Problem 52859. Easy Sequences 35: Cutting a donut to Semi-prime pieces

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The figure below illustrates how a torus (donut shape) can be cut in </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>13</w:t></w:r></w:customXml><w:r><w:t> pieces with only </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>3</w:t></w:r></w:customXml><w:r><w:t> cuts:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"248\"/><w:attr w:name=\"width\" w:val=\"339\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>In fact, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>13</w:t></w:r></w:customXml><w:r><w:t> is the maximum number of pieces a torus can be sliced with </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>3</w:t></w:r></w:customXml><w:r><w:t> cuts.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Wikipedia's article on </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Torus\"><w:r><w:t>Torus</w:t></w:r></w:hyperlink><w:r><w:t>, gives an amazing formula for calculating the maximum number of pieces using </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> number of cuts on a single Torus:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>C(n)\\ = \\ \\frac{n^3+3n^2+8n}{6}</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Therefore for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n = 3</w:t></w:r></w:customXml><w:r><w:t>: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>C(3) = 1/6\\times (3^3+3\\times 3^2+8\\times 3) = 13</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Given a cutting limit </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, write a function to find all positive integers </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n\\le x</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, such that </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>C(n)</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> is a semi-prime.</w:t></w:r><w:r><w:t> A semi-prime is a positive integer that has only </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>2</w:t></w:r></w:customXml><w:r><w:t> and exactly </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>2</w:t></w:r></w:customXml><w:r><w:t> prime factors. A few example of semi-primes are: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{4,6,9,10,14,15,21,...\\}</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>As an example for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x=20</w:t></w:r></w:customXml><w:r><w:t>, the only semi-prime </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>C(n)</w:t></w:r></w:customXml><w:r><w:t>'s are </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>C(2) = 6, \\ C(6)=62,\\ C(7)=91,\\ C(15)=695</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>C(19)=1349</w:t></w:r></w:customXml><w:r><w:t>, therefore the function output should be </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" 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FFLK2ils4RXPIaEBGbCXoUcK1b1iogxoHby0BYk00KzKhfgv3ccPYZZwYfFQIgbSYSrK4huiWfFOYdv53Rc0oQIhRVpaHi9aXSS33Hv7VfpmEbPZ4TZ2nEs92fSmhZAylOL7oZ3yGjDe2QYHYjir1UTCHj/EHjgkUkPEFZAAJP1fEOhMyISTCQn9xIc4jfi7njUXoZRGVPPsYkEBoi2S4EqxnkRgXZpzTMNgG/4w52YCDk5HX+G7vyHhXZIK6iIlYppHI1YVAIWvGJCoOMmCYUY4ntojXmGoCqF4LdJPhV5RemJQnYTuLN5SO2D5eKXSY1TXXtI4ZhGrHVWQw9xx395T0+FFGdVz6dpFCEYnbJjfUxmOWZ2Zow1nohIYc9pZamJAusVr/ZIkZhH9yGXJqhJSGxYRZmG7/GGA2aX5V95cfKZlA8YkdtCtO2Yeo2VmnFE+LSVjx6IMeaWJlVpI9M0GeQ1WYZG8NlpkhgUNkeZaaGF8c04PvB5J7SJoNJ5Vtp4tyVy4lJza3ARhXxRcfBJnzRFbPJJNTWVTed5t1iZYlAVdQKXRlgy2a05QnkPlrmGmWieiQAah0hSNoE4l2O6l2PJGe1nU/0TV5kvgu1QdMXPk0uJEhtPEuWkJ57Pd8jmhN/TaWjBmaCmmeJMGCfUl0K9RJo7OKg/WbwZRxGeQygbmHzBlMpzRmebih19ea+5miSwZA+4JzwORB8+ERuwSj6AWdRehYb+JaFcqHKHOYD6mPPtla6AEiK2JhulmE/8FJdhuBQ6r5aIjIEM/3nkq1kNGVFkmqbhE1Vvm5cOLjfPiJMqYpbq+5d4mJcWw1Sk3pmEbakW+aitijPYTZTfskopdJnxpxSzd5Yj5ZR4V3Wy5aYFhEVd2JRirVVwbqnH5FnnAKdOJFqNl0RsqJZXnlmO81ptxXp0bhO1sjn1D6oSYhYGynlsrXRqSqqEZ1bLflqaeZqHv3V6mqZ16ZMoKxho95Ec/XVwIIePiTp+wGNlkno+WCpId6O3KJZJe5p1JKfnR5dGU2n4MjqyhKlvLCoxjxqIy4lAOKftiHQheKrCIoh68naEy0UpwVU3sZkzGqceCaFDMFnuQWnxa5gf/uNo1Elptv2KaIWTdaOqs3maVHZoq+qniruKK+Ok+mNWqgSq6bqWVy0qqe2ZkocaP+OZTPOE1/lq8UajkWapyCWa7xep8waRJpRZismqqZx0DVCBKheBEddxE7Skb6+npy8q4wK6lQ5qdJoTDEep+78pIjganuxqpBt4DIOHTzObS0RqLy2LGbiLHjyrMc5YoWobEwBrHeeEbEOlpYS3sYCprU1xa7eqVsiFlGKxLolH/fx0+ZqntY5IjbeKoG+Knmin1VqoJ9y39721l5d2XktW+oqrPGmqyvKnOCtqznmV0D60bNJJzBFLFOAy/F6VgV+6QFVK2TerIJ44B6pZb/SftWFltFf8sQM9uzE3tWk+dmUltGF5O6v/aZJTGNjvtdsetV+JqWR3k4OztfQpue3up9/cm5MYaw+gm1oQZPOIZ0bqu1IdSEXtU0u6pYa3mIiNqnlgtb86oWhxta0LqxATe3ivpeD9uUyJtya6pU/Rm5WAZknMVyJ/iFKwZXtNu8iTu93dtwsJi2D2icFjuS3+u9/ZsUQtp0GSVJaWm6A6urrchv6+tYAGuUBBm9WzO2RFqBOyUnHAwu4qiZEhtCgzulVcRd3LqUAxyVBfyzxdoWEBuH6LhK5Lt/5gu4VlupybXCUeSwWQs2E4yB5gUuZeZozhq4vwaJIEq1ZPvC/zvVnZuLuCV7sH54EoBaw9hWsQpsmfw2qKZbZxa1vwx0RXwqdLAIiouZwvB5VBocfibXgfVGWko8l0wcmWobYv2nxmq0w3dDW/BLsFgMcw58dP1Gucv1uzbLimxIwSUZjPY6hm1bqZrlpuWFgV75OpQqxy1MbqJLs1J0w6KZnGV7sR+MR0qYu7ZTykqhf3rIxT28oUhLPlNjUtgUxCBlftxFpKSVnBdYk0FWpY1HiZ3FZJAKqqBsRCb6lmBKU/qhxwLZvniMiikhY0naUrBHyFFqkRx2F5dHf2s3TWdIoAyhNj9YzJMHixAWHFQBIlD0nayVtRXVOVZBIRfzJxx0zGoWJs3LVcSDmMmq5peVDDbAl1/47GkvxxYp48x01LvWsktNcS0ggjeeolCEk7Yi2zQeo5U4BT2H5nEXvFnhU0MpMnYp87ezk500YyYko8y0ha24RpXI7M8MBtBCB9MGTTIuLbgHPc1B7JGt/xyiPKxSZiY7LNPRyapBRL1AFE1Pb8wRcfJqgcEvs4IvMLVExTtFULQgA0I3srMCmQEijPWWj6XQ4yxiYs1YPS3QMq2fj/zD4RmOdaxxQV2yBZ282byGFRTVUf0u3cxoFqmgk4cXUDTD92rETpJXmHKAtCxhblIgTgQ39lyDYh2dpuRcl5xG+VtCZyzF4QdZU7XWGZrK1bxZe41nT93WpIWv9EgZimMhJwQmUOHKliM8FcVQWmVQfTwrvSQgY9NABcXNE6lDfBEVYUM3GGg8xTxBDZXTrQu0NQlIYCSz0FvTKOV5kZ1gxkLWILzTcE0vExl4qjxZbDvXW7vXH9MSFf9kLi3ToSeKYYCBLUDToeHCbbSxIPW1PSk5IVjxPN+jnnrRahPdbkQl3DbUaqgGkNnEpG9VFextPEVsRtXs0IF8bl2sx7Jj0xTG0EyxIhbzVjNx3fwCNbl7H7c93L0Bw32rG+xJHLidEQcqzMlL3CsS3dOEFWfTViCmG31xvWriJBO3rOKU1vd4iYPh4CCDS0u92QA+vgIzyzPxL6/dLR8dejOu476dQ8NpPekaVAJCGToCQ/zSn1upkkJOfx5W5vF1SEkt1U9yNGu2XG1I3lgz5xYI4zeRGKxNWbQ5N4i01AxaJDyTdZmBF9jmZpDRmzL1FAr6JmXMu5jV1HQe6aX/geipqFZ3+jbmfTOUTtsyZRjRSzZ7AeQ0o9FlrdhVN1hTLumqvuosAeKiAj3FYVJ9fbSQjVPdmJZhlSDhcxjoY8iEvE+Fy+rCPuwtxRaU7hJ7yUg71EOP+20RDSowIhWKcRXC8RiKsSJkoSdgIURfQeojTuzgHu7w4+qzDuBz9OK3UiglAu3TbiCUM+1ZWSM1sik2YhzIgRyOMx9tsjn6Lu7+/u83dkjonu4EX/DqTkhbYjzXaTE0FDbl8fAR1BV99CgSrx53Ah2AdCYAv/Ex08sDb/AgH/IiP/LoItHs7pIEud5hge3ZnhVeBDVbDSvAw/GK4sglNEzIojL5IUjLq7E59tIoxyE1AgIc9C7vrI0VzdM9Sn/yKlnkTn+VJB/1Un8lCsr0Vn/t8m4ZRY8eQo/vNO+PcTna4Q7lLU8WhGHfV3/yoF4hU9/2bk/wtHEimALfWlEgmPJWvCEcV/FW+/436BMwubUmu2jnUfTtXy8kQP8bLBLfEC82M8IgDPL2kj/5lB8irbErqnT4mg8UzZH4/VEpBBIgk5JVWR/fWk3cjgHqMuT0ld/6gf8S9n9MVZs/++riwbDSRzJf9jEk7UzC15nu+lYS9mIPT7FP+8Z//DBlH2pyLGnyGwfl+V+CLbtxHgDSFRB/3cJPZNRT/Mjf/d6vKm8OVh9mPIVxQM7NNS54WA0C0rK6/B3kOwNuX98///SvRhreqPrMTu3ktfnvpACx4t9Agv+uXSv4j9VBhg0dMmRFcAVDKwYpWmxY8Z+VhoESKnwYEqJEkSE1DixpJRBHh4EClWyZEubMgywhLqSZ8yBOnT19/gQaVOhQokWNHkWaVOlSpiE9/ntZUiDGkBF5Xov4UOJAnBurUhV5cuCKQKxwanRZ0WdEkjXBemU4dexFjCh7br3/CnMrWLcDbR78N/FmSIGCHaodyTNwS5BYGwPGyMrK5MAr5Oa0yjDqw7/XVkw2y2pl4LweO/csC3HlyslM81ZtGhuoWdm1bd/GPfPpZsJ2S0J1+BjhYsg1DQf36fGhwIa+aTq/GNwm24MCcWZt/vq3Reglny6EztalX4ZwiwcnbZJq5msaGV8Xjvja048rtD9kj1B9848FedLvLie4+gtQJyvIygisySjzD7/TqmuwqgdlM4s1+ibMDaKdMryNtobu49Ax83o7LqQRETLMo+Myw86h/AS86sUWZ5qxoc8Ow8i68ixSLsG7DANOp8aIOw/C8niTbye+fBwpwRKpAqtH/8aCMq+7JF3CKiL7luOqyJ7kA02zJXWTyzcpISuIrLzYGoi3Mrt0qEyggoQpopfY/GilhWosKhCBeDtMsYTws2w