 1531, 467, 2246, 1530, 466}], Line3DBox[{1553, 1857, 2061, 1856, 2262, 1552, 1855, 2060, 1854, 2261, 1551, 1853, 2059, 1255, 1550, 1852, 2058, 1851, 1549, 1254, 2057, 1850, 1548, 2260, 1849, 2056, 1848, 1547, 2259, 1847, 2055, 1846, 1546, 1845, 2054, 1844, 2258, 1545, 1843, 2053, 1842, 2257, 1544, 1841, 2052, 1246, 1543, 1840, 2051, 2291, 2141, 1542, 1243, 2050, 1839, 1541, 2256, 1838, 2049, 1837, 1540, 2255, 1836, 2048, 1835, 1860}], Line3DBox[{1567, 1877, 2075, 1876, 2264, 1566, 1875, 2074, 1277, 1565, 1874, 2073, 2294, 2146, 1564, 1873, 2072, 1872, 1563, 2145, 2183, 2071, 1871, 1562, 1273, 2070, 1870, 1561, 2266, 1869, 2069, 1868, 1560, 1867, 2068, 1866, 2263, 1559, 1865, 2067, 1268, 1558, 1864, 2066, 2293, 2144, 1557, 1863, 2065, 2292, 2143, 1556, 2142, 2182, 2064, 1862, 1555, 1262, 2063, 1861, 1554, 2265, 1859, 2062, 1858, 1879}], Line3DBox[{1581, 1893, 2089, 1312, 1580, 1892, 2088, 2299, 2155, 1579, 1891, 2087, 2298, 2154, 1578, 1890, 2086, 1889, 1577, 2153, 2187, 2085, 1888, 1576, 2152, 2186, 2084, 1887, 1575, 1300, 2083, 1886, 1574, 1885, 2082, 1297, 1573, 1884, 2081, 2297, 2151, 1572, 1883, 2080, 2296, 2150, 1571, 1882, 2079, 2295, 2149, 1570, 2148, 2185, 2078, 1881, 1569, 2147, 2184, 2077, 1880, 1568, 1282, 2076, 1878, 1894}]}}}, VertexNormals->CompressedData[" 1:eJxsfHk8Vd8XtkoTpZQyhiKVlDQK3VMRFSFDSjQIKZEGU1SkzEMpKlPzPJCp EvdEmYnMpciQMTSSQu959j1+n+/7ft7+uR+rdZ+99rPXWnvtdc6+M60OGtmM 5OPj+zuOj28U81ny+x/zr4eyu3uf+RfHsYSQL45zTNPFML3iC1XZeuhl5uta atkqV4vSybGc+IUepld/NFF2hac/v+Jvp7h0s7RaTBzHZckvbqhHEaVzKU4+ ZnEPZazi6ShQG8MpCq4JDfcoomm1ni/RjDx5w+4rz57EcV45/JK99qOJjlqx WhM4Zi0jCI6g/rYMZlz6T5L6AM2Mu3V9h7xUXRzHY4DYSRsuHzF/z2szrjgf z07FcLVE6I8w3K/48nUtfav2LNHfeGbcBOD3LPtqzODTZb3PpsUOxHJM9cbN hz2PNa99Z+yhi+NuE3vG2jVND2Ps95OPkmHsp0dOKbgGuefrcwcw31FakuXA 8X65tM7wQAznyhRdc/CTdzL2IsMPvYtvHuHnVj+Pz6XpK96v/RHF3cLyGb2W x2eNlEHzdZNojnIXj9ek4sGykv52as2FKx6v+d9R22UlnkB+O9MwvaS/gVov N0XlRGALNffHygLI71/v4nO9l09dKuD4xEsyeEkHMiH3f7Eo6Ni9fNqPK20M +Y2ClkTIJYXsD5f2N9CXUhfePs7gJKrfS4G86ULEotL+dtr2ocj7LGbclxmi hZA7aRM76T2ne3f8kd/CTejg2bl6fu1s6I++dX3MK/539HNWf5n+6V3AzzF1 Tmbw6UcsvvjW5MWwx8lg/lbGHvoaa4/OkTnWsN8x5etxyBOz/9CQa6yf8Bbz zX9WoMDMlz7f0UFw1HILqsFPSH7KJoYfWsjWOw9yXdY/247+zH25+RJXkeWz eVTqNqyXV/DmjqWjznNua89uhH9trn+TAXy5HlMjDcO3lKHijwbIfb/GHpVo qKE+RO5Lj15cT/Vpfa+HvEmmO35ZVia1qrXb7NwRxt97vxN/l3+wcIZqViY9 dfD9Cshjvho3Qe5RdGSvZEMNnfA++1sUg6NvRJNxW8/FjQQ/8qOtl6tj3EnX ybjeY4md9J26i+1/vxlyw9fx7LzJN/CXsZMO4XzfzOjTBqx+8+52I+Dvu7Bz HGMnzf/1zSfIJ9mod6xg7KlvCVvL2EP/iND8CPnazDH9sN8hbYQF5FFjA8m8 FsklBmK+mVURN4GjfKeR4C+JfvMa/Mwv1FrG8ENvYvmx4+fxecu3++LqwrPc Gyyfn5KEHyDeh4LqzsSqe3DKZ2bORtzbWdoR/2xT6rm2++kz6oJoJ5Hnr1dP gD2Vrhs0s7VyqEzv10Te4DIxc7r5PepjmfZq7utCyuDyKyL3jkhdJmF+jz6S kz4e8vX7B4k8Wi99z3Jmvjoh4SmvGZx/M5KJvLu22ZYZlz5wKnvSLmbcK8+v Erl0GrGTDkrWNClwV+XeYe3kX3bOEvpL/L2XM/r0sP7+q1oGwPcTy3jJ4NOv +HqIvDLs22dxxh6d7stijD20Y+h+Im9v5JMUZezX/yCvDrkha3+ykvkrzHd8 1/ilzHzp4fn6Jl4XJv5/WciL4Yd+kXqEyK8n8/jcVBLYuLrPlVvG2qkYtITk z7PlvZNdBDy4CXd/kzyq5pLshfh6f9NmrA2Ds//K1C7IX9L50vDPhwuHdPOY cT/19hF9fadOwuffKEeBLMbOyJUDRG4hoP9wBmP/13vFNZmMvDu5m8i9iuVK GRyqpOQFncvgWIR2EHmFbk4LMy61ZXSwwx5m3DjxViLfdY7YSbllb03s+7Gc c5q183Wf8Efo2wa9i2D0qVhWv1/6URrwVdVb8hl86u3XlcR++8xcU9hjeiHj I2MP1cXas2L07guwX0IrYRxjPxWim0fkQmeTlDHfgXXeHGa+VB073ztHJ4WB H+3rVbXWzLhOaZ+IvJHl80xkS92SQVfOMJ+7XdXJfqTz0fXWjDHnuZv9Ksi+ 9MXU8RDid1/81wHERf3sXUT+UNqHxHv9moqeGCaOPsY8J/LV86UOw3+eHF0o Hc7E3WSrJUSebKdXifkezR/qRzx+2aGqBfnM9XW7pJh4XJgXogCco3nHiPyH 9+IUZlzqxpsPn5AHImdVEpyhY8RO6rU53++G2YYcDV+enWOubXoM/QmG6v+Q Z3IV/YncyFJwPfCdbjtpMPhUMh9Pv7rz4nnYY3qBO4g81snaI3044Rbsz/a+ LM7YT50LcCdyl/QAb8x3F9/UWuDUsvPtVNvpCn5uuPg1Iq8mzHhE5J9ZPrNj rf/0F57l6LN8Omzi7e+Po4b+7q2P5iY/5+3z671psh+tOK/6Dnm+0/rXINn/ p4cMIR+WL94TiH3BRy2F6B+Q/uqM+H0auvIL9hGR01uIvsfsqY3wtyT5fWmQ u/THEP3JW18ng5+lnXP6sU+tUThM5IN/T15gxqXyL2/VwL62LzeRyPdsJnZS nLlhloqfTDhLn/Ls3NksEwR9P0NtW0af+hzD9wdyzaau68CnnTTHYr++11pO 9PXqOkNhj4zeIhr7MnXtGJEHih57Bfu/tBS1Qi7M2r9I+PJU8LnGMcodOCfY +e7bd0wd/EhdvB2POsFKTfMv5BRbL8ko2WZe1LrEecTyacHWS+TjZBy3xdA7 YMBlG3fen8/60L+x42sO6paKs977GuK2cbM/ZplhP1I1S8J+Rg+WP06UOrqN ++S2aDLyp7bxKuQjuvedfXuXuDl336T5YYh3jQCSF+hLRXltkA+y/qnO80s6 vfDKQ+AM87mExyO9//UxW4z79x+vXjLSJ/Zx2E/uqQhS11GqxqSuozRy8oh+ 9OAU1HVUz6dW1HWUbZb6I+Bvu7JxAew5o+OFuo761FdD7EkL7pzG1HV0g95d 1HWU4ZPtxP7Rc4ZQ19FdNa/LSDyECZD5Gv7cjbqOTvXjoK6jfEaoEH4UBnl8 rjB4Tk38E8X5zPIZfI5Xf7qc4HyDP6eZ8urQKXH8c7Bene7vSuDPjStKiHxI MKYf/vxCQ8QL/jwhtJ/Ia6632MMfRvFXN8Bvz+1Mngd51eWpNfCf+jjneMi3 hGjOh9zQJvcR/G3lbeuv8OcIrSGCk3elPBD+qXxy7BL484frGwiOD8vnoy/e pvBndR6vtMeVU17Qj1/sZAl/lpn+mOi76UdFA9/VsmkIdeN5Fn/eofrTJP/f X5gMv3U3sCT2lPwpew77tWnrj5CHsvarnVeeAH8u6Oxwgj8HUxJKkG9aI6UC fiz9em7Bnz+w/Oxi6/lVg+OfwZ+TWT7P2FwURD4x9sk/h/ysfXCjCfzLOfvi DuDXVhR2ID/bZEwg8qJfJZuRr9698ytEXj3gf5DI63UGdyC/je/XGI/8/OmP CZF/KQl/hXwo9G5aK/Lzzb0p5NwwZLl2A/Kn9DnTscCZ0yjCG7diP4n3iXo5 b5Cf7wYfJXK5fcROasMD3Vbk50WOPDtjhxYSPp9PePsF+fkOq28tJ7sQ+Nsf C0giry4eeEzkUxad9oY9U9K+tSM/j4naT+TqkYPnYb905vIxyM/1rP27j22z w3wF5I6/AM52x0pif27ODBvws0wjuQT5eQ/Lz3hbHp+HxfnbkZ/XsnzOvkzi iBZ5+SvZmak3knjxRG90sFDCfto7X+Exs5/SQSdPE7nut+YG1J+XDlz/hzrB 9VogkYfW9tahXrLw7n6AumJdEk8//UaaCfb3CvUGN8hX/gwi8jv+RmQ/2hvu dgQ4/xw9iHy8b1YI/E3Dzk8M9cYaQX8it2Dj/a7eamvUG36snY6HThL/3Hsp cDXqjR3yPkT+4aA44XPBp6NeqDeOiIcQee/2pUNSjD1zFd4eR72hxtpz4Xqr GuoN82PxtyEftv/CHM0fmG95Qt434Lix89WNvbwC/Ky88/kM6o2fck5EXsfy yXmkE4J6Y5hPsYAEEZw37X6970D9vFE7jZw7M0wHdqM+dL3R8Q/1c6NABpGv GXvhO+rJsEcekaifq6YnEvmDiCgZ1J8WgQfvok6usH1A5Js3mlyC/UNP9J0h v7blCZH/6sm8Cf8Z8JEcC5yZ6S+JfNXb3GzE785+W1vUz/w2j4h8axixk/5O j4lH/SzN2ul8cRWJd8XpxaGon6PsyohcYcFx4p8J39ZPR91b+TCByM/K6VKw J77S9RjqZNHFPLm8n70r7P+2yv8q5PmXKoj8qfDp0QwOdXz/Wl/gHP/MJfJl N3QOgJ9OGcVK1M8NLD8fWD4/FOxTX8PUz7qsnZOOXiPn9zS+bQM4D/a8EiLn eOH2pmKcdy6vLd+NuPgm9JTI5U41ncb5KNfS/D3Og/dUz2F/oFd2jcwG/7/k xxxEPB5/NInoZ3Q8IvVntECkLuSz8xSJfKxkhQ/iUUl73yTgRPIfJTizTOun IB53HhXURh44vpoi+g9ciZ10gPu9fpwHa7N4dmrnlglC/17N5j3IM8P6V4s8 Sf0ZlzJDDue4y/O3E/kzMVfinx+W7TFEHrsyIEHGHbQew0/4fOBgD7kna393 csY1zFfKflEWcFr2dBH9IfvrFeAna7B0HfJqD8tPOMunyN7aOzgPfmH5fBR8 m/RDZt7v60J/w+nyzEjUF36KQ1U4v/88sD8Aef7dmOQIyDVeFWYB3873sTr2 hU1SQ0TfO/mfANZXfq95CPaRfZOViFx7vsc5xJed/+ZtkPv83HYJ8uUZV9zA z9gh5QfYpwwpM4Kf8ve5GvYX/TSHNvQ3RExWEP1TZ4mddEFjvi36G18jeXbW e74i+9H2axJTsG8qOy29APksJz2SP980+z7HPrtrWxnBaZ5gowp7vtfZ7sC+ fIK1Z6+iqQPsnzeQ4Qe5DWv/RuuOSsz386KDStj317Pzfexo2wh+DA4LmKNO qGD52R7C45OOCC5Ff2M/y6cr218SuMfr19mN5jgdEIrm1rD9EOU2Xh/k1NHR ssYq0dzFyrx+3YQiXr9uwZwXpme/RXGL2X7dXbZfR3eeT/wwLZp7JoTXrwtU 5/Xr9qidVraRiObqOPL6dZQqr18XouK+BThFbP2ZlMyrO4U4S8m4M9l6qYjt 19mN5NnZz+7v+Wy/Tsxti3pbaxQ3he3XuSzn9etSbtsQ/AmbeP06dy1ev256 vBex5yXbrzOazevXHUywJvI7bL9uBduvq/R80rOOsWeA7dfN8uL165Y9Hk/s 3PSHx2cm26/byfLp3p7Qbbm/m+qZaeP9ismfK742RFxgxhPeqi630LqNOlQi uwb779tfSgmQ322eqAi5gm9OPc6hr779c0Md0FoTXwoerRbetA8+Ecsx29t0 HPoLJPT/ZjE8RvIt8IDeYYPYGeh/Ztw7XuMzpZa6I+n+Bn4uvsY0FvqPjuls ORTWRAV1vDXB/t5annAG38upq1kE3itNjLoxvz8SRxXQ/7R1UYkP+xTKPVvL G1/Mhjfu+8rs2dUplVSd8rT3iJfvh228gBOut7o2QfYs1+0vj49Otr+aflPy wpkptfStzbQ17FEoEgsmPOzwnxw0IYB7llrZj3lULc4/DhzJjq39WNd9v2y9 yPkprd8cfVG3bwlZDD/0wO6Tx5En90Z3eAFHTtXAvyalku4NGvCBPWXiqt7A OThmVzTWT8/4aCLWkxY/TvrDaz7lzt2xv5terHc8mWbWpbeyaR9w7Hcefsfw Q0/YNFEG+Xa246ITwDHalyoI/6gpO3rkLKMnEyrFsBLDEbnxXg44HzduEnrJ 7Dt7z3jbAueEmq8B7Pzw82ol9sdHxu7EnvYEkzHAGQrPfsvg0BJfRh5Cf9v7 0uwk6NcbD55FXnVj51VKrdGFfMmFI7I5zP71kMVRiC8KInWZ7kA28n2i//3P XYKxnI8yO23A8+GVfE7IG7Isz0s5ssWYl3DMj1XIz8Pzcq4LKwDPlg33gxBP kVOvEp6zF34705zpz23lrTs9lV33l/Ui+8Fz1YnJ55HHjhrbEf8M/vY6dsAl gFvLW3e6lV33PT0VI08zfng/rz2H5DeR50eAIyVRKj5e4DT3PW/d6Up23TsX PtoOP/TWGtkMezzHNZjBnkCXhhWIi/QCowWotz8P3HYAzvjNh3Xghw6e/W9h Txfrh6ZTCiYgv3CMVtsgH0yXphvQb6/Ia/iJeNwwuUWEiUd6MRuPOgdv2iAu /uzeuBD1+Wc2Lo65va+B32ePyO4+z6zXqwX1ZN0vvePFg2aMQpmmdRR3ExuP X5MtFsLOoIs6F9A3o9n45XafsoJfilYYLHzH2Jut0eAO+binck2I06mPDq9D vbftx9wv8PdMDV48ZP05vfhx9EXO+yU8fqQdhiLQFw7+el74MGNv59N0T8in vhRfDh4+bxZ4gXqgZ5JDB3COLsk5jP5md9PfPbDrzKIVxH82PejYmC6WR2nf UH2KfU1gegMZd41f+jHUzWs9bnCgv6o4g9hf9pz/98LZnlz9NcIaWJ8rqXGd 0Dc31c6GP61f/e8s+Nsoteo09DmNck0ZYnn0g1hPc+CXaj0k+knTHJ9inXp+ fsyDvYUZvLxlPk2Wy/xN15TWCcL+7x9nEP2Y1Tz/mPLy4/jxAiZcL9ZPpCpe TGT8ih4qWVGPOlN869su6Gs3mSUA32SCeDfwtl0QIjz/HZ0/Dvp5WV+Xod4T ZfUXjh37CPbPGHC5jvjYeeUi4XOr3Y+H+H5M2H4J1EujfRUJP1tfiy8AP50V qeqISw/XF4TPN1rnaMx32abT9sx86X/zq9qhP+1txCvwv9Jp507o+7D8Hzn6 NeexqAv3Ho9POo7lM7hCMRnrq/I1aDSzvnQru76iZ4W8sF4qSudTgL/tszNZ X+WkOmv41buFsvyMX9GTRj05Bf0kg2gt8Lvq/ru7sL+b9QejVTy/CijxbKmV iuBWs3518VX9N/jhykSXvzgfjVB8QuwXsdrZdmBcGLfq7CdK2PQAdyTbZ1m0 iucHr1NlI1ZYBXKmPuXZPybDpLO70Z/7N2LC5js1PtxRrP7l+rWcJVc8uHNv KKhnPgr+H87aoD2eT+4pr/r6s2nni4qw/+lbxXPGLLviwTnuIlT68j/6b5+e Celp9Oc0Pm70v/0ffEcfLXmHcWEc80w/o4n/sZMv9LY05M9Vficzcs6w/vcN mceBk7/0bgyDwxnWl453fb+UGTe579J7Ztz/6S/cn7Ep1GTeKsNfxM7/6Yul XXbAvHLDXyoz8/qffM6+JUPgYYf0npV3/oPfxPIWV3/r2Y9dftzJLG8B6dN7 wHNfslLBZMbOYf3Jp2MvIp/HVn9vQX/eoESC7If3enh8jdnnXZq1hZMxrG+a dyMY+bniqvcb1Nt6/JFEf/7y2bXwzxhKRxf14ZxSQyKfEz/p4kUfD87IEn2y 3xbv3UfkCnd+76EZf3M/JdaBOrak5xOR96ynxJC//PrHyAC/QeA2kS+y+JnP 2El5XpU4bsXY+U9h6CTkHfP8syFfHBBTwMipYXnhy+WCwInS6lyEc1Ow336C 871r9EqMG9py8Cf6SG/Ycd9Jbr30U8KFY8yzkxq2U2vH6kHMa9KU3xTOBYEl A0SetX1bDHhYlv4mDfi6LA/Hv/J4U2oTizxfqbZqeH3p38FR4DlaXP04wzM1 p6uC6MvzS+Qgbu3GuRzOZ+I+lv9fPOqI4gIeX8myEkdvXQrkrrHj2fPn9NiP yCMPzwbMimXySvkOxSfQfzZ6WiLySU/Xc0fU7ft7NpJ6RMyl5Y+UaQBnzT2H GOznlPosoi9WcV4S/KTP3yAO/a36HgmQG+303Ya8v1FIvhN5q/5YNZHLfdzx Dfl674m/e1EneHnsJThRr8S7IHdSK01k5NSwfKl+pR5wZtPnBFAHFlz7R3DM L0/5xfBGWaxfMAvnqW0m7UQuHvZ2i2ujD+c8z05qFWvn75c+1ZiXW//GvdAv 4DtF9DUXX2oHD262Y0YxPFClLA9hhTzeprf7iAfu8ONQLG8tspb54HnNo6gZ DM/UQecuou9TdvwH8nnK2RWpyG9z/kkRuYB/Banf5kRLvcQ+rmO3xxV12frb PB4jUg+8PL3nEnetBs9Oi8c/toOv9BK1cORV/80riVy18o8RxnWaKmWHuuJJ 5Ag34GgKG09Cv2D9NrPRysz//1g/jmfPopsTsI/41B0cncDUM4+Ll5B6UKw+ cALq9aWzM94DT29sOvETC7/DZ6U9wzj6//xI/ehqc90F+onW7yPAu5zmZxHY s2SiNcEPMArKQbzIDvFFo14aJXWH4P/S1tkAft+PGWEKv+bc1CE8PzSR+Ir1 XbNQ6AbqxnMPDIn9Rvd56xQelZP7IsaY06bG+pXvqt0Mb9TIg1KNTN1L12zI Ivon0xJWA99ytagr1l/jfgrB3/fj1nboL+2V0mLqW+odq2/ibOMK+9uVBWbC j4btv9bn0AB7vtx7mYL6fGbEZGfo07OWZ6HP9eyk7Uf8/yy3+0R/w6mqy5iv c9brWzgXDEry5lvke8EU/J8fwRnB8E/5npQn+lvWVAQ6XPHnJPH4pJxZPoWc c05gfU0Vt56GPafZ9Q1S0l6O9do/VfAv8HenjXUn+Gu2/YVfJf6LiECcybN+ lToh1gbrd/OcwGacy6S9Mo9Cf+Idnl9Nc5VWrxCI4HBYvzrxNkoZfshRjt+A 8526ojjxw4lnDu3H+nV5JYT5MuO/X3aP8BA+pZ2cFxa9jHsBv/VdVV6Cc0DC AM8/FLucBQo8YrnP9vLmpbXLfyPWtXzbl+XwwzczVQnO6GO9+rBzymCrNfzW 4tmEMuCsOqqkjP7XqEalYxjnxOQsgnNc481Y8FAavJ8Pfls242MF9MVPF39D X9LB2kAT+u37HhF8tT+Lg+C3E5N455UbkbzzSltk10TwUlDaGEXyouw84g/p jysysY60slQk5p3HV0PsOfC1ohK895yPKMX4u3XbCP8vXk38Aj8YFVx+BfNz KZtaDn0zPn+yrqUNV9JFVbdynlrzeHigaWcBP5z3LvEj/Pb75BuEt6saDQXA 57oLD+GcsYPF/5NQugX6uruSKPjtN1Z/87PYP/DLLPsN9zG+DWt/jqQU8cvt 2fqJ+P/fvc2V0L8W8iUC/Hh/PLceeI3z9xB+fOpkIjDfKT/rr2L8bHa+8zWv hYP/cGGvo9B3Y/m393vuC7914vFJXWH5nNiov5O8V1EppAA/DwrQJfbPlv6j Ar6Euy/0Av/gjFJi//25h5zJ80jBUVaMX1FvWb/yCj+yG+vR8unZJqyPMesP ewd5fnVM/GHX5S1RnETWr7bfvqOI9T68UXEd/NYqYmop9LcMPLIB/ss28SD4 rWGHEcFxe3A9Gfj7in2ssA8ukXDJwbnTkT3P3s8JGg2/bbzEm1e6rpwO5lUb en8x/LZ9903ib4IR80qxL0i1jRLC/qjgVEzOrytLbiuCN6smVWfYlWVSSOY7 eE/sFvYXg12c3dgHH+UIEf3qG2pdWBfrNj0O9D0VXhD91H12HdhPN36RC0a8 qnSGEv2zhjkC4OWEb3ck5rFKtojM9/4rsYmI//HaqwWAP2q+HdEf0LF+C96D 3+gXYR0O96wj+lKfi8m+OVPhfRXyTa8Lh+hPTeatq8/uyGfw28YIHg/Nxd9J PvzO37oN+/LlU6uIvvIFJ5yHKePkgn747TC+RfIj4oeFL1/cxH49rD9Je0sf /PJLvtJt/P+IfSaEz7EivRTsYQ5HvehXbH59k+gH3TA6B37KHvghrqmtJ/4S fjpN17cgvxfOKZuCfG91Yz1ZR7E4yVDw/2NK8EHoc1n+lxyr34B9P4rHJ6XM 8ukopkzeBwrrlpsFvxUQlyLzjYg4gXMd/e9xohnwpZ2WE/wfVx6RfoTRkQOW 8NsNrF9tWpv2Af4wmOHVjf1EnvUHuSc8v3quuL4dflvL+tWMWQ5p5Bzl0jcJ dcL0Djmi399xrhn53OlAzR3UCe+8G4g8xDLSFnXduG9Kz1E/P5yrFoy+gmE7 zz8e/ghKQJ2w9AtvXmbZ7jpYVx0N6zPYl6+fLyVyb/5De7HvhrhVJ6DudSoX IDgznTv5sE/dXnn2F+yKcDIm+pXXjBNQl+pqlkmj3i44sJjoBx63HcA+KPBR iNQ7NtnuhB8LcY29qMPv/xyfj/roce44oj8rwMobvPzqnzQO9khy+gn+mBPq GqiTZ8pUvUR9fj2nlfRvqLklK8G7QbWENuxduamE6L/5l/gd6y7ILRoB+5+1 SBB88y7euiZ1jniBOuFdB4+HkKeyl5DfPCbFGqCe9wvQI/rj7vmR9whVlh63 A94wvv6Z5PPQv94nHYs635fVd5rvsAf2WzaeRp1Dxf9yI/rTI9d+xvePNt6e gvp82J6hEuNk8PNzp8ob+Hla1UqiL5G9XhjzVfBZUIhzwTV2vh4tm3TA//uR 0aT+na28hujv2d15COeFfh6f1DCf34P09mN92yO9XWHPFXZ9J2vyVWG9Lpxa IYpzROmPTwR/lbnDF/iVd+1yP+SJKtavVk0qdAG/yhG1MbBfiX8OwRfp4PnV Cyf7BagTFrF+Zaf3xgF+mKS52wTni4h/DQSfb4vkjcByf+5kcyGPo/dtuTt4 5xHa+SvPD1y+1q3D+WJWHs9+h4ZP1nSbDzftrrTYhMyT/9N37IkQ7RVz4bqd f/Zg7zff/8md2HPrPrY/Nyx/nZnl1SfmwhloaDf5r/57q5XNDD7n3Nw31QL/ wZepDCtl7ORsnLLW9NB/7JRxFS6CXN5h5E1GzhmW66qcrwLORKPxfxic/8n3 +a01x7j75ZR3MOP+T6787ITuLU35Vak8O/8nP2ckqop5XWtuvvFf/dXWsw+D BwXPml7B/+Av/8bj7XpK89cA5nwhw/K28YXTXfA8eCNixtH/2Ln6cuBo5F+L 8pA96L8V6T5ugv6iLh5f0uWTftqtU80Y1hfSjNZFX8WjbFER+lQ5HsVE/5/N dWf0Z2rV3KvQ75q9oI7I70xrE1Oe7clV6vKxwLn/Q/gbIk9yjeiHv0WH3XGF /k+OEul3KsXaVSF/TjHVkCHP9QxuEH3ha5Kq2IcizrWOxvNc0XnmRP65bO4S yFtOX7UgfS1WLjVuIsnDx2eOXYT+T07jWyKPdJ5bgXHXHHjogz7SJrUzRK66 JPMT+lG+PDvpWtZOG2/qEuZVHyn3Bvry7Lx01lmYgwfN6ITnBJ/l4R3LW/Wv ZQH3XJetGuZt4+s21J/UtMILk/DcP/8HReYbedh1JeLW8PfbLzg/pbtRpF87 qZ3HV5LUryT0lwzP8+wxm0Y5oM94aKWzE/JKSPIOa+j/CGtbAXsmh3Z0ox+2 uufLHsinTY6Ux/OFnNTVE5HnfM4+IPoyy71IfyBrU9VF6E9L0CPjLnLYQM6t v5sNVbGfmlzPI/rTtWTJuaC2OKkd/fwGrftE/8dMBVJ3ZWXYKmN//8TKe3T7 yL42fekKM+QbIxaHE/QU5yv679MnV5FXRNhx5SbVzkM/fNJTYid9irVzk9Be wvPkXaqfoV897iTR/9RX5w4etDsLDdGvDmR5yGR5a9nZV47+0iaWN3PDwlXg WdV2x3X0patuKhAcwa23DmH+BTUTKeS3ViE1ghP6O7UPffIR864HoD7cn/3w B/rfvUk8HnN22q9DX9rvHM/OlPFiD9G3fJLxmJwHteUMiHzvsaL5GFci95cO 6q/sKvmvwJFy3OOHvqjwvLPHSN/irBLRj/ijWY8+ZG1vdTXqI/vwuB7oK3qc 8EffdapCyiboRwpYEPtFqj6n4vmUVrIb6dPvCHD5BX1PkZhG8P7nRMtN8DR+ 1lqiXxD+ORp52COg8gDwz8kVkb7+02THPPDrqtRaCb432R4g9uRv9cnD+ork DJxC/fV31TyCX8au04SUNnH0pRew69X1XoicB/c6qKbhuZK62MR+6E9staKB v+SzyB/EpaVqMdHXOPBtHvQND3yYiudHw/p8yjNzYL9U6K0n8KO5Sz8Tf16n lPoM9ihoFkei/hpg7VEwPbwW/CStFzPG/4/tuUv0w/ekHsB8W/ZccUX91V9f 3Qf9cROW1ID/bSk/nEkdwvKffV06GM99onl80ltZPkfqTSvA+j6+akr6FUrC Dwmf62f7oa9O5ZWbFgP/u/7939BPW5V1DH71VX2ZOOqxJtavCpbOJH643fqU Cs6t9duHiD1+yTy/Cs/b04e+tA/rVx3VrYPwQ3VRuRk4L+9h/fCumLE61s/S 86kd6smCf2+/Qd5cVv4WfrD8TAt5npchGkGe58Y84fnHQVW+I3h+GhfEm5fP xKR5WNcjLj2TUMfeEVr4HfK37HNV8RG85xMZh4rJc+Tflzv48R7MqUtLyXlw 9e40gnOynvf8NMKU9/y0W3sDeS589E8KjfeTjGfvEIb+1YrSv9BvZZ+TyvDe r6TmjuI9Lz5spdeNdW122HgEPIW0byTx4sw+D81hn4c+F5Ig+MlvHO6A9wjN vttYB43RZT+hLzKW99yzlH3u6TgoTOxfk8JbV1EDlawKSzNujD+Phwfs8815 5bznm95TDhHeXtksjQX+XA+Ht9hnhvE3svX5lvO8uvynrhF57p947cV72K9z KfgU/Cpl3iiC78Y+rxynx3teaWZvQJ6nBy+9aQ1+bDzmiyIOnoxyI+tYyj6X TGOfS375LE3mm3XS2Br8L2/OWgt9NZb/Kd95+443+77qbJZP5QZzCuvrrmY0 BHumG7T0EvuVec8Zm9nnjKEL3UNvyURzJ6/z1oFfiV6cuRzn3yzWr4LY54n7 2OeJqWlXu2H/pkSeXwk5p9fgOWAE61eV7HND0ZG854Yfnp0lfIqz/nn8NM8/ lTaJxuF+kFDsdhWMqzdGeif8ObMnPgn/P6gUvRzyuxMuLvC8l09pfo7PxnsZ L4LnzsW82kMcxsJvjZMjXKGveUdiB+Lu0+GGTLwneMv961vojx9L9WQwvJUP hq6GHzZ1eYdA/5573nzUH2I3TS3x/ubR9fHkvQ//kc+fY10WyogIQH9CmsoJ 6HctSzSPdwvmHljHe0/EsJP3nkjOYEYb1l28dfVB+O3oqUbW0D/peCMT5xMz qU0D5P2UbjEu9Ce3xV+DX2X5HbwGv7W65030Uza4fEOe9H8pi/c9qWYJcXJf KeQD7zn05SSLdPjtFmve81bvNdoOwLkxRzvOjeHnWUpjGvRHK9+6QPpvo5Tz 4bd1ywyjoa/Ylm9H8pSJ/A9Gn/bKdXoOfXt+/UryPlPhjuPwk6uF6wmfmdvz WmBPXpnFTLy/EzClgNwnmnzihCX4EbAwmwQ/FGD5ObnzTSTmW749dgzeAxqe b/fUPRbw26QUEzXo17D8b9y9QPxQjy83jccnrcfyWfc+Rw3rKxV64Tfs2cqu b9DgMn2sV5qzoCnwHdj1Oi6+fTX8JPwDRxl+K2Dd4An9QI/fh+EP5tWh8bCf PnQtA/pZCnFriX5ZYp4Hw8OUEouHkPe1hMlj3Pf3izRWZmVS046dI+/7XCz/ G4n8Py026J1kQw3Vcime3N+JKQ5LUmPq1PSw3TJYLzHRKHKPqSrP7NyV3z7c kDG8ez817L2kcpV7JagXv0fdqcF7TDZXtAj+7qZGc+x3E8dersV7ZJcd6WbI f5kZb8K6fH4YW4L3zmr+OpL7RBnRpRsgj5eXn4j31Ibl9CIrbeBMTtD/xeDQ wzjbRHyfYtwNUloteG965rj75B7TrF+aiYH1J7l5PDvpatbOOYqupZjX9yZ7 MfAmws7L1lbrBnk+OyIiFe/NDXgGt0I+4W0oiUenP9m9eI9PmOVttOzsP4i7 T87SNZLm9yhBVz9yH+doI+2E/XfuPNkUzOtkzSci/ynxz3QnU9+vv5AVjPe/ JET/Erl5ttuR6aEHuB7PePd7EofvSWmu7MF7k20vbi6A/liRN0T+LmbKKJyL Dyf/4wO+hXYWkYelvV+EPo+b+7FdYow9Lbc2EbmFwmElyN0H0h8xcnpYnjXF /hfuL2UtcpyK9zENtqUSedV7+SyM++n0SVW8vzk87tBDw/D7Obbctzw76Ses nQO9Zd6YV8dknSDoq6f6EPkLnR+nwcN1mx9Xgf+68QmRj3NU7gVvgiUFdgxv dLORhALkmxfvyiTv+55RMZBh5GnfefeALA444H1cWuvxaxnGb2lZ4zYilzz4 JRX9i4UmkpPh544fxpP7QS4WR5LSJx7gvArj3eMJY+/veGR66OEcGPu95zHe yxM5Poro080NQjif2C/2ccL6bjuXT/QNvgT+QJ+NfnKqEHYmRPNwPhm0dUNu p8aVwnvB8ax8uvEUvN9MKT5z88J7xI/yvxC5fKHITIxbbbznOd47Hh7Xrntd cFiGLWfqWd69qGE7v4w1qse8spUoAWZe1JG+KiJPL+cPAw+6E44KIX7NdtcT ecz2I7ngbfnsF83SjD3DvIWnv8B74fRRlbG94E38y0RyT2dvat8bEkdDRSVS jJ8bXFxK5I939pP3R78v7Swj+fDMNCLP1y1dZ658mjOad2+D9mbvE01pLzyB /siVBXGh0Dd3VSP6DqkbyfOvCdt9qxFHexdLEHms17hJOCeEVBudRFzP6R5H cJpTUwQh7xlz7jkjp+ay8p/tgT7AmVQj9x15Sa+Un8h15p6ywrgjCxQvIi+F l/5ZC3l3tdv4Dt+THB32fsmwnZ9UXx/HvA4YpxRB35edF/+QYxN4aJstl4r3 6/VYHg6IxfSAt9nvTj4Cz7/GJhP8PYVS17G/CG99FcLs13TPeGXe/eNH8uS9 z+qwXaPfMjzEzTlL7t1ETD/qh3P1SU/dl8jnY33eEPk//qsmVxYGc6wMee9F VrL3hqyU98mgP1VVpL8D+iGNzeTe0G6L/PXoy+koz9kMnm1WlhMc/prL5PmL a+J6fnfGHoHwNoIz7uV00t82bdxuzMip8azct2su6R8u6VC0Bg8yCibkPtHz lr2/0HdbLHTADnVCIDvuppb8KRG9vpzHPDupMtZO2YeuDzGvJU27n0J/BDuv 8/PO5IKHL7u3/QD+ZZaHvtHUXfD2N+zdLNQ5yU8mEJycuQfKsO/vHeO+k9nP 6C+inuQ+zu79SqjPaRMtM9Tn9M/Gunu4dzO91mAx+hc6Qr+7SD/iyWwb3LvJ 6+O9t8HH9iP62PtBXtH+v9EfPDjzMupqWrJb3g76wYduoH6m2t7IoH6m0xJ/ xANfYk4FeT4lWGF/CHVv2sZZ5B7QFLb//4nX96fW7ppC5K1TrwWR+3P/FqPP S83dvZXgzOzl9SV9eX1Jqj+5Yi/Gtf3B639ZsO8lDNv5uJvXl0nm9WUor78H yLxCMlpRl9KL5SRtyHtXnYH3gW+X3ELqfLmK7i6m/qR+vAslvP0OTr4InjV/ rj0N/9xpcHouOVdsin+EdRlaMGsk/LOuW5Hcu9HcHuSJdewddEiFv804Fkze txXZnrkB/nnqAu893Fr2HpBW0opp8M8S9+fG0N92+RG519OxNpqCX9nJztOF f5YvUyD4DfWfyPO73JgTf1CP9T+NIDiN5XvI85HCzRc3wD/Lf3kQeZP/EdJ/ 1r7lbgH/MW/VJvIV4vO+wD9rdWNIHWvGjjs3qHs8/PMNz06qhrUzSXDyTczL o47/EfSrx8wlcvGT88g5fdnzFV+A/57lITDtZwx4My8MFIN/qrfJk/tHmfbj qpAHXrwWaEb+zNScT+6/VLZWkPfK0r5pPkP+zP9qReSGHo7kPrajyHrU53Ro fS95T/maU/ci5E9FO959Ghf2vk9zzAIH5LFiQ2NP6BvttSfyJcrvnJH3Iqcc 4SJ/dnnIEbmIgDHuhVK6Y7ztkT9bKwuIfOTdib2Q2x8uvIX82VRHE/lVUUcr 4GxxraxE/pTo3kXk78NSDTDuY/E7PuQ+4s3VRJ4kU9vWzuRPe56d1FHWTlE+ /QOY10rhC2nQl7w+k8jnRk59BR6EJ12NRf7MZXmw2mv9DryJyq64jPwp6/KJ yLnZNlbYp7Q6d7Qz+xRtZsC7d6MUV7MI+5qEnncr9t/aK85E7tq+dg/2QcqM g32T1lTh3aPhl+Ezwf5Ox/LuzZxn78v4cYT+4D7PtEWWW6EfJupJ5OXCOZnY l933SywCvkIZ756OhPsq8vx36ECaM/b3EYbHiXzLwPWzkOtc3JuDum5YXjt9 ZxJwJuhJaGF/T5pzhHff5w3nDcY1et5uhf39LDtuR3gLB/v7pDjePaRhO0eN Kw7EvA5NXPcE+g8refO9IuRG+jyPZtm9Bf57lgf6/rm94E3BXyUE+/vMczz7 F9keIOcOn0APUdQhIhYfyHvui1RTclB3zbrj1ov6MObfU949mkOiKajTnlqe 6EE9aafPu/9yb7PFR9SfqSG8+zHz2Xsxq8d16KHvvE2xMxT6p7/eJPKaw04m qD8TVyhrAl9MNYfIy3ftPYc6M+VJZDzqz/gdj4n8ZqRIMORUfsME3Pcalrsu 7iDPdzbOnLQF9aG8+T0i93h2fQbGDfA5fhH1pOTPfCJfviCnBfXnhFDefaN5 rJ2bL4m+x7wUtb+0QD/qXQrPTi3TKvBQ/PJTI/CjWR7q917cA948vUOLsO4y iklEPhhhooE46qk8aQS/9dosS+65vE3/kohzgZOL7U/E0e5wPd59nF9euThH yKy2Xoy46Jl3guhP79W5ifNRqgvvHowse//Fsu9CE+LozYktXTgfmfT9Ivor KrQ9EUda2kf7cD7alb2P6G/OLNiBOKr6GVYPnt8cmU3k00av3w559YHpM5AH ill5SdtEO+CMW2Q5CXnjytdsIjdbcvY1xk0q2P4D56NwM74KyP8eOV6K89F3 np20NGun7i/zJsxrVco4JeQlyTEcYmfegRTSJ2w+cb4K+DtYHpSlf3DIexcO KwSRJ/3DVhP5i8t/1yDPvx79ZwXy6ssDK8m9lVtPvfbj3Kp/KD8fvI3zWEbk m1suLcX5V8fW0xZ521/Hi9xn2fI70xp9Cc8w3n2Xsxd591wEbtvk4zwuY7Sd H/rZ0n3kfs2LYzvI+z+DumNFgF/H707wRR9Ek/crPFobbqGfkJRiRe55SMSX kefXa3eVkn2qd5Mckf8YiCHPBykZfwXw8IHFMb/SfhXjjn4nIYR98DU7rrre +pk47xfy7KSDWTuV/n4ww7yOD03eCf1Le46Hk3tJrnakj3r9ejXu8dOjWB5i k6aTPtXb17lFONecWbr5MuR53hpFmy73UCrKU1UueaRT9wtSv724l069KvR9 C7nE5hsrL3qk035KWw9D/oczVAp5YpXFMujvnFcVm3YvnR6nsbwC8r+9QhrQ 3zH6WCLk5s+EDx8v6qG+XcgVzaiP5Wz9N8kLOI+cpJwhP+Y37S709v2e/mDs 0jiOb6n7IcgTUlXuQ2/B012/glZGc/u0ePp6H0OCdKqiuPEfZpLv1ZXw9MVZ /VozXY2PSnGcMc95414qGvCHvgE77kYW5yLfDQnY85TF2XeIJ5/lz7PnxZTI HeFtUdyEPkdr45gO6sG6/l3bhKqo9K5wbYFPtVRXxvzEDItm6v63W1e4zGd1 y9bjS9trKcsbpwa3MHqKkuqf8L2AwXuboc/Hx/f/veeSZfny3jmvGnrhkPzx j2FdVJavk9SrmFiOfpPrpbirLfSVUN+lzCf1IPlxUklxHOdC5dNERo+2tF96 56xXDaVEi14cPBbH4Z59GM+MR/8devDJTKiKTlI0M8O4AePOb2DsowP0gybj c3eprA3szFlGOW9l9L7VtpzH9zTfVOhCf1zH4ZHAPXy0tgLj1DrdkIA9WZoC vbGMHXILflbBrshXOz22R8VwTslv3A67Z92YtSmcmceAiZTjbplYTsJ2m0W1 uxqpuX+/Viq5vqG2Lbl1zGtyOzU194WxneQHSkMk5fI+5vPZyPWPHUTaKd9K UZ95jN71qqu++N6MmIme0M8I87Rj/qYD9oTkKbq+obdMdnSHfGSJiCTzfTr4 0LRiBo/mP5AVD5yQ9xGX5jN6sSIWW/A958YOF+jrhh20rlEpoOreT/4hmppC CdnN1HBb2kOVGhWbiIx+Te3aeHH1NOZzidncEaLLeijfI+IXpzF68/S16/E9 7wOriX6/SHsq8zfdvFf6+PTUFDrQtk4d8vC65BYGhy5Y5PgYn/N+KxKcDJXW Ccx4dHf+rEh8b5rTGIJjWCjZV8v8nXP/QrcE8/9r3KpHQb72w3kRUeb7sSO/ /MHn1IavedMZHKmG7lAxRq84vPfoB+Z7i9RqiP707QU6zN/UiMaxR8QZextm pRM5Z3nTNeb71IOAhfvxuWO6SD5wBFfFjmTGo5ZXP5+L72W9Kib6NSVW7eDr tXHO6IUMf5KvOmtPMrztXrLOHjxbxd5I2M98HuCWCIPnrrbODKxHwccq6gPz PdkPJh+gf33OCxnmb8rNRa+fWQeq2beD4EiM37Sc+T6VPhTVinXfeXo1wVF9 PzEb/hG3r1wA36ua/Jroa+uV58AvV5urJDNxR0dvHhUyjvFPk0KdkfDj/VG+ Pfi83Op+fzHjz3PVH26G3y8VvLnOhPme1oTKIOgfe145nfmbunXZchnj75TY xL2BkC/YNS0CcVu8zNUCn1V/Vz4ATkdVfB70hFSUfiN+W591Ev2oeQOGiIdL 0R9PwM+vVvRpVX/Yxs1XuNnIxAVdtMm8A3GxVX7NR7PYbdxrp79XhTF6FYL1 H/G9UdGSa6F/baTgPcQL/eBzJeJs6ZblmpB3W4v5Is49prRo4/NYjCHBCWgf 787kByqaf5Ufvmdh2Ub0jSpL0sGPVHrDA/Dj513+nLGTVpFM62fyEv1i8942 8JN1TLWGmRfN2SmzHvxE+viog5+bGpPSoO+kJj4B/Ej/O7gA8/6i8ZDgbM72 CgEvE7iWJvi0y/5LcObq73sJvbHRS7tIfmvf+gL6blvUquA//hFNnxcwfuEr aP2FWUe6KfyMAfyn9ZFVOPynqXfSLGbd6Sr7WbHwn6mf1y6A/wTkHSL6R6Xq BOEHwmtCauA/D3/1Ebma9gUx+M8uKigP/mO6bD3BKZ6ueBP+c1N0Vh/yxoIV yUR/s43gVcSXturHOMTXgwTt8Yyf07l5mm+mM3FFeQQ8Q3xN+m3/hokLWl1I ax3iS39IVgrxtXePPtH/J/Gii8GhTIKXzkV8rfqzjsh/H1LeibgSNFo+B59e 0k4EJ031+HPo3XhcXkK+t0GT6L96opWDPDKQH7CGGYfq4J+9HHKpG2OvIf/M et0TiPzzokL6L3A+K+t1IP9sUT2o+Y75nstVUaKvH3p9KvM33Xl3fSHyz1X3 OUQ+b9+sxcz36eqtkX+Qf5aLiBKcwy1cC+Qf9Zftv5B/cqpnEv1sfu+14Guy Z/Z38Jd/ZIE9kydpik9oP/Lz0VLTVPBs9XjEVfA8bbPnbeRnJ7u8KHzvwrTI /dDvNqlyw7pPNchtwXrWCMwmOH159sux7qmpia3Iz/ahNwlO2MrLj5GfJyx6 vgffG1x3mOiLFXjvhz8Nfa44gH22subfbGY/ol10al9gn53fonAPfqi6e9s6 Zv+i1YVdRzP+TMmbPW/H95pTpedAf/TltDTEheopkw74e7uKJ8Hp+talj3hQ Gp06DZ9FWw5oA8dY7vZx7IPTti+JxvdO/DSYB/1rfNmbEW+muiIeTLxTr+1C 2s7oRXOf6Mc3YB8smmnQiTiVqNxsv2xGNFfvvGg1E+/UT/NqxDvVpKG430o3 mjv0TwDxToffI/FOa7SleU8SieYe2qOEeKebJpUh3ukDwkfeaq6K5trUfke8 04npExDvdNZqvnaMS1GeN/hMOilN14JVUgerKCWR5RqNUTXU6KD78UMHP1Ne xTuLj1KfKVXjxb7P11RSTyc+kOx5Vk0F8U+5JWLxhTpREVfZmvuWmnA68yuD QzfwyaRIHKyip5Z92wgch5V5uv8Ofqb53u1dxuDQ9iqCTsBZK/7+8ddn1bRq rJURg0MPblErBM4TUf6N5U+bKJlZa89GZZVQviquHkc6W6n2aRreaQqfqPvp kptmnqintretzr+a2EKpNyTPnXm9jOJbdtFO/stn6tG+nD96Oz5TZyTHeTM4 dLSe9fZLWSW0q+OgJ3CWJqT8YnDofWKUreyJerrw9JEc4AyJmNnMul5Gj9hw aAGDQ3+e4/gdOKO4WTp/3Espb6kFFmtqnlG+8a9u1rzqpjwvxUWaFL+hmuLl xi2+VUTdinFVH7+ymxL34s4zznpFjdn9eWr6tiqqvKlPfsv5Lkr128qjDA5d 5S97hqp5RpcuySQ4UqILdpgWv6GzR5yUV7lVRL+LX6UBnGWlts4mWa/o5p8j ql5sq6JPd5bMAs6MQ2+mOW15RbfUB9wddTWRNr9bN3FUcA+14MaDzsG6J7TQ 2tCRH+xS6bF/9E+i7owVkUupcwugHRWnmx9seUB/Pbo4TOVHD1V11WE7g0Nt ypwWPvJqImW+P5vgfFI/5T9U94QaU3nxZK1dKqVxfifBue5RWNPgFkApzlJZ wOBQj2NVCE6cf/KlxL5P9IeulL8zNIrphSsP3S+X7aDkzOIbAj2q6WSvUZru R2potftZavryjJ/dWPug+lYOc16UbTO894FOT5y+MFPwC3Wv9WgRg0OpexWK SWkUU5kzogmOw6m74UEe1dQJSumy25EayjLiBcE5tcBR492tHGr8y3WRDA71 SiaT4JSN1zzkk99OG0dztrQ/q6TfrJj23HhiPfXd7W1o4e9GOv1xaG+rdhMd 17Hs1BiJBsrLyrl57O1y+pH5H2EP2Tbasnr3lciIRir360WawaEO5a7+3Pqs klIqHPEUOMan9SSKfjdS/YH2DgwOJZAlRHBO18ZqjL9dTrUfzS06JttGSQes jgPOQ2OdYxe9uuhD3XsepvnW0A9XOy5Z8fIh5bnltvbJIy10VrJbTJ9PC/1n nK1+QHU6Vf1LNer99Bp63wqFlrFzumjKpqBg3tlsKnihfxmDQ8V8fD7quW8N pVw4fhlwLvkpdTA41KkHbv29Pi2UYmGoLnAep0xe8WF6DdWR8+4sg0N9qxcp BE5Dh9J3xKnm6NW+TLzTImHBMZ+iauibzZYtTLzTuWP4xjszcXpZZuaLp2sq 6YrwkfpMvNOR5/ubEKezhOVGtOS+pU19OtaOYPKGWVbsIBPvlMW2ymjgNGy3 8GLinYpwtnBA3vBcvjwdODM10uqYeKduu6w8i7xxN6eCDzj6tv9aEKdcb79L 0UyctqXLNh/ubKVPPe7tQ5xOvDlz+SwmTpcEfZVj4pTO1rh+hYl3+uk7xQHE 6dLRhzcwcUqLvF8uU8HkDc/qnXaXmbyx//A6guPzWtDuBZM3elXfGSBvvP0y SR44y/THVTPxTvVwJz9H3uD7bLsROJnOBrV/mTgNke8frcXE6VmjmbZMnNID v0Z+3sLEqchW611LmTjdembT93Eru+l4/7B9iNPrSRvPZTBxuvxdaInp+S56 04eGsQNM3hAuNFBcy+SNIjFFgjO5vj7JjMkbMrrTvZcweaP6njnBKXxcf8uU yRv/Ig7rMThUttF2gqMwzqT2ABOn850v9vMxcdqTWbeEiVN6xDn/jt9MnKp3 bRhfzcTpHrULl5g4pT9f0a7PY+J0U/MaNSsmTqu6uNFMnNK91cIzHJi88drx YNO/K4n0UF0HwREMdAnuZ/JGZamOfxWTNwzrzxMcpxX0yCImb2hkCE9gcOj5 ajTBEbi5suMJE6dyz/g/IU7vu0cqV8h20LvPpxUFMHHa3v9vCeI05nRSEhOn 9J9bGw5VMXHalPTB2YCJ01vW/jFMnNKUZIo08sZY74AhCSZv5C5aQHDsHMOP I2/YlVX6uzJ5o6jvH8E57bt4TA2TN+q/fZ/D4NA6d/gITlSS63jE6RvdO+OY eKfKBGavN51YT4uHGK1g4p2avaLvKuLUseml5liJBjrutewxJt4pR5fqS4hT /oUvt16MaKSv+UttRd64aHzqAhPvtFeGhg5win/VZSJvrFMTEkPeqG/fpQUc 5xzLsnFM3shTLNjM4NB9xiPMgVNwO90RcbpV2fgqE+9UN79g3LqXD+njxcEq iNPYuyNCmHinRN1VHc9Wp9OcnE43Jt6pQ7HTXyFOTwyN2rLgbDa9Wu5DNvLG 81q/wWdM3uh9IO4PnOSdRpXIG67Vl9uZeKcjK/SOAOfjdTcRJt5p7W3ZDsgb 9PHjFsC5quHiAHvSzKSJPdsD1/zWZvKG7YtfC2CPzmi9QNhzI/zw3XNM3jCZ lTQSfO51TRpoY/h8kjVgy/BASbL1yTK2PnFQbiB9A4W6rKOwP+SlYgbsX/gg oY0Zl0rYcHMu+M8XLL8A/hvuPd/N8EYlh/PqGV22nokzVpox+1Qch48v4fF/ f99jMvs7D3x8L4k8jJXLsvKtc/bZYx1T8z76Yh3Np/85wvBPtWksosCDWeze HbBnxe6hdthjnrb/I+oNkws31yP/6NSvIfXGCD5Z8rsf4ezvfgz//sMIvtVE HsbK37Fy7ZuLPoN/geKwCuRboyUdruAt73uKBeocSSljeeS90KAJpM6xeFnW Dj/ZLFCxEnaq32s/DDtvDQWeQr2hL24gg/wjYXuW1C2ZStnFWHc/ge1vmHWn jvUmuusw6zVSurcfeVsl6ocf8u2Qlrou6qvzzkty4Z/jx4bzgefls75uBc9b y5eNYPIe7Wh4UJepc6jXludyUedEG815TfxqfsIA/Morx9gF+HFWaUbw/473 hTuw37U8fXIC6563RtoP+fn8qy5ppo6iYjx5ddRGtv78dpdXf+6S9ZDCOvbe /F0Gfjbukm2FfzqKjbUGP+P0YjYAf7Hv7wDEV+eaXIIvzNarx9l6dflT+chp ybGcN4sXTsI6Tq8wsoM/T57fR9bRqrbrKebrLnJ5EuLxfRNvvmPZ+nYFW98e T1Yj/a6Dav654H/WbgVtxGlZ0x978H/usPQV+O3K+aopwFfKM64Gvk2yzXrU t1MDVeOw360ruJkNP/k5W0YL8eI6os8F+/W1bRrSmFdr1NBr1Mk7iwO4qG+N BI7ZY92bTm8+B/9M329yEuN2VmcQ/5ygKayLevWH7vw92L80Emp+Y93XCT9x QZzKOCcfQZ1Qe96dxOkrL/V7qM+nHHk7Efv12Ln2+lj3sFhHdcTXxXOHfcHD 7C/TLMGD/NbnoaiT7039uYDZ72jLOS4FWPeSJd/GIK65C6aWMnFNd9dKuYF/ L4edhqi3P9Rs3szU27RtyWFSb6uvibFqE26luEc2zJwiU05d+as1aefIZuo7 dfMd8v8qm1uvkf/XHlqnweRt6ouUQn/qrQZKpFg39ynzqfL0pprh2GaqL27T c+wLP1d/lMS+sDhhSwbqtzXnacHJDO6T0xKFGGejzNrpwB/Bt4jE3Tk27qrZ uHvLNdPFPvJy62wj7CPL7obfQb0nKpPkKixTTi/XGvQCzmbTLBHg8PHt6sPv hGxmfydk+Hct+PhKiXwjK7/KytcnL/Zj7KYPz5FeCftnv8sk9rd4JUhi35Es mj2gz4zLfS15G+OOu6EcgX3fYOTqXKY+p852riN1/nr5Dw8YO+hj9z8mYn7X hLZPgT26EQpu2NfSEo0smX2NWlL7mwseXgW/d0f9f3TEpslM/U+1xD4k54iO gdFTsT8qd7bdZ/ZHKvtFDOFZTGLQDecItRFyRsw5grJ/nEXOESvij93CuEIy WjXMuPTSPzmTMW7Kzj0TgbO126oe+6yuZBTB4Wb/Oob5jnz/YAM+LRx/Lsd8 r1WZ28DOy8+1nLD/NhpkEztFg1TMwLOaeUgQxklM3Erwd0qr/EQ9/7rughD2 5a8HrW+AH60iRWXMv6q36BX0LxxcQdZXIjdsHPj9FfT0KcY9xCkgPJs2DZ3B +iZPUjIGTvLTbTeBcyMlxgznqWXGylOY8xQtsm2XHHh+L+hog/VetWDyb9h1 YmzdNOAbDMQVwt+c5oSNYfyNnvxSidg/++S7xzivbQ6Q78Y5yyXdhfD8pPPW J/jziTNrwxh/pnV2H1UHPxfLxhvh3Nd1SnERc+6jN57/dgM8D/rnuqEe2/XX 4A7qsSWX96ri3GQcFmyGeqxCPsy5CvXY9JPRODclLjWzz2HqsR7L5vRdTD3m ump+LM5NpE3/RHkV46f/1++NEPkNIt/1X/kyxTnN+Uw9ti5TyBc4IlULCc6D pDTlRgZ/upr6XJzvhs9lMVcWT0BdJ3T1V0slY09J7zFij227QhzOd19H2Tsz 5zvaLUqXnO9yzwnkMPOiP1npujH1IRV9cBWZ1+rEDCucE1f3px4ZifMme05c bz6Khr5KjEcE6slhfVf3c30MD3RByZzvzLj01twAMu7T26IXYP+SOdMjGPvp a0mzif3hF55mg59ZKulPIR/mp05gqkg9o++pvWMrzpuCaspkXlL2BfvB8/a2 5baoV61Ynne9TxjA+Tf+xN+fOLcOn3/3XC49g/Wa2F4ZwqwX/aRDjtj5M/SW LM7RQlfT/ZhzNBVSnEnmxccfjLqdnlX4zQT1v9jfZTux7gZKevOYup22SP14 E/X/o8uf25m6nbK9sj8MeeDb9zdc1P+LsnZlM3U7s441kbhHOfSG9zsTb9jf CRnBt4vIx/w/v3PiV7O0B/X/xMHVB4Ejwf+M4JTqWTrgnNsQExmM87L/2ixy zo1fN3/SVsafp9aFPGLOEfTnmFZij/G85Fs4Lx+WmX4G/i8gKqcO/3cbeV8N 55HBaeZazHmEXmo9nsyrVHxhGc7dLiLzGiQZ/z8Tk0vO3S6qLcug3+Su6oLz S2KcINFv/GjWh/PLpcn5r3F+8akU7MC4P7lW+bBfseSeK84vcuEpxP53fwYf g5+eC39TIJcUTSPy8/6/3iJvPK3T+Yjzu4pCG5lXd9+dNeD59hrNQIZnSrei k8zLdQXdi7yk+eT2Qncmf247WED6APw3b07EekXfdhZn1osyXTib2NnUfiUW ea/N81HODCZ/ni/+SeYlFpXZj3rmmZ/iM5w3D/aOL2POiZS51RR+1Es1c0SM cd5st1wvjH3T7lflA5w3TVKiBWcz+/WkhG/LsV+P4Dv7f/1eyhr2d0hG8DkR uSYr57DyC4E/x8sx+76w4qws7PuKFv+WAcfn6Bpr9A1uaLe/Rp3A4QzGom+g 6P7eG+dWQT5zQ+zjayb4EnuKLnLnof/w8oPFDuz7SzQ/e6P/INpSuQLn37cl gjrM+Zfujs4g8/rNfZyLfX9ks1A66q77Bj+foY+xqeKcCvTtn+T74bysf8qf 6B87O9cZ4/pcXm6P83Ke6Soy7qPxkc04L9/YmpOPevV13ybCg+iIzDfgp3aQ fzTDD3V9vyiR974PFEDdFXpyjaAHU/fu/yNA+iFLhX5PBs/ZGx6qMjxTvZma BH9lRMoV1HX0j5EtqGNPHJIhfZXvXyb9w3od4rYcY9aLksqlees13vIY6kn5 j2uVcO7727uCzMuiKLwP+82XqyFRTN1CF4YFa+9g9gXB1Kw/qJ8FgptDUEfd 9nU6+Impo9renDmIfejK/lCNZ8ynx8ox9gbMfsQX2NuBfoi6Wcsk9EMKFvGF PGXqup6acwHYX+VE51m3M+NszEnT2UHqDa//7+/nWGf9M0L/RMnYrQP15Dwh wbefmXrScbxnP7NvUZPXGIoDp7BWltg5ko+P/E6LAfs7Ld7s74qM5PsaBrkh Kz/Eykv9Xg5gP6076BKPefjGte6H/Q89eiZ9Y+rYLfn2IRhXJWMyGfev+zob 9IVkpuj7oe4dtUuU9IUC7/FrMnZQ7zK2KmM/LRbfQuw5bH0nEv2c3NNPrFDf uiv0BIOHmR75f1EPuzdUkzr/5/gy0r+SvnLFBH2hS0YvatAHbthb6AieJwju +ID6Nm7s3gqcO3KXCJL+VYOgpzrGzRe2NAIfDqJ3ybjOCUJ6wFnZ9Zpfkjnv CE9MOgCc2YeedWO+QT4OGfj8Et1L5qvxdp0v7Czfa3EE5y+3ezuJnWIZCuXA TUmOksU4rZYNBP/WsnNN6EfFf02JxHkwUWOoFPzIWp5/jPXl8F2yhH5UmjPR N/I9fQL8rrtwdQHjJ1SKeR8ZVyRuvSfWd8714w3A8SyjyoGzv1o0B3282sqG DziHhpQuKwHP8uN3DcE/S4odXVFXl3wTI/4z9ajoP/hbT2PeX9iv461G7D+U 0GWO89QIR0N/nNMHI9RIf2/jw2R+hh/6xoVLO9G3n1rm6gB+rMpqT+N8t8bF 0x3n/W1rDUi/8UxX0P09pV9oH1OB0LqGanr9lrFWljFFVIdmixvpT4amPMC5 QzyoLUv15UM6IWOjcMzEFlrG89LUWOZz5wHrmzZ3iign35M4B9Faa15E4Ry0 3853cmB1On1aoau3lsH9Ziu01JoZJ3qfyS7gj2D9dtif3Vi/bfvqHQl+9hxc 3wg/fGE3RlnxbDY95+T99I8N1ZSW6vgq2Kv/dwvB4eNLCPzv78BEs79bwsf3 ksgnsPIHrNx3bXwWYz/1e3CSFeaxO0DmNuz3k7i2G/5fkXvKB+NqiDgtwLj9 M8UFES8bH37zRbyo76gm/cl71yvGM/OhMn5MyfzAzK/3e54N7NE1v9oP/5/f K9YC/18tHS8MHrJ8xc/BDx98uWOBeDlTcIz0UR0fDr2H/6/ofVoO/w+u6yY8 3+mWIn6uPELhLeLFK/E06aOGfF/Ah3F1l97uYcal5g7lk3G7S+a+Bc6SIgHS B+537iI4EpyrTzDfltGrj+AzYGQAWa/s2p5W2Hlu+6M+9Cue3b0pAjuFlPb9 n7q+PK7n7fm/FJIlWQopVAhRorTo/ZJkaRMtpEWUIlmjUhJKpVRoEe2Wiixt iPJ+tUhUKtopWpQWUZJs1e/1PO839+N+7++v+7jPxpw5c+bMmTNz5vUOgp6t 0ne/ZfRMHYpXJnpmmTgsgX4ij44LgN3Khuwh+um+flcS879z6P58yCXFe8UG 9Dd2qcyGfjeoRQ9hXKtJvWTcwU+puVjfUW7GteBTf2rWAvDJtqtyxn4x3er1 GvtlX5H2ELNf6PxlGelYb1XndnPGPqmzLVLEPhV3Zm2Gvb03OeMN+89fnkzs LdFP6zv2S5443Yf9ImxaS/S8WNbVE/bcZljiAvs/mmeSB/2o2t3+Sfy/duYm 7JfH+pkk751Sf+saxr3W8fM09sX0WbxsZlxaRMlvB86XuXKL9FBHyA83b2XO Fzon32ss5lumUSyEfTHmZQyvbUIxfWDVnVM4vwSSR3zAuRzAVgpnzi/a/tGt z9gXV3R+LcK+yN2tnA3+/7bn3981OrdGtxb1CDnDCcNRj/DfJ5LGnJt0usiJ DKzX1XFjXkBeSjCWzeHDQ74zo8P9zszv76Lw8Mwk+FoursDFc2P5aayTWaWd JeYxSlqfB/JH8PNsRhxSWP7gHuIQb55rZFwqNukXzn0Z7cYUkm/3PUfy7aLj 1YbDDmojNR/BLhS8YrMgz+ihtBmIT/LiHxhBD5nDWi9AD5erTUlcsfnhdCXE MyNCTpF8/tMz9lmIT5bPlUtDfLJCMewd9Kx76cFsxCcn4sVkEM+MKFhO8vkD W0N+wl6311d1Yl/sCooj4/Lqn08DH1ev9Drkr4bqOgmf6u85tzDfooV2+/Bf pZ9+fJhvlqXgeMjZUPTZGvFGu6Y4WS/bVyx/6PnOeYdXGGeX61Wi50uhs+Sh H9NAUzbyeFYf1qZDP2eS30hg/ulvhedAH6YhxkSelhbPWdDvRtFPPzHu65sD Q8y+oMcY/xzA+u7e+foX+LgZjCN8lH+OyUEcVfdq6RfEVys7DEk9okGu5g7W e67Uq83YF3aHVxB5nPu3hcLeDtmb1UH+bROciPwyEfwkjl3gv1AC8ZVLWhLR 89iJUXthz+JfJkghXto64VYL9DNhh0sX4quVml+3IL6qy29thp638ze+xzmV LpQUgDgq4VuGGXNO0ZF52l6Iqz9P83qFet+eScMfMnE1zTO6yhrn4/Mdb+UR R6nejfJgzkfa4e6LPMTt5y1DZqEO2DMyey3y+e1Hu9xxzioM+2mM+Cdcpm4L +PPwjP/P7yZlPB/njftCVnl3Ju5Bkbs01JD/F/vl/gHn+88E11Hgs26WO5GT lyfWFves2//6jg0PjwD5vk08F7/DxZOWSfcgnlBWqL6CeUQJWRH5DWzqtXH/ ql311hrjjhZ4r4pxJz9NKcJ9pztv1Crc19iPLUi9xituzxLEDYuM9SQRR4nu 2UPkORpQ6o17WZzdGVvcy2izVKIHW+ezhbhPzTQ9uwv3uC4bTl1pomzGI9zL AnmmZeNeNuOTFdGzbaTbGNzLch1ufENegr9AltSVDt+dKYtx98zw14I+ZOsd yLi/jj28Dz5Boir9DB+Kf4o94RNYJdOM+SqMfZ+C/84ark/mOz5g00HI2fbw iwvydW2HfhA5PcuUnoDvE/e5whgntOIp4V+lWDIV+hnbKLQH97hPVSPJutTJ 2MdhfensV3qgl12eTei35VYchH6PBvXMQhx1qCqQjJttUXIH63u6LykdfJr2 8hI+wzSz/XF/rL3V7of7o1OLMdHzUqONn2CfrKJqe8RRgbOcCH8t79HVsDf2 0kAh3BM/XIsn8qelKw+gfqfqpqeFe+VYfwui53YDaT/Y87augau4J5Y+/foA +tlkuK0RdUB2hGGJJnOvtBs5nOg55KzBo30mefSW022mqL9rU7+EUUd748Sy RP5hbUIRyas8Sp16EnU0tlDn2jqX0/S9216te1qT6IyK0LOoo5E8j/48dR6e FdH/+z0cgpsT/K/v5HhVv81963KaCl+tnAY+KmvDCJ/tY5eao073ZV7TCNT7 LHQ5dbrOq8/HI8+juSun7RUjz7e3k4k8d4cqopAXOtg36II81bX2C6Tet03r 7gjkeQqNV8ggz9OpMUjmJT/79BzUDS8tHZaPvNDzpkpSNxw3LXOI0QP16Yrd arwfOOz6k9AL+BwaZPRALYkp7WPGpbI2TCPjxl/u3g35zRctymDkp37LP2qj zjXoJ0qbagT+Wz/+tNuyZwz9G2VtBdQfC91zyLxYZRn7oOdW19d2yPP81rOK S+gA8kLLJb58Q15I3ZEzLwWeonysl3FxqBryPOfTu4mc9+snNyMvdEnJqhZ5 od911WFGYw6T9x5W22/gvUdG4b0orPt9Z/HnyB+mROWvxHuPgrJTS0cx9vM9 omA98pOHcnYr473Hjceu000Y+2TOd/K9HRnu93bqud+xYdaV4HJc/Pf3bZad GHsTdv5s/ZEO5JN13l4nfILmnl+M/LPI9EPTkfcWmZZN6p52jVGpyBvbBhzS Rd5Y4fExIk+Yi3gw7L9+o5MT8swHbFxJ/fRz+bYE5I2nJEhGIW9cyrpE5jV6 wzVp2L+orGMB8sw582RJHbbSaE8c6LX9d77Ae5UFJx4R+vnleyIwrkX1Nxvk Ud1FOHqouLfWD/KPPqv6Be9VzgmqEfkjdtnug35YpnMXI39rQPkS3LpROQL5 3gsdD/Yg3+uafozMa1qQZwv03LL+51xGz/RUlUDC38Apvgl53Q9n90nAf8r+ KCPzqtBwP4L1WtAzdAj+8BFfEZFz/KHLn5DXnWesloS87mX5x2Rea5UWbUG9 QyxgXhLeF92wbdvtyJx3r47lnUPdxKH3Gcl7KPnUpuLcTDJYp4J6jYzbzmM4 l4eGFzTgXOblWUG+55PP/Z7PKe53V5i4i+AFXPwEF89xcAxBva9hauIS8JnZ +bQRfFp/2H9HnqRPvmId4oH7t/hJHfme+UWSJ+k5fNEO9bvPkznyvNnU+gLn vlqswCic+5lnfEhdW2uZ+kWc44PP1i5Hnc6FjiLzqorI2YpzX9dimgPiIu1C MW3UtY30v5wHfWqFhCveR1VY3CD0Gtd1+TDusFtrTuB9lPtOuzSMa9026gDk 37LaQw1xoOjQYSJ/3y4lM+jn1aCYE/Bbai0Ev6F1MRb1L1/LKWcRT3p9+mSK eaXs3BoDPS+84433GPRw6W9kXlfMTdagnnV6s+o5xI3CEx6SebEPmFthvdbu nLYX9SlhrUYi5/rE8RNJPWvDlteoZ3lIfSH1+vWXvx9AXSA6LVIO58KG0lk/ yDk1rZ/U0Rzt1LQR/182nzSpiYn/tS47C+L8MzUMqsJ/07d8EjdgzqNx71Qy UNez1paqxv2CNzp2+QPmfuFcPG466hrrtpxuwDiHPOO/c+IW+f/8vlPcCbYk 6okNTafu4L4j7X3s9HvmvvNyY7ov4gP2gdJg8JGUHvrB4bOffEdIk/sdIVvu d294eKz++r6QCRcXbUkIw3na33oBdRxKrSZaAvJ7v/zyDvVuA/nNGzDuDtE7 ZNyhL+xVqKu+qRa3wb0s4uslY7wTKNgpycZ5Kl7JojG/4jFGRJ75hYesUde+ 0bJuPvRwpHqA6GHByGbcK+nRX0Wqca/06VtJ3iGkfrTmQ14ieSApGHVq/ycJ ItBzwFXbUtzLBiZLlKKufWHmwyt4z1Cta30P40pcVG9GvPB81HUyrp+/Nrmv 1Ve5s3Ev3nkufCL4zApYfxrzTXHK3IT/vnrWSdbre8yTDZCTn31dDffuqGM1 LMi50mWZDfScfO1JBMZxvuRD+O+d2XYX+vn5KXEL7vsP9EcEQD+NYdNXYP6r o4RqQC8mWkronYYZT4F+w/07UN+kE8bGED1PcFyI91GU0cwuvIek5avzz4DP m06zK6gvCx4cfIA8w6iaqRbQs9TdN0ew3l+PPhmFuFrjjjDh/1U4sRD2tih9 zGPIvz72IpHfZGhQC/d3kWO6Lsi3rEtRPAY9v7WXSoc9O+XcnoJ8puFlIWLP +9z6nZEfyNRtJ3Xk0+M0yfuT/kY3V9xnptdd24V7xP6ZvE1WzD1ic+y9DxHM /WSv9uFPuKeU76+U2sXcU1YXjCpl7q1U1odb/LjXnJXparCK/L92+Ps7V2Jl vaHMvYmeMt0sHuNMTmttBD0vtz9lJvf7QvO438NJuXogGvcjC7WL6hj31kGH 2Rh3hiWnb+U6t2/FsJnzTvVAeXUt7kGrncwice8z649rAf8Wbj+LUhCnn0Vj nAx5N6texeln6eX2sygP+0Xe2R4ObigDnxlZ0QW4t53ckUD4GAy7fAby0CLK 6/FfJfH8uZDHdUmLLebV8LCW3MPyloxsBf3HaqEf0E+c6mbcR2nv6uT3wKft NeHBfMbc3vAafNpDZOeDjy23/+UTt//l5O2W60uoCPaUxKWnoK9bq9sUkX9Y 8XiQ6O0Lty/GiNsX0xVus2yjRQS7idsXc4DbFzP2RCOZ12zuu+Jv2px3xbfF isn7h9HvYvaDf0f6+m1Y9/QTdyO3RTLxi/CO91j3FyIn30NemQqVAkZOSkhd uwDzsswuJPfsJ+t4/bZx8m+3/+v3d65baSGPRKu/NIsG/YT2CUc49Cv+8/s8 aknZ4dCLSEyVMsb1mDszHuPOXRIbi/fSY2zf++Hd9bKuetI3ZKnWXA79upnu uYB1X54/zgT8K0M/bsJ7683TUwbxjjvYz3Af+o+qogoy8N566rsd6XjHffDb RdKvVHm68in4bJmXmI11X1544hj4pDWI+0CeH3Lp6/DfJVWRdyDPnam7rDCv ae0TEvHvSvcMuIC+1e7hF+gn8pLxF+CZZYftgd+4ZvwT+lwtvKoKfN4vG0bm tfrXfSnIcXKbUw3kehY5hfRtRdu7uUNfgWti5bDu45QcHMFndoZmAeazaJ7T OcwvhXfxLszrZdTS3dDL1ND6xejLqBk/8Lv/6z+/bxNtF/sM7+F5Ug+tw7v6 GMME0vc0rOCOHN7Piy1+n473+HRdbjL6ZSYVmO3Fu/mednbQfOcSqufiftIP FbGwKhvv878f3n0Sf/9WdpD0W51P/GaDfy+8XOMo+H2enp4CPpnlt5UwXumZ x+GyzPhGubcJPXOv/8/vxsxUSFVGH8F1jTV+6GOIfrGA9DHlDuT3o9/gYWJs DPoYpDMnkr6nz7G8NPoNzovYmojcu0uFONSTPqk7Kcp56GuwW9RQh7+fq20h +MI5rjvx791qGxehj2GXzCTCZ/tSq/0Yz/9LVhHGT3D/SOgZff7n91iehA8u RH9T2d2EGejjOFdfQvqbdN/4pKNP40ewuAX6PpRrXpG+qmvDVA3QB3VG64r2 VIZ/NyuT0I/3Gf0A/SADSTP34+9m368Q/PIKE2n8+3p/r07wK1brInw2H7bl w3hWUeHZGN/XLJXQ8/IcJ985GcH9zslJ7vdDss/z8ixk1svH/BAf+l/WUCmk f+rzwigd9Ll0iGqVYr3U9KdOwHq1Hrs/G30xbpdHPoK9iI4WI/Qr3kf2oO9C JURAFX93t75O8KKmsyfx7wvvW1wEP+8ZJaTfKkvN5hPsw19xVDHGP2j6nvRb 8fLIk++HWHO/H1LF/S7HFdHiz+j3kS7Y/Qn7IldwOOmrMo/4eg39GPVJjTqw //opFqQPS8emWwL9RO3tz0fDT5jbbzoD+hTzdc7ox5hoXK2Ov0+NeEX4CO3p m4h/P/fT+3rwy6b0CR+ehPNlGK9jR5gP+kHi3kwm9Nx3GP/nuxzypvNwHlE5 uqtwHtHWDxeQ/qyokdo4d6gz+9Jx7tAN49aTvqqtno9x7lBj9Pvj8S7uqFc/ 6c+ij/+E/6dvzqfh/ynxXBbBe6fqws/TTmap8POUcr0h4WPmbwk/T7ezsnXh z+taqsi4vDwG5HsXntzvXdRxvyMRNlDcDn0uPR3zDvObnWtJ+qcObH4Qhfmf VNiyCvp4yL+N9FsdtmyeBH1FWXvwQZ97l+uQ/qwpnWn7oM/PnluX4O8/Cjj9 X3defh+Nf++j01pJ+mWE+wkfQ7HX+RjPV6/jGPR5teEN6f/i4Yn9z+9IlLr9 bEBfkHpwWzfsxbvhGumr+s56Iwd70me3psK+bGa8nIW+nvXnp0yA/VU65kXC PotCegh9Z0n5S9hnxMDRufi7pfpFgjcYntuBf1/UL+oOfrMaawmfXfoj6zCe U7fPDdinUyhnXB6es4b/9X2G4NELW9BvZVJ4+wn6vXK8VpF+K722E/uwPzVG Z4hgvyo2HCD9WReqy/vQlzUvaCoP9ntRzVpCv8ho917sd+vCiknY76Jv1Qm+ iafgLfrFxkSciwc/j2ucPq/hivnXMd7z79KHsd+jFygTeh6e7rr/+u7BMW1T f/ivJfsUPsKf2RWM5PRzZQpowN9Jfgloh/9b9F2W9G3VV22VQJ9Xnr1BHPzn rVFjCH3ksZHC+P81VcPV8PfK0ukEPzFxQyr+/cKnw4+AX8yq2YSPSN6TUoxn 9FZ0CuZXkzhFiSvnlf/6nsBoPYMPWD//w8MscT4sCPtM+ryK5TL0sV6qR4pe 4DxRzvsWQ9b9FK8H1uuLrkUSzqOLoZKkn2tc/9QGnEfHKkVD8fe3EdsIH9nz B7zw73eLrY0Avxemi0lf2Pg3K9divNwVTfdwHtUdOEH4MPuI9Om7c/v0z3H7 33tldROwH4Tenz+P87bxsS7p2zppOMYK9n9WWWE47F9a/foq9HktMbyWC/v/ IaaVjXOe/6avDOhVHyvI4v/fHPBrwt8tWlulgK+UOfYc53vIJ48L4Ldk/Q7S d+ZlaXcI440wyFLD+X5wwjjSd/bt0loS1408Xz2jhSeS9TzOwR3+IKrUHv2h 1K8Z/BFfD4Sy9l0ORp8oFXNX4HgafxUlZjHLdmBpPnUg7m3r8uAuKne6fT3e XT+WM1dX0fNhvf7lUwe+3t1JevuOlFDXXnhImYqVU/19GoSex27FjvDsu9SU w2sHdpZXU3YLI98D7/VotIjIvksP7YgoB96/UJPgP16EuO4/UkLvLRyRuJnh 81z5JeEzZBZTychD27npjP7FyNP0+CjBNYLlXVftr6GH9cgLv6tZxfY9+Yjg C+/6PQd95O1Xsgw9/Zv+rOFMS/C/1uOXzvCnJ1THEfyg2SNxyDPWe24jIw89 1VarBXj/5g8PIf/ZN6FDwHsd5hH60xMD7DFfyZNak5n50uPFUwm+ovqxH/Sm yvtiFaM3WtnUkuCts06PL3h4hv3OYub9kDdubF7ue7xJI5+E+37xZDcsVthy oMX3z+987bw2e9Ivcwd20775nlVTgv7glh+O5EnudmAdiD89NEsjiM09Z6jO i8qBb5s8Waq/Jlts7/mHj1x/cbXZ/TOs9GrXRcdj3P7gEapWzoUtQazHn/nC zg60/fm9raaqWr+V6cw5+3BUkeVNtz+/2zWQcpI/7ZUnS3Jm+E3Zdt8/vyP2 qPLCu/QlDizXmAGNW58CWcO5+KXSxJIfJxzYSf1lPPFL/5yHlO12q4e7mzzZ 5eETZzX3+v7h3/dm6wTFK2fY/P5zNksFubH4/7xj5LxrZO4Nof/7+1Z66o9k 7jLrmyBqODTI6Fn109FT0HP10qVhB5j1PSdYdm4Lsy4/FzsSnG3/a/IlZn3X fjpSbM+so4abKcGLjn0YEcWsb83yhFjgi0pPEfzU8skFB5n1Fb3nJwo+zzac Jfj5MhN3ZlxKbWtDHNbXZY4dwW9Z8G9Yvb+G8l/nq7ad1mT1jHAl+IUt3w+B /sqvWU+wjy7mGhP8tqBPPPg7NG2RYvhTPhHZBD+qlZ8Ryciz+s30a4w81EKu PPOdoswgf++8+U+B636yJ3j3Of67mG/xde9T4PODO98jQUWLoR/Fcp56Rj+U uuImzryWXCP3YrFn/PF7Y7xYDpfnk/vxnHktAt+2v6Nfq2lFx18upwfsBpbA D9xJKPJYvayO8ZdyHq+SG+mvPcvJ/fjmLU2RdqnH9PCt0sOthVrpDwmvCL2q XXdhp9RjSmZ7bP12Bj9sW0NwPWeNiDXL6igTD6+x4FNW8ojwYb9RNmHGpSqf JllcY8ZdqfmW0NukZZG46KXQFBetwQ2sx3kahD5Dcoc+6D8pCx9j6KmpW1sI fZCrtQf4Hxs9bSrDn+pV20royz5be0Ge3WE5DYw81MDAfYJPP3bZEPL3idXy MPJT18xjCe51eVc05rvu1o+D4POFO1+Xj6+EoJ9j60KOM/qhpMfOI7hcMpGT vjZPOmuMYDDr+2OOnC2jRYV2Xe6gp4WoUHMTamk9q6JE3NvX6McsP7q3iV7q bjq3ePp7er1EAckrCJr2vhxhUEjvoNJKZrz8QF/KPUDoJd9+2SxoUEgFH7CK AF41P5fQa+gPfGX4ULGbks8XMXwC73USXH7PgsPMuFRYbNaF2cy4GQIbCZ8C 4asknjyr46HhVGbM6mkIJvRf5untBn1MbXouQ0/pRagj3qS+sdPegf+ZJ4vj GP6UxcxlhM8N9jI+yDPGQjeWkYfS+hpN+EjHm88Zych/pbT7GfALXPn3vrq5 AfPlG7lPhJkvZemrQfBbRU1ToZ/5860mMfqhGj7fI+OmjrvK+X5I55Qrku/D WQrNHDlzBjl9IiG6i2Lyd0ayR93m9ItEpswnfR/Bw/qtf1SHsuXyykn/h96R 6UPpjP0bXb1RAf9QUTI7iLF/2ukd+V4BnZXWHDh+vw9bZDj5bgHdGLHdEvuo wMRwN/Y7lb+S0Bvmre28yOy77EU9UfAPmqZKBJeYYlCPfepz3ckR+JY50wie IzsiEPv6TOzsXpwLJRXiBE9QNdoIP8CjdtsFfmPlNA2Cb989QhJ+Q+9SxGT4 jf0L5Qh+4MzzdaBXdAyIhN/QLFIjOJ/ZoT3g/3VxxSDO2fwCQ4J7BpcEQp7i BXOc4R8aRDQJ3tW0azH8xsa87ovAV3Lld7jS5or5zjQqsoLfaOudQXAXyZSR 8BtT8npT4TeacoUI3ig11/97izd7UdrSGsGhw+yt3PsNv9RW8/psD/bruq8L Fj31/INvPWH+Oszflq0yVfBr8kPfP/ixVtnTOo62rN5FkcEbMv/BVYbXSJ9O 92B1/gqoON30Dx/lhzqaBi+9WQfMuqWGJJz+4Acb55g22p1m3fy5a1cEc379 xs9sKx+v1OXNivpRbFMu5vTndzE+fryh9vaqB2ubZZF1QJkn6zf9p/HFea0+ tqz0wWfDjj7w/YPLZLtm771ly36eXj7Zo8z3D5/LS4xzpyV4sJfeyLdOeP0P n8vWEtYPu7zZLnXDXQMn/jPu7U4qCfHAi5bsIKzjx59f66DPjmOCXogfXg1S 67COQZmJBI/Sbg9GvGGXHiK/i1mvCiE2wc+oHPFHfLJ92BA/8D1RhQQP4/34 APHM9VVOzxEv5Q6mENwoeAkP7P/OjKcKiJeEvnHoE1TX3UC8tDDGShXx0te+ 5wS/6f7yK+Il2ePqJoiXssf2EtyO9Skc/H/GPKlFvGReUUHwu2KvV0CewDEu gow89Kt+f4I/C3RqgPxtXzYvAJ58s4PgWdPXxWO+NlE5qtgXBnuKCL5p3YM0 6OfLviAH7Isurn6KfKpInrMrWa3teKwX26X8Ccl3XlE0P9zP+P+ul5snwQ/T nZUkr7k8bO1dLcb/V2tl88BvV1UoE3yLR7lrG+P/t+iy7OD/g97vJ3iIzjhF 5lygnTYWsoAHnxxVDZyWyHwB/7/evT6wluEzXSaM0GsEpuUx49IDFiWlV5lx M+lEgqdfNSL37jD1jP6vERvZ98uuE9ypJTQT9PVzH3Qz9PRq3wqC24Xq3gX/ hw3Glxj+tMMBN4L7hfr0djDyfNv5SRPn5pbYG5XAhXwW50H+ufLi1sADuPKH zq58ifmqmHT2gs+bJkEif0GOiTv0c360Ui/O0yyufo7FETmpe17GfTkTgtld LzhyzpbzpXcy/l+2WOn7HMYPn7zOjzwBfTjNYCT8f/sWxSb4/45p40ie2N3+ ujNzTlHNE4Nc4edj46oIvcEufyHmXKDXuQVpARd7rbYeePqi9Bz4/1X8/Xrg Y740SAf4suy62fD/K/VG6+PcuSe4Xh94vqoFyVc8dHa5bhtowl534Qnhf0vP aTrorQUFXXCu2dQqET6fjrNug3/usFhznIMVO4oJnxFGcXdHMfJUf/2sjXNz v+hwgosJPKyF/GfDvh4CHsWVf+Q4STHM1+GDxkvwGV0XQeab+UuuCPoJ/Fzy lNEPfYyrn5vLiJzU0atn+I5+CWf7X+TIWTjnnmlbXjO15V6O8LW+Fsps35qz 70NrqF8fQ1NMg8oo5W/fAkzMP1A7r3w/0M7gAqGHZyzdnUcnqpttDpHqorZp d6iiLy9Z8lCoAX8jXXwtWCl6dhu1yjCdBTyNx72Ot7SdbpladiaGXUd5JPKQ Pr6IXzM+T3XvoiMMKj+Y89+kHimP0wTuPnXHD0YeWqFEzOdqXwudm9jhCnlK rjZomwWV0blLJI0ZeehTZwNtIM8pyrZOfnce1b2Y9wgjD+1dz68FPuzZTW3r +RuprDNvkhl5aDV5QfJ9D6OTB50YeagvtW2Dsew6+oNo/jrgMjfPv2PkoXI2 zx5nz3+TPjhZeS3wp+vzPR63lVBWAqtPFSq0UJ8/zc4VTWmlopQvP1HqSqFV /dsXDhxopTavSiR9pvN/XX1R71lN/3Tknyu0opk6saHzKXDp+Tf8hT430fcX 794qebSG0m5oJ9/fUD/+ZUzwNmZ/Dy6LueV6jwqbkEXoNQZetD5pK6E719qb MOPS2o+CHmDc4qufHi/uSqE+2POsYMaljYeH5YP+R4dWdp1nNXXZ+IQbMy79 wkaY8Hl76e5iZlzKVvvcTqmjNfTBZnfSF8nnk/Dr/DZG3i/x11Jd79HU1dbH wE88ma1T53aarj+qcsXZgdFjpArp75v40it2TNwT2tq5wv9lYiUVFz+b4LLi LsFHL5TTErPOWHcoPqcye9ikTy3K3LtHeKCajivN/iB3OZXaNhQ2G3hot+3y J26nmXvkzusMf7rqlyTh0zkY6TA67gklv8WtgeFPP961lfAZt2DBQoY/lawb cKxT8TldULGM4NbOlXUMf6pme1GSwuVU+vr6evKdkPKx6iGwH2eVW5sYe6a7 T2i+agmtodP0KloZe6YNV5o2w35Kdy14zNgV3b97mAVjz5SEjtQt2M+Bo3Oj 8D627IPoM8aeqaCnp4/CfszmKRH8uomY7DDGfoQO729i7JmuftJB3i3XREto T2Psp/SWwAwLxn4ydm0k72ynxj9QaGf218/59U8Ze6b8lWqIPHvuznJm7Jny rrmTiP1VG7ksH/IUHz0nsZjZXzaZX0uxv0I7RxI+MSLW07G/Th2Z9RX760NX EpFneNHqfOyvIa3XG+OY/SWq0kfojR5fUWfkoR2j16sx9kw5OO8juFfRqS35 jF1tkhsnXcTY1Y7Ni8UYu6JL9BYfWsbYlU5lwQvY1cqNLuT9ZKiwiu8bxq5c RGelwq78R8QTPG1dvuh4xq68Mu4Iwq5WVRUQ/MxcuVTGnqlBhfdzbzN2VdyX QvDIYQ9TC5h9pBB2+QP20RjdN2Rctsm4HQrMPtr6NLAR+2jG21pCv9/u2UHs o/xHUSPGM/sos4yD669Ty8Y+mmd6ZKo0s4/qqJcEr4lVicY+mq6cJpXG7CPv uZcJ/vlCyOK3jL0tNpZUP8LYW/zSA+QdXVWZx+JxjL2tKrP4XM7Y2zsFI4J/ i4ludGfsrfC+jPIHxt5KZdwIfuvF2DMTGXvT75nJt5ixt02vLhHcZfaerc+Y /cIb37SS4U/xTtxL8CT3ZT+xX47YWWpWMPulQtyE4Pt3bz3C8Kc9PGvXdzH7 Zc9HV4I7rFjowPCnAx/13VnC7BfDLEOC33k0oRl+ae2kTTG74Sd1tIhfOjo3 zQF+bKvF5flYd5cRYRTwScE7f2Bff485pAI9SI+tIPtaLr+kHP7QoPjoQ9hP qnGYAegPVHrOgX+IHnzux6wjxVa8RPzDj+DvV+BPdsq5nYIf28H+RPwVH7cf X57bj/+L24+/hdt3v/9fffdjuhu74edfJwYZWjL7Qk4gbiXoO0c4jzW2aqEf xowNUMksptrHtSfOS2fs5pJNGez5q5VuBvaXZcdnPdLvX0QLYn0N4iXkYFct VbeJf9u9a9RJ7ItYmxWrsE95hR+Rc0dg2PSTsJNoze6jjL+l6+O6iPy7hJ7n LWH214vbsubY7yJZ7eT8ypjokAF7Wy14fSnsXOB8Yx7oK41GroSfHyM7qIB9 MThSi+jzMbc/XYjbn87H7U+f/a8+dHNuH3piBCefWX5O8Kcbc/4+5eYz22Jb 642sWiivbLMetcxies8NzWvQQ8YJ1x2Iiy4M9fEhbmwcntaGe/q7Tu8X8HsF 3gHdjN+jXve7Ev+53MU9DvGVn1tpN+LAY/2vCP1yyxkz4T/bpTZEM/6TMuyz J/7znNelHYjTzPYOrUc8ObFk7UfQ68qGUPDD4WGuzfDzbzR+EP4FL+ulEX/S vIYLQX9gdT/h7/R0eDriw7wN349i3Nyhyi7gItw+8c3cPvFAbp+42cnsVMSZ rD3zchCXVtiItYNe4oyLi3PYS3rkis6M8uRS6pVqy6ovDP3WcpLvpQvc9N4j XlWM4+R7RwmpX2HFVNOlrjXqhjUZVJmEsxToEz73JIF/2PlXjYhjR+XPJnKq 1j3rwnmkL7RXVZ7Zv3wKoeQ8OujyIgryx09N9EdcGrVxDZHnde+6UzjXTpzX OMaca/RKoYNE/nuDu5oR95rtspdHfDu65gKh1xXOOI793jlS9RLOr2cLBIie h/+4lQo9f+k3hJ5pPv14Ij9vQklqLeM3JrKGX8M5WOoyyDk3r3zKxDqu/Pz6 HeS5euAL4X+d2w+u8q9+cI21T3fBTvRkMt4ifjaefucD6CckPRVg9EmdPbg+ vyK5lJZguRB9ypRx8uebGs+8Q1y9m5s/NxvK9mT0SVk8uvTZuCaD7spJnAl6 Xp6G9w4CQexHZxsoYWOHP33ZvDzdBOfl4fkL5+Fp6PjY5Mvm4akxSKjx/B9c oJODJ/6F8/LEqi+JcWP4ZKvm3DrzP7gAi4Pf/Av/nz7xv/rHeXn4RyjGuLF4 eUJKs//iEzucgyf/hfPwKAd8avJl8fC4+Mb/Jed4Lp74F87LUya1RyCI4RO7 YexfesgmuFGOz8axf+lhpgTw5MXf0hmc9Q8uT3Dm73/hvDwG7hiXl2d/JDPu /+D7ufiKv3BGz7VLmXnx8Kx4xczrf3DWKw4+/S+cl/vumpdb7/0LN/8v3GoP R/+r5HL+5sPFrf6FNwxgfXl5vikn/CV/NheXUflffLs4py5z2i3zKe7Ltdy6 DKPfjxy7WvFs/F/6OUvw5nTZwv/FT4znC8e5+aKncv5SZl9nh6iSPuvR+tby Kxj/cGxv9trNjD3f2Kia10vsmWM3zDzKck1Yj37zaVWSCsa57FYhncScy3Rn VzDhc7uYX9eF8UtL33utqWb2kZP77VbwMVs+S3Ass99F/EY7Mec7XbV5M6Hf cejBacQb543v7EG80e1kS/BW2xJLxBvrboqLgV40Oo3gITknixj+lN7MN2JV DP+MlPuEv0m03KhjjN+e5zF8H+KQZ7Qfofc6MdeamRdVlGW6HvtU4clkMq+9 178+QnySKhA4G/EJvXY2oX9aG/0Q+LDVXrsZnCo/IUnwVNUIS/D5xdMczPCh Qr+IEj6h7XMHEf9450wOYsalHiVbE/pnkgI05Hz7wVGFkZMK3p1K5JzYM1EF 