A δ-Invariant for QR-Submanifolds in Quaternion Space Forms
Year 2018,
, 8 - 17, 30.11.2018
Gabriel Macsim
Adela Mihai
Abstract
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GRlN0oJMlFFzcgnC4zj36FlZS181PyG89cXDSSsL6I0iLfExfi0uShLJAkusgWzxr0l+IsO21DmW7KjgmpITOCxjOJflQ4XW4QORHVpX1P45cekSZkOXOIdpT4J0lk55JqO1RQyupx8vYT5lH0OzMpLK1SzEZYSHFLmQu5ybTuco34mFTHcbQ6pYJIyksWJy1oM4/kW02T0kZuAZUnf0t+XEcKFMW4ZJoTc1EVQhv2pVJ+Y3Ogy4GlDCcZu7fHx+T4NO9UxVOIHVqKZ+awFDs1eYO0wE6YS7u+iBL5O784jkKY4o87n3bmiTNACx/ZXFFAjaQMA219Wp3MymypDBQiYU0GRb7zHoVfrqCm+9H0joVMLIumZbxB67PEk/LkKQiJlxJKjnifogsV81MdZa0PbD31piyOlnjKTOWQJ0jEL6XsC3tp+UgLAqbRupS7VFj4kGr493Xwe+ZCcjfl1NdR4cXLyn1Pa3upw1hReCb3aesH6ugq8wnmOkaJ/yoRocXX1PBoax7RqR+T6w7Qfb6Aqi78jwKYPMqdKfIzIT+XohXGDWHJEVrKjHfSXCuTC7y/Fk8bksarQhxJj0t0bqSKzCh6X3RTSpIXZeipyy1K8yCPCuO/oalus8XyC+vo/sFlNEPZNE5metIbLoSRX1JcXpXohpywNIsu5jdPG5TK2jImScdV6fjXEr/cqeF0oZwZJ/MoPnSq6KZaS+0km5+1x7pj/FSJT6qMXz6VaFEXtcZBSPU5f9Jnfi+Iaywhn2pyDtEKP03Fsxb8VMqqbKxSFmjiY/JPSlXer9YH12sm/u9AOsrvXEb8zp+xPGgUuLiB2P98ifUpqt985PSZgdD5XjCEAbp5D8cEO6C2rA485ppU9s9pEAY5cmFoNwC+9m15Ja83+nv1ghHHFI6DBsEJQEVuiXglkPpbSNhxGrVmDnC0NQI43dDbnXk02AW2gwMQOMIehrKyiLa7wtp9ILwdzUV7HK4VbO1sFR7JOmPooD4wMrTDYF9zFKSdxy0Ygcs1an5c1AW2jq6wQy0yE6/jnuy7a+iN/u49YMAxh/tgL5gBMPP0hBNXHwa9vTDUyQyoKERJpapVRbqgz6xPMJ95uUffAt4jh8MOj1BWp7i8jRn69PdEbyMDGDn214JuKyDkD/TxgldvU3CM+mDQUGcAZcgtqQExL7bcOozvvzsCIw9H2BpywDHvBfc+Zqg9noSL93h4dO4XzH49CoazJ2O4pSE4RrbweWGEyFbyTLTZ01Z/bWgptuGgi/tozH7REUiOwcFLVQCVInVPGsbMHgEbdVNeFElJ99XZoTsGT3sd47k5OLDjJG7xGSxPYGvFREwd0E1Mof4u0k5cB2ACrnHz5Bw9azgO6gkgG4nXHqhYXUML2lIZlW2ok7sG2QmHcbLWCh6OPWAIfZj3dhJPcbIdjIDA4bA3bANYbfaxtrxIoiZvQAvsOE6YFfom3A050O/mgZET3IDaGtS1WkpJNlf0VpJvGOy19Wl1MiuzobJjj3Br97cId3kHCwaaQ89uAPzGVOH4jQfi5eFE0zK6oYdFFyWd65Fz+Tzujh8G7+cUJoo13sSJrfkIXjwBbrKjSzdr9OaLp3IoIQgYWMN9cD84mhkBMATX8jnY2VmB25ing9+bwWlofzgamcBu8EDlvqe1vXTEuLPotgKLwL9zDD+uXYu1kn+/JaFIbjxVI3tb84hO/Zic4QpbA310cx8AH9Hg5op+Tt3AMbCDt8K4UZ+TjhO3agGuKYybp1Tp2TpikB2AzHRcuycb16riSKKzIcz7BWLhv8Yqz4sqc0sroMUHqs9h/aJViHUajwn9zcHhmMDu+XewcpJT6+lHHCt4jugPbsqXmOjQC55+c/Dhr5fRKJ0mpoKHisNmnv3gbsGMk33g9+57eMsCqD2Vgds1soWELlgzswC1zVcSPJXUU8rkVRW/BrXI0akuaiZOd/Hnso/wzY3RmDnRFUYcA3Cdh2Hs0B7KuMsc04Kfnopco6OdFDKfjAwym1R7D9kV5vCw58LCcSD8mX+zXsM4u1fx4jc5OHerFMLR1jI9JJsEQUUW4qL24DwG4+Xn6yUnHu+vsQtGTh4A/HwNl25Wwm9QFTIv5ILrNx/B/vYy82fbI5YAj6pVLyzDtTIVzzOWS3Lt4cdHRdYxREVdAEZNwPMNHUa4jUIR6u/dxnlmbnz891g0d7Mouej1fRffTh4I3x5C3DuTjkwATLnX/r9O1t/QDRODJsHiz62I2n8RC535OFgQgGDf7u0XvRWFlmL92J97EHtlAiZdOA+n4P/CTVJ8CupRXVbbqqf4gAmsTLuq8GMtaKugqvmwGdxHvgBPbEb6pRxU+3FRmXkFd7iT8HHwWNi3oW5Wz1OTj7W+BFZPT9NZLbATlCErbieiznMw6mUfyA7zmqi3Pt/JPi3LsOEaYsMLMDPCC6L1LDhdYdrdEt7PdUfzTEzZ1vLbwnyk7svAC6+uhotsgYwG3D+4GXtGhGL3y71U+KM8KY17bfZ7FZQ71F4yPDqLrgwL8WYVLm5fgw+WnWo+Y4FR6xLwARNr2gwBbcWzrf1aya94gCB4VIMyxcOSfa4ZTHV+p8YAxlzGq63g3MNM5IfaQCNhKfsrfHAb527Uyr30xDF3hpf4nppsUwDdMOAf63DcNgBHzhzHoU07sO7UDkRe4OHinnfgrjGwFMjJ7HKMTNDNCOAO7wtHrlzQybTSYvOx+alEFi3rIklzyW/NHVw61ZZ1l7Tk11aHkMgHLdd5psJ4/HD8nnxsSu/eemCMl23rqzCGCd1F9KJpeGUNH+PmvoIRrj2a1wqVkeBxbHJ6wG/Fr4h8pQyHvl2C+Z/8gYJRYbgY8ynG2Gh1/aCFlN3gOngguKhBYVGFwrJMFhgwwgO2HVhMUH4MFo2YgjXCMZj7ynC42rTlbr0WamndhAMDEzNYMe3d30boH5uxefNmbPphJT79YAYGmneFeY+esEARLpy5hgftdN7O198QduNm4B+ewI2Yfdi6eQ+Kp45tKWa1xkXLhpJiHWcQGfF/+OFPD7w52ralADFzwuBxLgBKUVSu+LkKT4zwtGlpq8hSE23F9lrv68PS71NERwag/FAYFs//NzYUDEPExSgsGyMju9b0NDXU5GPtGJ1UsVaLXSPyo0Mw4pVNEI6bhVdGuMGma9sHts73aRkly/NxNaMv+jo0v+7XUIzcDE9MHd5b7EecruDaKdeFiq8hKXkg3hzjLFNoM2vhb0b4hZH49avxUNrVkAvTrjomwfb4vYy64s2OtVcL+c6i28KhZcscI/5zkplu2fyvHGc/GARlzwda+shstRXPtvaTYa18Uw9mrgMxjgugsBjlio+kBwyCp62uF8U8lBeVgusXhKDn25eH9GxdMdyTC1xIQ+YDTQu3VuN6XBa6TVmIr8L34ULpDUTN80RtTjHKNXVVDo70KFWWoqDGBzNfHwF75WEpbat643H6qUSKNtZFRpbo5WQBFKXj0i3VNyUlXFp+28ivhYDWW1qYgcArL0Rq1B4cz69rLqAJgqIkbIu6Cr8VX2D+EOZunAFMujHPZ8pw49I5pJ27goLyIty+WgzUZCHldCLi/ojCviJtZGsZJGtuXEJy2gVkFMgs3K8NCbk2j3DnyEZEnOqFl16dhlfGDIS9aQUyE44h4WI+attZyIlZdYG930y85wlkRh1GankTQA+Rduw0ityC8PE0T+0TnJzsynYI9YW5uCpaASUFp1OO4I/NcdAKWmXkOuQYByaDJmPRVEfU7vgGy388jmsFRSgqykXGqUso4OvDxvdFvO7GRcWmlfjo6z8Qvet3rPl+V6t1fTnWDvBhElbyHmzcfRIpR7chMuaqjJQdqb9qX+NY9Mf4wAHArZ+xdGNPLAjoo7pAlZGubZsyxfqGgyidOQEDZFcK4NjDb+5r8ESa6E54OQFUnoFjsblwC56Paf1k1zxQlEADbcXmWu8zj5CP46eIi3B+aSoCXxmDQfZGqMxMRFxCOgpqVX0fTkmuUBw0lcqgycc6JJAVOKvD7hEKb+eiFiVITzmDlLjt2LwvW6G/trsd5dOq/VlOkuf646VpfNTxGBs1ofp8HA74z8MUN2baBAB9S/TuV4jcQsULNQEepBzH3kETMcaDubvXgIfXjiEi+G2svO6DT1bNhJdkFQFZhqV5uGrcB7bddbzAaZffywrAbHekvWRpdxTdtsaFrCwattuKZ1v7aRCHOc2xH425740EMg9if2opCE0oTzuJ2CJfBH88Bf26aHPBdQ9X0nNQKWhERUYMfrswDjs2vI8RFjr6m6K8Zl6Y9PZYcCu24t+fRyD+Wj6KivJx8+YDhRtkzM3CMlzdewTpRY9EdRLHwAAGMIXfG6PhYcwBOJZw9GEmlKYiamMMEplxOzK21fgnEaEm/TzSCh+BeHdxLPIAun4djtAZriqmfEl6qfvtKD9Vx0PxXBvroi7umLhgEriIw1effIn1u/Zg648/Y/fVSkUGCvtt5KdARZtd/S+//PJLTQ2biIPujVmI+3ktfth/AgkH/0Ts2Wp4vbsSK+cNb14mqyusbc2hV3wJOzakomn0q5g+zB2OfbqgOPMoUssd4D9zCLoe2I3knBoI7LwwzKoAh2P2IYHvAB/hA1TrcWHt4AgbIz0YWveArV4Zru/YgVNNwzD7VQcUJ+xHdEwWzH0sUF6uB0sbDkqT4hAdcxwZ5RyYOzjAw8sF1nUZ2PZTLHL0LOHg7AYvNwvwci8gMX4Lft0Qhd27dzf/244tvyWhcsgkvOzeXb4wYr5oc2wfoqMPIiHrAfSMLWFu0BWWfYS4vj8GexMq4erThLxqPXCt7eFiYwyOqROef3kobMsO4/s125B4Nhm3rKYh7LtFmORoCg6/AKkxMdgrlbcPnEyLEb9/L/48exuNXWzh4O4J7958XNm2GbE5jVKdGExa/jgwtLZDH+NyZEZfQLnbWMwcpocDu48ip1oPdv29YZWfgJi9sTieUQQ9855w9vCEm3UdLquly3zhKB57ow/hlrknepZXQd/SDvZdcnE4JgYxxy+jXIqpJeou78NPsVkt9O0c4DPxJQy1LkPytlAsCdmOi6VNsBk0HEOcLdHVzBVjJ3jDtDQZmzZdhsHwWfjodTsk/RKLHJdALH7LB1ZMjjHuhX5DHGD88Cz2JhbB3Hcqpjrcwu9SXn3h1ddZtf4ePcBLPYpokY2EeNBgAlt7B3Dvn1bQrSecXXrAzEbB16b7iJcz45jgOYtKnPwtGeZLV+KrCX1UJy6Jv8j6Z6/n0CUnXms7cIwtwa1KQmT6WKwNfwN9TWVtrgdTl2F4eaQ1yo78iDXbEnA2MRdWc1biuw/Hw9GoEQWpBxCz9zT4rg4QPmiAiW0fuPcWP4ZXTVuZzc2hX3oOR6I1+48V7w5SEuPw268bZOJqF3Zs2YaDlQPw2sseMGs19inmimmYYpWD2A7wMcVxliqv4djeaMTc6gafntUo17dAL3s95BzeLxOHqvJGD9FUK9XYdYV1bxsYF19EdGo13PwnYVjXNOxOzka1wAr9h5kjn+GjmCus63GdyS1yvuIET218Wpo7VMus0p9bEgjAMYdL/0fY8UMcimuycOh8L4QsewVO0jvnhkBJPGIaRiCwryQ3NqIocT2+WBGJ86k78cvK7xCVVgET2wF4+V9L8dbw3jAVfzFLlpNoPkHDzcP4ljcQS8Y7KX36KLLTnmhExyYgq5xgbMuFQRcruPS2QDdd/D6vGnpcazi4KFuOU0t7aYGx/FKfHUXXHr0VxtBXHUuRoOi/zuIxUg7kVmOLKv+whZUueErziLZ2kMkZTiYoi9+PrX+exd1GLmwdnOHp3ROCKwrjRo8ecHl+LEbaFuLI999jW2ISEm9ZYk7YKnw4yRlGguZxUzGOmDGXHiJdNKYJYEwXsWHFNtx4biI+XzUPw58zBod5F6fgHGI05hY32JQmI1pu7GPGBwe4jRoHf8cueJAUiY9DtuBiKR9WPsPh29NUvmaAEA1Vlwl8UOkAACAASURBVLA99FtEnjiB2N1nUT96KVa+NwY9mbjimMC+nxccjR/gzN5EFJoPxRtTe+Lc7wdlahUrNFxPxt1eg+HDuY6YlZ/jp/NdMOQfX+CzqX3RXRRfvOZcryvWAzHSp4/mfKXB//vaPERitHxO7WlRh/SD+5TEb3foq62LTCAQ2UdSB5ajwaQH7N0d4TxoJPwdTfDw7A7E5Dlj+uI5GFhwEFvOlqCLbW+4e3rCvnvrmQOa6jAwY4LSXKPFlDWZoOMw7w3K7D+bm1SFm4c2YNP9Ufho7nBRcQ7iofTc73g34ANc+Gc8bnzjj+ZXs55NDJ5QrYQ3N2KSxwIcGx+J7CPz4S5bLz4JMjdeRviL34Eb+av45cwnQaYnRoYm1N48gh83FcPvozcx3IZZV10IXuk5/PbuHCy58Abib6yGf7cnzahPDIBPsCCExoyfEBDhhD2/TEGPVhdAuoheh2sR/8KPvVfjlykdNBdaF/Zs22cXAeENbJzkjwXHXkBk9hbMd29+cvLsasxq9oQg8DcY1Ui0ysOMV87Bzc9HXDgz4HOMYOPVD55mLhg32Em02sUTYhNWjCcIAXpwExkDZ2GS29/pM8FaGuDReayb8U+ccnsew0SFM9NPD0Y2bvD2tAJ33EC4mv0NUoyWcD1dzTjoMiAQSwSncKaonRM2H13D4eMD8a5/T4U7dU8XIqy0LAIsAiwCEgT+FiObYQ9nDHW7hD/jMlAhaL7RLihDxt7dSJqwHP+Z3JlzWSVQs79PDQKCIly5VAAe/x4SNqZi0HtjYdeuO29Pjea6CWpoDdeh1kj+8zguVUgKLD4qMmKxNWkI1v1nYiesuKGbiGzrdiDAsccrnw/Dyd+SwMyxb9vfI9zcuQ/8T97CYNk5/G0jxvZiEWARYBF4IhBoPWHkiRCrI4XgwNB5Or7bx0XU1l8wI+Br9OpjDj3jXvD1n4dd64fBXm4+cUfyZmmpQ0A0zzHuPPKZRvnnEbe/H4xfGaZ8fVZ1hDr4HJVfxPqXXkEEPwBLN3yPVZK1ljuYz1NPztAVM77bAtOobfhxxgSU9bKHlZ4J7HxfxPu7vsNwe8U5gU+9xn8zBcS5c8WLvyN8d0/8e7YndHsoLkBp0mZsNw3Cv0das3ed/2be0+nqMvO8DxzF+XxmNYa7OB93GF7GL2OEvW5e2ulysgyeSQT+HnOen0nTsUp1HgJC8CofotbAUuGjOJ3HkaXMIsAiwCLAIsAiwCLwdCDAFs9Ph51YKVkEWARYBFgEWARYBFgEWASeAAT+FnOeW+MsBK/2EVR9+Lp1+7/LEYJAoGpt3r8LBu3RkyCoU/Lp+faQZPuyCDw2BDozLwpQV9sg/6Gtx6YXy4hFQBMCbRj7qAG1dVpUEYJHqOXJflJbkyx/s/Na4kO8OtRJ3llrK0Ta2kwL+n+j4plZ7zEF2yPWYkXwJHjP2Ilc1p+bXYT56M1ZRASPgUWf5UiofgKAqU7AZz05MBs2F8vD/kCSwhv/xCvBtXOZKJIGEx9FSX8gbPlcDDPjoOdnCajWIgA6oglVZuHQxnCEhryBEX1DkVzTWfgxc0jXInDILKxJevCUFSJCNPAaW2SmB0haMwtDAtciqVSLAUitoToPF2rgoeXL953HR616nXGSGsFrYPy0M/Mis4b4EWwMD0XIrFHou+osdPlWWGeoLaYp1nlb6Jtw53DA4bjDb9bbmPv2FAwxM4Or3ztYsTFFJrcAVHoaawJHI3DNaZS2+eXJztOorZSfVb3k8VAXt7qOfTwUpOxGxNrlCH5xOGbsug2l2Z5Z9//QHwgP/RizRgRgVXK5vEjP6p40r2hQUFt8+AVI2R6BtSv+gRe9F2BXboOYsE7jh5Y20yCy4um/UfHMgaH9SLzub4lzvx5T+VUfRYCe/f0m1GZtx+J5+2C24EckbA6EM/M1pCfizw6jgj/HV5/Ow2g7Q0BQjYKMBOwK/wyzXxiEfu8eQF6jRFBD2I2eh0+/+hzBo+wkBx/LL8e8Hya/5o3qqF242N46UK3EDSjJSkXCxVScyiqBZH0LtV3+8pNMoZKEjasXwP+jYy2FB78EWadScTEhFVklzQmxzbJ2Ai78fCRtXIV5/v/BcWlx3wl82qxzWzvyUJC0BavnTcdHx4tA6My8qA9zrwl4zbsOUXsuPEFP+sQ6v7l4AV4VpYpBeHv179i89QBSszYj4P5erFrwCdYlMl+7Y/4I/JIbOJVwBgmnbqCE/6xUz8+qXoqxoSpu2zL2GcF+5FT4W2bj15Mlioxa9jmW8Jo8Bd7Vp7HnYnvzWwvZJ3dLMa9okFRbfAztMfL1cbA8dxAnc2QuU3QaP7S0mQaRFU//DVbbUFSZ3ZdFgMpPYfVrwYjosw4f+g568j5SIhGW7mDX3GDE+byPhT62qLxYBIx/Dpbyn/qStH5Gf03R793fcWVMFSzcHTrwc++dCReh/tYRLFv+BxDytuiLfSJuXfrj3V2JGFPRHe5O6j4tro1snYBL/W0cXLYCW/A55kpX4+kEPtqo16FtanHrYDiWbwFC5nZlV8CQw5YDgz5jMPNVD0R8W4z80rrmsxx06Tcfu66MQ4WFM5wUP2MpR+Np2nlW9VK0gfK4fWrGPkV1nsj9x5xXOnT8aBugOhbPAtQ+LAPPyEq7VQiIh8riSgi41i3t6RGKLh1H7NFkpGc/hJHjUIybPh1TBvZAizBC8B4WosLIDjaCAmTlVMPEwR2u1kbgCCpwJysX5YbPwcO9F7gGsndJBagtKkSNWS/YGpTgetYDoIcL3O27ydDWFSiCoLYU9yoM0NveUkxHmV5Ssk2ovZOCQ3HxSDmfi4qudujv/wbenTkQ5iJRGXrFuFfDhYOtHh5cz0YhbJTowhDUhLd4VYgKgQlsrLlt0pEe5iH9Ri3QR6qAeEMrOzF4F6DC2ByC9CM4WDEIC6Z7gfmcCPEeIq/CCA42fNzNuoNqE3t4uDKfzOWj8s515JQboIeHO+y5LVZXkEB+l+OAaZEHMMuoC+jmxg4Y9NVgSzw8zKuEkYMVBHevI6faFA4eTrCWFlHyoum0J6hF0b1amDnYgqvoD3ZccKDBfwws4OhMyCuqAFfij2rx1kk6+cZa+YAu/syQZ+YWCmFgoA8D8z5wpkIUlZnA3qqrlHebfEcRF0EtHpbWKLk73wVmNpYyeYORvxylvK5qY4gEAggNDKCvyEcktRC8onTExR5DSvpNlBg5Yvi4QMyYMhA2MvlJtV5S1VtvqPRFDgSVecjKqYBhe3IcNUEg1IP8I8jmGFXi98S7j0txh3A0JR3ZJV3hONwf02dMwECbFvu1VkLxiAYfV2iuHU81Y4YCPbW71IBH1Q0Adzhe8nlOJs8YwtzRAZRXjDJuL1jJ2FU9PVW5RAv7iXy4AUZy/irmpp0vaYOJGr3U8Ge+0Kt7jlQjj9pxndG5nflaSdyqHPuYr6RqEc9q7a7qJFXjzpmjiDtxFufvVqGrrTf857yDmQMtZXxNsTOj+0PUSJ94cGBoxtRU+hA8zMG1elv0t+cCvEoUV9SLn5YYmqnNZ4octNvXIW6b84qBPjPIaZdjIfIB2VpBnVQcJeOHDvLpxEuFHMznuTX+CasoNyGSQiZ7Ms+rCNwXKHhLBtUIVfQU1lJ+0qaW9hhHq1MqiKiGsre8T27cQApLLiY+v5iSwwKJC18Kjs4lfkM2HVi7nBZP9SUuJtOqzT/QPDeumKfbexSZfJp2LA0gLiMD7MnvvyephJGhMZ+St/1Ey4NGEReB9O2OCAoeaifuh4E0e22SuB0RNWVH0nim//hIym5qlp9fRtnxkbT8/SCa6RdAM0Mi6GhOFQmplrJjQymIocWdTKHJpSQkPpWc/poC54XRgawykodASI05O+kdt4m0OrGY+NRE9be30fxFB6hYWE/5ybvol+VBNJRrRwHfbqY/gl9o1oVLbrPXUXIJXyyQRrybqD4/iSJDAslFhAWXvFcnUx3TW6UurW0lrL9HFyIXkSdDw2UczQwKoqCPoim3SYOdGvMocdP/aJkI7wBaHPImuQFkF7KPzh0Ip+WLp5Ev1478Vv1Ov8zzabaDD82LPEnJOz6lcVxRfBPXL5ROS3RWFK8qnkLs7Gh85HWSmEnSRKkNpSevU+R4O7ILiacqyTHZX5XYCqkh+yCtXb6IpvraEfy+oA0/vCPSi/H51rIKqCb3ZLMN3MjvrRk0htHL7nOKr1KUWEiN+Ym06YcvxL4k8j0BVVzeSz8sE/uDWE91/iOgisxYWh+6mCa7cJv1q6VsWbyX/0w/BEnwlokPkf48KknbRaFL5lNQ0EyaPHkOLQ3bQ6cvpFFa2k0q5ct7ssZYJW38uZH4hado3TwmLsU2B3wp5MQNytwXQaFLppILsx9fSsTEmqwuWvuOMlzEcT5xaBAt+zaMwsJW0pLm3MUN+B9dqBIQkaz9GNnsaGhwFGXWCIj49+j0undpaLOfMva3CzlKd1vhzwArpPrsKJrn5kgBYWeojN9AZclrKYDLJbfgaMrjK+il1kYSR1X0xf/S5l/ebfZFLrnN20DJydto6Tj75nw8if57uqglF6nMATwqPB1O86S5scVfpTGlzu/rs2jLPB/iBqyl5LIG4pedobAAe4LbEorOq5cITyQbYy4B9NZMcZ4Tx6Q6H28hId3SxFNuzJhEyzeEUZBkzOAq4CIl2rwhyjGM7WdSZHY9kbCW8uJWUsDIhbQ++T41Z2MSVlylfetDxT4kG98qcW6f/YQ1tykh8jNRnItyz9DFtCWzUjweycaIKl/SEhNVeqnmr6iXphzZjLOcPDqM60x3WV9icoi09tBWFuX5QfXYpymemTxZT9mRM0U5Q3F8asHOglz8ZtPMMUyMSnJcHeXsXEhuI7+mxLJGkb/djvqQFh241xK7ij4qwqCMsuJ+pxA/hpYFDV2ynuKY2kOYTwcW+pLFO9F0X8iMMakUve598nSbR2EHMqmCEVWljypjpK69urhVlVcaZcZIhRwrYl9K8SG+BPjQ4g2bKXRqc30pm4uZdk3iMb0lTsuUjB/q5GOItNjMT1XcqIBE1WGoOiF3XJhLu76IouxGIfGL4yjEk0vgzqedeQ1yzUQ7/AKKD51BblN/pss1AhLW36WDIYtEyUlYcoSWMoltVDhdbhAP1tKk7f01pdQJZYAaSUsP5BFfWEYXRAU2iNtMk58XTcEMHYsldKC4OcVJAR5JS/fdpnphI1VkRtH7okQqKd6VFM/CIjr930lkERgp0k9YdoI+8+QSNyCcLjPykJAasyMpkAviBnxPyVd308LAMEouZwZgxb8Gyts5n7gIoBVxOVTDFCTCEsq4WECNoqYSA3LJc+k+yqsXEL8ig7a8zziQTAGsFm8eFcZ/Q1PdZlP45QoSCuvo/sFlNIMpMjXqIiuvkPilN+lC9HIaySSlgHWUcr+QCktriK+TnXwpeFc21TcW0sU0Rk9ZHQ/Qfb6Aqi78jwKYQoQ7UywzP5eigxmdvSlYVeLotOJZvS9L/dHzY9qXV0vC+mza1UrWWsqJXUZ+notpV04tCfmVlHNkJfmpLJ7FuEtpSy/cJFhJLhI0+U8TVcV/TnaiYk5ycSChIfEpPtXn7FaIDwGVJ39LflxHCozMokYSUFn8MtFFE9cvhDbsS6X8RnE8SjxEq1iVs7Uqf1YmM8NFkjglAwtzTFYXXXynNY+m7D/ofdGFl5D49w/QUlHOavY/kZINlLcrjCKz60TFclzIKAJc6I2dueKBTFJYyRZL1JoPCQspbulQAibTuss1YvikuUiSd2T1YnBSZiNxV9n/pf7i+SkduM8jYVWquFiFI00NT6MaYT3lRS8RFdUWwcwFOpOuNOUzZbjL5EWVfs+nkrgQcoMFjVqXTuLM36KX9OK9/hbFfjaJPIN3Uw6T32pu0ZEVk0QXT+LiWZOPyyKgJU8p3pLcX0s5uxbL4yJLVrItsTFm0M/RkbRwnJtoIH9n583mfC1pSESSthJ/0IizLKY62I8xYd5e+kIUpw1UHPe5OE7f2El5ohBtwVw8hqjwJW0xUdRLI39ZvdTlSBnsmE1ZeXQZ19WOhdrKohi3asY+neJZkrcZBYVUn/Mnfeb3gng8FPKpJucQrRAVvM05TphLO99wIYz8kuLyqkQXZ8LSLLqYL3PhqQBby24dZUfOIa40/lrqEnBn0PrMWtENgbL45TRGciNNCx9toa8pd/A01DbK8oqGHCsdAxxp6rpUKucLqP7+CQplLshlc7HUd5ovckVCK/LTlFe0jBs5QNTvyD+tU3F3GhwnzGLeTDbkQL+bB0ZOcANqa1DXavkVIapTIrHoP8lwCvRHf64+OEa98fy7H2CScxfU56TjxK1agGsK4+bHXnq2jhjEvLSRmY5r92Qn1vdGf/ceMOCYw32wF8wAmHl6womrD4PeXhjqZAZUFKKkUvENrd7o79ULRhxDmPcLxMJ/jQWQjcRrD5S8FUvg3zqM7787AiMPR9gacsAx7wX3PmaoPZ6EiyJ5ODB0fw1fhU4Djq/C2/PP4aXwf2Gkhb4StAxh7TkII7nHsXKiC8w8/fH6hxuQ0ain8EjGDH36e6K3EfPouj9mL5yLUahFZuJ13GPmxKvDu/oc1i9ahVin8ZjQ3xwcjgnsnn8HKyc5okmjLrIic2Bg7YbB3o4ibMHhwtLWDnbWpmjUyU7OGDqoD4wM7TDYtzcMpSwYHV1ha6CPbu4D4CMyoCv6OXUDx8AO3kOdAZQht6RGdEtS2q2zN9RhK8u7jxe8epuCY9QHgxRkpfyDWDZnNW5MnYaJzqbgGHSH86jnMZTRsV1/2vqPMiYSnzKAkWN/hfioQXbCYZystYKHYw8YQh/mvZ3EM3VsByMgcLjCVx1Jx1iV8Fbhz8rEVXus/b6j5z4XEfM9oSe4i9hVX+KHG26Y98uXeG+geXMsdkGfWZ9gvrsJoG8B75HDYYdHKKvTcTm1+rtIO3EdgAm4xs1TkPSs4Tiop5K8I8FJmY3UANLHE+62XcHp5oLBPj0AWMGznwO4HCP09h4AJwAVuSWoJG3ymRo+zCmVfl+LnLTzuAUjcLlGzVPEusDW0RV20tzViPw/12DONyWYOtMPzkx+4zpj1NhB4hwjYq2Lj2vDU1YfSe43heOgQTK4yLZRtq0HI+8AvB3gDi7SsWn5ehxVWN1HvpeOOGttPzEXTp8ZCJ3vBUMYoJv3cEywA2rLFJfA1NaXdMdEO/7qfEUeLfk9Hcf1DsjX8vyZPVVjHxcGOsWzDGW6iz+XfYRvbozGzImuMOIYgOs8DGOHMvHa/MexgueI/uCmfImJDr3g6TcHH/56GY1aTQEyhqPvCAxABa6kZuOBsBRJG2NhMMkP3NqjWLc1FeVUhsvHcjD+xb4wYV5y1ake0NReqGVtI1GW+dU2x1rB09sFFgb6MOo5Fu9+MB0WyMGpS3d0WJ1H27yibdzI6qF8W7sJp4IyZMXtRNR5Dka97APZEleebCMe3MrCDSaupCf0Ye7mDnMIUf2oBmXS4wobXDOYdsScUjmyBjDmMjNwreDcw0w0aDLPOVv+CPX3buN8LVAT/z0Wzd0smvun1/ddfDt5IHx7SErBbhjw1r+waP0JfHP9HkpqFAt2CUUOTAbMR+Txnjh45CTiDsVg17pT2BWZCf7F3zHfXdm1CgcGxqbgArBw7iGeF60Gb+GD2zinMEeZY+4ML3Mhqq9ro4tEVlW/BMFjt5MqWTrhuBpsteMmRM3tDJyq1a61bq00+U9bPztrBveRL8ATm5F+KQfVflxUZl7BHe4kfBw8Fvayrw2IBNbWB2TefpYqqsSfpece98Yj5EaH4d8R2XAL3oyv3ugr83lpPiqyjiEq6gIwagKeb1mPTjchBfWoLlPlDCawMn2cL+Vpm890U1HcWoBH1aoXmuNamcKIU43blzKgCg0xHU0+zuRryZ82PEUTCSUd2vFrgxEL/43PT1zBf07+jk/XTcaoNS/CslVsMCw6E2eCoCILcVF7cB6D8fLz9e3QqS1d/2r+CjK3O18r0NO029Z4rrmDS6dyNFDvhgH/WIfjtgE4cuY4Dm3agXWndiDyAg8X97wjujmpmgAHXdyG4GVvLpLjUnA5wwDHCqYh9MfecL36Kr75LRon5zTgQsYQzFzRvQ0+qsmnu8Cku7raRpnkbcmxejAyMYERHDHc215UFymj3PqYpryirPZqTUWXI1oUz43Ijw7BiNcz8M/4OLwyAkjYp0qQLrB16wdP7MGFM9fw4B1P9JQmHz2YuQ7EOC6wo7AY5TwCTKQngQGD4GkrKVZ1UUFdWx7Ki0rB9QtC0PO2SopnDgxMzGAFoMb9bYT+MRt9ZERqofwId44fR/nYyfD89RC+/+4Qxv86C86Gio0Jj64n4mK3ACz8agYWfvkNcrZ/iKFv3UJRObOmmrLih8ArL0YhdzI+CRoBG456vPVsXTHck4tjF9KQ+eBtuPeUYKatLi1aKd/6K+ykXJKOP6oeW+34cWBkZSe6q5WclI5bj/zgK+vH2hFR0aot/qOClNxhfVj6fYroyEIEbQ3D4qzecBg0DBEXV2CMu7IXVbT1AWWX0Yr+DB3uHsgJ3c4dAi8rCh++ux63PD/FgeWT0ccA4BdcwXVjL/R/FINFI17HqX/G48Yrw4GEA23jZ+aEweNcgB2lKCrnKcS4J0Z42ig8dWobG+16dVQOUMatG1wHDwQX2SgsqgCjaUuZa4EBIzxgyzFCRS9bAMlIunQHj/ytZdpIaGry8RaqgDY8O6p4BjgWI/DuZ3Ow9eQ3uPHzj9j4mg8+HqIsPjoRZ7qL6EXT8PqpWYi/8QpG4BT2SaB7HL9/NX85HTsiX8sR1LzT1ng2skQvJwsgOR2XbtXA35cpYBX/qnE9LgvdpizEV7P+iS+/zcb2hdPwVloxypl1R5mhXFCHSl5XmCt7kd7EHWNeHQSsikfE8kIM/OgnuD9nhDcWvoSflxxE+Bd3YDJpDVY2j0fa1TYSGTX5NOHRNXW1jYROyy/ltyXHClBZWowat0l4/fleCi8yt9BuvaUpryirvVpT0eWIqipYhsYjFN7ORS1KkJ5yBilx27F5X7bMedlNPZh5v4i3/exRsWk1Pv/xOK4VFKGo4DZuFj0Cx3405r43Esg8iP2pzBqaTShPO4nYIl8EfzwF/TpkCaB7uJKeg0pBIyoyYvDbhXHYseF9jFA6zYIDk0GTsWiqI2p3fIPlEnmLcpFx6hIKRG+3NqE2YzOWnR6GZeHfImyhB25tCkPYgbtK1i3l4+HVI4hNLwJzbQCOPgwN9GDk9zL8PWSf6dcg/8oV3KpshKAiHTt/y8KrO/6HD0ZYgwMNeJt5YdLbY8Gt2Ip/fx6B+Gv5KCrKx82bxdDTqIusrVRvPx47qebfeWc0YKsVYw66eL2IBYGOQMo6fPLFT9gVvQU/hu/BVaaiUPPHsXaAjycXSN6DjbtPIuXoNkTGXJXpoa3/yHTRapPAv3McP0VchPNLUxH4yhgMsjdCZWYi4hLSUVDb+quSuvmAOn+WSco3LiE57QIyCiRLgGklfJsaUcVZfL94NWIxGaEbQzC5J7MaRB2u7duGtHI+6gtzcZV54pSegtMpR/DH5jgUyXIyMEY3Ky5QcxOXks/jXMY9UcEo20S0zbGH39zX4Ik0RO2/iHICqDwDx2Jz4RY8H9P6tXcZvlYc1RzQJp8ZwKQbk4vKcOPSOaSdu4ICUbJSQ1Z0qgvs/WbiPU8gM+owUsubAHqItGOnUeQWhI+neaILTOE1cToCuRVI+eo/+GL9DkRv/Rnhu9NlsNPFx7XhqUluXc4boMf4RQhb6AvU/omvVu3FNaXYaIOzLnxl2tY/wO2rxUBNFlJOJyLujyjsk3NMmbadsflX85fTqSPytRxBzTttjecu7pi4YBK4iMNXn3yJ9bv2YOuPP2P31coWnlSGq3uPIL3okWiqIsfAAAYwhd8bo+FhVITE7z5A4Igp+L/z5SqmMnaHxzBfWCATSQYT8c5o5sLcDF4TX8GL3AIkHtLHpLGuzUuY6uqjmto3aqhtFPNKBrJv3VafY6XIlCA9NQOFPAF4+QmI3GGIrzcvwwxn2QtpaWMVG7rkFRUkdDys/+WXX36pvk9XWPe2gXHxRUSnVsPNfxKGdU3D7uRsVAus0P/5Aehp3FKDc4ztMXL8SDia3EfShv8iZHMqSvnW8Bk1CD1Nu8Pl+bEYaVuII99/j22JSUi8ZYk5Yavw4SRnGAkKkBoTg70xx5FRzoG5Qx84mRYjfv9e/Hn2Nhq72MLB3RPevfm4sm0zYnMaYe7gAA8vF9h0LUe66JgAxnQRG1Zsw43nJuLzVfMw/DljcERf0jqHmJh9SOA7wEdYjgaTHrD3GoyxL7+EodZlSN4WiiUh23GxtAk2g4ZjiLMJHiSEY/HH+Xjz50UYam4Bp77muHdkEzYcuwU979EYy8zhlQFQ2FCGy9vX4pvIIzgZuw8n60dixcp5GNuTkUGAsvR9+Cn2Nrob1+HShjBsvGGNSZ//B+8O74muIkKa8B6BYf7+8HfsggdJkfg4ZAsulvJh5TMcvn2c4DNRlS6WkL82Yb7+FY890fsQm3AV5Xpc2JobooulA3p3t9DOTgmVcPVpQl61HrjW9nCx4eBe6gHE7I3F8Ywi6Jn3hLOTCcri92Prn2dxt5ELWwdneHr3hOAKg0OWuI2HJ9xsGHxk/hru4MRPMXjgPxdv+TAXFQBVXsPxQ0dwaPsWbE67i8biGgi4DKqWcOndHaJZ6PRQ5AcJttPxrwAnyC+gpR5bj951SD2yHzHHL6NczxIOzm7wcrNE3WUFWW3tMWDscDgaP8DZ9QeQ5/kqFr/jjYJNW3G2RqKjPbqLlulp0Ylj3Av9hjjA+OFZ7E0sgrnvVEx1uIXfZXBw6fZIhf90QdW1eOyNPoRb5p7oWV4FfUtz6Jeew5FoGbwZLK3rcFkhPqx4WeN6+gAAIABJREFUd5CSGIffft2A3bt3N//bhR1btuFg5QC89rIHzGQNwDFT7wOittr4MweG1j1gq1eG6zt24FTTMMx+1QHFCfsRHZMFcx8LlJfrwbLXc+iSE98G33GDTWkyouVw6YrC/Svw7sYrQJduMK5Jx7E/Y7AjfAU+iDBC4OLpGOZhjz7G5ciMvoByt7GYOUwPB3YfRU61Huz6D8Mgh56wteWg+Pp+bDhFGD17AhyLkxTw7wlnl+dg5TIML4+0RtmRH7FmWwLOJubCas5KfPfheDgaNaJAMSZU2MhGOm2N+bAMk6tiZHyxF0zLkrF/60GcvVuHLra94e7pid6Cq9j2UyxyJP7a1xsj1OaArrC2NYde8SXs2JCKptHTMMUqB7FyvJT7vbujF154eShsyw7j+zXbkHg2GbespiHsu0WY5GgKDjjQt/LCWH83GD9MxPqYQnhO/wfeGViMTVvOoEaUvz3gZSPAFZU5siVemC2OqROeV8eTrzhmiMcD67oMeVzcerSsMQ7mLtqfWPfjJmw7eg3lqEE1n4fG7m4Y7NALLv1tUHroMJJTUnChwBAeHka4cXQ/Ym51g0/PapTrW6CX+zAETBuvYtywAOdeG+3n5QHXPl1QnHkUqeUO8J85BF0P7EZyTg0Edk7ozbukOd7dDJFzeL/MOKock742D5EYHS2vl4cPfNyNVPD3wjCrAhzWwlfk8nkrG2k7rnuhr+tzKmsP7fK1svzQAxYNV3AwRtnY1wWmWsXzafBdHSB80AAT2z5w722NHv1Hwt/RBA/P7kBMnjOmL56DgQUHseVsiThePVxgQ1exPfRbRJ44gdjdZ1E/eilWvjcGdlVJ+Gb2UvzZfzkiPnke1gpjhzgq9GBiLkBe5Hk4/HsF3htgIY45S1tYlCYiSm86/u+TF2Ar6WvQA4PU5gL5WIOG9gZqaxvFvPIqXh8/AM7qcqxdA64n5KLXSDdwbsRg5T8icL7bUPzjqyWY6mEhvuss8R1RrSHEgwYT2PY2R3XqQYXxwxFOKsdOJXWJxhysgI2SXQ7zPqGS40/fIeENbJzkjwXHXkBk9hbMd+/42/TtB4WHmxuD4LHgDMZHJuAI80JT+4k+mxSYz3N7voXLq3XEqdkPlg2Kwo1v/NHt2URHR62aUHvzCH7cVAy/j97EcBsjcJi1TEvP4bd352DJhTcQf2M1/Lvp6o2sP+toCLY5iwCLAIuAAgKER6n/h+EB5/Hemc34YCA7aikA9ETu6jpaPpFKsEI9qwgUIXnrD/h67R9IUvv2O6M/H0VJf2Dt1z9ga/LjfM75FGD/6DzWzfgnTrk9j2GiwpmRWQ9GNm7w9rQCd9xAuJqxqeApsCQrIosAi8CzhgCVInX/cdh8/jHeHsAWzk+LebV4YfBpUYWV85lCoJs/vikkfKO1UoawGz0PnzD/lkVo3etv0dDQGq5DrfF/fx7HpVddMMSCeTOFj4qMWGxNGoJ1v09UsuLG3wIZVkkWARYBFoG/FoH6ahi++AO2jfaGhezUub9WKpa7BgSejeKZmRdz4CjO5zNLKd3F+bjD8DJ+GSPsn6SpGzwUpB5G3Pm7zNoeyD9/FPu9TPHKCHuZtZE1WIs9zSLQFgQMXTHjuy0wjdqGH2dMQFkve1jpmcDO90W8v+s7DLdn5qvq+sf6s66Ise1ZBFgEWARaIWDiitEBrY6yB55wBJ6dOc9PONCseCwCLAIsAiwCLAIsAiwCLAJPPwLsRMen34asBiwCLAJ/YwQEF8MRHFPwN0aAVZ1FgEWAReDxIsAWz48Xbw3cCII6xc+waujCnlaPADWgtk7VFyHVd+2ws9QEQdPjX9SGeHWoEzx+vh2G2zNOiGpzceVuZ655LcDDazdQ1CE+IEBdrY6fLpfYr0mADhFBQk+rXzaXagWTxkbtsLtG2o+pgc75Vwhe7SMl33FQlPcZwEZRJXZfawTY4llrqDqvIVVm4dDGcISGvIERfUORXNP82WN6gKQ1szAkcC2SSh9fAUilp7EmcDQC15xG6VNZe/FQkLIbEWuXI/jF4Zix6zYkH5JWrZsQDbxGFYvTt9X2DShK+Q3Bw+3R54uTqG4rGS36UQMPoi9M8wuQsj0Ca1f8Ay96L8CuXGVfAdSCoJomqjFU06nTTwlQmrQWgUNmYU3Sgw62IyO8rv5Ri5v7wxG6+gNMcbWE66sbca2xJZioOg2/f3ce+tbN72UICpG6dTXmDusJDocj/891AoJDtyO1SFdb6sPcohDbw44gv03VK7MW/BFsDA9FyKxR6LvqrG5fi6Qq3Nz/FQI9LNDn3zE4t3MpRo1aip031X/Auz2uojKXtodoh/QVgld0EfsjvsIHr8/C63PnYu6sCfALXIzQjYeRUSpjWyaGt63G6+5m4HDM4Or3GubOfRNThvQEx9Ufc1dsaYMv6KJEO+2uC6t2tlWfi3TJv8za6inYHrEWK4InwXvGTuRKBg05GTsWG/XyyzF+gnd0zY3tUaWz87wOsjHrPLN/TwACVfEUYgeC3ecUX9UkFqghg9aPtydwZ9D6zNrHJKSQGjIjaDwXxB0fQZkNwsfEt6PZ1FN25EwC7Gh85HUSI6pMNyE15idS5Kp5NGrhASruKHWFlZS5ZQmNXxpF5y+n0rGUu9TY0Soy9BrzKDFyJQWN+ogOFPPFHJquU+R4OwJmUmR2fQdzVYZhB7NoE7laylw/g7iwp/HrM6ihTTSUdWqjf/DT6H+rE4mJWmFNLqVeLqRm6xAJ71Pcxx/Tltt1IobCmgyKXPgRRVx4QHxeCq12dKGg6HymJ/FLM+lo5Gc02YVLXL8v6URha834aevofVF7ZfILqCrle5q/PoPa5glNVBX/OdkBZBcST1XKWCg7xi+g+NA3aXbYEbp8OZEOJSbRn0uHEjCUlsYVUkeFmTLWpCyXKm34uA7yqPDEKvLj+lBQ+CnKr2/O7ySgmpwDtNzPnuD2HkVmVsrgUkrxIb7y+YufS9HBzDEueX52gso6FcQ22v1xQSrioyYXtTH/NmVH0niAMD6SsiVmaqVTR2GjRv5WPJ/EA23Mje1SpbPyvO5CQfcubI9OQUBpwhcSv+IOZeWWtwy8ncJckWgjVeTeoNyKTin3FJl10r6y4plhpahbRyVCWTUEVBa/jDzlCnfZ8x24rcxvOrV4VoZhB+rTHlL8csrNukMV/I6sKtroH8I8ip6/SFogt6glpLq072nS6mQSl84PKXH5NAqKzKAaplFhNAXBl0LiS1u6kICqEleSN0AuYWmtcoH64pmpwXNp55sfUvT9tsRzW/Svo+zIOcRV0ENYX0jXrxdSfUeaRwYl6aaymJCefNwbwv9n70rAoqzW/2/YwQ8EBGNUFsEBRBQISTEtoYtrgWm4VJfcSvx7bY/K1LomdQtvqXXTSjQNFVTEQBMXXJBAEUQUVFJQwEBAFgVkmWHe//MNM8PMMBuLZjY8D898yznv+57fu5z3O+d856PG8+spiB2MCImmglbFxktiBQjuyymlWiAWUEnyTB26YObEUrEiqV5tWgevLj009aoM2hBTjOdsHQmmsgMn2tAierDJMyuTMvm1k/XPL/Un2ch9ifNdR7OLW9UJ0HC7Gs0m/WDDdK0qNdehorYNjK01GIP2jbGo+Q+cSz6AQxk5KKg0htOoQEyfMRFetjIfVRY0oPx6HUy5LchJOI5a35mY7mEBqLquZtSdXWOYdiAZRzOycaPWCHbD/4EXF06Dl6Xow87tNG82wNyxPwxu/Y78MiH6u7nCXqatWsnMfr3tdhlqTbiwFZQiv/AuzBxdMcSG/bJbV/44MLB0gDOVobzaDPb9OnCh5tsorjWBoy0fN/Kv466ZPdyG2Mp8grYrfBTLGsLSyRFUXIFqZiD6ifXFTl33TrsU+Sk7F6ChvAz15gPBZRT1YwdGCiRB0FCDqmZj2Now0GyVim1T5E0QNN9FXa0AJrbWMGmuQVWDPqweswDu1KDZxBwGDQ2AZYcdK1Jg91C+faMAVwA4KNzUyn66YdsSNiQQQKiwGEtQd6MHNiihLPuriKFEGersg40dt1HPlyxdMIK5BN/6VvZDzDA0t5GJK+r0ytpGKWpNLSHIOYj9td5YMN0DZgZWcHImFJfXgrG3lrEFdbSArvkSQSAQwsBAbJOysMgec7gYPVWIkW//hBHbF8FLYsOoQfYv5xEYsgBmovLmGPH2dvxkaSaKDYKyIvyGQXjXrv1uO0l9WIx5HkvGfo3FF4tRBV9wZXlpOubY46npfMxPLsS0B/JV03u4WVAAxcUZHJPH4GRTgvLqFgy2kcQydTajqWG9c18rn+x27KtBdvwuHGngYkLwGAwxlPiKRHZ9WI+egpc912J53j7sTg9HwLMDVfQTQjTfu4dmOOGZfwwHV5GUhKTotw0N1zNwIDkFGZlFqDXmYnjgHCwM9YKlqJ628VVClI+665dReLcPHN0Gw0b6Kfn2+6p9SFyvxqBTXyquqSZ+a2MbymJRD+OvpMld+tWEtypiyuQHG5Rwu7gOJo79ILihGndVVLW73gUbEDTgdlWLqE+U5G+deWgZG9mKqvo4bdqtNM6zy6JykJx4GBk5v6PSxAmjxodgxrNesJXmL12N9Z1bKHdFq3xbeIeKjkVTxFR3tucjMGMpfFsu1Wvx5CtsKqZT4mlHUV3PzyijUUjUlE/b5voQE7SG0qtbiF+dRlFB7PTVGxRf3CSaSt+ydhmF+XEJ48MpIsyHAB9auiGOOl8Xj9Twq6kgJZpWLAqj0IAgCo3YSIcK77RPhbX+TrHz/Mh/9Umq5gtJ2HSFYuZ/IJrqbi1Jp+3frWjnFRRJO39aSn6MaNkkgfcSrUm/1U5Dg8zUUkBJa1bQ0mBfYjCZVmyKojAeI8ZsMn18slxmWk5A9UXHKToihFzAo4CXZ9BTLE/Jsg1hNeUlbKTIN4LJRTqC00AFSetpxdJp5MtwKWDF/2itCBdWVnsK+Pg4VUp0wr9FWbFf0BtzwygsNJimznqLovYcp7NZWZRVUNVp9EpiB8Lai5SwIZLeYHUtkaUr7VKnAzETYdNNyopfQ+EBPGJ8Z1HE+l30646vaOPp2vZlCFu+puVhY4gRLztgl1VIdS6dTpPFj20/l/zCYyivXjJy03nkuXPbBMQvO0Hr5rK8xPqGL70Xd5SSouYST2TrkygiOo1KWhupJH0DLXJ3ooCIOMqrlfCRICf5baOmstMUHc5OUTPkMn4GhYXNo7fjr1GbBvuRa6fU5hVHISV8iIh/k06uW9hhq5KpdenIswYb1EJXMtxEh50xbCOt7F5YT8WpG2iuyB98aVF0OpXUt1J9SSbFRgQQL2w9pRSxvqpGr+wSFaltBNHSiJdEOuJGHKIbeYm0IXKpaHlDx0iZGlqkjS8JldqH/KiwIkLsOTsdf4jWfxBOM3zsyW/lCaqR+GXzWYryW9axNEuuOp/K4hd1+J3cvRKKD3MhqzeSqVruOpHGkWdqH1GbNDeeyiRyKNCQO5WN9y5B9HLoWJF/dODK2p6KWCuso4Kkz2mWJO6J/MqLQt97k0LFuhfh16sxRVbPSmKpXOMUTjT4pFa2rUBS7rQlh9aNsSJIY7jc3fYT4U1KCvckwIrGrMsRLzlSHHluo6big7QyKIgWbUijMrWzK0JqLYylebxJtDq1gvjURk3XttP8JUlU0SLrQ+3LuuTijjS+yowqLt1IuyNnkIs4RjJ+S2mbaImJgg99+iN9N5ftp9lY6kNzo49T+s73aLy4L2UCIulkpWTxkqzOFOK3lrahNBaxbe1m/GWVoXLkWa1PqMFbjb91ll9ALQX7ac2KJRTsyyUELKNNa+e190MAyeOnxI5kLwkbqSwrnqLCJ5AL40ehEetpz6/baNXGM9QoF0fV2QC75OwaHZPJ3zp0ryY2qooN1L7MQ9qXS/s4H1oStVGLdguoVmmcF1JTQQzN5TlRUFQaVfNbqDp9DQUxDPHC46mYr2Cn6vImWQw1HGu3bENYRHHLYkRTTvyKZIpwZwjMfIot7rz+roMfC+5Rigz2o+D1WVQvbKOmPw5QxAx2LRGfKpMjiCcXLCTJDkOe4ilNqSHzllJcYT21luVSVklTh4HLXi8uopMfTyYr8dSYsPoove/OEBO0ns43CklYHEtzGCvyX3mQiutZB+ZTVW4ulYin0aS83N+hhOIGEvKrKW/bknbDFSX8rVrJTNLExZ/eTLhGTcIGKoxbKqJjFS5ZU9tAhYnLKcCdbRfLq44KD66iANnkWQSkJIDKJlAdOLm/mUDFTXxqKtxF4WzHZPVG+7pXYRWlR04lhnmRogsaiYQVlPL+mPYEO+J7SsgoUb/+Vtm0pzbtEpar1YEoqciPpTcDQikqvYL4wiaqzIoWJ1Qy63OlvDquSfUjDe4tVBwX1d4+/k1KjmDb50JzYovEDygSnBSm7jq1TaaTkF3TKVlvjqm07rxoQp2oMZOiJnxAydIOoMPaO46aqargNMWvCBIl9EHr0uiPsnKqqm/Syn6k7ZS17RI1q1U7tYftASRrntXYoEZddbSo01F3eVItZaweL68ndnnDvFCKyqoTs9GgV2nbfCk8roCaWssoO6uUWmWmtDuSPA20SGIjDKn0JaV0OyEic0FA9Xk/0bw539H5+ib6I34xWUn8ki3FLssYu4HylT571VHG6rGEsHgqk6EoOhRcpA1jndrX77ddp+SvvqSoqCjR/xdvhJB/2DLpedRn2ylL8t6EhE51Mr3hHkVZktxFcl3xt+kqJb4/mdzDd1Fhk4D49Vfp4MrJ8smzRttRFreUXJPqsid2qm0sVWwoe65dP6SVPykjz16T+Iq65Jkk2MiuK5dc49KE/8XR9sVB5AKGePNiqbDT0g9F5i1UHDufGATRyuRCqmcTbWEl5WazfiIbH9TF1464yASvp7M1rcQOhKVEBotsoWPZiKwPJdEffAHdOfu1aJkKmFBaf76WhNK12p4UnnRTHJ81+KY2tiGLr2Sgh3op/kr7GSLS6BMa8FZUj+y5xD6k8ssk8JJcpKmA4kRr3WXxkyUifyysv0ixb06lCaJEUkBNlZkULXqokekLpfiqswEiYfEeWhadT63UQhXJH5I7m8RLlwx12Ig05mqMDTLtU+jjpH2f2nYr41lGyaL3KWT6amn7xtPqjFpWieJ3oNTFenkcNZ0pTPDKDUp3nHAGY2bkS3A15EDfwg3+E3lAQz0am5W+jiquV4OMDZ/go0QnhEwcBoajBxOuPxaumgJnvQYUZmXiKkzAMCbi6VUj2DkNARcNyEu9jJuypAd7w9uJgSF3BHxlvxoovT4cI5qP46v/HoSJmxPsDDngWA6Eq4M5Go6cQvbNFnBseBjtzyBj1WQ4mnsgYPa7+D73HmRG9NvldvCAx6A+4BhYY9ishfjXGCsgLweXblZ3TWYMwnCPgTDh9IGTtzcGA6gtqkQdAVSyH8tfXI0rwdMwyZnl1RfOY56En3kH5JqPzOEw3B2DTAxg4jQcfoPNgdoyVNYJgKarOLbzJBrMHeFkZwJwLDDIdSAAI9g9HoSQHn3VUFW7CPyrv6rVAe5lYt2shVhrOAnBo/rDgGMCW58xGMfK3uU/IzjMfBfzXc0AfSt4+o8CF/dQ3djN7bQU+RsNQeCscWBwEj/uv4h7aEPN6SQkPRWMcbbqFocYw8bVC55OliKKHKYf7Lh2sGGau2Y/UttWsHlFOdWe90BXaumqu6mKJ1unLx6fNhsTmEIk7TyOq3zWZo7i59pJCB5hISaqrV6d4eftABNDLh73HaTiK53a0lLjS+qaquwevwC7PoqDy+tz4MWYgOvjj6dqc3GltFlUWrQsw7k/rJSt+mgrxfnkm5jwtAcek6NNaM07jp/zQ7D02SHQ03PCxLfew7vvviv6j1i7D+lbI6Xn7374InwtFEK7hQ0G8a+hWO2uPa0o+eVzvPhFJYJDA+Bsog8DxhljnvZGh4dq4edysmtzospmNPPqWSztYj+kJqarbKWBKSz6MQBacPeepthkhcEDrdHpu7gmHpj4zyA4MA24uiUKaw7dFE2TsQO8/OuH8c2aNVgj+f/hFMrJEDbu3vBnjmDVJBeYuwdi9lubkNuqp2I5iErpRTfM3YfB1coQHBMHBCx8FS9bAQ0ncnFNsitUeyk4DB8COwN9WLiOgA9rMOZDMGywBTgGXHj6OQOoRlFlvVh2bX1TlW2okrmX4q+UvDY+0bt4S1lLchETB3h3wk9aSuGgDmfWLcXstWaYFewLawN9mNgOx9hxQxTKaXfKcZiByPkeMIQBLDxHYSIXaKhWtZ2uZn+V46qqj+tqu5tuIOvoZQBmYEzFfbOeDZy8BwAoQOqlW9LdtoDei/XqsoCOdgqqkZ8ci5hMDsZM8YHMpjodZRSPhFW4eqYQkF2dx7ECz4MteBv37rKf0lb+x/Tr08W1u4Smm9eQ2QDUp3yFJa9sBdt16A1diC+nesG3vyFg5o3XonfBbv8hpCUnYUvcOpyI+wVn+Qewe74HlPVlMGhP7mE1AP0toZ3MkiWdypsm2vKq/louTiguCFRZvhs3TF3gP3UE8L9LOPd7HQK87yDvbBGYgPkID7TvVgDVLIVmHQhvXkZqXgPA2nSP//iozT+MmJizwJiJeFK0T1uPicoQMANv0gyEWu3AlphfcXrxIPD31+KVcC/xWlWZolodCrSzH61o9bSQZl31lIPy+hwYuY7DrGeccPiX3Ui8MBGTz2ZicPjH4EnXgvamXnuTlvIWyV8ltFz4Fetzx2KjT1/RLY5JH/TFQDxmbShfVMmZsDATCWleeP57B1H8khYRFGP/xmMYvfMbTOmvXciW1u3SwV1cO5fbaa2yPIkHaTuaeOmh/lxPYqmWPqkxpssjJHdm6gCvsU5A3g2k5Zag6dmBneNH603kpRUB8MKUJ5xgJEeAPTGA1eh5iPzwJCZ8dAAb3vsBL4z5BIHW9cje8TleX35CXMMKY9Ydw+scDoxGzEf0kQHYf/A4kg/sRdy6E4iLzgM/+0fM714eJeLBMTGDhQnAjBoKJ0bhAa2T3OouPGjf1FLXnUTWxic4MFOHNzvA86D+hLdwKbUAgG0vcCQIavORHLMbmXgcU55s0kBTk79qjoEaGCi/LWjC3WpVCZUZ+vUxvi85jxaRuBUl8REYPTsX/5eSjOdGA8cStHAaPVvwRrkAhy8iLa8S81wdZBpggSGPe4FBAcrKa8GOyXSYlxVGjHaDndqXIRQx5MDAzBz9ANS7/hORP82Cg2L9e5eQnG2BZxd/jJmLV+DLwlgs9luErPI74APKk+fmWpSXGSPg3RfwpK016rWRWWOg5cCkH1c0Ep1+KgdX7wXA10xRWMX2dfGc0x8BK79HdMli/PzlG8gf4AzvMVHI/nwsXC21UHkX2bUX16wDau0PZysAZ7OQd+ufcB3QfWeikr1YMno2TvxfCq48Nwo4ltQtqdVV4nDH4uXXxmDLF4ew72dj3K4Yi//wOixVXd3O93rb5jtz0P6KZl1pT6uLJQ15mBQ2GVa//Izojf9BwU03hMfbSWNDb+q1N2lp18o21BRfQ+5TE+BozPo0oaWsCLkTAvGRY/sLchxTRnY4QYasABV5Z5E+dhK+dpOxMUEZMjb8iLPjP8W/JwyST6plamt1aMigj0guVaVN0G+gHYB0nDp3HfcCbWTisqTOg7QdTbwIrT2KpVr6pMaYLsFGyS/HDmNCp8F942rkiR7Cn0CgtexQDeHe5VPYf6EWTPAcTPNuf+jqRIljg9EL/4VXfz6Jr69sxX82P4uR74zC6I+Ogz5SLM3STEW2RRAW/3sGFn/yBQp3vAW/l6+ivIZ9Obf7f1RXhdJ6H4TOHg17LdIAVZwevG9qqetOAmvjE5rwlvHnTvR7+QLHHP2d2UxIWd7VRV50A/FLpmH2iZlIufIcRuMEEtSS0OSvait3/6b5YDw+3gXYWYXyGjablJ27ccdod1tp/9J9Jp1ramH+91B2rQgNqERORhoykndgawL7ZKPpzxKek4MRwFzBlg8+wTcpeSgtL0fp74UobzaEfUAoXnVHe0CpaQPoNrIOn0Q5LwzvTHNX8vStjh8HZt5TsSTYCQ07v8CKb47gUmk5ysuLkHviHEr5BLp9EXsSz6NctNSEAwNDA8DkacwJ5MFUlnRJHnKu1kAgqEZu7Hacff4bbHrdH1Yco16SmQMjj2ewIMQJyFiHd5d9i7j4bfhm/W5cbJ/ZlZWmm8f3cP3gZmw8MRD/eH4annvKC/Z9apF37DCOZZegoSedgUqJNOuAY+uFqbN9gdqf8cHbX2BbfCyiP1+LmEKFWQiONZx82IUupxGzeS9SMw7ip+hEsPMY7X+EprIiXGRnGnIycJK9vzUZ5ZLbXfqVcfgr55CedRa5peKvvnH6wXtCINxxFt+8eRAOCwJg3+3nnN6yH4XGSaaF63/HufRMnMm9KXoYVSilcKpZVwoVevHUENzxM/CaO3Bl035UhU7ECOnDY2/qtbdoqbGPTqgY4DHvJzHtrnhak2qQmZiFwLcngSeOtPq2gzAsowhlit88ojJkJKXB+6WxcGNzK0EVLh3egPBpX+LymNfx6SxPmR1mOjHWfKGqGBdNHWDXVzZxU6zWBx6TpiOEqUXGvz/Csg07Ef/z/7B+V46MTT1I29HECz2MpffJJ+Vg1Yd1wFuIWT8HLlfWYslHscirZYdr2L82NBQdwH/eikKG36fYt/EVDDNRHWA4/Z/Be1GvgodSHPn319hxSdVoGx+3Lx5EYk45mtlYz9GHoYEeTAKmINDNHNAYX8XiiX/qczKRVXYP1HwDh6OTYPzZekTOGKJiqZR8XeVnveWbyqkrv9pdXWvjExrwVi7Q/bnK6Q/fqUHggc27PsRn23YjLvq/+CrmvDw/bWyg6RauXawA6vORcTIVyT/FIEGuk1WMjVm4av2U2jxMXoheOuPYI+CVF+COLMRsFZg6AAAgAElEQVTsy0YNuzS2JheHE4vAC5+PacP69BIjeTL6n3zyySfylxTPjGEzyBamFdmIP30XvMDJeMI4C7vSC3BX0A/DnxyBAabKcnA9mNqPxIRAHsxuncCmd1Zha3Y5+P08McZ3IPowg/HkFD/YVf+Krz7fjtTf0nG13zRE/XcJJjuZQVB6Bnv3JuAY3xE+wlu4q8fAxtERllWZSq47wZaxg/ekf8DPphrp2yPxRsQOZFe1wdZ7FEY6W8OImnHn/A5EfrEVR48nYdfxJoxbuQyvPj0I7GAMVedg+7eJKOxrAjq3BSs3X8Vjk9/EpwtH4zHj9vZx+qiTuQ84/FKc3rsXe/YeQW4NB5aOjnDzcIFNY247bT1rODrz4OHuAb/xo+Bkegu/bUhCsfvzWDrPE6VbfsZv9QzsHJ3hPozBH0cTEL83H5Y+Vqip0YP1wMdgVJiCvXsScSS3HHqWA+Ds5g6eTSPOb9+KxMJWMU8HGJZlIzVlG77fFINdu3aJ/3dg2w+nUDdyMqa49lX6NEZ1l3B4Tzz2XrWAz4C7qNG3wkB7PRT+uk9zu4Z6YrQ6HXD6gvf0U/DuU4kzW3bhrMHjmPP2DAw6tQeJhQ4IWfo8fPoZABwz2A/zEOGTticVZZZ+mBM8AGd+3I9CMYZe/iPgalqDvPizqOE9jdAn9JC06xAK7+qBO9wT/UqOYe+ek+APcYTwVgvM7BzAY/7AUcW2OQ/GgEGPwU6vGpd37sSJticwa7qPeHs+PZg+Zo7m43twxHIe1vx7IuylywsU/UR8TjW4dDgB8fH7cSz/FvRMrWFpYAxrl4Hoa+HcDZt3gq3CtlBynA2tYGfHQcXlfdh0gjDueU80n9zfC7qS4yI96ZF98PqLlmNxTK3B3DmF6JynsWb9HAztI4kfHBjacOGgSq9u/dF8+hDij9VhiE8biu/qgbGxh4utEe5cSsGe+AO4aumOATV3oG89EG6jtLERTb40RI19SGGRHnAsnTCcvw9rDxSj/tJxZA5YiOXThohijKiQqRCVB4+gJWgChpqL2y38A6lff4KV3x3C6YQNWPXvOGTVG8NuxBT864M5GDWA6dmIMzsC/vuv+LLZC29MGAzJJnFSoaUHHOj388DT7IDC7VRs2FsG9+mvYZ5XBbZsS0O9kR0cXd3hOZgHX1V+bt+Ic3v3IH7fEZy50QhDKyvY2luBfzYRO3cfEl0zsnsMdrYcVJ1KRrymWKkppujbYPjTGmKppz366itPSnstpottWwql7AHHFAOemITnJw0Dc+MgvnrnC+zJTMPBrZux83wrPEM/wNqP5+DxfuKZuHuXsHfd//DT9mRcqqlBxV0BqLUveI8PBtfFFQOr0rAr/QhOnr0FIzc/+Duad4rlwpZqnN+xBl9EH8TxxAQcb/LHylVz8fQAU3C0iK8evH5ouZyOGwMfhw/nMvau+hDfZhph5GvL8H7wUPTVY/FsRunpJPn+aLAZqlP24edffsONVnFf5jkAggsJ+DYxX9xnDYXHUGfNfq7BNoba3kZqvEJfNdgCVam/9EL8rUGLWX/Yuw6CVf9hGnzCDR62AlxQhbesLcgcd46llrDVv4VTB/dh75HzqJHkCzxrNJ6Xxc8dPFvTTjpvJ60Pc95oTPQ2R9WZXdhyVh+j5izC7EH5+C6xBC4hr+BlHxvtbMDDDUMcjFCRdwinaxwRGDoSxkm7kF5YDwF3GJ70HggL2/7yfeesSXjm2SAVeZgVODfV5XV7NbSbB9uqdMTLxfkBcHZ5DP1cnsAUfxtUH/wGn28/ht9Si9DvxVX471sT4GTS2tlOleZNLur7WhndsYcc9o1ChWt/y1Ph75sx2W0BDk+IRsHB+XCV9Od/RTTYz+Ie2IQtf4zB26+MajcIakbVmR+xMOh1nGWXOnwRCMkrWn9qE4VXsHlyIBYcHovogm2Y7yo75fKnSiZm3oDc9XPxMbNKtDa++wtNHoa26GT48xFg7WkRNjp/ie9U7ufb21I24tLGf+GbQasfIM/ebsOjQI/dC/gkYtatQ9x1ezw16Sk8PcYfTwwbJP32waPQSl0bHjYEmvH75jC4LUjDhOhjOPhA9np/2DDofXn+yili76PxSFAk3DvzHWY8dwa8AJ+OJyl2ZwuPYXA3d8H4xwfLvD3/SDT6/jWCqnAll4eFk3k9mKa8f+LpKP/VEGAw4oUZEPxyBuUPatji3iX8esQLCwMHqBit+qth+FeUV4CqtO3YcqYNw4IXYP4kG1TsXo5nvD3gHTQX76+JRuzP3+DrQyXi3Sj+im3UyaxD4O+DgC55fgR1bdjfGX68c/glORe1AnEPza7h3rMLpyauwEdTZV/efAQB6HGTWlB+4QJKm++h/FgcDnuHIpCrG3PuMaw6AiIEOAMm4cN/5OCH45UPIFG6h99jE8B/92U8Ll1brlPEg0fAALZjw7B0dhDGBQbjn4s/wcZjl1Bflo24FSFwM2qFnut0LJ6gi80PXjc6jjoEuo7A/dp6oeuS/Gk1CPzSTCQlZ6KElaEkE8n7hsH0uSc0r2/902RWx5gDQ+fp+G8Cg5ifv8OMoM8w0MESeqYD4Rs4F3EbnoC9ujW06kj39j3R+uAjyCxhXxi8gczkX+FhOgWjZffy7m2e2tCj28je8BKe23gH49+Mwv8+7e72dNow05X5+yFgBueZS/DM2q3YNWgxZrmy+wDfjz8Bqk5txY4+YfjA30Y36nw/IO4RTQMwXFf4sv+BPSKkq6xDQAUCbai7dBzJmTfYvchQknkI+zz64LkefetBBau/2WXdmue/mcJ1zdUOAWquQ0WDAWxsGPFHfLSrpyulQ0CHgA4BHQI6BHQIPNoI6JLnR1u/utbpENAhoENAh4AOAR0COgR0CPQiAro1z70Ipo6UDgEdAjoEdAjoENAhoENAh8CjjcDfI3mmNgjaHtSr7Y+2wfwlWtddfVMLGhoVv17xl2jxAxaSIGgUfwjkAXPWsdMhoB4BARobWh7Ai5jqpXjY7lJzIxolL48/bMJpJY8QzQ338GCjsy7OaaWav2mhRzx5bkF5xg8IH2UPh2XHcfcvqGSqOonPQ8Yh5POTqOqt/J9a0dwi/AuioUlk7fVNLc1oEeHZjNKMXdi4ZgXCnxmFGXHX8Cgiowk5be5TXT4ObF6PyIg5GD00Eun1OqS0wa3Xyjw0fnsXl+I/xkxXc3A4HHBcZ+L9709Jt96jmhR8MG4ljrFfjmX/qAynfvgU4QEOMA/4P3xzqqyXk1v2paiD2Lw+EhEzx2Dop79B4ZulnVXQJSzZFy/XIGTkTHx+6lYvy95ZtF67wi9Fxo6NWLPyNTzjuQBxRS1dIt0RI1kd3sKpz2diZMganKp6UCks+zJ/BnZsXIOV4ZPhOSMWRSpDTu/pqNfjXJdsrUsquu+Fe55/CNHS3KrZZ+6TffVcftUQP7rJM91B/s/vY+6uPljwYwK2Pu8i/xlu1Zg8RHcI/MorOHEsDcdOXEElv6fZczNKT23D6rnT8faRcs0G/RAhoVEUbfXNL8GpzZ9ibuBHOCLqBExg7x+MQOsCfH+8UiObv3MBjuUwTH3BE3dj4pD9oPrPvzPg0rY/bH5rAY8Zb+HtV0aKJLR6JgzvvDYOXNFH/PgoPxGPH9JScPh8dXuM4QzAuNcWY+YTQ/HyOx/hX+N6e79pfVh6TMQLno2I2X1Ww+hkd7BsQWX+aRzLPo0T+ZWQfFxbqp6H9cDQHv6zx8P6zH4cL1SZdXaWvlOMBMCvRP6J08g+dhr5lV1Lwjsz0PYKB4b2/pgdaI0z3x9Godpqvaej3otz3bE1tY18wDd7kn+wDz6nsHn1AgS+fVjzwN99sa+eyK8Z6kc0eW5DzfE1eCFsFzDcF75eoxA02vEv+JELDoyGzUfchSu4EDcfw4yUf2JWs5olJRpwdf96rNh2C+Zmxo/Q1lVd0HfTNexfvhLbrhvD7GHZsk+iHt2vDgGlCDyMfsvA2csLVgBqL1xHueTBnn8VydsOohYXsDfpHG5LnvdbbyIv3RHjR9j+yXGnO1j2wbCFP+JCfiriFg6HkVIdPUIXlcVIo+FYGJeK/As/YuGwPg9hYx9GHXXH1h4maHuSfxCarh7E8hU/4bq5GUw0pS73xb56Ir9mPWi3zzPdxfW0Q0g++hsyb9yBsZ0nAl+ch1Ava3EgFKChvAz15gNhZ1CJy/m3gP4ucLW3UNjmiyBoqEFVszFsVW0BRs2oq6iDgLGBDaOdeJ2bycftGwW4AsBB4SY1/4FzyQdwKCMHBZXGcBoViOkzJsLL1rijpKAB5dfrYMptQU7CcdT6zsR0D/Zj1kI03y5DrQkXtoJS5BfehZmjK4bYmIAjqMX1/CLUGD4GN9eB0s+tUkMR0g4k42hGNm7UGsFu+D/w4sJp8LLU7+Cn9sgQlk6OoOIKVDMD0c9AYoVqZFFLT+YmuzZYqAcDfQlNmXtyh6zebuF6rTG4ggtI2H8HvguC4WHGATXfRnGtCRxt+biRfx13zezhNsQWJhw+6q5fRmGNAfq7ucJeqkv2E7UZOJCcgozMItQaczE8cA4WhnrBUpUYdA/l544g8VA6cgpuw8TJD+OnT8ezXv3F9qVa33LNUHJCAgGEimYm0qVsW5RU1PJSz/XPMurwLy4jthvWRm82wNzRDowsboIG3K5qgYmttdQGpaKqtGtpiV4+UGOjKvxFawHUtZOacbu4DiaO/SC4cRmFd/vA0W0wbLR8WBJtU1jbBkYOQy11IIdxMq4PDMLkoebiZhnB3NYaJs01qKpvBcCBoblsnNMiPrKUpH4LCBoqcLOegSOX6RSLpbYisp9S1JpaQpBzEPtrvbFgugfMtAZbWUED2LiOgB+AwxfO48otPrwcDHHvwkFE5+nDCQ24umk3jr0ViFkORhDevIiTNqPxeQ8+NqRV7JaKKo4/mnQvxVLsRKrsysAKTs6E4vJaMPbWHf1aj2xNgIbb1Wg26adlX8faYG/qUTv+7THSAAaWDnCmMpRXm8G+n7i/1BibWYWoiQNifWkfJ9XoVamOWJ8S+4idHm5dLkAZbOX6aKnJqDwgCOpuyPf3KsuquUHtuU0TSZ4oJf6vD8HtQlxqssNwewZgt0mtbWqftTE0V50rqWGl7JbqvlpZacm13so/CAKBEAYG+mzQUppfKbWvHtuOKvnb26c81kvaruGXNP41UmHsYuL5f0ap1a1Ewga6FvMWLUm6ScLWEkrf/i2tCBtDDELoy50bKdyPy1oGAV40a80pqhSyDARUX3ScoiNCyEV0j0t+4TGUVy/o4C5soJJTWyhiqru4/nhanVHbfp9fTQUp0bRiURiFBgRRaMRGOlR4h0SkOyiIj9qoqew0RYf7EcCQy/gZFBY2j96Ov0ZtTfm0ba4PMUFrKL26hfjVaRQVZE/gvUHxxU3UWpJKW9YuozC2DePDKSLMhwBfijiQSklrVtDSYF9iMJU+3bqW5vKYdjl5r1J0+kna+WYQMaK22VPAx8fb2936O8XO8yP/1Sepmi8kYdMVipn/ASVV8DtJreyCsPYiJWyIpDdYTLgfUsqdNqKWAhlZJtOKTVEUJpGFmUwfnyxXgUszlZ1cT3Ol+kEHTZX4NlFJagytXR5GfgyXxi99q50X91WK+ukrWrF0GvkyXAr49Ef6bi6LFat3H5obfZzSd75H4xmR/xMTEEknK9k2C6m1MJbm8SbR6tQK4lMbNV3bTvOXJFGFcmUSUT0VbFtEPCaEotIriM+voPSoEGLgS+HxRe00VOlbEVT+TTq5biH5ieVi5eVGpNAdaqKC6FACuBSw4n+0VqR3VnYZXbK0VOKkyEh8ro3+hY1UlhVPUeETyIXxo9CI9bTn1220auMZamwtptQtX9NykX+FUnSBgo1OiKaCtnZewvprdCz6fZrq0m6XjN9S2pZXR0IWc1V2nVKlRZtkfZdHAS/PoKdY/CT2qKzpcjbaBX9haWnAWF07Wwr205oVSyjYl0sIWEab1s4jnsgmIWODygQWY9hUTKdkMITnZ5RRd0MLHajCGOSzKEIcK3xpUXQ6ldS3Un1JJsVGBBAvbD2lFLFxTBZj1u5k46Myv11MG/ZtlfrlhOjL1CaspvNx6+RsheTsJ4iWRrwkwkNk8xpwVo2SzJ3GdFrtydrbWFqReptIWEEp70+jxXv2048hTgQ4UUh0PrUSnyqS3qKn1uVQi6R6V/lriN1EbXQn5UPisj69dCPtjpwh7mtAHb6gDMv2uKrargRUm5dIGyKXinyrPV4IqUe2JrxDRceiO/o6ZiyFb8ulelUxsCd6bLtM0RPYPrk9fojgV8dfWYx8bwedSthIkW8EkwvbH7JxQ/SnITbLxQE1fZWGONlWEE0TWD9W6dPKdNREJelx9N2K9r4r6Mut9FP4WHEfzRBv1jpKF/VJ4qYo/txJoQguG+f+RZt2R1KwOK5CUVcq7ViJrfWfSau3b6SIAHsCrMjvjQ2UnF9NQmEJJS32Jat58fSHkI0lpyl+3SJy582lqKQ8qmXtQiUfseAq7zdQQdL6jr5aXf+mgEH38w8h8ctO0Lq5bF7YngOwecHSDXHK86ujVyhP0b56wXaUyi9uo1BZrG9U5YAKwIhPofyyzFVhEcXOcSH4f0LJxXdIlAJV5VN2SVN7Ialz+tObCdeoSdhKtXkxtEiU0EkS4BYqjoui6IJGIv5NSo4YQ4ALzYktak/0+KWUEjmDeMH/o/P1AhI23aD9EUtEyQIJy+nkx5PJKiSaClqFJKw+Su+7M8QErafzShvbTFUFpyl+RZCoEwpal0Z/lJVTVX0TVSZHEA9WNEYaxCVJE0Oeq9OpkYikjspbSnGF9dRalktZbFtl25lUTHxhNZ0VJXEgRiw3vziewtl2W70hSpCFxbE0h7Ei/5UHqbieRY5PVbm5VNLaBSVJnVicPLOoy8oiwryBCuOWijpGq3B1iWgVpUT4tj8QSAKgRnw7MOKF76LCpkYqyz5PJa0d193fTKI/+AK6c/ZrCmITKyaU1p+vJSG/iOLDWX6eFM4+bFELFcfOJwZBtDK5kOr5QiJhJeVml1KrjMnJHgorD9KbLKZj1tP5lnbcpDpik5vGJhX6VvGAogxPafLMkPubCVTcxKemwl1yuuy6HRJp0r+w/iLFvjmVJkSlUTVfQE2VmRQtegjhkighktN1R+cnbb9s8ly8h5aJEpUWqkj+kNwBYubEUrHY1KR1ZO26uEiDbzVQYeJyCnBnfaGBhPw6Kjy4igI0Jc9ycvvTm1r6izYYC7Vtp/s7lFDcQMKmAoqTs0FZ65Ics8H+KEUG+1Hw+iyqF7ZR0x8HKGKG+OFE6m/qdaAU45Iyylg9Xj7eCYspfl4oRWXViQXQEB9Jid9KbVa9rXTECl8KjyugptYyyj57ho50KaZKcFL4Fd6kpHBPUSLAxtRm1lfHrKCU6kaxn4OYCRspr+U2pa54qWMwRGPMUeBDfC1id0fyzASvp7M1rcR2kCmRwaIOvMMXlGHJ+qo6/+mg3Z48t8sn1XeXbI0dQyiiuGUxov6MX5FMEe4MgZlPscXSRwtFAGRifhf1qMR2NfJXGiM746Y5Ngtl5JbkB537Kk1xUjuclelIto9i47qA+LW5tG0R2yd19PmdwSYiCQZMKK07W0V8YSP9kfK5uH8T60qjHXfGjKiRCqJfJEaahwiptSCaQkT95gzakNcgGmysTllBT4lzEo1xUaMcijgo6d+UgiCDg+xgidSmVOtU7mFWNECl4DOy/ZAol1SClRZ8NNmOVI9S+TXEelU4KLmuec0zpx/cRw8Hk/EJJjkOhHvAi3jr+/NolS4fkAxtD8Jwj4Ew4RjCclgIFv/raQAFSL10C0IYwWHmu5jvagboW8HTfxS4uIfqRnZLISHuZkRjyUfpGBwSiOGMPjgmg/Dkwtcx2dkY/Ku/4qv/HoSJmxPsDDngWA6Eq4M5Go6cQvZNZS8uGMPG1QueTpYiwThMP9hx7WDDNKMwKxNXYQKGMRFPuxnBzmkIuGhAXupl3JR9p2KwN7ydGBhyR8BX7nPRgzDctT8MOJZwfdwD7ISsubs7BjP6MBjkAb/B5kBtGSrrBODY8DDan0HGqslwNPdAwOx38X3uPXSCTgJhl38lmPeBk7c3BrPrD4sqUceOAWv1R13A1xyD/YbDycQM3Me9YG8oYWAOh+FDYGegDwvXEfARATIEwwZbgGPAhaefM4BqFFXWg2AIG3dv+DNHsGqSC8zdAzH7rU3IbdVTsQ6S0FSYg6NXGwCmD0zFwOnZOcGbCyAvB5duQoW+FddiSORV98u2xR2DTAxg4jRcTpddt0No0H8dzqxbitlrzTAr2BfWBvowsR2OseOGqBNQ5T2OwwxEzveAIQxg4TkKE7lAQ7WS7eSkdj0cI5qPq/UtKtmP5S+uxpXgaZjk3Accg75wHvMk/CSrEFRKI3tDe3/RBmOt2+ngAY9BfcAxcYC3nA3KyiY5rkHGhk/wUaITQiYOA8PRgwnXHwtXTYGz5ggpIdLxK8WYjR12eHzabExgCpG08ziu8lmfO4qfaycheAS7FIz9UxcfxUV6/OMMP28HmBjaYbhFHr7tUkxVwZxjA48x3mBQi8uXryE3JRE3FszGOGsz2AeGYiGPQcPhWOxLz0FOlgv8XVnD6UrMkfBt6FLsNncfBlcrQ5HuAxa+ipetgIYTubimZncYre1KIpLsb5dsjV2tMxgzI1+CqyEH+hZu8J/IAxrq0dgs2wHJMpA97gU99oi/RBZtYrNs/6y6r9K6n+wqzhJRIYnr+jCwHI5Zi1/BGGV9vrS8zIH5EHi6WsOAY4YBAf/E6y97Ag25OHftThf6Thl6MIWT72iMYN8KOF2AW8IqnNqcCIPJAWAaDmHdz6dRQ9U4f7gQE54ZCjMt/EWbuNkugQSHzv2brITaH6vWqUYacjHSRENx1Xy0th0ph96L9VpkGBYY8do6HLELwsG0IziwZSfWndiJ6LPNyN49D65Kl+4awJRhV9T1g3N/c3DAR23+YcTEnAXGTMST7XuEiZvTiltX8xXWJ+vDkucKSzaxvnkNmQ1AfcpXWPLKVrB9md7Qhfhyqhd8+0szOCk0qg8EuHdX9QZGTL8+mhe1qyau/I6ZN16L3gW7/YeQlpyELXHrcCLuF5zlH8BuUaKjvNqDu0po0ohvb75bzoHZiPmIPjIA+w8eR/KBvYhbdwJx0XngZ//Y/nAl13iC4F49quWuyZww5ugjWseqTacjU6/Lh0ItcFJCVJ3+5+rhUmoBAFslFbt6iSCozUdyzG5k4nFMebJJCwKadK+H+nO5ONGgBaleKaINxt1ppxbCCatw9Qz7Lj/7RCb+41iB5yE56ckvB0au4zDrGScc/mU3Ei9MxOSzmRgc/jF4hpLF6uriY094K6urSe9dialGsON5wIl9jj3xM9ZUDcWCb3jtL2bbjsasV0Zi7fIsxHy7ES5OczHbiu0stNGzotzdj90cEzNYmADMqKFwYlQ9Cd0nu1JshuRcUI385FjEZHIwZooPZFNMSRHNvz3QYy/x1y42a24J1MXJ+R5QmmJoQVZ5EQ4MTPuAAWDl3F/1ezbKKnOMYWZhDDBD4enUB003upObcGDEG4kpngzSkzNwPtcAh0unIfKbQRhy8Xl88UM8jr/YgrO5IxG6sq/oYVN9H62HpnOa5OjNPlwZMH/iNQ220yma9WKs1yJ5vovLyfmweHYx/j3z//DJlwXYsXgaXs6qQA2rE6WW3Yya8iowAWEIe9IOKNmDJaNn48T/peDKc6OAY0kyaLMBeBjcsRtn0y7h1jx3DJD0KeDAwMwc/QDUu/4TkT/NgoP0ngwJrQ4tMORxLzAoQFl5LZoBmRdmrDBitBvsuk1bhQD3riA52wLPLv4YMxevwJeFsVjstwhZ5XdE2x2JFCtoRF2zMSylL9SpoHVfLmuDb286HuHe5VRkWwRh8b9nYPEnX6Bwx1vwe/kqymvYF6gUX2HSg/kQL4xngJ1lFahpJsBMRkkjvOFux6LYve5He0i1wUkJNXX65zigvzNr2ReRlleJea4OKkbfldBVvEQ3EL9kGmafmImUK89hNE4gQbFMp3NNbSK09uOKZjPST+Xg6r0A+Mpi34leTy9okoftR653o51ayKVnC94oF+BwL+hCGTtDHiaFTYbVLz8jeuN/UHDTDeHxdlJ9U8leNfFRGcGeXNMCZ7SgKjcTBabDMJoddVPJjgNT5+EYawXkXTmGyy9/gEDpC4F920fc/3MCh+PPwyd2GGxFrqsNf0WG2sVuNqYr/lFdFUrrfRA6ezTsVebO3fEfRU7anreiJD4Co2fn4v9SkvHcaOBYgirB1NHsDo4svd7ir21sVtcG8T11cVJViqEFWeVFCM01FShjpuLdsNFim1RestNVqkdV6V3wQp/Fk/YmMKjsZm5i5oqnnvcGPk3BxhVl8Hr7W7g+ZoI5i/+B/72xH+uXXYfZ5M+xShxv1edAhHsac6Te7MM7ofLnXtBgO52S516M9Zq9lqpxcc9B5JTfE6385hgYwAB9EDBnHNxMZRIZ3MSFnELUCVpRm7sXP5wdj52bFmG0lR6ayopwkR09zsnAyYyD+GlrMsqlkOvB3PMZ/DPAHrVbVuPDb47gUmk5ykuv4ffyJph5T8WSYCc07PwCKyT3youQe+IcSiXbI0lpqTswgn1AKF51B/JifsVpdgN/uo2swydRzgvDO9Pce30LIrp9EXsSz6NcNB3HgYGhAWDyNOYE8mBKZUj97+sIGf0s/pNZI8JWnfS9c88AZhbs1Gk1rpw7g6wzF1HtNqWX8NVGQj5uXzyIxJxysHkwOPowNNCDScAUBLopXwvAsR+HV171B/L2Y9/pKhDaUJN1HInlvgh/59mub99nYAqLfgxQ/zvOpWfiTO5N0YOUeuk53bJDtfrn9Ifv1CDwcAVbPvgQn23bjbjo/+KrmPPyotnf11EAACAASURBVHCs4eTDLsg5jZjNe5HK+k90ovyep023cO1iBVCfj4yTqUj+KQYJHQ4mT096pqlNgJHHM1gQ4gRkrMO7y75FXPw2fLN+Ny4qy1KkdLt7oEkeArrVTm3ksYTn5GAEMKwuPsE3KXkoLS9H6e+FKGcNVRsdqGVjCO74GXjNHbiyaT+qQidihPRBhDTER5awot9eQGmzAWyc3OCOcqTHbMOu1DQc+ukn7C1UPbvWLqJmnIVFu/Da2Kcw7tnVSC5X3/FybIdh/CQXgAnGW6FeMo+/HSPugDtGu0u2qNPMvzOUXYvd9TmZyCq7B2q+gcPRSTD+bD0iZwwRb1WqBMua8m74T2cptbtyD2XXitCASuRkpCEjeQe2JrAzUF396w6OLA8t+GsZI3srNquNk12FRWn5epRcuICrda0Q1OYg9od8PL/za7w+2kb6AKu0GnuxPh+ns26imRpRcng7dhq/ia2R0+BsqKdFn6DE1kQdX1+4PeELK+ThlMEkzBvH+oY5PCY9h2eYUqQe0Mfkp4eI8xFNeoYWcqhs3X28IfNwd+Uc0rPOIre0sdf5dd12NMT6Lkio/8knn3yivrwQLXfOYUfkl4g+ehSJu35D07g3serVpzDAWE+UgOZs34rEQgFMKRubVm7Hlccm4cNP52LUY6bgsNsx2XDhYFqDvPizqOE9jdAn9JC06xAK7+qBO/wJ+Di7YcwEfziZ/YFTmz5GxNbTqOLbwGeMNwZY2MF70j/gZ1ON9O2ReCNiB7Kr2mDrPQojna3RaetjqsGlwwmIj9+PY/m3oGdqDUsDY1i7DERfC2c8OcUPdtW/4qvPtyP1t3Rc7TcNUf9dgslOZhCUnsHevQk4xneEj/AW7uoxsHF0gq3+Hzi9dy/27D2C3BoOLB0dMLhPBVL27cEvv11Dq5EdHF3d4TmIjwsiLFph6egIV7cBMLoSi8gvtuLo8STsOt6EcSuX4dWnB8Go6iS+mPUmfhm+AhvffRI2SraLo7pLOLwnHnuvWsBnwF3U6FthoL0eCn/dJyOLI9w8XGDTmIvt3yaiUM8ajs48ePD6K1mGYgwbO0voVZzDzk2n0TbueUz3G4aRKvE1Q8WZJOzdcxL8IY4QFt+FHmMDRxdzVImuJ+JIbjn0LAfAebAZqlP24edffsONVgZ2js5w9xwAwYUEfJuY317GzR0uFvdwfscafBF9EMcTE3C8yR8rV83F0wNYW1HyxzGHy5NPw9+uDAe/+grbU08h9ao1Xoz6FG9NdoYJ1OhbCaYwtIKdHQcVl/dh0wnCuFkB6Hf1MPbukWmLmzt4No04L6NLtxH+CJo2QXs7ZJsibMad8zuU6t+Yow9z3mhM9Gax3IUtZ/Uxas4izB6Uj+8SS+AS8gpe9rEBh2MG+2EecDK9