1DEPEj0CCDs1tN5gEYvTEx5IEjCU6s/PpUuaCAzSsCU+U79LMKKVUL5uIfA6nM0tEEbCrSB2zuif/gy5IGYUrD8TfbNKRSZM6fUq6n0ptbrYu7VTyMFa12kg0KCNt1sNMHzzTK48MXTK/AkWS7MAyr3sSyMBGW4/AEk+arCxdaaIPyE4PUlGlpyZD0MXLcGPr0Klm4kqs5k6DqzUXYxUJ1RM9W1ardxHGKt0q81pMLtoOFsmjqwjmtDzDTkNMuP8zGfburc00Oo5IXHGtFCj59u0o1pU4w/VjmviMC+OCebWIT4w3NXFhJdediWdfEXpwzMdeLAnPsQCllOcRn+bt5ZYD+wjoisfy7dL2tLvxK4kYTWreRynm76N/H+rxQKw+tFnY8jhOGLmC+9sMV7X+HFSnwuj9U0ie2OOr46s+1hqrqBCrqG+39Ks51+C0I7vOHAli2ztWAyycX25RFpA/x4s1VapDOV9rSctsLPpd4UiPc6OoupY7uur+mpHYll2U9ictCXtyzITbRJQtXRWXaiIPoew0VPeSnbY5Vk9/btfQUnYVx1YN97m3/oTcrMXAuUNy9YlWG00wpYFfHMz/umjnPPKkJ2e8vPe1Khrs2G1EFTXXlweM2dEABpFK9MI6IZnoLxRD4MWyFzITDYwiT+JN5jCFlPzFpTO2M13cbCM8mCSOXxDLCKtCtSjm3YV9nAEbzap3NsD0zjMLHKBWhHTAz30OepA5oEHEMh2o2ER955HSma5lQJWdyiDVuo/MEGg/0LFtLj8B0OqYRZDXsI4rrBDajtynOfoNzYINRJ1QlsQXjKhogot7FAzvwkAvyq+LiBJR9oIVuibOJ3CGYU5ELPUTSYmscwV7o2PQQ7ShHIyAW6uSD99ylsmhSj5KdCAaCRm/alXweskRV5HIJrXbLUeDYHTKtsISq5Pp/8qKBVkYmz5ZsIXUCyFIetANxZQnMb7mOKOZZWVOFEWTMJEmatuc9XrGpVU2RTxji1Rn3tKZLaERUlvUyprMo0JPQgRICnOemMDTtoIBi4AFsWO5RgalVnKnk+05WSTReZGyQMk+aCmcJXVjxCNRL1EmsqUa64jPTJFShnoJoNXcIlD8UbF/YQzkSKhmGWiyEj3bGyhBvLkRK2inIgsiKO/m5znCvGsqrsSN2KQiwbfdz44XOyfLkuM1id7lJfzT2oj06BhLFdOh0ZRcmhIFlSzKJSroG46fWurG5kRlVU/sC3F61Tjd4XFjINnkkiDJx+Fx00smFdhv4qZPMQFlX++bUtCyEChMrwIKa8RpTMeMFrS8CQV2oAznzUImT2PCSSSQ4pdZ0dYmSkmmNqwZlkHjshwTAbUoGZ1NYZxSohvSpzoXexJL+NSp3N3Vql1tIf5ME5aECa2hj4OJzGJ4U1lpZkFsuw9J4WXSnFwUMllEoOrISlV11rAuKMNYVoui20BSbUnAfN9liXLMkb5rQd9JV2FCQxu5GG+5z4VudPd0HdpcxyhYgmN2h8tHyfoyNiYDlGKTth2ViPI3A3tqP38zOAJdpTAMtctZh4rD/wGlktXUilhrm6k1XS4qWOSPXgGKFOD2pjiitR3bbGoUw/9yKXmKgnCEJTxhCle4IAxaFKQs4y1vbXgln/HTgkDjEgtJ18Sqmm6WpqddFtuXq0EhWS1x5Fs+xuo0kKroSHUaTt9qrblH8RPMCsvPfa7xn0WVJA6bNGAK4ue/4DzoINkl3EKqlngtpu6Jp6dl6brkuSOm14I2PObPlPlAZy7zhcv8GQu32c1tflN/LPMZklFNxHSmjJlFvGc+91klZrFPt/akGcRmKJXmbXGii1Ir75awyEEqMLyCFEUSRvkohUmLXUEm6dJYjZpK4aCOFT1qUgulun/b8olJnBaVyMvPdz5zmMM85gNthM0JifOb95JrXecavhZm6JgDc2bWvLr/z+qqEJejq2INqRi6pZ5NS16sGbhuyCckozPlhvMmkF47TUDL8ZTDPdMOaZqY0EZ3utW97ths2drdslC6jB1rMeNZLLrGd74TMmsOb5hvn8EiWVa9atE8e9nZXfBQSCZvc+uuKfdu9FBCfbWEs9viF8d4xjVuTC2vmizyWrOZ5xzrkd9b3ycvuVzovfI9t6c9khXNtDOemgwR17JU3njOdb5znvc83c/NUlmE7uWY62neHBYz39CcYaw117e8Npecpd7jfNPZ6nu2kNAlo6eGkZh/h224Zn0+drKX3exnR7t2tfO3tXWk1aw+Op81bOuT43xu+vps2vW+d7733e9/6g/R+SLcbVOTh7yAR3ziFb94xje+TtF9ibpAHfaaydzxl8d85jW/+b5PPJSW53zoRT960pc+u54/t+lVv3rWt971SEF96yr+etrX3va3X7xGqmp33Pfe978HPsYpD6HZB9/4xzdQc/fWc7PUesK8pnOhkW/fBj90+tfHfk8WAqBb91iAGseiRH6tEDtZiKISESrVLyz97E9NVxUBffvlz3oMr98zA6ILRdkdZ/ahZEvk6S4eMQiu8K0LmT9j+Sa6OsAFND3WMJfDAZKpAI9tUghtQ7c2ab5yohPKOZ3dSRGL+L/qQAhVQTQGlP80AsIrE1TB0Qu/NNmwnaqJ8OEIkIA/yGA/2aArmFoMtJqIHBGMI+KIHIMS3rs+6kCmFURCzVMlutsRr+uLGRSn+LGLLGoxBYSQrpiP4agUADso4KBBz7iYG5y+2OOP4kvCM9w5PfkoSdqUp2CzujEILLqYGcSJNjyk3FCtluEIq+hBc/o+YALCrYmf9oi/MTQvpELDREw77suhgIGfSbo/SxtBlzOSdarCittBOlyMrKgLEfSMDaETBBFD40OL4CpE+cs7RWwx5+sxnsihn3GmcRKkJYvAJAu8EuyiI+rBLfyplwKPhrHESbzD+fuOuYo4BsRFVTw9nyLBcRmoi9j/E4yoiFY6FeM5jg5UDEs5RaLwC8TKipeZiBv5xhh8Oc/YQzuSJCIMvq8rLDMkxmRUxhARrIEZIsf4G5AIIhCsm5cAKa/gIaJCFKhARMxQCGtkHI4wn/HhiJfZI4upoSSco+3YRuwbtomMR9gzqBQMDo2cJq/wK0mzNHMCHR9iCdEKkSujiRQcH4NQE5aQLEL8RJG6SCM8vIt0HHW0SaNoQSGbIsWIoO3LpvhhjiB7oE8kKpy8NHisDGAMxNcRwdTYPnhkQHZklmOcP+wYxpx8OL+INHSMpg08oDvBFKKcxGY6KFcUjATjEDIMJZd8oXHUD4YMyvFCwmLcnFRExtex/0qtXDTI2i90DMV/nBGLyKqcyYhzpAiAbLHN+qMX0o8j6h+ak4zqu6cVZEvIsEjkowp35EtTu5zOQJobQZ4m+YuuaSa1+b7+EQ1qk8REG764YMiXIL/5aKW2wzTUqMtDxMsDrJbO5BAqjETWikMoOZuSOUprAwx+tCCaJDULvJqhe6U4URKkPEDdM8WclKXU9E3bcJQpEU6vnEXV3Azo+T4AYy9BvL88ZDGNNCB5GQ7E7MPMfEfWYc54BItP206l0KHTqJEaAQ6eMUu1McscOZK8GJ+Ssji7pJ8/QyegRKe9hMjXfM26vJxRzE8B0SFW4aTZkRs6iaD5OJWzqJvlMGaq3VQ7S4IKqekRs5BKZVTQwrJQ5OvKDb1Qo9DO4uCTbgMLUSyj8awJijgV2QHSy1w3Kxm26oi8gaxRdGIdjYDQ62ufJUUKs8SfcJPOyhnLHDGqPfRReKkbZTLRUXvRx5CIGH287Ov/zrmRT+AzmieVUhqpvhulUqKEC+/5UXJEzhlBlrHTyLQcCzOF0+wrxTtVKEAFPprbqzdVuFVik8PgDLn5yPb4wcgzqhUhKvHiEMpcNC/EmjUlE+yLyFDKygUkvMFSVOoTqBbcpMNgiQGFl1YlKi5UjpNAlGdyUy6Z0NowVM57Uf+5SIKx0lMlyEKbTGj6SODqGh5JzGXVJc4MCsdaocm71Zwc1LnZ1d7rSiwVVp0QQ1XFkBHdCVidD8FwpSebVgOpNMwaO4ySv1AdMvtcl1LdVgrhtmD1xNVquyykzbhwlnPVjUW5D1nCuG5RlGvdPOuUyHhkVOqc17VYDW5bCNp5/9Wa2D5BGVWiIBmguVhu9VesKBPCY5PuWS5s1dRw8tTbo1FAalhuwRcHnK/juVItxA0JzBRPVc+Zsb/nUL/6wKgVKz13nTGDtT15PYyTVUSG5VYR0ZrDWS2V+qtcrTYKYr8WZNCVmsx3cov0o7C3YjyEFVWjrT2rclatVMvbaK5Bo8SgKreNPaewiThUOgo92pKyzVcIKdm+A1opU0Su1YuVxSksK5N0edANmoptxE+hYKI0TYp8kUTsCgvN+DHE89p3PdprG1u/1dU3AVsRIVqvulzQ4pcwzQlXAs2cuaD7HNcj9btedSKhfT2BDVTMxbjNtaPPzRhQe78WhSJpVN0m1vwiBH3CvqNKvUVDKutY2R21jALOpEDa0MJUXW0M/1RMD30XZ2neUavWvbre2jtctDley9zeRCMo3S2dpbjR4W23DUQpfK2n8FwhPPle7VLcGUNX2l08ckuO+DVB3kK3SGUK8v2J5RWKfAzf97GJ3gTGJnor4tCS4YwWsmNdhVIjsXBdwMMT6dNfBuxcRSPLpRDg/7VdEB2OCp4b4nSjDSXLa6wLB00q0U009D3BFDopNyThRWypG9WblbXXCzTYD24Ktq0Y8AjhTMkS2Dzh4/i+DR2S7BGNvbFfD//WTY1lScFIP9qbR6MM4AzmTYvDYSC72x+OUZmUR4OEFzyKvLCMVim5z4RplydOSoIR42AaRHQaYrRj3CPjI+RdvNRAyaeloC/+4U681DNuIhOOTiRTsA95XnWL4Ca0XHtpFtGjD5+xux3e1ha0Ny1ezPTADbqdsprQ5KFB1NNUlSVDVDV2GzFZGKiVX1Ei0qhVWjdeNzdcIDP0XylNF1XdWYD1WbNjz9q4Wb0YpxpOz+7xoR/cCVlM20ksYiF9xmROwbwdtStmFsQySR6T5VHzKQORvlvOT5NTEzJRFEvOOQDmI868T0DmRvDxXaKULDP2WHWlCsKhCieVplBWGQn/ZVvVKtZsPr2lyShyTkliBj6lodK1CA3+w2em+OWl2MmhWJY4Roo5slOQRE8g2b59TLJLMRi+EI3y4mRSg+E4or7WMmeL+yjp41sDWWjcE4s6DtcLGy6CZpbY2Bcp8eZHuU79FKrSOuQeEUVeYV+hzMa5vKQWBsSW/iV9ljGTBmIPnkhaxljeK2A27canNhaJw+rrssLkSIgJ9N2Y+MuapqBWFUmi5MJ6yZm0tCaiqhbDeJFFbiPtotntYL/LauicS7/L7V6VxU5Odlx8AWIXjltWTglw2sW6rQoNtZ8+1h2O/kVC5REsPMvP4UJmBk8hqqDmu5F63GSMUedh6iea/1aKSdZPhVPq1WPHqh6loCDtDjJRqu0hSjxQ+4LruNmdAQ6POGTrg/q+IDGfoyzROqKTaWQM9DPiVWTqQkLA19Zqw/aJg9Y+1n7ds4Ie6g6lsYPHlxakitIhLE4OY94PJs3n2jwbEHSj46lYdcoRn2xfmd0R6ZbUrrYN54TRQiq+RhbTpZEN/jWyvY2SHINpk9Zum7Fe7hAglvzEjw6KDW5mCOGqa6mQcnFMQcYuBEFUi3bcjUkvDr2IBylWrnRuugjdQuS9kW7lYCaKDh6WEedVu0ic1ojY1IbFnkswPCGxEZxB2gSwHA9gy8vtmXCtrJgV1NyjfY3OpW1VVZEsQ//e0OXln7NwcRSHbrQpRA9SNDYh6L6+KzQ07lfqFqdz8RH+IHWLa7wYwV0MwiB0ua1TGaJw2oF5ltWEXL86Vi+tHuAYzyNnZjIN0t9VZAiT65kdPv0uoE1lMap97UJ08CLkq8qw15No9K3UoAGfaBocC7XAEoVQzoVcyBEsuDkxCuBEGk5EDqfcV+ziDhBKYMa5oRYh3RvrRulyPkSZXDk/RcK+P39GExd3VksvvcAVsfnisUgOyK2+jQJRPtmM54mgwyD8bgRRccUsvAhqFtfqn3787TKej5+612UVGC7cTPjYp/ocoGymcpy87OE6aW+jb2AWQ+zmPMfGn1vCtbSHMLR2hyOUWE2E7Hb98Hem5W1zfGzm1SG0EkjCdHYf4UcspPNVdzs8xRIr9R7F8EvYfsCQEiUnZTAz9ezYyF7tcuGVxr6+Sba1q8FZKna/0BPXvTKB1lWYF5NfTg3IDDRBQm//hm39BCrl6JXvToyX8vYLF0/qgWckpuIUKZkJ0VrQWK7xqPJ8/6bPqE9UjET2q5l27nxSece8+PqILkYV6jA86JP5xz6VqIZdu9Y+ifGRcKxUQTSeRstWiB5OjZFZ45GOiEXmh49MVMfiI1rfQRxNmHFGIaf6uyhZQ//vS0daala0Xx9zwFMqB2F7dT0Pp8kZlxXxo+gS6pyzkPrlCQxEfdTXnqhjEMwZdsaiwIYLqQGJSdWPoDbVLDyXEgqVwir72wV5UZpf5obiJ6VhdVPHdYfSn6qo+yhWBUqQl3oqtosYOUO2okO2wZC0FQERoBPfuo7McvzBhf+Sq8+Y5eGRH1z3rpEaAWpVZhcgLgSmu0EoV8LHNXYfVqss+SawQj/8hLL6wv8L6XQDiH/XBhIsaPAgQYEIFzJs6PAhxIgSJzYM9O+fxYsaL1oJhNDKvxUFFRK0aOWaRYIgWV1jFfIayYvXVoSkuVGjzZs4M8bEiJCnT4pCJ4LkGOjkwBUsFQo8SpHm0IZQUb5kxRLmQIweVf5jyWqrFZEiZ3oUaIWl02thk55FmvUqSZdZtw60OLag1aI6L1pNeDWqVL4Mi/4F7NcwQ8ESXb5E7BiiUsRpH1OubJkozp9hcbqF2VVlYZheSVqEezKm17EgqdZtiVGk1YxWCA+Mffn2wq827w48GUhkR6GrK9O8OhXpv5OzC8tt6VYk05MiA3kMZHwr8L+sVD8va3D/am+dZ0NTzbyCrmXaiT9TTonbInqErPRGxn17tmOS9vfzB1w0fm6z2YRUaQSdV5B7zVEF11FbNRccVjCd5ltnao2VXG/9aVgQSPUlxdIKFUZUHGU21fWZQu6NR1Bz8yUUYYhqoQSigdjJWBJyfwkU2gp3MbYiRLGF5OJ9MjWkGGWN3cZYbjiRt6FhMSJ2IJRVWplQUEJlVBt7ZI2kGknDYXXXWqKhBBtTcxmUpppX8qdejlGBhxhGX2Vl1lZpatcUkWP21hZKWRnI0mr6pUimkViymOVQNIlJXKILRZrkk5StVNBubhInolAKavrpbZMO5dKFOvKGIWvhcRkhTNWx/ylTjC6hZ5aPnIJKGWNG6idcl4D5FJ1HSAUn0KlX6ThTVsp5eddYPbL6oI67JjpnbQJeFOJstnq2q2M2VXongJJxm15Iv5V762POdvstuu2OGNdRe1F55I76SelaQm41ptVVv/UWrHJNXcibUtq6a9l8GhkM0aWG/fqnsjOJddBnHkK3FHXSeZeUmmEiN9KssLX2Z04cWXtTR4VtCWmvFDNKKX+5HuyYdY9tNzPOEam4EYR15ZTyQlB5iupMMdEVVFcxvYiVe6pNlxS1LOZcWZmINRzVZ2uFdbGFWBWGoZLElnWUWEstnbVKtSGKqUaz8vxQvApzyNuUSCIU9WOP2v/n3tQGzbZXSGdZNm7ffScHkuBw30ReSo8SnSVpCvWIX9dqSbeUb2hVd+dghBdOM90PkQrYXTsKHplcxGIKnb5d15mdgnmi9FxvOrrN2+iA8YRjiaKu2TLM/b2M7lGb3TS5gH9vxK5E1H3+fGbVZmv8kAaZS/SJqQq6avZvcdy6oDev5qKLwHn+7/OWrUyR7xCRFCOGzmOl3NGElm45WX19dbNzrNnpvVs81aqRAA8vVvkKdSpFk8jMK0oXCReXCugYAb7nfBrKC+BCtxCQrC9K6eubt+6kkwNtp3p+e+CaBtib0h3NQSlKYO1WyLQDCQtZSvpg+tpXkbukBCr+mp//WlooMbXhLzkuWo5bpEO/pa0tXyOx1W9KhpO21Yxtp0mXDsFlH+xtEYL2Ud5O+oKXg3goIWCRoEQoh0N35e5aEMmIBm+IFcgZKy5Gm4vSBNWVr1wxQhRc463adhCTTER+ghJamqqWFeCQaYjnER+g+hccD/lGiKri3gkP50XnlIxyD6ubBVG4xQ1ZsD2c0Q1DJjMog/CPS5sUXSkBScqmyDEvyxmkIJ+IoOSEiVnM2soPC3aYmcxnPJEs1URoUkVZIuxbTIpIhwblnkQG6zDNcUpK0HYU/t2MhnQRS/1ciclFNTCN1AuUGuVkN1auMz0avIwcycURMqYydPYMjUsW/+aQxDFTU7Dqkl720rMT9SpSdjmWGbvHqo4AEylyEdx8rOMUvHXuJq/sJ6T0abnh1IxNsNPXaGpjo4d1NG0+6Zl0ShKTsfyxjCzqSFHOM5tlss1AoHRIFh+DxsrsdFQ4eedAWXkQERFueIvRKEYvAxV1xVSM1ospO091qp4Zkm/vsxFdjqaWAzI0KbGM4Gm04sakCq+UF6qW1xIpMu8p6GMomh2y8BWcJEasaCey0Qk/Ari9xKdFX5VUOwnYH0Puh2/dutZVoPjOPqUthZK6KEPeSdYKqmVHjopICSs0J+xh5H26DOIlM2ac0UKoR0v5azQNpJBcpeyAk01SFh+EHSk7ySVGMQLp9sQoEKaUhZt4IuafbuQZzpmJnAf50QKpkzGyHS9xwYTsBv+z2MFRaqinDBMli570xzPRE0GSNSz7kPpahwmqQBRJrUpHMrfh9ExB9/sXMMciUabQUiLtfFRAdzJew8QLgpf9YWNkhr/SwYVQHrFTdFpFuwORiZ8wmU7Fvja8ax3UIdeTWxX/SsbYBtZS2OWPhtm2EUkFrVJE9ds7u5LOQgbuJMzb71OgkxzoApadi3oigEG2PS+BdmkJBBOrGsIYycqKlQf8isJoDGPBUqw59F0Vdup6VS85BTm9vd+w/CLV4SrIJU+ClZLLQx2N+AxrHb7Tizu1G8buh4sOKSG2CDWuoJb5uCdGULim6Ste6nfJ5HWUdmJK54XYBS8xCeBuQfT/F3UxVb7LlK9vDllKxrzYzaz8mZ8xM6s+Jriy+MNPHmsDXMEpBD9KuZ9TjOajX3lk1fj0lkvT6JPcDfohJmIIpdUnN7aQUmcLvNu4ikpivxVm0I1RZCHBtLg0Z3okXaaPFCeHU/0oKEumPTCZ3rtQTHklkp11n3hzyhWOMHvJRZZQhiLEntU4C37j5FhcGQybe1lWuD2iy0PrtTQChohRfOxRBgeqzFSF2Kto/E/vhrfdy4AXl0blChk5ZWluDdTBXnW2maNXHo2UG8a/Jmil+KjxoXbJqk+smHrhXdx7yU9AlY2luL9j3WqVLEQdT2quOCKledcIf/7qF+NE7bdk/xkIOqzCSGd2uzHggtU10dIkTVsyn59hxywYEq9q0ZiRmx83I14sp31irdpvRjZ04/qhYzlUbPL0Sm/N++l5TILBZlv4XPhqnk3ynKUyTeZH+GtTfSAUFgchJUStBjvFJCvkh+M6btfCOkYHT70HomoqJPSiLRGo3OUQPruiIbBb/NUUAm3Z6SsM88tZyhnGBy2nMcf1yIfdn+1Oyu1O1PFQ7xYazSKEW2J3H6r00q8k073JKdfShxO6Y2vva5hV/OFZGtq/fUe24J+NymZQ/1owcsSzLVF5zvc6QhEZ/kU+Mrq2i3s1yJNcta6B/K0J/foNW1r+G1IXV8LF+JeNK//WQaWpS9EZ/rHPotGXYsQL18kS2jFdVPidoYGPYRlJfQRFWhDJLaEEtt1eKlmfzOWH9i1ZTjAd4LRFmk0dYvEO9S2SdQiLviAHtR1Xv5kMTE3PfxASa9heRUjXmUXXzK0J+w2FveiQ5whQAQEIm91LXGGKfCieVJzRiXQEwAlOhdFdliwgsIXRcX2YmJRJZ3AQXP0d2nGHg1RHnliQl+kUBx5fs1mXbijM4xXPByJLTljH4wQKlhDJNQXfYuUEtlgLwPEM9wkLsWBdUeRgD75cAu7Ym1hdZ0GQFeIF7sTR3RAbh1CM7AkF2NiUzAmUn3WZ5xgPQ1GPS3UQ3zSL22z/z3BUG1sA04GF1LTxFBMqTvHFosN90RyuStJNy4GxB7W0oRHlRtRlElgsHfCdz3RV3yEGDS3mxzy1CRl9S3wAT6zRzQA20P+cUCI6Sp7gE19YRSctGR2RnN3JXy31iZE4hadcymdMRh4h3fbcYkPg4J5ZTRoW32CJ0oGpxHmEifYkyvXUWtFci5NEF1x8IWSc2TGKYyJSTByOCNhJ0Pl0xiMSVrqphEReZO/VH/CBCN2YF4tc2A/mTLVpVjMGyccp34ONDLWdlIuFyTbK4SIRH04tZGIsY/XZY+Hc4l8w1Gr11iIRlMW91AmimNgVyIH8FcdV1LcgXGW0Em5sF1RK/5YiBdtQoYcqfV9J6F8SCoXl2RgP5lJSTYVhIc6eJV0d1QXAMFmzlMRaphpQCJWk2CT7yKVe4aREIN7eCEa/DB6h5MXF2VVu7MbC5JN82Msyxl+NXRpYWgZe6pQX4aDi8caK8Rhb7pJ3qV371WNNhMacnWAJxRMgrVbkhOTvYFzlnBWWBEurpZefyMaMQGLr8QdFvR3OSNHxHA480aRPvY9WTIxoEp3LLKbiAEgEvgsaPVNL8ARpBkk9Lh5O+ReunQoMdtc4LaDEnUYi2sWuNBAcPQlTypKTGUfo/FuI9KFrESQmfYaLsKNcOE/SidAOVkoyAmGd1MZ5vlFzDs6QTP9P3OSXUSykbvpK4fWhjOjb37HNIwloFiYWLSKmOCpF7O0HQPLXYBLOVeLea35H7qmhKkkciMThjnwNAfUV2UxegFrJWlRROYWf+CFe7DyZjKhi4QkX/ywP8M3NLO1VhzgVLrERL5Xg5ElRUOIMhpzaNtGhmQhQ7nSLiKiiremgcPbabTho++legCih31SIg61kJVpij2FfElYNo9BHWNwSH55oddHFijEGZFnFQOLevhiHCPqlTFkkurEPatwjrDDQbh3Oz2SLobXLNCVjMS2Hm77phn5KuYgPiACqcP3k4nGGwTxic/zeLp0Pm37KZOaH9jyWfHhROKYdWqphkElR4hCRDtm0ScmN46X+oUbOTJcwR/L5WkmmpJkMxyfZXEt+01hhouyA2N4lFD8ljbyoB6jwJl0GyEZYZX4aRpGV2pDFkAYOlV6UqW0SZ8s4y4WK/2M8gmaVJOubwWhiEFrIeQx1olVjUZ+pWip+eo0pQtwmrhOZQU90LSdB8erdxU+iEVON6sur6kyzrge3QWpcrCVVMFcJoUsD1arVxF8wuskeYcw5muUgnelgGE9ftQyb0MvCzB9lUc2hdetPfCJCBaoabimppgoSAqFrrGNPGFp8/iu6BFvARtBLlonkgBYSASaVmlle7shfTpO+gAWvyVXNRsWFJiVsHS1inCExqae9ZOwvvtQmHeMN3QzrFc0mGaumNCZXvueRfFm52qmoYmVddIZ0Wk+z2OskbeycXNabvV/hOGXRptLkGYVSqtvhnUk3IZC6ZS2eTimqGOg18f/QoahqH93KH/FEQ0Ii0/JXmjTLX6iSA25cc+nddhqKbQSGwUTpldSsNRrj2UkWaYgITbUX2pLdU3mPs/JWUDjOEDreTRSOlnbsT03PmtlfWryKDZXHJcFT415q0fnRrEVOYpWFCxbXzHYrozzsdcEqcCDLAgKUkhQFpyhnRloPe/gLE/Zs1qGpf4DrJGZp2PZeZNHO6qKgIg7rIH2MBwLns7wMkt2udiTM4zpGZ9DtCcUiVPWe/DhPjGyJjBEXbsgsLHFpivCi+72IkxHL/QIh8zgguzrEygaSgZVq4T2OTVovO0WjnC6M9xqcu4jvULHdJs0ZBLXSNGroMN3dVr7/CLI1YAK3CXxwiMIASfWB7wShLStli9KaZDxJcEtcyLnUCwlHxKwGCRw9YMWUWunYy2mMGVPosGFsai3SCRVXsVlMH8FFhrnAFGc47+xEypIOMYJM2/mEEPHYa3B5adBopaQYS+g4mGTOSrqq13xGVr7koYRhnvHQGxtTjUpkFcrsGYBM7ADN64LkaOAgMcPuznChW8Iwq2fgnwFXCVLmcUIccQH/xvRiTHnsY4v5p/OS5SabLHchI/MeTLNWcOUQ2kfYihq9jCIZkuMUpCWCrr8qlGt4kXJy1Txtq5uY46J0HPUQFVHpCS1plZUU07JmS4PEzXgCYqkJZAAqcngE//Lg0BhyQhPD+uipnXL3hdWQVot47O8Ct3GQBachZjHW0IywpVK4LJa5iqpTJl2UbRgnp52TfYe2DFxhvoYmIwx3tPBPZMzxtCGP7AphrgWE5UnwAsahil/xuKq8XLRAjhVzeavihhjijMeRNQhDlUxOmhDTjJUrNx7Gwmw6iyC9ROQOWskEw9L1ns+cNQmWkqpk7iRYkB/TegjasAjpNugPa8runvISykvNPTKjXNYW4+o+2wep5FfcxAfiKNc2OfNeRTR1yZr4KfXn+GOf3lXr9gqJqJAZv/AmBsZAg2yvyjBFOmMWUmuJ9dzAZiVrTp8V1rD6EPGkuPK5bRASev/hp7gncownKctHbHyna5wKLUEYQAPSAtHkfX5Occjlr0Eo5khIURdOKd5apPjnDWtL/6IZWk8SqEKpO99liwEuTm3VR5QvC1dlZeIZKpdqnYUHV68JoSjiOnMJeeTXH+eJNnPl5hCmd/GMkrmmBkbT4D6wXV5JbTEbcm2uAe52deWIuLLpkRXq8ZAjohDjjqT2wcW08OwJFqv1gY4vZg4Svu2KFQIUQqmRRwIvjmribQMleXwmKLsJ+8Ls34Dowh5NeeJydI/X/EGV0b1cEj9PSphEWHGFeJ0kO9lRqv7LNdKfIYJKYEsr9u2i+UYWPkGQvTBH7dp1hKBdW4tONAr/yyHDrH6Ior82uGyipGdccOvCNuu2RZFG9YGPMMx92xYDRXF/brA4sKLwCgThV69Gb+ulsXlv0ZdVsZW17wa6saheZUd2h12f5Zt4JbcEBZxFkMmsYBhxMIpSn67Yii2J8cWRiFU9648vmSl33b5EBppjt3RbnViCZppNYQcuCmetB5SvuK+gRcRJdKiZZohjKKOvs8XxEA9lVZ2H3UKvLBeiSuUG9B7ReAF/yAIXkGiT25P4UKd1xT7OuZ8p592WYUh4OjPNrqeNm3g0ZqUnOZmnoIix9Wq/tKz7dnidbcUOxu5xypbik/WMUXIPCXTzMgFnjykPJXO+DZRsbOr4fR42P5W0ExebgJqeq3q72K9FdRKP7tdyVLPBzZrUUI9/AY9BJU1FsjMyfjsF1wRbUmAautdHfAtDa5BTvkx8RF3xvKlrR0loxLe5eFVIfmYMj5KY/DB9WLVtWpSOSIdYmEXigjvd1Zx19Lq7kFkD41t3ay+5uUx8vK11TAxg/4lus49sk2xso7CU6ZJuog4d2Sq70KV7PKV0ZcT1vMjNrU+EbmHgBYkNUpeHxD2e30TR4qjbW6hYkWt8zjSIqkvJrwjLxP+nPmb7dEUKnmjLNwuvlexUDWsmMLGdAlVIXDOgWiubRYlsf5iqrXJ0Fn71fs6e6sBvS4U9MDZ9iC641Ad+sz14n1pvCjteF8qvWaOK/JBuFnHt7MWil3ntQ7wubS+hV5JvSVT447UWZFQX44y18u5Q53s+QfELf3hyBqfsZPtHkhmY/gq+7E9W6sjGhPZw3nGJiDhYal0IiXOYoRPFMu5W61IIlpftb6c1vAUUafp4PMaRrrzSWwaJXv8souQYSjRGdfih+Ox3P1nlU8mTTjOKSq88q2o++StCydVQ8ObOI/mZmJYS53t3NtZ4fLx/yayPrL3vpoSCCUBYuTbw34qBAwP9O7iQ4TUr/yBCtDIxkJVACyP+E3jNYEOPH0GGFDmSZEmTJ1GmVLmSZUuXBzX+u/iSoMJrrDQyXMFqYcKBPC1+hDgTJESaJf/xRNmx5QqjDCt+xMmQFVOYGx9CVErz4dGQgbYu7GrTY1aiDSfeFFnQq06BWZU6FUtWakSKK7JmZHtzqMxrdNsGFjyYcGHDh4s+daiX8UaRCS/iPPvXMUeFbycfdGq1YULAha10ZMUq0Aqnoa2EPRj/1aXnhpwxvkZbcKjgqYerfpRbtjZVp7Qh/paYmmFOwRq7bvSp+fPqrCsydw7O96JC2IixZ9e+nXvbpDCRjxbPaqLwnWtn7j0YFCZ0h9H/KubdfLDNjNBL5/2OET7Kh1YrY4g9mML6LcDA9jPsPI8S/Ek+jIzzaLTQImKqwaN+e4+gg3A6sKaC+ktswxG7K9HEE1EskT2/SCLPrqI22o1ACHlSDbzrwKMvMJ/Uk/C/hW57CaeCbJRtofOq6s2wCwdjjUGiOvToNP9+40lHlrr6C6EYWYSKSKj0K2hKnS4zKLcU0UxTzTVVCko54Qoizscei1OKTrqiTAxHhB4kLKcr/49MUE6akmQytiOFK3KwtBDTMcjmMmRJuBDbFAivDXG6bkjVzJvI04mCq0wumchj09RTUV1zQIm2sig4RcdsiCz5goxP0fiuHLJRQIWyqdajPFOUUb4MNexXwoZl0KEAI/WNsWfdu8Y17wSyTyKPgiVzwa+uHWisCFMNV9xx/