89LTUpNGnFOtXkXo5XaXydQzepgxR38v4qIRLhw9hLYffoB4qZu67Qg8U9+E 4EfWj5GBPg0lnu4GH5NZRQTfd33AFPqfXOI8h9E/9XlmGhk3XTEvFuvlnvbJ B3HU/OvHCP10oU1Lse4PBCd93MTMy+17LJnXFYt5l2AnOi/LShBf5bSkEvqD GxNvI674tV++lImXaP2nT8bjvHZ0zTmJ+KSjoU1WnTmX90uI9sgw53KdAqce cfDopkfIx+7l1iMUltx/gnijRDpDm4lL6ZLGmaS/O0hGyg5xhVao1wwmjqW9 rtIEfzlP2Rvx9sOn95oRV2Qd9SS4VltMBOLtvAePchCHDPFuJ7irWvZcxNuP Fs2TQLzdkSRPcHX7ioeMnJTwIddTqoyc2ScFPkNO27lOjxGHu89crIR46V60 I6FXfbgmF/himbZcBqfGvXAg+IxOpbvgw3e78xnDh3o6p43M96dYhTjGVXir p474kPVkAqG3bohwg5xHI+8WIT5U8FIm+Ku4jk4mXqL2741pQTy/hvYhOFth lDPifNf76b3Ad5fdJvi0let8oJ803VgRxPnC578S/YefGlkGfc74fnAh4vzh JylC33PC1gfrUnbb8f1yRs5NPxXJfAeDVJKxjis3nVyMuLf5WRKh3z7qlBbu QRe27Z/kwMSfI6rUSV/26TucOojH1ZrDyMMPcusgU+mjOYg/pwTM9GHiaroo spD0y4v5qo1FnNk59duYGCbO3LSkh/Qdv9UMtMH9UV3o7j3Ek7/OGRP+Om0/ S3B/5New90Jcmpk1SOiF2YeW4v5oFD6zE/Gt/YUsQp9zNtkQ98fuZgcp3B/t fC0ILrfLciNwkWgpTyZ+pgpu7id43dmIeeBzyk91UiwT/9d4LSd94tqqrzMx 7uPtL84hzq9p1yH0cU9GCUJOm2aXh7hXvm8048gZ1TQb980dmxfUAi+o+0Hw leeOSWK+hlseD4DP5Lxigj+Wm1sC/dw/X2eGe4d67WIyL8knK9dAz21XKijc N9dtVyP03jva1YD7lvYKQf8BsdvIPbR1LKdu0he4NxH1ERVu3UR6nfgD8J+/ weEY9N80KELuuWdb2gUgj/rPHj7o/5WuAcHXOhevhX5O2dHHoJ8pgTsI/9d2 h2dCPx9GPxkN/XSKHyf4yqSUu9BPtJaSH+ZlGrCE8JnMe3gY9BN0sz4Zevhq YE7wadUXRyCPZ35ozDLUxX5OXlWFOs70EMUI2NvOgw1s+I26tKXk+4oiahOV kd+TCTojgXqZ59YbhD7yecw92LNvosgy+IdxF16R+2nWEoNC1NE0nqXmI7/3 vk2c1Iku8GYYY18otscIwW8Uaz4i9M/LLA1Qz5rz5ts50Av2rSf8O7J4e5AP NHoh54984H1fVYJbyr52QL1s+/OHQchDxvfWVgC/zP1utuE4N1XU13I438+m F984fh1+QGn30G74k5tV5vzMfYTWyDHZDj46XhKZyH9eOzCX8/2zhzzYdxSl Gp0OfyItw+m7PPfW7g3kUZvXfpHkUWOvEnl0Cy+NhT85aHRmHvzJogM9hD5Q KuzHKGZejZI1YcjHhlrt5uh580db+JkpGx0y4WdSQ6yJnrfG8UmgfndH4kM2 6Ju5ejsuer4W/mfn1HXl8DPjXjYT/jKXduhgXZrGDhdCXW/6oEQ16Gf+6h+P 9dVLHhiNut5X7voG/P7OWztfBOp6fNz6nc3mUCf4nx2Cjs/hf258mEr0w8Pq 6Me9I9yjIwD16FszqkhdzzTpvi3OHeH6pQKIT9SyzpJ7fevbcHvcO8LlIveh vjzdfcQa0OeO3eWAc21J2wRHxCGsGkdCf3aC43DUf0X2P/iMe0RLNZvw71V0 eIV7x5X+Mm3EFUlefoR+50H6AerI4l1jikB/8VA7oV9pwHcKdWcnq/lDuF9E HGkhuJ1s3yrUqVl9gnokD58jQOR5t9wjAee++yX3ukomPlkbG93NnKe0811S x6SaaK1dqHf35XDqmJoZWgqIK2wyj4kiPjHpCX4O+q09c9TBf23q4T2og//m P3bYPV/EJ4KLRNchPtk9MZzIL5FusRNyZvzaL4j6yOzaYYQ+zn1jFeKTmroL JohP9BcdIfQdmZsOYb47niwsxf20zZsm8nwIDxyD+GT94tKf5UxcIV/H6Vfd qXhaE/pc9F3pE+hPht0j9K7BSWV1TNySOTsH+SIqS5GTL7qzZJcP1sudHWgD eR5Ou0PoeSLnDGHdE/3r9+GefoO77guC+JQQt7g3NrQgXuK1vEX0ppHKqf8+ DPe8ifr7Am791+pQwEjELbarzz1A3CITu5LobUYLp/57Pn+aO94/TOLWf/d4 n/mGPEDoYrGRiGdCjm8m/WXutTsjcY9bEdxiZcLwmfJ13bQvqCOP27AceYCr 1ufykAfoHThI6Cf8ejoR98Qj+V8mMOtLhaT5qYP+eK7OfuQBnvNuGg698RVx 6DN2DtxCfvh8dtdT5IfPBe0muOmMwBzY4dSLtUnIG0zbn07w4Pan53Gvz3Uz 6cC93vCuI+HPijiegvv1oiQTf+SNhd8YEPqPUpNLca8fLlu4H/d66z5BIv+R x+kSE5h91Dvz3Sjm/k7NXSpN6Mes+jYNuMK2c5twr39mK0lwR5+iZ+DTo66f xfCh493FCJ+nBdOuYVy7xKzruNdnTjtG6B/8KDgFOZM694zEfXn3kD+Rs/fU qDjMa6Pjq3u41zsXswj9uxv2Y14xevCxDH2G+3uL6h6Cv3YYfxH57QTp7SXA 56W5EXyzlWwQ9HlNX3AAfHiK3AmeunrdLOi/qJi3F+O2WgeRcYU0M9divSba 6V5G3jvclqP/VpWDMVjfW6YVIsz60o2RCWRec9L1f8Ae6vyuPkQ+PKjjEaEX G2wcDf+8RT5/NeKiq+tsSF9bww3dNuSd6ixNdODHLtuYhcCPyXLrmO2iQ1Z4 L3eEW8d8O/ujKvKEmpOPxsFvLxc6SPhsvMJ/D3nCGHWxcPjnwgBn0tc2yyYC fpj+dNJsJfyweuhSQr85kd2Bc61MakgZ9K5OCwj+nb0mEuejim7kIdRHVG2N CJ4pJDkL/tZCqioBecKZ4quJnGFffs3C+fsgZ3w66ibe0jcJvdq9lhnAl37P ZSHuXegaRnD+n9Fi4DPAutLG8KG9I0wIH5s77ucxLk31n0ee8MsRA0I/0bL1 GeQM7D68EnG4+J54guevrNfBvL5fe7AKcfv3H5FkvorLj5WhLrPojtNG4M9e yBH6CyEjqqCfHZHSAeDz+MoRznwzk1dBnxsrN3sing9dsofgp743dWFdAo4d H8WsC33mkR6R85LNnHFYx14DgXTUa76s5dA/1ajtQn54gN8uEflh/WZH0g/V G8upnzoHttzCO8lubv20t6T/IPLGYiszVBC/SRdfJ/1lOzW+1SI//GvioXzE RTF6xwifKTeeSqPeR9u+3oq4yNvGmPS1TdO6H4F47Imnmjro1V6uIHzWVHa0 IH7r58+9hHpfwbE5hL72YNpP5IFps6bPqPft8hacDHz+FqsfwDXq7UyRH34p y0fwILFpr8Hnes7yx4iTi5uFCf+QazN9MO6ZvqfaiKulJw0TBe758sZT5HWT B1OsEYd3hBiScVd0pDajPrgyruMk8BDJWDKvNTUJXZhv5Ju198HnpUcCGXfb 9vce0I/MPBdBxJ8L7oUR+pXypp+g59a1iqKoDw6/ZUvwASVOXdXI22Ye3qme 49ZVi1KeZ6AOW3Oe1Yk6dZxZqzPyvfeGzZFEvFLy2P/eaCbeyfJf6wU8P+w9 L+Kl1dtaqxEvZQqoEVwiRmeoEPGTr/FYd+bvfr0vzgLnG5xuj7rwtIuH9oOf lCLfceDJvob+0sx4lPnwdYjXMq11TwDPHZEggHr3vUOmLFLvFuNzBC5+wX3k O8UAdlYUJz8tGsvJS48w35yJeKm94cVayMMamHYQ+NjtybKoK2uMc2zB/B49 WkPoebflkXq3i1mFBuLDqbOunwS+7XhsGOLRWbYOhpife7/KKeB0NBmPNvd4 HIe6uXcMZ9yFqZJbENeavYydKMDMb++4Qqfz5J1VO4nTvPPbHRDHHlQWPQ3c a/EpY9Bb7ZC2Z+hpg1FrDgOv7n6VCPmj0r6bYPy+AKNDwFVGGvvh/1/NGbMT f7+6KIjQ5z8ouY36+9O3RzTBbypXP73mN3kw3+wVY7qZ+dKZ3Pl+PaVVBv1/ 7a+zB71ReQt+x4YqWvsowO64D3scd34iXH0q6H2cjPkrf5lUjPFTqbNEnpPV mslYL4VySgPze5VgfxS43TvJHOh3do/vI4y/RMXbE/jzl9smYT1qzFN+QP60 haZHyDo+UZbFuspfLdBn7IqevIjeD/x+6fapiG/0z5ru+sDER492kd/VoZyH +axFvv7ZmiBFxFkOCw+T/L+XyJyFyMtrRfm+RF65QjWU5JM979o3j07wZlu8 5OSPPbl5eBsh/72IFwXl7niCfr1ZK8n/FycqZSG+DF0YNI2JmyiR8csJnzaL CSsQjy7afCWRib+og4rV5Lva6xVllgPfuZHVhbjsABffKvU6GXwm8I1ehvhr MpfPDo9Vhhg3NHrJecRfV59ktQI3krvtJTjtJDuWIyd9kivnxpTLupjXoQe9 haAv486rXO2CIfSw9E3/eEYP9Nmpy3qAX7A9Kw69/WqeOZPRG/2Qq7c1rXsD dZqrqQcnCyLES+9Sl+SLuHnLBm4+fP9f+fA06nH+ZJlyStZf5nZuQAkVHlr4 GvQ8PN3cPHn2X/nwR4WJcjM08ymNRy80tk+sosJTnOo5/Mu4efLkv/Lhi7d4 iQUVubAPz+TkU49z86g8PA1uKdf/b568Q/9h2EzNfPqWyNjubQx/g+NhXPnL uHny2L/y5IX2F1giMuW0unKFSw4jf+AnBS7/mdw8+dm/8uSdj6m7jH7orc93 RE5j9MOjV8yVP5ubPx//V5589Z7+ZNAvsXB8z9DTv+l/588Z/n/lyRs2vpGD PNf3rg5m5GHi+Aau/FbcPLnVX3nyqF4rJ8z3ZonlIDNf+qq9JVf/PNw8ufxf efLaI2MrZ550ZD/m6JP2+JOXttILNPq/eXLt8foWWK8ws2MrmPWix+cnvubQ y3Pz5AZ/5cmH5yuVwx5M0q4GMPZAvwy+x6Uv4+bJx/+VJ5cP0L0Ie7uYstaE sTf6l5Etl/4sN0+e/VeeXEf/moEeo8+vole1ZjD0IiafjhK/7sc7X5TRm+oB 5bbHzLhbtTU476iPZzyDftaMn9xszcj//PIsgs8TlR1+U8OFFaPEyXdO4uY5 Sx3ipCWZ+aYLRgSAvuTiMYKHFU26xvCndnamp+Ux/G3LWQSvPddylJGHSjm6 cOV0Rp7cnc1Enitbf7oAN5/xzJvBqd+4ZKLeRfAZ+evBS4YPtXPjHMLnSEvZ 4CxmXHrgbhgzLvV7XB7e4F2Ono6sVo6c1ESunIsU9rRhXvIV2bWgnyfFoU+b cXMZ9PB81cInjB6ol67qBB+yOWcIvfV/DmyTYORpfGdP8Bv7RpH7c+31deO7 GD9wNOYNeb/dtMjyNfySj9arqWsZv1HQ6Ubyh93sgmLUHeuHup3x/vpS0QeC +/Bc0Zv63ptlkcrJO07k5htFXowXxr1ReOjmfNCLi8gT3Nm9XQf3TCnhlTzw S4YuawieaXygF35pT7K4DuqQ9XFdRJ5k9Rhyj+3umhDI4FQdFw+dzKMBPlb8 luLw8y3GWQQXuGr5CfdwKQHzJbiXe4bcJHjhhUzfyk8nWAkcOSlhrpwGn5M+ YF4FJ2QOgF5nvgTB95VUtUIPOw9PHgD/fK4eXJ0P4R5Om9Mfs3Hu6E78Qfh/ LrA+ifMy7+omoTHMOXWQHUvyfo/2WhngXBRp2arNxDn0kkxlgvPcot5I47wf JnuZvL8LrCHvrmdbb/efOzuAlT+ek0f0bOTkD0WvXj2OeOvs22B10K96tZjQ 23qJvMO5+Utzwjmcm/30YUJvv9T8Ps7NszymDogf2KNMyXvvwcWBqcD3Tg3I RhzyG7+2/1YF+IwZlLyK8zx3ojrBG9i5xhjXUOn9GsRdK7jjFvpVV81092GJ ct+zH+fKKb70DD/iGNHewnDQm1zwIfihwI6t0EPGR75liPdaxaoJn4b4e77Q W03jyDjEjW9OuxN6T9ftR4Bv7ZMYCX3mr1pK8nt1fcWrwefM54VroE+tmH6C N/HWVECfP8VPXoR+ohrNSb4rUOnrCegzlpfkBWmjm5x8V9XiN86Yl4qr81LQ G2sMEfroOsU66CFUv9Af+rxZM4HQP3u86Db0tmvkN2voU25kAcEFnthcB25b KJcBfUrLpBHc/cSz5+DTrO4aBX0KzV9N+MvLpulhXOun0Szox4g7rnTX0lLo s4cjJ7WBK+ekkysGMC813l9BoBdKcSb4EsuozdDDxW3V8tDnSq4e2gfFPKA3 L3nNcOgzapEAyQeGr1PJIHX6K9OHcO7PiZtP8k5bpPyLYef94df5sN+fdQ2Q vE1nSH8W9sXLz8Y7sX9r9tgTPOZytSr2+/50Tr5nVS4nz3NkSjMPec9R2jAV 9Lc+VnB+/6E6TB37dG7frnbEOWe1LxJ8i30j6QN5uX6BKvZ7VU4/wWdvn4x+ Fapl8hx37Pdpfj0Ep5qXK4DP0pR6fuzHkB0dnLxfrtsb7Hf1nPJZ2L97F0uS eTncGO6K/f6AIye1kivnO4GVdZgXX7m4FeifW3HydQZdijXQg/h321bwL+Dq 4Sdvdxb0JlU+Ihn7XejgN4JvjbwzA35VQGatCM4jDdGtJH+1KbKHD35Ywn7j LZxHBlUqBH/m9DYafrvJOPwezhevZnOCW6lNrkxiziOVNk4+LJPz+430eqP1 v3Au9M+KtgZ9+8bZBB83XcQD54jvuEPOOI/yf2oTPPWdjQ7OnUj28Mk4j85m 7eTg993WAHf3CDLFefQbH/KWdgSfXHZdKM4j/sOaBJe5faAK4xaoZzngfPk9 rv7cVytxHnlw5KQecuXsnqWejXm5Pnt7B/T5MyUIziuUIQw9tMRfPY3zaH2A LsH39xXPht6cZj1h4zwymcrhf8HGMx3xwOXmFQ8Rf4p1kr5qWtXtUAPiiqSQ zmrEmQmz8gmuuCnMDPGJ0dHAHYgnjRVeEPyDvZ4G4sZ6P06+R4Kb52m7JZ4G OZUGe4RB39/5k+AKEfVbEHfdWboiHnGgzuI7BB8xS6sR8duYJsc8xHsLXQ4R XGLr2zrgyZ+9xosxev6NL1Fy1AefXVM0HyN+sy3LIfjXFaPOYdxSWenpiKN+ lkYSPGVD42fEYwv9iZz0bzmF0gxcMa9TpxUsQa+rW0rwyuGnu6CH5rvi9xFf xXP10KkheR9666s9cQBx1PnxQpXAk8veyGIfpayNcYXdJrnvIHkSmaEkM9wL Xl9+swF2/kvsBsG3a0evwD3i+Nb3rbjv3IviJfg1yS39uB+lXeHkXYZz8y0y Yp9P4p5y5Lp+OOinRb8juMKnh8Sf3NA+pYj7Udq5DoLX+SkbYR9p9Chm4n40 un4eeSc/Z/QhA+Anu5YP4H4kyMW1JjrlgI/2lZkb4De8KiUIrshqtsK4T2xf xeC+03rDjeDjuyJCcD/6ypGT5ufKeSb1/VbMq9js0RvQm0wKJvj9ft6d0IN7 2kcFxCHfuXqQrtiP90+UaYH5YvhJz3sDBDe56b+Q5Be8e7PhV1c+rSfv3iNN NEfDz689vX0y/PDy5P0Ev7Zoewjuvwt/DDOE3zaYZUXyJymLHIWRl8hR4eRX 6rjv6kVdZRRxH/48lfUR92O9aYvIO/muGzkx8PMjUzq24BzJdlUj9HXxm7bD z1t3S4jh3BmaPJ/QL9l40AL4/O64Azinxsp+5/ze8tiks+Djp1G1B+cam8tn u2eGIMZ9fmrZN+QBJhaqk34B1zk5objvT+L2AdRy5Typt+AB5qU5P0Yb52ZO zCZt4M4WfmLQQ2TrDR6cyz8PmhP6vEKBJURvzUNGuL/LiY4g/Mdyf1+ygfv7 ksLc35e8+F6xBnlCE62ypcjfyuxYR94NOq7uG4k8p6B5ZAnynA6/2si7SsV/ /f5jIff3H0dEbXNCPvlxdZYC6gWpT49K4t1Xj53jT6ewl5TH3YB3FcmllHAL 5/1YmYBxNPLq0p/afZFXZ908TN7dLe/5sBP584UZoS/Kk0tp6ag7WsDVuL/n 2Pav33NclsTaDznToqgJeF/xLjmW1NFsLTKvkPqjsGQy3iFcXbCT4COzbvKg PmK564IQ3vMYSJ4g9ZHR9EoZ1FmOBzmNxPuc8idhpM5i1vhkIepQJqu+mOF9 y7I0Th0qRlgkAvUsRW+Z76h30CbxhN5x1DkX5AlV+nqOIs+5qHzMauj5w/VF Lug7eDXFUx/vtG9MCSd9B5IVnvOR71WYoctCfttSfyH5Xc6gtrrR7XnN9OjT 253x3rvqQSfpX9i1rE+ioK2EFg02Wof3z2t8eHPwnn/6le5G9FncXLrSF+/S JVbn7wb/jWXv9qIvY2rVyuF4x26tV+ICPrmfvuejH8Gvr+gk+gI+Kh5lg0/l 7baLeW6nKYv0cTdQl9nZKk3eK27m/k5HO/d3OpZwf6djrulFgwK307SXzQe8 w6EvptoTvIP7exbS3N+zkOb+nkUZ9/cs2rm/ZyHO/T2LyhErD+A9+YU2W0W8 Jz9hOXYU5Nm5nq+T0Q99+4TQV+TDZ4tMJu8xppRITXzKyC8QvvAb5Lc82SAA +hNB44rwPvzKRr9B6MemT5jwsU51TQF/H5Hzcgx/6ryOAMHj1UddxDv/7NMb raAf3Y2fk1oY/TxraOnEO/8DPX4foM+Vo4zDoLdv3gmlzPrSD80f1CEPPD1g LnnXMeViezze4U/R+pYE+u/splDQ86/31Ma7fU2n2Gz0oexnFRD+EwwtVYBL vptYhvU9Z3aX4BbOM4+Cj587lQo72WGWRfhQm9kTtzDyhJSdbQWefWfCBeAf DFNvQX6bmxV66LsxeHue8JloNPop5Lww2rcccm4sWULeLaxo/RgH/vYTD16G nErX5Ui/gF2n6irIo2St9ABySha5kP6CvMIRQhhXf+hiPcZdVxKZB/qOB8IJ GDf2+aHVGNfhstpr0NMHE6uxXvuSl5D3SNNMv5G6eTPfmp9Yl2Ehb1qxXk4/ J5J3+zHRYy5iXXb73hfHuugfKyT4Lknh708Yu5Ka56cJu9od7EDqp1edU77B PtfLm5fCPvXWOZD6lOQTnSjYc6FLUQTWvfVg+A3wCen+SmF/XX2tZYT95W69 iFOX0T+pjn3Uc+GFBehZrzSTQN+0ovY7+mUcBK7aQE6D3njCp3v207fgv9D3 Vwjw/bd1CP03f5dt2F/LhJZNhx4+yH7dAP1o+yXcx3508nseDr0tG2xXY/Yj fcDB+zj8A31mvA/8g9CQH6fOslnZHf7B/56WCeiL823UQf9s3ckJ8APVD8a6 w046c3UI/zV934ag/xqtn2ewXo0eQ4bAk/K81pP+pvj75ljfkUL7WeAjuX7a e8izrfLGOeDBMo3LgW9w0j0E+cVlBgVh/6mHPm8En4YRo0k+/9G/8vlnD74y GrhdRaucL7uSu6aTyhH06k8Iq6GypoWsb/74js6p2Hc5uOodpV2ZmeUWU0M5 TCsv+Xm7inKTdP/C0NOCjXrfQb+1dVZm08d3VO/mOSohVe9om3DT+6DfMnMa yQ+bc/PDXty8q9tH+bwFgS9oaeE7NWdL3lE/7Kjg8TdbqQ3GTyPmB76gwnsn Tz1X8o7WkTc6B9zSaT3JZx76Vz6ztN3zr/upMffeV2fqEcrMi3o9aUEf5BRn VW+MD2P2RVHdGWZe1O3+2EZmXrRtgb2Ia0wNPWVvgfAvRg8sc/HVeYweKiZr bwB97fjqfmZetMsMeWdmXlTN2FZCvzrT/z/vcWND0zRlGfkX6L06CPlVrzR9 ELrJ3LPsYqdgvvPk9qUwONWev7kL+Kx3bytwf1H61/3Fguuf3//LP3/k+mGp f/lhl/3dI8B/QEblGcadbtT9iuFPFXa0LII8fKXO/hi3y20jwfP9izsxr7um U89hvbbXzWo7wqzXAS2THmZ96ZyqtZsYPdCjxIZLMXqgenyme0JvccUTvsMe pMyVCP3J2ZMOQs8uVo4jobfROtskQV82I9Yf62h+I2oJxhVqEzvKrCO9T0E0 DXJuSXD+wqw7vbu2nuBNZ8XvwH6OWjhsgJ7tj4wOdIOedyndhr3t4J04AvxD OzY/Y+yNvlaeoAX7XM++9wDraGlzOwj0dgUX5WHPR43n3cW6K4z7UQT6gg9L LEpa31H8pxskU/iY9TFuHDYvuZX6HUc1ceOoCdw46kWBRThDT2+79r3/Dt8L etWvXfyg/x0v7f7X72XTG21Yl0KqqNVuvdtuaORSY+LVnCMudFFW/Udkx5x4 QR3p6AzW/lRGfbM4uu4yg5ty+2IO/KsvZhy3P8LsX/0RHstORUOerGuK1Yw8 VIBCM5Hn6egfKQx/OtYodgT4Jzr3Ef6zx2zyZuSh536U+ZXIyHMpX4/Is612 gwdw1wyRGdc1cunQCh2C7+h/exl8LlgITmT40BOP22uDz7J/xWme3Djtdz9L 0r9+VzH+/9OP0KQnvx36f2bWMJTM6LPRsJbIP1C6QBX6CT75yAvjjuiNI/Kv 2PBjHfQp2MWjweiTPiOs4wQ5BxzP7/XYGMB2Xr4qWX67y596wWlBkcy4Q97s TQnL7/Vu8mb//n5L45yO6b6GLuzmkqh701YH/MHzf4q4Gxi7sN5PEBs7ySCA /fs7Lb8qZ/i27fZmnVr1bV2VxT98wu9qnKteH8Ayn/n+yMQlLn/oWzQnWfvq BbCMPIen3Vju8ud7L5fffK8pt/NmPWMXL35o6v3nezLm8Soj9+q7sPLmzx9q UwtgjeDiJu7aPlM3u7BbaH7BQd2AP3xUMzQeJ+/2ZvtEvps0ees/fHQsfdbd WRHA9h/4XEbPcfmD1xilMje5KjrKNa8oidHbKkVeUehtuvrYfWOZ9W248L1W h9Gz3wipzjgGfy7e9JXBKZVXwnrAn4UpEvyM4xelSEb/XnZO1tB/34wPIuCT l/JODri63hQf2PmjFS0Ep0/OaQcfMY2WLQwfausUTcLHeP4pd4x7fmlVIfB9 j+YRfL3NpD7IKbI46xojJzVCYDyRc16g1ZpSxk4W3P9iDTt54detL8PYyRyh vYIMTo9qXRyI/SttI7seeMKIi/zAy4bsbzM4naJ3gtDbDFxbAT7i/rqnGD7U VZlmgt86U/KZ7KO1vjGgvxp2ZxuD0/a26nKgjz180gn0EddSCX6X70sO5Fzg 8hJy0tu+ls5k5KSnFRbrYV777ufch96uTuj9wsyLrhs1Sgl8ImctN4b8ZsNv ET5jhVZXQj9jWwoWgH7k7B5CP8Hw/SjoUy8rnQU9O4z9RPibN9LDgJ82mrAd el5izMGjLYILwMcvcaUK9HmJT7APfBR/xHzHvCaxdT2gn6HIg2TczUvyzCCn aazAdbIumQNkXP7CX88wryMdX45D/7HH0wj/eRHxn2/b+LAHDSvX7VnryLbi 2BUtJTphdXLnCbbC4bj25JIT7G1c3LP0y3aHA47smHnXpzdu8/lDr91udubg XkfWgqGospHb/8Hny6keudd2gnXYfMO7p69P/MEX/xo0+mrsw7KY3p+zwMrx D//vtdvCZex9WOkzxU2/WDiyftPHii89nv/uBMv1xaj60pcnWL/ped2U5b/v d2RlvNuiE7LN5w99TZLx4ouHHdlqW5Ir1tj9g18wsXxj1nKC3ccS+2VSc+IP buL/5puvvQ87oWkG77NN/4ybPOqbHfySj9a+U1gXvr6Pe6C3Uw4vteDHZlcO S4YfXiOaocH4MVrZdFYJ/GrXgYtSwN194gk+Lcg+BX74XdWgBOOHqbGabMKn xm/XdeDlvis14Z8LZN8SfKzlVxp84ui9i+En76s9JnxmbPMywrjvJ3jEAh8Y xsEnXIjeCzlXpV7AeUR39I/eCz6f39Ulw05GVmq04BwZPs6sB3Yi28x3CP5Z ovqGEPZF8FJngpd+UN8DPORFljzsSsn+BMEFfYVugI9W1dfhsPPnnu4ErzWs vIZzvFg/bg3OcfeG3BLEgVdDpsbjHD8Ve/8n4sxtO4oGETf+7htV4PaNDnD7 Run1JRTOd4Hc8jSc76VKx0k8KbxaSwbnu8Eo0Vs4379YuJF49Xff5cR/9V1e r3F1RRxSGiohgTjkcudcEmfqynokIA7hVz7WijhEwOuTP/DZV3v5Ud+M4tY3 J3PrhuX/n3uu95T1/1m/O6X8bAPirm8+3Z6Ix7J0XEnc9XLLtzkYd3pPRy7k MdztTfCRij1+/1u3OsWtBznMmBSF+Cq/3n0Q87U74ULiq8vPs4MRj4V22rVB P248o0k8tjlx1RTEsZVBI9cjXkqyeETitxabR4OI93Y4KR7DuoxYkvQe9LPT 1VqA992c4oc4MFt5Polvl4XotiMOvGxhro848G3CKBI/b+IxO4px5V34PiMO 3NsyWRT09dE/7CFnYuUwyElds3lJ6G0fbfjO6J8ez3cvA3pQufGQxMObeTbN hH7kyu8dgR5WDNtH4mHRgMkk//yam3+ewc3rRp4f9p951GV8wpXQZ5rF2i7c I7LFmkg8uVOwPQnrXrhDQhbjSls+Inh02tD4/8ofJs1Ybg67atYxvgn5I7pa CxE3WshN3gQ7vDCMnYj5Xst/E4A4U9PuTBWJSxf1DmBddn2Tfwr6uGSZHNj/ hK28FPRplSdA4tL/BzNiim4= "]], Axes->True, DisplayFunction->Identity, FaceGridsStyle->Automatic, Method->{}, PlotRange->{{-2.999999999999899, 2.999999999999597}, {-2.9999999999998237`, 2.9999999999998237`}, {-0.9999999999999748, 0.9999999999999748}}, PlotRangePadding->{ Scaled[0.02], Scaled[0.02], Scaled[0.02]}, Ticks->{Automatic, Automatic, Automatic}]], "Output", CellChangeTimes->{{3.6228122304477577`*^9, 3.622812235369383*^9}, 3.622813324596197*^9}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Direct solution (unsuccessful)", "Subsection", CellChangeTimes->{{3.6225957589276247`*^9, 3.622595787690277*^9}, 3.62281224786847*^9, {3.6228124294840326`*^9, 3.6228124345796795`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MinValue", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Norm", "[", RowBox[{"par", "-", "p"}], "]"}], ",", RowBox[{ RowBox[{"0", "\[LessEqual]", "a", "<", RowBox[{"2", "Pi"}]}], "&&", RowBox[{"0", "\[LessEqual]", "b", "<", RowBox[{"2", "Pi"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.6225955818696413`*^9, 3.6225955818711414`*^9}, { 3.622595794588653*^9, 3.622595859786932*^9}, {3.6225959318115783`*^9, 3.622595966651002*^9}, {3.6228123287292385`*^9, 3.6228123669415903`*^9}, 3.622813333703354*^9}], Cell[BoxData[ RowBox[{"MinValue", "[", RowBox[{ RowBox[{"{", RowBox[{ SqrtBox[ RowBox[{ SuperscriptBox[ RowBox[{"Abs", "[", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{ RowBox[{"Cos", "[", "a", "]"}], " ", RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", "b", "]"}]}], ")"}]}]}], "]"}], "2"], "+", SuperscriptBox[ RowBox[{"Abs", "[", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", "b", "]"}]}], ")"}], " ", RowBox[{"Sin", "[", "a", "]"}]}]}], "]"}], "2"], "+", SuperscriptBox[ RowBox[{"Abs", "[", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"Sin", "[", "b", "]"}]}], "]"}], "2"]}]], ",", RowBox[{ RowBox[{"0", "\[LessEqual]", "a", "<", RowBox[{"2", " ", "\[Pi]"}]}], "&&", RowBox[{"0", "\[LessEqual]", "b", "<", RowBox[{"2", " ", "\[Pi]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}]], "Output", CellChangeTimes->{{3.6225959592885675`*^9, 3.6225959680761833`*^9}, 3.622596279571238*^9, 3.6228123869316287`*^9, {3.622813327447059*^9, 3.622813334431446*^9}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Reduce to analytic objective function in a bounded box", "Subsection", CellChangeTimes->{{3.6225957589276247`*^9, 3.622595787690277*^9}, 3.62281224786847*^9, {3.6228124294840326`*^9, 3.6228124345796795`*^9}, { 3.622812545052208*^9, 3.6228125739643793`*^9}}], Cell["\<\ The \[OpenCurlyDoubleQuote]analytic objective function in a bounded box\ \[CloseCurlyDoubleQuote] method is not used for the last input, because the \ use of square root in the objective function adds an inequality constraint. \ The constraint is always true, but the method is used only if there are no \ inequalities other than box bounds (checked syntactically).\ \>", "Text", CellChangeTimes->{{3.590495719669221*^9, 3.5904957664958572`*^9}, { 3.5904958952316313`*^9, 3.590496000166148*^9}, {3.5904960460377064`*^9, 3.5904961976548166`*^9}, {3.5904962300991354`*^9, 3.5904962304990377`*^9}, 3.590496269178705*^9, {3.5905001446396117`*^9, 3.5905002032308903`*^9}, { 3.590500236367592*^9, 3.590500254614165*^9}, {3.6223845824010396`*^9, 3.6223845945605836`*^9}, {3.6224211783006287`*^9, 3.6224211826201773`*^9}, {3.6225956468413916`*^9, 3.6225957206572647`*^9}, {3.622812109083847*^9, 3.6228121456919956`*^9}, { 3.622812204419953*^9, 3.622812204908015*^9}, {3.6228122856857724`*^9, 3.622812285893799*^9}, {3.622812637452941*^9, 3.6228126783881392`*^9}, { 3.6228127135961103`*^9, 3.6228127676679764`*^9}, {3.622812809404276*^9, 3.6228128372363105`*^9}, {3.622812870980595*^9, 3.6228129817971673`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"MinValue", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"par", "-", "p"}], ")"}], ".", RowBox[{"(", RowBox[{"par", "-", "p"}], ")"}]}], ",", RowBox[{ RowBox[{"0", "\[LessEqual]", "a", "<", RowBox[{"2", "Pi"}]}], "&&", RowBox[{"0", "\[LessEqual]", "b", "<", RowBox[{"2", "Pi"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}], "//", "Timing"}]], "Input", CellChangeTimes->{{3.6225955818696413`*^9, 3.6225955818711414`*^9}, { 3.622595794588653*^9, 3.622595859786932*^9}, {3.6225959318115783`*^9, 3.622595966651002*^9}, {3.6228123287292385`*^9, 3.6228123669415903`*^9}, { 3.622812586774006*^9, 3.62281259515707*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"0.79560509999999995400798979972023516893`5.921297471662085", ",", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", " ", RowBox[{"ArcTan", "[", RowBox[{"1", "-", SqrtBox["2"]}], "]"}]}], "]"}], " ", RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", RowBox[{"2", " ", RowBox[{"ArcTan", "[", RowBox[{ FractionBox["1", "3"], " ", RowBox[{"(", RowBox[{"2", "-", RowBox[{"3", " ", SqrtBox["2"]}], "+", SqrtBox[ RowBox[{"31", "-", RowBox[{"12", " ", SqrtBox["2"]}]}]]}], ")"}]}], "]"}]}], "]"}]}], ")"}]}]}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "-", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", RowBox[{"2", " ", RowBox[{"ArcTan", "[", RowBox[{ FractionBox["1", "3"], " ", RowBox[{"(", RowBox[{"2", "-", RowBox[{"3", " ", SqrtBox["2"]}], "+", SqrtBox[ RowBox[{"31", "-", RowBox[{"12", " ", SqrtBox["2"]}]}]]}], ")"}]}], "]"}]}], "]"}]}], ")"}], " ", RowBox[{"Sin", "[", RowBox[{"2", " ", RowBox[{"ArcTan", "[", RowBox[{"1", "-", SqrtBox["2"]}], "]"}]}], "]"}]}]}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"Sin", "[", RowBox[{"2", " ", RowBox[{"ArcTan", "[", RowBox[{ FractionBox["1", "3"], " ", RowBox[{"(", RowBox[{"2", "-", RowBox[{"3", " ", SqrtBox["2"]}], "+", SqrtBox[ RowBox[{"31", "-", RowBox[{"12", " ", SqrtBox["2"]}]}]]}], ")"}]}], "]"}]}], "]"}]}], ")"}], "2"]}]}], "}"}]], "Output", CellChangeTimes->{3.6228125977473993`*^9, 3.622813340534221*^9}] }, Closed]], Cell["Specifying the bounds on a and b is necessary.", "Text", CellChangeTimes->{{3.590495719669221*^9, 3.5904957664958572`*^9}, { 3.5904958952316313`*^9, 3.590496000166148*^9}, {3.5904960460377064`*^9, 3.5904961976548166`*^9}, {3.5904962300991354`*^9, 3.5904962304990377`*^9}, 3.590496269178705*^9, {3.5905001446396117`*^9, 3.5905002032308903`*^9}, { 3.590500236367592*^9, 3.590500254614165*^9}, {3.6223845824010396`*^9, 3.6223845945605836`*^9}, {3.6224211783006287`*^9, 3.6224211826201773`*^9}, {3.6225956468413916`*^9, 3.6225957206572647`*^9}, {3.622812109083847*^9, 3.6228121456919956`*^9}, { 3.622812204419953*^9, 3.622812204908015*^9}, {3.6228122856857724`*^9, 3.622812285893799*^9}, {3.6228130206290984`*^9, 3.6228130350044236`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MinValue", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"par", "-", "p"}], ")"}], ".", RowBox[{"(", RowBox[{"par", "-", "p"}], ")"}]}], ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.6228130495337687`*^9, 3.6228130524296365`*^9}}], Cell[BoxData[ RowBox[{"MinValue", "[", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{ RowBox[{"Cos", "[", "a", "]"}], " ", RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", "b", "]"}]}], ")"}]}]}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", "b", "]"}]}], ")"}], " ", RowBox[{"Sin", "[", "a", "]"}]}]}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"Sin", "[", "b", "]"}]}], ")"}], "2"]}], ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}]], "Output", CellChangeTimes->{3.6228130531987343`*^9, 3.622813344809264*^9}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Reduce to a polynomial problem", "Subsection", CellChangeTimes->{{3.6225957589276247`*^9, 3.622595787690277*^9}, { 3.6225960544976573`*^9, 3.622596060969479*^9}, {3.622813070948488*^9, 3.622813091636115*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"eqs", "=", RowBox[{"Join", "[", RowBox[{ RowBox[{"Thread", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", "par"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Sin", "[", "a", "]"}], "^", "2"}], "+", RowBox[{ RowBox[{"Cos", "[", "a", "]"}], "^", "2"}], "-", "1"}], ",", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "b", "]"}], "^", "2"}], "+", RowBox[{ RowBox[{"Cos", "[", "b", "]"}], "^", "2"}], "-", "1"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"GroebnerBasis", "[", RowBox[{"eqs", ",", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Sin", "[", "a", "]"}], ",", RowBox[{"Cos", "[", "a", "]"}], ",", RowBox[{"Sin", "[", "b", "]"}], ",", RowBox[{"Cos", "[", "b", "]"}]}], "}"}]}], "]"}], "//", "Timing"}]}], "Input", CellChangeTimes->{{3.6225955818696413`*^9, 3.6225955818711414`*^9}, { 3.622595794588653*^9, 3.622595859786932*^9}, {3.6225959318115783`*^9, 3.622595966651002*^9}, {3.622596102015191*^9, 3.6225961830024757`*^9}, { 3.6228131250538588`*^9, 3.6228131945101786`*^9}, {3.6228132906388855`*^9, 3.622813295838546*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"0.`", ",", RowBox[{"{", RowBox[{"9", "-", RowBox[{"10", " ", SuperscriptBox["x", "2"]}], "+", SuperscriptBox["x", "4"], "-", RowBox[{"10", " ", SuperscriptBox["y", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["x", "2"], " ", SuperscriptBox["y", "2"]}], "+", SuperscriptBox["y", "4"], "+", RowBox[{"6", " ", SuperscriptBox["z", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["x", "2"], " ", SuperscriptBox["z", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["y", "2"], " ", SuperscriptBox["z", "2"]}], "+", SuperscriptBox["z", "4"]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.6225964602096763`*^9, {3.6228131821891136`*^9, 3.622813195330282*^9}, 3.6228132967306585`*^9, 3.6228133482131963`*^9}] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"poly", "=", RowBox[{"%", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.6228133587430334`*^9, 3.6228133653978786`*^9}}], Cell[BoxData[ RowBox[{"9", "-", RowBox[{"10", " ", SuperscriptBox["x", "2"]}], "+", SuperscriptBox["x", "4"], "-", RowBox[{"10", " ", SuperscriptBox["y", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["x", "2"], " ", SuperscriptBox["y", "2"]}], "+", SuperscriptBox["y", "4"], "+", RowBox[{"6", " ", SuperscriptBox["z", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["x", "2"], " ", SuperscriptBox["z", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["y", "2"], " ", SuperscriptBox["z", "2"]}], "+", SuperscriptBox["z", "4"]}]], "Output", CellChangeTimes->{3.622813367128098*^9}] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"MinValue", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Norm", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], "-", "p"}], "]"}], ",", RowBox[{"poly", "\[Equal]", "0"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}], "//", "Timing"}]], "Input", CellChangeTimes->{{3.622813215926898*^9, 3.6228132696782236`*^9}, { 3.6228133707770615`*^9, 3.6228133713096294`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.20280129999999998990922733810293721035`5.3276706478709865", ",", SqrtBox[ RowBox[{"Root", "[", RowBox[{ RowBox[{ RowBox[{"374544", "-", RowBox[{"82944", " ", "#1"}], "+", RowBox[{"5320", " ", SuperscriptBox["#1", "2"]}], "-", RowBox[{"128", " ", SuperscriptBox["#1", "3"]}], "+", SuperscriptBox["#1", "4"]}], "&"}], ",", "1"}], "]"}]]}], "}"}]], "Output", CellChangeTimes->{{3.622813254425787*^9, 3.6228132710153933`*^9}, 3.622813373947464*^9}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Region formulations", "Subsection", CellChangeTimes->{{3.6225957589276247`*^9, 3.622595787690277*^9}, { 3.6225960544976573`*^9, 3.622596060969479*^9}, {3.622596218025923*^9, 3.622596224729774*^9}, {3.6228136140374517`*^9, 3.622813615189098*^9}, 3.622813848773759*^9}], Cell[CellGroupData[{ Cell["\<\ Trigonometric parametric description with no parameter bounds\ \>", "Subsubsection", CellChangeTimes->{{3.62281385877903*^9, 3.6228138792776327`*^9}, { 3.6228141009172773`*^9, 3.6228141315411663`*^9}}], Cell["\<\ The heursitcs successfully reduce the problem, but it takes a long time.\ \>", "Text", CellChangeTimes->{{3.590495719669221*^9, 3.5904957664958572`*^9}, { 3.5904958952316313`*^9, 3.590496000166148*^9}, {3.5904960460377064`*^9, 3.5904961976548166`*^9}, {3.5904962300991354`*^9, 3.5904962304990377`*^9}, 3.590496269178705*^9, {3.5905001446396117`*^9, 3.5905002032308903`*^9}, { 3.590500236367592*^9, 3.590500254614165*^9}, {3.6223845824010396`*^9, 3.6223845945605836`*^9}, {3.6224211783006287`*^9, 3.6224211826201773`*^9}, {3.6225956468413916`*^9, 3.6225957206572647`*^9}, 3.6225964415118017`*^9, {3.62281372419694*^9, 3.6228137869734116`*^9}, { 3.622813995861437*^9, 3.62281402305339*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"R1", "=", RowBox[{"ParametricRegion", "[", RowBox[{"par", ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6225955818696413`*^9, 3.6225955818711414`*^9}, { 3.622595794588653*^9, 3.622595859786932*^9}, {3.6225959318115783`*^9, 3.622595966651002*^9}, {3.622596102015191*^9, 3.6225961830024757`*^9}, { 3.622596237681919*^9, 3.622596249450413*^9}, {3.6228134864862547`*^9, 3.6228135280780363`*^9}}], Cell[BoxData[ RowBox[{"ParametricRegion", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Cos", "[", "a", "]"}], " ", RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", "b", "]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", "b", "]"}]}], ")"}], " ", RowBox[{"Sin", "[", "a", "]"}]}], ",", RowBox[{"Sin", "[", "b", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}]], "Output", CellChangeTimes->{3.622596489911948*^9, 3.6228135290411587`*^9}] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"RegionDistance", "[", RowBox[{"R1", ",", RowBox[{"{", RowBox[{"3", ",", "3", ",", "3"}], "}"}]}], "]"}], "//", "Timing"}]], "Input", CellChangeTimes->{{3.622813544874669*^9, 3.622813559181986*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "21.99614100000000149748302646912634372711`7.362946408219529", ",", SqrtBox[ RowBox[{"Root", "[", RowBox[{ RowBox[{ RowBox[{"374544", "-", RowBox[{"82944", " ", "#1"}], "+", RowBox[{"5320", " ", SuperscriptBox["#1", "2"]}], "-", RowBox[{"128", " ", SuperscriptBox["#1", "3"]}], "+", SuperscriptBox["#1", "4"]}], "&"}], ",", "1"}], "]"}]]}], "}"}]], "Output", CellChangeTimes->{3.6228135818743677`*^9}] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", "%", "]"}]], "Input", CellChangeTimes->{{3.6228142315193615`*^9, 3.6228142466402817`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"21.996141`", ",", "2.7455890393265063`"}], "}"}]], "Output", CellChangeTimes->{3.6228142401554585`*^9}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Trigonometric parametric description with parameter bounds", \ "Subsubsection", CellChangeTimes->{{3.62281385877903*^9, 3.6228138792776327`*^9}, { 3.6228140405091066`*^9, 3.6228140407896423`*^9}, 3.622814142981619*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"R2", "=", RowBox[{"ParametricRegion", "[", RowBox[{ RowBox[{"{", RowBox[{"par", ",", RowBox[{ RowBox[{"0", "\[LessEqual]", "a", "<", RowBox[{"2", "Pi"}]}], "&&", RowBox[{"0", "\[LessEqual]", "b", "<", RowBox[{"2", "Pi"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6225955818696413`*^9, 3.6225955818711414`*^9}, { 3.622595794588653*^9, 3.622595859786932*^9}, {3.6225959318115783`*^9, 3.622595966651002*^9}, {3.622596102015191*^9, 3.6225961830024757`*^9}, { 3.622596237681919*^9, 3.622596249450413*^9}, {3.6228134864862547`*^9, 3.6228135280780363`*^9}, {3.6228136295989275`*^9, 3.622813655982778*^9}}], Cell[BoxData[ RowBox[{"ParametricRegion", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Cos", "[", "a", "]"}], " ", RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", "b", "]"}]}], ")"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", "b", "]"}]}], ")"}], " ", RowBox[{"Sin", "[", "a", "]"}]}], ",", RowBox[{"Sin", "[", "b", "]"}]}], "}"}], ",", RowBox[{ RowBox[{"0", "\[LessEqual]", "a", "<", RowBox[{"2", " ", "\[Pi]"}]}], "&&", RowBox[{"0", "\[LessEqual]", "b", "<", RowBox[{"2", " ", "\[Pi]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}]], "Output", CellChangeTimes->{3.622596489911948*^9, 3.6228135290411587`*^9, 3.6228136572554398`*^9}] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"RegionDistance", "[", RowBox[{"R2", ",", RowBox[{"{", RowBox[{"3", ",", "3", ",", "3"}], "}"}]}], "]"}], "//", "Timing"}]], "Input", CellChangeTimes->{{3.622813544874669*^9, 3.622813559181986*^9}, 3.62281366316669*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"0.74880480000000004814353360416134819388`5.894968532939736", ",", RowBox[{"\[Sqrt]", RowBox[{"(", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", " ", RowBox[{"ArcTan", "[", RowBox[{"1", "-", SqrtBox["2"]}], "]"}]}], "]"}], " ", RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", RowBox[{"2", " ", RowBox[{"ArcTan", "[", RowBox[{ FractionBox["1", "3"], " ", RowBox[{"(", RowBox[{"2", "-", RowBox[{"3", " ", SqrtBox["2"]}], "+", SqrtBox[ RowBox[{"31", "-", RowBox[{"12", " ", SqrtBox["2"]}]}]]}], ")"}]}], "]"}]}], "]"}]}], ")"}]}]}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "-", RowBox[{ RowBox[{"(", RowBox[{"2", "+", RowBox[{"Cos", "[", RowBox[{"2", " ", RowBox[{"ArcTan", "[", RowBox[{ FractionBox["1", "3"], " ", RowBox[{"(", RowBox[{"2", "-", RowBox[{"3", " ", SqrtBox["2"]}], "+", SqrtBox[ RowBox[{"31", "-", RowBox[{"12", " ", SqrtBox["2"]}]}]]}], ")"}]}], "]"}]}], "]"}]}], ")"}], " ", RowBox[{"Sin", "[", RowBox[{"2", " ", RowBox[{"ArcTan", "[", RowBox[{"1", "-", SqrtBox["2"]}], "]"}]}], "]"}]}]}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"Sin", "[", RowBox[{"2", " ", RowBox[{"ArcTan", "[", RowBox[{ FractionBox["1", "3"], " ", RowBox[{"(", RowBox[{"2", "-", RowBox[{"3", " ", SqrtBox["2"]}], "+", SqrtBox[ RowBox[{"31", "-", RowBox[{"12", " ", SqrtBox["2"]}]}]]}], ")"}]}], "]"}]}], "]"}]}], ")"}], "2"]}], ")"}]}]}], "}"}]], "Output", CellChangeTimes->{3.6228135818743677`*^9, 3.6228136649639187`*^9}] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", "%", "]"}]], "Input", CellChangeTimes->{{3.62281428395302*^9, 3.6228142909584093`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"0.7488048`", ",", "2.7455890393265063`"}], "}"}]], "Output", CellChangeTimes->{3.622814286676366*^9}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Polynomial implicit description", "Subsubsection", CellChangeTimes->{{3.62281385877903*^9, 3.6228138792776327`*^9}, { 3.6228140405091066`*^9, 3.622814084581203*^9}, {3.622814152445321*^9, 3.6228141613974576`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"R3", "=", RowBox[{"ImplicitRegion", "[", RowBox[{ RowBox[{"poly", "\[Equal]", "0"}], ",", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6225955818696413`*^9, 3.6225955818711414`*^9}, { 3.622595794588653*^9, 3.622595859786932*^9}, {3.6225959318115783`*^9, 3.622595966651002*^9}, {3.622596102015191*^9, 3.6225961830024757`*^9}, { 3.622596237681919*^9, 3.622596249450413*^9}, {3.6228134864862547`*^9, 3.6228135280780363`*^9}, {3.6228136295989275`*^9, 3.622813655982778*^9}, { 3.6228141658950286`*^9, 3.6228141873752565`*^9}}], Cell[BoxData[ RowBox[{"ImplicitRegion", "[", RowBox[{ RowBox[{ RowBox[{"9", "-", RowBox[{"10", " ", SuperscriptBox["x", "2"]}], "+", SuperscriptBox["x", "4"], "-", RowBox[{"10", " ", SuperscriptBox["y", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["x", "2"], " ", SuperscriptBox["y", "2"]}], "+", SuperscriptBox["y", "4"], "+", RowBox[{"6", " ", SuperscriptBox["z", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["x", "2"], " ", SuperscriptBox["z", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["y", "2"], " ", SuperscriptBox["z", "2"]}], "+", SuperscriptBox["z", "4"]}], "\[Equal]", "0"}], ",", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}]], "Output", CellChangeTimes->{3.622596489911948*^9, 3.6228135290411587`*^9, 3.6228136572554398`*^9, 3.6228141884253893`*^9}] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"RegionDistance", "[", RowBox[{"R3", ",", RowBox[{"{", RowBox[{"3", ",", "3", ",", "3"}], "}"}]}], "]"}], "//", "Timing"}]], "Input", CellChangeTimes->{{3.622813544874669*^9, 3.622813559181986*^9}, 3.62281366316669*^9, 3.6228141953517694`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"0.01560010000000000042474912476109238924`4.21372729556415", ",", RowBox[{"\[Sqrt]", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"Root", "[", RowBox[{ RowBox[{ RowBox[{"1953", "+", RowBox[{"432", " ", "#1"}], "-", RowBox[{"3086", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"673", " ", SuperscriptBox["#1", "4"]}]}], "&"}], ",", "4"}], "]"}]}], ")"}], "2"]}], "+", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", FractionBox["863469", "258002"]}], "-", FractionBox[ RowBox[{"948021", " ", RowBox[{"Root", "[", RowBox[{ RowBox[{ RowBox[{"1953", "+", RowBox[{"432", " ", "#1"}], "-", RowBox[{"3086", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"673", " ", SuperscriptBox["#1", "4"]}]}], "&"}], ",", "4"}], "]"}]}], "903007"], "+", FractionBox[ RowBox[{"413895", " ", SuperscriptBox[ RowBox[{"Root", "[", RowBox[{ RowBox[{ RowBox[{"1953", "+", RowBox[{"432", " ", "#1"}], "-", RowBox[{"3086", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"673", " ", SuperscriptBox["#1", "4"]}]}], "&"}], ",", "4"}], "]"}], "2"]}], "1806014"], "+", FractionBox[ RowBox[{"335154", " ", SuperscriptBox[ RowBox[{"Root", "[", RowBox[{ RowBox[{ RowBox[{"1953", "+", RowBox[{"432", " ", "#1"}], "-", RowBox[{"3086", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"673", " ", SuperscriptBox["#1", "4"]}]}], "&"}], ",", "4"}], "]"}], "3"]}], "903007"]}], ")"}], "2"]}], ")"}]}]}], "}"}]], "Output", CellChangeTimes->{3.6228135818743677`*^9, 3.6228136649639187`*^9, 3.622814196193376*^9}] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", "%", "]"}]], "Input", CellChangeTimes->{{3.6228142990134325`*^9, 3.6228143049826903`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"0.0156001`", ",", "2.745589039326506`"}], "}"}]], "Output", CellChangeTimes->{3.6228143018012867`*^9}] }, Closed]] }, Closed]] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Solving for real variables vs. solving over the reals", "Section", CellChangeTimes->{ 3.483202458955147*^9, {3.514308340990994*^9, 3.514308352103572*^9}, { 3.5904954665145655`*^9, 3.590495477705966*^9}, {3.6223028190867653`*^9, 3.622302822686513*^9}, 3.6225937958723483`*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SqrtBox["x"], " ", SqrtBox["y"]}], "\[Equal]", SqrtBox["z"]}], "&&", RowBox[{ RowBox[{ SqrtBox[ RowBox[{"x", "-", "y"}]], " ", SqrtBox[ RowBox[{"x", "+", "y"}]]}], "\[Equal]", RowBox[{"2", " ", SqrtBox[ RowBox[{"z", "-", "1"}]]}]}], "&&", RowBox[{ RowBox[{ SuperscriptBox["x", "3"], "+", SuperscriptBox["y", "3"], "+", SuperscriptBox["z", "3"]}], "\[Equal]", "7"}], "&&", RowBox[{ RowBox[{"(", RowBox[{"x", "|", "y", "|", "z"}], ")"}], "\[Element]", "Reals"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}], "//", "Timing"}]], "Input", CellChangeTimes->{{3.3914452187452817`*^9, 3.39144522238593*^9}, { 3.39144566381063*^9, 3.391445669154414*^9}, {3.3932633708668423`*^9, 3.393263377554428*^9}, 3.622374438409622*^9, {3.622374980057269*^9, 3.622374982272597*^9}, {3.6223750343328*^9, 3.6223750362205095`*^9}, { 3.622375070261673*^9, 3.6223750865646133`*^9}, 3.6223751834462023`*^9, 3.6223843834638553`*^9, 3.6223918753814087`*^9, {3.6225841534824204`*^9, 3.622584205642044*^9}, {3.622584298051278*^9, 3.6225843219058075`*^9}, { 3.6225843728117714`*^9, 3.622584534914356*^9}, {3.6225845836585455`*^9, 3.6225846162111797`*^9}, {3.622584649309882*^9, 3.6225848327401752`*^9}, { 3.6225851459414463`*^9, 3.6225851475546513`*^9}, {3.622585269469133*^9, 3.622585333571273*^9}, {3.6225853850618114`*^9, 3.622585402563033*^9}, { 3.622585442452099*^9, 3.622585479148759*^9}, {3.6225903181377325`*^9, 3.622590394896479*^9}, 3.622590448412775*^9, {3.6225905217565885`*^9, 3.6225905278253593`*^9}, {3.622828368411519*^9, 3.622828369851202*^9}}, FontSize->16], Cell[BoxData[ RowBox[{"{", RowBox[{ "11.34127269999999931826550891855731606483`7.075261706423187", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{"Root", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1695"}], "+", RowBox[{"24576", " ", "#1"}], "-", RowBox[{"62976", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"86496", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"70800", " ", SuperscriptBox["#1", "4"]}], "+", RowBox[{"31008", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"5426", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"32", " ", SuperscriptBox["#1", "9"]}], "+", SuperscriptBox["#1", "12"]}], "&"}], ",", RowBox[{ RowBox[{"53208614832751665", "-", RowBox[{"787594273805002767", " ", "#1"}], "+", RowBox[{"1728275115271227921", " ", SuperscriptBox["#1", "2"]}], "-", RowBox[{"1987234063898096409", " ", SuperscriptBox["#1", "3"]}], "+", RowBox[{"1144587091148369463", " ", SuperscriptBox["#1", "4"]}], "-", RowBox[{"248347199722637937", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"1492906121703969", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"1476325005540257", " ", SuperscriptBox["#1", "7"]}], "-", RowBox[{"1396759209347961", " ", SuperscriptBox["#1", "8"]}], "+", RowBox[{"49594071947721", " ", SuperscriptBox["#1", "9"]}], "+", RowBox[{"48470803196393", " ", SuperscriptBox["#1", "10"]}], "+", RowBox[{"45460783051449", " ", SuperscriptBox["#1", "11"]}], "+", RowBox[{"62595796172722320", " ", "#2"}]}], "&"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "]"}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{"Root", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1695"}], "+", RowBox[{"24576", " ", "#1"}], "-", RowBox[{"62976", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"86496", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"70800", " ", SuperscriptBox["#1", "4"]}], "+", RowBox[{"31008", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"5426", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"32", " ", SuperscriptBox["#1", "9"]}], "+", SuperscriptBox["#1", "12"]}], "&"}], ",", RowBox[{ RowBox[{ RowBox[{"-", "150727873288265265"}], "+", RowBox[{"401476268183829519", " ", "#1"}], "-", RowBox[{"493232081043071697", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"315073184812299033", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"77887985011498551", " ", SuperscriptBox["#1", "4"]}], "-", RowBox[{"10674432865166751", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"1236413705218527", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"537502632324191", " ", SuperscriptBox["#1", "7"]}], "+", RowBox[{"45520073334217", " ", SuperscriptBox["#1", "8"]}], "+", RowBox[{"47616451789623", " ", SuperscriptBox["#1", "9"]}], "+", RowBox[{"22190552103959", " ", SuperscriptBox["#1", "10"]}], "+", RowBox[{"1515193133927", " ", SuperscriptBox["#1", "11"]}], "+", RowBox[{"62595796172722320", " ", "#2"}]}], "&"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "]"}]}], ",", RowBox[{"z", "\[Rule]", RowBox[{"Root", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1695"}], "+", RowBox[{"24576", " ", "#1"}], "-", RowBox[{"62976", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"86496", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"70800", " ", SuperscriptBox["#1", "4"]}], "+", RowBox[{"31008", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"5426", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"32", " ", SuperscriptBox["#1", "9"]}], "+", SuperscriptBox["#1", "12"]}], "&"}], ",", "1"}], "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{"Root", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1695"}], "+", RowBox[{"24576", " ", "#1"}], "-", RowBox[{"62976", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"86496", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"70800", " ", SuperscriptBox["#1", "4"]}], "+", RowBox[{"31008", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"5426", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"32", " ", SuperscriptBox["#1", "9"]}], "+", SuperscriptBox["#1", "12"]}], "&"}], ",", RowBox[{ RowBox[{"53208614832751665", "-", RowBox[{"787594273805002767", " ", "#1"}], "+", RowBox[{"1728275115271227921", " ", SuperscriptBox["#1", "2"]}], "-", RowBox[{"1987234063898096409", " ", SuperscriptBox["#1", "3"]}], "+", RowBox[{"1144587091148369463", " ", SuperscriptBox["#1", "4"]}], "-", RowBox[{"248347199722637937", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"1492906121703969", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"1476325005540257", " ", SuperscriptBox["#1", "7"]}], "-", RowBox[{"1396759209347961", " ", SuperscriptBox["#1", "8"]}], "+", RowBox[{"49594071947721", " ", SuperscriptBox["#1", "9"]}], "+", RowBox[{"48470803196393", " ", SuperscriptBox["#1", "10"]}], "+", RowBox[{"45460783051449", " ", SuperscriptBox["#1", "11"]}], "+", RowBox[{"62595796172722320", " ", "#2"}]}], "&"}]}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}]}], "]"}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{"Root", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1695"}], "+", RowBox[{"24576", " ", "#1"}], "-", RowBox[{"62976", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"86496", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"70800", " ", SuperscriptBox["#1", "4"]}], "+", RowBox[{"31008", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"5426", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"32", " ", SuperscriptBox["#1", "9"]}], "+", SuperscriptBox["#1", "12"]}], "&"}], ",", RowBox[{ RowBox[{ RowBox[{"-", "150727873288265265"}], "+", RowBox[{"401476268183829519", " ", "#1"}], "-", RowBox[{"493232081043071697", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"315073184812299033", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"77887985011498551", " ", SuperscriptBox["#1", "4"]}], "-", RowBox[{"10674432865166751", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"1236413705218527", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"537502632324191", " ", SuperscriptBox["#1", "7"]}], "+", RowBox[{"45520073334217", " ", SuperscriptBox["#1", "8"]}], "+", RowBox[{"47616451789623", " ", SuperscriptBox["#1", "9"]}], "+", RowBox[{"22190552103959", " ", SuperscriptBox["#1", "10"]}], "+", RowBox[{"1515193133927", " ", SuperscriptBox["#1", "11"]}], "+", RowBox[{"62595796172722320", " ", "#2"}]}], "&"}]}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "1"}], "}"}]}], "]"}]}], ",", RowBox[{"z", "\[Rule]", RowBox[{"Root", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1695"}], "+", RowBox[{"24576", " ", "#1"}], "-", RowBox[{"62976", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"86496", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"70800", " ", SuperscriptBox["#1", "4"]}], "+", RowBox[{"31008", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"5426", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"32", " ", SuperscriptBox["#1", "9"]}], "+", SuperscriptBox["#1", "12"]}], "&"}], ",", "2"}], "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{"Root", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1695"}], "+", RowBox[{"24576", " ", "#1"}], "-", RowBox[{"62976", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"86496", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"70800", " ", SuperscriptBox["#1", "4"]}], "+", RowBox[{"31008", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"5426", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"32", " ", SuperscriptBox["#1", "9"]}], "+", SuperscriptBox["#1", "12"]}], "&"}], ",", RowBox[{ RowBox[{"53208614832751665", "-", RowBox[{"787594273805002767", " ", "#1"}], "+", RowBox[{"1728275115271227921", " ", SuperscriptBox["#1", "2"]}], "-", RowBox[{"1987234063898096409", " ", SuperscriptBox["#1", "3"]}], "+", RowBox[{"1144587091148369463", " ", SuperscriptBox["#1", "4"]}], "-", RowBox[{"248347199722637937", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"1492906121703969", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"1476325005540257", " ", SuperscriptBox["#1", "7"]}], "-", RowBox[{"1396759209347961", " ", SuperscriptBox["#1", "8"]}], "+", RowBox[{"49594071947721", " ", SuperscriptBox["#1", "9"]}], "+", RowBox[{"48470803196393", " ", SuperscriptBox["#1", "10"]}], "+", RowBox[{"45460783051449", " ", SuperscriptBox["#1", "11"]}], "+", RowBox[{"62595796172722320", " ", "#2"}]}], "&"}]}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "1"}], "}"}]}], "]"}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{"Root", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1695"}], "+", RowBox[{"24576", " ", "#1"}], "-", RowBox[{"62976", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"86496", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"70800", " ", SuperscriptBox["#1", "4"]}], "+", RowBox[{"31008", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"5426", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"32", " ", SuperscriptBox["#1", "9"]}], "+", SuperscriptBox["#1", "12"]}], "&"}], ",", RowBox[{ RowBox[{ RowBox[{"-", "150727873288265265"}], "+", RowBox[{"401476268183829519", " ", "#1"}], "-", RowBox[{"493232081043071697", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"315073184812299033", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"77887985011498551", " ", SuperscriptBox["#1", "4"]}], "-", RowBox[{"10674432865166751", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"1236413705218527", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"537502632324191", " ", SuperscriptBox["#1", "7"]}], "+", RowBox[{"45520073334217", " ", SuperscriptBox["#1", "8"]}], "+", RowBox[{"47616451789623", " ", SuperscriptBox["#1", "9"]}], "+", RowBox[{"22190552103959", " ", SuperscriptBox["#1", "10"]}], "+", RowBox[{"1515193133927", " ", SuperscriptBox["#1", "11"]}], "+", RowBox[{"62595796172722320", " ", "#2"}]}], "&"}]}], "}"}], ",", RowBox[{"{", RowBox[{"3", ",", "1"}], "}"}]}], "]"}]}], ",", RowBox[{"z", "\[Rule]", RowBox[{"Root", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1695"}], "+", RowBox[{"24576", " ", "#1"}], "-", RowBox[{"62976", " ", SuperscriptBox["#1", "2"]}], "+", RowBox[{"86496", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"70800", " ", SuperscriptBox["#1", "4"]}], "+", RowBox[{"31008", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"5426", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"32", " ", SuperscriptBox["#1", "9"]}], "+", SuperscriptBox["#1", "12"]}], "&"}], ",", "3"}], "]"}]}]}], "}"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.622585483035252*^9, {3.6225903321015053`*^9, 3.622590355550983*^9}, { 3.6225903887597*^9, 3.622590407381565*^9}, 3.6225906253552437`*^9}] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SqrtBox["x"], " ", SqrtBox["y"]}], "\[Equal]", SqrtBox["z"]}], "&&", RowBox[{ RowBox[{ SqrtBox[ RowBox[{"x", "-", "y"}]], " ", SqrtBox[ RowBox[{"x", "+", "y"}]]}], "\[Equal]", RowBox[{"2", " ", SqrtBox[ RowBox[{"z", "-", "1"}]]}]}], "&&", RowBox[{ RowBox[{ SuperscriptBox["x", "3"], "+", SuperscriptBox["y", "3"], "+", SuperscriptBox["z", "3"]}], "\[Equal]", "7"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", "Reals"}], "]"}], "//", "Timing"}]], "Input", CellChangeTimes->{{3.3914452187452817`*^9, 3.39144522238593*^9}, { 3.39144566381063*^9, 3.391445669154414*^9}, {3.3932633708668423`*^9, 3.393263377554428*^9}, 3.622374438409622*^9, {3.622374980057269*^9, 3.622374982272597*^9}, {3.6223750343328*^9, 3.6223750362205095`*^9}, { 3.622375070261673*^9, 3.6223750865646133`*^9}, 3.6223751834462023`*^9, 3.6223843834638553`*^9, 3.6223918753814087`*^9, {3.6225841534824204`*^9, 3.622584205642044*^9}, {3.622584298051278*^9, 3.6225843219058075`*^9}, { 3.6225843728117714`*^9, 3.622584534914356*^9}, {3.6225845836585455`*^9, 3.6225846162111797`*^9}, {3.622584649309882*^9, 3.6225848327401752`*^9}, { 3.6225851459414463`*^9, 3.6225851475546513`*^9}, {3.622585269469133*^9, 3.622585333571273*^9}, {3.6225853850618114`*^9, 3.622585402563033*^9}, { 3.622585442452099*^9, 3.622585479148759*^9}, {3.6225903181377325`*^9, 3.622590394896479*^9}, {3.6225904279751797`*^9, 3.622590457255898*^9}, { 3.622590534929261*^9, 3.6225905393043165`*^9}}, FontSize->16], Cell[BoxData[ RowBox[{"{", RowBox[{"0.03120020000000000084949824952218477847`4.514757291228131", ",", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{"Root", "[", RowBox[{ RowBox[{ RowBox[{"15", "-", RowBox[{"336", " ", "#1"}], "+", RowBox[{"48", " ", SuperscriptBox["#1", "2"]}], "-", RowBox[{"390", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"276", " ", SuperscriptBox["#1", "4"]}], "+", RowBox[{"96", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"392", " ", SuperscriptBox["#1", "6"]}], "+", RowBox[{"72", " ", SuperscriptBox["#1", "7"]}], "+", RowBox[{"48", " ", SuperscriptBox["#1", "8"]}], "+", RowBox[{"78", " ", SuperscriptBox["#1", "9"]}], "+", RowBox[{"12", " ", SuperscriptBox["#1", "10"]}], "+", SuperscriptBox["#1", "12"]}], "&"}], ",", "4"}], "]"}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{"Root", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"15", "-", RowBox[{"336", " ", "#1"}], "+", RowBox[{"48", " ", SuperscriptBox["#1", "2"]}], "-", RowBox[{"390", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"276", " ", SuperscriptBox["#1", "4"]}], "+", RowBox[{"96", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"392", " ", SuperscriptBox["#1", "6"]}], "+", RowBox[{"72", " ", SuperscriptBox["#1", "7"]}], "+", RowBox[{"48", " ", SuperscriptBox["#1", "8"]}], "+", RowBox[{"78", " ", SuperscriptBox["#1", "9"]}], "+", RowBox[{"12", " ", SuperscriptBox["#1", "10"]}], "+", SuperscriptBox["#1", "12"]}], "&"}], ",", RowBox[{ RowBox[{ RowBox[{"-", "45676543216"}], "+", RowBox[{"64176019967", " ", "#1"}], "-", RowBox[{"96357120244", " ", SuperscriptBox["#1", "2"]}], "-", RowBox[{"36284349888", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"23452728469", " ", SuperscriptBox["#1", "4"]}], "-", RowBox[{"74597760600", " ", SuperscriptBox["#1", "5"]}], "+", RowBox[{"13127794640", " ", SuperscriptBox["#1", "6"]}], "+", RowBox[{"13527085501", " ", SuperscriptBox["#1", "7"]}], "+", RowBox[{"15532809152", " ", SuperscriptBox["#1", "8"]}], "+", RowBox[{"2226010400", " ", SuperscriptBox["#1", "9"]}], "+", RowBox[{"65820617", " ", SuperscriptBox["#1", "10"]}], "+", RowBox[{"189210884", " ", SuperscriptBox["#1", "11"]}], "+", RowBox[{"22477794952", " ", "#2"}]}], "&"}]}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "1"}], "}"}]}], "]"}]}], ",", RowBox[{"z", "\[Rule]", RowBox[{"Root", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"15", "-", RowBox[{"336", " ", "#1"}], "+", RowBox[{"48", " ", SuperscriptBox["#1", "2"]}], "-", RowBox[{"390", " ", SuperscriptBox["#1", "3"]}], "-", RowBox[{"276", " ", SuperscriptBox["#1", "4"]}], "+", RowBox[{"96", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"392", " ", SuperscriptBox["#1", "6"]}], "+", RowBox[{"72", " ", SuperscriptBox["#1", "7"]}], "+", RowBox[{"48", " ", SuperscriptBox["#1", "8"]}], "+", RowBox[{"78", " ", SuperscriptBox["#1", "9"]}], "+", RowBox[{"12", " ", SuperscriptBox["#1", "10"]}], "+", SuperscriptBox["#1", "12"]}], "&"}], ",", RowBox[{ RowBox[{ RowBox[{"-", "2838163260"}], "+", RowBox[{"17898313808", " ", "#1"}], "+", RowBox[{"55093897535", " ", SuperscriptBox["#1", "2"]}], "-", RowBox[{"22564875484", " ", SuperscriptBox["#1", "3"]}], "+", RowBox[{"15937854096", " ", SuperscriptBox["#1", "4"]}], "-", RowBox[{"41616973333", " ", SuperscriptBox["#1", "5"]}], "-", RowBox[{"427094072", " ", SuperscriptBox["#1", "6"]}], "-", RowBox[{"495389008", " ", SuperscriptBox["#1", "7"]}], "+", RowBox[{"4444963069", " ", SuperscriptBox["#1", "8"]}], "+", RowBox[{"774360200", " ", SuperscriptBox["#1", "9"]}], "-", RowBox[{"44520208", " ", SuperscriptBox["#1", "10"]}], "+", RowBox[{"65820617", " ", SuperscriptBox["#1", "11"]}], "+", RowBox[{"22477794952", " ", "#2"}]}], "&"}]}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "1"}], "}"}]}], "]"}]}]}], "}"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.6225904337239094`*^9, 3.622590631813064*^9}] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Symbolic Integration", "Section", CellChangeTimes->{{3.6219397657619414`*^9, 3.6219397703954086`*^9}}], Cell[CellGroupData[{ Cell[" Scope of Integrate", "Subsection", ShowGroupOpener->True, CellChangeTimes->{{3.623075552580637*^9, 3.6230755645513554`*^9}, 3.623153092714595*^9}], Cell[TextData[{ ButtonBox["Integrate", BaseStyle->"Link", ButtonData->"paclet:ref/Integrate"], " can compute:" }], "Text", CellChangeTimes->{{3.3691474811256*^9, 3.3691475712205*^9}, { 3.36914767534684*^9, 3.36914768711261*^9}, {3.36914775209782*^9, 3.36914776289483*^9}, {3.36914782145808*^9, 3.36914782187996*^9}, 3.36914785930232*^9, {3.3693017674333115`*^9, 3.3693017685896425`*^9}, { 3.3799476906272397`*^9, 3.3799476913459854`*^9}, {3.3907557717906*^9, 3.3907557799625273`*^9}, 3.393348348022973*^9, {3.6231474717339883`*^9, 3.6231474717339883`*^9}}], Cell[CellGroupData[{ Cell[" A wide variety of indefinite integrals ", "Item"], Cell["\<\ Definite integrals over finite and infinite intervals \ \>", "Item"], Cell["Multiple integrals in an arbitrary number of dimensions", "Item"], Cell["Integrals of piecewise functions and distributions", "Item"], Cell["Integrals over regions, including areas and volumes", "Item"] }, Open ]], Cell["", "Spacer"] }, Closed]], Cell[CellGroupData[{ Cell[" Integral of a Rational Function", "Subsection", ShowGroupOpener->True, CellChangeTimes->{{3.622383070238083*^9, 3.622383131222001*^9}, { 3.622478989651311*^9, 3.6224789998542995`*^9}, {3.6224793067864065`*^9, 3.6224793101718016`*^9}, 3.6231530940186787`*^9}], Cell[TextData[{ "The indefinite integral of this ", StyleBox["rational function", FontColor->GrayLevel[0]], " has three parts - polynomial, rational, and logarithmic." }], "Text", CellChangeTimes->{{3.3933267495052023`*^9, 3.3933267802714186`*^9}, { 3.393326913836483*^9, 3.393326915086507*^9}, {3.3933273227662086`*^9, 3.3933273306101093`*^9}, {3.6223831437807255`*^9, 3.622383179506787*^9}, 3.6223857559642963`*^9}], Cell[BoxData[ RowBox[{"\[Integral]", RowBox[{ FractionBox[ RowBox[{"3", "+", RowBox[{"15", " ", "x"}], "+", RowBox[{"37", " ", SuperscriptBox["x", "2"]}], "+", RowBox[{"36", " ", SuperscriptBox["x", "3"]}], "+", RowBox[{"14", " ", SuperscriptBox["x", "4"]}]}], RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "x"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"4", "+", RowBox[{"7", " ", "x"}]}], ")"}]}]], RowBox[{"\[DifferentialD]", "x"}]}]}]], "Input", CellChangeTimes->{{3.3914452187452817`*^9, 3.39144522238593*^9}, { 3.39144566381063*^9, 3.391445669154414*^9}, {3.3932633708668423`*^9, 3.393263377554428*^9}, 3.622374438409622*^9, {3.622374980057269*^9, 3.622374982272597*^9}, {3.6223750343328*^9, 3.6223750362205095`*^9}, { 3.622375070261673*^9, 3.6223750865646133`*^9}, 3.6223751834462023`*^9, 3.6223843834638553`*^9, 3.6223918753814087`*^9}], Cell[TextData[{ "We can use ", Cell[BoxData[ ButtonBox["D", BaseStyle->"Link", ButtonData->"paclet:ref/D"]], "InlineFormula"], " to ", StyleBox["verify", FontColor->GrayLevel[0]], " the result." }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{"D", "[", RowBox[{"%", ",", "x"}], "]"}], "//", "Together"}]], "Input", CellChangeTimes->{{3.3914465432537584`*^9, 3.3914465523163166`*^9}, 3.6223744384408236`*^9, 3.622375183477404*^9, {3.622375317801153*^9, 3.6223753286125765`*^9}, 3.622384383495056*^9, {3.6223885681969547`*^9, 3.62238857106752*^9}, {3.6223918754438124`*^9, 3.6223918905454836`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell[" A Rational-Exponential integral", "Subsection", ShowGroupOpener->True, CellChangeTimes->{{3.622383070238083*^9, 3.622383131222001*^9}, { 3.622478989651311*^9, 3.622479028544355*^9}, {3.622479312636744*^9, 3.622479315897332*^9}, 3.623153095426888*^9}], Cell[TextData[{ "Now consider the following", StyleBox[" rational-exponential indefinite integral.", FontColor->GrayLevel[0]], "\n" }], "Text", CellChangeTimes->{{3.6223751641010866`*^9, 3.62237516814172*^9}, { 3.622479087999385*^9, 3.622479095690628*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"\[Integral]", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["\[ExponentialE]", "x"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[ExponentialE]", "x"], " ", "x"}], "-", RowBox[{"8", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"2", " ", "x"}]], " ", "x"}], "-", RowBox[{"15", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"3", " ", "x"}]], " ", "x"}], "-", RowBox[{"3", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"4", " ", "x"}]], " ", "x"}], "+", RowBox[{"3", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"5", " ", "x"}]], " ", "x"}], "+", RowBox[{"4", " ", "x"}], "-", RowBox[{"5", " ", SuperscriptBox["\[ExponentialE]", "x"]}], "-", SuperscriptBox["\[ExponentialE]", RowBox[{"2", " ", "x"}]], "+", SuperscriptBox["\[ExponentialE]", RowBox[{"3", " ", "x"}]], "-", "3"}], ")"}]}], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", SuperscriptBox["\[ExponentialE]", "x"]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["\[ExponentialE]", "x"]}], ")"}], "2"], " ", "x"}]], RowBox[{"\[DifferentialD]", "x"}]}]}], Background->GrayLevel[0.85]]], "Input", Evaluatable->False, CellChangeTimes->{{3.391600958619855*^9, 3.391600967526162*^9}, 3.622375183508606*^9, 3.6223843835418572`*^9, 3.622391875490615*^9}, FontSize->16], Cell[TextData[{ "\nTo guess the answer, we replace exponentials by powers of a new variable ", StyleBox["t", "MR", FontSlant->"Italic"], " and then apply ", Cell[BoxData[ ButtonBox["Apart", BaseStyle->"Link", ButtonData->"paclet:ref/Apart"]], "InlineFormula"], " to the integrand." }], "Text", CellChangeTimes->{{3.622389764474636*^9, 3.6223897858010664`*^9}, 3.622479099060423*^9, {3.622480676673218*^9, 3.6224806823207436`*^9}}], Cell[BoxData[ RowBox[{"Apart", "[", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["\[ExponentialE]", "x"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[ExponentialE]", "x"], " ", "x"}], "-", RowBox[{"8", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"2", " ", "x"}]], " ", "x"}], "-", RowBox[{"15", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"3", " ", "x"}]], " ", "x"}], "-", RowBox[{"3", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"4", " ", "x"}]], " ", "x"}], "+", RowBox[{"3", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"5", " ", "x"}]], " ", "x"}], "+", RowBox[{"4", " ", "x"}], "-", RowBox[{"5", " ", SuperscriptBox["\[ExponentialE]", "x"]}], "-", SuperscriptBox["\[ExponentialE]", RowBox[{"2", " ", "x"}]], "+", SuperscriptBox["\[ExponentialE]", RowBox[{"3", " ", "x"}]], "-", "3"}], ")"}]}], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", SuperscriptBox["\[ExponentialE]", "x"]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["\[ExponentialE]", "x"]}], ")"}], "2"], " ", "x"}]], "/.", "\[VeryThinSpace]", RowBox[{"{", RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{"a_.", " ", "x"}]], "\[RuleDelayed]", SuperscriptBox["t", "a"]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.392898830549589*^9, 3.3928988538936377`*^9}, { 3.3928989154881763`*^9, 3.392898927347703*^9}, {3.393596678005888*^9, 3.3935967015218143`*^9}, 3.622375183539808*^9, 3.622384383573058*^9, 3.6223918755530186`*^9, 3.6225671636772237`*^9, {3.6228015618356085`*^9, 3.622801566047852*^9}, 3.6228260388504963`*^9}, FontSize->16], Cell[TextData[{ StyleBox["Exercise", FontWeight->"Bold"], ": Use the second argument of Apart to get the desired output for the \ above." }], "Text", CellChangeTimes->{{3.622825325884523*^9, 3.622825361672988*^9}, { 3.623076220958072*^9, 3.623076245319534*^9}, {3.623090794080905*^9, 3.6230908006488843`*^9}}], Cell[TextData[{ "\nAfter evaluation, the integral has ", StyleBox["four", FontColor->GrayLevel[0]], " parts - polynomial, fractional, logarithmic and transcendental.\n" }], "Text", CellChangeTimes->{{3.3933302920578413`*^9, 3.3933303283071456`*^9}, { 3.3933303869622693`*^9, 3.3933304307583036`*^9}, {3.393330512710369*^9, 3.3933305136634884`*^9}, {3.393331589333707*^9, 3.393331615130582*^9}, { 3.622375431545458*^9, 3.6223754553368306`*^9}, {3.6223832110830083`*^9, 3.6223832346247663`*^9}, {3.6223897890772552`*^9, 3.6223897899821076`*^9}, { 3.622479102071397*^9, 3.6224791040683117`*^9}, {3.623090811881532*^9, 3.6230908215072875`*^9}}], Cell[BoxData[ RowBox[{"\[Integral]", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["\[ExponentialE]", "x"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["\[ExponentialE]", "x"], " ", "x"}], "-", RowBox[{"8", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"2", " ", "x"}]], " ", "x"}], "-", RowBox[{"15", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"3", " ", "x"}]], " ", "x"}], "-", RowBox[{"3", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"4", " ", "x"}]], " ", "x"}], "+", RowBox[{"3", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"5", " ", "x"}]], " ", "x"}], "+", RowBox[{"4", " ", "x"}], "-", RowBox[{"5", " ", SuperscriptBox["\[ExponentialE]", "x"]}], "-", SuperscriptBox["\[ExponentialE]", RowBox[{"2", " ", "x"}]], "+", SuperscriptBox["\[ExponentialE]", RowBox[{"3", " ", "x"}]], "-", "3"}], ")"}]}], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", SuperscriptBox["\[ExponentialE]", "x"]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["\[ExponentialE]", "x"]}], ")"}], "2"], " ", "x"}]], RowBox[{"\[DifferentialD]", "x"}]}]}]], "Input", CellChangeTimes->{3.6223751835710096`*^9, 3.6223843836042585`*^9, 3.6223918755998216`*^9}, FontSize->16], Cell[TextData[{ "\nOnce again, we can use ", Cell[BoxData[ ButtonBox["D", BaseStyle->"Link", ButtonData->"paclet:ref/D"]], "InlineFormula"], " to verify the result." }], "Text", CellChangeTimes->{{3.6223857775871434`*^9, 3.6223857828446465`*^9}, 3.6224791072352943`*^9}], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{"D", "[", RowBox[{"%", ",", "x"}], "]"}], "//", "Together"}]}]], "Input", CellChangeTimes->{{3.393331628630582*^9, 3.393331636130582*^9}, { 3.3936046131699567`*^9, 3.393604618513775*^9}, 3.6223751836022115`*^9, { 3.622375297083158*^9, 3.622375299610504*^9}, {3.6223754637925186`*^9, 3.6223754684259853`*^9}, 3.62238438363546*^9, {3.62238857538897*^9, 3.622388578087926*^9}, {3.6223918756622252`*^9, 3.622391900623665*^9}, 3.6224791098874474`*^9}, FontSize->16] }, Closed]], Cell[CellGroupData[{ Cell["\<\ A Gaussian Integral \ \>", "Subsection", ShowGroupOpener->True, CellChangeTimes->{{3.6224791401843953`*^9, 3.6224791509490166`*^9}, { 3.622479297332261*^9, 3.622479319095516*^9}}], Cell[TextData[{ "The following Gaussian ", StyleBox["definite integral", FontColor->GrayLevel[0]], " has an elegant closed form answer.\n" }], "Text", CellChangeTimes->{{3.6223837264653625`*^9, 3.622383728274638*^9}, { 3.622383985226*^9, 3.6223839879559298`*^9}, {3.6223847151190977`*^9, 3.6223847199553146`*^9}, {3.622480368268789*^9, 3.622480374165929*^9}}], Cell[BoxData[ RowBox[{ SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[{ RowBox[{ SuperscriptBox["x", "12"], " ", SuperscriptBox["\[ExponentialE]", RowBox[{"-", SuperscriptBox["x", "2"]}]]}], RowBox[{"\[DifferentialD]", "x"}]}]}]], "Input", CellChangeTimes->{{3.39144774813647*^9, 3.391447838012045*^9}, { 3.391448069732278*^9, 3.391448101341855*^9}, {3.3933276724447975`*^9, 3.393327672788554*^9}, 3.6223744385500298`*^9, 3.6223751836334133`*^9, { 3.6223837210843287`*^9, 3.6223837473032217`*^9}, {3.622383854284417*^9, 3.622383920846451*^9}, {3.622383968425231*^9, 3.6223839689088182`*^9}, { 3.622384009202585*^9, 3.622384038951022*^9}, 3.6223843836666603`*^9, 3.622384572932812*^9, {3.622384610140482*^9, 3.6223846220438156`*^9}, 3.622391875709028*^9}, FontSize->16], Cell[BoxData[ RowBox[{"N", "[", "%", "]"}]], "Input", CellChangeTimes->{{3.393327743508662*^9, 3.393327744805562*^9}, 3.622374438581232*^9, 3.6223751836646147`*^9, 3.622384383697861*^9, 3.6223918757714314`*^9}, FontSize->16], Cell[TextData[{ "We can use ", ButtonBox["NIntegrate", BaseStyle->"Link", ButtonData->"paclet:ref/NIntegrate"], " to verify the result." }], "Text", CellChangeTimes->{{3.6223832822387133`*^9, 3.6223833125964684`*^9}}], Cell[BoxData[ RowBox[{"NIntegrate", "[", RowBox[{ RowBox[{ SuperscriptBox["x", "12"], " ", SuperscriptBox["\[ExponentialE]", RowBox[{"-", SuperscriptBox["x", "2"]}]]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "\[Infinity]"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.39144774813647*^9, 3.391447838012045*^9}, { 3.391448069732278*^9, 3.391448101341855*^9}, {3.3933276724447975`*^9, 3.393327672788554*^9}, 3.6223744385500298`*^9, 3.6223751836334133`*^9, { 3.6223837210843287`*^9, 3.6223837679851093`*^9}, {3.6223838614123373`*^9, 3.6223838616462955`*^9}, {3.6223839551031723`*^9, 3.6223839742438817`*^9}, {3.622384045518454*^9, 3.6223840479831905`*^9}, 3.622384383729062*^9, 3.62238458001553*^9, {3.6223846279876823`*^9, 3.62238462883012*^9}, 3.622391875818234*^9}, FontSize->16], Cell[TextData[{ StyleBox["Exercise", FontWeight->"Bold"], ": Derive the symbolic result using differentiation under the integral \ sign." }], "Text", CellChangeTimes->{{3.622825325884523*^9, 3.622825361672988*^9}}], Cell["\<\ \ \>", "Text", CellChangeTimes->{{3.6223858204896183`*^9, 3.6223858346864376`*^9}}] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Exact Solutions of Differential Equations", "Section", CellChangeTimes->{{3.6219427613617373`*^9, 3.6219427723759727`*^9}}], Cell[CellGroupData[{ Cell[" Scope of DSolve", "Subsection", ShowGroupOpener->True, CellChangeTimes->{3.623153081954789*^9}], Cell[TextData[{ Cell[BoxData[ ButtonBox["DSolve", BaseStyle->"Link", ButtonData->"paclet:ref/DSolve"]], "InlineFormula"], " can find exact solutions for the following:" }], "Text"], Cell[CellGroupData[{ Cell["\<\ Ordinary differential equations (linear, nonlinear, single, system)\ \>", "Item"], Cell["\<\ Partial differential equations (general first-order PDEs, some higher order \ equations)\ \>", "Item"], Cell["\<\ Differential-algebraic equations (linear constant coefficient systems)\ \>", "Item"], Cell["Delay differential equations.", "Item"], Cell["Hybrid differential equations (ODEs with events).", "Item"] }, Open ]], Cell["", "Spacer"] }, Closed]], Cell[CellGroupData[{ Cell[" The Aging Spring", "Subsection", ShowGroupOpener->True, CellChangeTimes->{{3.622373821330676*^9, 3.6223738423762903`*^9}, { 3.6224791563157263`*^9, 3.622479161167606*^9}, 3.6231530837067547`*^9}], Cell[TextData[{ "This ODE is a model for an", StyleBox[" ", FontColor->RGBColor[0, 0, 1]], StyleBox["aging spring", FontColor->GrayLevel[0]], ". It has an exponential function in its coefficient and is solved by \ transforming it to Bessel\[CloseCurlyQuote]s equation." }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{"AgingSpring", "=", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["x", "\[Prime]\[Prime]", MultilineFunction->None], "[", "t", "]"}], "+", RowBox[{"4", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"-", FractionBox["t", "4"]}]], " ", RowBox[{"x", "[", "t", "]"}]}]}], "\[Equal]", "0"}]}], ";"}]], "Input", CellChangeTimes->{{3.3802947716311984`*^9, 3.3802948093354144`*^9}, 3.622374438862048*^9, 3.6223751839298306`*^9, 3.622384384009869*^9, 3.6223918761926556`*^9}], Cell["The solution is expressed in terms of Bessel functions.", "Text", CellChangeTimes->{{3.6223904789077845`*^9, 3.622390491107688*^9}}], Cell[BoxData[ RowBox[{"sol", "=", RowBox[{"DSolve", "[", RowBox[{ RowBox[{"{", RowBox[{"AgingSpring", ",", RowBox[{ RowBox[{"x", "[", "0", "]"}], "\[Equal]", "1"}], ",", RowBox[{ RowBox[{ SuperscriptBox["x", "\[Prime]", MultilineFunction->None], "[", "0", "]"}], "\[Equal]", "2"}]}], "}"}], ",", "x", ",", "t"}], "]"}]}]], "Input", CellChangeTimes->{ 3.3802947738844385`*^9, {3.38029482093209*^9, 3.3802948251882095`*^9}, 3.62237443889325*^9, 3.622375183961032*^9, 3.62238438404107*^9, 3.6223918762550592`*^9, {3.6230762975826693`*^9, 3.623076314453682*^9}}], Cell["The solution can be verified as follows.", "Text", CellChangeTimes->{{3.6223904789077845`*^9, 3.622390491107688*^9}, { 3.622799911482557*^9, 3.622799915554392*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"AgingSpring", ",", RowBox[{ RowBox[{"x", "[", "0", "]"}], "\[Equal]", "1"}], ",", RowBox[{ RowBox[{ SuperscriptBox["x", "\[Prime]", MultilineFunction->None], "[", "0", "]"}], "\[Equal]", "2"}]}], "}"}], "/.", RowBox[{"sol", "[", RowBox[{"[", "1", "]"}], "]"}]}], "//", "FullSimplify"}]], "Input", CellChangeTimes->{{3.622799861559677*^9, 3.6227998952888227`*^9}}], Cell["Here is a plot of the solution.", "Text", CellChangeTimes->{{3.6223905075978394`*^9, 3.62239051522668*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"x", "[", "t", "]"}], "/.", "\[VeryThinSpace]", RowBox[{"sol", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "30"}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"Thickness", "[", "0.0075", "]"}], ",", "Red"}], "}"}]}], ",", RowBox[{"Background", "\[Rule]", "LightYellow"}]}], "]"}]], "Input", CellChangeTimes->{{3.379956619990835*^9, 3.379956628037813*^9}, 3.3802947774595795`*^9, {3.3802948523072047`*^9, 3.380294874899691*^9}, { 3.3802949240703955`*^9, 3.380294925131922*^9}, {3.392665541075152*^9, 3.3926655838432403`*^9}, 3.393332150021207*^9, {3.6223700452946334`*^9, 3.6223700460434766`*^9}, 3.622374438924452*^9, 3.622375183992234*^9, 3.622384384072271*^9, 3.6223905271925697`*^9, 3.622391876301862*^9}], Cell["", "Spacer"] }, Closed]], Cell[CellGroupData[{ Cell[" Ball in a Square Box", "Subsection", ShowGroupOpener->True, CellChangeTimes->{{3.6219429214113708`*^9, 3.621942929352229*^9}, { 3.6223700849053183`*^9, 3.622370092019329*^9}, {3.622385367889408*^9, 3.6223853989508*^9}, {3.622388950469864*^9, 3.622388977880645*^9}, 3.622389717422322*^9, {3.622479353495501*^9, 3.622479361311552*^9}, 3.623155105206386*^9}], Cell[TextData[{ "The following models ", StyleBox["a ball in a square box", FontColor->GrayLevel[0]], ", that changes direction upon impact with the side walls. Try varying the \ second argument of ", ButtonBox["Rationalize", BaseStyle->"Link", ButtonData->"paclet:ref/Rationalize"], "." }], "Text", CellChangeTimes->{{3.622389281021733*^9, 3.622389312987977*^9}, { 3.6227999329961977`*^9, 3.622799969065479*^9}}, CellID->38646030], Cell[BoxData[ RowBox[{ RowBox[{"sol", "=", RowBox[{"DSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["x", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", RowBox[{"a", "[", "t", "]"}]}], ",", RowBox[{ RowBox[{ SuperscriptBox["y", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", RowBox[{"b", "[", "t", "]"}]}], ",", RowBox[{ RowBox[{"x", "[", "0", "]"}], "\[Equal]", "0"}], ",", RowBox[{ RowBox[{"y", "[", "0", "]"}], "\[Equal]", "0"}], ",", RowBox[{ RowBox[{"a", "[", "0", "]"}], "\[Equal]", "1"}], ",", RowBox[{ RowBox[{"b", "[", "0", "]"}], "\[Equal]", RowBox[{"Rationalize", "[", RowBox[{ RowBox[{"N", "[", SqrtBox["2"], "]"}], ",", "0.1"}], "]"}]}], ",", RowBox[{"WhenEvent", "[", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"x", "[", "t", "]"}], "2"], "\[Equal]", "1"}], ",", RowBox[{ RowBox[{"a", "[", "t", "]"}], "\[Rule]", RowBox[{"-", RowBox[{"a", "[", "t", "]"}]}]}]}], "]"}], ",", RowBox[{"WhenEvent", "[", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"y", "[", "t", "]"}], "2"], "\[Equal]", "1"}], ",", RowBox[{ RowBox[{"b", "[", "t", "]"}], "\[Rule]", RowBox[{"-", RowBox[{"b", "[", "t", "]"}]}]}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "100"}], "}"}], ",", RowBox[{"DiscreteVariables", "\[Rule]", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.622389325421894*^9, 3.622389327886836*^9}, 3.6223893648609695`*^9, 3.6223894041752377`*^9, {3.6223894364378986`*^9, 3.6223894517735834`*^9}, {3.6223894939116144`*^9, 3.6223894950972824`*^9}, {3.622389557859703*^9, 3.6223895726337557`*^9}, { 3.6223896371868935`*^9, 3.622389644644123*^9}, 3.62239187712871*^9, { 3.6227999754774485`*^9, 3.622800026929217*^9}, {3.622800934082553*^9, 3.6228009511343365`*^9}, {3.6228237933586087`*^9, 3.6228238183356495`*^9}, {3.6228261503071833`*^9, 3.622826151867277*^9}}, CellID->5558107], Cell[BoxData[ RowBox[{"ParametricPlot", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"x", "[", "t", "]"}], ",", RowBox[{"y", "[", "t", "]"}]}], "}"}], "/.", "\[VeryThinSpace]", "sol"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "100"}], "}"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"FrameTicks", "\[Rule]", "None"}], ",", RowBox[{"PlotRange", "\[Rule]", "1"}], ",", RowBox[{"Axes", "\[Rule]", "False"}], ",", RowBox[{"PlotPoints", "\[Rule]", "300"}]}], "]"}]], "Input", CellChangeTimes->{{3.622389355890452*^9, 3.6223893714133472`*^9}, { 3.6223894209774065`*^9, 3.6223894297295113`*^9}, 3.6223918771911135`*^9, { 3.622800019206771*^9, 3.6228000193627806`*^9}, {3.6228009444415503`*^9, 3.622800945346402*^9}}, CellID->175288610] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Symbolic Summation", "Section", CellChangeTimes->{{3.621942830879348*^9, 3.621942836027645*^9}, { 3.622800224733028*^9, 3.622800233313523*^9}}], Cell[CellGroupData[{ Cell["Scope of Sum", "Subsection", ShowGroupOpener->True, CellChangeTimes->{{3.623072283524782*^9, 3.6230722848347297`*^9}, 3.623153053090457*^9}], Cell[TextData[{ ButtonBox["Sum", BaseStyle->"Link", ButtonData->"paclet:ref/Sum"], " can compute:" }], "Text", CellChangeTimes->{{3.3691474811256*^9, 3.3691475712205*^9}, { 3.36914767534684*^9, 3.36914768711261*^9}, {3.36914775209782*^9, 3.36914776289483*^9}, {3.36914782145808*^9, 3.36914782187996*^9}, 3.36914785930232*^9, {3.3693017674333115`*^9, 3.3693017685896425`*^9}, { 3.3799476906272397`*^9, 3.3799476913459854`*^9}, {3.3907557717906*^9, 3.3907557799625273`*^9}, 3.393348348022973*^9, {3.443467117567151*^9, 3.443467118815199*^9}, {3.4447369150924077`*^9, 3.4447369151080084`*^9}}], Cell[CellGroupData[{ Cell[" A wide variety of indefinite sums ", "Item", ShowGroupOpener->False, CellChangeTimes->{{3.4434671222473307`*^9, 3.4434671229649587`*^9}}], Cell["\<\ Definite sums over finite and infinite intervals \ \>", "Item", ShowGroupOpener->False, CellChangeTimes->{{3.4434671309992676`*^9, 3.443467132855739*^9}}], Cell["Multiple sums in an arbitrary number of dimensions", "Item", ShowGroupOpener->False, CellChangeTimes->{{3.443467137021099*^9, 3.4434671529025097`*^9}, { 3.443467199548304*^9, 3.44346721920506*^9}}], Cell[TextData[{ "Sums of piecewise functions, ", Cell[BoxData[ FormBox["q", TraditionalForm]]], "-functions, etc. " }], "Item", ShowGroupOpener->False] }, Open ]], Cell["", "Spacer"] }, Closed]], Cell[CellGroupData[{ Cell["Procedural vs Symbolic Summation", "Subsection", ShowGroupOpener->True, CellChangeTimes->{{3.4316963186960897`*^9, 3.4316963548270793`*^9}, { 3.4316964360906043`*^9, 3.431696438961115*^9}, 3.6222931329506903`*^9, { 3.62247938589857*^9, 3.622479395227908*^9}, 3.623153049514697*^9}], Cell[TextData[{ "The sum of the ", StyleBox["squares of the first thousand natural numbers", FontColor->GrayLevel[0]], " can be found as follows:" }], "Text"], Cell[BoxData[ RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"k", "=", "1"}], SuperscriptBox["10", "3"]], SuperscriptBox["k", "2"]}]], "Input", CellChangeTimes->{ 3.6223744395328865`*^9, 3.6223751846318707`*^9, 3.622384384743088*^9, { 3.6223871855500154`*^9, 3.6223871857996297`*^9}, {3.622390933143589*^9, 3.62239093524971*^9}, 3.6223918775655346`*^9, {3.6224830199500504`*^9, 3.6224830861440554`*^9}, {3.6225513925873713`*^9, 3.622551401823104*^9}, { 3.622800489003476*^9, 3.6228005317499423`*^9}, {3.6228207686702833`*^9, 3.6228207691383104`*^9}, {3.622826197159994*^9, 3.622826209490734*^9}, { 3.623071347592935*^9, 3.6230713523332195`*^9}}], Cell["The same answer can be obtained using symbolic summation:", "Text", CellChangeTimes->{{3.6223871472654066`*^9, 3.6223871710411787`*^9}, { 3.622387252587083*^9, 3.6223872614015913`*^9}}], Cell[BoxData[ RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"k", "=", "1"}], "n"], SuperscriptBox["k", "2"]}]], "Input", CellChangeTimes->{3.622374439564089*^9, 3.6223751846630726`*^9, 3.622384384774289*^9, 3.6223918776123376`*^9}], Cell[BoxData[ RowBox[{"%", "/.", "\[VeryThinSpace]", RowBox[{"{", RowBox[{"n", "\[Rule]", SuperscriptBox["10", "3"]}], "}"}]}]], "Input", CellChangeTimes->{ 3.62237443959529*^9, 3.6223751846942744`*^9, 3.6223843848210897`*^9, { 3.622387193865295*^9, 3.622387194005703*^9}, {3.6223909431905684`*^9, 3.622390945140681*^9}, 3.6223918776747413`*^9, {3.6224830282808247`*^9, 3.62248302929487*^9}, {3.622820780324156*^9, 3.622820780324156*^9}}], Cell[TextData[{ "There is a built-in threshold of ", Cell[BoxData[ FormBox[ SuperscriptBox["10", "6"], TraditionalForm]]], " beyond which symbolic summation is typically invoked. This threshold can \ be controlled using Method -> \[OpenCurlyDoubleQuote]Procedural\ \[CloseCurlyDoubleQuote]/\[CloseCurlyDoubleQuote]Symbolic\ \[CloseCurlyDoubleQuote]." }], "Text", CellChangeTimes->{{3.6224829496688967`*^9, 3.6224830011668077`*^9}, 3.6224831455366817`*^9, {3.622820816440239*^9, 3.622820836206579*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Infinite Hypergeometric Series", "Subsection", ShowGroupOpener->True, CellChangeTimes->{{3.4316963186960897`*^9, 3.4316963548270793`*^9}, { 3.4316964360906043`*^9, 3.431696438961115*^9}, 3.6222931329506903`*^9, { 3.62247938589857*^9, 3.622479395227908*^9}, {3.6224802217451363`*^9, 3.6224802288747473`*^9}, 3.6231530637871733`*^9}], Cell[TextData[{ StyleBox["Hypergeometric functions", FontColor->GrayLevel[0]], " often have simple expressions for certain discrete ranges of their \ parameters." }], "Text", CellChangeTimes->{{3.4444849229467964`*^9, 3.4444849465349035`*^9}, { 3.444484986113626*^9, 3.4444850032898865`*^9}, {3.444489246107634*^9, 3.4444892874336233`*^9}, {3.44448942308084*^9, 3.4444894294926867`*^9}, { 3.44448950367354*^9, 3.4444895111774282`*^9}}], Cell[BoxData[ RowBox[{"Hypergeometric2F1", "[", RowBox[{"a", ",", "b", ",", "c", ",", "x"}], "]"}]], "Input", CellChangeTimes->{ 3.622374439501685*^9, 3.622375184600669*^9, 3.6223843847118874`*^9, 3.622391877503131*^9, {3.6228001306596007`*^9, 3.622800151221587*^9}, 3.6228262224215097`*^9, {3.6230712234254856`*^9, 3.6230712438067083`*^9}}], Cell[TextData[{ StyleBox["Exercise", FontWeight->"Bold"], ": Find a value of the parameter \[OpenCurlyQuote]a\[CloseCurlyQuote] for \ which the above expression is a polynomial in \[OpenCurlyQuote]x\ \[CloseCurlyQuote]." }], "Text", CellChangeTimes->{{3.622825325884523*^9, 3.622825361672988*^9}, { 3.623071203484289*^9, 3.623071238286377*^9}, {3.623072319023362*^9, 3.6230723229232063`*^9}, {3.6231550444810038`*^9, 3.623155047269315*^9}}], Cell["\<\ Hypergeometric simplification is applied internally for evaluating series \ such as the following:\ \>", "Text", CellChangeTimes->{{3.6223870609768286`*^9, 3.622387084502986*^9}, { 3.622800358829567*^9, 3.62280041349512*^9}, {3.623071267688141*^9, 3.62307127249843*^9}}], Cell[BoxData[ RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"n", "=", "0"}], "\[Infinity]"], FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"2", "/", RowBox[{"(", RowBox[{"5", "E"}], ")"}]}], ")"}], "n"], " ", RowBox[{"Binomial", "[", RowBox[{ RowBox[{"2", " ", "n"}], ",", "n"}], "]"}]}], RowBox[{" ", RowBox[{"(", RowBox[{"n", "+", "3"}], ")"}]}]]}]], "Input", CellChangeTimes->{ 3.622391613546504*^9, 3.6223918777215443`*^9, 3.6224799968893642`*^9, { 3.6224800567656183`*^9, 3.622480058559722*^9}, {3.6224801501994085`*^9, 3.6224801653946853`*^9}, {3.622480311122692*^9, 3.6224803240246363`*^9}}], Cell["Before proceeding, let us verify the result numerically:", "Text", CellChangeTimes->{{3.6223870609768286`*^9, 3.622387084502986*^9}, { 3.622800358829567*^9, 3.62280041349512*^9}, {3.623071267688141*^9, 3.6230713115107703`*^9}, 3.6231475455574474`*^9}], Cell[BoxData[ RowBox[{"N", "[", "%", "]"}]], "Input", CellChangeTimes->{{3.622480177859804*^9, 3.6224801790922756`*^9}}], Cell[BoxData[ RowBox[{"NSum", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "/", "5"}], ")"}], "^", RowBox[{"(", "n", " ", ")"}]}], "*", RowBox[{"Binomial", "[", RowBox[{ RowBox[{"2", "*", "n"}], ",", " ", "n"}], "]"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"E", "^", "n"}], "*", RowBox[{"(", RowBox[{"n", " ", "+", " ", "3"}], ")"}]}], ")"}]}], ",", " ", RowBox[{"{", RowBox[{"n", ",", " ", "0", ",", " ", "Infinity"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.6224802017447824`*^9, 3.6224802045061417`*^9}}], Cell["\<\ The internal conversion to HypergeometricPFQ may be seen as follows:\ \>", "Text", CellChangeTimes->{{3.6224802464569616`*^9, 3.6224802706227555`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", "/", "5"}], ")"}], "^", RowBox[{"(", "n", " ", ")"}]}], "*", RowBox[{"Binomial", "[", RowBox[{ RowBox[{"2", "*", "n"}], ",", " ", "n"}], "]"}]}], ")"}], "/", RowBox[{"(", RowBox[{ RowBox[{"E", "^", "n"}], "*", RowBox[{"(", RowBox[{"n", " ", "+", " ", "3"}], ")"}]}], ")"}]}], ",", " ", RowBox[{"{", RowBox[{"n", ",", " ", "0", ",", " ", "Infinity"}], "}"}], ",", RowBox[{"Method", "\[Rule]", "\"\\""}]}], "]"}], "//", "TraditionalForm"}]], "Input", CellChangeTimes->{{3.622480008044008*^9, 3.6224800284655857`*^9}, { 3.6224800706660204`*^9, 3.622480071071644*^9}, {3.6224801684524612`*^9, 3.622480170246565*^9}, {3.622480330483409*^9, 3.6224803326519337`*^9}, { 3.623159991340968*^9, 3.6231600043486996`*^9}}], Cell[BoxData[ RowBox[{"Activate", "[", "%", "]"}]], "Input", CellChangeTimes->{{3.622480034175515*^9, 3.6224800370928836`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["The Calculus Navigator", "Subsection", ShowGroupOpener->True, CellChangeTimes->{{3.6219434182703376`*^9, 3.6219434317495155`*^9}, 3.622293307221146*^9, 3.6223873009654737`*^9, {3.622393036617771*^9, 3.622393037273009*^9}, {3.622480343213743*^9, 3.6224803531827183`*^9}, { 3.6228000754948187`*^9, 3.622800081547968*^9}, 3.623155058414172*^9}], Cell[TextData[{ "A poster for navigating Calculus functions in ", StyleBox["Mathematica", FontSlant->"Italic"], " is available ", ButtonBox["here", BaseStyle->"Hyperlink", ButtonData->{ URL["http://library.wolfram.com/infocenter/Courseware/8960/"], None}, ButtonNote->"http://library.wolfram.com/infocenter/Courseware/8960/"], "." }], "Text", CellChangeTimes->{{3.6223876216493053`*^9, 3.6223876370941963`*^9}, { 3.6223877150707307`*^9, 3.6223877185029287`*^9}, {3.62238779861355*^9, 3.622387802326565*^9}, {3.6223878428577027`*^9, 3.6223878428577027`*^9}, 3.62280011070605*^9, {3.62307152019088*^9, 3.6230715244811373`*^9}, { 3.623072399089344*^9, 3.623072399089344*^9}}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.622551442057825*^9}] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Vector Calculus", "Section"], Cell["Calculus on Fields: Grad, Div, Curl, Laplacian (9+)", "Subsection"], Cell["\<\ Calculus on Parametric Regions: ArcLength, ArcCurvature, FrenetSerretSystem, \ Area, Volume (10+)\ \>", "Subsection"], Cell[CellGroupData[{ Cell["\<\ Coordinate Systems: CoordinateChartData, CoordinateTransformData, \ TransformedField, CoordinateTransform (9+)\ \>", "Subsection"], Cell[TextData[{ "Structure of a coordinate system: ", Cell[BoxData[ FormBox[GridBox[{ {"{", "metric", ",", "chart", ",", RowBox[{"dim", " "}], "}"}, {" ", RowBox[{ "typically", " ", "omitted", " ", "if", " ", "in", " ", "Euclidean", " ", "space"}], " ", RowBox[{"always", " ", "needed"}], " ", RowBox[{ "typically", " ", "omitted", " ", "as", " ", "it", " ", "can", " ", "usually", " ", "be", " ", "inferred", " ", "from", " ", "other", " ", "arguments"}], " "} }], TraditionalForm]]], ", \n\nwhere metric and chart can each be either \[OpenCurlyDoubleQuote]name\ \[CloseCurlyDoubleQuote] or {\[OpenCurlyDoubleQuote]name\ \[CloseCurlyDoubleQuote], params}. " }], "Text"], Cell["Simple example (though note answer is an orthnormal basis):", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Grad", "[", RowBox[{ RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]"}], "]"}], ",", " ", RowBox[{"{", RowBox[{"r", ",", "\[Theta]"}], "}"}], ",", "\"\\""}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]"}], "]"}], ",", FractionBox[ RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"0", ",", "1"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]"}], "]"}], "r"]}], "}"}]], "Output"] }, Open ]], Cell["Here we need to specify the dimension:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CoordinateChartData", "[", RowBox[{ RowBox[{"{", RowBox[{"\"\\"", ",", "2"}], "}"}], ",", " ", "\"\\""}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"\[FormalAlpha]", ">", "\[FormalBeta]", ">", "0"}]], "Output"] }, Open ]], Cell["A Euclidean chart with a parameter specified", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ArcLength", "[", RowBox[{ RowBox[{"{", RowBox[{"t", ",", SuperscriptBox["t", "2"], ",", SqrtBox["t"]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"t", ",", ".5", ",", "1.5"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"{", "1", "}"}]}], "}"}], "}"}]}], "]"}]], "Input"], Cell[BoxData["3.518162612521188`"], "Output"] }, Open ]] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Assumptions", "Section"], Cell[CellGroupData[{ Cell["\<\ Integrate-like functions\[LongDash]ArcLength, Area, Volume\[LongDash]take and \ can really benefit from the Assumptions option.