hbQ9qSiz9MOc4AE48+P+Dl17uGGIgxEq8g7hdI0jAkNHwjhpF9IL6yHgeuCJfqX4VZldMxp8S98Gw58eJeL924YkFLs/j6XzPFG65Wf8Vi/RsT36KuLML+2Wv2jE2MgagzS2cy/2HjmPGqkfWKPxvLwN8mwVbU0PpvYjMSGQB7NbJ7DpnVXYml0Ofj9PjPEdCDONOhgCnkmRcozF2+NxTK3B3DmF6JynsWb9HAztIxm30BwfvQdYwVbRb737w9zeHSOdzHA77QBSyyzgO2ciHM/sQ2Jhe/xx4xm2x4pjdRji04biu3pgbOzhwnWEj0qfZ2NqM6p+z8Vtjxfw6rQRMttjKvNPQ7T9cQIxfWbiv6/6oK+sE+v3RT/OJWy64o0P3w/EIMkyFYP+XYvp7HN2n8FqYncfcNCGO5fScWPg4/DhXMbeVR/i20wjjHxtGd4PHoq+ehLBlMTAJ1zhpNKu3OBhdBkH9h7AVUt3DKi5A31rLuyNWH13x9aMYTPIFqYV2Yg/fRe8wMl4wjgLu9ILcFfQD8OfHIEBphLbEOMt8aeu6lEg9kNRPSFutZjBzn4ovD0GqOdvYS0fI2eOhlH2AcTvzYeljxVqavRgPdAJLv37q4/NEv7SflNFX+VijhalcXIg9G6yfbImnHmwrUpHfLysjgbA2cVK7PvX0Ne0Eec2RWHzFRtM/vAjLBw1AMYSk1Bi1nTnMo7deAz+PoQrez/Da9/mwGLkK/j3+8/Bra94LkajHSuxNW9bGEAPZpYCFEdnwvGDlXh1hJUoT9K3toNVVSpi9KbjP++OhZ0krmriY6jOnyR9uIb+zcMFtgpbefY0/zC37Q87vWpc3rkTJ9r88PzIFpxM3Nc5vzKua8/ZZO3LloOqU8mI77btDILRHSX5k7MzHHh+amK9EmNQcYnDvkSo4p52l4VXsHlyIBYcHovogm2Y76pp8bd2ZB/tUoR7p/+DUUGZeDVtK173krw49Gi3Wtc6TQg04/fNYXBbkIYJ0cdwcL67aI2/plq6+zoEdAjoENAhoIiALp4qIqI77z0EFB5xe4+wjpIaBKgKp/cdge2H7+Cf0jfu1ZTX3dIhoENAh4AOAR0COgR0COgQeCgQUP0uyEMh3iMqRNNdGD6zFtvHecJKzdTRI9p6XbN0COgQ0CGgQ0CHgA4BHQJ/WQR6NvLMrsXadwiZJexLKjeQmfwrTpfel7eJ/rIAKxXcbAjGBY0AV2GNkdKyuot/EwTaUHfpOJIzb7BvqaAk8xD2nS4V7cryNwFA10wdAjoEdAj0EgLNKD39qy6e9hKaOjKdEej5mufONHVXdAjoENAhoENAh4AOAR0COgR0CDySCPRs5PmRhETXKB0COgR0COgQ0CGgQ0CHgA4BHQLKEXgIkmeCoFHJZ4SVy6u7qkOg6whQGwRtPdtUputMH+YaAjQ2tDygvcXvEw5d1qkQzQ33INAozoPEhiAQtGmUSFfg74qAzj7+rprXtfvhR+BPS56pLh8HNq9HZMQcjB4aifT6+/iJZWpFc4tm+lR1Ep+HjEPI5ydR1Yu5Vk/p9rT+fTFDuoVTn8/EyJA1OFWlOSXpugxCtDS39jDBa0F5xg8IH2UPh2XHcbfrQmioIURzeTb2bfw3Xp89E7NfeQWvzJyIgJCliNz8K3KrZL58yC9FxvbVmO1qDg7HHEMCXsArr7yEZ0cOAGdIIF5ZuQ2ny2XKa+Dc9dvsmuqD2Lw+EhEzx2Dop79B0+c0us6jd2qot/eu6JTAL83Ajo1rsDJ8MjxnxKJIaRh40NgQBOW/YWP4U7ByWIFjd5UK1TtgaktFyxipLTm15e577FDL/S9w8yG0j78AajoRdQg8SAT+tOSZYzkMU1/wxN2YOGTfj9xLhGIzSk9tw+q50/H2kXINiRiBX3kFJ46l4diJK6js0tcL1amsp3R7Wl+dbD24x69E/onTyD52GvmVvZn0sQnPKWxevQCBbx/u/kMM3UH+z+9j7q4+WPBjArY+7wLTHjS3c9UWlKd8himuryKBPx7v/RSL2K1bsXXXr0j6eiJaYsLh/eRSbM6/0253hvbwfykcrz3vBsAcLv9cjS1bt2P/6d8QH3QX2z5dgnnr0lDTiw9t8jLrw9JjIl7wbETM7rNajMDK135wZ2rsvcs65cDQ3h+zA61x5vvD8l9llGvQg8SmDQ35O7B0bgLMF3yDY1tD4Cz3pVY5wR7ASVdiZC+Jc99iRy/J96eSedjs408FQ8dch8DDiwD7kZQ/7e9OCkVwQeB+SCl32u6DGFWUEuFLgC9FpFRpQb+VaouuUFFtqxZlu1Kkp3R7Wr8rsmpbVkj82uuUX1RDfG2raFWuje6kfEhcgLgRKXRHqzqKhQRUnbKc3MGlCdGXqfctS0iN59dTEANiQqKpoFWoIICEPwjuyymlWiC+L7FHWbk62svMiaViRVIKlHt22sGr+9j2TALtaiuzdwmmsthpR62tIJomAIQJ0VSg0hgeDDbC6qP0vjujQRbt2tU7pSQ2qW2M7A2u9yt29IZsfy6Nh88+/lw8dNx1CDysCHRxn2cBGm5Xo9mkH2wYharUjNvFdTBx7AfBjcsovNsHjm6DYXNft2MjCBqqcLPWAIPsrSGSiJpRV1EHAWMDG0bhoYVdJynUgwH72UtBA8qv18GU24KchOOo9Z2J6R4WsHRyBBVXoJoZKPNZWiGab5eh1oQLW0Ep8gvvwszRFUNsTKSflKaGIqQdSMbRjGzcqDWC3fB/4MWF0+BlqQ/AUAVdVj4hmutuo1ZgBlsbpr0NCmKrrq9OLlZXt1EvHUE3grmtNUyaa1BV38p+8BaG5ixGEj2yWNagqtlYiRwCNJSXotbUEoKcg9hf640F0z1gZukAZypDebUZ7PsZy0itjhZAzbdRXGsCR1s+buRfx10ze7gNsVXyOXGWJLvuTwgD/UZcTzuE5KO/IfPGHRjbeSLwxXkI9bKW6qBDAD5u3yjAFQAOHRdFR9T8B84lH8ChjBwUVBrDaVQgps+YCC9bGflV2EYHqRpkx+/CkQYuJgSPwRDJZ4elBfRhPXoKXvZci+V5+7A7PRwBzw5UIidbQYjme/fQDCc884/h4Krd97sNDdczcCA5BRmZRag15mJ44BwsDPWCpagei3sFbtYzcOQyYn6s7spQbz4QXEaROB9111X7qmo9ievVGKC/myvspTYkAaCn+lfmLz3UqUS0Lv6q92sFYnQP5eeOIPFQOnIKbsPEyQ/jp0/Hs179pX5Nt4uRc6Whs2EqkNL6lLXVmw0wd7RDu3qV2QBLTb1OpPxkY6T0orIDlt4tXK81BldwAQn778B3QTA8zDha+DcHBkpih1a+yfqLhlgsL20XfMZOD7cuF6AMtnBzHQjGQNFf1PR/IqbaxHJ56RTPVNsHu0QsB8mJh5GR8zsqTZwwanwIZjzrBVupnN3RiSpf1oSbouS6cx0CfzMEtMrqhXeo6Fg0RUx1ZyeVCcxYCt+WS/VCIbUU7Kc1K5ZQsC+XELCMNq2dRzy2DEBMQCSdrJQdlxRQfdFxio4IIRfwKODlGfQUo2HkmV9NBSnRtGJRGIUGBFFoxEY6VHiHhNRABYmRFObHJTBTKTK9ioTEp8qTn1HI3ChKyi+jP06up7nsfbE84H5ABy8cpy1rl7XXGx9OEWE+opHp9+KOUMKGSHqDbaNkJLylgJLWrKClwb7EYDKt2BRFYTxGjMFk+vhkOYkGClt/p9h5fuS/+iRV84UkbLpCMfM/oKQKPglrL3amKwK9jZpKTomxYPFiyHN1OjUqKERpfW3kEtZTceoGmiuS15cWRadTSX0r1ZdkUmxEAPHC1lNKEYujrE5YObjkFx5DefUCotZiSt3yNS0PG0MMgmhpxEsi3XLf20GnEjZS5BvB5CI3qq+GFquvpPW0Yuk08mW4FLDif7RWhD3L054CPj5OlUIh8ctO0Lq5LL92G2qfNSimwtjFxPP/jFKrW4mEDXQt5i1aknSzHX85zNqoqew0RYf7iTB1GT+DwsLm0dvx16itKZ+2zfUhJmgNpVe3EL86jaKC7Am8Nyi+uIlaS1KV2kanWYuWHFo3xkr9jIbwJiWFexJgRWPW5VCLSEbJKJ9k9LSNmooP0sqgIFq0IY3K+OqGnYXUWhhL83iTaHVqBfGpjZqubaf5S5KoQthEJakxtHZ5GPkxYtrCajoft06su1CKLmgiIpnR1aUbaXfkDHKR+KrfUtqWV9fuV7J6+vRH+m4u6yOsPnxobvRxSt/5Ho1n/baTj/dU/6TCX7qvUxZ2lSPPsnHNJYheDh0rsjvpqLwav5YzOdFJPRVsW0Q8JoSi0iuIz6+g9KgQYuBL4fFFotkZYdNNOhu9hNxZLF3GU2hYGIW9HU9FKkbD2fJZ8WsoPIBHjO8sili/i37d8RVtPF0jb6uiEXUB1Z7fI28DIrnU6aSZyjrFSPEsoMq4K29r45e+1R4Tua9S1E9fafBvIhJWU56y2KHBN0mbmNdJKRp8Jj2OvlvR7jNBX26ln8Lb9c/GYt6sdZQu6btk7YTVnbT/kzBUE8tV4iip2/Gr2j6E1FQQQ3N5ThQUlUbV/BaqTl9DQQxDvPB4Kubfk/N/lTrR2pfV4dYhr+5Ih8DfGQFo1XhhEcUtixFNT/MrkimCnXZk5lNscXtKIO2c3N+hhOIGEjYVUFw4u1zCk8KlCU4DFSYupwD3pRRX2EBCfh0VHlxFAeqSZ2E5nfx4MlmJp8YlU1pM0Ho638gmGkJqLYimEHb6POgrSr+4ixaHRFF6jeI0ufyUpFReHitLPbWW5VJWSRORsmUkbZcpegKbgPvTmwnXqEnYQIVxS0VJpFU4m7gQCYtjaQ5jRf4rD1JxPfuwwKeq3FwqkUznd6LbTGUpX1AwbxatP19LQmEj/bF/Oc1QtcSgU302I9AsF1EtZaweT4ALzYktak80hcUUPy+UorLqxKpvoeK4KIouaCTi36TkiDHy5aV8fCk8roCaWssoO6uU/r+9c4Gqqkof+O9cL8jjgrx0QEQuIHDFF2gqWEramM/IHk7ZTDVZ9s+/U2NT00yPKbNxyjQLq2XThKb5REFFDRTzgSgKIpLvEFJ0uCqCBQgIyJl1kIv3XrhwYWAtY/Zdi3XPOfecb3/79+3v298+Z+9DlWxIBI3ZtiBLrpDPxEytS2p1szfK5yuq5YrcWPkFJcF3/WPdYMMkwTNM26jNk9dOC5CJmCMnnf/5ViJSeELOVGzW6FMpF545KMf9bWzdQGBsdKr87wK9XFhaIV9Jek0ONElmb+tjGLhYbBvG5RjsYTJwMD5B2TbwMZ5+YjjmJd//+Tp51cyxcoDSUT+zVs41tBVzMQ37N+Tza6fXDWLeTsqVS5VEu/aKnJ2p2EL5GOpiSMyN20jj5FkTtVjOKK6SayvOy9/Ni6pLGm9PGzHI0si62Vvkf1fXyD9nfFw3TQXN1FtttjpPjmvk4+1hf7kJP2wnmxpP26jIkRP+MkHWvRAr51bUyNWlOXLi2xNMkucW/brBNoopEuXZSjsesVg+euPWIKihLfX/h5x2/aZcXfiDnBH3NzlCScDGRstp/y6QCwpLm5j2VCOXnlgrzx499VYiXlshXzkcUz8QNtiyqUGBwW5GbUBuySaGNmnkxy3GXUM5SvKm8LsuF2QelfOrbh+37N8KNPMyq63yTetinpFRlLpb5TNKO1fiUY1cfS1bXvF/St9ldDOj2f6vmVjeIkdjXWstt4/aAjlptnIzYJIcfbT01kUNcfle+e9p14z8vzmbWOvLLXEz1ltsCwL/mwSsWzAo+fGbeb8lyEaii3MwEeMCoayU65Vmq8R7hxDSyxHJrjehQ/2BIvKulN66RZW/lbee+Duno6Yw3t8RSd0N/xF3M9TJ0q1+meqcb1n0USJ2wVo8bSQkF2+CejtRlryPzIvKIjUJm6BHeXfeFEh+jyenH+LXi/9AhKsyVcKKj18ooVoNNl4DGeJj18IFvRgQ4o2d5Ig2NBQ/4FreFX6SQfIIJDxCQ9rcCfg6hTD68Vf5Z3Y5DU/TzCWXHGLJrPdI8LufcQNckCQHvO5+hrkT/LDOIMYCLesF3Rg85XHu1+SyZc1ucqoVpjv55tp4ogY61wuxpfdvXmV6kAN0caV/xHC8KKfouvmrzPwZGtobOxsvBg/phY2xCg3b1spyovcAHb3s1NhpBzDUzwmuFXDlJwsrRyV3dOED0KTNYbyvN7rRT/DyP49S1STgrngEDaK/1qVOK0njjqeXJx6aSnIPp5ODHRqNXf1jdFs8tX3woozjKae4aNycm2sbanuc3ZU5QTcoKTfn1ACjfsMVP283GrUuuxDGPTmW3poycpYtYOH2i3V+ouRV1T/u4NOFC1lo+PtyH3rZBg9dKBGaZOaOD8BJN4bHX/6K7CqVhekg5nqY7jvp+hHkalPnq6Ofm8HvXKFsTzZnTd56o9ipD57qLjgHDSRM8VWnPvTzc0ZSe9HfzMehg+xPO9m0AUEV+Zvf54n5V4iaOhp/uy6oNf6MiAzFOBxZ79cyFblZ7MwpA40j9vXtUuWpJdQLOJ7FyYtVqD0CGdxfe6sMSYObpxdeTU3VKk8n+rHn+MRmPFHDe6CW7OgeNoKRip+0+mOtTQyCrYm7hnOd8Bs6AK2dA16DB+HTEBRa6d+Utc43aS7mGXRTvq31GYO+XVC7DOCxmU8zwjgmNNf/WYzlWm622H8Z6ypZbh8V5zi88xTggMa+fpqdygNtaE/