{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":60431,"title":"Calculating the Union Area of Overlapping Rectangles","description":"Calculate the area covered by a union of multiple rectangles. Each rectangle is represented by 4 integers: the first two integers denote the coordinates of the bottom-left corner, and the next two integers denote the coordinates of the top-right corner. The input is provided as a matrix where each row represents one rectangle.\r\nThe rectangles can overlap, meaning that simply summing up the areas of each rectangle will not yield the correct total area. Instead, the overlapping regions should be counted only once.\r\n\r\nExample:\r\nGiven the rectangles [ 4  8 11 10;  6  3  8 10; 16  8 19 11 ] the area covered by the union of these rectangles is 33.\r\n\r\n\r\n","description_html":"\u003cdiv 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; \"\u003e\u003cdiv style=\"block-size: 757.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 378.517px; transform-origin: 406.5px 378.517px; vertical-align: baseline; \"\u003e\u003cdiv 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: 383.5px 31.5px; text-align: left; transform-origin: 383.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 381.342px 7.81667px; transform-origin: 381.342px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the area covered by a union of multiple rectangles. Each rectangle is represented by 4 integers: the first two integers denote the coordinates of the bottom-left corner, and the next two integers denote the coordinates of the top-right corner. The input is provided as a matrix where each row represents one rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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: 383.5px 21px; text-align: left; transform-origin: 383.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 383.5px 7.81667px; transform-origin: 383.5px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe rectangles can overlap, meaning that simply summing up the areas of each rectangle will not yield the correct total area. Instead, the overlapping regions should be counted only once.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 0px 7.81667px; transform-origin: 0px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 33.5px 7.81667px; transform-origin: 33.5px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 367.383px 7.81667px; transform-origin: 367.383px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the rectangles [ 4  8 11 10;  6  3  8 10; 16  8 19 11 ] the area covered by the union of these rectangles is 33.