\ \>", "Item", CellChangeTimes->{{3.623155743760192*^9, 3.623155745271371*^9}}], Cell["\<\ D-like functions\[LongDash]Grad, Div, Curl, Laplacian, ArcCurvature, \ FrenetSerretSystem, TransformedField\[LongDash]do not take an Assumptions \ option.\ \>", "Item", CellChangeTimes->{{3.623155746551194*^9, 3.623155747703223*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Problem: Simplify the following formula for the length of a sine curve.\ \>", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ArcLength", "[", RowBox[{ RowBox[{"a", " ", RowBox[{"Sin", "[", RowBox[{"b", " ", "x"}], "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "c", ",", "d"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"ConditionalExpression", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SqrtBox[ RowBox[{"2", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "c"}], "]"}]}]}]]}], " ", SqrtBox[ FractionBox[ RowBox[{"2", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "d"}], "]"}]}]}], RowBox[{"1", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]}]]], " ", RowBox[{"EllipticE", "[", RowBox[{ RowBox[{"b", " ", "c"}], ",", FractionBox[ RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], RowBox[{"1", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]}]]}], "]"}]}], "+", RowBox[{ SqrtBox[ FractionBox[ RowBox[{"2", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "c"}], "]"}]}]}], RowBox[{"1", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]}]]], " ", SqrtBox[ RowBox[{"2", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "d"}], "]"}]}]}]], " ", RowBox[{"EllipticE", "[", RowBox[{ RowBox[{"b", " ", "d"}], ",", FractionBox[ RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], RowBox[{"1", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]}]]}], "]"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{"b", " ", SqrtBox[ FractionBox[ RowBox[{"2", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "c"}], "]"}]}]}], RowBox[{"1", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]}]]], " ", SqrtBox[ FractionBox[ RowBox[{"2", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "d"}], "]"}]}]}], RowBox[{"1", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]}]]]}], ")"}]}], ",", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[ RowBox[{"Cos", "[", RowBox[{"b", " ", "d"}], "]"}], "2"]}], "\[NotEqual]", RowBox[{"-", "1"}]}], "&&", RowBox[{"(", RowBox[{ RowBox[{"d", "<", "0"}], "||", RowBox[{"c", ">", "0"}]}], ")"}], "&&", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Re", "[", FractionBox[ RowBox[{"2", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "c"}], "]"}]}]}], RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "c"}], "]"}], "-", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "d"}], "]"}]}], ")"}]}]], "]"}], "<", "0"}], "||", RowBox[{ RowBox[{"Re", "[", FractionBox[ RowBox[{"2", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "c"}], "]"}]}]}], RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "c"}], "]"}], "-", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "d"}], "]"}]}], ")"}]}]], "]"}], ">", "1"}], "||", RowBox[{ FractionBox[ RowBox[{"2", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "c"}], "]"}]}]}], RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "c"}], "]"}], "-", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "d"}], "]"}]}], ")"}]}]], "\[NotElement]", "Reals"}]}], ")"}], "&&", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Re", "[", FractionBox[ RowBox[{"2", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "d"}], "]"}]}]}], RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "c"}], "]"}], "-", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "d"}], "]"}]}], ")"}]}]], "]"}], "<", RowBox[{"-", "1"}]}], "||", RowBox[{ RowBox[{"Re", "[", FractionBox[ RowBox[{"2", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "d"}], "]"}]}]}], RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "c"}], "]"}], "-", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "d"}], "]"}]}], ")"}]}]], "]"}], ">", "0"}], "||", RowBox[{ FractionBox[ RowBox[{"2", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "d"}], "]"}]}]}], RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "c"}], "]"}], "-", RowBox[{"Cos", "[", RowBox[{"2", " ", "b", " ", "d"}], "]"}]}], ")"}]}]], "\[NotElement]", "Reals"}]}], ")"}]}]}], "]"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Solution/Discussion", "Subsection"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " defaults to assuming that symbolic parameters are complex. When there are \ complicated conditions on real and imaginary parts, a good place to start is \ to assert that the parameters are real:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ArcLength", "[", RowBox[{ RowBox[{"a", " ", RowBox[{"Sin", "[", RowBox[{"b", " ", "x"}], "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "c", ",", "d"}], "}"}], ",", " ", RowBox[{"Assumptions", "\[Rule]", RowBox[{ RowBox[{"(", RowBox[{"a", "|", "b", "|", "c", "|", "d"}], ")"}], "\[Element]", "Reals"}]}]}], "]"}]], "Input"], Cell[BoxData[ FractionBox[ RowBox[{ SqrtBox[ RowBox[{"1", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]}]], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"EllipticE", "[", RowBox[{ RowBox[{"b", " ", "c"}], ",", RowBox[{"1", "-", FractionBox["1", RowBox[{"1", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]}]]}]}], "]"}]}], "+", RowBox[{"EllipticE", "[", RowBox[{ RowBox[{"b", " ", "d"}], ",", RowBox[{"1", "-", FractionBox["1", RowBox[{"1", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]}]]}]}], "]"}]}], ")"}]}], "b"]], "Output"] }, Open ]], Cell[TextData[{ "In this particular, we only need to put assumptions and ", Cell[BoxData[ FormBox["a", TraditionalForm]]], " and ", Cell[BoxData[ FormBox["b", TraditionalForm]]], ". This can be seen from the condition ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"d", "<", "0"}], " ", "||", " ", RowBox[{"c", ">", "0"}]}], TraditionalForm]]], ", which implies that ", Cell[BoxData[ FormBox["c", TraditionalForm]]], " and ", Cell[BoxData[ FormBox["d", TraditionalForm]]], " are real." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ArcLength", "[", RowBox[{ RowBox[{"a", " ", RowBox[{"Sin", "[", RowBox[{"b", " ", "x"}], "]"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "c", ",", "d"}], "}"}], ",", " ", RowBox[{"Assumptions", "\[Rule]", RowBox[{ RowBox[{"(", RowBox[{"a", "|", "b"}], ")"}], "\[Element]", "Reals"}]}]}], "]"}]], "Input"], Cell[BoxData[ FractionBox[ RowBox[{ SqrtBox[ RowBox[{"1", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]}]], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"EllipticE", "[", RowBox[{ RowBox[{"b", " ", "c"}], ",", RowBox[{"1", "-", FractionBox["1", RowBox[{"1", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]}]]}]}], "]"}]}], "+", RowBox[{"EllipticE", "[", RowBox[{ RowBox[{"b", " ", "d"}], ",", RowBox[{"1", "-", FractionBox["1", RowBox[{"1", "+", RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]}]]}]}], "]"}]}], ")"}]}], "b"]], "Output"] }, Open ]], Cell["\<\ Good assumptions can be so important to integration that ArcLength (and \ Area/Volume) will attempt to add useful assumptions automatically:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ArcLength", "[", RowBox[{ RowBox[{"f", "[", "x", "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "c", ",", "d"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ SqrtBox[ RowBox[{"1", "+", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "x", "]"}], "2"]}]], ",", RowBox[{"{", RowBox[{"x", ",", "c", ",", "d"}], "}"}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{"c", "<", "d"}]}]}], "]"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ArcLength", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"f", "[", "t", "]"}], ",", RowBox[{"g", "[", "t", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", "c", ",", "d"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"{", RowBox[{"\"\\"", ",", "a"}], "}"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ SqrtBox[ RowBox[{ RowBox[{ FractionBox["1", "2"], " ", SuperscriptBox["a", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"Cos", "[", RowBox[{"2", " ", RowBox[{"g", "[", "t", "]"}]}], "]"}]}], "+", RowBox[{"Cosh", "[", RowBox[{"2", " ", RowBox[{"f", "[", "t", "]"}]}], "]"}]}], ")"}], " ", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "2"]}], "+", RowBox[{ FractionBox["1", "2"], " ", SuperscriptBox["a", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{"Cos", "[", RowBox[{"2", " ", RowBox[{"g", "[", "t", "]"}]}], "]"}]}], "+", RowBox[{"Cosh", "[", RowBox[{"2", " ", RowBox[{"f", "[", "t", "]"}]}], "]"}]}], ")"}], " ", SuperscriptBox[ RowBox[{ SuperscriptBox["g", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "2"]}]}]], ",", RowBox[{"{", RowBox[{"t", ",", "c", ",", "d"}], "}"}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{ RowBox[{"c", "<", "d"}], "&&", RowBox[{"a", ">", "0"}]}]}]}], "]"}]], "Output"] }, Open ]], Cell["\<\ Note that the condition that the endpoints are order isn\[CloseCurlyQuote]t \ just useful, it\[CloseCurlyQuote]s necessary for a correct answer:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ArcLength", "[", RowBox[{ RowBox[{"f", "[", "x", "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "1", ",", "0"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"-", RowBox[{ SubsuperscriptBox["\[Integral]", "1", "0"], RowBox[{ SqrtBox[ RowBox[{"1", "+", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "x", "]"}], "2"]}]], RowBox[{"\[DifferentialD]", "x"}]}]}]}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Homework (Needs 10.0.2): Simplify the following formula for the area of an \ ellipse with semi-major axes of length ", Cell[BoxData[ FormBox["a", TraditionalForm]], "None"], " and ", Cell[BoxData[ FormBox["b", TraditionalForm]], "None"], "." }], "Subsection", CellChangeTimes->{{3.623155018998558*^9, 3.623155020189106*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Area", "[", RowBox[{ RowBox[{"{", RowBox[{"r", ",", "v"}], "}"}], ",", RowBox[{"{", RowBox[{"r", ",", "0", ",", RowBox[{"ArcSech", "[", SqrtBox[ RowBox[{"1", "-", FractionBox[ SuperscriptBox["b", "2"], SuperscriptBox["a", "2"]]}]], "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"v", ",", " ", "0", ",", " ", RowBox[{"2", "Pi"}]}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"\"\\"", ",", SqrtBox[ RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]}]]}], "}"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"-", FractionBox["1", "2"]}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]}], ")"}], " ", "\[Pi]", " ", RowBox[{"Sinh", "[", RowBox[{ RowBox[{"Log", "[", RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]}], "]"}], "-", RowBox[{"2", " ", RowBox[{"Log", "[", RowBox[{ RowBox[{"Abs", "[", "a", "]"}], "+", RowBox[{"Abs", "[", "b", "]"}]}], "]"}]}]}], "]"}]}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Homework solution", "Subsection"], Cell[TextData[{ "The presence of ", Cell[BoxData[ FormBox[ RowBox[{"Abs", "[", "a", "]"}], TraditionalForm]]], " and ", Cell[BoxData[ FormBox[ RowBox[{"Abs", "[", "b", "]"}], TraditionalForm]]], " strongly suggest the need to add the conditions ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"a", ">", "0"}], "&&", " ", RowBox[{"b", ">", "0"}]}], TraditionalForm]]], " (they are lengths):" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Area", "[", RowBox[{ RowBox[{"{", RowBox[{"r", ",", "v"}], "}"}], ",", RowBox[{"{", RowBox[{"r", ",", "0", ",", RowBox[{"ArcSech", "[", SqrtBox[ RowBox[{"1", "-", FractionBox[ SuperscriptBox["b", "2"], SuperscriptBox["a", "2"]]}]], "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"v", ",", " ", "0", ",", " ", RowBox[{"2", "Pi"}]}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"\"\\"", ",", SqrtBox[ RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]}]]}], "}"}], "}"}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{ RowBox[{"a", ">", "0"}], "&&", RowBox[{"b", ">", "0"}]}]}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"a", " ", "b", " ", "\[Pi]"}]], "Output"] }, Open ]], Cell[TextData[{ "Your exact starting point can affect the needed assumptions. For example, \ here we only need the assumption ", Cell[BoxData[ FormBox[ RowBox[{"b", ">", "0"}], TraditionalForm]]], " (why?):" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Area", "[", RowBox[{ RowBox[{"{", RowBox[{"r", ",", "v"}], "}"}], ",", RowBox[{"{", RowBox[{"r", ",", "0", ",", RowBox[{"ArcSech", "[", SqrtBox[ RowBox[{"1", "-", FractionBox[ SuperscriptBox["b", "2"], SuperscriptBox["a", "2"]]}]], "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"v", ",", " ", "0", ",", " ", RowBox[{"2", "Pi"}]}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"a", SqrtBox[ RowBox[{"1", "-", FractionBox[ SuperscriptBox["b", "2"], SuperscriptBox["a", "2"]]}]]}]}], "}"}], "}"}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{"b", ">", "0"}]}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"a", " ", "b", " ", "\[Pi]"}]], "Output"] }, Open ]], Cell["\<\ Had we used a direct parametrization of an ellipse, our starting point would \ have been much simpler:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Area", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"a", " ", "r", " ", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], ",", " ", RowBox[{"b", " ", "r", " ", RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"\[Theta]", ",", "0", ",", RowBox[{"2", "Pi"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"r", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{ SqrtBox[ RowBox[{ SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]}]], " ", "\[Pi]"}]], "Output"] }, Open ]], Cell[TextData[{ "But note that even this needs the assumptions on ", Cell[BoxData[ FormBox["a", TraditionalForm]]], " and ", Cell[BoxData[ FormBox["b", TraditionalForm]]], " to fully simplify:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Area", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"a", " ", "r", " ", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], ",", " ", RowBox[{"b", " ", "r", " ", RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"\[Theta]", ",", "0", ",", RowBox[{"2", "Pi"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"r", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{ RowBox[{"a", ">", "0"}], "&&", RowBox[{"b", ">", "0"}]}]}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"a", " ", "b", " ", "\[Pi]"}]], "Output"] }, Open ]], Cell[TextData[{ "Finally, had we entered a ", ButtonBox["disk region with two radii", BaseStyle->"Link", ButtonData->"ref/Disk"], ", the assumptions that ", Cell[BoxData[ FormBox["a", TraditionalForm]]], " and ", Cell[BoxData[ FormBox["b", TraditionalForm]]], " are positive would have been inferred from their meaning as radii:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Area", "[", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"a", " ", "b", " ", "\[Pi]"}]], "Output"] }, Open ]] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Spherical Harmonics", "Section"], Cell[CellGroupData[{ Cell["\<\ Problem: Show that spherical harmonics are eigenfunctions of the Laplacian\ \>", "Subsection"], Cell["\<\ It is a well known fact that the spherical harmonics are eigenfunctions of \ the Laplacian on the sphere. That means \ \>", "Text"], Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{ RowBox[{ UnderscriptBox[ SuperscriptBox["\[Del]", "2"], "sphere"], RowBox[{ SubsuperscriptBox["Y", "l", "m"], "(", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], ")"}]}], "\[LongEqual]", RowBox[{"constant", " ", RowBox[{ SubsuperscriptBox["Y", "l", "m"], "(", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], ")"}]}]}]}], TraditionalForm]], "Input", Evaluateable -> False], Cell["\<\ One way to show this is to divide by the Laplacian by the original function. \ For example:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Table", "[", RowBox[{ FractionBox[ RowBox[{"Laplacian", "[", RowBox[{ RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "0", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], "}"}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "1"}], "}"}]}], "}"}]}], "]"}], RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "0", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]], ",", RowBox[{"{", RowBox[{"l", ",", "0", ",", "4"}], "}"}]}], "]"}], "//", "Simplify"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "2"}], ",", RowBox[{"-", "6"}], ",", RowBox[{"-", "12"}], ",", RowBox[{"-", "20"}]}], "}"}]], "Output"] }, Open ]], Cell["However, the Laplacian looks like this:", "Text"], Cell[BoxData[ RowBox[{"Laplacian", "[", RowBox[{ RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], "}"}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "1"}], "}"}]}], "}"}]}], "]"}]], "Input"], Cell[TextData[{ "And dividing by ", Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["Y", "l", "m"], "(", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], ")"}], TraditionalForm]], CellChangeTimes->{{3.622563571937787*^9, 3.622563633395677*^9}}, Evaluateable -> False], " doesn\[CloseCurlyQuote]t simplify it very much (as in, at all):" }], "Text"], Cell[BoxData[ RowBox[{"%", "/", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}]], "Input"], Cell["How can this be simplified?", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Solution/discussion", "Subsection"], Cell["With no assumptions, FullSimplify does a reasonable job:", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearSystemCache", "[", "]"}], "\n", RowBox[{"AbsoluteTiming", "[", RowBox[{"noAssums", "=", RowBox[{"TimeConstrained", "[", RowBox[{ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"Laplacian", "[", RowBox[{ RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], "}"}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "1"}], "}"}]}], "}"}]}], "]"}], "/", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], "]"}], ",", "30"}], "]"}]}], "]"}]}], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"10.29972700000000074282979767303913831711`7.03342562692025", ",", RowBox[{ RowBox[{ RowBox[{"-", "m"}], " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}]}], "+", FractionBox[ RowBox[{ RowBox[{"LegendreP", "[", RowBox[{"l", ",", RowBox[{"2", "+", "m"}], ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}], " ", RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{"Csc", "[", "\[Theta]", "]"}], " ", RowBox[{"LegendreP", "[", RowBox[{"l", ",", RowBox[{"1", "+", "m"}], ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}], " ", SqrtBox[ SuperscriptBox[ RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]]}]}], RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]]}]}], "}"}]], "Output"] }, Open ]], Cell["\<\ If we just put assumptions on the angles, it will take a really long time and \ I wasn\[CloseCurlyQuote]t willing to wait for more than 10 minutes:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearSystemCache", "[", "]"}], "\n", RowBox[{"AbsoluteTiming", "[", RowBox[{"angleAssums", "=", RowBox[{"TimeConstrained", "[", RowBox[{ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{ RowBox[{"Laplacian", "[", RowBox[{ RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], "}"}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "1"}], "}"}]}], "}"}]}], "]"}], "/", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], ",", RowBox[{ RowBox[{"0", "<", "\[Theta]", "<", "Pi"}], "&&", RowBox[{ RowBox[{"-", "Pi"}], "<", "\[CurlyPhi]", "<", "Pi"}]}]}], "]"}], ",", "600"}], "]"}]}], "]"}]}], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "600.06431199999997261329554021358489990234`8.798797711746513", ",", "$Aborted"}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "If we just put in the conditions on ", StyleBox["l", FontSlant->"Italic"], " and ", StyleBox["m", FontSlant->"Italic"], ", the run time increases but a factor of 3, but all we get is from the \ effort is a common demoniator:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearSystemCache", "[", "]"}], "\n", RowBox[{"AbsoluteTiming", "[", RowBox[{"lmRangeAssums", "=", RowBox[{"TimeConstrained", "[", RowBox[{ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{ RowBox[{"Laplacian", "[", RowBox[{ RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], "}"}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "1"}], "}"}]}], "}"}]}], "]"}], "/", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], ",", RowBox[{ RowBox[{"-", "l"}], "<", "m", "<", "l"}]}], "]"}], ",", "600"}], "]"}]}], "]"}]}], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "31.62133800000000150021151057444512844086`7.520580155653892", ",", RowBox[{ FractionBox["1", RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "m"}], " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}], " ", RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], "+", RowBox[{"LegendreP", "[", RowBox[{"l", ",", RowBox[{"2", "+", "m"}], ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}], " ", RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{"Csc", "[", "\[Theta]", "]"}], " ", RowBox[{"LegendreP", "[", RowBox[{"l", ",", RowBox[{"1", "+", "m"}], ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}], " ", SqrtBox[ SuperscriptBox[ RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]]}]}], ")"}]}]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearSystemCache", "[", "]"}], "\n", RowBox[{"AbsoluteTiming", "[", RowBox[{"lmRangeIntegerAssums", "=", RowBox[{"TimeConstrained", "[", RowBox[{ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{ RowBox[{"Laplacian", "[", RowBox[{ RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], "}"}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "1"}], "}"}]}], "}"}]}], "]"}], "/", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"l", "|", "m"}], ")"}], "\[Element]", "Integers"}], "&&", RowBox[{ RowBox[{"-", "l"}], "<", "m", "<", "l"}]}]}], "]"}], ",", "600"}], "]"}]}], "]"}]}], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "39.55385199999999912279236014001071453094`7.617788697469397", ",", RowBox[{ FractionBox["1", RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "m"}], " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}], " ", RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], "+", RowBox[{"LegendreP", "[", RowBox[{"l", ",", RowBox[{"2", "+", "m"}], ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}], " ", RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{"Csc", "[", "\[Theta]", "]"}], " ", RowBox[{"LegendreP", "[", RowBox[{"l", ",", RowBox[{"1", "+", "m"}], ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}], " ", SqrtBox[ SuperscriptBox[ RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]]}]}], ")"}]}]}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "Lest you think the assumption is ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"{", RowBox[{"l", ",", "m"}], "}"}], "\[Element]", "\[DoubleStruckCapitalZ]"}], TraditionalForm]]], " is superfluous, the ", Cell[BoxData[ FormBox[ SubsuperscriptBox["Y", "m", "l"], TraditionalForm]]], " are perfectly analytic in ", Cell[BoxData[ FormBox["l", TraditionalForm]]], " and ", Cell[BoxData[ FormBox["m", TraditionalForm]]], ":" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"SphericalHarmonicY", "[", RowBox[{ SqrtBox["2"], ",", ".35", ",", RowBox[{"Pi", "/", "2"}], ",", "0"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"-", "0.29443433113246553`"}]], "Output"] }, Open ]], Cell["\<\ But if we combine the assumptions, we get something that returns quickly and \ is simpler:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearSystemCache", "[", "]"}], "\n", RowBox[{"AbsoluteTiming", "[", RowBox[{"lmRangeAngleAssums", "=", RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{ RowBox[{"Laplacian", "[", RowBox[{ RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], "}"}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "1"}], "}"}]}], "}"}]}], "]"}], "/", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], ",", RowBox[{ RowBox[{ RowBox[{"-", "l"}], "<", "m", "<", "l"}], "&&", RowBox[{"0", "<", "\[Theta]", "<", "Pi"}], "&&", RowBox[{ RowBox[{"-", "Pi"}], "<", "\[CurlyPhi]", "<", "Pi"}]}]}], "]"}]}], "]"}]}], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"5.43814400000000031099034458748064935207`6.756050616637282", ",", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "m"}], " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}], " ", RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}], " ", RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{"LegendreP", "[", RowBox[{"l", ",", RowBox[{"1", "+", "m"}], ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], "+", RowBox[{"LegendreP", "[", RowBox[{"l", ",", RowBox[{"2", "+", "m"}], ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearSystemCache", "[", "]"}], "\n", RowBox[{"AbsoluteTiming", "[", RowBox[{"fullAssums", "=", RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{ RowBox[{"Laplacian", "[", RowBox[{ RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], "}"}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "1"}], "}"}]}], "}"}]}], "]"}], "/", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"l", "|", "m"}], ")"}], "\[Element]", "Integers"}], "&&", RowBox[{ RowBox[{"-", "l"}], "<", "m", "<", "l"}], "&&", RowBox[{"0", "<", "\[Theta]", "<", "Pi"}], "&&", RowBox[{ RowBox[{"-", "Pi"}], "<", "\[CurlyPhi]", "<", "Pi"}]}]}], "]"}]}], "]"}]}], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"5.66672499999999956799001665785908699036`6.773932050593715", ",", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "m"}], " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}], " ", RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}], " ", RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{"LegendreP", "[", RowBox[{"l", ",", RowBox[{"1", "+", "m"}], ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], "+", RowBox[{"LegendreP", "[", RowBox[{"l", ",", RowBox[{"2", "+", "m"}], ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]]}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "In this particular case, the assumption the ", Cell[BoxData[ FormBox["l", TraditionalForm]]], " and ", Cell[BoxData[ FormBox["m", TraditionalForm]]], " are integers was not particularly helpful:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"lmRangeAngleAssums", "===", "fullAssums"}]], "Input"], Cell[BoxData["True"], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Bonus: how to get the desired answer", "Subsection"], Cell["\<\ We need to apply the recurrence relation obeyed by LegendreP at the right \ moment. That moment is the answer we got with the full assumptions. The \ function Simplify`SimplifyRecurrence will do this for us:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Simplify`SimplifyRecurrence", "@", "fullAssums"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"-", "m"}], " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}], " ", RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "l", "-", "m"}], ")"}], " ", SqrtBox[ RowBox[{"1", "-", RowBox[{"Cos", "[", "\[Theta]", "]"}]}]], " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"Cos", "[", "\[Theta]", "]"}]}]], " ", RowBox[{"LegendreP", "[", RowBox[{ RowBox[{"1", "+", "l"}], ",", "m", ",", "2", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], "+", RowBox[{ RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", RowBox[{"LegendreP", "[", RowBox[{ RowBox[{"1", "+", "l"}], ",", RowBox[{"1", "+", "m"}], ",", "2", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "l", "-", "m"}], ")"}], " ", RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", RowBox[{"LegendreP", "[", RowBox[{ RowBox[{"1", "+", "l"}], ",", "m", ",", "2", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], RowBox[{"1", "+", "l", "+", "m"}]], "-", FractionBox[ RowBox[{ SqrtBox[ RowBox[{"1", "-", RowBox[{"Cos", "[", "\[Theta]", "]"}]}]], " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"Cos", "[", "\[Theta]", "]"}]}]], " ", RowBox[{"LegendreP", "[", RowBox[{ RowBox[{"1", "+", "l"}], ",", RowBox[{"1", "+", "m"}], ",", "2", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], RowBox[{"1", "+", "l", "+", "m"}]]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "-", RowBox[{"3", " ", "l", " ", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "-", RowBox[{ SuperscriptBox["l", "2"], " ", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "+", RowBox[{"m", " ", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "+", RowBox[{ SuperscriptBox["m", "2"], " ", RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}], ")"}], " ", RowBox[{"LegendreP", "[", RowBox[{ RowBox[{"1", "+", "l"}], ",", "m", ",", "2", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"l", "-", "m", "-", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"]}], "-", RowBox[{"l", " ", SuperscriptBox[ RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"]}], "-", RowBox[{"m", " ", SuperscriptBox[ RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"]}]}], ")"}], " ", RowBox[{"LegendreP", "[", RowBox[{ RowBox[{"1", "+", "l"}], ",", RowBox[{"1", "+", "m"}], ",", "2", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], RowBox[{ SqrtBox[ RowBox[{"1", "-", RowBox[{"Cos", "[", "\[Theta]", "]"}]}]], " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"Cos", "[", "\[Theta]", "]"}]}]]}]]}], ")"}], "/", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "l", "-", "m"}], ")"}], " ", RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", RowBox[{"LegendreP", "[", RowBox[{ RowBox[{"1", "+", "l"}], ",", "m", ",", "2", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], RowBox[{"1", "+", "l", "+", "m"}]], "-", FractionBox[ RowBox[{ SqrtBox[ RowBox[{"1", "-", RowBox[{"Cos", "[", "\[Theta]", "]"}]}]], " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"Cos", "[", "\[Theta]", "]"}]}]], " ", RowBox[{"LegendreP", "[", RowBox[{ RowBox[{"1", "+", "l"}], ",", RowBox[{"1", "+", "m"}], ",", "2", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], RowBox[{"1", "+", "l", "+", "m"}]]}], ")"}]}]}]], "Output"] }, Open ]], Cell["We can now simplify down to an obvious constant:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{" ", RowBox[{ RowBox[{"Simplify", "[", RowBox[{"%", ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"l", "|", "m"}], ")"}], "\[Element]", "Integers"}], "&&", RowBox[{ RowBox[{"-", "l"}], "<", "m", "<", "l"}], "&&", RowBox[{"0", "<", "\[Theta]", "<", "Pi"}], "&&", RowBox[{ RowBox[{"-", "Pi"}], "<", "\[CurlyPhi]", "<", "Pi"}]}]}], "]"}], "//", "TraditionalForm"}]}]], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"-", "l"}], " ", RowBox[{"(", RowBox[{"l", "+", "1"}], ")"}]}], TraditionalForm]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Homework", "Subsection"], Cell[TextData[{ "Assuming the functions ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["f", RowBox[{"n", "\[InvisibleSpace]", "l", "\[InvisibleSpace]", "m"}]], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], " ", ":=", RowBox[{ RowBox[{ SubscriptBox["R", RowBox[{"n", "\[InvisibleSpace]", "l"}]], "[", "r", "]"}], RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}]}], TraditionalForm]], "None"], " are eigenfunctions of the Laplacian in three-dimensional space, find the \ form of the functions ", Cell[BoxData[ FormBox[ SubscriptBox["R", RowBox[{"n", "\[InvisibleSpace]", RowBox[{"l", "[", "r", "]"}]}]], TraditionalForm]], "None"], ". " }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Homework solution", "Subsection"], Cell[TextData[{ "We wish to show ", Cell[BoxData[ FormBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["\[Del]", "2"], RowBox[{ SubscriptBox["f", RowBox[{"n", "\[InvisibleSpace]", "l", "\[InvisibleSpace]", "m"}]], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], RowBox[{" ", RowBox[{ SubscriptBox["f", RowBox[{"n", "\[InvisibleSpace]", "l", "\[InvisibleSpace]", "m"}]], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}]], "=", "\[Lambda]"}], TraditionalForm]]], " for some constant ", Cell[BoxData[ FormBox["\[Lambda]", TraditionalForm]]], " which might depend on ", Cell[BoxData[ FormBox["n", TraditionalForm]]], ", ", Cell[BoxData[ FormBox["l", TraditionalForm]]], ", and ", Cell[BoxData[ FormBox["m", TraditionalForm]]], ". So we begin by substituing a generic function ", Cell[BoxData[ FormBox[ RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], TraditionalForm]]], ":" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"eqn", " ", "=", " ", RowBox[{"Expand", "[", RowBox[{ RowBox[{ RowBox[{"Laplacian", "[", RowBox[{ RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], ",", RowBox[{"{", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "}"}], ",", "\"\\""}], "]"}], "/", RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], "\[Equal]", "\[Lambda]"}], "]"}]}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"Csc", "[", "\[Theta]", "]"}], "2"], " ", RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"0", ",", "0", ",", "2"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], RowBox[{ SuperscriptBox["r", "2"], " ", RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}]], "+", FractionBox[ RowBox[{ RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"0", ",", "1", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], RowBox[{ SuperscriptBox["r", "2"], " ", RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"0", ",", "2", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], RowBox[{ SuperscriptBox["r", "2"], " ", RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}]], "+", FractionBox[ RowBox[{"2", " ", RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"1", ",", "0", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], RowBox[{"r", " ", RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"2", ",", "0", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]]}], "\[Equal]", "\[Lambda]"}]], "Output"] }, Open ]], Cell["At this point we can either use brute force or be clever. ", "Text"], Cell[CellGroupData[{ Cell["Brute force:", "Subsubsection"], Cell[TextData[{ "The obvious next step is to substitute in our form for the function ", Cell[BoxData[ FormBox["f", TraditionalForm]]], ". Because there are derivatives, it is important that we substitute it in \ a as a function ", Cell[BoxData[ FormBox["f", TraditionalForm]]], " rather than as an expression ", Cell[BoxData[ FormBox[ RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], TraditionalForm]]], ". We therefore use ", ButtonBox["pure function", BaseStyle->"Link", ButtonData->"ref/Function"], " notation with ", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "}"}], TraditionalForm]]], " replaced by ", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{"#1", ",", "#2", ",", "#3"}], "}"}], TraditionalForm]]], ":" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"eqn", "/.", " ", RowBox[{"f", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"R", "[", "#1", "]"}], RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "#2", ",", "#3"}], "]"}]}], "&"}], ")"}]}]}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{ SuperscriptBox["m", "2"], " ", SuperscriptBox[ RowBox[{"Csc", "[", "\[Theta]", "]"}], "2"]}], SuperscriptBox["r", "2"]]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"m", " ", RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], "+", FractionBox[ RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "\[CurlyPhi]"}]], " ", SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"1", "+", "l", "-", "m"}], "]"}]], " ", SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"2", "+", "l", "+", "m"}], "]"}]], " ", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", RowBox[{"1", "+", "m"}], ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], RowBox[{ SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"l", "-", "m"}], "]"}]], " ", SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"1", "+", "l", "+", "m"}], "]"}]]}]]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ SuperscriptBox["r", "2"], " ", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], ")"}]}], "+", RowBox[{ FractionBox["1", RowBox[{ SuperscriptBox["r", "2"], " ", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "m"}], " ", SuperscriptBox[ RowBox[{"Csc", "[", "\[Theta]", "]"}], "2"], " ", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], "+", RowBox[{"m", " ", RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"m", " ", RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], "+", FractionBox[ RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "\[CurlyPhi]"}]], " ", SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"1", "+", "l", "-", "m"}], "]"}]], " ", SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"2", "+", "l", "+", "m"}], "]"}]], " ", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", RowBox[{"1", "+", "m"}], ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], RowBox[{ SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"l", "-", "m"}], "]"}]], " ", SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"1", "+", "l", "+", "m"}], "]"}]]}]]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "\[CurlyPhi]"}]], " ", SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"1", "+", "l", "-", "m"}], "]"}]], " ", SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"2", "+", "l", "+", "m"}], "]"}]], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}], " ", RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", RowBox[{"1", "+", "m"}], ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], "+", FractionBox[ RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "\[CurlyPhi]"}]], " ", SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"l", "-", "m"}], "]"}]], " ", SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"3", "+", "l", "+", "m"}], "]"}]], " ", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", RowBox[{"2", "+", "m"}], ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], RowBox[{ SqrtBox[ RowBox[{"Gamma", "[", RowBox[{ RowBox[{"-", "1"}], "+", "l", "-", "m"}], "]"}]], " ", SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"2", "+", "l", "+", "m"}], "]"}]]}]]}], ")"}]}], ")"}], "/", RowBox[{"(", RowBox[{ SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"l", "-", "m"}], "]"}]], " ", SqrtBox[ RowBox[{"Gamma", "[", RowBox[{"1", "+", "l", "+", "m"}], "]"}]]}], ")"}]}]}], ")"}]}], "+", FractionBox[ RowBox[{"2", " ", RowBox[{ SuperscriptBox["R", "\[Prime]", MultilineFunction->None], "[", "r", "]"}]}], RowBox[{"r", " ", RowBox[{"R", "[", "r", "]"}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox["R", "\[Prime]\[Prime]", MultilineFunction->None], "[", "r", "]"}], RowBox[{"R", "[", "r", "]"}]]}], "\[Equal]", "\[Lambda]"}]], "Output"] }, Open ]], Cell["\<\ We now have something that looks like similar to the spherical harmonic \ equations we saw above. We therefore try to simplify it:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FullSimplify", "[", RowBox[{"%", ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"l", "|", "m"}], ")"}], "\[Element]", "Integers"}], "&&", RowBox[{ RowBox[{"-", "l"}], "<", "m", "<", "l"}], "&&", RowBox[{"0", "<", "\[Theta]", "<", "Pi"}], "&&", RowBox[{ RowBox[{"-", "Pi"}], "<", "\[CurlyPhi]", "<", "Pi"}]}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}], " ", RowBox[{"Cot", "[", "\[Theta]", "]"}], " ", RowBox[{"LegendreP", "[", RowBox[{"l", ",", RowBox[{"1", "+", "m"}], ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], "+", RowBox[{"LegendreP", "[", RowBox[{"l", ",", RowBox[{"2", "+", "m"}], ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}]}], ")"}], " ", RowBox[{"R", "[", "r", "]"}]}], "+", RowBox[{"r", " ", RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{ SuperscriptBox["R", "\[Prime]", MultilineFunction->None], "[", "r", "]"}]}], "+", RowBox[{"r", " ", RowBox[{ SuperscriptBox["R", "\[Prime]\[Prime]", MultilineFunction->None], "[", "r", "]"}]}]}], ")"}]}]}], ")"}], "/", RowBox[{"(", RowBox[{ SuperscriptBox["r", "2"], " ", RowBox[{"LegendreP", "[", RowBox[{"l", ",", "m", ",", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], "]"}], " ", RowBox[{"R", "[", "r", "]"}]}], ")"}]}], "\[Equal]", RowBox[{ FractionBox[ RowBox[{"m", " ", RowBox[{"(", RowBox[{"1", "+", "m"}], ")"}]}], SuperscriptBox["r", "2"]], "+", "\[Lambda]"}]}]], "Output"] }, Open ]], Cell["\<\ Progress, but we still haven\[CloseCurlyQuote]t gotten all the way to \ something that only depends on r. So let us try SimplifyRecurrence followed \ by another Simplify as was done above:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Reqn", " ", "=", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"Simplify`SimplifyRecurrence", "[", "%", "]"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"l", "|", "m"}], ")"}], "\[Element]", "Integers"}], "&&", RowBox[{ RowBox[{"-", "l"}], "<", "m", "<", "l"}], "&&", RowBox[{"0", "<", "\[Theta]", "<", "Pi"}], "&&", RowBox[{ RowBox[{"-", "Pi"}], "<", "\[CurlyPhi]", "<", "Pi"}]}]}], "]"}]}]], "Input"], Cell[BoxData[ RowBox[{ FractionBox[ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"l", "+", SuperscriptBox["l", "2"], "+", RowBox[{ SuperscriptBox["r", "2"], " ", "\[Lambda]"}]}], ")"}], " ", RowBox[{"R", "[", "r", "]"}]}], "-", RowBox[{"r", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{ SuperscriptBox["R", "\[Prime]", MultilineFunction->None], "[", "r", "]"}]}], "+", RowBox[{"r", " ", RowBox[{ SuperscriptBox["R", "\[Prime]\[Prime]", MultilineFunction->None], "[", "r", "]"}]}]}], ")"}]}]}], RowBox[{"r", " ", RowBox[{"R", "[", "r", "]"}]}]], "\[Equal]", "0"}]], "Output"] }, Open ]], Cell["\<\ Or, rearranged to its traditional form, we see a spherical Bessel equation:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"MapAt", "[", RowBox[{"Expand", ",", RowBox[{"-", " ", RowBox[{"Simplify", "[", RowBox[{ RowBox[{"First", "[", "Reqn", "]"}], " ", "r", " ", RowBox[{"R", "[", "r", "]"}]}], "]"}]}], ",", "2"}], "]"}], "\[Equal]", "0"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"l", "+", SuperscriptBox["l", "2"], "+", RowBox[{ SuperscriptBox["r", "2"], " ", "\[Lambda]"}]}], ")"}]}], " ", RowBox[{"R", "[", "r", "]"}]}], "+", RowBox[{"2", " ", "r", " ", RowBox[{ SuperscriptBox["R", "\[Prime]", MultilineFunction->None], "[", "r", "]"}]}], "+", RowBox[{ SuperscriptBox["r", "2"], " ", RowBox[{ SuperscriptBox["R", "\[Prime]\[Prime]", MultilineFunction->None], "[", "r", "]"}]}]}], "\[Equal]", "0"}]], "Output"] }, Open ]], Cell[TextData[{ "As it is a well known 2nd-order ODE, ", ButtonBox["DSolve ", BaseStyle->"Link", ButtonData->"paclet:ref/DSolve"], "can quickly return an answer in terms of known special functions:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DSolve", "[", RowBox[{"Reqn", ",", RowBox[{"R", "[", "r", "]"}], ",", "r"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"R", "[", "r", "]"}], "\[Rule]", RowBox[{ RowBox[{ RowBox[{"C", "[", "1", "]"}], " ", RowBox[{"SphericalBesselJ", "[", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "-", "l"}], ",", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "r", " ", SqrtBox["\[Lambda]"]}]}], "]"}]}], "+", RowBox[{ RowBox[{"C", "[", "2", "]"}], " ", RowBox[{"SphericalBesselY", "[", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "-", "l"}], ",", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "r", " ", SqrtBox["\[Lambda]"]}]}], "]"}]}]}]}], "}"}], "}"}]], "Output"] }, Open ]], Cell["\<\ Spherical Bessel functions are really just particular combinations of \ \[OpenCurlyDoubleQuote]ordinary\[CloseCurlyDoubleQuote] Bessel functions.