RxoN9J4OsuzL4tjcjnLenIsIj257bOtd1N6asB7I+J0pxdL3DMwgX9krstAQQRrNA5HK226+Nq61KCIonNqsoJNyhbig8nt2OOPTXpWZOjSrVBdJk1jDqMak9Lx4Y/y8vCoYkvajdemhiOtwhRv5upWysArMquULP5LYJQSsiihhf9l/azP0UwLLWqmHfwuqVJBzlrrrRerEM4486N4vR7zxIipLPniaGJF5w3JqJ5Vghskn5Jt8us0wS3sWAgJ8nBolt7++aQh8QXy4E2duy+QxVFrjKCJZeRa8slPLVrCsGvDGK72ZLWQrIkW3rPbusocLOWXfDraq7goxS607KKVMk4PtXqJLbnXqv01wJLmM1TBb6oouN9+a53y45E3VnUOp40cdPA6h97c1UD6W7facUdKQvJMwwu1Qb0sbbvCS3QSN0DtpRMk0rrv3iKlwLqUpulUe1Cxl7cXDywy76M5+f8B6JW8kQQyiykQWSJHkK3s5Tzig9kA2wUU450kQUOXqlB5KoIX4Ryoe9yJ3YmyB7ifkW9vN/nacLwXJpjMTCFUk0xxOqIkIIVJZI5Z2tsCmEMdHuU2IuMY3/5yMpuQr0tsyc3i6OW2/YQQJKejGPCC16dmZYeJ3tEO1q4HmOasy1P7C4mLIlPFnlhnbPXbiPpwBaKGiMdb+7HTTaC4QznO0UGp0d14Nscgm3wQYtKCDVleaKb+jP+uV5qRWUpu85BDcussPJEfFZenoEUOLCRKm9UfIdii203wiy1bIZn6pkcbuUgvqflVAumYSlXmKCPg812RnpK3LD3oXXIx5SHxJx26iNFs8ZlkJw/Ey3yl6HXZMZ9Qztg0210Gdd1yZQ+v0yCHhYooX4PSD1eZTR1qzIQSmcxmbLQXju3mkeZaIOhIk5grcROVKXlI2VqiO2/9si1oK58wTVLC4kjrLDKMJxJd0rZjWS06LFoXHy3TF+DEkJPadKjW0Oi7D2LsKgS5mH3qByGwDBKbq6GVMNuGENMwBqG82ed2OoodfS6qdfjSlVTW9az3tSuSdWFU3cRXzhkVT0L/BgJSG0P6UKGuriIK86DqSLmVTMlqRnOxKKI45BeOCmxamoljUazyqsigKy9HK1vdGoUifFKQJA+ZJkdJNUoKvcpc+MSKl+AlK1DhMqUnHepdVRJTkWWnK+v62UtDWae0CQijhzLXtvRIsD6JMUj/+WteQhQh/x2Hnshq6EtK2jR7tbGyN8mLla5alOnxhyOJxVGSOEOaLrJRWp3FKwAPBNDgnRAvi8tINz8TWk1GBixZWaQiYTKZ5ezrqbWSbR+v99vFutYtxAptHhmElbGWZKWHOSZiIknIsVUxIQapKYxKq5mJBciCRVrXak7ow9f+r0Y/GY/7TOapkWnkpQhk/xFga+Id8wZnkKJxWjKZKi1AkqWqelzn06p4mbrmjm17vKxL2qnS6dbMeORDbmcoMpKgruR1lVEwYatiI9/maKZj9BV+1zsuUgbHhxnJIFzsYqBLnskn75LnwUrzXSWGirjl1WNbA3y6MQKZRBtu15WsdyTmtlFLLklSkeRS3ePoVoDcceBIjgmuQrXYlW2lMlyZUiqn8ZMqowPnGovHqQmnuEkXnKYRfzSk2GXpNhbDWqZ6qBDWADe/OuGKTCqy1lAxT54q+4tqZiklOylngVcyMsLKouMNIbYlBVbZkl1SzO4s+Dghs5Bj4ARWzyZKJ5Ius7SsSmn7RE96u6MZp/+1yVr3gjCifczT1fZD5yFehig5sVN1fj0TeEpFtwcGl6UPrUDB2vOTOFGKY5jdrkVWSVlEyySQTgifAnop2odZs0mIi5hwg1eyk3W1h223T87wqH7XzMyQAhSzDH77J5gmTDrvIrUWkzTD2Kk136Z1O6VEiVE8Muz0euikzUIIbua2lVPtyjv7ZGZBPfTojkMyxZ5I2l7koeGn/hMdFAsY1l4R8nZE7W0KStbeJOdcS4a1tMlcjTP2/OEULbiZCi08a6rdt869CZYL6llnejE1SnhOJiTusVoDL2wQ1cKnqLtnJoGWbknGLStO9i6qRrryU6FuOM65UWCPZg4ui63/mpg+73o4ijY3/W2ilgNu6wg8eqCIzJJ0zhN8UxlzU6NqFXgXp5r05iuoKCY8sdkSL2xFdVdo/CeFJD3TuHspQ5ss4BHlZlVGnUqplqackgPqpRWBonwKxyg++uozWfWjZjDexIV3222Gc/hcmnOsWPl77ivB4hXlljILt2nVAYU9YPBz0fUwq0uEa9c3DW8svVz4NLvO0HOYEuWNONtoF0bQgyHWQytxTn6XuqZDzKklzrfxy176+Z7smcBZFagjmq73pUWqxJ9pXLAmOVvJZWeUOIby+KU7zoQ7APDQOmpCKIQibsXZQGomvKtO/sjp2mUuoG/d8q5jrMdqXO90/15HLnqHRfoKfuzDUu6uk3zvOxyohbZvjxyEzBRof9Jif/SMT9rPd9KqqEZqKLhuNjCCWbyFM5bISDQPfsqurvhvyLDu6loDgnokyRoF/IyvO4ZPtGTnPmjIi2zPdgTC9BpJI5RP2VotrqKKLuDEu24vRapv/tSm60jQSs4I2PLLi2aJDtvihVbwqVKGRSSmoi6ptHwinfTsLeTGgqBlv6Rq3GyuOGIErjjiYnqttZYl9rJoLUImjHgICpkiP6gwr6KvKHLwnwZn3fxpNrTrnSDMIN6iQPbOsE5OPu7EOAqlgdgiwtikvmblcVZj/EZEqooPaCwkPUjkKGgvZFqo+J18xSCujOh+YmI2RGFaaG2oq5U8cXEUTxEvIjRsREYKx8FOSvcIpFR06sgqKemkLBrXLH1EYzFQqveIBh5XAneK6DPCZFvkTCzgkYzwJCkCRLLwLri6sCYqY+A2cE2Mw6xYkPXI8NBuA2sWcrCSjSE1Dxfn8RP5ghX1zDpiaLSSzUIisckapiaQ6olIYgFj6b8MbZ40Tywwj7TccfJy/ydElpDwsKxaqOLNRIZSnCKcZuXaBOMKkSUFSZGCHMYxtiyF1mpbZNF2pJE/UmsXu64Mt+0HEwr2BAwjAwOwPm+PbCItamXyZsJNJo4SB6v+yjIBRyIdz/EXq4MlmUYEx3ECqQa65iOzsPCBHGTmDq7JnKZGao4hL+JozK6tbmayxOTIuDAnN6guMsOIZFI71PIJQShfoE27qMJ6+Awva4bmuu4fx3KXemlsypBwSmZBkK07zEKwlsNmHAnacHJEbCawIO/pghFDes/itASggrGFrAr9Zg5QPIMKV+pR6OJdaoU4vi7sgmkcF6ww42N5hNKvVrJFpIbSwG5l/E4eS/9CKOvjROyPgM4IAFUxlK7LP/Ss1zZK7IpR01xqVipj24rx5U7kPLNEfhCoGPUs+5Qt0UIpKCLPHa0ooKgxJzAvPwEqLd6COQhzMkttxAKMI0RlGDnkjMIiS8IzWv7kr3KJf5CiP0hNIt3pFB9kNcvT30ZxmCoT6TIIkRLEL0DKhFYIfPCzn/pyifgyNr6RAEtEKospLR5p6VZDE6HOxpTNDf8tJbxzLTdyQ77jUlRvtFLGU4iFUnhUw2Iil2wsLAbsSPLv4kTUIWIoNpUoRFJTKGDkRVPUMohQiwiMKE9iSfWrPh8Mm74nsyTrPJeCfWJQiz7JXOSln2Kofrh0NLT/SCPhVDB2gzXyM7ymR7bG9BcvLp1YQzerDMJi0zRAryOIEf00pCssZ24cVCjOYvfQJkGuTMh4M+ICbCp+CTNxz/9kRp4sEj0FNQhXRjLXNGO0sgpLkX8kwjyCsww5TGm8ZRuZULaC5ADjagD7iUx5MWhMZT86IlqAlCiAFL1GBEB7rRUzDyt6lQn1rkkP7a1QzVPHUqRqNTtpYjmtMlqY9UV7gsl+0yEyqiZaB1Y9Sm5yr/m+DVz24lfYkiZOzrq4cyUKtqwsBEemqTJ0TUgiZCd+73RKNVCnMjx7JHVE5enOTE3qbBtBTUaPbxJD0i+7TnxYowURJEWLz1jPhDjq/28w/yVJw5SFDqZHCGwraol2XBIhZs4ETxIo4S53WI1dveJE3+YxdxUplpYkEjWe4sZQoagnPcpK4LQ2XDWrLuLruvRPkY8u+uo4yxLS7gVL0lNkTZZAnCQq9q7GFmi0pBIolZQop/RYJdBbpLRaoJM5wlVWrGSXzgYkNUPYAIlDOnGIOKXqDrOuzjQv/7QlqYt7KkRR9PAqq811QtGuTIQzP8IzBI2/sKVLakyYVFF87A9xtdVbdHaP7pVeG8QrY3BsuPNK5wMr7dVRKVFUikwgVjd4HPVSmHV+RvF1kKh3UjbHAPUUe6Vp/YxPem0rrBVbpfInYnewjmlFfikfRf9Vx2rl93JFtTSolRCvWLokYY12SZg341JkYBHmLZTGt8JpdUcuXxxpG1vlK3FVP7fWT6OqfmHSDQmNXfbwCTl1PVTXOTz1sJItbdBtNztxPpupJSCSL/yXWICqpmhXRR1kgRT3cQMRIQCPBQNTQEXC+WQveyKEC8OzakIFPxTFc6NL6iQkc7ENdg4WYTEt67pmWA1zTf8Qd/3QsGLu6fLuIbPqjPwrHImnyzSsb3dGQHo3QEDWqg7whxv1X+/Ogc7DQEkzPhoqg90pQoMENZGSUwlscNH4mMTH4TxDYGpSBdMPgtv4r0KXY7jv2szXT9IXZp4WaqO2Xjys19zqBhP/ONkGZECYkneJ8H/v908/6PMeJ2aYGMPy0EDkZYbO1YAdFWXXgxW3UQJ9sZ4KLZ++Um+RRPjkVpkOI1Ql8nTG2LDciHXWg0iDsOH+bTPiJhnpkyDXSN8aIywsDTIIUztWuM3Q5BhPOE40KFnw674GOUEPJUG2pYEbJHbKz4Y+J2ShCka/sGVc7AFlzRgnVyeAQkA8MuxiUEGx4i36eHBDqM4mpnz7BenaGauiUHCZE4Ek8ECGRUPrh1+VkGaFYkIE0kGiyRrlBLKACDwoBZkRRMLwRiXAiLbmYoHeCLO6hcBgsKlkCyz5d0SQUzTvL1cLC0gN0S5AjjHuzSTVGSpA/xiBoRdvlyM3ylGAmGs5ogJgU1mVw+rCDGqI+PNLl7V6i0mnBBo8pg2MOWslLcwqdywutAh41hBT4w5N5PRyZOdZY7eYkW5oDtAvsOhROJgjLrSa0uN5V3KieE1KPfkXgeNZEGPtMm+kj0sIpw72Uo6F4hTagIZNc1kyd3lW7vYnqqmpNBSBb7cvHwM63xhLiRpSLG84DUiTFzs72FdS1KSKatqn90iQbIdPE5gFYdOD5xOQRCP7XO9xoS5uX/OpiEMrBu6zEGPF6AtvZw3wmuwRo/GGQzeSmlFCTRjpaPjgIjaJK5FEbgopSeRMTm45S1hf2+ruooQEc+uoexvsHLduVOkXu3ibw3LwreMTDQurV6tVTD+JC1X14pJFyKi1i4eQecQukcrbLN3EttRJu9HTLoTtAtejnBf4C+s5uUYCNeN5VK2bUP5RXuYQud/kTxfctucad2D4hOMpvKVjH5NxMKvRmAJ8jYZ7LaUbGFP4RZMRO1VUU0UPwksWUjXcsB5yehuyQYh3nz1rS8wljHhlXfq2ReS6L3l3sMn6sscVUMxPwVpup/NQac+bdTVZrG2bvb2WuYL/Owth7nClA8uihmQKyWhqKq9XtqfRZKrBZF9ZZJfI1cl+bflunLLl9fdecUXSIyzCUrDc8Ec5NYwiqRZ3vKz0m3rFQlqeLdCFvNJo5nVkgs/iZs+7UyM+SKOV7VHYHFyPO/N2TUmhOzoJXbUhF80uqAdPcZb4dY9Dt1FEfW6bQrhiqdegMQ+XSLdJ5P8S+1ibzYx1AlsLsjdl/bjhHGmIZ9PExmyIAltDWTLpY0GUuqK6A5zk+ZNW5NnSVYbxTXCn4qqbJrIOHC06MkI3bp4fqNBmE9w+HL+dtsOJRiv9hqCCq7vL/KJt+xW52LAciFGkSaTFy7wH63Pg56xXYsK3/0POkBAp41ZF6AQCkVwoyF3DLtmQWJI1rJVT3/b1hmUXxdx3kjoF6YbiYIOnOpPEC/kku3uGD4OrERB1PMRSu0sw7tN2l0M98Bex/fyB83fS+TAu2B2B7GQUqc3XmcSZGxIBK4jb5/HjtYe4L/pzbNwsRZIVE96X9l15DQbmmEnb+8zSjaNDNQx2FF3qTQSfToO8gjGPA4pMP2e+02YxG/hM/i6OPyn7aqSwD3iBcWbiCeWJo46sIXh8pkM+5/HgB9zM+sl/g3jz8Jkj2byKVlOdJNgfsd0Rn9BqsofafbVc1nd2F2pSv7LDp92ROxXqFvnog+KYyqnmmFFwIbWpCv8+d0x8trsKltDEPAhd6Jn25M+5mKzjBJHbwRObURlrlLUl8Z/JTVlo2DPR37L+SErd//r2TJIkxWtM6JPFDZX/Nqu4U4PJhn4W0GV4WwZ/xy0IRRq2/1JkacYV9vmco7U2iODZI/HZkTqZhAGHyI+dWN8QTIHF6pmUiiSJZ+6ln75SLAEiEKtrBAsaPIgw4cF/gQr+czjQSsNrVlZQHFiwosON1yYafFhwBUaCrEBaJKjxGshrK06qdLhSocyZ//5ZmYkzp86ONWtasRJzp9ChCP+53MmQqNKcQf9hdFqwZEeLIKVeRInxJtaVD60u/Whz5oqaXx1qNXjUa0JWP1f//PyZs2RQoUDLDg1rd2ago3mX1u2LEqjbrCDDGgVMk+NLlhPD8l0xkdVJuIcNSv54EDLKkCRdwiUIcq9bxAYD1RxJmijbsXhTAy7pkelZ10JZj/zLKjbUh1CtWsnaMCXFpAQDmQZsWyxZuxIRHiV+UG7P6T5ZWZfZmihU2tHnklbLHadmxDVN1zy5/KHw8GNBk9TKdTPakBhHZ2eccfZi4xwDnf3dn3XeIVdZeAYeqNBNANI0IIJgXVPSWemNJNVDHvWm1XXQHRfVdnn1hFpRy5XF1kEcqhQbSdVhR11CnykFXnj3pdagg4u5dhlx7UH2ooG7FTfRSf4Vd9BZLnXl/6F7nJVmUmQnjQbaSEIONCNiQOlnY5a0ARXig1omdJ6KGRGHmlPGXUbRk+/dyFNBpnX5lVxYgsWXUj2q9FSKLCWJk3VABbVXWQUeyCdp432JUp2IHfcZUOZl6dRkTxHUUkezlajkSyMWtxKaEJEUklazddokhJumZpqeiK5ql6IquZplSVRlyJV3GlHFUW8CHfXXX4jJpSpMNeqEaa4pPvrVaR3aNeyizcYZrIOFGkrVRH9G69pYT06q0k2HpslpcSLdByV+mBWFkUfFpgSgdHD2BZuWc7JaFl/mPRuerIqJhNJyZb7E72LNsVWsSoW9+5V52PaUV8F1rScXYK3hq//