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 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rectangles_union(R)\r\n\r\nend","test_suite":"%% Example \r\nR =  [  4 8 11 10; 6 3 8 10; 16 8 19 11  ]\r\na = rectangles_union(R)\r\na_correct = 33\r\nassert(isequal(a,a_correct))\r\n\r\n%%  \r\nR =  [  4 8 11 10; 6 3 8 10; 16 8 19 11; 6 8 8 12  ]\r\na = rectangles_union(R)\r\na_correct = 37\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nR =  [  4 8 11 10; 4 8 6 12; 6 3 8 10; 16 8 19 11  ]\r\na = rectangles_union(R)\r\na_correct = 37\r\nassert(isequal(a,a_correct))\r\n\r\n%% Not overlapping\r\nR =  [  4 8 11 10; 16 8 19 11  ]\r\na = rectangles_union(R)\r\na_correct = 23\r\nassert(isequal(a,a_correct))\r\n\r\n%% Partial overlapping\r\nr = [ -3 -3 -1 -1 ];\r\nR =  [ r; r+1; r+2  ]\r\na = rectangles_union(R)\r\na_correct = 10\r\nassert(isequal(a,a_correct))\r\n\r\n%% Full Overlapping\r\nx1 = randi([10,20]);\r\ny1 = randi([10,20]);\r\na = randi([1,10]);\r\nb = randi([1,10]);\r\ns = a*b;\r\nR =  [  x1 y1 x1+a y1+b ; x1 y1 x1+a y1+b ]\r\na = rectangles_union(R)\r\na_correct = s\r\nassert(isequal(a,a_correct))\r\n\r\n%% Partial Overlapping\r\nx1 = randi([10,20]);\r\ny1 = randi([10,20]);\r\na = randi([1,10]);\r\nb = randi([1,10]);\r\nr1 = [x1 y1 x1+a y1+b];\r\nR =  [  r1 ; r1+1 ]\r\ns = 2*a*b-(a-1)*(b-1);\r\na = rectangles_union(R)\r\na_correct = s\r\nassert(isequal(a,a_correct))\r\n\r\n%% Partial Overlapping\r\na = randi([1,10]);\r\nb = randi([1,10]);\r\ns = a*b;\r\nR =  [  4, 8, 11, 10; 6, 3, 8, 10; 16, 8, 16+a, 8+b  ]\r\na = rectangles_union(R)\r\na_correct = 24 + s\r\nassert(isequal(a,a_correct))\r\n\r\n\r\n%% \r\nx1 = randi([10,20]);\r\ny1 = randi([10,20]);\r\nR = [x1 y1 x1 y1]\r\na = rectangles_union(R)\r\na_correct = 0\r\nassert(isequal(a,a_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":208445,"edited_by":223089,"edited_at":"2024-06-16T05:19:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-02T15:58:47.000Z","updated_at":"2024-06-16T05:19:18.000Z","published_at":"2024-06-02T15:58:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the area covered by a union of multiple rectangles. 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zK9Qnetuy0/UCwEzUJ4GwU4+Zdl6U30mfOCGllE6n++9OxMerG9PTZVSULCxUf72tTAzIy5OdOsnc3CpFRUZe1qLi4mRh4a+iPBNIT3fvSmtL25USpe3KK21tTV7/aVczgYSE/IoS0KK2b9eRts9+U46lBtP2mUBCQn7VT3fACezdqz5xWrCgJk+3V9p8wtTmVqhP9LZlp+sFgJmoTwJhpx4z7bwYN6xLi9LWsTViWJe2KyusyVvNYV1alDK+y9DhcE6nTEjIr+Lprk4CLpfLuGFd2q74hKnNrVCf6G3LTtcLADNRnwTCTj1m2vpdRhcn6b+sY2tocVJsgTV5a6o4UY7F6OLE+ctfTjThr0AaXZxER/MJU6tboT7R25adrhcAZqI+CYSdesy0v38ipVywwH3