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Simplify", "[", RowBox[{"%", "//", "FunctionExpand"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"R", "[", "r", "]"}], "\[Rule]", RowBox[{ FractionBox["1", SqrtBox[ RowBox[{"2", " ", "\[Pi]"}]]], RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "r", " ", SqrtBox["\[Lambda]"]}], ")"}], RowBox[{"-", "l"}]], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"r", " ", SqrtBox["\[Lambda]"]}], ")"}], RowBox[{ RowBox[{"-", FractionBox["1", "2"]}], "-", "l"}]], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "r", " ", SqrtBox["\[Lambda]"]}], ")"}], RowBox[{"2", " ", "l"}]], " ", RowBox[{"BesselK", "[", RowBox[{ RowBox[{ RowBox[{"-", FractionBox["1", "2"]}], "-", "l"}], ",", RowBox[{"r", " ", SqrtBox["\[Lambda]"]}]}], "]"}], " ", RowBox[{"C", "[", "2", "]"}]}], "+", RowBox[{"\[Pi]", " ", RowBox[{"BesselI", "[", RowBox[{ RowBox[{ RowBox[{"-", FractionBox["1", "2"]}], "-", "l"}], ",", RowBox[{"r", " ", SqrtBox["\[Lambda]"]}]}], "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "r", " ", SqrtBox["\[Lambda]"]}], ")"}], RowBox[{"2", " ", "l"}]], " ", RowBox[{"C", "[", "2", "]"}], " ", RowBox[{"Sec", "[", RowBox[{"l", " ", "\[Pi]"}], "]"}]}], "+", RowBox[{"\[ImaginaryI]", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"r", " ", SqrtBox["\[Lambda]"]}], ")"}], RowBox[{"2", " ", "l"}]], " ", RowBox[{"(", RowBox[{ RowBox[{"C", "[", "1", "]"}], "+", RowBox[{ RowBox[{"C", "[", "2", "]"}], " ", RowBox[{"Tan", "[", RowBox[{"l", " ", "\[Pi]"}], "]"}]}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}]}], "}"}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Clever:", "Subsubsection"], Cell[TextData[{ "If we\[CloseCurlyQuote]re clever, we recognize that the first three terms \ are ", Cell[BoxData[ FormBox[ FractionBox["1", SuperscriptBox["r", "2"]], TraditionalForm]]], " times the eigenfunction equation for the Laplacian on the unit sphere:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"First", "[", "eqn", "]"}], "-", RowBox[{ FractionBox["1", SuperscriptBox["r", "2"]], FractionBox[ RowBox[{"Laplacian", "[", RowBox[{ RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], "}"}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "1"}], "}"}]}], "}"}]}], "]"}], RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]]}]}], "//", "Expand"}]], "Input"], Cell[BoxData[ RowBox[{ FractionBox[ RowBox[{"2", " ", RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"1", ",", "0", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], RowBox[{"r", " ", RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"2", ",", "0", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]]}]], "Output"] }, Open ]], Cell[TextData[{ "Equivalently, the first three terms are the eigenfunction equation for the \ Laplacian on a sphere of radius ", Cell[BoxData[ FormBox["r", TraditionalForm]]], ":" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"First", "[", "eqn", "]"}], "-", FractionBox[ RowBox[{"Laplacian", "[", RowBox[{ RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "\[CurlyPhi]"}], "}"}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "r"}], "}"}]}], "}"}]}], "]"}], RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]]}], "//", "Expand"}]], "Input"], Cell[BoxData[ RowBox[{ FractionBox[ RowBox[{"2", " ", RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"1", ",", "0", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], RowBox[{"r", " ", RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"2", ",", "0", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]]}]], "Output"] }, Open ]], Cell[TextData[{ "The function ", Cell[BoxData[ FormBox[ SubscriptBox["R", RowBox[{"n", "\[InvisibleSpace]", "l"}]], TraditionalForm]]], "will just come along for the ride and cancel on those three terms, and we\ \[CloseCurlyQuote]ll get the eigenvalue ", Cell[BoxData[ FormBox[ RowBox[{"-", RowBox[{"l", "(", RowBox[{"l", "+", "1"}], ")"}]}], TraditionalForm]]], " found above. Thus, we can rewrite ", Cell[BoxData[ FormBox["eqn", TraditionalForm]]], " as " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"eqnNew", " ", "=", " ", RowBox[{ RowBox[{ FractionBox[ RowBox[{ RowBox[{"-", "l"}], RowBox[{"(", RowBox[{"l", "+", "1"}], ")"}]}], SuperscriptBox["r", "2"]], "+", FractionBox[ RowBox[{"2", " ", RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"1", ",", "0", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], RowBox[{"r", " ", RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"2", ",", "0", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]]}], "\[Equal]", "\[Lambda]"}]}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"l", " ", RowBox[{"(", RowBox[{"1", "+", "l"}], ")"}]}], SuperscriptBox["r", "2"]]}], "+", FractionBox[ RowBox[{"2", " ", RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"1", ",", "0", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}], RowBox[{"r", " ", RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox["f", TagBox[ RowBox[{"(", RowBox[{"2", ",", "0", ",", "0"}], ")"}], Derivative], MultilineFunction->None], "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}], RowBox[{"f", "[", RowBox[{"r", ",", "\[Theta]", ",", "\[CurlyPhi]"}], "]"}]]}], "\[Equal]", "\[Lambda]"}]], "Output"] }, Open ]], Cell[TextData[{ "We know that all \[Theta],\[CurlyPhi] dependence has been removed, so we \ can just replace ", Cell[BoxData[ FormBox["f", TraditionalForm]]], " with ", Cell[BoxData[ FormBox["R", TraditionalForm]]], ", again using pure function notation so that derivatives are computed \ correctly." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"eqnNew", " ", "/.", " ", RowBox[{"f", "\[Rule]", RowBox[{"(", RowBox[{ RowBox[{"R", "[", "#", "]"}], "&"}], ")"}]}]}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"l", " ", RowBox[{"(", RowBox[{"1", "+", "l"}], ")"}]}], SuperscriptBox["r", "2"]]}], "+", FractionBox[ RowBox[{"2", " ", RowBox[{ SuperscriptBox["R", "\[Prime]", MultilineFunction->None], "[", "r", "]"}]}], RowBox[{"r", " ", RowBox[{"R", "[", "r", "]"}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox["R", "\[Prime]\[Prime]", MultilineFunction->None], "[", "r", "]"}], RowBox[{"R", "[", "r", "]"}]]}], "\[Equal]", "\[Lambda]"}]], "Output"] }, Open ]], Cell[TextData[{ "This is ", Cell[BoxData[ FormBox[ FractionBox["1", "r"], TraditionalForm]]], " times the equation ", Cell[BoxData[ FormBox["Reqn", TraditionalForm]]], " found above, which DSolve has no problem dealing with." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DSolve", "[", RowBox[{"%", ",", RowBox[{"R", "[", "r", "]"}], ",", "r"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"R", "[", "r", "]"}], "\[Rule]", RowBox[{ RowBox[{ RowBox[{"C", "[", "1", "]"}], " ", RowBox[{"SphericalBesselJ", "[", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "-", "l"}], ",", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "r", " ", SqrtBox["\[Lambda]"]}]}], "]"}]}], "+", RowBox[{ RowBox[{"C", "[", "2", "]"}], " ", RowBox[{"SphericalBesselY", "[", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "-", "l"}], ",", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "r", " ", SqrtBox["\[Lambda]"]}]}], "]"}]}]}]}], "}"}], "}"}]], "Output"] }, Open ]] }, Closed]] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Some Problems from Calculus", "Section", CellChangeTimes->{{3.6231504063401976`*^9, 3.623150412159333*^9}}], Cell[CellGroupData[{ Cell[TextData[{ "P1: Evaluation of ", Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["\[Integral]", "0", FractionBox["\[Pi]", "2"]], RowBox[{ RowBox[{"log", "(", RowBox[{ SuperscriptBox["sin", "2"], "(", "x", ")"}], ")"}], RowBox[{"\[DifferentialD]", "x"}]}]}], TraditionalForm]]] }], "Subsection", CellChangeTimes->{{3.6231132388265743`*^9, 3.6231132471725893`*^9}, { 3.623114163488574*^9, 3.623114163784974*^9}, {3.623114541593622*^9, 3.623114561168742*^9}, {3.623154417619364*^9, 3.623154423267149*^9}, { 3.623154732190089*^9, 3.623154734604343*^9}}], Cell[TextData[{ "Source: ", ButtonBox["math.stackexchange.com/questions/58654", BaseStyle->"Hyperlink", ButtonData->{ URL["http://math.stackexchange.com/questions/58654"], None}, ButtonNote->"http://math.stackexchange.com/questions/58654"] }], "Text", CellChangeTimes->{{3.623113340039552*^9, 3.623113362612792*^9}}], Cell[CellGroupData[{ Cell["Built\[Hyphen]in", "Subsubsection", CellChangeTimes->{{3.62311415581336*^9, 3.623114156733762*^9}, { 3.6231141950006294`*^9, 3.623114197902234*^9}, 3.6231529077452927`*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{"Log", "[", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], "^", "2"}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", RowBox[{"Pi", "/", "2"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.623114177060598*^9, 3.6231141785582004`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"-", "\[Pi]"}], " ", RowBox[{"Log", "[", "2", "]"}]}]], "Output", CellChangeTimes->{3.623114179587802*^9}] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Derivation", "Subsubsection", CellChangeTimes->{{3.6231142009442396`*^9, 3.6231142042358456`*^9}, { 3.6231529157610703`*^9, 3.623152917217112*^9}}], Cell[TextData[{ "Make a substitution ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], "\[Equal]", "t"}], TraditionalForm]]] }], "Text", CellChangeTimes->{{3.6231142809567804`*^9, 3.623114294045203*^9}, { 3.6231143702669373`*^9, 3.6231143761481476`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Log", "[", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], "^", "2"}], "]"}], RowBox[{"Dt", "[", "x", "]"}]}], "/.", RowBox[{"x", "\[Rule]", RowBox[{"ArcSin", "[", "t", "]"}]}]}]], "Input", CellChangeTimes->{{3.6231143876297674`*^9, 3.6231143961161823`*^9}}], Cell["Or use a nice function built especially for this task.", "Text", CellChangeTimes->{{3.6231144021377935`*^9, 3.6231144156162167`*^9}}], Cell[BoxData[ RowBox[{"int", "=", RowBox[{"ChangeIntegrationVariables", "[", RowBox[{ TemplateBox[{RowBox[{"Log", "[", SuperscriptBox[ RowBox[{"Sin", "[", "x", "]"}], "2"], "]"}],"x","0",FractionBox[ "\[Pi]", "2"]}, "InactiveIntegrate", DisplayFunction->(RowBox[{ SubsuperscriptBox[ StyleBox["\[Integral]", "Inactive"], #3, #4], RowBox[{#, RowBox[{ StyleBox["\[DifferentialD]", "Inactive"], #2}]}]}]& ), InterpretationFunction->(RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{#, ",", RowBox[{"{", RowBox[{#2, ",", #3, ",", #4}], "}"}]}], "]"}]& )], ",", RowBox[{"t", "\[Equal]", RowBox[{"Sin", "[", "x", "]"}]}], ",", "t"}], "]"}]}]], "Input", CellChangeTimes->{{3.623113403240136*^9, 3.6231134312037363`*^9}, { 3.6231142559031363`*^9, 3.6231142565739374`*^9}, {3.6231144189546223`*^9, 3.6231144189546223`*^9}}], Cell[TextData[{ "Representing ", Cell[BoxData[ FormBox[ RowBox[{"Log", "[", "t", "]"}], TraditionalForm]]], " as a parametric derivative (Feynman trick ?)" }], "Text", CellChangeTimes->{{3.6231144331828475`*^9, 3.6231144727143173`*^9}, { 3.6231145102648306`*^9, 3.623114514050047*^9}}], Cell[BoxData[ RowBox[{"Limit", "[", RowBox[{ RowBox[{"D", "[", RowBox[{ SuperscriptBox["t", RowBox[{"s", "-", "1"}]], ",", "s"}], "]"}], ",", RowBox[{"s", "\[Rule]", "1"}]}], "]"}]], "Input", CellChangeTimes->{{3.623114251160728*^9, 3.623114271924364*^9}}], Cell[BoxData[ RowBox[{"Assuming", "[", RowBox[{ RowBox[{"s", "\[GreaterEqual]", "1"}], ",", RowBox[{"Activate", "[", RowBox[{"int", "/.", RowBox[{ RowBox[{"Log", "[", "t", "]"}], "\[Rule]", SuperscriptBox["t", RowBox[{"s", "-", "1"}]]}]}], "]"}]}], "]"}]], "Input", CellChangeTimes->{{3.623114086674039*^9, 3.6231141189192953`*^9}, { 3.6231142766043725`*^9, 3.6231142769163733`*^9}, {3.6231146659946814`*^9, 3.623114674387496*^9}}], Cell[BoxData[ RowBox[{"Limit", "[", RowBox[{ RowBox[{"D", "[", RowBox[{"%", ",", "s"}], "]"}], ",", RowBox[{"s", "\[Rule]", "1"}], ",", RowBox[{"Direction", "\[Rule]", RowBox[{"-", "1"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.6231141272029104`*^9, 3.6231141389185305`*^9}, { 3.6231142116302586`*^9, 3.6231142125974603`*^9}, {3.6231146794107046`*^9, 3.6231146831235113`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"FunctionExpand", "[", "%", "]"}], "//", "Simplify"}]], "Input", CellChangeTimes->{{3.623114214375863*^9, 3.62311421847867*^9}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "P2: Asymptotic expansion of ", Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["\[Integral]", "n", "\[Infinity]"], RowBox[{ RowBox[{ RowBox[{"exp", "(", RowBox[{"-", "t"}], ")"}], " ", SuperscriptBox["t", "n"]}], RowBox[{"\[DifferentialD]", "t"}]}]}], TraditionalForm]]] }], "Subsection", CellChangeTimes->{{3.6231092334137855`*^9, 3.623109270526251*^9}, { 3.6231145622188025`*^9, 3.623114563106853*^9}}], Cell[TextData[{ "Source: ", ButtonBox["math.stackexchange.com/questions/327525\n", BaseStyle->"Hyperlink", ButtonData->{ URL["http://math.stackexchange.com/questions/327525"], None}, ButtonNote->"http://math.stackexchange.com/questions/327525"], "Source: problem 11353 of AMM\nSource: ", ButtonBox["math.stackexchange.com/questions/71447", BaseStyle->"Hyperlink", ButtonData->{ URL["http://math.stackexchange.com/questions/71447"], None}, ButtonNote->"http://math.stackexchange.com/questions/71447"] }], "Text", CellChangeTimes->{{3.62310930406631*^9, 3.6231093678198686`*^9}, { 3.623113082123299*^9, 3.623113117895162*^9}, {3.6231133046742897`*^9, 3.6231133265143285`*^9}}], Cell[CellGroupData[{ Cell["Built\[Hyphen]in", "Subsubsection", CellChangeTimes->{{3.6231094214129343`*^9, 3.6231094243161*^9}}], Cell[BoxData[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"t", "^", "n"}], " ", RowBox[{"Exp", "[", RowBox[{"-", "t"}], "]"}]}], ",", RowBox[{"{", RowBox[{"t", ",", "n", ",", "Infinity"}], "}"}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{"n", ">", "0"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.623109381237636*^9, 3.6231093976075726`*^9}, { 3.6231131587204337`*^9, 3.6231131614504385`*^9}}], Cell[BoxData[ RowBox[{"Series", "[", RowBox[{"%", ",", RowBox[{"{", RowBox[{"n", ",", "Infinity", ",", "3"}], "}"}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{"n", ">", "100"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.623109399764696*^9, 3.6231094130484557`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Derivation", "Subsubsection", CellChangeTimes->{{3.623109429858417*^9, 3.623109431386504*^9}}], Cell[TextData[{ "Change variables ", Cell[BoxData[ FormBox[ RowBox[{"t", "\[Equal]", RowBox[{"n", " ", RowBox[{"(", RowBox[{"u", "+", "1"}], ")"}]}]}], TraditionalForm]]], "." }], "Text", CellChangeTimes->{{3.6231103377262783`*^9, 3.6231103476946955`*^9}, { 3.6231118572841473`*^9, 3.6231118657861624`*^9}}], Cell[BoxData[ RowBox[{"int", "=", RowBox[{"Assuming", "[", RowBox[{ RowBox[{"n", ">", "0"}], ",", RowBox[{"ChangeIntegrationVariables", "[", RowBox[{ RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{ RowBox[{ RowBox[{"t", "^", "n"}], " ", RowBox[{"Exp", "[", RowBox[{"-", "t"}], "]"}]}], ",", RowBox[{"{", RowBox[{"t", ",", "n", ",", "Infinity"}], "}"}]}], "]"}], ",", RowBox[{"t", "\[Equal]", RowBox[{"n", "+", RowBox[{"n", " ", "u"}]}]}], ",", "u"}], "]"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6231103636379237`*^9, 3.623110419955023*^9}, 3.6231110132562647`*^9, {3.6231117927468348`*^9, 3.623111792980835*^9}, { 3.6231119038658295`*^9, 3.6231119191850567`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"factor", "=", RowBox[{ RowBox[{"Exp", "[", RowBox[{"-", "n"}], "]"}], RowBox[{"n", "^", RowBox[{"(", RowBox[{"n", "+", "1"}], ")"}]}]}]}], ";"}]], "Input", CellChangeTimes->{{3.6231119893227797`*^9, 3.623111991413183*^9}, { 3.6231125484765615`*^9, 3.623112564154589*^9}, {3.623112595354644*^9, 3.623112595604244*^9}}], Cell[BoxData[ RowBox[{"int", "=", RowBox[{"Assuming", "[", RowBox[{ RowBox[{"n", ">", "0"}], ",", RowBox[{"PullConstantOut", "[", RowBox[{"int", ",", "factor"}], "]"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6231103636379237`*^9, 3.623110419955023*^9}, 3.6231110132562647`*^9, {3.623111132317674*^9, 3.623111153346511*^9}, { 3.6231114127905664`*^9, 3.623111413913769*^9}, {3.6231119091074386`*^9, 3.6231119094506392`*^9}, {3.6231119947983894`*^9, 3.62311199557839*^9}}], Cell[TextData[{ "Apply ", ButtonBox["Watson\[CloseCurlyQuote]s lemma", BaseStyle->"Hyperlink", ButtonData->{ URL["http://en.wikipedia.org/wiki/Watson%27s_lemma"], None}, ButtonNote->"http://en.wikipedia.org/wiki/Watson%27s_lemma"], ". The integrand attains maximum at the lower integration limit." }], "Text", CellChangeTimes->{{3.623109744027411*^9, 3.6231097654974995`*^9}, { 3.6231097986653967`*^9, 3.623109837852638*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"\[Phi]", "[", "u_", "]"}], "=", RowBox[{"FunctionExpand", "[", RowBox[{ RowBox[{"Log", "[", RowBox[{ RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "n"}], " ", "u"}], "]"}], SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "u"}], ")"}], "n"]}], "]"}], ",", RowBox[{ RowBox[{"u", ">", "0"}], "&&", RowBox[{"n", ">", "0"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6231099058083196`*^9, 3.6231099542152047`*^9}, { 3.6231111780101547`*^9, 3.6231111969641876`*^9}, {3.623111929309474*^9, 3.623111933334281*^9}, {3.6231125781322136`*^9, 3.623112602062656*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"{", "sol", "}"}], "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[Phi]", "'"}], "[", "u", "]"}], "\[Equal]", "0"}], ",", "u"}], "]"}]}]], "Input", CellChangeTimes->{{3.6231097729479256`*^9, 3.6231097856856537`*^9}, { 3.6231098222167435`*^9, 3.6231098240968513`*^9}, {3.623109931080364*^9, 3.6231099887380652`*^9}, {3.6231112006925945`*^9, 3.6231112027205977`*^9}}], Cell["Develop the series exponent into series about the maximum.", "Text", CellChangeTimes->{{3.623109855810232*^9, 3.6231098933126974`*^9}, { 3.6231126036538587`*^9, 3.62311260437146*^9}, {3.6231131706076546`*^9, 3.6231131712316556`*^9}}], Cell[BoxData[ RowBox[{"ser", "=", RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"Series", "[", RowBox[{ RowBox[{"\[Phi]", "[", "u", "]"}], ",", RowBox[{"{", RowBox[{"u", ",", "0", ",", "20"}], "}"}]}], "]"}], ",", RowBox[{"n", ">", "0"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6231099684580297`*^9, 3.623110003979292*^9}, { 3.6231112130790157`*^9, 3.623111215793421*^9}, {3.623112127960223*^9, 3.623112128085023*^9}, 3.6231121938859386`*^9, 3.6231122272231975`*^9, { 3.623112996696549*^9, 3.623112996821349*^9}}], Cell[BoxData[ RowBox[{"quadratic", "=", RowBox[{"Normal", "[", RowBox[{"ser", "+", RowBox[{ RowBox[{"O", "[", "u", "]"}], "^", "3"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.623110061980194*^9, 3.623110084350633*^9}, { 3.6231112343574533`*^9, 3.6231112398018627`*^9}}], Cell[BoxData[ RowBox[{"rest", "=", RowBox[{"ser", "-", "quadratic"}]}]], "Input", CellChangeTimes->{{3.6231100894986424`*^9, 3.623110098078657*^9}, 3.6231112442634706`*^9}], Cell[TextData[{ "Represent the integral as ", Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[{ RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "n"}], " ", RowBox[{ RowBox[{"u", "^", "2"}], "/", "2"}]}], "]"}], RowBox[{"(", RowBox[{ SubscriptBox["\[Sum]", "k"], RowBox[{ SubscriptBox["c", "k"], SuperscriptBox["u", "k"]}]}], ")"}], RowBox[{"\[DifferentialD]", "u"}]}]}], TraditionalForm]]] }], "Text", CellChangeTimes->{{3.623112839760273*^9, 3.6231128784795413`*^9}}], Cell[BoxData[ RowBox[{"coeffs", "=", RowBox[{"Expand", "[", RowBox[{"CoefficientList", "[", RowBox[{ RowBox[{"Exp", "[", "rest", "]"}], ",", "u"}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.623111262671503*^9, 3.623111374367699*^9}, { 3.623111464660658*^9, 3.6231115138163443`*^9}, {3.623111581676463*^9, 3.6231115830336657`*^9}, {3.62311220021955*^9, 3.6231122101255674`*^9}, { 3.6231122951301165`*^9, 3.6231122979693213`*^9}}], Cell[BoxData[ RowBox[{"ints", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"u", "^", "k"}], " ", RowBox[{"Exp", "[", "quadratic", "]"}]}], ",", RowBox[{"{", RowBox[{"u", ",", "0", ",", "Infinity"}], "}"}], ",", RowBox[{"Assumptions", "\[Rule]", RowBox[{"n", ">", "0"}]}]}], "]"}], ",", RowBox[{"{", RowBox[{"k", ",", "0", ",", RowBox[{ RowBox[{"Length", "[", "coeffs", "]"}], "-", "1"}]}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.62311151712355*^9, 3.623111552878813*^9}, { 3.623111584749669*^9, 3.62311158542047*^9}, {3.6231121366962385`*^9, 3.623112140627445*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Series", "[", RowBox[{ RowBox[{"Accumulate", "[", RowBox[{"coeffs", " ", "ints"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "Infinity", ",", "4"}], "}"}]}], "]"}], "//", "Differences"}], "//", RowBox[{ RowBox[{"Take", "[", RowBox[{"#", ",", RowBox[{"-", "4"}]}], "]"}], "&"}]}]], "Input", CellChangeTimes->{{3.6231115884624753`*^9, 3.6231115935792847`*^9}, { 3.6231120805361395`*^9, 3.623112101502577*^9}, {3.623112262292059*^9, 3.6231123408225965`*^9}, {3.623112909102395*^9, 3.623112959194083*^9}}], Cell[BoxData[ RowBox[{"res", "=", RowBox[{"factor", " ", RowBox[{"Series", "[", RowBox[{ RowBox[{"coeffs", ".", "ints"}], ",", RowBox[{"{", RowBox[{"n", ",", "Infinity", ",", "3"}], "}"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.6231123550030217`*^9, 3.623112367295843*^9}, { 3.6231124432221766`*^9, 3.6231124438617783`*^9}, {3.6231129858077297`*^9, 3.6231130115633755`*^9}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "P3: Evaluation of ", Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["tan", RowBox[{"-", "1"}]], "(", RowBox[{"a", " ", RowBox[{ SuperscriptBox["sin", "2"], "(", "x", ")"}]}], ")"}], SuperscriptBox["x", "2"]], RowBox[{"\[DifferentialD]", "x"}]}]}], TraditionalForm]]] }], "Subsection", CellChangeTimes->{{3.62311531453662*^9, 3.623115318046627*^9}, { 3.623115365311864*^9, 3.6231153884781885`*^9}}], Cell[TextData[{ "Source: ", ButtonBox["math.stackexchange.com/questions/174258", BaseStyle->"Hyperlink", ButtonData->{ URL["http://math.stackexchange.com/questions/174258"], None}, ButtonNote->"http://math.stackexchange.com/questions/174258"] }], "Text", CellChangeTimes->{{3.6231153234130363`*^9, 3.6231153463294764`*^9}}], Cell[CellGroupData[{ Cell["Built-in:", "Subsubsection", CellChangeTimes->{{3.623154556119296*^9, 3.6231545622758837`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[{ FractionBox[ RowBox[{"ArcTan", "[", RowBox[{"a", " ", SuperscriptBox[ RowBox[{"Sin", "[", "x", "]"}], "2"]}], "]"}], SuperscriptBox["x", "2"]], RowBox[{"\[DifferentialD]", "x"}]}]}]], "Input", CellChangeTimes->{3.623154495459817*^9}], Cell[BoxData[ RowBox[{ SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[{ FractionBox[ RowBox[{"ArcTan", "[", RowBox[{"a", " ", SuperscriptBox[ RowBox[{"Sin", "[", "x", "]"}], "2"]}], "]"}], SuperscriptBox["x", "2"]], RowBox[{"\[DifferentialD]", "x"}]}]}]], "Output", CellChangeTimes->{3.623154542849209*^9}] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Derivation:", "Subsubsection", CellChangeTimes->{{3.623154469131858*^9, 3.623154471387561*^9}}], Cell["\<\ Key: develop a series with respect to parameter, integrate term\[Hyphen]wise.\ \ \>", "Text", CellChangeTimes->{{3.623115403823066*^9, 3.623115421226062*^9}}], Cell[BoxData[ RowBox[{"term", "=", RowBox[{"Assuming", "[", RowBox[{ RowBox[{ RowBox[{"n", "\[Element]", "Integers"}], "&&", RowBox[{"n", "\[GreaterEqual]", "0"}]}], ",", RowBox[{ RowBox[{"SeriesCoefficient", "[", RowBox[{ RowBox[{ RowBox[{"ArcTan", "[", RowBox[{"a", " ", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], "^", "2"}]}], "]"}], "/", RowBox[{"x", "^", "2"}]}], ",", RowBox[{"{", RowBox[{"a", ",", "0", ",", RowBox[{ RowBox[{"2", "n"}], "+", "1"}]}], "}"}]}], "]"}], "//", "FullSimplify"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.623115395622597*^9, 3.6231154518872185`*^9}}], Cell["Evaluate first few terms.", "Text", CellChangeTimes->{{3.623115487798482*^9, 3.6231155144277287`*^9}}], Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"n", ",", RowBox[{"Integrate", "[", RowBox[{"term", ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "Infinity"}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "12"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.6231154623392367`*^9, 3.623115507392116*^9}}], Cell["Guess a closed form.", "Text", CellChangeTimes->{{3.6231155178753347`*^9, 3.6231155244585457`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"integratedTerm", "[", "n_", "]"}], "=", RowBox[{"FindSequenceFunction", "[", RowBox[{"%", ",", "n"}], "]"}]}]], "Input", CellChangeTimes->{{3.62311552681415*^9, 3.6231155315877585`*^9}, { 3.6231155652370176`*^9, 3.623115581726247*^9}}], Cell["Resum.", "Text", CellChangeTimes->{{3.6231155355657654`*^9, 3.6231155376249695`*^9}}], Cell[BoxData[ RowBox[{"Sum", "[", RowBox[{ RowBox[{ RowBox[{"integratedTerm", "[", "n", "]"}], " ", SuperscriptBox["a", RowBox[{ RowBox[{"2", "n"}], "+", "1"}]]}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "Infinity"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.623115538529771*^9, 3.6231155879818573`*^9}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "P4: Find ", Cell[BoxData[ FormBox[ RowBox[{ UnderscriptBox["lim", RowBox[{"x", "\[Rule]", "\[Infinity]"}]], "\[ThinSpace]", RowBox[{"(", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"n", "=", "1"}], "\[Infinity]"], FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "n"], " ", SuperscriptBox["x", RowBox[{ RowBox[{"2", " ", "n"}], "-", "1"}]]}], RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", " ", "n"}], ")"}], "!"}], " ", RowBox[{"log", "(", RowBox[{"2", " ", "n"}], ")"}]}]]}], ")"}]}], TraditionalForm]]] }], "Subsection", CellChangeTimes->{{3.6231156065146904`*^9, 3.6231156445943575`*^9}}], Cell[TextData[{ "Source: ", ButtonBox["math.stackexchange.com/questions/191008", BaseStyle->"Hyperlink", ButtonData->{ URL["http://math.stackexchange.com/questions/191008"], None}, ButtonNote->"http://math.stackexchange.com/questions/191008"] }], "Text", CellChangeTimes->{{3.6231156503039675`*^9, 3.6231156696168013`*^9}}], Cell[CellGroupData[{ Cell["Built-in:", "Subsubsection", CellChangeTimes->{{3.623154655820999*^9, 3.623154662428163*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Limit", "[", RowBox[{ RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"n", "=", "1"}], "\[Infinity]"], FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "n"], " ", SuperscriptBox["x", RowBox[{ RowBox[{"2", " ", "n"}], "-", "1"}]]}], RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", " ", "n"}], ")"}], "!"}], " ", RowBox[{"Log", "[", RowBox[{"2", " ", "n"}], "]"}]}]]}], ",", RowBox[{"x", "\[Rule]", "\[Infinity]"}]}], "]"}]], "Input", CellChangeTimes->{3.623154667092141*^9}], Cell[BoxData[ RowBox[{"Limit", "[", RowBox[{ RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"n", "=", "1"}], "\[Infinity]"], FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "n"], " ", SuperscriptBox["x", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "n"}]}]]}], RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", " ", "n"}], ")"}], "!"}], " ", RowBox[{"Log", "[", RowBox[{"2", " ", "n"}], "]"}]}]]}], ",", RowBox[{"x", "\[Rule]", "\[Infinity]"}]}], "]"}]], "Output", CellChangeTimes->{3.623154669434825*^9}] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Derivation:", "Subsubsection", CellChangeTimes->{{3.623154637556135*^9, 3.623154664444182*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{ SuperscriptBox["a", RowBox[{"-", "t"}]], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "Infinity"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.6231485762753563`*^9, 3.6231486191598315`*^9}}], Cell[BoxData[ TemplateBox[{SuperscriptBox["a", RowBox[{"-", "t"}]],"t","0","\[Infinity]"}, "InactiveIntegrate", DisplayFunction->(RowBox[{ SubsuperscriptBox[ StyleBox["\[Integral]", "Inactive"], #3, #4], RowBox[{#, RowBox[{ StyleBox["\[DifferentialD]", "Inactive"], #2}]}]}]& ), InterpretationFunction->(RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{#, ",", RowBox[{"{", RowBox[{#2, ",", #3, ",", #4}], "}"}]}], "]"}]& )]], "Output", CellChangeTimes->{{3.623148592577385*^9, 3.6231486195186324`*^9}, 3.6231493288350782`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Assuming", "[", RowBox[{ RowBox[{"a", ">", "1"}], ",", RowBox[{"Activate", "[", "%", "]"}]}], "]"}]], "Input", CellChangeTimes->{{3.623148620407834*^9, 3.623148628161048*^9}}], Cell[BoxData[ FractionBox["1", RowBox[{"Log", "[", "a", "]"}]]], "Output", CellChangeTimes->{3.623148628831849*^9, 3.6231493295838795`*^9}] }, Open ]], Cell[BoxData[ RowBox[{"sumOfint", "=", RowBox[{ RowBox[{ RowBox[{"Inactive", "[", "Sum", "]"}], "[", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "n"], FractionBox[ SuperscriptBox["x", RowBox[{ RowBox[{"2", "n"}], "-", "1"}]], RowBox[{ RowBox[{"(", RowBox[{"2", "n"}], ")"}], "!"}]], FractionBox["1", RowBox[{"Log", "[", RowBox[{"2", "n"}], "]"}]]}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", "Infinity"}], "}"}]}], "]"}], "/.", " ", RowBox[{ FractionBox["1", RowBox[{"Log", "[", RowBox[{"2", "n"}], "]"}]], "\[RuleDelayed]", RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"2", "n"}], ")"}], RowBox[{"-", "t"}]], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "Infinity"}], "}"}]}], "]"}]}]}]}]], "Input", CellChangeTimes->{{3.623148634713059*^9, 3.6231486947419643`*^9}, { 3.6231488070621614`*^9, 3.6231488143941746`*^9}, 3.6231491172229066`*^9}], Cell[BoxData[ RowBox[{ RowBox[{"sumOfint2intOfsumRule", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Inactive", "[", "Sum", "]"}], "[", RowBox[{ RowBox[{"c_.", RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{"e_", ",", "iiter_"}], "]"}]}], ",", "siter_"}], "]"}], ":>", RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{ RowBox[{ RowBox[{"Inactive", "[", "Sum", "]"}], "[", RowBox[{ RowBox[{"c", " ", "e"}], ",", "siter"}], "]"}], ",", "iiter"}], "]"}]}], "}"}]}], ";"}]], "Input", CellChangeTimes->{{3.62314895983423*^9, 3.6231489675718436`*^9}}], Cell[BoxData[ RowBox[{"intOfsum", "=", RowBox[{"sumOfint", "/.", "sumOfint2intOfsumRule"}]}]], "Input", CellChangeTimes->{{3.6231487113559933`*^9, 3.623148773600103*^9}, { 3.6231488213517866`*^9, 3.623148827076997*^9}, 3.6231489724234524`*^9}], Cell["Using ", "Text", CellChangeTimes->{{3.6231488449858284`*^9, 3.623148849509836*^9}}], Cell[BoxData[ RowBox[{"eulerInt", "=", RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{ RowBox[{ SuperscriptBox["u", RowBox[{"t", "-", "1"}]], RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "2"}], "n", " ", "u"}], "]"}]}], ",", RowBox[{"{", RowBox[{"u", ",", "0", ",", "Infinity"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6231488525206413`*^9, 3.6231488741422796`*^9}, { 3.6231489227217646`*^9, 3.6231489272613726`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"eulerInt", "\[Equal]", RowBox[{"Assuming", "[", RowBox[{ RowBox[{ RowBox[{"n", ">", "0"}], "&&", RowBox[{"t", ">", "0"}]}], ",", RowBox[{"Activate", "[", "eulerInt", "]"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6231488827534947`*^9, 3.6231488977139206`*^9}, { 3.6231489320037813`*^9, 3.6231489342813854`*^9}}], Cell[BoxData[ RowBox[{ TemplateBox[{RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "2"}], " ", "n", " ", "u"}]], " ", SuperscriptBox["u", RowBox[{ RowBox[{"-", "1"}], "+", "t"}]]}],"u","0","\[Infinity]"}, "InactiveIntegrate", DisplayFunction->(RowBox[{ SubsuperscriptBox[ StyleBox["\[Integral]", "Inactive"], #3, #4], RowBox[{#, RowBox[{ StyleBox["\[DifferentialD]", "Inactive"], #2}]}]}]& ), InterpretationFunction->(RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{#, ",", RowBox[{"{", RowBox[{#2, ",", #3, ",", #4}], "}"}]}], "]"}]& )], "\[Equal]", RowBox[{ SuperscriptBox["2", RowBox[{"-", "t"}]], " ", SuperscriptBox["n", RowBox[{"-", "t"}]], " ", RowBox[{"Gamma", "[", "t", "]"}]}]}]], "Output", CellChangeTimes->{ 3.6231489001787252`*^9, 3.6231489363405886`*^9, 3.6231489767290597`*^9, 3.6231491235253177`*^9, {3.623149320473464*^9, 3.6231493360154905`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"res1", "=", RowBox[{ RowBox[{"intOfsum", "/.", RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox["2", RowBox[{"-", "t"}]], " ", SuperscriptBox["n", RowBox[{"-", "t"}]]}], ":>", RowBox[{"eulerInt", "/", RowBox[{"Gamma", "[", "t", "]"}]}]}], "}"}]}], "/.", "sumOfint2intOfsumRule"}]}]], "Input", CellChangeTimes->{{3.623148909835142*^9, 3.6231489394917946`*^9}, { 3.6231489774778614`*^9, 3.623148978039462*^9}, {3.6231493116438484`*^9, 3.623149343659504*^9}}], Cell[BoxData[ TemplateBox[{TemplateBox[{ TemplateBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "n"], " ", SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "2"}], " ", "n", " ", "u"}]], " ", SuperscriptBox["u", RowBox[{ RowBox[{"-", "1"}], "+", "t"}]], " ", SuperscriptBox["x", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "n"}]}]]}], RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2", " ", "n"}], ")"}], "!"