gDCknL3E7dDVnE2t92VpuxvqLbUHgf4uAYcJr87WuKeJE0lpWpkuMmBhG69+tUEvp2Wz2lDVfjOmvMhUXz5JeBqXfLWLW08vrEktV3+f4cNIghvQwRGpnBv7uD8xaspP5py5ypdRCAmYqvH33HEJ5PiYWz63bSU3awrJ10exZt5mM6m2snx7SKNGsvXSWQ2bzHiUXf0Ju5XvtqJuEbdBIHrtPy47N60n4fhwTMtLxe+EdAhvm6VZz7cQOVq7MgBHjuPuG8jS+rZ/2lGWsgzMDn48m2XMsianJbFu2hug9a4jJqCRz/TN1gzrjs5verqG8xPLL2TTujhbmXDchzb43g+7RwvFzpGbnUzHZGwfz06oucjw1DxjExGFabM1/R41r+DPMe30v97+5jSV//pJHR8xhjFspmavf56W39tRf4cqI6F28JEnYDpxOTHJPtibuJmlbPOui97Au5jjVmf9ielDrh10GlSQ7B5ztQDO8L1pN2+VAR9nfoKn5d1ttWsLZI9m0GI6s9muZmvJSiszVM+xrnHBsxdqP2ounSDleBkpu9F9/WmsTa+Ju9X+tlakAK+3Y6tAk4dBqn5FQ2zuiDI1d/XvcWkvQTP9nOZbXUnLKmv7LlESTezUVlBRZaq0OuDt2bdMAusmy6g62xK1RtLMsSvwiCHRSAlb0lFXkx71G+APLqL33NzwQHkj3rlZcZgJMws7dq+5urX5fFjnl1kRBCbWDE+6KnKAnmff1cpYvX86yT+by55ceqV+Ip/xYzo/JyRRHTkJXto1FH20jr2GRnIkSHbdTfpqkTGcmz3yHxZvTKTy7it+7XiVX/zNNdTMqzz4M12kg4zDHLzV1RjuqahPI+Kcm4EoqMV98wCebg/ntSM+GYCvnxzMrfDLv147i6QeG06d721/o1p6yTAmUcCrpBM6TZ/Lu4o1kFJ5m5e91lOVepthqfM70GTwIDaUU6K9RaVKAKwPDg/E0Xx9kco7RjuTJiKlT0Cl3p1Z+y8Fi8390IVN+ah9bv7+GJmoaU0K7GV1stCl5EP7cH5ihtIXTy/lg6WFKZBfC39ytTKeq/ytm/0uh2KLITCHTeSwz3/2MzRk5nF05A9eyAvTFygLQtn/knwq5UBrG1MfD8WmtaxsV23H2NyrEZLOtNrXD3dsTyGPfkR8pN5FptGO1X6tw6jOIe5WMq+AyxZVm8W1gKDpPw2DfSL6FTcmlB/6utEt8aL1NrI27FpRv0+G22rGlwtriMzKVxZcp0Ezi1afC6S413/9ZjuXtyNHJj8H3BgCF6ItNIxfoCNd1b4jnLRGx7veWuN2gMHsfqT8U38GvvLSupuIsQaCtBKzoKsspOJtHGVfISkslLWk1yzeeaWV5ErYh9/Hsg1pIi+bVNz5jXdwKPl28nmPmsaBBsoRD6CRmRWkpWzOfv32azMkLevT6PLL3HOFCXYJ8k7Ls5by1dxhvLf6QBTOD6x6BL9hyrt6p1Tg4K486izh95BCHD33PBfOOraG8tm/IV4+xIeEo+rppLBJqGzXYRTJtTGDT7xZ2CmHCk5Forn3DX1//gu9O5qPX5/PDD5fMkrq263T7Shu87n2E53Vw+qutFE4dx0AHQ5YoU1GQxzHl7n5WGnvTEvl6eRL62xe3Yqu9ZN3udEpPH+HA4Qyy889xbEMiWfryuqkNklqNGkdGTxtJsNXvyLXFZ/RUZui4nfDKVzm8Yy/6wKd4ZYquibvDlqrfBbfRL7Ny8TQCTn/CrDfXcvyaIYu/SVneNj54eQFpQ99j0xdP08/OwLuxPKnHffx5wQwCuUDyux+z+qSlO0zVXD2WSEKWnromLHXBRq3CbvRExgQrbdwGD20wOvQcWLmC2JRUtn/9NfG5Td9tL81K53BBOXLlOXbEbKHrPxYz75E+jZ6SNNbY0pH2sr8l+U0db6tNHQkZ/zAPaq6R9u6bvLFkDXHffM7i2CwT/2uNX0s+I3l6RgQc38qmg4XI3KT48G4S9EN44ZXJ9LO13AbMayZ1H8Skx4eAEh/+NJ8VcWuJef8TVprZUvLwJUwZeB1Yz9LY3aRtX0VM/DEjcdbYxDxGHqMoeGILcdeoiHbZbKsdWyq8JZ8xXF9K/vffk/NTFTXXslj75QkeWvMxL4V7INFC/2cxll9G1WL/ZSi/hW/Jh9FPP4qOw6zclFn3Lni5OJsdCXkEvjCdKf0cWxDQ2p+b51abF8vz94xi5OS/k6Q3xL3WliHOFwR+2QS6zJkzZ07zVeiKR6/u2F/OJO5gCYFjJjCs62FiD5yhpMad4F7XOZi4ifjkoxSr3PD1DyQk0I3rRzfyWcIJVC498Q/WEejpw8DI4WjtL7F/yRbO6x7ixWf6c2HZN+wv1eDp64+uvw/dlNfIGT7qHoSO/zVDPYo4sGoef3xtNZmFN+keOpy7/B24tGsxL76Sz28/n8VQF1f8+rpwMXEZX+3IQdV/JJF+3enu6YLq8hHWfHWQmyOnMNk9l4T4jeyq9iWs9hIlKg0evlo8Kk+zY0Mc8TnOhPUsobiLK94+KnK/3cSG+GSyiyVcfH0JDgnA43o2qz5LINdQ3wAnbhxdzbz5y9m5ewuxuysY+fYbzIjshe3PJxvL9Q9h8OgxjNHacmlfDK+8toLMwmrcw4YzpKejyV0E+acmrrdWr8AedVMRJHs3ND/vIyYrkoWLp9HX0TBmkrDx8KK3fTHH4zIoDoxk6jAVW2K3k1uiwiu4B5UHtxO36yf6hN3kfIkKjYcPAR4VnNqxkbj4E7iEuVJcrMLN2w9dX3/Lsgb0xz1/F/EbR1HS6gAABUJJREFUEkjO1t9uFx7XObpqOQm5VfV8+9Cz16/wVBVxas0a9twcxmMPD0RzPYvV8z4kZudOEmL3UzFyNnNnjKKn+VMQuZiTim5xW9l14hIqezdc1F1xC/Cmm7M/d08cimfRtyx6fxUp+w+Q4z6FBR/NYoLWgZoLh4hvom10b+qRu2RPz2HjeWh8PzTnEln0ynw2pKeSuHwpa45W0X/qX/nknWkMdq+/41h+kvjoz/l6VRIni4u5XFKDXNWNwMF+eAUE4V2YSuyBZPZmXMI2eCgRvk4m7UBxidobRRxdvZD5MYnsTtjI7ooI3p77eyJ72iOhwt5Hx11aB66mbiOlwJkh08bhe2iTEVsttnkHOec9mDDpFPFzX+ezdFvuev4N/hLVl24qxfcquXBwi6md/Bwo+m4T32zez7kqg6/2pOZ7Yx/vS0g72D/Iq5KsbRtN/dDPmcKUze1g02JuOPTAJ6gXrj36EakMbq+msCS+AN3Dz/PMoMssW5FKqa0nvkE6+nvbUmrBr7saham6cCU5EXB3JBGeBSQuWsSqlH2k5LjxxIL3eHmCP3aS8l8Mv2N93EYSdh2jWKXB08UGWzdfenUzmz0ndSMwchShjlc4tCyWDPVgpv3pEXrt20BCbm8efPEhwtzVSPbe9LvLF/ur+9mQosdlSBRRvjn8qyHutmSTYYT2dDWLkQ/x8NB+3NVM3L18SGkfe6nu40vt+RJUGg98A5worDvegn/3db1lS5PYoSVAG8I9Fn3TEan6Agfj41uOxfUxz9CFNO8zNRRlKW34LN3sr3PkqwUsPe3BhNff5LnhPbll4+b7vwF3hzNsjIVY3tuPMIsc3TAdTzXXPmxxDBjGxAgPihI/5f1Vu9ifkof7E3P56OX70dpV1fusFTaxypd1BDiXNxNrKin8IZurIY8yY8pAo1e6GqiLb0Gg8xOQlHWSnb+aooaCQEcRUN6HupeV0dGs+9GHUeNHETkigmH9ejXxntiO0kHI7fQEak+zdMIYnt1xDzFnVjA9qNES1E6PoP0rWMkPS58i+NlU7o/ZReJ0XRsWbLe/VkKiICAI3PkEzG553PkKCw0FgTuHQA2FqatZe9GL0KhnmX7mCPvXv8V9/68n4N6HeWTSKMJ+VY6+x4PMHte70Z3kO6ceQhNBQBAQBAQBQUAQsJaASJ6tJSXOEwQaEVDT/Z6neLH++MgxUTw58y0W6vM4c+o42ccvowp6mJnDLP13wUYCxQFBQBAQBAQBQUAQuMMJiOT5DjeQUO+XRkCNxiuIIcrfmF+a7kLfO5JA3Tz+ZNLzlcWf50hP+pYQ+4mEt/hu+juyNneIUsrc/m9JSj8HlJKfvp1NIY48EO7zXyyavUOqJtQQBASBDicg5jx3OGJRgCAgCAgCgoAgIAgIAoJAZyFgeO1CZ6mPqIcgIAgIAoKAICAICAKCgCDQYQRE8txhaIVgQUAQEAQEAUFAEBAEBIHORkAkz53NoqI+goAgIAgIAoKAICAICAIdRkAkzx2GVggWBAQBQUAQEAQEAUFAEOhsBETy3NksKuojCAgCgoAgIAgIAoKAINBhBETy3GFohWBBQBAQBAQBQUAQEAQEgc5GQCTPnc2ioj6CgCAgCAgCgoAgIAgIAh1GQCTPHYZWCBYEBAFBQBAQBAQBQUAQ6GwERPLc2Swq6iMICAKCgCAgCAgCgoAg0GEERPLcYWiFYEFAEBAEBAFBQBAQBASBzkZAJM+dzaKiPoKAICAICAKCgCAgCAgCHUZAJM8dhlYIFgQEAUFAEBAEBAFBQBDobAT+AzrQBcHlYHepAAAAAElFTkSuQmCC)
References
- [1] Al-Solamy, F., Chen, B.-Y. and Deshmukh, S., Two optimal inequalities for anti-holomorphic submanifolds and their applications,
Taiwanese J. Math. 18 (2014), no.1, 199-217.
- [2] Bejancu, A., QR-submanifolds of quaternion Kaehler manifolds, Chinese J. Math. 14 (1986), no. 2, 81-94.
- [3] Chen, B.-Y., CR-submanifolds of a Kaehler manifold, J. Diff. Geom. 16 (1981), 305-323.
- [4] Chen, B.-Y., An optimal inequality for CR-warped products in complex space forms involving CR δ--invariant, Internat. J. Math. 23 (2012),
no. 3, 1250045 (17 pages).
- [5] Macsim, G. and Mihai, A., An inequality on quaternionic CR-submanifolds, Ann. Univ. Ovidius Constan¸ta, XXVI (2018), no. 3, to appear.
- [6] Nash, J. F., The imbedding problem for Riemannian manifolds, Ann. of Math. 63 (1956), 20-63.
- [7] Oprea, T., Optimizations on Riemannian submanifolds, Analele Univ. Buc. LIV 1 (2005), 127-136.
- [8] Sahin, B., On QR-submanifolds of a quaternionic space forms, Turkish J. Math. 25 (2001), 413-425.
Year 2018,
, 8 - 17, 30.11.2018
Gabriel Macsim
Adela Mihai
References
- [1] Al-Solamy, F., Chen, B.-Y. and Deshmukh, S., Two optimal inequalities for anti-holomorphic submanifolds and their applications,
Taiwanese J. Math. 18 (2014), no.1, 199-217.
- [2] Bejancu, A., QR-submanifolds of quaternion Kaehler manifolds, Chinese J. Math. 14 (1986), no. 2, 81-94.
- [3] Chen, B.-Y., CR-submanifolds of a Kaehler manifold, J. Diff. Geom. 16 (1981), 305-323.
- [4] Chen, B.-Y., An optimal inequality for CR-warped products in complex space forms involving CR δ--invariant, Internat. J. Math. 23 (2012),
no. 3, 1250045 (17 pages).
- [5] Macsim, G. and Mihai, A., An inequality on quaternionic CR-submanifolds, Ann. Univ. Ovidius Constan¸ta, XXVI (2018), no. 3, to appear.
- [6] Nash, J. F., The imbedding problem for Riemannian manifolds, Ann. of Math. 63 (1956), 20-63.
- [7] Oprea, T., Optimizations on Riemannian submanifolds, Analele Univ. Buc. LIV 1 (2005), 127-136.
- [8] Sahin, B., On QR-submanifolds of a quaternionic space forms, Turkish J. Math. 25 (2001), 413-425.
There are 8 citations in total.