bN3as+7Zv5Ej1bnXkSHXMUl6eHDBAfcOCBeqIneJiOX68unH7dh9Ru3YdnTzZfd+pjfPRdrV9u5w9W93VkCHuu1VtRVrPcT6eCWhpP/zn4zabf6Ic7PjxNdZvI0d699vBg65KT7eWgHa6K0pg5EjfCUyfnueVQFqa+8RVlLbPn7fyP6XazxufMLW5FeoTvW3Z6XoBYCbqk0DYqcfMXF/YuCcnStTAgRcMfXIS9DV5a/DJibIr5VmQ0U+cBg68YPQTJ+UpjaFPTrQnTt4/3Aaw07Vvp1aoT/S2ZafrBYCZqE8CYaceM7M+kUYWJ/Hx7jV5DR3nE6w1eWu8OJG/zKUxuqhTjsXQ4kRKuWvXUaOLE8Z31fJWqE/0tmWn6wWAmahPAmGnHjNzfeHCQhkX5x57o9329e6t3iyeOOG+WUxMVG8WfUYVFsqoKHeUco/rcrm0KM9daeN8PKM2bHDfrSYm+khg1iwfCXyUftxm47u0HtD6TVvNObB+08ZHaf3mcrkqOt1acaIlkJtbSQLbt/8qAS1t7YmTzygtgYrSrvTnTUmbT5ja3Ar1id627HS9ADAT9Ukg7NRjJrSijIopLpZxcfLwYSmlTE+XERHu30mnpkopZV6ebN/evbTrtGlqbFyce5VYLSoqSqakqFHDh7vX5FWi8vJkp07uKG1XWlR6uuzZ0/2r9HXrfCSg/SrdK21tTV4tbS0BLe3qJ6DN9vaKUnpAiaq03/z39vDh6vVSg2n77Lfk5KyKEqhmv2lR7dvLrVuPyV8/Oamo33Sdbq+0+YSpza1Qn+hty07XCwAzUZ8Ewk49Ztp5MW5Yl3bfqaxja/QkBJPX5DViWJeWtue8IOP6LTLysnHDurQol8tl3LAuLYpPmNrcCvWJ3rbsdL0AMBP1SSDs1GOmPT8xujgxc4a00cWJ85c1eQ0tTqTHvCBD++3gQZf/ExdAAuWjkpOzjC5O4uP5hKnVrVCf6G3LTtcLADNRnwTCTj1m5vrCaWnuATPaJIS8PNmmjXpfOG2a+y92DxmibtywQfbu7R2VnS3791fvO2fOlElJUkq5a9fRjh3VqHXr3LuKjXVPQtDG+Tz1lDsBLcpnAp5pR8Zn2mz+iVcPePab1tu6+k1bk1eLOnjQ5Xm6tROnRXnuasOGShKYOdNdnHimPXnyGe3E+U87LKyS060MIfP588YnTG1uhfpEb1t2ul4AmIn6JBB26jHTzouhT07kr9fkNXScjzlr8kZGXjb0yYkSpRyL0U+ctGMx6MmJEmXaEyfvH24D2Onat1Mr1Cd627LT9QLATNQngbBTj5l2XowuTrQ1eY2ehGDCmrzR0TI5Oatm0/bZb0IIE9bkVY7F0OJESnnwoMvo4kSp6KTx7HTt26kV6hO9bdnpegFgJuqTQNipx0wb32V0cWLODOl/nz1us/FdJjxxUuYFGVqcmPnESf8VoJttrn2btUJ9orctO10vAMxEfRIIO/WYCa1cvqzWJ717u9eW1eacOJ1y7lwpf5kDkJ0tpZTp6XLIEPccgO3b1aiRI9WbxaQkNSovT7Ztq0YlJ2fNnKnuqmdPNcrzbjUpyXcCWtTw4e7FbT0T0KL691d/xnwmkO6xJK6WtlcC2rLIbdv6SEBLOzk5SzvYxMQA+02LqqjflGNJT5fKBB4//aalXWm/KW15JrBr11FtzomWtt5+84zSKgrPflu16kfPBPz0mxZVab+NGeOdAJ8wtbkV6hO9bdnpegFgJuqTQNipx8wc32XckxMl6re+Jq9nlLImbw2m7bPflHlBRi97NXDgBUOfnGhPaYweDpfH+sK1uxXqE71t2el6AWCmECmlEOLIkSPCeLRSO1spKRFCiMce+7Fp06u7d9eZMOH2998/9fPPpS+/fLMQ4umnzx06JGbNajFnTv7PP5empdVbuvSWd9756cgRMXHibQkJZ5Wo+fObvvpqTmamWLZMjfLcVVpavV27Gjz99LlDh85pUR9/rO5KiYqMLKiRBIQQZ86cqTgBEVgCRqfts9+EEJ98csaUBHIqO3EVJlDFqH//u97SpVeM7jcTrhcFrVizlYsXL+YcOSKEaOPRYgtfGz1fNzp9+lKVo7RjqXpUYAn4PJaA0/YZJcw6LwDsRtrv91vGs1OPmdDK8ePqeTlxQrZvr/7Seto092+ytaVdU1JkVJT6m+yICPU32SdOuEfsaFGeu0pJUYcnHTzo0qK0XSlR2q60qKQkdwL9+/tIQPtV+okTcvhwdVePv3xciGBPGqnBf0IoPaD1W2pqJf2mLe9bUb+NHOndby6XSztxngO0tBPnmcD27epy0n5Ot5aA5+mOiFCfOM2e7SNtz583n2l7/rxpp1uLys5Wd8UnTG1uRfD8RGdbdrpeAJiJ+iQQduox086LMsxGmaXgdLr/7kR8vHsOQFSULCxUa4O0NCl/GWZTWPirKM9dec6diIy8rERpu1KitOkrngloURUloEV5JaAdixal7UpLWxkyVMUEPKO0tBMS8n1G1Wy/CSECTrvq/ZaQkO+ZQNX7zf/p9uq3vXtdftKufr8pUXzC1OZWqE/0tmWn6wWAmahPAmGnHjPtvBg05+S3viZvRVHamryG9pvwmBdkXL8p84KMmHPiGeVyuQydq6NE8QlTm1uhPtHblp2uFwBmoj4JhJ16zLT1u4wuTsycIW10cZL+y5q8Rhd1QggT1uT1OhYjihMpZUJCvtHFiZP1hWt3K9Qnetuy0/UCwEzUJ4GwU4+Z9vdPpJSJie5lZLU5J55Lu0ZEuIfZaHNOZs2SCxaoGzt2VKO2b3fvShtTlJyc5Tl1QdtVr15qVEUJxMb6S0CLysuTbWKO22/+SXq69Nlv/fpV0m9KlFe/jR/v3W+7dh3VTly6x1LCWpRnAlU53Vpx4pn2e+/9qEQNGFBJ2v36VfLzphUn5RPgE6Y2t0J9orctO10vAMxEfRIIO/WYaefF0Ccn8re2Jm+lUeHhV0144qQci9FPnLRjMejJiclPnKTx7HTt26kV6hO9bdnpegFgJuqTQNipx8ysT6SRxUl0tDx4UJ0hbeg4H89jMag46dxZ7tp1tGbT9tlvyvwTo4s65VgMLU6klLt2HTVhjhOfMLW5FeoTvW3Z6XoBYCbqk0DYqcfMXF+4sFDGxam3fRs2uG8We/dWbxZPnHDfLGrDbHJzZadOalRamrqxsNAdtX27e4Z0YqJ7V1rUggXuqGom8O7W4zYb36WNxapmv8XFqf2mRWn95nK5Nmxw3+WXP3GBnW6vtNu0uVrjp7t8AnzC1OZWqE/0tmWn6wWAmahPAmGnHjOhFWVUTHGxjItzrxKrTV3wXJF25Ej30q7aJIROnWRurho1a5a6Qy1K2ZW2ju2GDd5RTqc7qqIEtKi4ON8JaFHK+sIVJeB0uucz+EzAK0r7tX35tBMS8pUEqtNvWlRFCSjXi88EPNOOj69WvyUnZ2nL+1bUb7pOt89++/rrDM9dVeV0B9BvfMLU5laoT/S2ZafrBYCZqE8CYaceM+28GDesS4uy+Jq8uqKUNXkNHQ6n1I1GD4dLT3cfixHDurQoZX1ho4cR8glTm1uhPtHblp2uFwBmoj4JhJ16zLTnJ0YXJ2bOkDa6OHE6pcvlMro4kdJ9LIb2m3IshhYnUsqEhHwT5jjxCVObW6E+0duWna4XAGaiPgmEnXrMzPWF09JkRIT3HIA8j6Vdp01z/8VubWnXtDT3MBstStuVEqWMvfFcx1bbVXGxHDnSvSufCSgLHHsloK2um5bmXqY2Mj7TZvNPvHq70n6Lja2k37TlfbV+O3jQpfW2Z5kR8OnWEvBMe/LkM0rU+PGBnG7PBLTTXT4BPmFqcyvUJ3rbstP1AsBM1CeBsFOPmXZeDH1yIi28Jm9gg8EGDrxgwhMn5bmW0U+cIiMvG/rkxOQnTtJ4drr27dQK9Ynetux0vQAwE/VJIOzUY6adF6OLE2uuyRtYcRIf716T19B+E0KYsCavMi/I0OJESnnwoMuEOU58wtTmVqhP9LZlp+sFgJmoTwJhpx4zbXxXcbEsLJRRUeptX3a2+2YxKUm9Lzxxwn2zuH27urGw0H2zmJbmvllMSnLvSpshnZjojtLuVrUVaaufwEfpx202vivvlz+1bkS/KVEul8vrxNXI6fZKW3viVIOnu3wCfMLU5laoT/S2ZafrBYCZqE8CYaceM6GVy5fV+iQqSqakSCllXp7s39/9O+m5c9WN7du7l3b1nAOgrS2rTUJISnLvqm1bmZ0tpZQJCfla1PDh7l1pv0qvKIGZM/0lEBUlU1PdCSg/Y54JaFFOp760tScA5dNOTs5SpuVUp9880/aZgLa+cGD9lpTkI4HZs939pkQlJ2dpCdTI6fbZb1u3HlOiKu03/6fbf7/xCVObWxFCyLg47Qv3N3xu9Hz94YdVj3IfS9Wj9CfgcrlqNm2fUXa6XgCYifokEHbqMTPHdxk0rEu7W7XOmrwBD+vSEoiMvGz0cDjluZbRw+G0Y6nx0+2VtsvlMmGOE58wtbkVnp/obctO1wsAM1GfBMJOPWba+sJGFydmzpA2ujiJjpYHD7qMLk6UYzG6OFGOxYjT7ZV2cnKWCXOc+ISpza1Qn+hty07XCwAzUZ8Ewk49ZkIrx4+r5+XECTl8uHrbN3Om+2ZRG7GTkqIOGfK8Wdy+3f0nw7W1ZbOz3VFz56pRBw+6+vdXN6amuv9k+JAhalRFCbRpU0kCPXuqUVOXHLfZ/BPlYKvZb6mp7n4bOdK731wuV82ebq2i8Ez7P/7jipK2lkD1T3f5BPiEqc2tUJ/obctO1wsAM1GfBMJOPWbaeTH0yYm0xpq8NfLkRElbW5PX0H5T5gUZ/cRJ+8uJBj05MfmJkzSena59O7VCfaK3LTtdLwDMRH0SCDv1mGnnxejiJOhr8tZgcaKtyWt0UaecF6OLOmVekKHFSXGxPHjQZcIcJz5hanMr1Cd627LT9QLATNQngbBTj5m5fpe0ywxpo4uT9HTpcrlMeOKkHYtx/abMCzK6ODHziZM0nm2ufZu1Qn2ity07XS8AzER9Egg79Zhp9YmUMjFRXcU1L0927Oi+WVTWey0ulhERMi1N3ahNQkhMlBs2eEdpu1ImISjrCycnZ2lzJ7Rd5eXJIUPcu/KZwFNPVZLAunVqVJuY4/abf6IdbI3029ix3lG7dh2t2dOt7coz7ffe+1GJKp9AwKe7fAJ8wtTmVqhP9LZlp+sFgJmoTwJhpx4z7bwYvXxTepDW5K3xJydK1MCBF0x44qSsRWbckxMlKjz8qqFPTkx+4iSNZ6dr306tUJ/obctO1wsAM1GfBMJOPWZmfSLtMkPa6OIkPt6kNXmVv0tjaHHSubN7XpCh/bZr11ET5jjxCVObW6E+0duWna4XAGaiPgmEnXrM5PWF27dXb/vWrXPf9vXsqd4XpqTIqCj1ZlFb2vXECdmpkxo1bZoaVVgohw9XN6amumdIR0SoUYcPy7g477vV6ifw+MvHbTa+SxsfVVP95hml9JvL5TLidHulPWCA9xMnI37e+ISpza1Qn+hty07XCwAzUZ8Ewk49ZtrfZ1R+J33ihJRSpqfLxET1W9HRcvt2dWNUlCwslFJKp9M9C6JTJ5mbq27UouLj3bvq3VsWFqozpLWouDj3rmbNUjdWlIAy4cFPAkqUkoByT18jaWtPAMqnnZCQv2BBJWlXmoBn2j4T0I6lBvutfNrJyVk1e7p99tveva6KEqjO6fZKgE+Y2twK9Ynetux0vQAwE/VJIOzUY6adF6OXbzJzTV7jhnVpuzJnTV7PY6nxYV1alHIshg6HKy6WLpfLhDlOfMLU5laoT/S2ZafrBYCZglyffP7559OnT583b96pU6dqpBU7fRraphVl/S47zZA2ujhxmrUmr3YsxhUnyrEYXZxIs/4KJJ8wtbkV6hO9bdnpegFgpmDWJ2+99VZMTMzx48c//fTT22+//dKlS9VvxU6fhrZpRRu1n5bmXiW2Xz8fN4vTpqmDf/LyZK9e6n3hggXqQKPiYjlypLpx+3b33eqQIWrUrmQGXuMAACAASURBVF1HtSVxPYcn9e6tRlWUQK9elSSgRUXGZ9ps/on89VLCAfebMhQqL08OGOAddfCgKza2Jk+3VlF4pj1x4tmKEgj4dJdPgE+Y2twK9Ynetux0vQAwUzDrk6ioqJSUFOV19+7d//3vf1e/FTt9GtqpFeX39EYve2X0mrxKlOeavDWSts8HF+asyas81zLuyYkSpf3lRHs8cZLGs9O1b6dWqE/0tmWn6wWAmYJZnzz77LN9+/a9cOHCuXPnOnfuXKzcNVSPnT4N7dSKDdbk1aK0NXlrKm2fd/nmrMkrhDC6ONHmBRld1O3addSEOU58wtTmVqhP9LZlp+sFgJmCWZ9cu3btP/7jP5o3b96xY8f9+/fXSCt2+jS0TSva+K7CQhkVpd4XpqW5bxYTE9WNJ064bxYTE9WbxcJCGRfnHrGjRHnu6sQJ9wxpLcpzV2lp7l0FloAW9VH6cZuN79J6ILB+Kx+1fbt3lMvl8oxKSqqZ0+2VgPbEqfqn208CfMLU5laoT/S2ZafrBYCZHGVlZRkZGSIYnnvuuYceeqhz587vv//+//3f/3300UetW7f2fEN4eLgJabhcLhNaqeXMOZWACfjEqLX4HAuAOddLmzZtTGgFgGlCHA6HMOXaPnLkiGcreXl5hw4d+t///V8hRGRkpBAiPT197ty5niFS/f2LDg6HI4AovbyOhVYq5XK5bHMsdvoZs9Ox0AqtGN2KnT7HbNaK0U0AMNl1wWq4fv3658+fv3jxovJlZmZms2bNgpUMAAAAACsICVbDjRo1euWVV/r37x8dHf3NN980b9580qRJwUoGqKIT4oQQwiEchrfEaAUAAFArBa0+EUJMmDAhLi7u+PHjU6dOvfnmm4OYCVBFd4m7hBBS2GRMlBmFFgAAgB7BrE+EEPXq1WvXrl1wcwAAAABgEUGbfwIAAAAAXoL8/AT4bWH+CQAAgKGoTwAdmH8CAABgKMZ3AQAAALAKnp8AOjC+CwAAwFDUJ4AOjO8CAAAwFOO7AAAAAFgF9QkAAAAAq2B8F6AD808AAAAMRX0C6MD8EwAAAEMxvgsAAACAVfD8BNCB8V0AAACGoj4BdGB8FwAAgKEY3wUAAADAKqhPAAAAAFgF47sAHZh/AgAAYCjqE0AH5p8AAAAYivFdAAAAAKyC5yeADozvAgAAMBT1CaAD47sAAAAMxfguAAAAAFZBfQIAAADAKhjfBejA/BMAAABDUZ8AOjD/BAAAwFCM7wIAAABgFdQnAAAAAKyC8V2ADsw/AQAAMBTPTwAdtPknRv9zHXGZ0EqwuxMA4LZzp/rfmBhRUiKEEPPmqRvz80WXLiI/X904b54QQpSUiNGj1Y1aVEmJiIlxR40e7d6VEuW5q5073bvSonQlUFHU/v3G9hXszVFWVpaRkRHsNGpMeHi4y+UKdhawMzv9jNnpWADUWiasJmIOh8NWa5ZIyW/BECgppcvlksYzpxXliIxmpx6jFV2Oy+NCCCHt8o/rhVZohVZoxTKEENHRsrhYSimnTZPp6VJKefiw7NRJ5uVJKaXTKZ1OKaUsLJTDh6sbU1OlElVcLHv2dEfFxam70qJOnHDvat06daNnlLYrzwQ8ozwT8B9lzv9fYFfMPwF0YH1hAIBxPvtMhISIefPEwIHigQdEfr4YNUqkpYmmTcW8eeLKFfHKK6KkRDz2mPjrX0XTpmLnTvHKK2LzZiGE6N9fzJqlRjmd4r331F1df714/nmRny8GDxaffaZG7dkj5s8XJSWif3/x8svigQfUXW3c6J3A4MHuBIqK1KjBgyuJAqqD+gQAAMAS6tUT8+aJqCj1Lj86WmzdqtYGQqjFybhx4o031DJj7lx3cTJ3rho1dapYtUotGIRQixNtVzt3iq1b3cWJEqXtSomqKIGqRwHVwfx4AAAAS/C6y9ceXAghXnrJR3HyxRdClCtOPvzQXZy89NKvdqUUJ8quvMqML77wUWaUT6CKUUB18PwE0IH1hQEAxvnP/1Tv8vv0Ef/8p/ewrtGjxf/7f6JpU7F1q5gzR3z1lRBCxMa6i5OJE0VKiggJEdOniwYNxPz5Ij9fTJiglhlbt4rPPxd//asoKRF9+7oHaGllxvTp4uGHvRNYuNCdgBa1Y4dYuNBfFFAd1CeADsw/AQAYp2dP9RGEVpwIj2FdSnGyc6dYuFAtTryenCjFybx5onFjH09Odu5UixPPOSeez0BiY93PQMon4Bn18suVRwEBY3wXAACAJfzWh3VRnKBGUJ8AOmjju4z+F94m3IRWgt2dAIBf0e7y58wRQoiXXhJXr7qLk61b1dqgpEQ89JBaMJw+7S5OtKisLPeuduxQi5OrV91R2q5CQsTcuWqZ4RnlmYBWnPiMOn3aRxRQHYzvAnRgfBcAwDjr16uPIAoK1MWyxoxxLyWszTkZNEj813+pDy4mT3YP61Ki8vPFgAFi40Y1KjVV/OUvoqTEHaXtSonq3FndlRblmcCAAe4nJ1rU3LnuKM8nJ1oUUB3UJwAAAJZw553q+Chlosi4ceLtt93DurQ5J06njzknSpRSMHz5pXtYl1KcaFHarsoP0FKiPBPwmqmiRcXE+IsaNy5Y/VddUso9e/Z06NDh+uuv9//Oo0ePLly4UAgRFhY2e/ZsU7KreSdPnnQ6nUKI2267TXlhEdQnAAAAlvCbnnPimfbHH+s+9oyMjM3KH3MRokmTJt26dQsPD6+RXq26BQsWOJ3OzMzM2267zf87c3JyLl++PHfu3Pr163t9a/ny5ePGjWvYsKGf8P37969Zs6akpCQ2NrZHjx7+28rNzd24cWOzZs0GDhzof6OmtLR09+7dqampTqfzuuvU2RwFBQUfffRRdnb24MGDu3XrJoRo1qzZs88+K4QYMWKEpeoT5p8AOjD/BABgnLIy9S5/9Gi1ONm0Sbz4olqcaEsJnz4tJk5UixPlrlIpTh58UC0YNm0SX3zh3pUStWOHeOEFtcyYNctdZvTsqUY5ne4EtOJkxw41AWUpYW3Oic+oCRPUtAPQunXr/Pz85OTkPn36hIaGxsTELF26tOrhJ0+eDKTVX3vhhRcaNGhQxTc3bty4bdu2d955p+fGJUuWPP3005cvX/YTuHfv3ocffnjYsGFxcXFjxoz517/+5efNKSkpCxYsWLly5e7du/1v1BQUFCQkJKxfv37+/PlSqiPSS0pKYmJibrjhhscff3z69OkbN24UQoSGhrZt27Zt27ZVPGTTUJ8AOmjzT4z+5zriMqGVYHcnAOBX5s71Xkp40SL3X4ifNUutKGbMcA/rcjjcT07S09Wob75x/633qVPdiwJv3apGDR3qfgayY4f6DMThUBPwfHLy8svuvxCvLSX80EM+osaNE0uWqAkEIDQ0tGXLlg0aNGjXrl1sbOyMGTNWrlypfffSpUunT5/2fH9xcbFWkxw+fDgxMdHzu9nZ2VlZWdqXZWVlFy5cEEJ47eTatWs//vijn6xycnKUwKrYvHnz4cOH77jjDv9v++yzzwYOHPj73//+/vvvHzZs2FfKuL0KxMbGvv766126dKl0o6ZBgwZvvfXW9OnTPTf+4x//CA0NHT169B133PH888+/8MILVTum4KA+AQAAsITf+rAuLe3qu3LlSvPmzYUQJSUlkydPnjVr1vPPPz9y5EjlgcDy5cvHjh2bmpp67733HjlyZNKkSbt3754yZcq6detOnjzZu3fvjz/+OCEhYezYsUKIQ4cOPfDAA3379o2Li+vXr19kZKSyk7Vr1w4dOnTt2rUdO3YcNWrU22+/7ZlAdnb20KFD33zzzaFDh77xxhuVJpyRkbF48eKlS5c6HJUMT7j//vs//fTTI0eOSCn37dsXExMTcC9V3bZt27SBZN27d9+7d+/PP/9sQruBYf4JAACAJdijOPniC1G3boA9kJOTs2bNmmPHjv3www/K85MVK1YUFxe/++67Qoh77rlnx44djRs3XrRokcvlCgkJ+e6770JCQiZMmPDll18uX75cCLF3796IiIgZM2aMGjWqXbt2Qoj27dsPGjQoNzf3zTffFELcfvvt33//fdeuXWfOnLlmzZrIyMjTp0/Xr19/8uTJnplMnTp1xIgRjz76aFZWVnh4+JQpU/xMmr948eLEiRNXr14dGhpa6TEOHDjw4Ycf7t69e1hY2JQpUzp16hRgZ+nx008/3XPPPcrrJk2aCCFOnjypvLAg6hNAB23+ieEtGb62MADAchYvVu/yX3xRHdYVFeUe1jVxojqsa84cUVCgrtb14IPuYV0ffyyWLRMlJeKPfxTz56tlxquvqmXGnDnivvvUXfXp4/5b75cvi1df9Y5SElCiIiO9o7QESkrEkCHi3Xe90w5YaGjoLbfcsmvXrmPHjil3