QiYQibFegrFKcbEPbKQtpYblihZa1Wo173bmZBgbmmhmFKp9UEcpopIHt0ftdaRaNNe+BXFpW1ZGDgvZwYwOhCZluptIGLIOwChWTyCFNu9TMVwlqo8XfPW3gkAgiqSLGtEm9mEllcmtwQyk+l5meVnkNoWf19efTlh9z/dXNOO+Esd4iamneQPxRCl+eFqXMklvGwbfkghtBR5rCTve10sMS4q1Ubxy3LK3YybJ6J3eMPuU5jWZyxmFTaJN17FmDK+bRZ4fCXRVXVIJWZcaba7c7q6zVCzl3f84W8H6T4aouQw2hx21zHQbvLPRg9VybqA8dSX2Rb/20sMd5rZeob+9M+V56X+XG+LXfhwe5UKLhUhRbucUP5/LVxTt+1kilmmqUQFbmzhPMrWVviJKTjCaGtkpR5HGIM9hNCmO0jvgPd+VTSuAYlD2dsMtbYsLJn6hDnW+JKXTaqaCgsJUsE5JHS8QBoIzo5x7nxcQqxPmZflwCnu0470a8khKYBJei6YhwKan63pUIKB4U5gVZNBpXkKoioeIwLlBSag5IPpMU4zSGaoAx/w/1GNYw5slObOURT5iY9LqEiW8oWkNOBl3jKwfRcFXwOdjgZpMSHZEtU3BbmnymUr8bfYZ26YrK7T4oQJmURIVfcdRShmWdaP0MQW/qIs/MkinPSI0/QeGewOAjEIEIjosEkp6wJAYavWEsXrUpI6fWGBIlUo6RONGYvGRJmiu9EY5qC8tP9Heb1Z0MaBlBja88IySlgcZaR6pfe2QoGZAREZZD8RTUSDkWXEorkQo5Y3oaYhVPZRGcFoqNI49HKc38Bn2uuaBMtIUcTv2HJto0yJ/GRMv2ISiOiOFmPBE1lnwyZ4sCKRDxPrWYgr2OL8R53XYmGLd9Xah+GkHTSv9YU0+0UJNQfkMiU/w5Jl+ainF4olRkulI4llAoKSY5GVl+slGduLObQ0shDP9YlF0qBJ4GM19McULKRyLKKINhoUDtQhjcZWSiy4ShxXbYFDfpb0ksyxSFMmQkk0SJJf1yIXZ0ihCwaocqIGUVJ3dnGrdMZ6tZzNCRItJUD81sN+k6zCKzVjcWldU5D6ycqzqarD0K6qgy/ali8ApTaSJor6Qhi0FPSp89BXI8tgRXWKOISfhFJSpYhRmmfkSRvoK0pjkxjVhbiVCP6gSwelmOfQ4HNh7CTJ0eO5RhPFbXrdroTxg74xJ589Zu5tImp5pm51Izv8XGj7S0qezG/PP/H62cCD4uYZtJP6Iuh0ykstWlkJtqhhJrxbVfEhRMPZn7ztPuhJ+GzRI/38mQgcG2qcksDkYuc51KCUa7Jb0obzKK1LzSlLHEvJk1P6JemXwwwR8hbE7Al5dyOUhRxRWegz8EHTR5Cj0qu1GSFOUVx8nWTW6KHX8XU6kWWk1buGTnxv7m0T7Ct09gVNN+rne00GD2JkMqoqm8l1AQfUlyCpHOCjmUxmU1V8BY+xqAZdJGH7lFPxUeGxI3JalPRc1NUCwNnHZ4FNrNB0j2XSqlyOu8SlVXiDoJqoOifFckKvDBuTuPaenXngl2xcYLJFyfRYXdV3kIvQa6J4N+uhcO/4n4sMQCIXV2GGWiSFh0hnXx2Fri2269ub0dW1K5oIJHM0sQLT7048rG46vcxDK8CBWSerb7ako5xSbZ9GCNLmxrOFUZUTtsc5Lu1UH1WMRro4nMydI1bAhR1yE7U3VT6ahYETG4O5hSVaTXoq07QbcnFyIsp8E0bWJCyk08ZZPNnpwaq0m3uqG0ZzHJrCLMhjjUZxb11RwXH/o5Tyq2jK0raYqd3Ua7p6plox4tRNKb4LeZTF0QvyOqaaIVyZSbprgDG0tscDfa4pbhKTWv3VhD4bq0MAY5xgkYMUwF05rjqdxITqTAT+cv38/2sJJRfD3IcjWuTznPu94LcYEnif/JBff1GVM3EJEgbSN6lu5GjrZs3Eno2wYfFtGZs5w5PavcQ3EUa+8S7o8uKuwyVdU3beTmCUsvaeYk6c6VCqqVzRC8fKR5OOHjran2OXGaRdF51j4Xjttt0FTPEmta2FQtsk/i3w26RRTOY7wYcL/0EuWucUfgkl+WKZs7GpXWyiwEWbqahS8SduaLdo8OT0TGFNxJ1NIazJpapR206kpi93rm0V5JW8bizlmDpY5mviyGdiTOIFo13p5seYjDHoQaJ2o1e0Q0kkUikQecmr/oKbnUHsrhhXh4gZq8LxC26ddo0myBq/bfiYrNkMbjFdiT132K8dTrUgI3KPFnjv3/wQymNFMZ0RQUX7cxhpF27DF8/BN36lFIa6J3UuI/AJgy1+NVgDNwGpWADbZ3jIYufMMzXWIcQpRPFfgh5IFudEEVVaI8ZKdBIxdhSYIl7wcn04V3qXVMwRRZoZVZAMIhYSY453IyKXhSRmFMpWdBREWC4VF+cVIgSWdIJAFO9oYV1sEvBUJcLvg9FwgTJ7hTCoIaB5YZpSMXj/FBNhGCxpc5+xRTk0Yb9uFFImKEC4GFZXFnRFIUPBRd71ZSp1ZdGlhvzrEkvjFm/7JzlPF2DNETtBKHvJOE3DFEL2ht6rIuPBZLQNQaTKRaM4UQTZNuDGhP0TJ+QkYn1nZ4EgFWn6NHOVxYVT4iTdF2SeNWcFp4GUaiP7KHQzFhXRASP2uRbz2mTKaHKXDxQFMzbI6lhTjDfl+yUQWDecZkYtOnH+vkIoRGL7zFIKrYMlQmFq01cAB0LffSiHsYPr+ViC+EIh3CF0AXHjJGQFzXYCZ2YhoDNz2yZfD2h7chJOiURqERFYezfFx1e1CVjAVHgEW3UyCWHGxiITe3Mu8xkB5Vjv8sgo1FEYUcmFmbeHWpxCJbuCc6NX4fol73onDXZyipVX0nZiOPuDcD2RWbhVDEJiFGkj8xmR+r6DyyM2wrZYdLo0BX9HYioXD9Y5AIMZFDKWtwRR8HdV+SV4ZG2VW9JXgwMheuEmk+BibB8m/34UWeo5KNVTrf50ojkpF0GGgMiYo0MpTWyGj1WFKwp3c1h4vAsS+fcin8yBkL4pOx4ycH6JR9mTmd9HxPJ2uPFo6rQpIikoELIVcD0iBcZErZ8ZjT0Wvi1jW31hPZVFBopCIZKGPfEkeLWBosmC1NqE9tUm8nIn+KQY8umUnBhhYxmH5cNRiN4R8XeHl+iZu2tiD/dbKQrFFUuflKUCmaTPJyiqKOFHecuoGVxAUZkhkik3lphsQW4JgpPWI1EfeCFGlPFzWHYlGUOKIss5F/LfWHlmUpXJZa7AhIEPcXuCgky9IbVGF/rARwwGmf17QaFMlt98kkpPSQqFRinEOUNTIghxJnMBYdFeFoi7igZaR7ugUTJhlYirUplcGG5+eUbwgzmUJz53hd5cmWHbFqlmVXUYM2cOEZIrqdbTac/ElAmPhKi8afGrpTUUlEnoElzDiiGpcQzzEv6mgZoaSgLWoiynJnivY+s8d4ZwlU/XIU6hMRibkTzmWQ12KPXTJnCjlm62mao2ZqiMelP8kR0hUi/xHDNy6KpmLBL2zxn/wJfJNjjlcTpDuVGC4ik0UmPqWHUWOqVTUnow0FS320KZAWW8qYm7aRPYCZpJ8GgSP6Ik9yMjNZPxYyNx7xO2mKqYzHiG3qolbKIkS6oXMioyzRM43JkJmRPfw0htwBRuIyf/+Ri2VJjTOxaJ85UUyKKlJaaK0qoDeFQLWnpbanW/iTj53hpZFiMKCZqYpUHtA1qgqWMNy3rDxhcZxKOaxWJLoWLJEGHQBkdfZiE/RJHsrzia/6lmF6YmukKH7TGuMCOt9JScAXIpDjIbnoUO5Hf8dKVR6KWTqWrN05rUghRNOBfAGbJTDKehx1ntl6ld30Zf+kUqc9WlPd6hoL6YcK5CuQM0S+kacJYqLppKx3yJ9/EjCbciKXSHdsIkOkZpqCSmJt0p7RZLArqR4xAY7wOrNQdoxpg6F1Ap3mhp4YiWAKtpxg4qONtTOlaWC3x1DTCKFC4WwJYTFcgbNCoZ65qZYB13gLq2znkmEHszLFArYmkWk5O1QX4rOXCbA5u3qfqoZvV5PR4SrS82HbKLWMKbLk16dUFU4h2ncLEZR2cjg1OjWauio2apBsGq5f+Ldvh2+Bth4VdUV4hGyaphmvGDm6ap/06h2rMZZmS4efS3BfE0lts4lY2SVRy7W96ocmEnwXZldpwZYxcSeMSSUZ9X3/Zqd3iMuqy1qG9XEqtxe053hghRG4KuMUtwJ6Y1O1ucknBSmSa4upCKuY49Y6YYWVUhs/CMOtwuUcG4VkxJOLTYsWc6ukTEFFFXZ710NAS+iibxgiGmNbSRefmeFvRfpjErSfUga6bZa6HCcd4dq/fsGpoou086OjA6KeDVQjJHS1QWFkILmKjetyZSmhLLM5ncQnwoGsBBSyakdUltpLnKJ7zkVDVDKv0yEdXYmWAxyxRcE1v4RIz+rCE4dNvEsiTvGFwVcx1kYhTzMvBWusH7Ez1FTBL7OlaXRgVLo0HMOG4rqHQPoluGqfpchi1aUfWoNkSUttIvgl0hpjalOxmegnFqhRmztbwzQqsdK7nccCiC7iw1KYt2F4t0yCkhaExfZUJvDIgQW6OLVxeuJGxQdyoQEbwOXhSUAlNN7hEzhcw3QSUCWppoqks7MKupr4vc1bn0jMWQkCJ4fCNZ07INY0dDOBMfPYeiWzr+aJrTlFMY5JPOAEqp/jwtYhgAvKI23haGBpFMt7sHval49ymLRMxtNkrTmLyf+KqbnFTDKnqoemt8qu26NBPCr2q0acjFM62JAxwphX+727Rq/m4lGDPLOiAUKmKBHGVIYtocnfXB1QXHRnZKahJxutEpFpvLNo3E64eEM7pSoORz1J1sqZgUM8TMy9JmGf9saqvHlIEZRzm1UfvFps/MjiCEcq/Jy3iTOrGqNNZmvLqM+Z6qk01c7dhEOPUTEz6G7vpCoqSbtYotHdtF3EY8b/kSKqe76kSsNbOrql+SpDKdGgm6WvAXw7zasESVQaRYRKgTki2Rdp5cIJSVOzzCBrWWR0KkX0BMfe+6Fcxpd2HKb6EX8+O8fkJnjgAXTa58gOQkIVTSO45tQ7gbn/BVchEHzU6NtonMgsX22fyaxRVF3Vq0vNAirF09LWHzu0HRumSba+2ullKU1nQtuBQLt+bu0zXFiGO42nQS12UWZofUKq6+VST83ZX7Ozkbwxr6fH2NajHTbZ2iO1TyqyUowdjRGameHa6ErZcPtOFTMXJVLISETOlg21eWNnqhjTQ5Wk9hsbknEhp6FTLgHVSLXMNOufhdlEYQVlkp3TF8zKG1qeHMpIvVKcphveDbl7Pt3bHnuHfP0ltE3c12y1bdtP2E3IVzTK8mzY2GYvqIHanca2+bzWw+V+qCu3PL3Q0uzY4b2aqrE/Dfk6Qgw+TBxUw5xOEwfYElPSFU2C/4fXvPMMkVvUHaehRJ3LzupNvR5otp9NUxRNY53yLgJ9UFq7iVpHmTX302PVEancjwGa4Oi922ChxhdpKi7+IUbev6On1zYz4L2LeS3C2wmiTaEjGLRU3fRy14qJ5MpxXzQOhQi+EKqio+YWVeqNFD8ox35LKSEyaagYNYz8cqVNFB8Z3yWkYJb8P1tOq7UjlMwmU2A1t44Mxmk60mBi39whJz0jQrJNtGthdh1329bMOxsoY2reuAyePcz4Xl4x1H3Z6XXeMLzo3hK8fnxG5K3FRj+K58AasFlr6HpeS7sGHk+KMD8Lhgd2KTb+lzPEUJaao4GHqh4EglPJYffZ5P+gXlhXvufxnNXg3WZzfrdq5RO/5CeeV5sbPlS3GdIAZaodJsSd3NomgtJRQYqPVOYZEasSOj/NMi1DVLMuKuegC88sFO/iXncOzkZsbhPW06AEK9QC7pQsnoNl5qrQ2qM3rY1yzD9PNigS1iNzguu4OD4yXaT1blzIvs8veuwVez0PehcmZLN2CUNJp0nKXo0Cju3JUms3/oVPI60QlvDNTMTwfbfTN3flWtaClEHgnFNpmtwY79BXZvJxJ3aCBTVdR7ZFvpkqEjQb75T3bOgpn8Mxr4u5bU+KQqVNIYkdSOfdkbJsAobf3UKpSlwtHUSwPq5ALzFDv1qjfk34IhWBzYluP5+srNOh52jAy3qpEombrk6I5w3N3VHW9aonXJFgeJHQcsi6eVTPPQ2sBem8Fo+pkg93VsvClmFC2kL3Cx4XIpU60FGKFb33Ux35/926Pzvwua06UpXgo64vCmnG/2zGs8IU+lMnt9jqlA/vBEnFwMaqm8+6ynFmxki2ZRvV/9ru9kMlIHwiV9RDQoG3xz6+0rjjyI/inje+tY/z7K0Lb06verpv7MItESLB2HLuvlAjQGTh3F0hJcecs6Nv6H0dGr5Vyi8s/RM8ZwINwYfnT7wKEIGsXCNI8N/AggX/Jbx2kOFDglZWPFyYMNBEiRA1buTY0eNHhoH+sQJZ0uRJlCk//guk0mVBK/9kzsTIkBXJlzl1GsTJcYXMaysGtiTIauZOpEk9/hzJUSZRpVFhVrwmkmVVhlc3arWIsOAKqNeseL1p02vCkaxirui5lGtQmxMpZpXbke3DuwxjSuVrUmTYvoEFaxQ52CxNkWCBsgJs2HHhjjJvDpQYU2Zex/+ZQTJtS/GtZpVAC1qFWBfixdJZz44tyMr0NbUPrUC1/O/1xp+0Ad9uGFbgys9GGf7sDDrwX+PJlYoWrHbm2YqklT+mCvFpQ+eXi0+fbnm7wurcTX5eqzey9bAZp7YufpYg2K8tXct0X1p07K6yTYfXaPRieKp+4k08pfYi8MCSLBswJ4loMgg+9WayrT4EdULOpsUk/K5C0KzasCH+ONyqs/mswAk13OoTKiHhRqMKxdFUTIg1gqz67CGjmsKsKOtc/Oi33iwy6EYRX7JqwSIrDGS+l2ITiKnrrlpohYlsa2giKq9LUifLZqtKQvo+3NIw6fpjbszTQsyxIiRbzOr/zYTqcrOo+kxsrbqJcmxsONuoxGsu2EKEyMv39LISzZeeQ3RRAUu6SSAwn6ISIYwW8rIiTIekcFGQIqVyRU6V884pQReFES/bHNoqNbTgLJTFOl1tCK1SvzozIsAKI7LH9UCsNVTcDgUW0efsxEqssSK96K4VTcRpICnFwogohLQc9qSbxLxWMM5I3Ta+jearlcY4zWtVoc5u2/Gs137a9E7+4KP13ZAA1O5bj+ZDEt8DxY30uZ+CrCvTgWJbyOBADVJoX34bJrDbrZrC91cQ3+XPWFzPNQiwOtOjzTOJIwZVYfAo/go6yRyGSFyGVSbQ37dY2ivCKl0jacqWFkLt/ypQ3XX55wohXtnabdXjaM3GDLzTItMYg4lj2cJyemMWDxZWo9pCvDWyJWfa0+E1MQYa0Rzh+yvgWWPKuesgcZ4VKFUt+3psug1j6miitw25I7mzAqy6UyGD7bX6gPwKXVeJy5c+gZ41uWRCgb4pzLqH/Y8+d8+Wa6TCWJsokJbYMryoyyo3XTPL8H58TKU/Yiqs16YmmXSNX80PLWo7q84oel38V9uIWt7WxrlPRxPSLCVk6yqS1PIPPN7HAh1K4I23XqXUw91a7+qnuq6+6iKf9WnwWG0NoVOD6sm/qzsSqMHH91YZyt6vHx7Kf/+FP2X7+4/qbu2tbkxzcpTyhqbjlSXNiDZUaZ1CZEM7i4SFTSMrCQVXpbLLgaV7/rtWtsoCmw+ujIMjRAoAI+ayXf1Ibj1hF9OWhjhZ1ehww4lTT+hzEoqlb1v0I2EPffhDpZhQI9v7lgCxJiHBYUdIMOkJ2maULqIkcEa3+9KFXLcv8Q2rS0DkYhe9aBIhPqRMDnOikfCXQNkFBSqge2Gc3GM494ivhVcCCQEpssEDXU5sX+RjH794/5QAAk1+TcoauWDjG7SQSEYRSVciz6U24GgPWNmpnx8teUn7Ze+EP2tgUrKGuY0kUYbmGuX5puiiBPLPKd/pZJKsUklMxlKWddPkEIUXKiOihDFZk1cMg5Is+tjmScpbG2MkY0wJ1ah9YhRUCvvFFFjOUprTbFgYPTM2QxoGfmgkiQb3R5PLSEh6+MvfQdhIq+Itc3xJqg0eqflOeDKKiNAbWy53YiNPCeVRCRqL9Hjklu/Y0WhBK108DXpQh43KTPZEkwU148FscccqexLlQMWTNXciVKMbleg8v+TMIvJxLcU5U96Ss8XZcVSlK+VQLa3D0IYWj4Qe8hvpWukYlP/ijqU75Wl3PAqiutmxi7WETEZAGhV9zW2QPWVqU5UyxpdW7qg9VKVD4CNUvhxJTGV0ale96pLyeCuotxyh1wyiNJh+ZH8y1elX3frWTv30p/xaahfdBZTE9Oqpz2ErjtIKV8Cq1JqqMR1Xv1jUmbRlqj+CZk5UFVjIAhaqFImm3vpKwt2pcp0qsVFl8RZLP/2Tb2LMZkfSGFnsqel1pL0sosK60NNhlYu9/KXPEpYSBWXUJ38tbNz4E7Ic9QSfwrOR7m4YpBolrX1SJJdxk7syiPrTQrQ1bRb1la9dvg8hYtJQnBBjke7m67IONW0ybVK8yVaNtw31rP1CS7LgVqX/tR9d7wX7CEllUgQqt7opR/Dp3f/kLEDhySthxVKRHM0IU1TRSv4opKfTSDEo5v2och87pJ+SE5AGSmKCgWrTIbJkdEdMbPAGBciqcFdmUjPrEfelznpaUnDv/Wh/1btYI9VXkOEDH1G2FhP8lMRK+GVgpiAIQ1ldRUG9euxjp1dXDIdnTQMrX8UuvD0Y42g2/2mL4CSGmNeKsnaLmxKmKAQUAymOVhFpJsNQPDQdb8miXXTTINcUrpw65sJ05l9pv/zSFq+EKAFrnZVeFDIYs2SXTSEem4ekEPfI9kFfQovYFvPhpuD3tW01SQOJo1Aw0TZ6Ek6pR5DTomZianN7BUObDs/q/5Zaxdd4cf5ZgLR3m0YbxzWWTJkFjUISMU84JVoRTusCJjEg55evwFYWTzjMJgQvM9YOwS+No3wfBmf7VoP172si5bhUAdpav0aWR0JtuxsfJdcHdrRov7QvbpOO1uycNxnl07vSFVc8hu0i3PJEFHIrcZSlXYkNqfaehTS4wau+YWJw4hDI4HXBQ4rduCI16Rvrt93wast8ukdAYUlMJN387ZmRaOqDkCtEIy/LSNaitGdTWJl7Bu+0612km/PLTyOWTXgPlHOdJxxMgXq4AQ8szvrxDuFsBktugFqbR9uodkPWNqVG8pTw8NtF2XL68+40myvLheDSjiZXiV1kW/+lZ1M4dmiIyhhMkpNEPQYK6K7Su+brBfuHxf5OBqdHVsHY2H9qmWigdjScdT3lcipmiZqPLjGkkbs2AvaxcB9dlJGt6WbVobl38W7bm1GmxCNHrmnEDGUxUnY0ep1wXQppw1vSPJxggl24Kd7k7W6HvEePDNA55Hu9Het8z+kMTQmE49i+GTQyDxdvQuiaavHnnP1Z3x590jTv3pArF/FxQStm+C8la74i7A/IhE5hfJoU0n7l62Z5VPvwORh084x3oICPIL37UGY1UpD1sz9+qbg/TtEtpABAbCkS54kI/4oj80Ka5LgIbdEu/3u1jyBA2JiN5sGfDak/owC8aur/o+cItB+ZK8HIMtQ6wSTpvJaSK9Qbm/wbobBpEhLsCwFEQRs0Hg6cwVrjImCas9Rqr3uqwRscQheUKw9sGEmLLaaQFwOMmCZMlCMkQinsIZe6Jg5CvoSiibbwQRnULMMQwjHRQWOZPhZ5QpyyQJfoOzOEQe4oMTOJQn5JQpcRlyziCb5wDjhECcG7Hs1qsBtriWATDYmQoNbStDrsnUEcHJrrsjpUCShZI/xZGfwCCfxaltWCjZQgvCY5idYRHDIMieoJoRipud4jIS5UmTVxJt/TQZ14LDTcod+qvJIRjUEykBaTQ++REu87OBJTFOSCuaH7EReztD4BOHM6owQ5/xT86aXcAJ5PIrN08T4YEZ8wQjYEu6YN8ZctPJO7kzeqkpzZWMIIzEOQML7BwMIdA5SGQJ8GG4rfWjC6e5y8CpjO4jTtgQ6vULhDUsGq0QjqigjwOTkcWp+b4RjlOy0QWRJnFCfSWR428QonsiIk0xFvSzjXWzDG8bx6qZVuxEFyxD/iEzLNKLDAA8MKgbCGvMTHCq13fLUM6ZT9ghawsyHgubI+Oa5cwiqCa50tbC+haqCRuxppwyPicLp4HAjMQKvtCJm9ID1bWcenlC/3C7YqJEWqWkPxsBHAw8XlaEGdODwOUrP0qxbwohoaORTmaQqTSaK94BkGc0Z2OTf3G+DBEAu0T+o4e9oaArJFR6Khk0ARKxGcmakLyCCglpMZdbMWXdmuW4mZQaq/D/vGbYnBRvQJIMwJDwsMk1xBGNIKtII2clq/CSPB1mnL6GMbtcKTi7y2lrmpg9glBXsfwOBKzzgLkDOnkCMpRXM6vpGLiLMh1PywT0qsf2k9iQmY0HKpt9C87CtFH7I218pIExuPV0wtrJQkDkqMMmEwWskS30G4/ZqXThmYKtkv9RsaTrPFpoMlndyTUxQ4XdobwGk2uEAVn0uRy2MOh1A0RfGPI6mW9SmzCUNKoXuQmNmTM//ROngBos1EicbSC8D7SBm8ziGiUGBZQh9xN96roSGyiQJqPEyBnVtSmoBjt7lciSPastKBzr6kRGPJrNissj1R0JAozy/BiQSzReI0MxAZmAA10aH7C4mzIQpJIi/EkAZFkCBDQOrxR7J6z8yg0ZyQUFT8PS35R0dZHwmyGrD4j8qcl0+6nMvIkw95Cyz1nV0UCwXLCqETCoHovnAkolS8FakbDRxFsxDEFBbSmUPTNpggz4aEFPhTHS5Cx8GYPPepLEOVimXJKirdqeqswFlkPnFLFWITRXPbUlPbvagcxTllHigBy9b4lE35ECA5VQAdjTwplSU1sMdrF4+qSg7/os3BmDKRFLJI3Ym+WY4p5JBcTZT64rlpUj4k7TcLzcQm7bTxoDdWdJ8k7VVXOtaDahTtkdZvecHjeERHLIlP9NWYuEy8sNY4hNYbtK2tEFfueSiGfIlbElURMcFlnVU425XJqKML3KAvrRxMnUJzTZNn/T0ygaZIddc/GcBFXVP7ubPWmCiRcA8NLK9g/FN/fAsRVb5X2qD3+ZTlY8VWFYw3Bddq8qjzNEWQDRetlFZhZaZhOdKBdK+DcEVhmRP/2NehmQ1nUTAvzButwCcEAqfH0bD7QMjyMyU2UyUPWZ3a2K70KIpHaacRvDjkEjlYnR8W5KM4E1OvlFS9qCRO/92SDnSsTNJT0eTFE/WJE0pQrWHME2MwroUPAqNUv9rThWkcilPAuAqUliBRtfSUOrrJ/Wie44w/dNUMaoWtL9pD96GfXzUT18GXb3WJg71QhIjHy5i/mhvZGUGfmqIjjDOUGUJSB8EhBWOWFow/B+rH+JSShzNGHDUmlzgV7pzOA1tc5UjTjQTBjPKXwfXHxsWXssmof/3Cm6wIBfHFtOtaW3HDQHlRWumMeMRU3lHIlMCMq5FSRBsYGEWJ9BPNZBszk5iTaMOJkeHHaylcOBOpZk3W5KAYKF0UOjwJKXWYxGDIxy2RjlNUczIUqMWwGfFNEUQu7MlHDIkM2BNPSv9LsWQEUbFbsL9JQ20LXaMh32Gpv03rtwisDYLNjAk83Tl83AoynkKzlMzqMwaSKSIhNKhD3feQC6y6F9xiW1/KCvFdLjxV3oJrSEpbMu8tIBex2S/rWWEio1iF1xE6U6yN3AIx4brp1/MwnU6cXGby2fs0Py20IHHqV99iD8BFusrSW6iQ0oDpwN/6HAk+MfPEsJuJ4b7VmD+DFZa9UBNUOhBkv/wtkjN9j5INw6kiYnxBXtIqWg3a1AmR0645LhhKPzwtWj4+mexjEmdtFENbVTjNV9B1w4C7GgIs0bfEuA+KX0TJwd0tIsYx3i1J2VKrG9tVR3JFFunqWJ1QWLcugApmI5rfKUeC7VapQKBZtuFvycE8ppv3+d9SXhDEBRveZNxVHlcRUosMthxSC/86iwtelXLl9whlK90QJE5mbd4SJr7dbe4UZB68N5ZmNMnMb0YoYqWLc0ZR6/jl4VEnFuUkwtCyD5KIB23OdZ6ldHaRR7XBZgKib9WdIoRbANYwX0FQS22N+MBlXUJA2mXTV3xo8ltYSj4QCl7kb+YNP76eFD5lujoICsoezKBW5Eg1DqbFZDI7gXwp4YrTVTyYbxI5pSgbwGGhsuxfo23Wo0HU4izblbHmkuGICs7ngvVLL3IOSuln7ripvMITqmgR1pAdAUGeOwFcEzG6innT/r3p/PmRAPXKMAaTiJod6qJV0XAitClRyVvpAa2eflLhpH04DVIs4Sqo9HjqDQH/nVcatiEmZ466DVpN2JTJ5gM5RZS8tkPJmlmkLlXJNENDMjblPGAzkWK+vIRcHPLZy9hV4xPTmAhWLGVqoMr2lZIqujuyDnDLC6aEYTFaxoySVaYjaqcwyEt6Jb9+3TGtk71huS77jCkWOMijQNdEMSkTILTxZKg8bdEUM9rckSy+0VGVYXs0tbbcZASWbgwBXOU+YPikFZ3mE478bnKVn6z1IXfOo3CqOGtpJTfJFokDkIdLF+x9M0NjExYbj+jAXPDc7l/UbSGLIrWY3AVjIW9TjQCHJauBIT/Zp3WsU3K7kZBxovB2rDgWb2gVH2yVbaEWlK/VEvZ+zWWUN4e4/+TdYDCM2A93tEjsXgmy2Gd8hux27Dkhg7ZdYzeFqgpvUyys/izgnlSrMd69cGWuEBYk2WhSsTkNxxoUT/LptVRAUiem9prtGIvmyUcGzFADY85K+2+KaBnmALnoG9O0KBYV0xSmuzqI/Bu6xhYjWyfFo0kZp8oFY+FaiecK8qivZXII3WE9h1j6IAvCYNWMKustXcKrNg3r2yB1EvSNq3GFrpGmc8PkIV89+fLrkDBrk08yrehiy28O3mGWPMam4B0oWZi7JNsmf7Hb1iilcbU+BxoMrtzBnWr6++1N9PO+otl02+e9SFZHt6dUtCFaLDpzstlPd0R4xeht/nWgflH17HRx/iPsTMxzC8FAXY+yZsfE9U12pUbBaHN2cJfBbseu/oF2and24l31cF/3PzJB2NZwsWX3cgwweW8q8+25cUetaKn3o9Ew0WuTd6Fbfp//LY9q2HVvvPNeZwERjULe53WbuVQeeP+J+IVZ93eX+EY38TTJErloUonEeP/JwXyPLA8G+a1Q2yOrKdIzZBM1+ZDH8zLOZ6d0+XZOeSJp7CrxK5p/+fAeeZLf+Q5VCN0YlAXmXL1KeKAXkXs3FJ9P+huckwJbKlAJcv7xOpJ0eqC5aInG+iH8m9CtF6H3ce/h+noiXzsne35n6C6xNudIF6RH++noZoSFe7qHdrqvnKW3iK2/e77vezs2wTHVa8FfC6EIR5sFnu1wmvZYkulDVTYqCzIkPEDUUL+v/J2neKAtJ83ffM7vfM//fNDPp08ZfdL/FCf329JP/UF8OdW3/2fVBx2b/VjZj33al33GeBSFfFOI2n3eZ9reByHeD34PwsTnax7L53oXz/zQX37mb37nf37oj37pn37qr/7OByYxjxSb7Sfu737vh/1+SiDdh/wlcRaFvH3hH/7jt9os+1Trf3/4j3/5n3/6r3/7v3/8p37lT+/0Tn2AWCEwUCArK6wQLHgwIUKBCBNCJGjlGsWKFi9izKhxI8eOHj+CDClyJMmSGVf86/jvH0JWLl/CjClzJiuKNK/RrJnzZSBWBa/1ZIUQ6M6XVnwiTFpwqdKmTJmuKGjl4UGHAq9izap1q8B/Wr1uXXnV68qyZs+iTat2Ldu2bt/CjSt3Lt26dvnv4s2rdy3Ksl399g07FixXrE4PP0XcFKjSxEslEhRaEClTpEd51mwpWaLPojJxFgXteWXNjf8CmUytejXr1q5fl0R90WXF0hh9XhtKMXLu2psjAg8ufGqghcMXXjVosHDWhigHgyW7dzr16tavY8+ufTt3sys4eoWt2so/2+LPo0+vfj379u5v+/YcM6jUnlPv3w+a3yVx+8Tz54cSfgWd1RdL3SGYoIILZvfdRuS95xErK0XIGkEZmVehhhty2KGHH8KWoUU64VQiibSdaGJPF6KmU0IoChcjQ8pVdZ9xUCmkHI3L7XgQeVUd5BdLf4mVlkFzGejdgiL/gtikk09CGaWUU1JZpZVXYpmlllty2aWXX4IZpphjklmmmWeimaaaa7LZpptvwhmnnHPSWaedd+KZp557qicUS7JtRFuEDn6EIomtMbkRoHwy2qijj24pmVGLWhRIWYma1JNpmF5EHlpEhXTURSmFVN5FmkKaqqqrsopeZJbWROqpoor6nqmzTaTRrbGZN6FIu7YarLDDEssRK99FVdqFI8o6W6U2FQqtsxSRaptPqGLUbInTilirTdpuW5pt4ForbbHnopsunbhVm1uGulUq1reeorbrZSscexqoOHmaa3l94WQWpRR5u2955BGYa0XLVpSSUN9Sm69st+JrsMTq/2LcJLitgbsxbB3/mpHHIp+F3sh0/oTfNcCufBupy+o7oUsO+jrhRLjVGhW19ZpaK24aYesutcni62ul9AH8c8sr60tqeceWVutK9WZcdYcbN3uyyNm2B3Kpq2kdZdhXmkrbTyMqvLBsRt+qacUw21TThQ9HvLJsy9KdEcNATYwazOZZOtVLDufKtr8R7wrz4VYzHiHWFo0NOdfseQ1S5KZxeTmVk7l09tEYocq2si1+V622mtIt+m6jKwp4adVO3GmvKeHt9OtDF7fw67c33jvlTFO7FtMUUju55Esjn5Ksyyff8KiTM98y8c0XL33WxFdevVmjMj+908Br6z3ww/9jPz3k13evfIR+nibisbX5vfbi11RMv25Gq83vbqa2vfbA+QOwbA4CVsFaljfbaU9ud5sY73znwPNgz3kSpF74jBc96U1QfdVD3gYlGL0ILi1rwdOe9kpGvRN+D3weVJ4GQzhCFHaQhBRkIQdBNBlLtah9tzqNRGojwkqVJioE2uCy9iY7IFbPaAUDVs3aByHkiUpWtGpgAR9oRdVc8IcnPB/3JKe+7mGweF/MVlo2mEIXVpCCzyOZFs+Ywg/KEI5mnOAaj+fCOz7pRfDD1p8WtTdKCYpvRgPUzwIJnxEpqyI0Mw+hFmaTV+2mNqt75LaAIskrYhJsGbTjBe1IRwx+tnCMYGzhJ/HoxuClMYudrOMcrVfKN5JQfK18oSdbCUsvbayRIMlbJnuZqixy0oOv5NoYxRhGUNYwmadUIweXKcyttZGWMbzjG9O4xRhW7paaexLLeGmsSfkynJAC5iZlqMytjW+FazTfGZ9pSnO+83iPm+UyvaZNd66SmviMb6M4++lPK5HTjGUxXilnadAttlOgIIxnPAfasO2l0qGoHKY+J0rPh6oSfc/c5j876lGNYY6V4/woSUvqUY6uCqUmXSlLiaXSX7Y0pjKdKU1ratOb4jSnOt0pT3vq058CNahCHSpRi2rUoyI1qW8KCAA7","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 562.