}], " ", RowBox[{"Gamma", "[", "t", "]"}]}]], "n", "1", "\[Infinity]"}, "InactiveSum", DisplayFunction -> (RowBox[{ UnderoverscriptBox[ StyleBox["\[Sum]", "Inactive"], RowBox[{#2, "=", #3}], #4], #}]& ), InterpretationFunction -> (RowBox[{ RowBox[{"Inactive", "[", "Sum", "]"}], "[", RowBox[{#, ",", RowBox[{"{", RowBox[{#2, ",", #3, ",", #4}], "}"}]}], "]"}]& )], "u", "0", "\[Infinity]"}, "InactiveIntegrate", DisplayFunction -> (RowBox[{ SubsuperscriptBox[ StyleBox["\[Integral]", "Inactive"], #3, #4], RowBox[{#, RowBox[{ StyleBox["\[DifferentialD]", "Inactive"], #2}]}]}]& ), InterpretationFunction -> (RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{#, ",", RowBox[{"{", RowBox[{#2, ",", #3, ",", #4}], "}"}]}], "]"}]& )],"t","0", "\[Infinity]"}, "InactiveIntegrate", DisplayFunction->(RowBox[{ SubsuperscriptBox[ StyleBox["\[Integral]", "Inactive"], #3, #4], RowBox[{#, RowBox[{ StyleBox["\[DifferentialD]", "Inactive"], #2}]}]}]& ), InterpretationFunction->(RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{#, ",", RowBox[{"{", RowBox[{#2, ",", #3, ",", #4}], "}"}]}], "]"}]& )]], "Output", CellChangeTimes->{ 3.6231489402093954`*^9, 3.623148978585463*^9, 3.6231491235877175`*^9, { 3.623149298976626*^9, 3.623149343987105*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"res2", "=", RowBox[{"Activate", "[", RowBox[{"res1", ",", "Sum"}], "]"}]}]], "Input", CellChangeTimes->{{3.6231489825478697`*^9, 3.623148986385477*^9}, { 3.623149305169837*^9, 3.6231493083054423`*^9}, {3.623149348121112*^9, 3.6231493486671133`*^9}}], Cell[BoxData[ TemplateBox[{TemplateBox[{ FractionBox[ RowBox[{ SuperscriptBox["u", RowBox[{ RowBox[{"-", "1"}], "+", "t"}]], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"Cos", "[", RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{"-", "u"}]], " ", "x"}], "]"}]}], ")"}]}], RowBox[{"x", " ", RowBox[{"Gamma", "[", "t", "]"}]}]], "u", "0", "\[Infinity]"}, "InactiveIntegrate", DisplayFunction -> (RowBox[{ SubsuperscriptBox[ StyleBox["\[Integral]", "Inactive"], #3, #4], RowBox[{#, RowBox[{ StyleBox["\[DifferentialD]", "Inactive"], #2}]}]}]& ), InterpretationFunction -> (RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{#, ",", RowBox[{"{", RowBox[{#2, ",", #3, ",", #4}], "}"}]}], "]"}]& )],"t","0", "\[Infinity]"}, "InactiveIntegrate", DisplayFunction->(RowBox[{ SubsuperscriptBox[ StyleBox["\[Integral]", "Inactive"], #3, #4], RowBox[{#, RowBox[{ StyleBox["\[DifferentialD]", "Inactive"], #2}]}]}]& ), InterpretationFunction->(RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{#, ",", RowBox[{"{", RowBox[{#2, ",", #3, ",", #4}], "}"}]}], "]"}]& )]], "Output", CellChangeTimes->{3.6231489867910776`*^9, 3.6231491246953197`*^9, 3.6231493490571136`*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"exchangeIntegralsRule", "=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{ RowBox[{"c_.", RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{"e_", ",", "iiter_"}], "]"}]}], ",", "oiter_"}], "]"}], ":>", RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{ RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{ RowBox[{"c", " ", "e"}], ",", "oiter"}], "]"}], ",", "iiter"}], "]"}]}], "}"}]}], ";"}]], "Input", CellChangeTimes->{{3.6231490315319557`*^9, 3.623149066756818*^9}, { 3.623149407791217*^9, 3.6231494098348207`*^9}}], Cell[BoxData[ RowBox[{"res3", "=", RowBox[{"res2", "/.", "exchangeIntegralsRule"}]}]], "Input", CellChangeTimes->{{3.623149076631635*^9, 3.62314907912764*^9}, { 3.6231493530039206`*^9, 3.623149357761929*^9}}], Cell[BoxData[ RowBox[{"res4", "=", RowBox[{"res3", "/.", RowBox[{ RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{"e_Times", ",", RowBox[{"{", RowBox[{"t", ",", "lb_", ",", "ub_"}], "}"}]}], "]"}], "\[RuleDelayed]", RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{"f", "=", RowBox[{"Times", "@@", RowBox[{"Cases", "[", RowBox[{"e", ",", RowBox[{"ti_", "/;", RowBox[{"FreeQ", "[", RowBox[{"ti", ",", "t"}], "]"}]}], ",", RowBox[{"{", "1", "}"}]}], "]"}]}]}], "}"}], ",", RowBox[{"f", " ", RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{ RowBox[{"e", "/", "f"}], ",", RowBox[{"{", RowBox[{"t", ",", "lb", ",", "ub"}], "}"}]}], "]"}]}]}], "]"}]}]}]}]], "Input", CellChangeTimes->{{3.623149138298544*^9, 3.6231492173594823`*^9}, { 3.623149289398209*^9, 3.6231492906618114`*^9}, {3.623149359181532*^9, 3.6231493757487607`*^9}, {3.623149416371232*^9, 3.623149422892043*^9}}], Cell[TextData[{ "For large ", Cell[BoxData[ FormBox["x", TraditionalForm]]], ", the main contribution to the integral comes from large ", Cell[BoxData[ FormBox["u", TraditionalForm]]], ". The small ", Cell[BoxData[ FormBox["u", TraditionalForm]]], " part is averaged out to zero by fast oscillations." }], "Text", CellChangeTimes->{{3.623149461970112*^9, 3.6231494930453663`*^9}, { 3.6231495881753335`*^9, 3.623149596068948*^9}, {3.6231496655046697`*^9, 3.623149691463115*^9}, {3.623149740353601*^9, 3.623149756359229*^9}}], Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"Cos", "[", RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{"-", "u"}]], " ", "x"}], "]"}]}], ")"}], "/", "u"}], ",", RowBox[{"{", RowBox[{"u", ",", "0", ",", "10"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"{", RowBox[{"1", ",", "10", ",", "100", ",", "1000"}], "}"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.62314969414632*^9, 3.6231497259391756`*^9}, { 3.6231497657660456`*^9, 3.6231497897900877`*^9}}], Cell[TextData[{ "For large ", Cell[BoxData[ FormBox["u", TraditionalForm]]], " the innermost integral approaches ", Cell[BoxData[ FormBox[ RowBox[{"Exp", "[", "u", "]"}], TraditionalForm]]], ", as justified by Euler-McLauren formula" }], "Text", CellChangeTimes->{{3.623149461970112*^9, 3.6231494930453663`*^9}, { 3.6231495881753335`*^9, 3.623149596068948*^9}, {3.6231496655046697`*^9, 3.623149691463115*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"nint", "[", "u_Real", "]"}], ":=", RowBox[{"NIntegrate", "[", RowBox[{ RowBox[{ SuperscriptBox["u", RowBox[{"t", "-", "1"}]], "/", RowBox[{"Gamma", "[", "t", "]"}]}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "Infinity"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6231494953853707`*^9, 3.6231495214686165`*^9}}], Cell[BoxData[ RowBox[{"LogPlot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"nint", "[", "u", "]"}], ",", RowBox[{"Exp", "[", "u", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"u", ",", "0", ",", "5"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.623149525087823*^9, 3.6231495653982935`*^9}}], Cell[BoxData[ RowBox[{"res5", "=", RowBox[{"res4", "/.", RowBox[{ RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{ RowBox[{ SuperscriptBox["u", RowBox[{"t", "-", "1"}]], "/", RowBox[{"Gamma", "[", "t", "]"}]}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "Infinity"}], "}"}]}], "]"}], "\[RuleDelayed]", RowBox[{"Exp", "[", "u", "]"}]}]}]}]], "Input", CellChangeTimes->{{3.6231495683310986`*^9, 3.6231496068797665`*^9}}], Cell[BoxData[ RowBox[{"Activate", "[", "res5", "]"}]], "Input", CellChangeTimes->{{3.623149601357357*^9, 3.623149610155772*^9}}], Cell[BoxData[ RowBox[{"Limit", "[", RowBox[{"%", ",", RowBox[{"x", "\[Rule]", "Infinity"}]}], "]"}]], "Input", CellChangeTimes->{{3.6231496171133842`*^9, 3.6231496204361906`*^9}, { 3.6231498069969177`*^9, 3.6231498082137203`*^9}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Utilities", "Subsection", CellChangeTimes->{{3.623110988077821*^9, 3.6231109894662232`*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"Clear", "[", "ChangeIntegrationVariables", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ChangeIntegrationVariables", "[", RowBox[{ RowBox[{"int", ":", RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{"e_", ",", RowBox[{"{", RowBox[{"t_", ",", "lb_", ",", "ub_"}], "}"}]}], "]"}]}], ",", "eq_Equal", ",", "u_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"sol", ",", "invsol", ",", "ne", ",", "nlb", ",", "nub"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"sol", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{"eq", "&&", RowBox[{"lb", "<", "t", "<", "ub"}]}], ",", "t", ",", "Reals"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Length", "[", "sol", "]"}], "\[NotEqual]", "1"}], ",", RowBox[{"Return", "[", "int", "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"invsol", "=", RowBox[{"Solve", "[", RowBox[{ RowBox[{"eq", "&&", RowBox[{"lb", "<", "t", "<", "ub"}]}], ",", "u", ",", "Reals"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Length", "[", "invsol", "]"}], "\[NotEqual]", "1"}], ",", RowBox[{"Return", "[", "int", "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"sol", "=", RowBox[{"First", "[", "sol", "]"}]}], ";", RowBox[{"invsol", "=", RowBox[{"First", "[", "invsol", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ne", "=", RowBox[{"e", "/.", "sol"}]}], ";", "\[IndentingNewLine]", RowBox[{"nlb", "=", RowBox[{"Limit", "[", RowBox[{ RowBox[{"u", "/.", "invsol"}], ",", RowBox[{"t", "\[Rule]", "lb"}], ",", RowBox[{"Direction", "\[Rule]", RowBox[{"-", "1"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"nub", "=", RowBox[{"Limit", "[", RowBox[{ RowBox[{"u", "/.", "invsol"}], ",", RowBox[{"t", "\[Rule]", "ub"}], ",", RowBox[{"Direction", "\[Rule]", "1"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ne", "=", RowBox[{"Refine", "[", RowBox[{ RowBox[{"ne", " ", RowBox[{"D", "[", RowBox[{ RowBox[{"t", "/.", "sol"}], ",", "u"}], "]"}]}], ",", RowBox[{"nlb", "<", "u", "<", "nub"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{"ne", ",", RowBox[{"{", RowBox[{"u", ",", "nlb", ",", "nub"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}]}], "Input", CellChangeTimes->{{3.623112529194928*^9, 3.623112538773345*^9}, { 3.623113448520726*^9, 3.6231135382998753`*^9}, {3.6231135739147387`*^9, 3.6231136023847885`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"PullConstantOut", "[", RowBox[{ RowBox[{"int", ":", RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{"e_", ",", RowBox[{"{", RowBox[{"t_", ",", "lb_", ",", "ub_"}], "}"}]}], "]"}]}], ",", "const_"}], "]"}], ":=", RowBox[{"const", " ", RowBox[{ RowBox[{"Inactive", "[", "Integrate", "]"}], "[", RowBox[{ RowBox[{"FullSimplify", "[", RowBox[{ RowBox[{"e", "/", "const"}], ",", RowBox[{"lb", "<", "t", "<", "ub"}]}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "lb", ",", "ub"}], "}"}]}], "]"}]}]}]], "Input"] }, Closed]] }, Open ]] }, Open ]] }, ScreenStyleEnvironment->"SlideShow", WindowSize->{1920, 998}, WindowMargins->{{-8, Automatic}, {Automatic, -8}}, TaggingRules->{"SlideShow" -> True}, Magnification:>1.25 Inherited, FrontEndVersion->"10.0 for Microsoft Windows (64-bit) (September 9, 2014)", StyleDefinitions->Notebook[{ Cell[ StyleData[StyleDefinitions -> "Default.nb"]], Cell[ CellGroupData[{ Cell["Style Environment Names", "Section"], Cell[ StyleData[All, "Working"], DockedCells -> { Cell[ BoxData[ GraphicsBox[ TagBox[ RasterBox[CompressedData[" 1:eJztnWmQXNWV5x0z82E+TWNQA6pSqfYlq7Iys6pyr9yz9jVrV23aSwtCYkcY sMHd2MYL3YMAAZ4eMIuJ9rTZP9AsAtsRnpYE7rDHNgg7oiFoSRND2xGoCONl lpp/vlN59eptlSUElsP/f/yoeHnfOeeee/M9EXHuy/sqt181uuvffeYzn7nu P+LP6LaD6Wuv3fa5sf+AD5nPXb+w/d/joBv/fQan88ddXT3nzPz8FjNDQ7m+ vn7Q25unp6fPzr2zszuT6Ugm04lECnR0dDl3l0gkY7EE/sIlnc7qT/X1DVi6 TExMIqW5ufmpqenu7t7ih4aAO3fu2r59J7zQlwFk/nHmjRBCCCGEEEIIIYQQ Qgj5pOns7C6Svr6BoaHc+PjkzMzctm07FhZ24+/s7LyBkZGx7u5eRRFddGUy HalUZtUEstnOdDor6wVwUe2jo+NIZmxswtIL7cgKOdsZ2DE5uWnnzl0Yr6Qn pNMgi0zWFIoQQgghhBBCCCGEEEII+ZTJdnRZ0tnV09s3kBsZG5+Y2jQ9u3Xb DrBt+06wfccC2LFzF8DBzOw8DBRDwyN2MddKX//gwOBw/8CQoT2T7QQqT6Sx sGvPzoXds3Ob8dEcB6NAYpNT02vKDaFk1B2d3YlkGiRTICOcrzESQgghhBBC CCGEEEIIIZ8EUksHPb39/QNDw7nR8Ymp6Zm52bnNc/NbwPzmrWDzlm1btm63 WwWA2dSmGSE3MpbOdGhkBdXFWkHYhV17ZJUBxxOTmwYGh/U5g5HRcSn+ixny 7O7pM8SBy9j4JNwxNAyz+ARGxyYwUvxNpjKyBKDAAM95XIQQQgghhBBCCCGE EELIJ81wbnR0bGJyanpq04w8wD89MzczOw9m5zbrVwE2b9kmqwCyEGBYBUAj IiBObmQsmTKWys8N9L5zYTfioyPERxrICr0MDY90dvWITbajCwlL8V+ZdXX3 GkJhpGPjk2BkdBwuzv1mtNUQCY6YGHsqnY0nUno+zrgIIYQQQgghhBBCCCGE kE+aiclNgiwB6FcBZCFArQKoHwLoVwFkIUCWAHAMx9zIWCye1JNMZVLpbJEk kql4IhlPpHA8PjGFBJCGPLovSYKx8cnh3Ghv30Am2yleg0M5yQe5IUm4dHb1 GCKjZXRsYmR0fGBw2CGBnt5+DAFIBPSLsHBBSvpBSYaEEEIIIYQQQgghhBBC yIXJzMzc5OSmiYkp/J2amgabNs2A6elZgLNAXuw7P78FbN68FWzZsg1s3bod bNu2A2zfvnPHjgWY5XKj7e1xPclkWr0/15JEIhWNxkKhiN8fbGsLtLb6A4EQ 2ru7e/v7BxFwbGwCiSGT8fHJ4eGRoaEc/g4MDHV0dKkgXV09khuSRBqw158V +voGRkbG4Gs+JaAdfY2OjqNTdC1hMUZMDkYRiyWEeDwJkLbzuAghhBBCCCGE EEIIIYSQPxbbt+8EmzdvnZ6enZzc5LwKMDe3GahVABzj7NjYxNBQrru7N6VV 8mOxRDQaC4ejing8kUymLYExDILBcCAQAm1tgbY2v1b/D5qNM5mO3t7+XG50 eHikp6cPPRoMstlO5IyskC0OkBhS0hvg4+DgMLLt7x+0SwnBZY0Alul0Fi0Y 49at2xE8FotrnF0FsAtCCCGEEEIIIYQQQgghhPxxkaf3ha1bt8/Nbd60aUYt BBhWAfAXjTg1Ojo+ODjc1zfQ09PX1dWTzXZKqTweT7a3x6X+HwqFBXxMJFIG YBmJtIdCkWAwHAzmi//aw//54n9bWwCNZhdFR0cX+kWPlqckW+Q5MTE1MDBk MECqyBztOLAM3tnZncuNDg3lYINjtOBgy5Zt+BuLxQ0/bXBIkhBCCCGEEEII IYQQQgj5IzIwMCTb+GzZsk2e6pctdOQRetkaaHx8UnbFEVR5vK9voLu7t7Oz W9X/Y7FEe3s8EmmXp/oFfJQNcxTKJhQKy8P/YoZ2g6UdstZgSSbTIZkj7ZGR MeRmMOjt7e/vH+zp6bN0x5wMDg4DZYO+MCcIKD9t0KP2AiKEEEIIIYQQQggh hBBCLijaY4ncyNj85q1z81sEeeEvmJmd3zQ9OzI6Lu/DVQznRgeHcv0DQ719 A13dvR2d3ZlsZzKViSdSiBaJxsKR9mAokn+kXyMUjqJdEdUM0BiUh/9DkWh7 XG+AOBIKpLQX8qYzHXqD/GsLZufRrm/Ug6zGJ6ZGxyaQKvKMacNUIFVkDncc 2LnL6GAjmUxOTWNmcIzMhYgQjdnlQAghhBBCCCGEEEIIIYT8EYm2x8FwblQK /sL0zJywaXp2atOM1Pz1DA7l+voHe3r7u7p7sx1d6UyHof6/XCSPxiS+nrPF /1BEb5BIphGqs6sHf1PprDTieH7zVqQ0OjbR3dMXiyfRiANki9yQgyFymz8o xwODwyOj40PDIzjIZDsNOSBtBEFwc3oAY5HRwUYy6e0bQI/ITZIPR4T8GC0j EEIIIYQQQgghhBBCCCF/XCLRmDA4lFM1f2Fq04wwPjE1NDwitXSFVMg7u3rS mY5EMi1LCSqaM1L/Vx9j8WRXd688b48DiSmnMtnOufktyAo5DOdGYRNPpNCe 7eiamNw0OjYBY7FEQI/X1+zx+gMhiZkbGZPfKXT39BlyQ8LyywW7nNERvGCD BPAxmcrMzM5j1Mg8FI5oRIUih0wIIYQQQgghhBBCCCGEfKqorWwi7YODw/LC 36mpaUFeBCwv/B0YGOrvH+zrG+jt7e/p6evu7k0m03r3cyOdzsrbBBBcRc5k OuQsDubmNk9Pz46PTw4Pj8AgFkvIqUQilcuNwiuVyoTD0eZmL/B4vF5vCz7C AHHUNv6GVKPRWFdXT0dHV1x7DbGZzs5uuItNVJul2dn5sbEJ7Z0FET3SFyGE EEIIIYQQQgghhBByQREOR/X09w+qmv/ExJQg7//N5UalON/V1dPZ2d3R0ZXN dsZiCUOENZFOZxF2eHhkcHBYlgBkWaG9PS4G0WgMveDU6Oj40FAOnerd0Xtv b78Yt7S0ejxej8cHWlv9aEG7eklxJtNh7hqR0ZdlYqlURoYJm/wLC8JRJDAz M6d/r7EgSwCEEEIIIYQQQgghhBBCyAWF4Wl20NvbPz4+KYyNTYDR0XFhcHBY Vf7T6WwqlUkm09FozBykGBBhZGRM6v9DQ7m+voFYLGFnHNF+C+BgEAyGteL/ 8hKAVOaRJ4bT1dWDA0TQ2yMUAiIHy2jt7XEZqeq0p6dvZmYuHk8GAiE90hEh hBBCCCGEEEIIIYQQckFheJpd6Onpk7L/yMiYkMuNCn19A6ryn0ik4vGkPH5v GceBaDSmIg8Pj6BHczKdnd0OEXy+VqnzK1pb22QXINDa6kdLLJZAZMTJZDqQ p944rP0EQPYOsoyvljkQBB9xPD09i1EHAiG/P6iQJQBCCCGEEEIIIYQQQggh 5ILC8DS7oqurR6vMCyNDQ0JucDDX09MXjydjsUR7e1z2xpcSul0oS7QtfSZG RsZzubHe3n79qba2gNTV+/uH4vGUNIbD+V6QAMBZr9fndntAa6t/dnY+k+mQ sryq/09ObpJG/E2lMolEat++/Xv27AWIIDG1JYz8ewEkrCHDdDqbTnckkxmM FF4HDlz9xS/+9fXX37h7955du/bg78zMrCwBoAuJLCAf57GjL2cby3zQy6qR /yjsaW1TZLQv7oIF6X1q2Z5bR0NtAb3jJ5he4XKV2+QTciHnHfzLUOS/Mx+T 7tlN81/7qyue+C9g+os3J3p6HIxzB/bu+q+HxBhezsYq/vjBayIJ4y+qDMAA ZsUEJIQQQgghhBBCCCFm2vwBO7IdnYNDw2BgcEjoHxgUOjq7wpFoKBwJhsKB YMgfCDrEQYSe3r5ItB2W0tIei4+OjY+MjoGh4Zxqb2lta/Z4m9zNXl8LPmay HX39A+gF3eEAfT33/POLi4u+ltYmtxtmINrevrS09Npr35MIHq/P3ezZtn07 Ghd27ZbG666/Hl5LOn37iSckjVg8gfhvaDKkHU8kk6k0/u4/cGDJRq1tfvDg N79pPvX2229Pz8xaTsip06dhMDg4ZDdjyBbuhkaMHV6pdMbSZbq1bamhoUju 8nrP9uVyrWoPG3OPqTb/c83NZmM0Dra22aVnGUp4ze02p2dI8kGPx3bSNBu7 +Eip+GwNnU7bGFgi02Ke1Teamnbh+rZ3xFnYmGce0RDTcqJgbxnqdq/PbrZx 1cmFpBcu/l2799glZumC6/P227/ocAFDDgbKxtyOe9PudlNS97uAG3xVF3Nf CGJpidsTE3LXXX9jd6/ZOeol/8KYx2v3b4LMs+WNf/Zrvf2L8k+HflD4x8cy z2KSxBgtOwon4gt/d+jWN14xMLTf4iKB8YGnHyvS2Bx/7ODVDhcJ2HbPV2E2 91Wna4kQQgghhBBCCCGE2NLmdyCb7RgYGAT9/QNCX1+/kMlkg8FQIBD0a0Fa W9taWlrx1xAhFApPTk4NDg7hbyQSlcbu7p6xsfHR0TGQSCTRglDw9flaEET5 oove3j50Go8nOju70HL77bcvLS1NT894PF63uxlcddXVUstKpdIwgDsaDx++ Hy0SGcZLWrnyuuuuhw0+vvbaa/kC3befCIcjsVgcWS3X/1dm3t4eSyZT6Hr/ /gNarewu9H7zzTcvLOxSIGfw4IP5+j/i79q1W4CxlPsGBwcNYXG2UHy7y3LO JeGl/ALBCl9ZwkAvll67fC3F1/8fbPYoxyJdjEm2tDosHODUtO57NKRnd7Gp 6rc+PXOShshmG8vJcc4WBg4BLc9af3eO0wJu93otHdHuvP6iH7V+Mq/z+Qyh Uq1tZ5dLVs4kLi39Qhiu+VOnztaTcXmbE8P15uDy3HPPW38Xheq0+fo32Fhc Bm+8sWrh2nC3yg24qtbaUb5cPz1zXjJU48Xsyb9UFldp4V8Gy7OYahUcQfQ5 4B83c8xiksS8Wfa18Hd3S3F+26Gvbrr9JnDdi/8gLZ3TkwbjK574ZvHGAI3K AMDe4YYKx+OF1YTdRd6DhBBCCCGEEEIIIUSPVLAdSKczqubf29un6OnpTaXS UvYHPl+L1+sDsgqgSCZT4+MTAwODudyIahwZGZX6//BwDh/9/gACJhJJOSsB cYD4mUwW7dFoezbbgRbE0cpWD6I7t7u5udnzzDPPSH3ytttuF1+0v/XWCYBk 0PLaa6/BAHECgaAarywBdHR0tLfHwoXn/w0Dj0Si6DoWi1955X4YLyzsQsJI QNLTg3xgYHCfnp5G4ze+cZeh/bnnnkM+Wh31lOWEw0Wqc3rfa6+9TgqScLf0 ml5L/f8bHo9yLMZ+0eVa8Z2urHKfcrlea2p6zu0+pWuEQVJ3JSwUnkgHdlea rv7fbDilT+ZEY6Olu138geKyHVh53eoDLmgX0qpgvKesOkLC+vzN0a7VTY4M EF7wNaStn8/nCj8BMLTnV6MKP3M4tfJbw6UrdwouPFxOZ7+ahV0nTrwtl5y+ 3cEF7XIHLeXX0b5t8V3oyuB20yUGFpeBVrjGda5faDOABFYMWbsBMQoHF9yP lh3hLjMbI6AMHH/xL9jHz1A/J3a3MLzs5gSTrGZbRUZiMnAZe/GjU5iHBlLD g8tP5t94lWoMxWIHnn4UjQt/d7elcef0hN5477e/aTYGQ1fuFvuDP3ge4GDq tpsc7imchc11L/5DMTcgIYQQQgghhBBCCDFjrmabSaXSPT29iu7uHtDV1Q0S iaSU/T0eL2hu9rjdzbIKIGQy2dHRMXGUlkAgqB7+7+zsQksymervH2jTnt73 +VoEsQyHI5FIVErx6XQGlr/4xS/eeOMNqfOju8XFxWeeefbUqVOvvvqaxIfx 0tLS4cOHcRYfcfzCCy/Avb09hoBis7CwgPbdu/dEo+3o4vXX3wCGUaM9Hk/A a9++K7X6/4L8AkKfpPDAA/kqnHne0IhT+hakgcZnn33utttuk5hmL0kGIzpx 4oRqhAtGijGivZivDDzgXq4Dv97Y5GCmq0t71xoZ4Fh/6uvNHstTC7rn2+3C Ik/LmPok7Qz0Nob2Z5vc6tTXtUvCMttXm4yztNaZcZgWRFDF/FMul8FRrRrA xtCXXcx+3XKPXfttnhWDxSUkBW1chJZXHc6qm0jARyn+W7qoorTcFCumTifD LWCwscvEzst65rUb0HwLOyMdWd6DYNOm6cLC4m0fP0PDnFx77bVmA/lHyTwn mF6HmVReSLj40TnQu31eSu6G9sF9u6Rur2+cuu0gGg88/ahlEGBol0WEvd9+ MNqRxV+t/n/QLpNge7usEYzecNVaR0EIIYQQQgghhBBCBEMp245stkOV/Ts7 u/TEYnEp+4OmJndjYxPweLziCJdcbkR+LCAtkUhUiv8jI6PwRUtvb5+cRRzl qAgGQ6Ctze/1+nDw93//90tLS/F4Asay+Q/+Pv74t6UR9gcOXIXj8fEJGOAj jh9++Fs4FY22+/0BiYmPsv0FktHq/3kZ+g0EgkgPXvv27YPxzp0L8iMI9UsH xQMPPAADg/vXv/51NH7hC7eZG6emNuF4cXHx2WefNXhJYggoI5LulDGiKfdV eaDwiPjrjY0OZqpcvNM083aoevWrTU12/T7b1NSHeIVGBFcd2YV9vfCcPCLY JemQrWX8uO7RenNY/SyBuC7hc5iZRcdp+YJurWFKF/AaXbtlR49bzac+c/Sr Tqk5NH/pUiU2XJD6Cw8Xp9xB+kvRwSV/JZw6BQM4Wvb16quvyoHlFSunLC6D 11+XW6DIqzE/FdoNaL6FnZGOcF/bGeCO01brnv34Garxii9uZ/1UC8jEck5k dJhqu8jXXHOteRSrjs6OQDQ6csOBxGC/oT07NS4lfX3jlrvvRMvkFw6a44hx tCOjb0TYwX3LKUn939JXwClZcUBKax0FIYQQQgghhBBCCBEMpWxLEomkPO0v dHZ2dXR0Kvz+gFb8d6viv8vVKL8CAN3dPcPDOXglkylpCYcjqv6PY7TkciNy AC+Px2vo3aeV4lu1/S5gtmPHzqWlpauvvkZt/oMDfETj5z//BdhLozv/8wDE 8mn1/4dln39ZRBC0+v+DCBgKhaX+b+gXPba3x+B1xRX7tB02Try+Usry/vvz BbrHH38cB+DZZ5+FsbgYYspT/XIMe9ggMb2BDGRycgrg4Gtf+7pqxN/e3j7V uCr3N52t/zuYqeLzDm26VqVXV8m/urm5GBewQ1fltrNRtWtkbpfkKd1T9DGv 19LGrl+DvRDT/TDBMANrmplJz9mOJj3W9ip5/QDV14SzRU6mynyxobDi0Nhk GKwhZ7lrzNeb01dWcHGwkWvYfO+ovmSBwHwjKBuLy0ArXOM+Kn4q5AY0p+GM dIRhrjXsOWSoxotbWH5WYA5rN+HSHab6/I5urYxcv//WN1659h//m76xUMO/ 0Wwv9f/M5JhdQAdfAX05GxBCCCGEEEIIIYSQVZF9exyIxxNazX/5sf+OjjzZ bKdGRyAQVE/+q/o/DpQ7XAYGhuCCOKqxudkjPxmQjzAIhcI46Orq8fsDhgSQ JBpbWlrT6WxraxtaZM+fwuY/z4gZjo8ceRUHp06devrpZ5CDxF9aWnrooYdl n39xF2Q/DfQbDIaknm/oFz3K7kB7915hrv9LX8L999+vN5CaJxrRqT7g9u07 tEWKz8vHiYlJrZj/Nb0NxoWByDHiSC/6RvSi79qB+wvb6b/e2OhgpirG2wtf hzPbdTvSFGNfvJeu/t/kkKQ6fmylmWV8NQknXC67fk+cLctbByxmZs55gEcK jUccvyZLvqbb2ggJqPUF8zeOq04u0eKDy1Vtvi/MYc02Usf2FK556LHHHrez Mc7ScnX9/vObql1HyNDOADeaZebnkKF+vDJp5ntfzZXBUf49ufrqq8/v6NaK VONnvvIFfeOex/M1/InP32i2L9T/R+0COviC/r075eH/tnD4fA2BEEIIIYQQ Qggh5M8QKcXbEYvF9Vv9qGf+s9kOeaOulPENxX99BHl9MP62t8dUo3KRPfwR ORyO4ABhYWnIQd5T7PO1IFvZh/zIkSOnTp1Sm/+I2TPPPIOPExMT+HvLLbdI fLRr9f+HotH2UCgMXzHu7u6RB+mDwZDfHzh+/HVg6LdVewUwvPbs2atV0rbb zdLhw/nyo/oIS61s+JjBTDJEO+yFxcVFDERvo9X8j8gxLGGPzGWZQ9/o/K0t Z1XYTv+4q9HBTBWQn2lshIuZCe07Ojs63YY5xaRh9rLsBajyNY7tkszPQGFc WtHbbWmzpknAKct+LXspZoB2No9ZJWPXe5GcfXeAbnOk7pVfmbpEzRe50/VT hItc6uYLUt8oV6z5DrJ0zE/I8XzhGr2f31TtOrK7r2+9dblKr/6F+TgZGsaL e3xJ2wUI/14VOZkO//6cw+jWysTnb5B6fiid0rfvefwBrYZ/g8UEavbpiVG7 mA6+QJYbNv/nr8hH9Ju77srWUOi8DIcQQgghhBBCCCHkzwd5et+Mx+NNJlOW lX+p0re1+T2FF/6q+r+U9PVEo+3d3T0IlUgkVaPaJgh/9catrW39/QPoDsHx 0edrQYvfHwDhcAShZA//r371q1q577i2z8+yr2z7/9Zbb+EvIqhkYPODH/wg EokGgyEE1Bvv2LFTdhY6rsmQOXJAp/Das2cPjLdt2+4p7E2kVk/E8vDhwzDQ +0p9r6urW7UgAdn3wyxEFhvYa4sXt8rH8fH8WoaEQsL6zNVHBw4XHiw/7nI5 mC3p6saWII7e/hZd+X3VHBTbdE+qr7VHfZL5mdQ96I6DiJXNmibh+Nl1h0bL TreZrmqH2XaYFstk7Ho/4mrEKQNdpkwONDUZZu8Z0+ypS9R8kTuNqAgXXLpy DRu/r5WNcleeOnUKd4GdzdkJOX5cjI/bSH9b6VN1EP7FsOsI99fhlXr00cck Ybvhi6ODcOeavfTjVf8aoKMiJ1P9K1Ekzkmid8skLUmNj0gxf/zWGwynpIZv bgfiAl+7sA6+fXt2iHswtfx/jR3f/Ft8HL72yjVNAiGEEEIIIYQQQgiR0r2B 5mZPKpW2rPyr4r+UwVX9X+rtZgKBIIIkEkl4qUaXq7GhwQXq6xv0ls3apuXx eCIYDKElEom2t8dCoTC6w7Gy7OrqkiqW7POjUCU1WV+QlOQlnvPzmxEfCaMl HI7ARnbUkZ8VSF3RkHlraxu6htfu3fn6/9at2+RNxGgBfn8AWcnA77svX37U +0qG+vRuueUWtIyNjevNkAnSUGZ33plf14CvMjh58pQU6/ReaHn00UctZ1vP fa6z1WYHs1Wr8Yijt79TV+heNQfF1kZjmbr4HvVJyscxXbRXCqOzzKqYSVAV eEO/KuBWm2vbsiOHabFMZtXe9VhmoiLIrwDCll3ft1zML/4rK8YFN4Xcicbv a2UjLntpeeWVI3Y2Z4ezWnUdnVqm6iAYnENHuMtwh56XDM3jPXDggCE358m0 jOnAqkka/i2yI5BMHPzB87e+8cqexx8wny3U8K83n5ICfnIsZxfZwVdObf7b LxdjTAghhBBCCCGEEEIcUKVyhdvdnEymtX3+O9U+/5mMkE2nM35/QF4cbKj/ WwIDeIFYLA57aZTKf11dPcCxNKLHrq5ueRGAtITD0Xg8Adra/LFYQh/29OnT S0tLN954EMmo3p9++mk0PvLIo3rLgYHBDz/8cHHxwyeeeOLAgavuvPPOkydP wuzmm29RNvJTgvtW6oEHHhweziH+wsJu2G/ZslWK/1rlP9Damt+SSH7FAGMY GAYuycBLPr6lyTw/MEPXGDWOX3nlFeSmP4uxLOXXEZ7WN5rNLLmvUBY+7nI5 mKnS8dMu131WbNF+pqHYoit0r5qDpdcjNh2dPFv/NyZs7vE+XdF7v5ahZVbF TIKuAu+y7NQwA5bcXMS0WCZj1/uiVf3fMhP93Jqnbrlr7RLFdV78V1aMCy5v KSYbvy9To0SD9u8/YGezPCFa4RoXOYJbIjeLObjl/eWA6kh/1+OjJDY6Oubs COM1dWcer9zdqi/nyVT/kqxpdGq2zw2v37//qUeWX/vr95sNdj+WL8uP3XK9 +VSh/j9sF9zOFy7i60/Ei+mIEEIIIYQQQgghhDjgcjXqaWpyJ5Mp/dP+stW/ kEgkA4FgS0urof5vCGIgHk8gZiQSha+0NDS4amvrNGpramrxUboOhyOwTKXS bW1+tMAlnc6gLzlQAXH2oYce/vDDD4PBEJJR7Vu2bFlaWhoZGdX37vcH0PK9 731PPfh68uTJK6/cr7dRRT+DZmfn0NemTdNSo1OP/be2tqFfzICM5StfuRMG hlFjDhcXF5966mk5hoGhUwG5wUxO4eDee+8znDU73nzzzebuzNzbsFxYPqZN rx262rKT2dlJ1hXei7Ev3utYIeF7TQlb+r6le+g9aGNTzCTY9bummVnTAJ/S daQaH7HPcNVMVjXAdYVr5tix48V/ZcW4yB2HG8qYjybj8I/lK9K4yHHb2tko M8ON8PFTtesIQ9A3Ijf5GZFDAueQoeV40ZesReIvjmUyzXNSqP9vWVN3lqNb K/N/+yV5CW+kp9PSYPdj92tl+evMp6SGnxgdtgtu5yvt+FtkR4QQQgghhBBC CCHEAdmHR5Bn9Qs1/+UH/rVn/vOP/ScSKb8/IKVvff3fEMQMXGKxeDgciUSi yri2tq66ukZhcGlqcuNvPJ5AR9LSqP1qALjdHmSiBcwvKIilslFZqfZQKBIM huU3C855Gmhr88t4EVNS0hf/EQ291Nc3gDWF/dS4t1ATPtbglKEqHW8uLuxm nUuu6GT0XnY2xwoG95psLH1zuvZXdA/J6232FdGvMvjcx5gZ/QCzNjZvWQ3w kULjWzYZBoqIvGqqmzdvkdp78dfPvn1XSmnawebee+/VCu/HjPloMjTiXxUp rYu9pU3+Mjh2TKuu31t8qnZpOCMdYWYso0FI2MFxTRnajTeXG5H2Rx55RL4j s4109+Uvf+W8jK54Bq++Qmr4Pbu22tlIWX705uvMp8Q3PjK0Jt9wd6c4oh2+ iiuf/BYa5/7mSw4BCSGEEEIIIYQQQogZqWADt7tZiv/qaf90OqOQJ//b2vxA X//XR7DDpT3JD/z+AHylsa6uvqqqGlRWVlVUVFZVVZkd0YW5BZnE4wl5LwDS 0J/FRynR46CpyY2W5maP7OGPRlWuLwaMS0IhYXF0a28E1i9/oAvZwqj4sJ8m 9+jq/w5mqnQ8X3Rk5XKPVeR99Q0vm6LN67zswh6zD2vne4+u7G9pk9H53mTV 6T6dQe7jzYzztOgz2adrv0nXnrEKqwzO2E/dqqnidpbaci6XK/JbhqW4wNf2 K9OKzN/61iPGfDRZjOWmz8mpL3/5y3Y2EvOee+4tMs/8ZXDPcv2/eBfV0fz8 ZvMpeSz/qaeecnBcU4YOcyLJyzRa2iANNL788ivna3TFEOrqkDr81B23OJjh rKWNu6VF3HFg51uo/1+rb8RHcXRg7m/uOLdBEUIIIYQQQgghhPwZIhVst7s5 nc6o3X5U2T+VSoNEIhkMhqQeLjVweW1uQ4NL3FfF6/VJER5BXK5Gaaypqa2o qKyoqCgvX6a6usYuQmP+dQARpJRM5h/+j0bbEUrlL+8RkC7kiX05hWPJHAfF Zwtc2i5DMlJ0jZbmZo/htw8NhV2Mig/7aXJPoSx8TDdLZlTpeK6+2MhP6irS wytP4eMZVQbX9YvgqiO7sMfqLRwNSTp42dm8WWg/2dCQXnkKH0/qzn7MmXGY Fr8ujTMrO/LrOoKN334+n7T/HotJVWraL7/8suXZL30pX5C/6aabineZm5uX ejUOjPlosvRCNJw6c+aMnU2hun5PMXMuwFjq/8W7qI7MyQPMg6Q3PJw7Lxk6 z8mbb765pNOaksE/bviaEAEHRY5uVZp8Pnnn765H73e2HLhqD8yueeE7hvau nVtk4yAHXwSHzcjnrtU3pmcmV63/G1wIIYQQQgghhBBCiAO1tXUejzeVyhRe 75sHHzXyxf94PBEMhtV7b6UqDhfxLRIYt7S0iqPP16J8q6trNm4sB2VlGxUV FZVoF4P6+gY4RqOxbLYT6Wn5JNvbY8FgqOHsSwTy+HytUufHQWNjE1oatM1/ ZFEAnRafLXC7m9Um/8hBZkn7eHbjozptCQOsKfKnxqFCyf1ovdM3dbb4XJ+3 tOTllRGG6ur09fYn6+v31tXP1dU/XH+2WJ2vReuukDldjdouk6OFhA+ZEnbw TdXW6Ts12+zVdQ1LJDlnle1e0/VczMwc1HnZTQuGc1LXbh7dId3iCCy/pHnt NWWYKuJLnLO/K/fuvULKyE8++aTh1MGDyxXmhx/+lmW72WVoaFhq+EePHrPI R5NlGrgZVfHf0gYB0X7o0D1ruNQP3WOXiQPS0dzcnOVZqclbxjyHDJ3nRE2m nY0sxMAGlobJlDxxCv82Fj86Z2SznYM/eL7R63W29EUjhZr8NfrGa174Dhpn 77rDwXfXo4cNjufLmBBCCCGEEEIIIYQovF6fKvtrD/znSSbTyWRKnrQPhcLB YEi9+hb2jY1NUvfWl75Vix319Q1a2dzb1NSsKuegqqq6rGzjhg1lGzZsKC0V StEiZ93u5my2U36VgMRk53/kY+gRZn5/ULbrQS9y1udrUQ//u1xNq2YIqqtr 5MDj8Um1H9GkRXvsP/9RvfVYb38BcqjubP3fwcy8f44lBq8bV9a6zcBAbz+r q1HbZXK2/l9nTNjZ946VyZgNntQtAVjypKnHImfGMLerTotlR+DN+lUyNMyn Xaqzjnfik08+KRXmkydPPvzww4c0qYfPcYA7pRiXl156WRrPnDkzODhkkY8m uzRmZ+dUrdviMjh6VKuuH1rDpX7okCRz1F7I2bIjJOOcpNlAHDEhDt2Z83ee kzvu+JLDnGCS1QIBBiLfAr4a1XjjjQfPIcm9e/ea++o/sNvh2ftdjx5u9Hr0 9hN/dbOcuuaF7+CsFOrBjd9/3hsJO3xrYpm76ZpivuI1GRNCCCGEEEIIIYQQ hWGrHyCV/0Ri+TF7QfbAl+36NVVL6btWe0S/ocHlcjU2NjYBecOvVPj1b/iV l/w2NblrC2/+haMcyBJASUmpYsOGMjkFe/UyAlmP8Hp95rBq5x95ya8EVzv/ o9GcjCVqXLLPj8fjRQKyK5F67F+K/ximsr8wubtQiz5aX+9gVmT93+y4p7b2 jJUlGm9c+XJnMKOrUdtlour/yNwuyVV97WzuMP1MQGV7hynb4mfGPLd20wIe Mo1L0VJd85DN2sG/1tcjpvN3rYxnVrvO77770JKVvvvdJ3HNr8nl6NGjyWTS Oh9NDmk89NDDdjZSuEanq17hq2ZokGVHMzOztheVZvDmm29atjsLNmudExXW 8uzAwKBhmyDRv/7ryT179jpEc5DlJOduutp5+x1POGRwmfirzxlsrnnhO/5s 2vlb23r/N2DZt393MV/xmowJIYQQQgghhBBCiEJX9leV/3zxPxptb2lpa2xs qqqqLi+v2LixHH81VVZWVmmrANVS/6/TXoAr9f+mJrfb3ezxeL1en8/XIk/j o1Fe9avH621BXzBTLYhcVlZWUlKyfn1JaekGaURM+VUC8pFH8Q1x6rQdsNXO P6ov/c7/yM2cgBVVctDQ4JJN/tWqB1rUY/9NTc3y5l81Dxcmvqrq6ZoakNDW KewYqK4RM2fs3G+oqX2otu5oXT3AAT76bCwlzoB9MolCJuYIKslVB+sQ37eW bIucGbu53a3r6Lt1dX9dW+v8LagZgCXsxfHu2rrdpgveOdWiLgxfyw033PjQ Qw8dPXr0u9/97t133437vXiXl156CS4DAwNO+QwMTE/POAeEgaUNkkE7DIoZ iyGaA+aEJUmHjiSs2VEydMY8pZahiunOkDMmH18Bvggc7N69x/krWGuSQmSw 1462TMrSpTkU7Nu/a/jg1SAxNVbMtyYuDc3N592YEEIIIYQQQgghhCik5q+e +QfxeCIabQ8Egg0NrhrtFb2yRb8sAWirAJWgSvcTgDrt9btqCaC52aNfAkCL lMoVcAkGQ/Jbg3A4Akf9WelFjtGFPGlviCDglNqYCB2h3yrtFwpud7PsWSQb FknjqqilDbjL0/44kK5lUFrx3y0/c0C7TEUxkQkhhBBCCCGEEEIIIYSQTxl5 2l92+wmHo/Kq30AghAMQCoFIOBzBceFh/mbZwKey0m4XoPxPANQSgNeb35BH lgwUjY1NsVj+tcKRSHt7exx//f6gvBegSvshwKrADF1oT/gv7/wjdX6cQpDC zj/5h/+RWzEB1dIGxlUo/nuQp/SFY1X8lw2OZFlErYYQQgghhBBCCCGEEEII IRcUkUg0GAxpJXQ//ra1BWQ7Hb9fVgEEWQhYXgsIh6PwAjCQB+xlVxxtCaDR 5VreBcjt9shu+VVVNVJd11NdXRMIBBETEXAgOfh8+Wf4GxubamvrzC4K9CK5 qeK/PPmvha2V9QvZ+QehHOLo2ZhXvp5fV1cvW/1gFDU1tWhBMjgGGJoU/9EO 47KyjUUGJ4QQQgghhBBCCCGEEEI+ZXy+Fp+vtaUFtLW2CrIQIGsBQa2crtYC VvwoQLcW0A6iUfkFQUh2yCngrtDtIGSgtrYOXWuLCC2ywQ5oaGiUAruB6uoa 2Pj9AS2NkHrnL1zKtTcUyJqCtioRwCiam73SviplZRs3bCiT46amZq343yxr B2hpaHBpj/034QDU1zdUVlbBBRQTnBBCCCGEEEIIIYQQQgj59JEterRVALUQ oNYC5EcByz8HKKwFGH4UEFE/CpDtgxCwvr5B0dDgklK5AxXapj3y7gC41NbW SYEdvtrLdpuRDPpCL/grOxRpT/4HkCfsJUjhyf+gPPmPQZWXV6zatVBaumHD hjItSI3bvVz8R0ryhL967B991dXl09O7EEIIIYQQQgghhBBCCCEXIC5XY1OT W1sF8Mkbe+WlvUJra1vhtwD+wr5AgcIvAoKyEFDYGii/k4/2ggC3vBFAqK6u 2bChbE1sLDyQj95loyGp/GvF/5B64a88ny8uDQ0u/SkMoaKissjuSktLS0pK 5VjWIGSTfwmOsajH/uvq6mVtorR0g3IhhBBCCCGEEEIIIYQQQi5ASks3CBs3 5l9lq73J19XY6Nb9IsByX6AVvwjAR4/HJ7v919c3VFVVV1XVVFfnQUzVxVpB 7/L7gsKGP/kN/5FGY2PTxo3lYiNbGBmK/2gssouSktL160vwF8eVldWq+I95 QEuZ9hsE+SGDFP9ramoxacqFEEIIIYQQQgghhBBCCLkwKSkptaNUq65XV9fK C3A9Hq/lWoDP1yr79gs1NbXyZuHKyirZxsehC0GWIcztXq8vEAhpBNG7y9VY VVWt92pocMlZ2Q5I2/Pfs3Fj+ao9Ki6/fD2QY8SX4r/sWYQWdFeo/NfX1NTJ 0NavL4GLLAEQQgghhBBCCCGEEEIIIRcm69eXrIny8oqKiqra2jqXq8nrbdF2 y3frKbwbd/n9AqWlGxyi4Wx1dQ1CVVZWm89KBDvf6upaKftL5b+lpQ1xSkqc ujNw+eXrL7vscinmV1VVu1zuhobG+noXUpLcpPIvj/2jsaqqBo3itdZ5I4QQ QgghhBBCCCGEEEI+TeQB+HOjoSH/wLyBwp5Cy/sL2XWxXltKqKurl3cE429J 4Wl8Oy677PJLL71MkLq9x+NrbW1raZG3/VauKXkVDcdIGJmrTf6lyC+7IWmV /9qqqpqqqmokLF7SOyGEEEIIIYQQQgghhBBywXLZZZefG/B1uRoN1Nc36BYX 8r8vsHTcsKGssrKqurpG3hRcV5evuldUVDr3uG7dX15yyTr8/cu/vFSK8Aji 9fqqq2vR3RrzvwxBgHysra3XnvzPpyFFfgSUyr/22H+17GWERnSsvAghhBBC CCGEEEIIIYSQCxb1RP1aKSnZ0NDgMlBdXasiX77yiX1h/fqSsrKN2iZC+RcE VFVV19TUytb68IWLQ4+XXLLu4osvkSUAoJ7eP4fk1607u45QUVGFzGUNQvJH Y3l5pVT+AQyQLdKGvfIihBBCCCGEEEIIIYQQQi5k5DH4c2DDhrL6+gYD5eUV dvaXaQ/Vl2jv7S0r27hxYzmMZQlAdtfBMU459HjxxZd89rMX46/U/88580su WaetIuQjlJZuqK/PF/+1rX7q1q8vlUYtn3xKFRVVyFN+FLBuHRzXnXO/hBBC CCGEEEIIIYQQQsinxrpzVVlZWZ2mWp1KS0svKUhvvLxfz+Xavv8lJTDbUFgG qNBUXl6+URMs7Xo0hz0HXaxJ4iAl2YEIf6urq5GSpFpRkMoKacNFOVIURVEU RVEURVEURVEURVHUBa5LzlUVFRW1K1VTU3PppZderJN+LeDsrv2XXy5LAGVl ZfAqLy/HwQZNaJRK+yekz372sxdddBH+Skr64j+GIzZIprygjRs3Sm7iqx8R RVEURVEURVEURVEURVEURV3IuvhcVVlZWW3SZ62kHptXSwAlJSVVVVUNmuBV Wlpaomm9pnWFp/TPo5DGX2i66KKLJB/kX1NTU6WpoqJCOkXvGwtSqxJIWy0c nPfEKIqiKIqiKIqiKIqiKIqiKOqTkGXFvhhVWekvVuoiTapsfskll1x66aXl 5eW1tbV1OpWUlFyu6bLLLoOB1NvPo5DDf9KElCSZioqK6upqJFxZWYl81q1b h3Z0LWV/qfyXakJWcJexnN+sKIqiKIqiKIqiKIqiKIqiKOqTU4aiKIqiKIqi KIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi KIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi KIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi LgCdeOvEj3/84+PHj//whz/8/ve+f+TIkZdfevnFF1/8xxdeIIQQQgghhBBC CCGEEELIBc6LL7748ksvHzly5Pvf+/4Pf/jD48eP//jHPz7x1ol333nnF2+/ /fOf//wnP/nJP//oR2g/dvToP/33fyKEEEIIIYQQQgghhBBCyJ8Ex44ePX78 +D//6Ec/+clPfv7zn//i7bfffeed06dPv/fee+/8yzu//OUv3z7x9ptvvvkz 6Kc//en/IIQQQgghhBBCCCGEEELIhc7PfvrTn/3sZ2+++ebbJ97+5S9/+c6/ vPPee++dPn36V7/61fvvv4+DkydPouXdd9/FKfAvFEVRFEVRFEVRFEVRFEVR FEVd8JKq/rvvvvvee++dPHny9OnT77///q9+9avFxcUPPvjg17/+NY7/7f33 /5em/0lRFEVRFEVRFEVRFEVRFEVR1J+IpLb/b1rZ/9e//vUHH3ywuLj40Ucf /eY3v/nwww9xfAb6gKIoiqIoiqIoiqIoiqIoiqKoPzGdAWfOLC4ufvjhh7/5 zW8++uijP/zhD7///e9/97vf/fa3v/2IoiiKoiiKoiiKoiiKoiiKoqg/Wf32 t7/93e9+9/vf//4Pf/jD/ynof1MURVEURVEURVEURVEURVEU9ScuVfb/fwX9 X4qiKIqiKIqiKIqiKIqiKIqi/sSlyv7/HyiXBEA= "], {{0, 71}, {2048, 0}}, {0, 255}, ColorFunction -> RGBColor], BoxForm`ImageTag[ "Byte", ColorSpace -> "RGB", Interleaving -> True], Selectable -> False], BaseStyle -> "ImageGraphics", ImageSizeRaw -> {2048, 71}, PlotRange -> {{0, 2048}, {0, 71}}]], "", PageWidth -> DirectedInfinity[1], CellMargins -> 0, CellFrameMargins -> {{0, 0}, {0, 0}}, CellChangeTimes -> {{3.544379162237352*^9, 3.544379175555642*^9}, 3.574009622854604*^9, 3.5740096771925993`*^9, 3.606497282354394*^9, 3.606497322480124*^9, 3.607965342107291*^9, 3.607965382772916*^9}, Magnification -> 1.]}], Cell[ BoxData[ GraphicsBox[ TagBox[ RasterBox[CompressedData[" 1:eJztnWmQXNWV5x0z82E+TWNQA6pSqfYlq7Iys6pyr9yz9jVrV23aSwtCYkcY sMHd2MYL3YMAAZ4eMIuJ9rTZP9AsAtsRnpYE7rDHNgg7oiFoSRND2xGoCONl lpp/vlN59eptlSUElsP/f/yoeHnfOeeee/M9EXHuy/sqt181uuvffeYzn7nu P+LP6LaD6Wuv3fa5sf+AD5nPXb+w/d/joBv/fQan88ddXT3nzPz8FjNDQ7m+ vn7Q25unp6fPzr2zszuT6Ugm04lECnR0dDl3l0gkY7EE/sIlnc7qT/X1DVi6 TExMIqW5ufmpqenu7t7ih4aAO3fu2r59J7zQlwFk/nHmjRBCCCGEEEIIIYQQ Qgj5pOns7C6Svr6BoaHc+PjkzMzctm07FhZ24+/s7LyBkZGx7u5eRRFddGUy HalUZtUEstnOdDor6wVwUe2jo+NIZmxswtIL7cgKOdsZ2DE5uWnnzl0Yr6Qn pNMgi0zWFIoQQgghhBBCCCGEEEII+ZTJdnRZ0tnV09s3kBsZG5+Y2jQ9u3Xb DrBt+06wfccC2LFzF8DBzOw8DBRDwyN2MddKX//gwOBw/8CQoT2T7QQqT6Sx sGvPzoXds3Ob8dEcB6NAYpNT02vKDaFk1B2d3YlkGiRTICOcrzESQgghhBBC CCGEEEIIIZ8EUksHPb39/QNDw7nR8Ymp6Zm52bnNc/NbwPzmrWDzlm1btm63 WwWA2dSmGSE3MpbOdGhkBdXFWkHYhV17ZJUBxxOTmwYGh/U5g5HRcSn+ixny 7O7pM8SBy9j4JNwxNAyz+ARGxyYwUvxNpjKyBKDAAM95XIQQQgghhBBCCCGE EELIJ81wbnR0bGJyanpq04w8wD89MzczOw9m5zbrVwE2b9kmqwCyEGBYBUAj IiBObmQsmTKWys8N9L5zYTfioyPERxrICr0MDY90dvWITbajCwlL8V+ZdXX3 GkJhpGPjk2BkdBwuzv1mtNUQCY6YGHsqnY0nUno+zrgIIYQQQgghhBBCCCGE kE+aiclNgiwB6FcBZCFArQKoHwLoVwFkIUCWAHAMx9zIWCye1JNMZVLpbJEk kql4IhlPpHA8PjGFBJCGPLovSYKx8cnh3Ghv30Am2yleg0M5yQe5IUm4dHb1 GCKjZXRsYmR0fGBw2CGBnt5+DAFIBPSLsHBBSvpBSYaEEEIIIYQQQgghhBBC yIXJzMzc5OSmiYkp/J2amgabNs2A6elZgLNAXuw7P78FbN68FWzZsg1s3bod bNu2A2zfvnPHjgWY5XKj7e1xPclkWr0/15JEIhWNxkKhiN8fbGsLtLb6A4EQ 2ru7e/v7BxFwbGwCiSGT8fHJ4eGRoaEc/g4MDHV0dKkgXV09khuSRBqw158V +voGRkbG4Gs+JaAdfY2OjqNTdC1hMUZMDkYRiyWEeDwJkLbzuAghhBBCCCGE EEIIIYSQPxbbt+8EmzdvnZ6enZzc5LwKMDe3GahVABzj7NjYxNBQrru7N6VV 8mOxRDQaC4ejing8kUymLYExDILBcCAQAm1tgbY2v1b/D5qNM5mO3t7+XG50 eHikp6cPPRoMstlO5IyskC0OkBhS0hvg4+DgMLLt7x+0SwnBZY0Alul0Fi0Y 49at2xE8FotrnF0FsAtCCCGEEEIIIYQQQgghhPxxkaf3ha1bt8/Nbd60aUYt BBhWAfAXjTg1Ojo+ODjc1zfQ09PX1dWTzXZKqTweT7a3x6X+HwqFBXxMJFIG YBmJtIdCkWAwHAzmi//aw//54n9bWwCNZhdFR0cX+kWPlqckW+Q5MTE1MDBk MECqyBztOLAM3tnZncuNDg3lYINjtOBgy5Zt+BuLxQ0/bXBIkhBCCCGEEEII IYQQQgj5IzIwMCTb+GzZsk2e6pctdOQRetkaaHx8UnbFEVR5vK9voLu7t7Oz W9X/Y7FEe3s8EmmXp/oFfJQNcxTKJhQKy8P/YoZ2g6UdstZgSSbTIZkj7ZGR MeRmMOjt7e/vH+zp6bN0x5wMDg4DZYO+MCcIKD9t0KP2AiKEEEIIIYQQQggh hBBCLijaY4ncyNj85q1z81sEeeEvmJmd3zQ9OzI6Lu/DVQznRgeHcv0DQ719 A13dvR2d3ZlsZzKViSdSiBaJxsKR9mAokn+kXyMUjqJdEdUM0BiUh/9DkWh7 XG+AOBIKpLQX8qYzHXqD/GsLZufRrm/Ug6zGJ6ZGxyaQKvKMacNUIFVkDncc 2LnL6GAjmUxOTWNmcIzMhYgQjdnlQAghhBBCCCGEEEIIIYT8EYm2x8FwblQK /sL0zJywaXp2atOM1Pz1DA7l+voHe3r7u7p7sx1d6UyHof6/XCSPxiS+nrPF /1BEb5BIphGqs6sHf1PprDTieH7zVqQ0OjbR3dMXiyfRiANki9yQgyFymz8o xwODwyOj40PDIzjIZDsNOSBtBEFwc3oAY5HRwUYy6e0bQI/ITZIPR4T8GC0j EEIIIYQQQgghhBBCCCF/XCLRmDA4lFM1f2Fq04wwPjE1NDwitXSFVMg7u3rS mY5EMi1LCSqaM1L/Vx9j8WRXd688b48DiSmnMtnOufktyAo5DOdGYRNPpNCe 7eiamNw0OjYBY7FEQI/X1+zx+gMhiZkbGZPfKXT39BlyQ8LyywW7nNERvGCD BPAxmcrMzM5j1Mg8FI5oRIUih0wIIYQQQgghhBBCCCGEfKqorWwi7YODw/LC 36mpaUFeBCwv/B0YGOrvH+zrG+jt7e/p6evu7k0m03r3cyOdzsrbBBBcRc5k OuQsDubmNk9Pz46PTw4Pj8AgFkvIqUQilcuNwiuVyoTD0eZmL/B4vF5vCz7C AHHUNv6GVKPRWFdXT0dHV1x7DbGZzs5uuItNVJul2dn5sbEJ7Z0FET3SFyGE EEIIIYQQQgghhBByQREOR/X09w+qmv/ExJQg7//N5UalON/V1dPZ2d3R0ZXN dsZiCUOENZFOZxF2eHhkcHBYlgBkWaG9PS4G0WgMveDU6Oj40FAOnerd0Xtv b78Yt7S0ejxej8cHWlv9aEG7eklxJtNh7hqR0ZdlYqlURoYJm/wLC8JRJDAz M6d/r7EgSwCEEEIIIYQQQgghhBBCyAWF4Wl20NvbPz4+KYyNTYDR0XFhcHBY Vf7T6WwqlUkm09FozBykGBBhZGRM6v9DQ7m+voFYLGFnHNF+C+BgEAyGteL/ 8hKAVOaRJ4bT1dWDA0TQ2yMUAiIHy2jt7XEZqeq0p6dvZmYuHk8GAiE90hEh hBBCCCGEEEIIIYQQckFheJpd6Onpk7L/yMiYkMuNCn19A6ryn0ik4vGkPH5v GceBaDSmIg8Pj6BHczKdnd0OEXy+VqnzK1pb22QXINDa6kdLLJZAZMTJZDqQ p944rP0EQPYOsoyvljkQBB9xPD09i1EHAiG/P6iQJQBCCCGEEEIIIYQQQggh 5ILC8DS7oqurR6vMCyNDQ0JucDDX09MXjydjsUR7e1z2xpcSul0oS7QtfSZG RsZzubHe3n79qba2gNTV+/uH4vGUNIbD+V6QAMBZr9fndntAa6t/dnY+k+mQ sryq/09ObpJG/E2lMolEat++/Xv27AWIIDG1JYz8ewEkrCHDdDqbTnckkxmM FF4HDlz9xS/+9fXX37h7955du/bg78zMrCwBoAuJLCAf57GjL2cby3zQy6qR /yjsaW1TZLQv7oIF6X1q2Z5bR0NtAb3jJ5he4XKV2+QTciHnHfzLUOS/Mx+T 7tlN81/7qyue+C9g+os3J3p6HIxzB/bu+q+HxBhezsYq/vjBayIJ4y+qDMAA ZsUEJIQQQgghhBBCCCFm2vwBO7IdnYNDw2BgcEjoHxgUOjq7wpFoKBwJhsKB YMgfCDrEQYSe3r5ItB2W0tIei4+OjY+MjoGh4Zxqb2lta/Z4m9zNXl8LPmay HX39A+gF3eEAfT33/POLi4u+ltYmtxtmINrevrS09Npr35MIHq/P3ezZtn07 Ghd27ZbG666/Hl5LOn37iSckjVg8gfhvaDKkHU8kk6k0/u4/cGDJRq1tfvDg N79pPvX2229Pz8xaTsip06dhMDg4ZDdjyBbuhkaMHV6pdMbSZbq1bamhoUju 8nrP9uVyrWoPG3OPqTb/c83NZmM0Dra22aVnGUp4ze02p2dI8kGPx3bSNBu7 +Eip+GwNnU7bGFgi02Ke1Teamnbh+rZ3xFnYmGce0RDTcqJgbxnqdq/PbrZx 1cmFpBcu/l2799glZumC6/P227/ocAFDDgbKxtyOe9PudlNS97uAG3xVF3Nf CGJpidsTE3LXXX9jd6/ZOeol/8KYx2v3b4LMs+WNf/Zrvf2L8k+HflD4x8cy z2KSxBgtOwon4gt/d+jWN14xMLTf4iKB8YGnHyvS2Bx/7ODVDhcJ2HbPV2E2 91Wna4kQQgghhBBCCCGE2NLmdyCb7RgYGAT9/QNCX1+/kMlkg8FQIBD0a0Fa W9taWlrx1xAhFApPTk4NDg7hbyQSlcbu7p6xsfHR0TGQSCTRglDw9flaEET5 oove3j50Go8nOju70HL77bcvLS1NT894PF63uxlcddXVUstKpdIwgDsaDx++ Hy0SGcZLWrnyuuuuhw0+vvbaa/kC3befCIcjsVgcWS3X/1dm3t4eSyZT6Hr/ /gNarewu9H7zzTcvLOxSIGfw4IP5+j/i79q1W4CxlPsGBwcNYXG2UHy7y3LO JeGl/ALBCl9ZwkAvll67fC3F1/8fbPYoxyJdjEm2tDosHODUtO57NKRnd7Gp 6rc+PXOShshmG8vJcc4WBg4BLc9af3eO0wJu93otHdHuvP6iH7V+Mq/z+Qyh Uq1tZ5dLVs4kLi39Qhiu+VOnztaTcXmbE8P15uDy3HPPW38Xheq0+fo32Fhc Bm+8sWrh2nC3yg24qtbaUb5cPz1zXjJU48Xsyb9UFldp4V8Gy7OYahUcQfQ5 4B83c8xiksS8Wfa18Hd3S3F+26Gvbrr9JnDdi/8gLZ3TkwbjK574ZvHGAI3K AMDe4YYKx+OF1YTdRd6DhBBCCCGEEEIIIUSPVLAdSKczqubf29un6OnpTaXS UvYHPl+L1+sDsgqgSCZT4+MTAwODudyIahwZGZX6//BwDh/9/gACJhJJOSsB cYD4mUwW7dFoezbbgRbE0cpWD6I7t7u5udnzzDPPSH3ytttuF1+0v/XWCYBk 0PLaa6/BAHECgaAarywBdHR0tLfHwoXn/w0Dj0Si6DoWi1955X4YLyzsQsJI QNLTg3xgYHCfnp5G4ze+cZeh/bnnnkM+Wh31lOWEw0Wqc3rfa6+9TgqScLf0 ml5L/f8bHo9yLMZ+0eVa8Z2urHKfcrlea2p6zu0+pWuEQVJ3JSwUnkgHdlea rv7fbDilT+ZEY6Olu138geKyHVh53eoDLmgX0qpgvKesOkLC+vzN0a7VTY4M EF7wNaStn8/nCj8BMLTnV6MKP3M4tfJbw6UrdwouPFxOZ7+ahV0nTrwtl5y+ 3cEF7XIHLeXX0b5t8V3oyuB20yUGFpeBVrjGda5faDOABFYMWbsBMQoHF9yP lh3hLjMbI6AMHH/xL9jHz1A/J3a3MLzs5gSTrGZbRUZiMnAZe/GjU5iHBlLD g8tP5t94lWoMxWIHnn4UjQt/d7elcef0hN5477e/aTYGQ1fuFvuDP3ge4GDq tpsc7imchc11L/5DMTcgIYQQQgghhBBCCDFjrmabSaXSPT29iu7uHtDV1Q0S iaSU/T0eL2hu9rjdzbIKIGQy2dHRMXGUlkAgqB7+7+zsQksymervH2jTnt73 +VoEsQyHI5FIVErx6XQGlr/4xS/eeOMNqfOju8XFxWeeefbUqVOvvvqaxIfx 0tLS4cOHcRYfcfzCCy/Avb09hoBis7CwgPbdu/dEo+3o4vXX3wCGUaM9Hk/A a9++K7X6/4L8AkKfpPDAA/kqnHne0IhT+hakgcZnn33utttuk5hmL0kGIzpx 4oRqhAtGijGivZivDDzgXq4Dv97Y5GCmq0t71xoZ4Fh/6uvNHstTC7rn2+3C Ik/LmPok7Qz0Nob2Z5vc6tTXtUvCMttXm4yztNaZcZgWRFDF/FMul8FRrRrA xtCXXcx+3XKPXfttnhWDxSUkBW1chJZXHc6qm0jARyn+W7qoorTcFCumTifD LWCwscvEzst65rUb0HwLOyMdWd6DYNOm6cLC4m0fP0PDnFx77bVmA/lHyTwn mF6HmVReSLj40TnQu31eSu6G9sF9u6Rur2+cuu0gGg88/ahlEGBol0WEvd9+ MNqRxV+t/n/QLpNge7usEYzecNVaR0EIIYQQQgghhBBCBEMp245stkOV/Ts7 u/TEYnEp+4OmJndjYxPweLziCJdcbkR+LCAtkUhUiv8jI6PwRUtvb5+cRRzl qAgGQ6Ctze/1+nDw93//90tLS/F4Asay+Q/+Pv74t6UR9gcOXIXj8fEJGOAj jh9++Fs4FY22+/0BiYmPsv0FktHq/3kZ+g0EgkgPXvv27YPxzp0L8iMI9UsH xQMPPAADg/vXv/51NH7hC7eZG6emNuF4cXHx2WefNXhJYggoI5LulDGiKfdV eaDwiPjrjY0OZqpcvNM083aoevWrTU12/T7b1NSHeIVGBFcd2YV9vfCcPCLY JemQrWX8uO7RenNY/SyBuC7hc5iZRcdp+YJurWFKF/AaXbtlR49bzac+c/Sr Tqk5NH/pUiU2XJD6Cw8Xp9xB+kvRwSV/JZw6BQM4Wvb16quvyoHlFSunLC6D 11+XW6DIqzE/FdoNaL6FnZGOcF/bGeCO01brnv34Garxii9uZ/1UC8jEck5k dJhqu8jXXHOteRSrjs6OQDQ6csOBxGC/oT07NS4lfX3jlrvvRMvkFw6a44hx tCOjb0TYwX3LKUn939JXwClZcUBKax0FIYQQQgghhBBCCBEMpWxLEomkPO0v dHZ2dXR0Kvz+gFb8d6viv8vVKL8CAN3dPcPDOXglkylpCYcjqv6PY7TkciNy AC+Px2vo3aeV4lu1/S5gtmPHzqWlpauvvkZt/oMDfETj5z//BdhLozv/8wDE 8mn1/4dln39ZRBC0+v+DCBgKhaX+b+gXPba3x+B1xRX7tB02Try+Usry/vvz BbrHH38cB+DZZ5+FsbgYYspT/XIMe9ggMb2BDGRycgrg4Gtf+7pqxN/e3j7V uCr3N52t/zuYqeLzDm26VqVXV8m/urm5GBewQ1fltrNRtWtkbpfkKd1T9DGv 19LGrl+DvRDT/TDBMANrmplJz9mOJj3W9ip5/QDV14SzRU6mynyxobDi0Nhk GKwhZ7lrzNeb01dWcHGwkWvYfO+ovmSBwHwjKBuLy0ArXOM+Kn4q5AY0p+GM dIRhrjXsOWSoxotbWH5WYA5rN+HSHab6/I5urYxcv//WN1659h//m76xUMO/ 0Wwv9f/M5JhdQAdfAX05GxBCCCGEEEIIIYSQVZF9exyIxxNazX/5sf+OjjzZ bKdGRyAQVE/+q/o/DpQ7XAYGhuCCOKqxudkjPxmQjzAIhcI46Orq8fsDhgSQ JBpbWlrT6WxraxtaZM+fwuY/z4gZjo8ceRUHp06devrpZ5CDxF9aWnrooYdl n39xF2Q/DfQbDIaknm/oFz3K7kB7915hrv9LX8L999+vN5CaJxrRqT7g9u07 tEWKz8vHiYlJrZj/Nb0NxoWByDHiSC/6RvSi79qB+wvb6b/e2OhgpirG2wtf hzPbdTvSFGNfvJeu/t/kkKQ6fmylmWV8NQknXC67fk+cLctbByxmZs55gEcK jUccvyZLvqbb2ggJqPUF8zeOq04u0eKDy1Vtvi/MYc02Usf2FK556LHHHrez Mc7ScnX9/vObql1HyNDOADeaZebnkKF+vDJp5ntfzZXBUf49ufrqq8/v6NaK VONnvvIFfeOex/M1/InP32i2L9T/R+0COviC/r075eH/tnD4fA2BEEIIIYQQ Qggh5M8QKcXbEYvF9Vv9qGf+s9kOeaOulPENxX99BHl9MP62t8dUo3KRPfwR ORyO4ABhYWnIQd5T7PO1IFvZh/zIkSOnTp1Sm/+I2TPPPIOPExMT+HvLLbdI fLRr9f+HotH2UCgMXzHu7u6RB+mDwZDfHzh+/HVg6LdVewUwvPbs2atV0rbb zdLhw/nyo/oIS61s+JjBTDJEO+yFxcVFDERvo9X8j8gxLGGPzGWZQ9/o/K0t Z1XYTv+4q9HBTBWQn2lshIuZCe07Ojs63YY5xaRh9rLsBajyNY7tkszPQGFc WtHbbWmzpknAKct+LXspZoB2No9ZJWPXe5GcfXeAbnOk7pVfmbpEzRe50/VT hItc6uYLUt8oV6z5DrJ0zE/I8XzhGr2f31TtOrK7r2+9dblKr/6F+TgZGsaL e3xJ2wUI/14VOZkO//6cw+jWysTnb5B6fiid0rfvefwBrYZ/g8UEavbpiVG7 mA6+QJYbNv/nr8hH9Ju77srWUOi8DIcQQgghhBBCCCHkzwd5et+Mx+NNJlOW lX+p0re1+T2FF/6q+r+U9PVEo+3d3T0IlUgkVaPaJgh/9catrW39/QPoDsHx 0edrQYvfHwDhcAShZA//r371q1q577i2z8+yr2z7/9Zbb+EvIqhkYPODH/wg EokGgyEE1Bvv2LFTdhY6rsmQOXJAp/Das2cPjLdt2+4p7E2kVk/E8vDhwzDQ +0p9r6urW7UgAdn3wyxEFhvYa4sXt8rH8fH8WoaEQsL6zNVHBw4XHiw/7nI5 mC3p6saWII7e/hZd+X3VHBTbdE+qr7VHfZL5mdQ96I6DiJXNmibh+Nl1h0bL TreZrmqH2XaYFstk7Ho/4mrEKQNdpkwONDUZZu8Z0+ypS9R8kTuNqAgXXLpy DRu/r5WNcleeOnUKd4GdzdkJOX5cjI/bSH9b6VN1EP7FsOsI99fhlXr00cck Ybvhi6ODcOeavfTjVf8aoKMiJ1P9K1Ekzkmid8skLUmNj0gxf/zWGwynpIZv bgfiAl+7sA6+fXt2iHswtfx/jR3f/Ft8HL72yjVNAiGEEEIIIYQQQgiR0r2B 5mZPKpW2rPyr4r+UwVX9X+rtZgKBIIIkEkl4qUaXq7GhwQXq6xv0ls3apuXx eCIYDKElEom2t8dCoTC6w7Gy7OrqkiqW7POjUCU1WV+QlOQlnvPzmxEfCaMl HI7ARnbUkZ8VSF3RkHlraxu6htfu3fn6/9at2+RNxGgBfn8AWcnA77svX37U +0qG+vRuueUWtIyNjevNkAnSUGZ33plf14CvMjh58pQU6/ReaHn00UctZ1vP fa6z1WYHs1Wr8Yijt79TV+heNQfF1kZjmbr4HvVJyscxXbRXCqOzzKqYSVAV eEO/KuBWm2vbsiOHabFMZtXe9VhmoiLIrwDCll3ft1zML/4rK8YFN4Xcicbv a2UjLntpeeWVI3Y2Z4ezWnUdnVqm6iAYnENHuMtwh56XDM3jPXDggCE358m0 jOnAqkka/i2yI5BMHPzB87e+8cqexx8wny3U8K83n5ICfnIsZxfZwVdObf7b LxdjTAghhBBCCCGEEEIcUKVyhdvdnEymtX3+O9U+/5mMkE2nM35/QF4cbKj/ WwIDeIFYLA57aZTKf11dPcCxNKLHrq5ueRGAtITD0Xg8Adra/LFYQh/29OnT S0tLN954EMmo3p9++mk0PvLIo3rLgYHBDz/8cHHxwyeeeOLAgavuvPPOkydP wuzmm29RNvJTgvtW6oEHHhweziH+wsJu2G/ZslWK/1rlP9Damt+SSH7FAGMY GAYuycBLPr6lyTw/MEPXGDWOX3nlFeSmP4uxLOXXEZ7WN5rNLLmvUBY+7nI5 mKnS8dMu131WbNF+pqHYoit0r5qDpdcjNh2dPFv/NyZs7vE+XdF7v5ahZVbF TIKuAu+y7NQwA5bcXMS0WCZj1/uiVf3fMhP93Jqnbrlr7RLFdV78V1aMCy5v KSYbvy9To0SD9u8/YGezPCFa4RoXOYJbIjeLObjl/eWA6kh/1+OjJDY6Oubs COM1dWcer9zdqi/nyVT/kqxpdGq2zw2v37//qUeWX/vr95sNdj+WL8uP3XK9 +VSh/j9sF9zOFy7i60/Ei+mIEEIIIYQQQgghhDjgcjXqaWpyJ5Mp/dP+stW/ kEgkA4FgS0urof5vCGIgHk8gZiQSha+0NDS4amvrNGpramrxUboOhyOwTKXS bW1+tMAlnc6gLzlQAXH2oYce/vDDD4PBEJJR7Vu2bFlaWhoZGdX37vcH0PK9 731PPfh68uTJK6/cr7dRRT+DZmfn0NemTdNSo1OP/be2tqFfzICM5StfuRMG hlFjDhcXF5966mk5hoGhUwG5wUxO4eDee+8znDU73nzzzebuzNzbsFxYPqZN rx262rKT2dlJ1hXei7Ev3utYIeF7TQlb+r6le+g9aGNTzCTY9bummVnTAJ/S daQaH7HPcNVMVjXAdYVr5tix48V/ZcW4yB2HG8qYjybj8I/lK9K4yHHb2tko M8ON8PFTtesIQ9A3Ijf5GZFDAueQoeV40ZesReIvjmUyzXNSqP9vWVN3lqNb K/N/+yV5CW+kp9PSYPdj92tl+evMp6SGnxgdtgtu5yvt+FtkR4QQQgghhBBC CCHEAdmHR5Bn9Qs1/+UH/rVn/vOP/ScSKb8/IKVvff3fEMQMXGKxeDgciUSi yri2tq66ukZhcGlqcuNvPJ5AR9LSqP1qALjdHmSiBcwvKIilslFZqfZQKBIM huU3C855Gmhr88t4EVNS0hf/EQ291Nc3gDWF/dS4t1ATPtbglKEqHW8uLuxm nUuu6GT0XnY2xwoG95psLH1zuvZXdA/J6232FdGvMvjcx5gZ/QCzNjZvWQ3w kULjWzYZBoqIvGqqmzdvkdp78dfPvn1XSmnawebee+/VCu/HjPloMjTiXxUp rYu9pU3+Mjh2TKuu31t8qnZpOCMdYWYso0FI2MFxTRnajTeXG5H2Rx55RL4j s4109+Uvf+W8jK54Bq++Qmr4Pbu22tlIWX705uvMp8Q3PjK0Jt9wd6c4oh2+ iiuf/BYa5/7mSw4BCSGEEEIIIYQQQogZqWADt7tZiv/qaf90OqOQJ//b2vxA X//XR7DDpT3JD/z+AHylsa6uvqqqGlRWVlVUVFZVVZkd0YW5BZnE4wl5LwDS 0J/FRynR46CpyY2W5maP7OGPRlWuLwaMS0IhYXF0a28E1i9/oAvZwqj4sJ8m 9+jq/w5mqnQ8X3Rk5XKPVeR99Q0vm6LN67zswh6zD2vne4+u7G9pk9H53mTV 6T6dQe7jzYzztOgz2adrv0nXnrEKqwzO2E/dqqnidpbaci6XK/JbhqW4wNf2 K9OKzN/61iPGfDRZjOWmz8mpL3/5y3Y2EvOee+4tMs/8ZXDPcv2/eBfV0fz8 ZvMpeSz/qaeecnBcU4YOcyLJyzRa2iANNL788ivna3TFEOrqkDr81B23OJjh rKWNu6VF3HFg51uo/1+rb8RHcXRg7m/uOLdBEUIIIYQQQgghhPwZIhVst7s5 nc6o3X5U2T+VSoNEIhkMhqQeLjVweW1uQ4NL3FfF6/VJER5BXK5Gaaypqa2o qKyoqCgvX6a6usYuQmP+dQARpJRM5h/+j0bbEUrlL+8RkC7kiX05hWPJHAfF Zwtc2i5DMlJ0jZbmZo/htw8NhV2Mig/7aXJPoSx8TDdLZlTpeK6+2MhP6irS wytP4eMZVQbX9YvgqiO7sMfqLRwNSTp42dm8WWg/2dCQXnkKH0/qzn7MmXGY Fr8ujTMrO/LrOoKN334+n7T/HotJVWraL7/8suXZL30pX5C/6aabineZm5uX ejUOjPlosvRCNJw6c+aMnU2hun5PMXMuwFjq/8W7qI7MyQPMg6Q3PJw7Lxk6 z8mbb765pNOaksE/bviaEAEHRY5uVZp8Pnnn765H73e2HLhqD8yueeE7hvau nVtk4yAHXwSHzcjnrtU3pmcmV63/G1wIIYQQQgghhBBCiAO1tXUejzeVyhRe 75sHHzXyxf94PBEMhtV7b6UqDhfxLRIYt7S0iqPP16J8q6trNm4sB2VlGxUV FZVoF4P6+gY4RqOxbLYT6Wn5JNvbY8FgqOHsSwTy+HytUufHQWNjE1oatM1/ ZFEAnRafLXC7m9Um/8hBZkn7eHbjozptCQOsKfKnxqFCyf1ovdM3dbb4XJ+3 tOTllRGG6ur09fYn6+v31tXP1dU/XH+2WJ2vReuukDldjdouk6OFhA+ZEnbw TdXW6Ts12+zVdQ1LJDlnle1e0/VczMwc1HnZTQuGc1LXbh7dId3iCCy/pHnt NWWYKuJLnLO/K/fuvULKyE8++aTh1MGDyxXmhx/+lmW72WVoaFhq+EePHrPI R5NlGrgZVfHf0gYB0X7o0D1ruNQP3WOXiQPS0dzcnOVZqclbxjyHDJ3nRE2m nY0sxMAGlobJlDxxCv82Fj86Z2SznYM/eL7R63W29EUjhZr8NfrGa174Dhpn 77rDwXfXo4cNjufLmBBCCCGEEEIIIYQovF6fKvtrD/znSSbTyWRKnrQPhcLB YEi9+hb2jY1NUvfWl75Vix319Q1a2dzb1NSsKuegqqq6rGzjhg1lGzZsKC0V StEiZ93u5my2U36VgMRk53/kY+gRZn5/ULbrQS9y1udrUQ//u1xNq2YIqqtr 5MDj8Um1H9GkRXvsP/9RvfVYb38BcqjubP3fwcy8f44lBq8bV9a6zcBAbz+r q1HbZXK2/l9nTNjZ946VyZgNntQtAVjypKnHImfGMLerTotlR+DN+lUyNMyn Xaqzjnfik08+KRXmkydPPvzww4c0qYfPcYA7pRiXl156WRrPnDkzODhkkY8m uzRmZ+dUrdviMjh6VKuuH1rDpX7okCRz1F7I2bIjJOOcpNlAHDEhDt2Z83ee kzvu+JLDnGCS1QIBBiLfAr4a1XjjjQfPIcm9e/ea++o/sNvh2ftdjx5u9Hr0 9hN/dbOcuuaF7+CsFOrBjd9/3hsJO3xrYpm76ZpivuI1GRNCCCGEEEIIIYQQ hWGrHyCV/0Ri+TF7QfbAl+36NVVL6btWe0S/ocHlcjU2NjYBecOvVPj1b/iV l/w2NblrC2/+haMcyBJASUmpYsOGMjkFe/UyAlmP8Hp95rBq5x95ya8EVzv/ o9GcjCVqXLLPj8fjRQKyK5F67F+K/ximsr8wubtQiz5aX+9gVmT93+y4p7b2 jJUlGm9c+XJnMKOrUdtlour/yNwuyVV97WzuMP1MQGV7hynb4mfGPLd20wIe Mo1L0VJd85DN2sG/1tcjpvN3rYxnVrvO77770JKVvvvdJ3HNr8nl6NGjyWTS Oh9NDmk89NDDdjZSuEanq17hq2ZokGVHMzOztheVZvDmm29atjsLNmudExXW 8uzAwKBhmyDRv/7ryT179jpEc5DlJOduutp5+x1POGRwmfirzxlsrnnhO/5s 2vlb23r/N2DZt393MV/xmowJIYQQQgghhBBCiEJX9leV/3zxPxptb2lpa2xs qqqqLi+v2LixHH81VVZWVmmrANVS/6/TXoAr9f+mJrfb3ezxeL1en8/XIk/j o1Fe9avH621BXzBTLYhcVlZWUlKyfn1JaekGaURM+VUC8pFH8Q1x6rQdsNXO P6ov/c7/yM2cgBVVctDQ4JJN/tWqB1rUY/9NTc3y5l81Dxcmvqrq6ZoakNDW KewYqK4RM2fs3G+oqX2otu5oXT3AAT76bCwlzoB9MolCJuYIKslVB+sQ37eW bIucGbu53a3r6Lt1dX9dW+v8LagZgCXsxfHu2rrdpgveOdWiLgxfyw033PjQ Qw8dPXr0u9/97t133437vXiXl156CS4DAwNO+QwMTE/POAeEgaUNkkE7DIoZ iyGaA+aEJUmHjiSs2VEydMY8pZahiunOkDMmH18Bvggc7N69x/krWGuSQmSw 1462TMrSpTkU7Nu/a/jg1SAxNVbMtyYuDc3N592YEEIIIYQQQgghhCik5q+e +QfxeCIabQ8Egg0NrhrtFb2yRb8sAWirAJWgSvcTgDrt9btqCaC52aNfAkCL lMoVcAkGQ/Jbg3A4Akf9WelFjtGFPGlviCDglNqYCB2h3yrtFwpud7PsWSQb FknjqqilDbjL0/44kK5lUFrx3y0/c0C7TEUxkQkhhBBCCCGEEEIIIYSQTxl5 2l92+wmHo/Kq30AghAMQCoFIOBzBceFh/mbZwKey0m4XoPxPANQSgNeb35BH lgwUjY1NsVj+tcKRSHt7exx//f6gvBegSvshwKrADF1oT/gv7/wjdX6cQpDC zj/5h/+RWzEB1dIGxlUo/nuQp/SFY1X8lw2OZFlErYYQQgghhBBCCCGEEEII IRcUkUg0GAxpJXQ//ra1BWQ7Hb9fVgEEWQhYXgsIh6PwAjCQB+xlVxxtCaDR 5VreBcjt9shu+VVVNVJd11NdXRMIBBETEXAgOfh8+Wf4GxubamvrzC4K9CK5 qeK/PPmvha2V9QvZ+QehHOLo2ZhXvp5fV1cvW/1gFDU1tWhBMjgGGJoU/9EO 47KyjUUGJ4QQQgghhBBCCCGEEEI+ZXy+Fp+vtaUFtLW2CrIQIGsBQa2crtYC VvwoQLcW0A6iUfkFQUh2yCngrtDtIGSgtrYOXWuLCC2ywQ5oaGiUAruB6uoa 2Pj9AS2NkHrnL1zKtTcUyJqCtioRwCiam73SviplZRs3bCiT46amZq343yxr B2hpaHBpj/034QDU1zdUVlbBBRQTnBBCCCGEEEIIIYQQQgj59JEterRVALUQ oNYC5EcByz8HKKwFGH4UEFE/CpDtgxCwvr5B0dDgklK5AxXapj3y7gC41NbW SYEdvtrLdpuRDPpCL/grOxRpT/4HkCfsJUjhyf+gPPmPQZWXV6zatVBaumHD hjItSI3bvVz8R0ryhL967B991dXl09O7EEIIIYQQQgghhBBCCCEXIC5XY1OT W1sF8Mkbe+WlvUJra1vhtwD+wr5AgcIvAoKyEFDYGii/k4/2ggC3vBFAqK6u 2bChbE1sLDyQj95loyGp/GvF/5B64a88ny8uDQ0u/SkMoaKissjuSktLS0pK 5VjWIGSTfwmOsajH/uvq6mVtorR0g3IhhBBCCCGEEEIIIYQQQi5ASks3CBs3 5l9lq73J19XY6Nb9IsByX6AVvwjAR4/HJ7v919c3VFVVV1XVVFfnQUzVxVpB 7/L7gsKGP/kN/5FGY2PTxo3lYiNbGBmK/2gssouSktL160vwF8eVldWq+I95 QEuZ9hsE+SGDFP9ramoxacqFEEIIIYQQQgghhBBCCLkwKSkptaNUq65XV9fK C3A9Hq/lWoDP1yr79gs1NbXyZuHKyirZxsehC0GWIcztXq8vEAhpBNG7y9VY VVWt92pocMlZ2Q5I2/Pfs3Fj+ao9Ki6/fD2QY8SX4r/sWYQWdFeo/NfX1NTJ 0NavL4GLLAEQQgghhBBCCCGEEEIIIRcm69eXrIny8oqKiqra2jqXq8nrbdF2 y3frKbwbd/n9AqWlGxyi4Wx1dQ1CVVZWm89KBDvf6upaKftL5b+lpQ1xSkqc ujNw+eXrL7vscinmV1VVu1zuhobG+noXUpLcpPIvj/2jsaqqBo3itdZ5I4QQ QgghhBBCCCGEEEI+TeQB+HOjoSH/wLyBwp5Cy/sL2XWxXltKqKurl3cE429J 4Wl8Oy677PJLL71MkLq9x+NrbW1raZG3/VauKXkVDcdIGJmrTf6lyC+7IWmV /9qqqpqqqmokLF7SOyGEEEIIIYQQQgghhBBywXLZZZefG/B1uRoN1Nc36BYX 8r8vsHTcsKGssrKqurpG3hRcV5evuldUVDr3uG7dX15yyTr8/cu/vFSK8Aji 9fqqq2vR3RrzvwxBgHysra3XnvzPpyFFfgSUyr/22H+17GWERnSsvAghhBBC CCGEEEIIIYSQCxb1RP1aKSnZ0NDgMlBdXasiX77yiX1h/fqSsrKN2iZC+RcE VFVV19TUytb68IWLQ4+XXLLu4osvkSUAoJ7eP4fk1607u45QUVGFzGUNQvJH Y3l5pVT+AQyQLdKGvfIihBBCCCGEEEIIIYQQQi5k5DH4c2DDhrL6+gYD5eUV dvaXaQ/Vl2jv7S0r27hxYzmMZQlAdtfBMU459HjxxZd89rMX46/U/88580su WaetIuQjlJZuqK/PF/+1rX7q1q8vlUYtn3xKFRVVyFN+FLBuHRzXnXO/hBBC CCGEEEIIIYQQQsinxrpzVVlZWZ2mWp1KS0svKUhvvLxfz+Xavv8lJTDbUFgG qNBUXl6+URMs7Xo0hz0HXaxJ4iAl2YEIf6urq5GSpFpRkMoKacNFOVIURVEU RVEURVEURVEURVHUBa5LzlUVFRW1K1VTU3PppZderJN+LeDsrv2XXy5LAGVl ZfAqLy/HwQZNaJRK+yekz372sxdddBH+Skr64j+GIzZIprygjRs3Sm7iqx8R RVEURVEURVEURVEURVEURV3IuvhcVVlZWW3SZ62kHptXSwAlJSVVVVUNmuBV Wlpaomm9pnWFp/TPo5DGX2i66KKLJB/kX1NTU6WpoqJCOkXvGwtSqxJIWy0c nPfEKIqiKIqiKIqiKIqiKIqiKOqTkGXFvhhVWekvVuoiTapsfskll1x66aXl 5eW1tbV1OpWUlFyu6bLLLoOB1NvPo5DDf9KElCSZioqK6upqJFxZWYl81q1b h3Z0LWV/qfyXakJWcJexnN+sKIqiKIqiKIqiKIqiKIqiKOqTU4aiKIqiKIqi KIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi KIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi KIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi LgCdeOvEj3/84+PHj//whz/8/ve+f+TIkZdfevnFF1/8xxdeIIQQQgghhBBC CCGEEELIBc6LL7748ksvHzly5Pvf+/4Pf/jD48eP//jHPz7x1ol333nnF2+/ /fOf//wnP/nJP//oR2g/dvToP/33fyKEEEIIIYQQQgghhBBCyJ8Ex44ePX78 +D//6Ec/+clPfv7zn//i7bfffeed06dPv/fee+/8yzu//OUv3z7x9ptvvvkz 6Kc//en/IIQQQgghhBBCCCGEEELIhc7PfvrTn/3sZ2+++ebbJ97+5S9/+c6/ vPPee++dPn36V7/61fvvv4+DkydPouXdd9/FKfAvFEVRFEVRFEVRFEVRFEVR FEVd8JKq/rvvvvvee++dPHny9OnT77///q9+9avFxcUPPvjg17/+NY7/7f33 /5em/0lRFEVRFEVRFEVRFEVRFEVR1J+IpLb/b1rZ/9e//vUHH3ywuLj40Ucf /eY3v/nwww9xfAb6gKIoiqIoiqIoiqIoiqIoiqKoPzGdAWfOLC4ufvjhh7/5 zW8++uijP/zhD7///e9/97vf/fa3v/2IoiiKoiiKoiiKoiiKoiiKoqg/Wf32 t7/93e9+9/vf//4Pf/jD/ynof1MURVEURVEURVEURVEURVEU9ScuVfb/fwX9 X4qiKIqiKIqiKIqiKIqiKIqi/sSlyv7/HyiXBEA= "], {{0, 71}, {2048, 0}}, {0, 255}, ColorFunction -> RGBColor], BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True], Selectable -> False], BaseStyle -> "ImageGraphics", ImageSizeRaw -> {2048, 71}, PlotRange -> {{0, 2048}, {0, 71}}]], "", PageWidth -> Infinity, CellMargins -> 0, CellFrameMargins -> {{0, 0}, {0, 0}}, CellChangeTimes -> {{3.544379162237352*^9, 3.544379175555642*^9}, 3.574009622854604*^9, 3.5740096771925993`*^9, 3.606497282354394*^9, 3.606497322480124*^9, 3.607965342107291*^9, 3.607965382772916*^9}, Magnification -> 1.], Cell[ CellGroupData[{ Cell[ BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ "Evaluate", " ", "the", " ", "following", " ", "to", " ", "copy", " ", "the", " ", "style", " ", "of", " ", "the", " ", "cell", " ", "above", " ", "into", " ", "\[IndentingNewLine]", "the", " ", "docked", " ", "cell", " ", "style", " ", "of", " ", RowBox[{"the", " ", "'"}], RowBox[{"Working", "'"}], " ", "definition", " ", RowBox[{"(", RowBox[{"2", " ", "cells", " ", "above"}], ")"}], " ", "\[IndentingNewLine]", "These", " ", "two", " ", "cell", " ", "can", " ", "be", " ", "removed", " ", "once", " ", "the", " ", "docked", " ", "cell", " ", "is", " ", RowBox[{"created", "."