z5s2bapTp46yRlZkZGRpaemWLVsiIiJCQkKEECtWrBBCbNu2TdtDly5dWrVqtXz58nPnzl27dk3bXqdOHeXF3XffnZ+fL4Ro3br12bNnhRBnz55t3bq1VyabN29u1arVoUOHhBD9+/c/f/58s2bNKkr70UcfjYqKOnbs2LFjx65evfr111/ff//9d911l883v/POOw0bNszJyVm1atXcuXNvvfXWYcOG6e8qfRo2bKj1RlFRkRCiUaNGRjcaMOoTQAf+/gkAwDgtW6qPILQ5J3/5i4+lhK+/Xv07J55zTrZuVYuT/v3FokU+noH07+9+BqIVJ0KoxYlXlDbnxGeUkoDy5OSDD9xPTrS0A9akSZOYmJiYmJhevXqtW7du4sSJpaWlQ4cOffzxx7X37Nmzp6CgoKI9bNiw4ZVXXlm1alXTpk3n+h1qtnLlymnTpm3atKl+/frPPfec57eklKWlpc8880xYWFhV0u7UqdPPP//86aefCiEKCgq++OKL0NDQiuqTJUuWbN68uX79+pMmTWrUqNEbb7xhQn0SFhZ26tQp5fWpU6dCQ0MrXaMsiJh/AgAAYAm/9WFdWtrVFx8fv3r1aiFETEzMe++9V1xcLIQoLS3Ny8uLjo5OS0s7cuSI8s5r1645HI7c3Fzly08++WTw4MF33XWX58MTn9q2bXvu3LmpU6cuW7bMazlgh8MRHR2tPJwRQly4cMFPRSSEmD9//pJf3HzzzS+//PKAAQMKCwu//fbb8m++8cYbMzMzldeZmZnKY5nTp09rRxSYAwcOKI+DfBo3blxqaqrSJ+vXrx8zZkylf+MlmKSULpdLGs+cVpQjMpqdeoxWdDkujwshhLTLP64XWqEVWqEVyxBCREXJ4mJZXCwjImR6upRSHj4s4+JkcbGUUk6bJp1OKaU8cUK2by/z8qSUMjVV3egZlZIilV1JKZ1OdaNnlLar4mLZs6ePqGnT3FGdOnlHFRbK4cPdCURHe6cdwP9f9u7d+8c//rFFixYfffSRlLKgoCAiIiI2NnbLli1/+tOfOnbsGBcXFx8fv2/fPinlihUr7rjjjv79+48ZM+b777/fv39/o0aNxowZs3nzZmXS/BNPPLFkyZJ69eotWrRo//79Dz74YNeuXfft25eamtq8efNRo0bl5+cfO3bs97//fe/evVu2bDl+/PirV6++9tprdevWfeaZZ4qKik6ePPnggw/27NnzkUceeeKJJy5cuOCZ7VdfffXkk0/6PJC77rorJydHSrlly5abbropXekRD99991337t1nzZr16KOP9uzZ88cff5RSOp3OW2+99erVq15v/umnn5566qmwsLAuXbpMnz69tLS0oo39+vXr16+fEvXOO+888sgjQognn3wyNTVV2fg///M/AwYMmDFjxkMPPXTmzBnPVjp06KD3fBmK+iQQduoxWtHLTj9jdjoWWqEVWqGV3zohRGGhLC6W0dEyLU1KKfPyZFycLCyUUkqnUyYmqhs7d5YnTkgpZXq6utEzKj1dRkW5o7RdaVHarpSo7dv9RXXqJHNzvaPi490J9O4ty6ddU/9/OX/+vHLzffXq1StXrnh999KlS9rrsrIy7XVRUZES5X/PYWFhxcXFys47d+68e/fu8m+7ePGi8h4vfuqT5cuXX758WXmdmJj49ddfl39PSUnJ0aNHlcpE069fv6KiIv9p+3Hp0qUhQ4b4f09RUVF+fn757VarT5h/AgAAYAkhId7Dulatcg/r0uaceA7r0v7OiecArdTUSgZoVT1q61bvKK9hXdqcE8+0a8pNN92kvPC5LtYNN9ygvfZc1bduFZYPy8nJOXXq1OHDhzt16nT8+PE777zzvvvuK/82P5PIDx069Pbbbzdv3txr9oi2DtiqVatCQ0MjIyPLx9apU8dzZouUMikp6bHHHqtK5hUdzvz58+fPn+//bXXr1r311lu1L8+ePbtu3brAWjQU9QkAAIAl/KbnnHim/fHHwevEqgkPD//www+dTmeLFi3uvffetWvXVmVpYM/wSZMmCSH8/L35Rx55pIpzPBwOx5w5c6ozIeSWW26pyp9e8XLdddcpNd7ChQsDbtoI1CeADqwvDAAwzosvqnf5M2e6i5PrrxfPPy/y88WECWrBsGOHSE0Vf/mLKCkRo0e7ywxtKeF588QDD6i7euopNUq5BVXKjNhYd9Qbb6hRL7wgHnpIjdLaWrhQTaCkREycqBYnO3aIZcvU4mT0aHfa06eraf8mjBo1atSoUYHFNm3aVPnjj37oqjeqOVs9sAcvTZo0qfQoguI38hMEWAPrCwMAjNOzp48nJ0px4vnk5Msv1eKkZp+cDBxY1ScnL79c+SJjQMBYXxgAAMASfuvDuihOUCOoTwAdtPFdRv8LbxNuQivB7k4AwK9od/lz5gghxEsviawsERWlFgxbt6rFydWr4qGH1Npgxw53mTFnjlpmZGW5ywxtWJdn1NatlURpCVy9Kh59VC1OtKiSEveusrJ8pA1UB+O7AB0Y3wUAMM7f/qY+gigoUFfrGjxYfPaZ+uDi88/FX/8qSkrEoEHiv/5LfQby4oti61Y16r771KcZAwaIjRu9n4F4Rs2ZI776