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 281.25px; transform-origin: 407px 281.25px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 214px 8px; transform-origin: 214px 8px; unicode-bidi: normal; ">The figure below illustrates how a torus (donut shape) can be cut in <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABHklEQVRYhe2WWw3DMAxFD4cwKIESKIIiGIMxKINSKIZCCIdSGIZS2D5iqw9tfSRWVWm5Un4ixzlxEtuQlZV1LxWAO7mmBCpZawrSAW/ZYE9O7EdZo+MlcNFSx3One0AOGASmBRqgX/mIgqrFWS0bHAXycoj11ZZMEfMxQHM1B4EqQjR+SaM9XgVUs/141c9wFdCeNELPOwA5wlV5zqcOcyD9eb0FTAqQAx4s85HHIEnGAOmP8yxzkP6yJCiLN7SO1FZ6uAQIQlQUaiThPVkBQSgnyb4sgaq7AiWVD0ugh/hp7wLkCX1Rkp+jQPpgfzViWsvqFJhCNlCgZsN23cx5sW+YSkd0ZArCif2X0fG9YjuZn9u2MmfaU2dlZWX9jT5uooJ0ozaDuAAAAABJRU5ErkJggg==" style="width: 18px; height: 18px;" width="18" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; "> pieces with only 3<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; "> cuts:</div><div style="block-size: 253.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 126.75px; text-align: left; transform-origin: 384px 126.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96px 8px; transform-origin: 96px 8px; unicode-bidi: normal; "> <img class="imageNode" style="vertical-align: baseline;width: 339px;height: 248px" 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" data-image-state="image-loaded" width="339" height="248"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; ">In fact, <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABHklEQVRYhe2WWw3DMAxFD4cwKIESKIIiGIMxKINSKIZCCIdSGIZS2D5iqw9tfSRWVWm5Un4ixzlxEtuQlZV1LxWAO7mmBCpZawrSAW/ZYE9O7EdZo+MlcNFSx3One0AOGASmBRqgX/mIgqrFWS0bHAXycoj11ZZMEfMxQHM1B4EqQjR+SaM9XgVUs/141c9wFdCeNELPOwA5wlV5zqcOcyD9eb0FTAqQAx4s85HHIEnGAOmP8yxzkP6yJCiLN7SO1FZ6uAQIQlQUaiThPVkBQSgnyb4sgaq7AiWVD0ugh/hp7wLkCX1Rkp+jQPpgfzViWsvqFJhCNlCgZsN23cx5sW+YSkd0ZArCif2X0fG9YjuZn9u2MmfaU2dlZWX9jT5uooJ0ozaDuAAAAABJRU5ErkJggg==" style="width: 18px; height: 18px;" width="18" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190px 8px; transform-origin: 190px 8px; unicode-bidi: normal; "> is the maximum number of pieces a torus can be sliced with 3<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; "> cuts.</div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.5px 8px; transform-origin: 68.5px 8px; unicode-bidi: normal; ">Wikipedia's article on <a target='_blank' href = "https://en.wikipedia.org/wiki/Torus">Torus</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 250.5px 8px; transform-origin: 250.5px 8px; unicode-bidi: normal; ">, gives an amazing formula for calculating the maximum number of pieces using n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36px 8px; transform-origin: 36px 8px; unicode-bidi: normal; "> number of cuts on a single Torus:</div><div style="block-size: 36px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18px; text-align: left; transform-origin: 384px 18px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 160px 8px; transform-origin: 160px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 146px; height: 36px;" width="146" height="36"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44px 8px; transform-origin: 44px 8px; unicode-bidi: normal; ">Therefore for <img src="data:image/png;base64,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" style="width: 36.5px; height: 18px;" width="36.5" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; ">: <img src="data:image/png;base64,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" style="width: 250px; height: 19.5px;" width="250" height="19.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">.</div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72px 8px; transform-origin: 72px 8px; unicode-bidi: normal; ">Given a cutting limit x<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157px 8px; transform-origin: 157px 8px; unicode-bidi: normal; ">, write a function to find all positive integers <img src="data:image/png;base64,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" style="width: 36.5px; height: 18px;" width="36.5" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.5px 8px; transform-origin: 38.5px 8px; unicode-bidi: normal; ">, such that <img src="data:image/png;base64,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" style="width: 33.5px; height: 18.5px;" width="33.5" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; "> is a semi-prime.<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.5px 8px; transform-origin: 8.5px 8px; unicode-bidi: normal; "> A semi-prime is a positive integer that has only 2<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; "> and exactly 2<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 156.5px 8px; transform-origin: 156.5px 8px; unicode-bidi: normal; "> prime factors. A few example of semi-primes are: <img src="data:image/png;base64,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" style="width: 155.5px; height: 18.5px;" width="155.5" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">.</div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.5px 8px; transform-origin: 58.5px 8px; unicode-bidi: normal; ">As an example for <img src="data:image/png;base64,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" style="width: 44px; height: 18px;" width="44" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67.5px 8px; transform-origin: 67.5px 8px; unicode-bidi: normal; ">, the only semi-prime <img src="data:image/png;base64,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" style="width: 33.5px; height: 18.5px;" width="33.5" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.5px 8px; transform-origin: 19.5px 8px; unicode-bidi: normal; ">'s are <img src="data:image/png;base64,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" style="width: 300px; height: 18.5px;" width="300" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "> and <img src="data:image/png;base64,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" style="width: 90px; height: 18.5px;" width="90" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129px 8px; transform-origin: 129px 8px; unicode-bidi: normal; ">, therefore the function output should be <img src="data:image/png;base64,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" style="width: 91px; height: 18.5px;" width="91" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">.</div></div></div>