}]}], "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SelectionMove", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "Previous", ",", "Cell", ",", "2"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"celldata", "=", RowBox[{"NotebookRead", "[", RowBox[{"SelectedNotebook", "[", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SelectionMove", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "Previous", ",", "Cell", ",", "1"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SetOptions", "[", RowBox[{ RowBox[{"NotebookSelection", "[", RowBox[{"SelectedNotebook", "[", "]"}], "]"}], ",", RowBox[{"DockedCells", "\[Rule]", RowBox[{"{", "celldata", "}"}]}]}], "]"}], ";"}]}]}]], "Input", CellChangeTimes -> { 3.5740143744052753`*^9, {3.574014994368063*^9, 3.5740150001730556`*^9}, 3.574015035375742*^9, { 3.574016128609118*^9, 3.574016129431505*^9}}, FontWeight -> "Bold"], Cell[ StyleData[All, "Presentation"], MenuSortingValue -> None], Cell[ StyleData[All, "Condensed"], MenuSortingValue -> None], Cell[ StyleData[All, "SlideShow"], DockedCells -> { FEPrivate`FrontEndResource["FEExpressions", "SlideshowToolbar"], Cell[ BoxData[ GraphicsBox[ TagBox[ RasterBox[CompressedData[" 1:eJztnWmQXNWV5x0z82E+TWNQA6pSqfYlq7Iys6pyr9yz9jVrV23aSwtCYkcY sMHd2MYL3YMAAZ4eMIuJ9rTZP9AsAtsRnpYE7rDHNgg7oiFoSRND2xGoCONl lpp/vlN59eptlSUElsP/f/yoeHnfOeeee/M9EXHuy/sqt181uuvffeYzn7nu P+LP6LaD6Wuv3fa5sf+AD5nPXb+w/d/joBv/fQan88ddXT3nzPz8FjNDQ7m+ vn7Q25unp6fPzr2zszuT6Ugm04lECnR0dDl3l0gkY7EE/sIlnc7qT/X1DVi6 TExMIqW5ufmpqenu7t7ih4aAO3fu2r59J7zQlwFk/nHmjRBCCCGEEEIIIYQQ Qgj5pOns7C6Svr6BoaHc+PjkzMzctm07FhZ24+/s7LyBkZGx7u5eRRFddGUy HalUZtUEstnOdDor6wVwUe2jo+NIZmxswtIL7cgKOdsZ2DE5uWnnzl0Yr6Qn pNMgi0zWFIoQQgghhBBCCCGEEEII+ZTJdnRZ0tnV09s3kBsZG5+Y2jQ9u3Xb DrBt+06wfccC2LFzF8DBzOw8DBRDwyN2MddKX//gwOBw/8CQoT2T7QQqT6Sx sGvPzoXds3Ob8dEcB6NAYpNT02vKDaFk1B2d3YlkGiRTICOcrzESQgghhBBC CCGEEEIIIZ8EUksHPb39/QNDw7nR8Ymp6Zm52bnNc/NbwPzmrWDzlm1btm63 WwWA2dSmGSE3MpbOdGhkBdXFWkHYhV17ZJUBxxOTmwYGh/U5g5HRcSn+ixny 7O7pM8SBy9j4JNwxNAyz+ARGxyYwUvxNpjKyBKDAAM95XIQQQgghhBBCCCGE EELIJ81wbnR0bGJyanpq04w8wD89MzczOw9m5zbrVwE2b9kmqwCyEGBYBUAj IiBObmQsmTKWys8N9L5zYTfioyPERxrICr0MDY90dvWITbajCwlL8V+ZdXX3 GkJhpGPjk2BkdBwuzv1mtNUQCY6YGHsqnY0nUno+zrgIIYQQQgghhBBCCCGE kE+aiclNgiwB6FcBZCFArQKoHwLoVwFkIUCWAHAMx9zIWCye1JNMZVLpbJEk kql4IhlPpHA8PjGFBJCGPLovSYKx8cnh3Ghv30Am2yleg0M5yQe5IUm4dHb1 GCKjZXRsYmR0fGBw2CGBnt5+DAFIBPSLsHBBSvpBSYaEEEIIIYQQQgghhBBC yIXJzMzc5OSmiYkp/J2amgabNs2A6elZgLNAXuw7P78FbN68FWzZsg1s3bod bNu2A2zfvnPHjgWY5XKj7e1xPclkWr0/15JEIhWNxkKhiN8fbGsLtLb6A4EQ 2ru7e/v7BxFwbGwCiSGT8fHJ4eGRoaEc/g4MDHV0dKkgXV09khuSRBqw158V +voGRkbG4Gs+JaAdfY2OjqNTdC1hMUZMDkYRiyWEeDwJkLbzuAghhBBCCCGE EEIIIYSQPxbbt+8EmzdvnZ6enZzc5LwKMDe3GahVABzj7NjYxNBQrru7N6VV 8mOxRDQaC4ejing8kUymLYExDILBcCAQAm1tgbY2v1b/D5qNM5mO3t7+XG50 eHikp6cPPRoMstlO5IyskC0OkBhS0hvg4+DgMLLt7x+0SwnBZY0Alul0Fi0Y 49at2xE8FotrnF0FsAtCCCGEEEIIIYQQQgghhPxxkaf3ha1bt8/Nbd60aUYt BBhWAfAXjTg1Ojo+ODjc1zfQ09PX1dWTzXZKqTweT7a3x6X+HwqFBXxMJFIG YBmJtIdCkWAwHAzmi//aw//54n9bWwCNZhdFR0cX+kWPlqckW+Q5MTE1MDBk MECqyBztOLAM3tnZncuNDg3lYINjtOBgy5Zt+BuLxQ0/bXBIkhBCCCGEEEII IYQQQgj5IzIwMCTb+GzZsk2e6pctdOQRetkaaHx8UnbFEVR5vK9voLu7t7Oz W9X/Y7FEe3s8EmmXp/oFfJQNcxTKJhQKy8P/YoZ2g6UdstZgSSbTIZkj7ZGR MeRmMOjt7e/vH+zp6bN0x5wMDg4DZYO+MCcIKD9t0KP2AiKEEEIIIYQQQggh hBBCLijaY4ncyNj85q1z81sEeeEvmJmd3zQ9OzI6Lu/DVQznRgeHcv0DQ719 A13dvR2d3ZlsZzKViSdSiBaJxsKR9mAokn+kXyMUjqJdEdUM0BiUh/9DkWh7 XG+AOBIKpLQX8qYzHXqD/GsLZufRrm/Ug6zGJ6ZGxyaQKvKMacNUIFVkDncc 2LnL6GAjmUxOTWNmcIzMhYgQjdnlQAghhBBCCCGEEEIIIYT8EYm2x8FwblQK /sL0zJywaXp2atOM1Pz1DA7l+voHe3r7u7p7sx1d6UyHof6/XCSPxiS+nrPF /1BEb5BIphGqs6sHf1PprDTieH7zVqQ0OjbR3dMXiyfRiANki9yQgyFymz8o xwODwyOj40PDIzjIZDsNOSBtBEFwc3oAY5HRwUYy6e0bQI/ITZIPR4T8GC0j EEIIIYQQQgghhBBCCCF/XCLRmDA4lFM1f2Fq04wwPjE1NDwitXSFVMg7u3rS mY5EMi1LCSqaM1L/Vx9j8WRXd688b48DiSmnMtnOufktyAo5DOdGYRNPpNCe 7eiamNw0OjYBY7FEQI/X1+zx+gMhiZkbGZPfKXT39BlyQ8LyywW7nNERvGCD BPAxmcrMzM5j1Mg8FI5oRIUih0wIIYQQQgghhBBCCCGEfKqorWwi7YODw/LC 36mpaUFeBCwv/B0YGOrvH+zrG+jt7e/p6evu7k0m03r3cyOdzsrbBBBcRc5k OuQsDubmNk9Pz46PTw4Pj8AgFkvIqUQilcuNwiuVyoTD0eZmL/B4vF5vCz7C AHHUNv6GVKPRWFdXT0dHV1x7DbGZzs5uuItNVJul2dn5sbEJ7Z0FET3SFyGE EEIIIYQQQgghhBByQREOR/X09w+qmv/ExJQg7//N5UalON/V1dPZ2d3R0ZXN dsZiCUOENZFOZxF2eHhkcHBYlgBkWaG9PS4G0WgMveDU6Oj40FAOnerd0Xtv b78Yt7S0ejxej8cHWlv9aEG7eklxJtNh7hqR0ZdlYqlURoYJm/wLC8JRJDAz M6d/r7EgSwCEEEIIIYQQQgghhBBCyAWF4Wl20NvbPz4+KYyNTYDR0XFhcHBY Vf7T6WwqlUkm09FozBykGBBhZGRM6v9DQ7m+voFYLGFnHNF+C+BgEAyGteL/ 8hKAVOaRJ4bT1dWDA0TQ2yMUAiIHy2jt7XEZqeq0p6dvZmYuHk8GAiE90hEh hBBCCCGEEEIIIYQQckFheJpd6Onpk7L/yMiYkMuNCn19A6ryn0ik4vGkPH5v GceBaDSmIg8Pj6BHczKdnd0OEXy+VqnzK1pb22QXINDa6kdLLJZAZMTJZDqQ p944rP0EQPYOsoyvljkQBB9xPD09i1EHAiG/P6iQJQBCCCGEEEIIIYQQQggh 5ILC8DS7oqurR6vMCyNDQ0JucDDX09MXjydjsUR7e1z2xpcSul0oS7QtfSZG RsZzubHe3n79qba2gNTV+/uH4vGUNIbD+V6QAMBZr9fndntAa6t/dnY+k+mQ sryq/09ObpJG/E2lMolEat++/Xv27AWIIDG1JYz8ewEkrCHDdDqbTnckkxmM FF4HDlz9xS/+9fXX37h7955du/bg78zMrCwBoAuJLCAf57GjL2cby3zQy6qR /yjsaW1TZLQv7oIF6X1q2Z5bR0NtAb3jJ5he4XKV2+QTciHnHfzLUOS/Mx+T 7tlN81/7qyue+C9g+os3J3p6HIxzB/bu+q+HxBhezsYq/vjBayIJ4y+qDMAA ZsUEJIQQQgghhBBCCCFm2vwBO7IdnYNDw2BgcEjoHxgUOjq7wpFoKBwJhsKB YMgfCDrEQYSe3r5ItB2W0tIei4+OjY+MjoGh4Zxqb2lta/Z4m9zNXl8LPmay HX39A+gF3eEAfT33/POLi4u+ltYmtxtmINrevrS09Npr35MIHq/P3ezZtn07 Ghd27ZbG666/Hl5LOn37iSckjVg8gfhvaDKkHU8kk6k0/u4/cGDJRq1tfvDg N79pPvX2229Pz8xaTsip06dhMDg4ZDdjyBbuhkaMHV6pdMbSZbq1bamhoUju 8nrP9uVyrWoPG3OPqTb/c83NZmM0Dra22aVnGUp4ze02p2dI8kGPx3bSNBu7 +Eip+GwNnU7bGFgi02Ke1Teamnbh+rZ3xFnYmGce0RDTcqJgbxnqdq/PbrZx 1cmFpBcu/l2799glZumC6/P227/ocAFDDgbKxtyOe9PudlNS97uAG3xVF3Nf CGJpidsTE3LXXX9jd6/ZOeol/8KYx2v3b4LMs+WNf/Zrvf2L8k+HflD4x8cy z2KSxBgtOwon4gt/d+jWN14xMLTf4iKB8YGnHyvS2Bx/7ODVDhcJ2HbPV2E2 91Wna4kQQgghhBBCCCGE2NLmdyCb7RgYGAT9/QNCX1+/kMlkg8FQIBD0a0Fa W9taWlrx1xAhFApPTk4NDg7hbyQSlcbu7p6xsfHR0TGQSCTRglDw9flaEET5 oove3j50Go8nOju70HL77bcvLS1NT894PF63uxlcddXVUstKpdIwgDsaDx++ Hy0SGcZLWrnyuuuuhw0+vvbaa/kC3befCIcjsVgcWS3X/1dm3t4eSyZT6Hr/ /gNarewu9H7zzTcvLOxSIGfw4IP5+j/i79q1W4CxlPsGBwcNYXG2UHy7y3LO JeGl/ALBCl9ZwkAvll67fC3F1/8fbPYoxyJdjEm2tDosHODUtO57NKRnd7Gp 6rc+PXOShshmG8vJcc4WBg4BLc9af3eO0wJu93otHdHuvP6iH7V+Mq/z+Qyh Uq1tZ5dLVs4kLi39Qhiu+VOnztaTcXmbE8P15uDy3HPPW38Xheq0+fo32Fhc Bm+8sWrh2nC3yg24qtbaUb5cPz1zXjJU48Xsyb9UFldp4V8Gy7OYahUcQfQ5 4B83c8xiksS8Wfa18Hd3S3F+26Gvbrr9JnDdi/8gLZ3TkwbjK574ZvHGAI3K AMDe4YYKx+OF1YTdRd6DhBBCCCGEEEIIIUSPVLAdSKczqubf29un6OnpTaXS UvYHPl+L1+sDsgqgSCZT4+MTAwODudyIahwZGZX6//BwDh/9/gACJhJJOSsB cYD4mUwW7dFoezbbgRbE0cpWD6I7t7u5udnzzDPPSH3ytttuF1+0v/XWCYBk 0PLaa6/BAHECgaAarywBdHR0tLfHwoXn/w0Dj0Si6DoWi1955X4YLyzsQsJI QNLTg3xgYHCfnp5G4ze+cZeh/bnnnkM+Wh31lOWEw0Wqc3rfa6+9TgqScLf0 ml5L/f8bHo9yLMZ+0eVa8Z2urHKfcrlea2p6zu0+pWuEQVJ3JSwUnkgHdlea rv7fbDilT+ZEY6Olu138geKyHVh53eoDLmgX0qpgvKesOkLC+vzN0a7VTY4M EF7wNaStn8/nCj8BMLTnV6MKP3M4tfJbw6UrdwouPFxOZ7+ahV0nTrwtl5y+ 3cEF7XIHLeXX0b5t8V3oyuB20yUGFpeBVrjGda5faDOABFYMWbsBMQoHF9yP lh3hLjMbI6AMHH/xL9jHz1A/J3a3MLzs5gSTrGZbRUZiMnAZe/GjU5iHBlLD g8tP5t94lWoMxWIHnn4UjQt/d7elcef0hN5477e/aTYGQ1fuFvuDP3ge4GDq tpsc7imchc11L/5DMTcgIYQQQgghhBBCCDFjrmabSaXSPT29iu7uHtDV1Q0S iaSU/T0eL2hu9rjdzbIKIGQy2dHRMXGUlkAgqB7+7+zsQksymervH2jTnt73 +VoEsQyHI5FIVErx6XQGlr/4xS/eeOMNqfOju8XFxWeeefbUqVOvvvqaxIfx 0tLS4cOHcRYfcfzCCy/Avb09hoBis7CwgPbdu/dEo+3o4vXX3wCGUaM9Hk/A a9++K7X6/4L8AkKfpPDAA/kqnHne0IhT+hakgcZnn33utttuk5hmL0kGIzpx 4oRqhAtGijGivZivDDzgXq4Dv97Y5GCmq0t71xoZ4Fh/6uvNHstTC7rn2+3C Ik/LmPok7Qz0Nob2Z5vc6tTXtUvCMttXm4yztNaZcZgWRFDF/FMul8FRrRrA xtCXXcx+3XKPXfttnhWDxSUkBW1chJZXHc6qm0jARyn+W7qoorTcFCumTifD LWCwscvEzst65rUb0HwLOyMdWd6DYNOm6cLC4m0fP0PDnFx77bVmA/lHyTwn mF6HmVReSLj40TnQu31eSu6G9sF9u6Rur2+cuu0gGg88/ahlEGBol0WEvd9+ MNqRxV+t/n/QLpNge7usEYzecNVaR0EIIYQQQgghhBBCBEMp245stkOV/Ts7 u/TEYnEp+4OmJndjYxPweLziCJdcbkR+LCAtkUhUiv8jI6PwRUtvb5+cRRzl qAgGQ6Ctze/1+nDw93//90tLS/F4Asay+Q/+Pv74t6UR9gcOXIXj8fEJGOAj jh9++Fs4FY22+/0BiYmPsv0FktHq/3kZ+g0EgkgPXvv27YPxzp0L8iMI9UsH xQMPPAADg/vXv/51NH7hC7eZG6emNuF4cXHx2WefNXhJYggoI5LulDGiKfdV eaDwiPjrjY0OZqpcvNM083aoevWrTU12/T7b1NSHeIVGBFcd2YV9vfCcPCLY JemQrWX8uO7RenNY/SyBuC7hc5iZRcdp+YJurWFKF/AaXbtlR49bzac+c/Sr Tqk5NH/pUiU2XJD6Cw8Xp9xB+kvRwSV/JZw6BQM4Wvb16quvyoHlFSunLC6D 11+XW6DIqzE/FdoNaL6FnZGOcF/bGeCO01brnv34Garxii9uZ/1UC8jEck5k dJhqu8jXXHOteRSrjs6OQDQ6csOBxGC/oT07NS4lfX3jlrvvRMvkFw6a44hx tCOjb0TYwX3LKUn939JXwClZcUBKax0FIYQQQgghhBBCCBEMpWxLEomkPO0v dHZ2dXR0Kvz+gFb8d6viv8vVKL8CAN3dPcPDOXglkylpCYcjqv6PY7TkciNy AC+Px2vo3aeV4lu1/S5gtmPHzqWlpauvvkZt/oMDfETj5z//BdhLozv/8wDE 8mn1/4dln39ZRBC0+v+DCBgKhaX+b+gXPba3x+B1xRX7tB02Try+Usry/vvz BbrHH38cB+DZZ5+FsbgYYspT/XIMe9ggMb2BDGRycgrg4Gtf+7pqxN/e3j7V uCr3N52t/zuYqeLzDm26VqVXV8m/urm5GBewQ1fltrNRtWtkbpfkKd1T9DGv 19LGrl+DvRDT/TDBMANrmplJz9mOJj3W9ip5/QDV14SzRU6mynyxobDi0Nhk GKwhZ7lrzNeb01dWcHGwkWvYfO+ovmSBwHwjKBuLy0ArXOM+Kn4q5AY0p+GM dIRhrjXsOWSoxotbWH5WYA5rN+HSHab6/I5urYxcv//WN1659h//m76xUMO/ 0Wwv9f/M5JhdQAdfAX05GxBCCCGEEEIIIYSQVZF9exyIxxNazX/5sf+OjjzZ bKdGRyAQVE/+q/o/DpQ7XAYGhuCCOKqxudkjPxmQjzAIhcI46Orq8fsDhgSQ JBpbWlrT6WxraxtaZM+fwuY/z4gZjo8ceRUHp06devrpZ5CDxF9aWnrooYdl n39xF2Q/DfQbDIaknm/oFz3K7kB7915hrv9LX8L999+vN5CaJxrRqT7g9u07 tEWKz8vHiYlJrZj/Nb0NxoWByDHiSC/6RvSi79qB+wvb6b/e2OhgpirG2wtf hzPbdTvSFGNfvJeu/t/kkKQ6fmylmWV8NQknXC67fk+cLctbByxmZs55gEcK jUccvyZLvqbb2ggJqPUF8zeOq04u0eKDy1Vtvi/MYc02Usf2FK556LHHHrez Mc7ScnX9/vObql1HyNDOADeaZebnkKF+vDJp5ntfzZXBUf49ufrqq8/v6NaK VONnvvIFfeOex/M1/InP32i2L9T/R+0COviC/r075eH/tnD4fA2BEEIIIYQQ Qggh5M8QKcXbEYvF9Vv9qGf+s9kOeaOulPENxX99BHl9MP62t8dUo3KRPfwR ORyO4ABhYWnIQd5T7PO1IFvZh/zIkSOnTp1Sm/+I2TPPPIOPExMT+HvLLbdI fLRr9f+HotH2UCgMXzHu7u6RB+mDwZDfHzh+/HVg6LdVewUwvPbs2atV0rbb zdLhw/nyo/oIS61s+JjBTDJEO+yFxcVFDERvo9X8j8gxLGGPzGWZQ9/o/K0t Z1XYTv+4q9HBTBWQn2lshIuZCe07Ojs63YY5xaRh9rLsBajyNY7tkszPQGFc WtHbbWmzpknAKct+LXspZoB2No9ZJWPXe5GcfXeAbnOk7pVfmbpEzRe50/VT hItc6uYLUt8oV6z5DrJ0zE/I8XzhGr2f31TtOrK7r2+9dblKr/6F+TgZGsaL e3xJ2wUI/14VOZkO//6cw+jWysTnb5B6fiid0rfvefwBrYZ/g8UEavbpiVG7 mA6+QJYbNv/nr8hH9Ju77srWUOi8DIcQQgghhBBCCCHkzwd5et+Mx+NNJlOW lX+p0re1+T2FF/6q+r+U9PVEo+3d3T0IlUgkVaPaJgh/9catrW39/QPoDsHx 0edrQYvfHwDhcAShZA//r371q1q577i2z8+yr2z7/9Zbb+EvIqhkYPODH/wg EokGgyEE1Bvv2LFTdhY6rsmQOXJAp/Das2cPjLdt2+4p7E2kVk/E8vDhwzDQ +0p9r6urW7UgAdn3wyxEFhvYa4sXt8rH8fH8WoaEQsL6zNVHBw4XHiw/7nI5 mC3p6saWII7e/hZd+X3VHBTbdE+qr7VHfZL5mdQ96I6DiJXNmibh+Nl1h0bL TreZrmqH2XaYFstk7Ho/4mrEKQNdpkwONDUZZu8Z0+ypS9R8kTuNqAgXXLpy DRu/r5WNcleeOnUKd4GdzdkJOX5cjI/bSH9b6VN1EP7FsOsI99fhlXr00cck Ybvhi6ODcOeavfTjVf8aoKMiJ1P9K1Ekzkmid8skLUmNj0gxf/zWGwynpIZv bgfiAl+7sA6+fXt2iHswtfx/jR3f/Ft8HL72yjVNAiGEEEIIIYQQQgiR0r2B 5mZPKpW2rPyr4r+UwVX9X+rtZgKBIIIkEkl4qUaXq7GhwQXq6xv0ls3apuXx eCIYDKElEom2t8dCoTC6w7Gy7OrqkiqW7POjUCU1WV+QlOQlnvPzmxEfCaMl HI7ARnbUkZ8VSF3RkHlraxu6htfu3fn6/9at2+RNxGgBfn8AWcnA77svX37U +0qG+vRuueUWtIyNjevNkAnSUGZ33plf14CvMjh58pQU6/ReaHn00UctZ1vP fa6z1WYHs1Wr8Yijt79TV+heNQfF1kZjmbr4HvVJyscxXbRXCqOzzKqYSVAV eEO/KuBWm2vbsiOHabFMZtXe9VhmoiLIrwDCll3ft1zML/4rK8YFN4Xcicbv a2UjLntpeeWVI3Y2Z4ezWnUdnVqm6iAYnENHuMtwh56XDM3jPXDggCE358m0 jOnAqkka/i2yI5BMHPzB87e+8cqexx8wny3U8K83n5ICfnIsZxfZwVdObf7b LxdjTAghhBBCCCGEEEIcUKVyhdvdnEymtX3+O9U+/5mMkE2nM35/QF4cbKj/ WwIDeIFYLA57aZTKf11dPcCxNKLHrq5ueRGAtITD0Xg8Adra/LFYQh/29OnT S0tLN954EMmo3p9++mk0PvLIo3rLgYHBDz/8cHHxwyeeeOLAgavuvPPOkydP wuzmm29RNvJTgvtW6oEHHhweziH+wsJu2G/ZslWK/1rlP9Damt+SSH7FAGMY GAYuycBLPr6lyTw/MEPXGDWOX3nlFeSmP4uxLOXXEZ7WN5rNLLmvUBY+7nI5 mKnS8dMu131WbNF+pqHYoit0r5qDpdcjNh2dPFv/NyZs7vE+XdF7v5ahZVbF TIKuAu+y7NQwA5bcXMS0WCZj1/uiVf3fMhP93Jqnbrlr7RLFdV78V1aMCy5v KSYbvy9To0SD9u8/YGezPCFa4RoXOYJbIjeLObjl/eWA6kh/1+OjJDY6Oubs COM1dWcer9zdqi/nyVT/kqxpdGq2zw2v37//qUeWX/vr95sNdj+WL8uP3XK9 +VSh/j9sF9zOFy7i60/Ei+mIEEIIIYQQQgghhDjgcjXqaWpyJ5Mp/dP+stW/ kEgkA4FgS0urof5vCGIgHk8gZiQSha+0NDS4amvrNGpramrxUboOhyOwTKXS bW1+tMAlnc6gLzlQAXH2oYce/vDDD4PBEJJR7Vu2bFlaWhoZGdX37vcH0PK9 731PPfh68uTJK6/cr7dRRT+DZmfn0NemTdNSo1OP/be2tqFfzICM5StfuRMG hlFjDhcXF5966mk5hoGhUwG5wUxO4eDee+8znDU73nzzzebuzNzbsFxYPqZN rx262rKT2dlJ1hXei7Ev3utYIeF7TQlb+r6le+g9aGNTzCTY9bummVnTAJ/S daQaH7HPcNVMVjXAdYVr5tix48V/ZcW4yB2HG8qYjybj8I/lK9K4yHHb2tko M8ON8PFTtesIQ9A3Ijf5GZFDAueQoeV40ZesReIvjmUyzXNSqP9vWVN3lqNb K/N/+yV5CW+kp9PSYPdj92tl+evMp6SGnxgdtgtu5yvt+FtkR4QQQgghhBBC CCHEAdmHR5Bn9Qs1/+UH/rVn/vOP/ScSKb8/IKVvff3fEMQMXGKxeDgciUSi yri2tq66ukZhcGlqcuNvPJ5AR9LSqP1qALjdHmSiBcwvKIilslFZqfZQKBIM huU3C855Gmhr88t4EVNS0hf/EQ291Nc3gDWF/dS4t1ATPtbglKEqHW8uLuxm nUuu6GT0XnY2xwoG95psLH1zuvZXdA/J6232FdGvMvjcx5gZ/QCzNjZvWQ3w kULjWzYZBoqIvGqqmzdvkdp78dfPvn1XSmnawebee+/VCu/HjPloMjTiXxUp rYu9pU3+Mjh2TKuu31t8qnZpOCMdYWYso0FI2MFxTRnajTeXG5H2Rx55RL4j s4109+Uvf+W8jK54Bq++Qmr4Pbu22tlIWX705uvMp8Q3PjK0Jt9wd6c4oh2+ iiuf/BYa5/7mSw4BCSGEEEIIIYQQQogZqWADt7tZiv/qaf90OqOQJ//b2vxA X//XR7DDpT3JD/z+AHylsa6uvqqqGlRWVlVUVFZVVZkd0YW5BZnE4wl5LwDS 0J/FRynR46CpyY2W5maP7OGPRlWuLwaMS0IhYXF0a28E1i9/oAvZwqj4sJ8m 9+jq/w5mqnQ8X3Rk5XKPVeR99Q0vm6LN67zswh6zD2vne4+u7G9pk9H53mTV 6T6dQe7jzYzztOgz2adrv0nXnrEKqwzO2E/dqqnidpbaci6XK/JbhqW4wNf2 K9OKzN/61iPGfDRZjOWmz8mpL3/5y3Y2EvOee+4tMs/8ZXDPcv2/eBfV0fz8 ZvMpeSz/qaeecnBcU4YOcyLJyzRa2iANNL788ivna3TFEOrqkDr81B23OJjh rKWNu6VF3HFg51uo/1+rb8RHcXRg7m/uOLdBEUIIIYQQQgghhPwZIhVst7s5 nc6o3X5U2T+VSoNEIhkMhqQeLjVweW1uQ4NL3FfF6/VJER5BXK5Gaaypqa2o qKyoqCgvX6a6usYuQmP+dQARpJRM5h/+j0bbEUrlL+8RkC7kiX05hWPJHAfF Zwtc2i5DMlJ0jZbmZo/htw8NhV2Mig/7aXJPoSx8TDdLZlTpeK6+2MhP6irS wytP4eMZVQbX9YvgqiO7sMfqLRwNSTp42dm8WWg/2dCQXnkKH0/qzn7MmXGY Fr8ujTMrO/LrOoKN334+n7T/HotJVWraL7/8suXZL30pX5C/6aabineZm5uX ejUOjPlosvRCNJw6c+aMnU2hun5PMXMuwFjq/8W7qI7MyQPMg6Q3PJw7Lxk6 z8mbb765pNOaksE/bviaEAEHRY5uVZp8Pnnn765H73e2HLhqD8yueeE7hvau nVtk4yAHXwSHzcjnrtU3pmcmV63/G1wIIYQQQgghhBBCiAO1tXUejzeVyhRe 75sHHzXyxf94PBEMhtV7b6UqDhfxLRIYt7S0iqPP16J8q6trNm4sB2VlGxUV FZVoF4P6+gY4RqOxbLYT6Wn5JNvbY8FgqOHsSwTy+HytUufHQWNjE1oatM1/ ZFEAnRafLXC7m9Um/8hBZkn7eHbjozptCQOsKfKnxqFCyf1ovdM3dbb4XJ+3 tOTllRGG6ur09fYn6+v31tXP1dU/XH+2WJ2vReuukDldjdouk6OFhA+ZEnbw TdXW6Ts12+zVdQ1LJDlnle1e0/VczMwc1HnZTQuGc1LXbh7dId3iCCy/pHnt NWWYKuJLnLO/K/fuvULKyE8++aTh1MGDyxXmhx/+lmW72WVoaFhq+EePHrPI R5NlGrgZVfHf0gYB0X7o0D1ruNQP3WOXiQPS0dzcnOVZqclbxjyHDJ3nRE2m nY0sxMAGlobJlDxxCv82Fj86Z2SznYM/eL7R63W29EUjhZr8NfrGa174Dhpn 77rDwXfXo4cNjufLmBBCCCGEEEIIIYQovF6fKvtrD/znSSbTyWRKnrQPhcLB YEi9+hb2jY1NUvfWl75Vix319Q1a2dzb1NSsKuegqqq6rGzjhg1lGzZsKC0V StEiZ93u5my2U36VgMRk53/kY+gRZn5/ULbrQS9y1udrUQ//u1xNq2YIqqtr 5MDj8Um1H9GkRXvsP/9RvfVYb38BcqjubP3fwcy8f44lBq8bV9a6zcBAbz+r q1HbZXK2/l9nTNjZ946VyZgNntQtAVjypKnHImfGMLerTotlR+DN+lUyNMyn Xaqzjnfik08+KRXmkydPPvzww4c0qYfPcYA7pRiXl156WRrPnDkzODhkkY8m uzRmZ+dUrdviMjh6VKuuH1rDpX7okCRz1F7I2bIjJOOcpNlAHDEhDt2Z83ee kzvu+JLDnGCS1QIBBiLfAr4a1XjjjQfPIcm9e/ea++o/sNvh2ftdjx5u9Hr0 9hN/dbOcuuaF7+CsFOrBjd9/3hsJO3xrYpm76ZpivuI1GRNCCCGEEEIIIYQQ hWGrHyCV/0Ri+TF7QfbAl+36NVVL6btWe0S/ocHlcjU2NjYBecOvVPj1b/iV l/w2NblrC2/+haMcyBJASUmpYsOGMjkFe/UyAlmP8Hp95rBq5x95ya8EVzv/ o9GcjCVqXLLPj8fjRQKyK5F67F+K/ximsr8wubtQiz5aX+9gVmT93+y4p7b2 jJUlGm9c+XJnMKOrUdtlour/yNwuyVV97WzuMP1MQGV7hynb4mfGPLd20wIe Mo1L0VJd85DN2sG/1tcjpvN3rYxnVrvO77770JKVvvvdJ3HNr8nl6NGjyWTS Oh9NDmk89NDDdjZSuEanq17hq2ZokGVHMzOztheVZvDmm29atjsLNmudExXW 8uzAwKBhmyDRv/7ryT179jpEc5DlJOduutp5+x1POGRwmfirzxlsrnnhO/5s 2vlb23r/N2DZt393MV/xmowJIYQQQgghhBBCiEJX9leV/3zxPxptb2lpa2xs qqqqLi+v2LixHH81VVZWVmmrANVS/6/TXoAr9f+mJrfb3ezxeL1en8/XIk/j o1Fe9avH621BXzBTLYhcVlZWUlKyfn1JaekGaURM+VUC8pFH8Q1x6rQdsNXO P6ov/c7/yM2cgBVVctDQ4JJN/tWqB1rUY/9NTc3y5l81Dxcmvqrq6ZoakNDW KewYqK4RM2fs3G+oqX2otu5oXT3AAT76bCwlzoB9MolCJuYIKslVB+sQ37eW bIucGbu53a3r6Lt1dX9dW+v8LagZgCXsxfHu2rrdpgveOdWiLgxfyw033PjQ Qw8dPXr0u9/97t133437vXiXl156CS4DAwNO+QwMTE/POAeEgaUNkkE7DIoZ iyGaA+aEJUmHjiSs2VEydMY8pZahiunOkDMmH18Bvggc7N69x/krWGuSQmSw 1462TMrSpTkU7Nu/a/jg1SAxNVbMtyYuDc3N592YEEIIIYQQQgghhCik5q+e +QfxeCIabQ8Egg0NrhrtFb2yRb8sAWirAJWgSvcTgDrt9btqCaC52aNfAkCL lMoVcAkGQ/Jbg3A4Akf9WelFjtGFPGlviCDglNqYCB2h3yrtFwpud7PsWSQb FknjqqilDbjL0/44kK5lUFrx3y0/c0C7TEUxkQkhhBBCCCGEEEIIIYSQTxl5 2l92+wmHo/Kq30AghAMQCoFIOBzBceFh/mbZwKey0m4XoPxPANQSgNeb35BH lgwUjY1NsVj+tcKRSHt7exx//f6gvBegSvshwKrADF1oT/gv7/wjdX6cQpDC zj/5h/+RWzEB1dIGxlUo/nuQp/SFY1X8lw2OZFlErYYQQgghhBBCCCGEEEII IRcUkUg0GAxpJXQ//ra1BWQ7Hb9fVgEEWQhYXgsIh6PwAjCQB+xlVxxtCaDR 5VreBcjt9shu+VVVNVJd11NdXRMIBBETEXAgOfh8+Wf4GxubamvrzC4K9CK5 qeK/PPmvha2V9QvZ+QehHOLo2ZhXvp5fV1cvW/1gFDU1tWhBMjgGGJoU/9EO 47KyjUUGJ4QQQgghhBBCCCGEEEI+ZXy+Fp+vtaUFtLW2CrIQIGsBQa2crtYC VvwoQLcW0A6iUfkFQUh2yCngrtDtIGSgtrYOXWuLCC2ywQ5oaGiUAruB6uoa 2Pj9AS2NkHrnL1zKtTcUyJqCtioRwCiam73SviplZRs3bCiT46amZq343yxr B2hpaHBpj/034QDU1zdUVlbBBRQTnBBCCCGEEEIIIYQQQgj59JEterRVALUQ oNYC5EcByz8HKKwFGH4UEFE/CpDtgxCwvr5B0dDgklK5AxXapj3y7gC41NbW SYEdvtrLdpuRDPpCL/grOxRpT/4HkCfsJUjhyf+gPPmPQZWXV6zatVBaumHD hjItSI3bvVz8R0ryhL967B991dXl09O7EEIIIYQQQgghhBBCCCEXIC5XY1OT W1sF8Mkbe+WlvUJra1vhtwD+wr5AgcIvAoKyEFDYGii/k4/2ggC3vBFAqK6u 2bChbE1sLDyQj95loyGp/GvF/5B64a88ny8uDQ0u/SkMoaKissjuSktLS0pK 5VjWIGSTfwmOsajH/uvq6mVtorR0g3IhhBBCCCGEEEIIIYQQQi5ASks3CBs3 5l9lq73J19XY6Nb9IsByX6AVvwjAR4/HJ7v919c3VFVVV1XVVFfnQUzVxVpB 7/L7gsKGP/kN/5FGY2PTxo3lYiNbGBmK/2gssouSktL160vwF8eVldWq+I95 QEuZ9hsE+SGDFP9ramoxacqFEEIIIYQQQgghhBBCCLkwKSkptaNUq65XV9fK C3A9Hq/lWoDP1yr79gs1NbXyZuHKyirZxsehC0GWIcztXq8vEAhpBNG7y9VY VVWt92pocMlZ2Q5I2/Pfs3Fj+ao9Ki6/fD2QY8SX4r/sWYQWdFeo/NfX1NTJ 0NavL4GLLAEQQgghhBBCCCGEEEIIIRcm69eXrIny8oqKiqra2jqXq8nrbdF2 y3frKbwbd/n9AqWlGxyi4Wx1dQ1CVVZWm89KBDvf6upaKftL5b+lpQ1xSkqc ujNw+eXrL7vscinmV1VVu1zuhobG+noXUpLcpPIvj/2jsaqqBo3itdZ5I4QQ QgghhBBCCCGEEEI+TeQB+HOjoSH/wLyBwp5Cy/sL2XWxXltKqKurl3cE429J 4Wl8Oy677PJLL71MkLq9x+NrbW1raZG3/VauKXkVDcdIGJmrTf6lyC+7IWmV /9qqqpqqqmokLF7SOyGEEEIIIYQQQgghhBBywXLZZZefG/B1uRoN1Nc36BYX 8r8vsHTcsKGssrKqurpG3hRcV5evuldUVDr3uG7dX15yyTr8/cu/vFSK8Aji 9fqqq2vR3RrzvwxBgHysra3XnvzPpyFFfgSUyr/22H+17GWERnSsvAghhBBC CCGEEEIIIYSQCxb1RP1aKSnZ0NDgMlBdXasiX77yiX1h/fqSsrKN2iZC+RcE VFVV19TUytb68IWLQ4+XXLLu4osvkSUAoJ7eP4fk1607u45QUVGFzGUNQvJH Y3l5pVT+AQyQLdKGvfIihBBCCCGEEEIIIYQQQi5k5DH4c2DDhrL6+gYD5eUV dvaXaQ/Vl2jv7S0r27hxYzmMZQlAdtfBMU459HjxxZd89rMX46/U/88580su WaetIuQjlJZuqK/PF/+1rX7q1q8vlUYtn3xKFRVVyFN+FLBuHRzXnXO/hBBC CCGEEEIIIYQQQsinxrpzVVlZWZ2mWp1KS0svKUhvvLxfz+Xavv8lJTDbUFgG qNBUXl6+URMs7Xo0hz0HXaxJ4iAl2YEIf6urq5GSpFpRkMoKacNFOVIURVEU RVEURVEURVEURVHUBa5LzlUVFRW1K1VTU3PppZderJN+LeDsrv2XXy5LAGVl ZfAqLy/HwQZNaJRK+yekz372sxdddBH+Skr64j+GIzZIprygjRs3Sm7iqx8R RVEURVEURVEURVEURVEURV3IuvhcVVlZWW3SZ62kHptXSwAlJSVVVVUNmuBV Wlpaomm9pnWFp/TPo5DGX2i66KKLJB/kX1NTU6WpoqJCOkXvGwtSqxJIWy0c nPfEKIqiKIqiKIqiKIqiKIqiKOqTkGXFvhhVWekvVuoiTapsfskll1x66aXl 5eW1tbV1OpWUlFyu6bLLLoOB1NvPo5DDf9KElCSZioqK6upqJFxZWYl81q1b h3Z0LWV/qfyXakJWcJexnN+sKIqiKIqiKIqiKIqiKIqiKOqTU4aiKIqiKIqi KIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi KIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi KIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi LgCdeOvEj3/84+PHj//whz/8/ve+f+TIkZdfevnFF1/8xxdeIIQQQgghhBBC CCGEEELIBc6LL7748ksvHzly5Pvf+/4Pf/jD48eP//jHPz7x1ol333nnF2+/ /fOf//wnP/nJP//oR2g/dvToP/33fyKEEEIIIYQQQgghhBBCyJ8Ex44ePX78 +D//6Ec/+clPfv7zn//i7bfffeed06dPv/fee+/8yzu//OUv3z7x9ptvvvkz 6Kc//en/IIQQQgghhBBCCCGEEELIhc7PfvrTn/3sZ2+++ebbJ97+5S9/+c6/ vPPee++dPn36V7/61fvvv4+DkydPouXdd9/FKfAvFEVRFEVRFEVRFEVRFEVR FEVd8JKq/rvvvvvee++dPHny9OnT77///q9+9avFxcUPPvjg17/+NY7/7f33 /5em/0lRFEVRFEVRFEVRFEVRFEVR1J+IpLb/b1rZ/9e//vUHH3ywuLj40Ucf /eY3v/nwww9xfAb6gKIoiqIoiqIoiqIoiqIoiqKoPzGdAWfOLC4ufvjhh7/5 zW8++uijP/zhD7///e9/97vf/fa3v/2IoiiKoiiKoiiKoiiKoiiKoqg/Wf32 t7/93e9+9/vf//4Pf/jD/ynof1MURVEURVEURVEURVEURVEU9ScuVfb/fwX9 X4qiKIqiKIqiKIqiKIqiKIqi/sSlyv7/HyiXBEA= "], {{0, 71}, {2048, 0}}, {0, 255}, ColorFunction -> RGBColor], BoxForm`ImageTag[ "Byte", ColorSpace -> "RGB", Interleaving -> True], Selectable -> False], BaseStyle -> "ImageGraphics", ImageSizeRaw -> {2048, 71}, PlotRange -> {{0, 2048}, {0, 71}}]], "", PageWidth -> DirectedInfinity[1], CellMargins -> 0, CellFrameMargins -> {{0, 0}, {0, 0}}, CellChangeTimes -> {{3.544379162237352*^9, 3.544379175555642*^9}, 3.574009622854604*^9, 3.5740096771925993`*^9, { 3.6064973343114243`*^9, 3.60649734678067*^9}, { 3.60796539088447*^9, 3.6079654004078093`*^9}}, Magnification -> 1.]}, CellMargins -> 0, CellBracketOptions -> { "Color" -> RGBColor[0.739193, 0.750317, 0.747173]}]}, Open]], Cell[ BoxData[ GraphicsBox[ TagBox[ RasterBox[CompressedData[" 1:eJztnWmQXNWV5x0z82E+TWNQA6pSqfYlq7Iys6pyr9yz9jVrV23aSwtCYkcY sMHd2MYL3YMAAZ4eMIuJ9rTZP9AsAtsRnpYE7rDHNgg7oiFoSRND2xGoCONl lpp/vlN59eptlSUElsP/f/yoeHnfOeeee/M9EXHuy/sqt181uuvffeYzn7nu P+LP6LaD6Wuv3fa5sf+AD5nPXb+w/d/joBv/fQan88ddXT3nzPz8FjNDQ7m+ vn7Q25unp6fPzr2zszuT6Ugm04lECnR0dDl3l0gkY7EE/sIlnc7qT/X1DVi6 TExMIqW5ufmpqenu7t7ih4aAO3fu2r59J7zQlwFk/nHmjRBCCCGEEEIIIYQQ Qgj5pOns7C6Svr6BoaHc+PjkzMzctm07FhZ24+/s7LyBkZGx7u5eRRFddGUy HalUZtUEstnOdDor6wVwUe2jo+NIZmxswtIL7cgKOdsZ2DE5uWnnzl0Yr6Qn pNMgi0zWFIoQQgghhBBCCCGEEEII+ZTJdnRZ0tnV09s3kBsZG5+Y2jQ9u3Xb DrBt+06wfccC2LFzF8DBzOw8DBRDwyN2MddKX//gwOBw/8CQoT2T7QQqT6Sx sGvPzoXds3Ob8dEcB6NAYpNT02vKDaFk1B2d3YlkGiRTICOcrzESQgghhBBC CCGEEEIIIZ8EUksHPb39/QNDw7nR8Ymp6Zm52bnNc/NbwPzmrWDzlm1btm63 WwWA2dSmGSE3MpbOdGhkBdXFWkHYhV17ZJUBxxOTmwYGh/U5g5HRcSn+ixny 7O7pM8SBy9j4JNwxNAyz+ARGxyYwUvxNpjKyBKDAAM95XIQQQgghhBBCCCGE EELIJ81wbnR0bGJyanpq04w8wD89MzczOw9m5zbrVwE2b9kmqwCyEGBYBUAj IiBObmQsmTKWys8N9L5zYTfioyPERxrICr0MDY90dvWITbajCwlL8V+ZdXX3 GkJhpGPjk2BkdBwuzv1mtNUQCY6YGHsqnY0nUno+zrgIIYQQQgghhBBCCCGE kE+aiclNgiwB6FcBZCFArQKoHwLoVwFkIUCWAHAMx9zIWCye1JNMZVLpbJEk kql4IhlPpHA8PjGFBJCGPLovSYKx8cnh3Ghv30Am2yleg0M5yQe5IUm4dHb1 GCKjZXRsYmR0fGBw2CGBnt5+DAFIBPSLsHBBSvpBSYaEEEIIIYQQQgghhBBC yIXJzMzc5OSmiYkp/J2amgabNs2A6elZgLNAXuw7P78FbN68FWzZsg1s3bod bNu2A2zfvnPHjgWY5XKj7e1xPclkWr0/15JEIhWNxkKhiN8fbGsLtLb6A4EQ 2ru7e/v7BxFwbGwCiSGT8fHJ4eGRoaEc/g4MDHV0dKkgXV09khuSRBqw158V +voGRkbG4Gs+JaAdfY2OjqNTdC1hMUZMDkYRiyWEeDwJkLbzuAghhBBCCCGE EEIIIYSQPxbbt+8EmzdvnZ6enZzc5LwKMDe3GahVABzj7NjYxNBQrru7N6VV 8mOxRDQaC4ejing8kUymLYExDILBcCAQAm1tgbY2v1b/D5qNM5mO3t7+XG50 eHikp6cPPRoMstlO5IyskC0OkBhS0hvg4+DgMLLt7x+0SwnBZY0Alul0Fi0Y 49at2xE8FotrnF0FsAtCCCGEEEIIIYQQQgghhPxxkaf3ha1bt8/Nbd60aUYt BBhWAfAXjTg1Ojo+ODjc1zfQ09PX1dWTzXZKqTweT7a3x6X+HwqFBXxMJFIG YBmJtIdCkWAwHAzmi//aw//54n9bWwCNZhdFR0cX+kWPlqckW+Q5MTE1MDBk MECqyBztOLAM3tnZncuNDg3lYINjtOBgy5Zt+BuLxQ0/bXBIkhBCCCGEEEII IYQQQgj5IzIwMCTb+GzZsk2e6pctdOQRetkaaHx8UnbFEVR5vK9voLu7t7Oz W9X/Y7FEe3s8EmmXp/oFfJQNcxTKJhQKy8P/YoZ2g6UdstZgSSbTIZkj7ZGR MeRmMOjt7e/vH+zp6bN0x5wMDg4DZYO+MCcIKD9t0KP2AiKEEEIIIYQQQggh hBBCLijaY4ncyNj85q1z81sEeeEvmJmd3zQ9OzI6Lu/DVQznRgeHcv0DQ719 A13dvR2d3ZlsZzKViSdSiBaJxsKR9mAokn+kXyMUjqJdEdUM0BiUh/9DkWh7 XG+AOBIKpLQX8qYzHXqD/GsLZufRrm/Ug6zGJ6ZGxyaQKvKMacNUIFVkDncc 2LnL6GAjmUxOTWNmcIzMhYgQjdnlQAghhBBCCCGEEEIIIYT8EYm2x8FwblQK /sL0zJywaXp2atOM1Pz1DA7l+voHe3r7u7p7sx1d6UyHof6/XCSPxiS+nrPF /1BEb5BIphGqs6sHf1PprDTieH7zVqQ0OjbR3dMXiyfRiANki9yQgyFymz8o xwODwyOj40PDIzjIZDsNOSBtBEFwc3oAY5HRwUYy6e0bQI/ITZIPR4T8GC0j EEIIIYQQQgghhBBCCCF/XCLRmDA4lFM1f2Fq04wwPjE1NDwitXSFVMg7u3rS mY5EMi1LCSqaM1L/Vx9j8WRXd688b48DiSmnMtnOufktyAo5DOdGYRNPpNCe 7eiamNw0OjYBY7FEQI/X1+zx+gMhiZkbGZPfKXT39BlyQ8LyywW7nNERvGCD BPAxmcrMzM5j1Mg8FI5oRIUih0wIIYQQQgghhBBCCCGEfKqorWwi7YODw/LC 36mpaUFeBCwv/B0YGOrvH+zrG+jt7e/p6evu7k0m03r3cyOdzsrbBBBcRc5k OuQsDubmNk9Pz46PTw4Pj8AgFkvIqUQilcuNwiuVyoTD0eZmL/B4vF5vCz7C AHHUNv6GVKPRWFdXT0dHV1x7DbGZzs5uuItNVJul2dn5sbEJ7Z0FET3SFyGE EEIIIYQQQgghhBByQREOR/X09w+qmv/ExJQg7//N5UalON/V1dPZ2d3R0ZXN dsZiCUOENZFOZxF2eHhkcHBYlgBkWaG9PS4G0WgMveDU6Oj40FAOnerd0Xtv b78Yt7S0ejxej8cHWlv9aEG7eklxJtNh7hqR0ZdlYqlURoYJm/wLC8JRJDAz M6d/r7EgSwCEEEIIIYQQQgghhBBCyAWF4Wl20NvbPz4+KYyNTYDR0XFhcHBY Vf7T6WwqlUkm09FozBykGBBhZGRM6v9DQ7m+voFYLGFnHNF+C+BgEAyGteL/ 8hKAVOaRJ4bT1dWDA0TQ2yMUAiIHy2jt7XEZqeq0p6dvZmYuHk8GAiE90hEh hBBCCCGEEEIIIYQQckFheJpd6Onpk7L/yMiYkMuNCn19A6ryn0ik4vGkPH5v GceBaDSmIg8Pj6BHczKdnd0OEXy+VqnzK1pb22QXINDa6kdLLJZAZMTJZDqQ p944rP0EQPYOsoyvljkQBB9xPD09i1EHAiG/P6iQJQBCCCGEEEIIIYQQQggh 5ILC8DS7oqurR6vMCyNDQ0JucDDX09MXjydjsUR7e1z2xpcSul0oS7QtfSZG RsZzubHe3n79qba2gNTV+/uH4vGUNIbD+V6QAMBZr9fndntAa6t/dnY+k+mQ sryq/09ObpJG/E2lMolEat++/Xv27AWIIDG1JYz8ewEkrCHDdDqbTnckkxmM FF4HDlz9xS/+9fXX37h7955du/bg78zMrCwBoAuJLCAf57GjL2cby3zQy6qR /yjsaW1TZLQv7oIF6X1q2Z5bR0NtAb3jJ5he4XKV2+QTciHnHfzLUOS/Mx+T 7tlN81/7qyue+C9g+os3J3p6HIxzB/bu+q+HxBhezsYq/vjBayIJ4y+qDMAA ZsUEJIQQQgghhBBCCCFm2vwBO7IdnYNDw2BgcEjoHxgUOjq7wpFoKBwJhsKB YMgfCDrEQYSe3r5ItB2W0tIei4+OjY+MjoGh4Zxqb2lta/Z4m9zNXl8LPmay HX39A+gF3eEAfT33/POLi4u+ltYmtxtmINrevrS09Npr35MIHq/P3ezZtn07 Ghd27ZbG666/Hl5LOn37iSckjVg8gfhvaDKkHU8kk6k0/u4/cGDJRq1tfvDg N79pPvX2229Pz8xaTsip06dhMDg4ZDdjyBbuhkaMHV6pdMbSZbq1bamhoUju 8nrP9uVyrWoPG3OPqTb/c83NZmM0Dra22aVnGUp4ze02p2dI8kGPx3bSNBu7 +Eip+GwNnU7bGFgi02Ke1Teamnbh+rZ3xFnYmGce0RDTcqJgbxnqdq/PbrZx 1cmFpBcu/l2799glZumC6/P227/ocAFDDgbKxtyOe9PudlNS97uAG3xVF3Nf CGJpidsTE3LXXX9jd6/ZOeol/8KYx2v3b4LMs+WNf/Zrvf2L8k+HflD4x8cy z2KSxBgtOwon4gt/d+jWN14xMLTf4iKB8YGnHyvS2Bx/7ODVDhcJ2HbPV2E2 91Wna4kQQgghhBBCCCGE2NLmdyCb7RgYGAT9/QNCX1+/kMlkg8FQIBD0a0Fa W9taWlrx1xAhFApPTk4NDg7hbyQSlcbu7p6xsfHR0TGQSCTRglDw9flaEET5 oove3j50Go8nOju70HL77bcvLS1NT894PF63uxlcddXVUstKpdIwgDsaDx++ Hy0SGcZLWrnyuuuuhw0+vvbaa/kC3befCIcjsVgcWS3X/1dm3t4eSyZT6Hr/ /gNarewu9H7zzTcvLOxSIGfw4IP5+j/i79q1W4CxlPsGBwcNYXG2UHy7y3LO JeGl/ALBCl9ZwkAvll67fC3F1/8fbPYoxyJdjEm2tDosHODUtO57NKRnd7Gp 6rc+PXOShshmG8vJcc4WBg4BLc9af3eO0wJu93otHdHuvP6iH7V+Mq/z+Qyh Uq1tZ5dLVs4kLi39Qhiu+VOnztaTcXmbE8P15uDy3HPPW38Xheq0+fo32Fhc Bm+8sWrh2nC3yg24qtbaUb5cPz1zXjJU48Xsyb9UFldp4V8Gy7OYahUcQfQ5 4B83c8xiksS8Wfa18Hd3S3F+26Gvbrr9JnDdi/8gLZ3TkwbjK574ZvHGAI3K AMDe4YYKx+OF1YTdRd6DhBBCCCGEEEIIIUSPVLAdSKczqubf29un6OnpTaXS UvYHPl+L1+sDsgqgSCZT4+MTAwODudyIahwZGZX6//BwDh/9/gACJhJJOSsB cYD4mUwW7dFoezbbgRbE0cpWD6I7t7u5udnzzDPPSH3ytttuF1+0v/XWCYBk 0PLaa6/BAHECgaAarywBdHR0tLfHwoXn/w0Dj0Si6DoWi1955X4YLyzsQsJI QNLTg3xgYHCfnp5G4ze+cZeh/bnnnkM+Wh31lOWEw0Wqc3rfa6+9TgqScLf0 ml5L/f8bHo9yLMZ+0eVa8Z2urHKfcrlea2p6zu0+pWuEQVJ3JSwUnkgHdlea rv7fbDilT+ZEY6Olu138geKyHVh53eoDLmgX0qpgvKesOkLC+vzN0a7VTY4M EF7wNaStn8/nCj8BMLTnV6MKP3M4tfJbw6UrdwouPFxOZ7+ahV0nTrwtl5y+ 3cEF7XIHLeXX0b5t8V3oyuB20yUGFpeBVrjGda5faDOABFYMWbsBMQoHF9yP lh3hLjMbI6AMHH/xL9jHz1A/J3a3MLzs5gSTrGZbRUZiMnAZe/GjU5iHBlLD g8tP5t94lWoMxWIHnn4UjQt/d7elcef0hN5477e/aTYGQ1fuFvuDP3ge4GDq tpsc7imchc11L/5DMTcgIYQQQgghhBBCCDFjrmabSaXSPT29iu7uHtDV1Q0S iaSU/T0eL2hu9rjdzbIKIGQy2dHRMXGUlkAgqB7+7+zsQksymervH2jTnt73 +VoEsQyHI5FIVErx6XQGlr/4xS/eeOMNqfOju8XFxWeeefbUqVOvvvqaxIfx 0tLS4cOHcRYfcfzCCy/Avb09hoBis7CwgPbdu/dEo+3o4vXX3wCGUaM9Hk/A a9++K7X6/4L8AkKfpPDAA/kqnHne0IhT+hakgcZnn33utttuk5hmL0kGIzpx 4oRqhAtGijGivZivDDzgXq4Dv97Y5GCmq0t71xoZ4Fh/6uvNHstTC7rn2+3C Ik/LmPok7Qz0Nob2Z5vc6tTXtUvCMttXm4yztNaZcZgWRFDF/FMul8FRrRrA xtCXXcx+3XKPXfttnhWDxSUkBW1chJZXHc6qm0jARyn+W7qoorTcFCumTifD LWCwscvEzst65rUb0HwLOyMdWd6DYNOm6cLC4m0fP0PDnFx77bVmA/lHyTwn mF6HmVReSLj40TnQu31eSu6G9sF9u6Rur2+cuu0gGg88/ahlEGBol0WEvd9+ MNqRxV+t/n/QLpNge7usEYzecNVaR0EIIYQQQgghhBBCBEMp245stkOV/Ts7 u/TEYnEp+4OmJndjYxPweLziCJdcbkR+LCAtkUhUiv8jI6PwRUtvb5+cRRzl qAgGQ6Ctze/1+nDw93//90tLS/F4Asay+Q/+Pv74t6UR9gcOXIXj8fEJGOAj jh9++Fs4FY22+/0BiYmPsv0FktHq/3kZ+g0EgkgPXvv27YPxzp0L8iMI9UsH xQMPPAADg/vXv/51NH7hC7eZG6emNuF4cXHx2WefNXhJYggoI5LulDGiKfdV eaDwiPjrjY0OZqpcvNM083aoevWrTU12/T7b1NSHeIVGBFcd2YV9vfCcPCLY JemQrWX8uO7RenNY/SyBuC7hc5iZRcdp+YJurWFKF/AaXbtlR49bzac+c/Sr Tqk5NH/pUiU2XJD6Cw8Xp9xB+kvRwSV/JZw6BQM4Wvb16quvyoHlFSunLC6D 11+XW6DIqzE/FdoNaL6FnZGOcF/bGeCO01brnv34Garxii9uZ/1UC8jEck5k dJhqu8jXXHOteRSrjs6OQDQ6csOBxGC/oT07NS4lfX3jlrvvRMvkFw6a44hx tCOjb0TYwX3LKUn939JXwClZcUBKax0FIYQQQgghhBBCCBEMpWxLEomkPO0v dHZ2dXR0Kvz+gFb8d6viv8vVKL8CAN3dPcPDOXglkylpCYcjqv6PY7TkciNy AC+Px2vo3aeV4lu1/S5gtmPHzqWlpauvvkZt/oMDfETj5z//BdhLozv/8wDE 8mn1/4dln39ZRBC0+v+DCBgKhaX+b+gXPba3x+B1xRX7tB02Try+Usry/vvz BbrHH38cB+DZZ5+FsbgYYspT/XIMe9ggMb2BDGRycgrg4Gtf+7pqxN/e3j7V uCr3N52t/zuYqeLzDm26VqVXV8m/urm5GBewQ1fltrNRtWtkbpfkKd1T9DGv 19LGrl+DvRDT/TDBMANrmplJz9mOJj3W9ip5/QDV14SzRU6mynyxobDi0Nhk GKwhZ7lrzNeb01dWcHGwkWvYfO+ovmSBwHwjKBuLy0ArXOM+Kn4q5AY0p+GM dIRhrjXsOWSoxotbWH5WYA5rN+HSHab6/I5urYxcv//WN1659h//m76xUMO/ 0Wwv9f/M5JhdQAdfAX05GxBCCCGEEEIIIYSQVZF9exyIxxNazX/5sf+OjjzZ bKdGRyAQVE/+q/o/DpQ7XAYGhuCCOKqxudkjPxmQjzAIhcI46Orq8fsDhgSQ JBpbWlrT6WxraxtaZM+fwuY/z4gZjo8ceRUHp06devrpZ5CDxF9aWnrooYdl n39xF2Q/DfQbDIaknm/oFz3K7kB7915hrv9LX8L999+vN5CaJxrRqT7g9u07 tEWKz8vHiYlJrZj/Nb0NxoWByDHiSC/6RvSi79qB+wvb6b/e2OhgpirG2wtf hzPbdTvSFGNfvJeu/t/kkKQ6fmylmWV8NQknXC67fk+cLctbByxmZs55gEcK jUccvyZLvqbb2ggJqPUF8zeOq04u0eKDy1Vtvi/MYc02Usf2FK556LHHHrez Mc7ScnX9/vObql1HyNDOADeaZebnkKF+vDJp5ntfzZXBUf49ufrqq8/v6NaK VONnvvIFfeOex/M1/InP32i2L9T/R+0COviC/r075eH/tnD4fA2BEEIIIYQQ Qggh5M8QKcXbEYvF9Vv9qGf+s9kOeaOulPENxX99BHl9MP62t8dUo3KRPfwR ORyO4ABhYWnIQd5T7PO1IFvZh/zIkSOnTp1Sm/+I2TPPPIOPExMT+HvLLbdI fLRr9f+HotH2UCgMXzHu7u6RB+mDwZDfHzh+/HVg6LdVewUwvPbs2atV0rbb zdLhw/nyo/oIS61s+JjBTDJEO+yFxcVFDERvo9X8j8gxLGGPzGWZQ9/o/K0t Z1XYTv+4q9HBTBWQn2lshIuZCe07Ojs63YY5xaRh9rLsBajyNY7tkszPQGFc WtHbbWmzpknAKct+LXspZoB2No9ZJWPXe5GcfXeAbnOk7pVfmbpEzRe50/VT hItc6uYLUt8oV6z5DrJ0zE/I8XzhGr2f31TtOrK7r2+9dblKr/6F+TgZGsaL e3xJ2wUI/14VOZkO//6cw+jWysTnb5B6fiid0rfvefwBrYZ/g8UEavbpiVG7 mA6+QJYbNv/nr8hH9Ju77srWUOi8DIcQQgghhBBCCCHkzwd5et+Mx+NNJlOW lX+p0re1+T2FF/6q+r+U9PVEo+3d3T0IlUgkVaPaJgh/9catrW39/QPoDsHx 0edrQYvfHwDhcAShZA//r371q1q577i2z8+yr2z7/9Zbb+EvIqhkYPODH/wg EokGgyEE1Bvv2LFTdhY6rsmQOXJAp/Das2cPjLdt2+4p7E2kVk/E8vDhwzDQ +0p9r6urW7UgAdn3wyxEFhvYa4sXt8rH8fH8WoaEQsL6zNVHBw4XHiw/7nI5 mC3p6saWII7e/hZd+X3VHBTbdE+qr7VHfZL5mdQ96I6DiJXNmibh+Nl1h0bL TreZrmqH2XaYFstk7Ho/4mrEKQNdpkwONDUZZu8Z0+ypS9R8kTuNqAgXXLpy DRu/r5WNcleeOnUKd4GdzdkJOX5cjI/bSH9b6VN1EP7FsOsI99fhlXr00cck Ybvhi6ODcOeavfTjVf8aoKMiJ1P9K1Ekzkmid8skLUmNj0gxf/zWGwynpIZv bgfiAl+7sA6+fXt2iHswtfx/jR3f/Ft8HL72yjVNAiGEEEIIIYQQQgiR0r2B 5mZPKpW2rPyr4r+UwVX9X+rtZgKBIIIkEkl4qUaXq7GhwQXq6xv0ls3apuXx eCIYDKElEom2t8dCoTC6w7Gy7OrqkiqW7POjUCU1WV+QlOQlnvPzmxEfCaMl HI7ARnbUkZ8VSF3RkHlraxu6htfu3fn6/9at2+RNxGgBfn8AWcnA77svX37U +0qG+vRuueUWtIyNjevNkAnSUGZ33plf14CvMjh58pQU6/ReaHn00UctZ1vP fa6z1WYHs1Wr8Yijt79TV+heNQfF1kZjmbr4HvVJyscxXbRXCqOzzKqYSVAV eEO/KuBWm2vbsiOHabFMZtXe9VhmoiLIrwDCll3ft1zML/4rK8YFN4Xcicbv a2UjLntpeeWVI3Y2Z4ezWnUdnVqm6iAYnENHuMtwh56XDM3jPXDggCE358m0 jOnAqkka/i2yI5BMHPzB87e+8cqexx8wny3U8K83n5ICfnIsZxfZwVdObf7b LxdjTAghhBBCCCGEEEIcUKVyhdvdnEymtX3+O9U+/5mMkE2nM35/QF4cbKj/ WwIDeIFYLA57aZTKf11dPcCxNKLHrq5ueRGAtITD0Xg8Adra/LFYQh/29OnT S0tLN954EMmo3p9++mk0PvLIo3rLgYHBDz/8cHHxwyeeeOLAgavuvPPOkydP wuzmm29RNvJTgvtW6oEHHhweziH+wsJu2G/ZslWK/1rlP9Damt+SSH7FAGMY GAYuycBLPr6lyTw/MEPXGDWOX3nlFeSmP4uxLOXXEZ7WN5rNLLmvUBY+7nI5 mKnS8dMu131WbNF+pqHYoit0r5qDpdcjNh2dPFv/NyZs7vE+XdF7v5ahZVbF TIKuAu+y7NQwA5bcXMS0WCZj1/uiVf3fMhP93Jqnbrlr7RLFdV78V1aMCy5v KSYbvy9To0SD9u8/YGezPCFa4RoXOYJbIjeLObjl/eWA6kh/1+OjJDY6Oubs COM1dWcer9zdqi/nyVT/kqxpdGq2zw2v37//qUeWX/vr95sNdj+WL8uP3XK9 +VSh/j9sF9zOFy7i60/Ei+mIEEIIIYQQQgghhDjgcjXqaWpyJ5Mp/dP+stW/ kEgkA4FgS0urof5vCGIgHk8gZiQSha+0NDS4amvrNGpramrxUboOhyOwTKXS bW1+tMAlnc6gLzlQAXH2oYce/vDDD4PBEJJR7Vu2bFlaWhoZGdX37vcH0PK9 731PPfh68uTJK6/cr7dRRT+DZmfn0NemTdNSo1OP/be2tqFfzICM5StfuRMG hlFjDhcXF5966mk5hoGhUwG5wUxO4eDee+8znDU73nzzzebuzNzbsFxYPqZN rx262rKT2dlJ1hXei7Ev3utYIeF7TQlb+r6le+g9aGNTzCTY9bummVnTAJ/S daQaH7HPcNVMVjXAdYVr5tix48V/ZcW4yB2HG8qYjybj8I/lK9K4yHHb2tko M8ON8PFTtesIQ9A3Ijf5GZFDAueQoeV40ZesReIvjmUyzXNSqP9vWVN3lqNb K/N/+yV5CW+kp9PSYPdj92tl+evMp6SGnxgdtgtu5yvt+FtkR4QQQgghhBBC CCHEAdmHR5Bn9Qs1/+UH/rVn/vOP/ScSKb8/IKVvff3fEMQMXGKxeDgciUSi yri2tq66ukZhcGlqcuNvPJ5AR9LSqP1qALjdHmSiBcwvKIilslFZqfZQKBIM huU3C855Gmhr88t4EVNS0hf/EQ291Nc3gDWF/dS4t1ATPtbglKEqHW8uLuxm nUuu6GT0XnY2xwoG95psLH1zuvZXdA/J6232FdGvMvjcx5gZ/QCzNjZvWQ3w kULjWzYZBoqIvGqqmzdvkdp78dfPvn1XSmnawebee+/VCu/HjPloMjTiXxUp rYu9pU3+Mjh2TKuu31t8qnZpOCMdYWYso0FI2MFxTRnajTeXG5H2Rx55RL4j s4109+Uvf+W8jK54Bq++Qmr4Pbu22tlIWX705uvMp8Q3PjK0Jt9wd6c4oh2+ iiuf/BYa5/7mSw4BCSGEEEIIIYQQQogZqWADt7tZiv/qaf90OqOQJ//b2vxA X//XR7DDpT3JD/z+AHylsa6uvqqqGlRWVlVUVFZVVZkd0YW5BZnE4wl5LwDS 0J/FRynR46CpyY2W5maP7OGPRlWuLwaMS0IhYXF0a28E1i9/oAvZwqj4sJ8m 9+jq/w5mqnQ8X3Rk5XKPVeR99Q0vm6LN67zswh6zD2vne4+u7G9pk9H53mTV 6T6dQe7jzYzztOgz2adrv0nXnrEKqwzO2E/dqqnidpbaci6XK/JbhqW4wNf2 K9OKzN/61iPGfDRZjOWmz8mpL3/5y3Y2EvOee+4tMs/8ZXDPcv2/eBfV0fz8 ZvMpeSz/qaeecnBcU4YOcyLJyzRa2iANNL788ivna3TFEOrqkDr81B23OJjh rKWNu6VF3HFg51uo/1+rb8RHcXRg7m/uOLdBEUIIIYQQQgghhPwZIhVst7s5 nc6o3X5U2T+VSoNEIhkMhqQeLjVweW1uQ4NL3FfF6/VJER5BXK5Gaaypqa2o qKyoqCgvX6a6usYuQmP+dQARpJRM5h/+j0bbEUrlL+8RkC7kiX05hWPJHAfF Zwtc2i5DMlJ0jZbmZo/htw8NhV2Mig/7aXJPoSx8TDdLZlTpeK6+2MhP6irS wytP4eMZVQbX9YvgqiO7sMfqLRwNSTp42dm8WWg/2dCQXnkKH0/qzn7MmXGY Fr8ujTMrO/LrOoKN334+n7T/HotJVWraL7/8suXZL30pX5C/6aabineZm5uX ejUOjPlosvRCNJw6c+aMnU2hun5PMXMuwFjq/8W7qI7MyQPMg6Q3PJw7Lxk6 z8mbb765pNOaksE/bviaEAEHRY5uVZp8Pnnn765H73e2HLhqD8yueeE7hvau nVtk4yAHXwSHzcjnrtU3pmcmV63/G1wIIYQQQgghhBBCiAO1tXUejzeVyhRe 75sHHzXyxf94PBEMhtV7b6UqDhfxLRIYt7S0iqPP16J8q6trNm4sB2VlGxUV FZVoF4P6+gY4RqOxbLYT6Wn5JNvbY8FgqOHsSwTy+HytUufHQWNjE1oatM1/ ZFEAnRafLXC7m9Um/8hBZkn7eHbjozptCQOsKfKnxqFCyf1ovdM3dbb4XJ+3 tOTllRGG6ur09fYn6+v31tXP1dU/XH+2WJ2vReuukDldjdouk6OFhA+ZEnbw TdXW6Ts12+zVdQ1LJDlnle1e0/VczMwc1HnZTQuGc1LXbh7dId3iCCy/pHnt NWWYKuJLnLO/K/fuvULKyE8++aTh1MGDyxXmhx/+lmW72WVoaFhq+EePHrPI R5NlGrgZVfHf0gYB0X7o0D1ruNQP3WOXiQPS0dzcnOVZqclbxjyHDJ3nRE2m nY0sxMAGlobJlDxxCv82Fj86Z2SznYM/eL7R63W29EUjhZr8NfrGa174Dhpn 77rDwXfXo4cNjufLmBBCCCGEEEIIIYQovF6fKvtrD/znSSbTyWRKnrQPhcLB YEi9+hb2jY1NUvfWl75Vix319Q1a2dzb1NSsKuegqqq6rGzjhg1lGzZsKC0V StEiZ93u5my2U36VgMRk53/kY+gRZn5/ULbrQS9y1udrUQ//u1xNq2YIqqtr 5MDj8Um1H9GkRXvsP/9RvfVYb38BcqjubP3fwcy8f44lBq8bV9a6zcBAbz+r q1HbZXK2/l9nTNjZ946VyZgNntQtAVjypKnHImfGMLerTotlR+DN+lUyNMyn Xaqzjnfik08+KRXmkydPPvzww4c0qYfPcYA7pRiXl156WRrPnDkzODhkkY8m uzRmZ+dUrdviMjh6VKuuH1rDpX7okCRz1F7I2bIjJOOcpNlAHDEhDt2Z83ee kzvu+JLDnGCS1QIBBiLfAr4a1XjjjQfPIcm9e/ea++o/sNvh2ftdjx5u9Hr0 9hN/dbOcuuaF7+CsFOrBjd9/3hsJO3xrYpm76ZpivuI1GRNCCCGEEEIIIYQQ hWGrHyCV/0Ri+TF7QfbAl+36NVVL6btWe0S/ocHlcjU2NjYBecOvVPj1b/iV l/w2NblrC2/+haMcyBJASUmpYsOGMjkFe/UyAlmP8Hp95rBq5x95ya8EVzv/ o9GcjCVqXLLPj8fjRQKyK5F67F+K/ximsr8wubtQiz5aX+9gVmT93+y4p7b2 jJUlGm9c+XJnMKOrUdtlour/yNwuyVV97WzuMP1MQGV7hynb4mfGPLd20wIe Mo1L0VJd85DN2sG/1tcjpvN3rYxnVrvO77770JKVvvvdJ3HNr8nl6NGjyWTS Oh9NDmk89NDDdjZSuEanq17hq2ZokGVHMzOztheVZvDmm29atjsLNmudExXW 8uzAwKBhmyDRv/7ryT179jpEc5DlJOduutp5+x1POGRwmfirzxlsrnnhO/5s 2vlb23r/N2DZt393MV/xmowJIYQQQgghhBBCiEJX9leV/3zxPxptb2lpa2xs qqqqLi+v2LixHH81VVZWVmmrANVS/6/TXoAr9f+mJrfb3ezxeL1en8/XIk/j o1Fe9avH621BXzBTLYhcVlZWUlKyfn1JaekGaURM+VUC8pFH8Q1x6rQdsNXO P6ov/c7/yM2cgBVVctDQ4JJN/tWqB1rUY/9NTc3y5l81Dxcmvqrq6ZoakNDW KewYqK4RM2fs3G+oqX2otu5oXT3AAT76bCwlzoB9MolCJuYIKslVB+sQ37eW bIucGbu53a3r6Lt1dX9dW+v8LagZgCXsxfHu2rrdpgveOdWiLgxfyw033PjQ Qw8dPXr0u9/97t133437vXiXl156CS4DAwNO+QwMTE/POAeEgaUNkkE7DIoZ iyGaA+aEJUmHjiSs2VEydMY8pZahiunOkDMmH18Bvggc7N69x/krWGuSQmSw 1462TMrSpTkU7Nu/a/jg1SAxNVbMtyYuDc3N592YEEIIIYQQQgghhCik5q+e +QfxeCIabQ8Egg0NrhrtFb2yRb8sAWirAJWgSvcTgDrt9btqCaC52aNfAkCL lMoVcAkGQ/Jbg3A4Akf9WelFjtGFPGlviCDglNqYCB2h3yrtFwpud7PsWSQb FknjqqilDbjL0/44kK5lUFrx3y0/c0C7TEUxkQkhhBBCCCGEEEIIIYSQTxl5 2l92+wmHo/Kq30AghAMQCoFIOBzBceFh/mbZwKey0m4XoPxPANQSgNeb35BH lgwUjY1NsVj+tcKRSHt7exx//f6gvBegSvshwKrADF1oT/gv7/wjdX6cQpDC zj/5h/+RWzEB1dIGxlUo/nuQp/SFY1X8lw2OZFlErYYQQgghhBBCCCGEEEII IRcUkUg0GAxpJXQ//ra1BWQ7Hb9fVgEEWQhYXgsIh6PwAjCQB+xlVxxtCaDR 5VreBcjt9shu+VVVNVJd11NdXRMIBBETEXAgOfh8+Wf4GxubamvrzC4K9CK5 qeK/PPmvha2V9QvZ+QehHOLo2ZhXvp5fV1cvW/1gFDU1tWhBMjgGGJoU/9EO 47KyjUUGJ4QQQgghhBBCCCGEEEI+ZXy+Fp+vtaUFtLW2CrIQIGsBQa2crtYC VvwoQLcW0A6iUfkFQUh2yCngrtDtIGSgtrYOXWuLCC2ywQ5oaGiUAruB6uoa 2Pj9AS2NkHrnL1zKtTcUyJqCtioRwCiam73SviplZRs3bCiT46amZq343yxr B2hpaHBpj/034QDU1zdUVlbBBRQTnBBCCCGEEEIIIYQQQgj59JEterRVALUQ oNYC5EcByz8HKKwFGH4UEFE/CpDtgxCwvr5B0dDgklK5AxXapj3y7gC41NbW SYEdvtrLdpuRDPpCL/grOxRpT/4HkCfsJUjhyf+gPPmPQZWXV6zatVBaumHD hjItSI3bvVz8R0ryhL967B991dXl09O7EEIIIYQQQgghhBBCCCEXIC5XY1OT W1sF8Mkbe+WlvUJra1vhtwD+wr5AgcIvAoKyEFDYGii/k4/2ggC3vBFAqK6u 2bChbE1sLDyQj95loyGp/GvF/5B64a88ny8uDQ0u/SkMoaKissjuSktLS0pK 5VjWIGSTfwmOsajH/uvq6mVtorR0g3IhhBBCCCGEEEIIIYQQQi5ASks3CBs3 5l9lq73J19XY6Nb9IsByX6AVvwjAR4/HJ7v919c3VFVVV1XVVFfnQUzVxVpB 7/L7gsKGP/kN/5FGY2PTxo3lYiNbGBmK/2gssouSktL160vwF8eVldWq+I95 QEuZ9hsE+SGDFP9ramoxacqFEEIIIYQQQgghhBBCCLkwKSkptaNUq65XV9fK C3A9Hq/lWoDP1yr79gs1NbXyZuHKyirZxsehC0GWIcztXq8vEAhpBNG7y9VY VVWt92pocMlZ2Q5I2/Pfs3Fj+ao9Ki6/fD2QY8SX4r/sWYQWdFeo/NfX1NTJ 0NavL4GLLAEQQgghhBBCCCGEEEIIIRcm69eXrIny8oqKiqra2jqXq8nrbdF2 y3frKbwbd/n9AqWlGxyi4Wx1dQ1CVVZWm89KBDvf6upaKftL5b+lpQ1xSkqc ujNw+eXrL7vscinmV1VVu1zuhobG+noXUpLcpPIvj/2jsaqqBo3itdZ5I4QQ QgghhBBCCCGEEEI+TeQB+HOjoSH/wLyBwp5Cy/sL2XWxXltKqKurl3cE429J 4Wl8Oy677PJLL71MkLq9x+NrbW1raZG3/VauKXkVDcdIGJmrTf6lyC+7IWmV /9qqqpqqqmokLF7SOyGEEEIIIYQQQgghhBBywXLZZZefG/B1uRoN1Nc36BYX 8r8vsHTcsKGssrKqurpG3hRcV5evuldUVDr3uG7dX15yyTr8/cu/vFSK8Aji 9fqqq2vR3RrzvwxBgHysra3XnvzPpyFFfgSUyr/22H+17GWERnSsvAghhBBC CCGEEEIIIYSQCxb1RP1aKSnZ0NDgMlBdXasiX77yiX1h/fqSsrKN2iZC+RcE VFVV19TUytb68IWLQ4+XXLLu4osvkSUAoJ7eP4fk1607u45QUVGFzGUNQvJH Y3l5pVT+AQyQLdKGvfIihBBCCCGEEEIIIYQQQi5k5DH4c2DDhrL6+gYD5eUV dvaXaQ/Vl2jv7S0r27hxYzmMZQlAdtfBMU459HjxxZd89rMX46/U/88580su WaetIuQjlJZuqK/PF/+1rX7q1q8vlUYtn3xKFRVVyFN+FLBuHRzXnXO/hBBC CCGEEEIIIYQQQsinxrpzVVlZWZ2mWp1KS0svKUhvvLxfz+Xavv8lJTDbUFgG qNBUXl6+URMs7Xo0hz0HXaxJ4iAl2YEIf6urq5GSpFpRkMoKacNFOVIURVEU RVEURVEURVEURVHUBa5LzlUVFRW1K1VTU3PppZderJN+LeDsrv2XXy5LAGVl ZfAqLy/HwQZNaJRK+yekz372sxdddBH+Skr64j+GIzZIprygjRs3Sm7iqx8R RVEURVEURVEURVEURVEURV3IuvhcVVlZWW3SZ62kHptXSwAlJSVVVVUNmuBV Wlpaomm9pnWFp/TPo5DGX2i66KKLJB/kX1NTU6WpoqJCOkXvGwtSqxJIWy0c nPfEKIqiKIqiKIqiKIqiKIqiKOqTkGXFvhhVWekvVuoiTapsfskll1x66aXl 5eW1tbV1OpWUlFyu6bLLLoOB1NvPo5DDf9KElCSZioqK6upqJFxZWYl81q1b h3Z0LWV/qfyXakJWcJexnN+sKIqiKIqiKIqiKIqiKIqiKOqTU4aiKIqiKIqi KIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi KIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi KIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi LgCdeOvEj3/84+PHj//whz/8/ve+f+TIkZdfevnFF1/8xxdeIIQQQgghhBBC CCGEEELIBc6LL7748ksvHzly5Pvf+/4Pf/jD48eP//jHPz7x1ol333nnF2+/ /fOf//wnP/nJP//oR2g/dvToP/33fyKEEEIIIYQQQgghhBBCyJ8Ex44ePX78 +D//6Ec/+clPfv7zn//i7bfffeed06dPv/fee+/8yzu//OUv3z7x9ptvvvkz 6Kc//en/IIQQQgghhBBCCCGEEELIhc7PfvrTn/3sZ2+++ebbJ97+5S9/+c6/ vPPee++dPn36V7/61fvvv4+DkydPouXdd9/FKfAvFEVRFEVRFEVRFEVRFEVR FEVd8JKq/rvvvvvee++dPHny9OnT77///q9+9avFxcUPPvjg17/+NY7/7f33 /5em/0lRFEVRFEVRFEVRFEVRFEVR1J+IpLb/b1rZ/9e//vUHH3ywuLj40Ucf /eY3v/nwww9xfAb6gKIoiqIoiqIoiqIoiqIoiqKoPzGdAWfOLC4ufvjhh7/5 zW8++uijP/zhD7///e9/97vf/fa3v/2IoiiKoiiKoiiKoiiKoiiKoqg/Wf32 t7/93e9+9/vf//4Pf/jD/ynof1MURVEURVEURVEURVEURVEU9ScuVfb/fwX9 X4qiKIqiKIqiKIqiKIqiKIqi/sSlyv7/HyiXBEA= "], {{0, 71}, {2048, 0}}, {0, 255}, ColorFunction -> RGBColor], BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True], Selectable -> False], BaseStyle -> "ImageGraphics", ImageSizeRaw -> {2048, 71}, PlotRange -> {{0, 2048}, {0, 71}}]], "", PageWidth -> Infinity, CellMargins -> 0, CellFrameMargins -> {{0, 0}, {0, 0}}, CellChangeTimes -> {{3.544379162237352*^9, 3.544379175555642*^9}, 3.574009622854604*^9, 3.5740096771925993`*^9, { 3.6064973343114243`*^9, 3.60649734678067*^9}, {3.60796539088447*^9, 3.6079654004078093`*^9}}, Magnification -> 1.], Cell[ BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ "Evaluate", " ", "the", " ", "following", " ", "to", " ", "copy", " ", "the", " ", "style", " ", "of", " ", "the", " ", "cell", " ", "above", " ", "into", " ", "\[IndentingNewLine]", "the", " ", "docked", " ", "cell", " ", "style", " ", "of", " ", RowBox[{"the", " ", "'"}], RowBox[{"SlideShow", "'"}], " ", "definition", " ", RowBox[{"(", RowBox[{"2", " ", "cells", " ", "above"}], ")"}], " ", "\[IndentingNewLine]", "These", " ", "two", " ", "cell", " ", "can", " ", "be", " ", "removed", " ", "once", " ", "the", " ", "docked", " ", "cell", " ", "is", " ", RowBox[{"created", "."