Solve

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41 Solutions
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Last Solution submitted on Nov 17, 2022

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3 Comments

3 Comments

.M.A. on 28 Oct 2022

For n>330289
something weird happens in this series...
Many more numbers pop up as part of the solution.

For example:
330290 ## 463 * 12970537638763 = 6005358926747269
330321 ## 165161 * 36370874563 = 6007050013699643
330326 ## 2678131 * 2243102671 = 6007322799387901
These 3 examples are semi-primes.
You can check in MATLAB command window:
factor( C(330290) )
factor( C(330321) )
factor( C(330326) )
where C(n) is the equation for the cuts-pieces on a torus.

For this reason, the test 6 of this problem may be wrong and should updated for x=3e5.

GeeTwo on 10 Nov 2022

Actually, factor(C(330290)) would return:
[ 2 5 23 29 33029 27259489]
without rounding errors.

Flintmax ~ 9e15, so if you calculated ~6e15 as n/6, n was clearly above flintmax.

A key point to solve this quickly for large inputs is to notice that any prime factors of n other than 2 or 3 will necessarily be factors of C(n) because the polynomial has a zero constant term.

.M.A. on 14 Nov 2022

@GeeTwo
thank you for pointing out a crucial detail that I was missing!

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Problem 52859. Easy Sequences 35: Cutting a donut to Semi-prime pieces

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Problem 52859. Easy Sequences 35: Cutting a donut to Semi-prime pieces

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