}]}], "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SelectionMove", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "Previous", ",", "Cell", ",", "2"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"celldata", "=", RowBox[{"NotebookRead", "[", RowBox[{"SelectedNotebook", "[", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SelectionMove", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "Previous", ",", "Cell", ",", "1"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SetOptions", "[", RowBox[{ RowBox[{"NotebookSelection", "[", RowBox[{"SelectedNotebook", "[", "]"}], "]"}], ",", RowBox[{"DockedCells", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"FEPrivate`FrontEndResource", "[", RowBox[{ "\"FEExpressions\"", ",", "\"SlideshowToolbar\""}], "]"}], ",", "celldata"}], "}"}]}]}], "]"}], ";"}]}]}]], "Input", CellChangeTimes -> { 3.5740143744052753`*^9, {3.574014994368063*^9, 3.5740150001730556`*^9}, 3.574015035375742*^9, {3.574015802108987*^9, 3.5740158031783543`*^9}, {3.5740161341680937`*^9, 3.5740161359439573`*^9}}, FontWeight -> "Bold"]}, Open]], Cell[ CellGroupData[{ Cell["Notebook Options Settings", "Section"], Cell[ StyleData["Notebook"], CellBracketOptions -> { "Color" -> RGBColor[0.739193, 0.750317, 0.747173]}]}, Closed]], Cell[ CellGroupData[{ Cell["Styles for Title and Section Cells", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["Title"], ShowCellBracket -> Automatic, ShowGroupOpener -> False, CellMargins -> {{60, 0}, {14, 50}}, CellBracketOptions -> {"Margins" -> {0, 0}}, CellGroupingRules -> {"TitleGrouping", 0}, PageBreakBelow -> False, CellFrameMargins -> {{20, 20}, {20, 20}}, DefaultNewInlineCellStyle -> "None", InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, TextAlignment -> Left, LineSpacing -> {1, 0}, LanguageCategory -> "NaturalLanguage", CounterIncrements -> "Title", CounterAssignments -> {{"Section", 0}, {"Equation", 0}, { "Figure", 0}, {"Subtitle", 0}, {"Subsubtitle", 0}}, FontFamily -> "Helvetica", FontSize -> 40, FontWeight -> "Plain", FontSlant -> "Plain", FontTracking -> "Plain", FontVariations -> { "Masked" -> False, "Outline" -> False, "Shadow" -> False, "StrikeThrough" -> False, "Underline" -> False}, FontColor -> RGBColor[ 0.8156862745098039, 0.07058823529411765, 0.07058823529411765], Background -> None], Cell[ StyleData["Title", "Presentation", StyleDefinitions -> None], CellMargins -> {{55, 3}, {14, 125}}, LineSpacing -> {1, 5}, FontSize -> 48], Cell[ StyleData[ "Title", "SlideShow", StyleDefinitions -> StyleData["Title", "Presentation"]], CellMargins -> {{55, 3}, {14, 35}}], Cell[ StyleData["Title", "Printout", StyleDefinitions -> None], CellMargins -> {{2, 0}, {0, 20}}, FontSize -> 24]}, Open]], Cell[ CellGroupData[{ Cell[ StyleData["Subtitle"], ShowCellBracket -> False, CellMargins -> {{60, 0}, {0, 30}}, CellBracketOptions -> {"Margins" -> {0, 0}}, CellGroupingRules -> {"TitleGrouping", 10}, PageBreakBelow -> False, DefaultNewInlineCellStyle -> "None", InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, TextAlignment -> Left, LanguageCategory -> "NaturalLanguage", CounterIncrements -> "Subtitle", CounterAssignments -> {{"Section", 0}, {"Equation", 0}, { "Figure", 0}, {"Subsubtitle", 0}}, FontFamily -> "Helvetica", FontSize -> 28, FontWeight -> "Plain", FontSlant -> "Plain", FontColor -> RGBColor[0.4, 0.4, 0.4], Background -> None], Cell[ StyleData["Subtitle", "Presentation", StyleDefinitions -> None], FontSize -> 36], Cell[ StyleData[ "Subtitle", "SlideShow", StyleDefinitions -> StyleData["Subtitle", "Presentation"]]], Cell[ StyleData["Subtitle", "Printout", StyleDefinitions -> None], CellMargins -> {{2, 0}, {0, 5}}, FontSize -> 18, Background -> GrayLevel[1]]}, Open]], Cell[ CellGroupData[{ Cell[ StyleData["Subsubtitle", StyleDefinitions -> StyleData["Subtitle"]], FontSize -> 20], Cell[ StyleData["Subsubtitle", "Presentation"], FontSize -> 24], Cell[ StyleData[ "Subsubtitle", "SlideShow", StyleDefinitions -> StyleData["Subsubtitle", "Presentation"]]], Cell[ StyleData["Subsubtitle", "Printout"], FontSize -> 14]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Section"], CellFrame -> {{0, 0}, {0.2, 0}}, ShowGroupOpener -> False, CellMargins -> {{60, 50}, {7, 25}}, FontSize -> 36, FontWeight -> "Plain", FontColor -> RGBColor[ 0.8156862745098039, 0.07058823529411765, 0.07058823529411765]], Cell[ StyleData["Section", "Presentation"], CellFrame -> {{0, 0}, {0.2, 0}}, CellMargins -> {{58, 50}, {7, 35}}, CellChangeTimes -> {{3.62315433608323*^9, 3.623154337579108*^9}}], Cell[ StyleData[ "Section", "SlideShow", StyleDefinitions -> StyleData["Section", "Presentation"]], CellMargins -> {{58, 50}, {25, 35}}], Cell[ StyleData["Section", "Printout"], ShowGroupOpener -> False, CellMargins -> {{2, 0}, {4, 22}}, FontSize -> 20]}, Open]], Cell[ CellGroupData[{ Cell[ StyleData["Subsection"], CellDingbat -> None, ShowGroupOpener -> False, CellMargins -> {{60, Inherited}, {0, 15}}, CellGroupingRules -> {"SectionGrouping", 40}, PageBreakBelow -> False, DefaultNewInlineCellStyle -> "None", InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LanguageCategory -> "NaturalLanguage", CounterIncrements -> "Subsection", CounterAssignments -> {{"Subsubsection", 0}}, FontFamily -> "Helvetica", FontSize -> 24, FontWeight -> "Plain", FontSlant -> "Plain", FontColor -> RGBColor[0.4, 0.4, 0.4]], Cell[ StyleData["Subsection", "Presentation"], ShowGroupOpener -> True, WholeCellGroupOpener -> True, CellMargins -> {{60, 50}, {20, 20}}, LineSpacing -> {1, 0}, FontFamily -> "Helvetica"], Cell[ StyleData["Subsection", "SlideShow"], ShowGroupOpener -> True, WholeCellGroupOpener -> True, CellMargins -> {{60, 50}, {24, 12}}, LineSpacing -> {1, 0}, FontFamily -> "Helvetica"], Cell[ StyleData["Subsection", "Printout"], ShowGroupOpener -> False, CellMargins -> {{2, 0}, {0, 17}}, FontSize -> 16]}, Open]], Cell[ CellGroupData[{ Cell[ StyleData["Subsubsection"], CellDingbat -> None, ShowGroupOpener -> False, CellMargins -> {{60, Inherited}, {0, 15}}, CellGroupingRules -> {"SectionGrouping", 50}, PageBreakBelow -> False, DefaultNewInlineCellStyle -> "None", InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LanguageCategory -> "NaturalLanguage", CounterIncrements -> "Subsubsection", FontFamily -> "Helvetica", FontSize -> 20, FontWeight -> "Plain", FontSlant -> "Plain", FontColor -> RGBColor[0.4, 0.4, 0.4]], Cell[ StyleData["Subsubsection", "Presentation"], ShowGroupOpener -> True, WholeCellGroupOpener -> True, CellMargins -> {{60, 50}, {20, 20}}, LineSpacing -> {1, 0}], Cell[ StyleData[ "Subsubsection", "SlideShow", StyleDefinitions -> StyleData["Subsubsection", "Presentation"]]], Cell[ StyleData["Subsubsection", "Printout"], ShowGroupOpener -> False, CellMargins -> {{2, 0}, {0, 22}}, FontSize -> 14]}, Open]]}, Open]], Cell[ CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[ CellGroupData[{ Cell["Standard", "Subsection"], Cell[ CellGroupData[{ Cell[ StyleData["Text"], CellMargins -> {{60, 10}, {7, 7}}, InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LineSpacing -> {1, 3}, CounterIncrements -> "Text", FontFamily -> "Helvetica", FontSize -> 12], Cell[ StyleData["Text", "Presentation"], CellMargins -> {{60, 50}, {10, 10}}, FontSize -> 18], Cell[ StyleData[ "Text", "SlideShow", StyleDefinitions -> StyleData["Text", "Presentation"]]], Cell[ StyleData["Text", "Printout"], CellMargins -> {{2, 2}, {6, 6}}, TextJustification -> 0.5, Hyphenation -> True, FontSize -> 10]}, Open]]}, Closed]], Cell[ CellGroupData[{ Cell["Display", "Subsection"], Cell[ CellGroupData[{ Cell[ StyleData["Item", StyleDefinitions -> StyleData["Text"]], CellDingbat -> Cell["\[FilledSmallCircle]", FontWeight -> "Bold"], ShowGroupOpener -> False, CellMargins -> {{84, 10}, {7, 7}}, ReturnCreatesNewCell -> True, CellGroupingRules -> {"GroupTogetherNestedGrouping", 15000}, CounterIncrements -> "Item", FontSize -> 12], Cell[ StyleData["Item", "Presentation"], CellMargins -> {{124, 10}, {7, 7}}, FontSize -> 18], Cell[ StyleData[ "Item", "SlideShow", StyleDefinitions -> StyleData["Item", "Presentation"]]], Cell[ StyleData["Item", "Printout"], CellMargins -> {{39, 2}, {0, 6}}]}, Open]], Cell[ CellGroupData[{ Cell[ StyleData["Subitem", StyleDefinitions -> StyleData["Item"]], CellMargins -> {{108, 10}, {7, 7}}, ReturnCreatesNewCell -> True, CellGroupingRules -> {"GroupTogetherNestedGrouping", 15150}, CounterIncrements -> "Subitem"], Cell[ StyleData["Subitem", "Presentation"], CellMargins -> {{146, 10}, {7, 7}}], Cell[ StyleData[ "Subitem", "SlideShow", StyleDefinitions -> StyleData["Subitem", "Presentation"]]], Cell[ StyleData["Subitem", "Printout"], CellMargins -> {{67, 2}, {0, 6}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["ItemNumbered", StyleDefinitions -> StyleData["Text"]], CellDingbat -> Cell[ TextData[{ CounterBox["ItemNumbered"], "."}]], ShowGroupOpener -> False, CellMargins -> {{84, 10}, {7, 7}}, ReturnCreatesNewCell -> True, CellGroupingRules -> {"GroupTogetherNestedGrouping", 15000}, CounterIncrements -> "ItemNumbered"], Cell[ StyleData["ItemNumbered", "Presentation"], CellMargins -> {{124, 10}, {7, 7}}], Cell[ StyleData[ "ItemNumbered", "SlideShow", StyleDefinitions -> StyleData["ItemNumbered", "Presentation"]]], Cell[ StyleData["ItemNumbered", "Printout"], CellMargins -> {{39, 2}, {0, 6}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "SubitemNumbered", StyleDefinitions -> StyleData["ItemNumbered"]], CellDingbat -> Cell[ TextData[{ CounterBox["SubitemNumbered", CounterFunction :> (Part[ CharacterRange["a", "z"], #]& )], "."}]], CellMargins -> {{108, 10}, {7, 7}}, ReturnCreatesNewCell -> True, CellGroupingRules -> {"GroupTogetherNestedGrouping", 15150}, CounterIncrements -> "SubitemNumbered"], Cell[ StyleData["SubitemNumbered", "Presentation"], CellMargins -> {{146, 10}, {7, 7}}], Cell[ StyleData[ "SubitemNumbered", "SlideShow", StyleDefinitions -> StyleData["SubitemNumbered", "Presentation"]]], Cell[ StyleData["SubitemNumbered", "Printout"], CellMargins -> {{67, 2}, {0, 6}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "ItemParagraph", StyleDefinitions -> StyleData["Item"]], CellDingbat -> None, CellMargins -> {{84, 10}, {7, 7}}, ReturnCreatesNewCell -> True, CellGroupingRules -> {"GroupTogetherNestedGrouping", 15100}, CounterIncrements -> "ItemParagraph"], Cell[ StyleData["ItemParagraph", "Presentation"], CellMargins -> {{124, 10}, {7, 7}}], Cell[ StyleData[ "ItemParagraph", "SlideShow", StyleDefinitions -> StyleData["ItemParagraph", "Presentation"]]], Cell[ StyleData["ItemParagraph", "Printout"], CellMargins -> {{39, 2}, {0, 6}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "SubitemParagraph", StyleDefinitions -> StyleData["Subitem"]], CellDingbat -> None, ReturnCreatesNewCell -> True, CellGroupingRules -> {"GroupTogetherNestedGrouping", 15200}, CounterIncrements -> "SubitemParagraph"], Cell[ StyleData["SubitemParagraph", "Presentation"]], Cell[ StyleData[ "SubitemParagraph", "SlideShow", StyleDefinitions -> StyleData["SubitemParagraph", "Presentation"]]], Cell[ StyleData["SubitemParagraph", "Printout"]]}, Closed]]}, Closed]]}, Open]], Cell[ CellGroupData[{ Cell["Styles for Formulas and Programming", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["DisplayFormula"]], Cell[ StyleData["DisplayFormula", "Presentation"], CellMargins -> {{60, Inherited}, {Inherited 1.5, Inherited 1.5}}, FontSize -> 17], Cell[ StyleData[ "DisplayFormula", "SlideShow", StyleDefinitions -> StyleData["DisplayFormula", "Presentation"]]], Cell[ StyleData["DisplayFormula", "Printout"], CellMargins -> {{39, Inherited}, {Inherited, Inherited}}, FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "DisplayFormulaNumbered", StyleDefinitions -> StyleData["DisplayFormula"]], CellFrameLabels -> {{None, Cell[ TextData[{"(", CounterBox["DisplayFormulaNumbered"], ")"}]]}, {None, None}}, CounterIncrements -> "DisplayFormulaNumbered"], Cell[ StyleData["DisplayFormulaNumbered", "Presentation"], CellMargins -> {{60, Inherited}, {Inherited 1.5, Inherited 1.5}}, FontSize -> 17], Cell[ StyleData[ "DisplayFormulaNumbered", "SlideShow", StyleDefinitions -> StyleData["DisplayFormulaNumbered", "Presentation"]]], Cell[ StyleData["DisplayFormulaNumbered", "Printout"], CellMargins -> {{39, Inherited}, {Inherited, Inherited}}]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Styles for Inline Formatting", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["InlineFormula"]], Cell[ StyleData["InlineFormula", "Presentation"], FontSize -> 17], Cell[ StyleData[ "InlineFormula", "SlideShow", StyleDefinitions -> StyleData["InlineFormula", "Presentation"]]], Cell[ StyleData["InlineFormula", "Printout"]]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Styles for Input and Output Cells", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["Input"], ShowCellBracket -> True, ShowGroupOpener -> False, CellMargins -> {{103, 10}, {5, 7}}, CellBracketOptions -> { "Color" -> RGBColor[0.734936, 0.713848, 0.694041]}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, DefaultFormatType -> DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> {"HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, LanguageCategory -> "Mathematica", FormatType -> InputForm, ShowStringCharacters -> True, NumberMarks -> True, LinebreakAdjustments -> {0.85, 2, 10, 0, 1}, CounterIncrements -> "Input", FontWeight -> "Bold"], Cell[ StyleData["Input", "Presentation"], CellMargins -> {{110, 50}, {8, 10}}, LineSpacing -> {1, 0}, FontSize -> 17], Cell[ StyleData[ "Input", "SlideShow", StyleDefinitions -> StyleData["Input", "Presentation"]]], Cell[ StyleData["Input", "Printout"], CellMargins -> {{39, 0}, {4, 6}}, LinebreakAdjustments -> {0.85, 2, 10, 1, 1}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InputOnly"], ShowCellBracket -> True, ShowGroupOpener -> False, CellMargins -> {{103, 10}, {7, 7}}, CellBracketOptions -> { "Color" -> RGBColor[0.734936, 0.713848, 0.694041]}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, DefaultFormatType -> DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> {"HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, LanguageCategory -> "Mathematica", FormatType -> InputForm, ShowStringCharacters -> True, NumberMarks -> True, LinebreakAdjustments -> {0.85, 2, 10, 0, 1}, CounterIncrements -> "Input", MenuSortingValue -> 1550, FontWeight -> "Bold"], Cell[ StyleData["InputOnly", "Presentation"], CellMargins -> {{110, Inherited}, {8, 10}}, LineSpacing -> {1, 0}, FontSize -> 17], Cell[ StyleData[ "InputOnly", "SlideShow", StyleDefinitions -> StyleData["InputOnly", "Presentation"]]], Cell[ StyleData["InputOnly", "Printout"], CellMargins -> {{39, 0}, {4, 6}}, LinebreakAdjustments -> {0.85, 2, 10, 1, 1}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Output"], ShowCellBracket -> True, CellMargins -> {{103, 10}, {7, 5}}, CellBracketOptions -> { "Color" -> RGBColor[0.734936, 0.713848, 0.694041]}, CellEditDuplicate -> True, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, DefaultFormatType -> DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, LanguageCategory -> None, FormatType -> InputForm, CounterIncrements -> "Output"], Cell[ StyleData["Output", "Presentation"], CellMargins -> {{110, 50}, {10, 8}}, LineSpacing -> {1, 0}, FontSize -> 17], Cell[ StyleData[ "Output", "SlideShow", StyleDefinitions -> StyleData["Output", "Presentation"]]], Cell[ StyleData["Output", "Printout"], CellMargins -> {{39, 0}, {6, 4}}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Code"], CellMargins -> {{103, 10}, {5, 10}}], Cell[ StyleData["Code", "Presentation"], CellMargins -> {{110, 50}, {8, 10}}, LineSpacing -> {1, 0}, FontSize -> 17], Cell[ StyleData[ "Code", "SlideShow", StyleDefinitions -> StyleData["Code", "Presentation"]]], Cell[ StyleData["Code", "Printout"], CellMargins -> {{39, 0}, {4, 6}}, LinebreakAdjustments -> {0.85, 2, 10, 1, 1}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Print"], CellMargins -> {{103, Inherited}, {Inherited, Inherited}}, FontSize -> 14], Cell[ StyleData["Print", "Presentation"], CellMargins -> {{70, Inherited}, {Inherited 1.5, Inherited 1.5}}, FontSize -> 17, Magnification -> Inherited 1.5], Cell[ StyleData[ "Print", "SlideShow", StyleDefinitions -> StyleData["Print", "Presentation"]]], Cell[ StyleData["Print", "Printout"], CellMargins -> {{39, Inherited}, {Inherited, Inherited}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "WolframAlphaShortInput", StyleDefinitions -> StyleData["Input"]], CellMargins -> {{98, 10}, {5, 7}}, EvaluationMode -> "WolframAlphaShort", CellEventActions -> {"ReturnKeyDown" :> FrontEndTokenExecute[ EvaluationNotebook[], "HandleShiftReturn"]}, CellFrameLabels -> {{ Cell[ BoxData[ DynamicBox[ FEPrivate`FrontEndResource["WABitmaps", "Equal"]]], CellBaseline -> Baseline], None}, {None, None}}, FormatType -> TextForm, FontFamily -> "Helvetica"], Cell[ StyleData["WolframAlphaShortInput", "Presentation"], CellMargins -> {{107, 50}, {8, 10}}], Cell[ StyleData[ "WolframAlphaShortInput", "SlideShow", StyleDefinitions -> StyleData["WolframAlphaShortInput", "Presentation"]]], Cell[ StyleData["WolframAlphaShortInput", "Printout"], CellFrameLabelMargins -> 3]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "WolframAlphaLong", StyleDefinitions -> StyleData["Input"]], CellMargins -> {{100, 10}, {5, 7}}, StyleKeyMapping -> { "=" -> "Input", "Backspace" -> "WolframAlphaShort"}, EvaluationMode -> "WolframAlphaLong", CellEventActions -> {"ReturnKeyDown" :> FrontEndTokenExecute[ EvaluationNotebook[], "HandleShiftReturn"]}, CellFrameLabels -> {{ Cell[ BoxData[ DynamicBox[ FEPrivate`FrontEndResource["WABitmaps", "SpikeyEqual"]]]], None}, {None, None}}, DefaultFormatType -> TextForm, FormatType -> TextForm, FontFamily -> "Helvetica"], Cell[ StyleData["WolframAlphaLong", "Presentation"], CellMargins -> {{107, 50}, {8, 10}}], Cell[ StyleData[ "WolframAlphaLong", "SlideShow", StyleDefinitions -> StyleData["WolframAlphaLong", "Presentation"]], CellMargins -> {{107, 50}, {8, 10}}], Cell[ StyleData["WolframAlphaLong", "Printout"], CellFrameLabelMargins -> 3]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Program"], CellMargins -> {{60, 4}, {6, 8}}], Cell[ StyleData["Program", "Presentation"], CellMargins -> {{60, 50}, {8, 10}}, LineSpacing -> {1, 0}, FontSize -> 17], Cell[ StyleData[ "Program", "SlideShow", StyleDefinitions -> StyleData["Program", "Presentation"]]], Cell[ StyleData["Program", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["CellLabel"]], Cell[ StyleData["CellLabel", "Presentation"], FontSize -> 12], Cell[ StyleData[ "CellLabel", "SlideShow", StyleDefinitions -> StyleData["CellLabel", "Presentation"]]], Cell[ StyleData["CellLabel", "Printout"], FontSize -> 8, FontColor -> GrayLevel[0.]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["ManipulateLabel"]], Cell[ StyleData["ManipulateLabel", "Presentation"], FontSize -> 15], Cell[ StyleData[ "ManipulateLabel", "SlideShow", StyleDefinitions -> StyleData["ManipulateLabel", "Presentation"]]], Cell[ StyleData["ManipulateLabel", "Printout"], FontSize -> 8]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["GraphicsLabel"]], Cell[ StyleData["GraphicsLabel", "Presentation"], FontSize -> 14], Cell[ StyleData[ "GraphicsLabel", "SlideShow", StyleDefinitions -> StyleData["GraphicsLabel", "Presentation"]]], Cell[ StyleData["GraphicsLabel", "Printout"], FontSize -> 8]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Graphics3DLabel"]], Cell[ StyleData["Graphics3DLabel", "Presentation"], FontSize -> 14], Cell[ StyleData[ "Graphics3DLabel", "SlideShow", StyleDefinitions -> StyleData["Graphics3DLabel", "Presentation"]]], Cell[ StyleData["Graphics3DLabel", "Printout"], FontSize -> 8]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell[ "Styles for SlideShow", "Section", CellChangeTimes -> {{3.514665148412793*^9, 3.5146651505550737`*^9}}], Cell[ StyleData["slideshowheader"], ShowCellBracket -> False, CellMargins -> {{0, 0}, {0, -2}}, Evaluatable -> False, CellHorizontalScrolling -> False, PageBreakBelow -> False, CellFrameMargins -> 0, ImageMargins -> {{0, 0}, {0, 0}}, ImageRegion -> {{0, 1}, {0, 1}}, Magnification -> 1, Background -> GrayLevel[1], CellPadding -> 0, CellFramePadding -> 0], Cell[ CellGroupData[{ Cell[ StyleData["hidefromslideshowgraphic"], ShowCellBracket -> False, CellMargins -> {{0, 0}, {0, 0}}, Evaluatable -> False, CellHorizontalScrolling -> False, PageBreakBelow -> False, CellFrameMargins -> 0, ImageMargins -> {{0, 0}, {0, 0}}, ImageRegion -> {{0, 1}, {0, 1}}, Magnification -> 1, Background -> None, CellPadding -> 0], Cell[ StyleData["hidefromslideshowgraphic", "SlideShow"], ShowCellBracket -> False, CellElementSpacings -> { "CellMinHeight" -> 0, "ClosedCellHeight" -> 0, "ClosedGroupTopMargin" -> 0}, CellOpen -> False, CellHorizontalScrolling -> False], Cell[ StyleData["hidefromslideshowgraphic", "Printout"], Magnification -> 0.6]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["slideshowheader2"], ShowCellBracket -> False, CellMargins -> {{0, 0}, {0, 0}}, Evaluatable -> False, CellHorizontalScrolling -> False, PageBreakBelow -> False, ImageMargins -> {{0, 0}, {0, 0}}, ImageRegion -> {{0, 1}, {0, 1}}, Magnification -> 1, Background -> GrayLevel[1]], Cell[ StyleData["ConferenceGraphicCell", "SlideShow"], ShowCellBracket -> False, CellElementSpacings -> { "CellMinHeight" -> 0, "ClosedCellHeight" -> 0, "ClosedGroupTopMargin" -> 0}, CellOpen -> False, CellHorizontalScrolling -> True], Cell[ StyleData["slideshowheader", "Printout"], FontSize -> 8, Magnification -> 0.75]}, Closed]], Cell[ StyleData[ "ConferenceGraphicCellSlideShowOnly", StyleDefinitions -> StyleData["ConferenceCellGraphic"]], ShowCellBracket -> False, CellMargins -> 0, CellElementSpacings -> { "CellMinHeight" -> 0, "ClosedCellHeight" -> 0, "ClosedGroupTopMargin" -> 0}, CellOpen -> False], Cell[ CellGroupData[{ Cell[ StyleData["SlideShowNavigationBar"], Editable -> True, Selectable -> False, CellFrame -> 0, ShowGroupOpener -> False, CellMargins -> {{0, 0}, {3, 3}}, CellOpen -> True, CellFrameMargins -> 0, CellFrameColor -> None, Background -> None], Cell[ StyleData["SlideShowNavigationBar", "Printout"], PageBreakAbove -> Automatic]}, Closed]]}, Closed]]}, Visible -> False, FrontEndVersion -> "10.0 for Microsoft Windows (64-bit) (September 9, 2014)", StyleDefinitions -> "PrivateStylesheetFormatting.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ "SlideShowHeader"->{ Cell[580, 22, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[59137, 1029, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[61000, 1079, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[73963, 1463, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[233506, 4481, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[258878, 5104, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[273658, 5534, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[282550, 5798, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[293210, 6098, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[296306, 6216, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[319202, 7027, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[370739, 8739, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"]} } *) (*CellTagsIndex CellTagsIndex->{ {"SlideShowHeader", 528109, 12200} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[647, 25, 57607, 980, 541, "Title"], Cell[58257, 1007, 533, 10, 139, "Subtitle"], Cell[58793, 1019, 307, 5, 53, "Subsubtitle"] }, Open ]], Cell[CellGroupData[{ Cell[59137, 1029, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[59226, 1034, 110, 1, 142, "Section"], Cell[CellGroupData[{ Cell[59361, 1039, 301, 7, 90, "Subsection"], Cell[59665, 1048, 354, 5, 85, "Subsubsection"], Cell[60022, 1055, 347, 5, 64, "Subsubsection"], Cell[60372, 1062, 267, 4, 64, "Subsubsection"], Cell[60642, 1068, 297, 4, 64, "Subsubsection"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[61000, 1079, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[61089, 1084, 230, 3, 142, "Section"], Cell[CellGroupData[{ Cell[61344, 1091, 256, 4, 90, "Subsection"], Cell[61603, 1097, 966, 16, 257, "Text"], Cell[62572, 1115, 842, 16, 201, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[63451, 1136, 220, 3, 79, "Subsection"], Cell[63674, 1141, 658, 21, 185, "Input"], Cell[64335, 1164, 800, 18, 90, "Text"], Cell[CellGroupData[{ Cell[65160, 1186, 123, 1, 151, "Subsubsection"], Cell[CellGroupData[{ Cell[65308, 1191, 1308, 39, 366, "Input", Evaluatable->False], Cell[66619, 1232, 131, 2, 366, "Output"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[66799, 1240, 174, 2, 110, "Subsubsection"], Cell[CellGroupData[{ Cell[66998, 1246, 631, 15, 366, "Input"], Cell[67632, 1263, 2344, 70, 366, "Output"] }, Closed]], Cell[69991, 1336, 278, 8, 366, "Input"], Cell[CellGroupData[{ Cell[70294, 1348, 275, 9, 366, "Input"], Cell[70572, 1359, 273, 6, 366, "Output"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[70894, 1371, 215, 3, 110, "Subsubsection"], Cell[CellGroupData[{ Cell[71134, 1378, 298, 4, 366, "Input"], Cell[71435, 1384, 391, 12, 366, "Output"] }, Closed]], Cell[71841, 1399, 710, 11, 366, "Text"], Cell[72554, 1412, 774, 21, 366, "Input"], Cell[CellGroupData[{ Cell[73353, 1437, 275, 9, 366, "Input"], Cell[73631, 1448, 247, 6, 366, "Output"] }, Closed]] }, Closed]] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[73963, 1463, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[74052, 1468, 233, 3, 142, "Section"], Cell[CellGroupData[{ Cell[74310, 1475, 323, 5, 90, "Subsection"], Cell[74636, 1482, 1228, 19, 702, "Text"], Cell[75867, 1503, 724, 13, 202, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[76628, 1521, 99, 1, 79, "Subsection"], Cell[76730, 1524, 908, 18, 366, "Text"], Cell[77641, 1544, 779, 23, 366, "Input"], Cell[CellGroupData[{ Cell[78445, 1571, 470, 12, 366, "Input"], Cell[78918, 1585, 127238, 2068, 366, "Output"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[206205, 3659, 195, 2, 79, "Subsection"], Cell[CellGroupData[{ Cell[206425, 3665, 664, 17, 366, "Input"], Cell[207092, 3684, 1345, 39, 366, "Output"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[208486, 3729, 271, 3, 79, "Subsection"], Cell[208760, 3734, 1253, 18, 366, "Text"], Cell[CellGroupData[{ Cell[210038, 3756, 805, 21, 366, "Input"], Cell[210846, 3779, 2383, 73, 366, "Output"] }, Closed]], Cell[213244, 3855, 774, 10, 366, "Text"], Cell[CellGroupData[{ Cell[214043, 3869, 333, 10, 366, "Input"], Cell[214379, 3881, 897, 29, 366, "Output"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[215325, 3916, 220, 3, 79, "Subsection"], Cell[CellGroupData[{ Cell[215570, 3923, 1383, 38, 366, "Input"], Cell[216956, 3963, 872, 25, 366, "Output"] }, Closed]], Cell[CellGroupData[{ Cell[217865, 3993, 199, 5, 366, "Input"], Cell[218067, 4000, 639, 20, 366, "Output"] }, Closed]], Cell[CellGroupData[{ Cell[218743, 4025, 519, 15, 366, "Input"], Cell[219265, 4042, 580, 17, 366, "Output"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[219894, 4065, 285, 4, 79, "Subsection"], Cell[CellGroupData[{ Cell[220204, 4073, 214, 4, 366, "Subsubsection"], Cell[220421, 4079, 728, 11, 366, "Text"], Cell[CellGroupData[{ Cell[221174, 4094, 490, 10, 366, "Input"], Cell[221667, 4106, 602, 18, 366, "Output"] }, Closed]], Cell[CellGroupData[{ Cell[222306, 4129, 251, 7, 366, "Input"], Cell[222560, 4138, 530, 16, 366, "Output"] }, Closed]], Cell[CellGroupData[{ Cell[223127, 4159, 124, 2, 366, "Input"], Cell[223254, 4163, 144, 3, 366, "Output"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[223447, 4172, 228, 3, 366, "Subsubsection"], Cell[CellGroupData[{ Cell[223700, 4179, 765, 17, 366, "Input"], Cell[224468, 4198, 891, 26, 366, "Output"] }, Closed]], Cell[CellGroupData[{ Cell[225396, 4229, 276, 8, 366, "Input"], Cell[225675, 4239, 2584, 76, 366, "Output"] }, Closed]], Cell[CellGroupData[{ Cell[228296, 4320, 121, 2, 366, "Input"], Cell[228420, 4324, 142, 3, 366, "Output"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[228611, 4333, 225, 3, 366, "Subsubsection"], Cell[CellGroupData[{ Cell[228861, 4340, 632, 12, 366, "Input"], Cell[229496, 4354, 924, 26, 366, "Output"] }, Closed]], Cell[CellGroupData[{ Cell[230457, 4385, 300, 8, 366, "Input"], Cell[230760, 4395, 2354, 65, 366, "Output"] }, Closed]], Cell[CellGroupData[{ Cell[233151, 4465, 124, 2, 366, "Input"], Cell[233278, 4469, 143, 3, 366, "Output"] }, Closed]] }, Closed]] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[233506, 4481, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[233595, 4486, 291, 4, 142, "Section"], Cell[CellGroupData[{ Cell[233911, 4494, 1883, 45, 57, "Input"], Cell[235797, 4541, 15584, 368, 366, "Output"] }, Closed]], Cell[CellGroupData[{ Cell[251418, 4914, 1755, 41, 49, "Input"], Cell[253176, 4957, 5641, 140, 366, "Output"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[258878, 5104, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[258967, 5109, 109, 1, 142, "Section"], Cell[CellGroupData[{ Cell[259101, 5114, 161, 3, 90, "Subsection"], Cell[259265, 5119, 585, 12, 366, "Text"], Cell[CellGroupData[{ Cell[259875, 5135, 58, 0, 366, "Item"], Cell[259936, 5137, 92, 2, 366, "Item"], Cell[260031, 5141, 71, 0, 366, "Item"], Cell[260105, 5143, 66, 0, 366, "Item"], Cell[260174, 5145, 67, 0, 366, "Item"] }, Open ]], Cell[260256, 5148, 18, 0, 366, "Spacer"] }, Closed]], Cell[CellGroupData[{ Cell[260311, 5153, 276, 4, 79, "Subsection"], Cell[260590, 5159, 434, 9, 202, "Text"], Cell[261027, 5170, 977, 25, 375, "Input"], Cell[262007, 5197, 221, 10, 206, "Text"], Cell[262231, 5209, 404, 7, 188, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[262672, 5221, 268, 4, 79, "Subsection"], Cell[262943, 5227, 264, 7, 366, "Text"], Cell[263210, 5236, 1627, 44, 366, "Input", Evaluatable->False], Cell[264840, 5282, 450, 12, 366, "Text"], Cell[265293, 5296, 1890, 49, 366, "Input"], Cell[267186, 5347, 319, 8, 366, "Text"], Cell[267508, 5357, 661, 12, 366, "Text"], Cell[268172, 5371, 1482, 41, 366, "Input"], Cell[269657, 5414, 286, 9, 366, "Text"], Cell[269946, 5425, 554, 11, 366, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[270537, 5441, 196, 6, 124, "Subsection"], Cell[270736, 5449, 370, 8, 366, "Text"], Cell[271109, 5459, 844, 18, 366, "Input"], Cell[271956, 5479, 235, 5, 366, "Input"], Cell[272194, 5486, 225, 7, 366, "Text"], Cell[272422, 5495, 855, 18, 366, "Input"], Cell[273280, 5515, 219, 6, 366, "Text"], Cell[273502, 5523, 95, 4, 366, "Text"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[273658, 5534, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[273747, 5539, 130, 1, 142, "Section"], Cell[CellGroupData[{ Cell[273902, 5544, 106, 2, 90, "Subsection"], Cell[274011, 5548, 190, 6, 366, "Text"], Cell[CellGroupData[{ Cell[274226, 5558, 91, 2, 366, "Item"], Cell[274320, 5562, 114, 3, 366, "Item"], Cell[274437, 5567, 94, 2, 366, "Item"], Cell[274534, 5571, 45, 0, 366, "Item"], Cell[274582, 5573, 65, 0, 366, "Item"] }, Open ]], Cell[274662, 5576, 18, 0, 366, "Spacer"] }, Closed]], Cell[CellGroupData[{ Cell[274717, 5581, 209, 3, 79, "Subsection"], Cell[274929, 5586, 289, 8, 366, "Text"], Cell[275221, 5596, 569, 15, 366, "Input"], Cell[275793, 5613, 139, 1, 366, "Text"], Cell[275935, 5616, 638, 16, 366, "Input"], Cell[276576, 5634, 173, 2, 366, "Text"], Cell[276752, 5638, 481, 14, 366, "Input"], Cell[277236, 5654, 114, 1, 366, "Text"], Cell[277353, 5657, 973, 20, 366, "Input"], Cell[278329, 5679, 18, 0, 366, "Spacer"] }, Closed]], Cell[CellGroupData[{ Cell[278384, 5684, 381, 6, 79, "Subsection"], Cell[278768, 5692, 446, 13, 366, "Text", CellID->38646030], Cell[279217, 5707, 2436, 62, 366, "Input", CellID->5558107], Cell[281656, 5771, 833, 20, 366, "Input", CellID->175288610] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[282550, 5798, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[282639, 5803, 152, 2, 142, "Section"], Cell[CellGroupData[{ Cell[282816, 5809, 152, 3, 90, "Subsection"], Cell[282971, 5814, 619, 12, 366, "Text"], Cell[CellGroupData[{ Cell[283615, 5830, 147, 2, 366, "Item"], Cell[283765, 5834, 180, 4, 366, "Item"], Cell[283948, 5840, 207, 3, 366, "Item"], Cell[284158, 5845, 157, 6, 366, "Item"] }, Open ]], Cell[284330, 5854, 18, 0, 366, "Spacer"] }, Closed]], Cell[CellGroupData[{ Cell[284385, 5859, 295, 4, 79, "Subsection"], Cell[284683, 5865, 163, 5, 366, "Text"], Cell[284849, 5872, 682, 13, 366, "Input"], Cell[285534, 5887, 194, 2, 366, "Text"], Cell[285731, 5891, 245, 6, 366, "Input"], Cell[285979, 5899, 465, 9, 366, "Input"], Cell[286447, 5910, 515, 11, 366, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[286999, 5926, 349, 5, 79, "Subsection"], Cell[287351, 5933, 447, 9, 51, "Text"], Cell[287801, 5944, 356, 6, 45, "Input"], Cell[288160, 5952, 450, 9, 52, "Text"], Cell[288613, 5963, 286, 6, 51, "Text"], Cell[288902, 5971, 699, 20, 90, "Input"], Cell[289604, 5993, 265, 3, 51, "Text"], Cell[289872, 5998, 122, 2, 45, "Input"], Cell[289997, 6002, 670, 21, 45, "Input"], Cell[290670, 6025, 162, 3, 51, "Text"], Cell[290835, 6030, 988, 26, 45, "Input"], Cell[291826, 6058, 129, 2, 45, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[291992, 6065, 360, 5, 79, "Subsection"], Cell[292355, 6072, 704, 16, 366, "Text"], Cell[293062, 6090, 87, 1, 366, "Input"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[293210, 6098, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[293299, 6103, 34, 0, 268, "Section"], Cell[293336, 6105, 74, 0, 160, "Subsection"], Cell[293413, 6107, 127, 3, 215, "Subsection"], Cell[CellGroupData[{ Cell[293565, 6114, 140, 3, 215, "Subsection"], Cell[293708, 6119, 757, 19, 366, "Text"], Cell[294468, 6140, 75, 0, 366, "Text"], Cell[CellGroupData[{ Cell[294568, 6144, 227, 7, 366, "Input"], Cell[294798, 6153, 511, 19, 366, "Output"] }, Open ]], Cell[295324, 6175, 54, 0, 366, "Text"], Cell[CellGroupData[{ Cell[295403, 6179, 200, 5, 366, "Input"], Cell[295606, 6186, 85, 1, 366, "Output"] }, Open ]], Cell[295706, 6190, 60, 0, 366, "Text"], Cell[CellGroupData[{ Cell[295791, 6194, 394, 12, 366, "Input"], Cell[296188, 6208, 45, 0, 366, "Output"] }, Open ]] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[296306, 6216, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[296395, 6221, 30, 0, 268, "Section"], Cell[CellGroupData[{ Cell[296450, 6225, 217, 4, 76, "Item"], Cell[296670, 6231, 244, 5, 76, "Item"] }, Open ]], Cell[CellGroupData[{ Cell[296951, 6241, 101, 2, 160, "Subsection"], Cell[CellGroupData[{ Cell[297077, 6247, 226, 7, 188, "Input"], Cell[297306, 6256, 8681, 259, 2053, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[306036, 6521, 41, 0, 138, "Subsection"], Cell[306080, 6523, 276, 6, 146, "Text"], Cell[CellGroupData[{ Cell[306381, 6533, 398, 12, 87, "Input"], Cell[306782, 6547, 825, 29, 181, "Output"] }, Open ]], Cell[307622, 6579, 527, 20, 146, "Text"], Cell[CellGroupData[{ Cell[308174, 6603, 375, 12, 87, "Input"], Cell[308552, 6617, 825, 29, 181, "Output"] }, Open ]], Cell[309392, 6649, 164, 3, 90, "Text"], Cell[CellGroupData[{ Cell[309581, 6656, 173, 5, 83, "Input"], Cell[309757, 6663, 386, 12, 122, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[310180, 6680, 360, 11, 83, "Input"], Cell[310543, 6693, 1347, 42, 253, "Output"] }, Open ]], Cell[311905, 6738, 168, 3, 90, "Text"], Cell[CellGroupData[{ Cell[312098, 6745, 173, 5, 83, "Input"], Cell[312274, 6752, 332, 11, 138, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[312655, 6769, 351, 10, 215, "Subsection"], Cell[CellGroupData[{ Cell[313031, 6783, 668, 22, 202, "Input"], Cell[313702, 6807, 537, 18, 125, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[314288, 6831, 39, 0, 138, "Subsection"], Cell[314330, 6833, 428, 16, 202, "Text"], Cell[CellGroupData[{ Cell[314783, 6853, 796, 26, 676, "Input"], Cell[315582, 6881, 64, 1, 188, "Output"] }, Open ]], Cell[315661, 6885, 228, 7, 202, "Text"], Cell[CellGroupData[{ Cell[315914, 6896, 799, 26, 456, "Input"], Cell[316716, 6924, 64, 1, 188, "Output"] }, Open ]], Cell[316795, 6928, 126, 3, 202, "Text"], Cell[CellGroupData[{ Cell[316946, 6935, 457, 13, 188, "Input"], Cell[317406, 6950, 142, 5, 252, "Output"] }, Open ]], Cell[317563, 6958, 214, 8, 202, "Text"], Cell[CellGroupData[{ Cell[317802, 6970, 583, 17, 188, "Input"], Cell[318388, 6989, 64, 1, 188, "Output"] }, Open ]], Cell[318467, 6993, 356, 12, 328, "Text"], Cell[CellGroupData[{ Cell[318848, 7009, 214, 7, 188, "Input"], Cell[319065, 7018, 64, 1, 188, "Output"] }, Open ]] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[319202, 7027, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[319291, 7032, 38, 0, 268, "Section"], Cell[CellGroupData[{ Cell[319354, 7036, 104, 2, 160, "Subsection"], Cell[319461, 7040, 142, 3, 366, "Text"], Cell[319606, 7045, 474, 15, 366, "Input"], Cell[320083, 7062, 116, 3, 366, "Text"], Cell[CellGroupData[{ Cell[320224, 7069, 737, 21, 366, "Input"], Cell[320964, 7092, 181, 6, 366, "Output"] }, Open ]], Cell[321160, 7101, 55, 0, 366, "Text"], Cell[321218, 7103, 403, 11, 366, "Input"], Cell[321624, 7116, 363, 10, 366, "Text"], Cell[321990, 7128, 159, 4, 366, "Input"], Cell[322152, 7134, 43, 0, 366, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[322232, 7139, 41, 0, 138, "Subsection"], Cell[322276, 7141, 72, 0, 202, "Text"], Cell[CellGroupData[{ Cell[322373, 7145, 858, 22, 753, "Input"], Cell[323234, 7169, 1023, 28, 577, "Output"] }, Open ]], Cell[324272, 7200, 171, 3, 202, "Text"], Cell[CellGroupData[{ Cell[324468, 7207, 1066, 28, 753, "Input"], Cell[325537, 7237, 146, 4, 188, "Output"] }, Open ]], Cell[325698, 7244, 263, 9, 328, "Text"], Cell[CellGroupData[{ Cell[325986, 7257, 977, 26, 753, "Input"], Cell[326966, 7285, 1202, 34, 547, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[328205, 7324, 1121, 30, 760, "Input"], Cell[329329, 7356, 1202, 34, 547, "Output"] }, Open ]], Cell[330546, 7393, 482, 19, 240, "Text"], Cell[CellGroupData[{ Cell[331053, 7416, 154, 4, 253, "Input"], Cell[331210, 7422, 64, 1, 188, "Output"] }, Open ]], Cell[331289, 7426, 114, 3, 202, "Text"], Cell[CellGroupData[{ Cell[331428, 7433, 1017, 27, 641, "Input"], Cell[332448, 7462, 974, 26, 506, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[333459, 7493, 1120, 30, 647, "Input"], Cell[334582, 7525, 974, 26, 506, "Output"] }, Open ]], Cell[335571, 7554, 233, 8, 202, "Text"], Cell[CellGroupData[{ Cell[335829, 7566, 77, 1, 188, "Input"], Cell[335909, 7569, 31, 0, 188, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[335989, 7575, 58, 0, 138, "Subsection"], Cell[336050, 7577, 233, 4, 328, "Text"], Cell[CellGroupData[{ Cell[336308, 7585, 84, 1, 188, "Input"], Cell[336395, 7588, 4586, 134, 1903, "Output"] }, Open ]], Cell[340996, 7725, 64, 0, 202, "Text"], Cell[CellGroupData[{ Cell[341085, 7729, 473, 14, 196, "Input"], Cell[341561, 7745, 147, 5, 188, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[341757, 7756, 30, 0, 138, "Subsection"], Cell[341790, 7758, 819, 24, 366, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[342646, 7787, 39, 0, 138, "Subsection"], Cell[342688, 7789, 1091, 39, 487, "Text"], Cell[CellGroupData[{ Cell[343804, 7832, 521, 14, 188, "Input"], Cell[344328, 7848, 2252, 71, 647, "Output"] }, Open ]], Cell[346595, 7922, 75, 0, 202, "Text"], Cell[CellGroupData[{ Cell[346695, 7926, 37, 0, 338, "Subsubsection"], Cell[346735, 7928, 858, 30, 366, "Text"], Cell[CellGroupData[{ Cell[347618, 7962, 288, 9, 366, "Input"], Cell[347909, 7973, 5765, 162, 366, "Output"] }, Open ]], Cell[353689, 8138, 155, 3, 366, "Text"], Cell[CellGroupData[{ Cell[353869, 8145, 396, 11, 366, "Input"], Cell[354268, 8158, 1610, 48, 366, "Output"] }, Open ]], Cell[355893, 8209, 213, 4, 366, "Text"], Cell[CellGroupData[{ Cell[356131, 8217, 493, 14, 366, "Input"], Cell[356627, 8233, 726, 23, 366, "Output"] }, Open ]], Cell[357368, 8259, 99, 2, 366, "Text"], Cell[CellGroupData[{ Cell[357492, 8265, 303, 9, 366, "Input"], Cell[357798, 8276, 607, 20, 366, "Output"] }, Open ]], Cell[358420, 8299, 217, 6, 366, "Text"], Cell[CellGroupData[{ Cell[358662, 8309, 124, 3, 366, "Input"], Cell[358789, 8314, 738, 23, 366, "Output"] }, Open ]], Cell[359542, 8340, 169, 3, 366, "Text"], Cell[CellGroupData[{ Cell[359736, 8347, 98, 2, 366, "Input"], Cell[359837, 8351, 2440, 74, 366, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[362326, 8431, 32, 0, 247, "Subsubsection"], Cell[362361, 8433, 285, 8, 366, "Text"], Cell[CellGroupData[{ Cell[362671, 8445, 678, 20, 366, "Input"], Cell[363352, 8467, 780, 25, 366, "Output"] }, Open ]], Cell[364147, 8495, 196, 6, 366, "Text"], Cell[CellGroupData[{ Cell[364368, 8505, 596, 17, 366, "Input"], Cell[364967, 8524, 780, 25, 366, "Output"] }, Open ]], Cell[365762, 8552, 505, 17, 366, "Text"], Cell[CellGroupData[{ Cell[366292, 8573, 1066, 34, 366, "Input"], Cell[367361, 8609, 1005, 33, 366, "Output"] }, Open ]], Cell[368381, 8645, 321, 10, 366, "Text"], Cell[CellGroupData[{ Cell[368727, 8659, 169, 5, 366, "Input"], Cell[368899, 8666, 604, 20, 366, "Output"] }, Open ]], Cell[369518, 8689, 249, 9, 366, "Text"], Cell[CellGroupData[{ Cell[369792, 8702, 121, 3, 366, "Input"], Cell[369916, 8707, 738, 23, 366, "Output"] }, Open ]] }, Closed]] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[370739, 8739, 64, 1, 1, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[370828, 8744, 114, 1, 268, "Section"], Cell[CellGroupData[{ Cell[370967, 8749, 611, 16, 210, "Subsection"], Cell[371581, 8767, 329, 8, 202, "Text"], Cell[CellGroupData[{ Cell[371935, 8779, 182, 2, 338, "Subsubsection"], Cell[CellGroupData[{ Cell[372142, 8785, 328, 9, 366, "Input"], Cell[372473, 8796, 144, 4, 366, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[372666, 8806, 156, 2, 247, "Subsubsection"], Cell[372825, 8810, 285, 8, 366, "Text"], Cell[373113, 8820, 320, 9, 366, "Input"], Cell[373436, 8831, 140, 1, 366, "Text"], Cell[373579, 8834, 989, 24, 366, "Input"], Cell[374571, 8860, 296, 8, 366, "Text"], Cell[374870, 8870, 285, 8, 366, "Input"], Cell[375158, 8880, 480, 12, 366, "Input"], Cell[375641, 8894, 409, 10, 366, "Input"], Cell[376053, 8906, 163, 3, 366, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[376265, 8915, 474, 14, 168, "Subsection"], Cell[376742, 8931, 704, 16, 451, "Text"], Cell[CellGroupData[{ Cell[377471, 8951, 107, 1, 338, "Subsubsection"], Cell[377581, 8954, 449, 12, 366, "Input"], Cell[378033, 8968, 293, 7, 366, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[378363, 8980, 101, 1, 247, "Subsubsection"], Cell[378467, 8983, 336, 11, 366, "Text"], Cell[378806, 8996, 821, 21, 366, "Input"], Cell[379630, 9019, 390, 11, 366, "Input"], Cell[380023, 9032, 507, 10, 366, "Input"], Cell[380533, 9044, 441, 10, 366, "Text"], Cell[380977, 9056, 670, 18, 366, "Input"], Cell[381650, 9076, 448, 11, 366, "Input"], Cell[382101, 9089, 245, 3, 366, "Text"], Cell[382349, 9094, 571, 13, 366, "Input"], Cell[382923, 9109, 291, 7, 366, "Input"], Cell[383217, 9118, 181, 4, 366, "Input"], Cell[383401, 9124, 610, 20, 366, "Text"], Cell[384014, 9146, 459, 9, 366, "Input"], Cell[384476, 9157, 722, 20, 366, "Input"], Cell[385201, 9179, 606, 16, 366, "Input"], Cell[385810, 9197, 416, 10, 366, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[386275, 9213, 584, 18, 203, "Subsection"], Cell[386862, 9233, 336, 8, 202, "Text"], Cell[CellGroupData[{ Cell[387223, 9245, 102, 1, 338, "Subsubsection"], Cell[CellGroupData[{ Cell[387350, 9250, 362, 11, 366, "Input"], Cell[387715, 9263, 363, 11, 366, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[388127, 9280, 102, 1, 247, "Subsubsection"], Cell[388232, 9283, 169, 4, 366, "Text"], Cell[388404, 9289, 723, 21, 366, "Input"], Cell[389130, 9312, 109, 1, 366, "Text"], Cell[389242, 9315, 405, 12, 366, "Input"], Cell[389650, 9329, 106, 1, 366, "Text"], Cell[389759, 9332, 280, 6, 366, "Input"], Cell[390042, 9340, 92, 1, 366, "Text"], Cell[390137, 9343, 354, 10, 366, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[390540, 9359, 806, 26, 203, "Subsection"], Cell[391349, 9387, 336, 8, 202, "Text"], Cell[CellGroupData[{ Cell[391710, 9399, 100, 1, 338, "Subsubsection"], Cell[CellGroupData[{ Cell[391835, 9404, 639, 21, 366, "Input"], Cell[392477, 9427, 664, 22, 366, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[393190, 9455, 102, 1, 247, "Subsubsection"], Cell[CellGroupData[{ Cell[393317, 9460, 301, 8, 366, "Input"], Cell[393621, 9470, 625, 16, 366, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[394283, 9491, 210, 5, 366, "Input"], Cell[394496, 9498, 144, 3, 366, "Output"] }, Open ]], Cell[394655, 9504, 1167, 37, 366, "Input"], Cell[395825, 9543, 708, 20, 366, "Input"], Cell[396536, 9565, 251, 4, 366, "Input"], Cell[396790, 9571, 90, 1, 366, "Text"], Cell[396883, 9574, 505, 14, 366, "Input"], Cell[CellGroupData[{ Cell[397413, 9592, 367, 9, 366, "Input"], Cell[397783, 9603, 1063, 29, 366, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[398883, 9637, 558, 16, 366, "Input"], Cell[399444, 9655, 2218, 58, 366, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[401699, 9718, 286, 6, 366, "Input"], Cell[401988, 9726, 1525, 41, 366, "Output"] }, Open ]], Cell[403528, 9770, 772, 21, 366, "Input"], Cell[404303, 9793, 215, 4, 366, "Input"], Cell[404521, 9799, 1134, 31, 366, "Input"], Cell[405658, 9832, 542, 14, 366, "Text"], Cell[406203, 9848, 702, 21, 366, "Input"], Cell[406908, 9871, 427, 12, 366, "Text"], Cell[407338, 9885, 399, 11, 366, "Input"], Cell[407740, 9898, 326, 9, 366, "Input"], Cell[408069, 9909, 519, 15, 366, "Input"], Cell[408591, 9926, 130, 2, 366, "Input"], Cell[408724, 9930, 241, 5, 366, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[409014, 9941, 99, 1, 138, "Subsection"], Cell[409116, 9944, 3014, 81, 1653, "Input"], Cell[412133, 10027, 663, 20, 303, "Input"] }, Closed]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)