So364x99RCkJlJSIP/1JLFyoJqBECeHelTLnZPVq77SB6qA+AQAAsIR69dSK4q9//dXyvsqwLqU46d9fOJ3uAVpaceI5QOvLL30M6/KM0oqTiqKUtsaNE2++6R7WpRQn2q6UYV2ffOIe1qWlDVQH47sAAAAs4Tc958QzbaA6eH4C6MD6wgAA4xQVqeOj+vQR//ynaNpU/P3vYs8edahV377i5ZfV2SPaAK1Zs8TQoWrBoEVNny4aNFCjtKWEPaOeflrEx6tRDz4o0tN9RL3zjmjaVHz+uVi8WP0jjFoCp0+Lxx8X69erCTRoIObO/VUCQHXw/ATQQZt/YvQ/1xGXCa0EuzsBAL+i/YV45S5/505x6JD7b70rtcHOnWLhQvcALa040aLmzRONG7ujZs3yEaUVJ9HRanHiGTVunFqc7NwpXn/d/RfilQTy88WMGWpxMm+euOEGtTjxTBuoDuoTAAAAS/itD+vS0gaqg/oE0IH1hQEAxrFHccL6wqgmR1lZWUZGRrDTqDHh4eEulyvYWcDO7PQzZqdjAVBrmbAauzkcDlv92khKRhEjQA4ppTl/acGkv+fgcJhwPdipx2hFLzv9jNnpWGiFVmiFVgDYA+O7AAAAAFgF6wsDOrC+MAAAgKGoTwAdtPWFjW7IpPFdTJEHAAAWw/guAAAAAFZBfQIAAADAKhjfBejA/BMAAABDUZ8AOjD/BAAAwFCM7wIAAABgFTw/AXRgfBcAAIChqE8AHRjfBQAAYCjGdwEAAACwCuoTAAAAAFbB+C5AB+afAAAAGIr6BNCB+ScAAACGYnwXAAAAAKvg+QmgA+O7AAAADEV9AujA+C4AAABDMb4LAAAAgFVQnwAAAACwCsZ3ATow/wQAAMBQ1CeADsw/AQAAMBTjuwAAAABYBfUJAAAAAKtgfBegA/NPAAAADEV9AujA/BMAAABDMb4LAAAAgFXw/ATQgfFdAAAAhqI+AXRgfBcAAIChGN8FAAAAwCqoTwAAAABYBeO7AB2YfwIAAGAo6hNAB+afAAAAGMpRVlaWkZER7DRqTHh4uMvlCnYWsDM7/YzZ6VgA1Fom/DbHHA6HrX5nJKXhv8uDXTmklOb8ptak3wc7HCZcD3bqMVrR5YQ4cbfjbuMfn5jFYcb/P2xz9mmFVmil1rZiDofDwf9fAMH4LkAXxncBAIxjwv9fzMH/X1AdrN8FAAAAwCqoTwAAAABYBeO7AB1YXxgAYByGRQGC+gTQhfknAADjMP8EEIzvAgAAAGAd1CcAAAAArILxXYAOzD8BABiHYVGAoD4BdGH+CQDAOMw/CS4p5Z49ezp06HD99df7f+fRo0cXLlwohAgLC5s9e7Yp2VXLyZMnnU6nEOK2225TXlgZ9QkAAACCLCMjY/PmzcrrJk2adOvWLTw83OQcFixY4HQ6MzMzb7vtNv/vzMnJuXz58ty5c+vXr69tvHDhwmuvvZaZmfn000//4Q9/qChWSvnFF1/s3LmzQYMGo0ePvvvuu/23tXHjxq1btzZu3Pixxx4rn1hpaenu3btTU1OdTud116kTNwoKCj766KPs7OzBgwd369ZNCNGsWbNnn31WCDFixAjr1yfMPwF00MZ3Gf0vvE24Ca0EuzsBAL9iwie/Of8COPbWrVvn5+cnJyf36dMnNDQ0JiZm6dKlVQ8/efJkAI16eeGFFxo0aFDFNzdu3Lht27Z33nmn8uWBAwcefvjhgQMHJicn+ylOhBAvvvhiSkrK+PHjr7/++q5du+bk5Ph58/Lly19//fWEhITOnTtHRERcvnzZ87sFBQUJCQnr16+fP3++lOrDt5KSkpiYmBtuuOHxxx+fPn36xo0bhRChoaFt27Zt27ZtFY8uuKhPAB208V1G/3MdcZnQSrC7EwDwKyZ88pvzL4BjDw0NbdmyZYMGDdq1axcbGztjxoyVK1dq37106dLp06c9319cXKzVJIcPH05MTPT8bnZ2dlZWlvZlWVnZhQsXhBBeO7l27dqPP/7oJ6ucnBwl0D8p5RNPPLFw4cLIyMhK33zjjTeOHDmyTZs2M2fOvOmmm77//ns/b05JSZk8efJdd901dOjQli1bHjlyxPO7DRo0eOutt6ZPn+658R//+EdoaOjo0aPvuOOO559//oUXXqg0JathfBcAAACs5cqVK82bNxdClJSUPP300w6Ho6CgoKCgYO3atQ6HY/ny5V9++WV0dPSrr776+eefT5o0KTc3d8qUKX369ImIiBg3btygQYO2b99+4403fvTRR4cOHXr88cfLysruvvvuQ4cONWzY8Ouvv3Y4HGvXrv3b3/4WHR39/vvvt2/fvk+fPpMnT9YSyM7OnjJlSocOHb7++uthw4ZNnTrVT7ZpaWlFRUVnzpx57rnnbrvttokTJ/p5DjNr1izlxU8//RQSEtKrVy8/e77//vtXrFgRHR1dWlp67dq1zp07V9p127Zt69Gjh/K6e/fue/fu/fnnn5s0aVJpoHVQnwAAAMAScnJy1qxZc+zYsR9++EF5frJixYri4uJ3331XCHHPPffs2LGjcePGixYtcrlcISEh3333XUhIyIQJE7788svly5cLIfbu3RsRETFjxoxRo0a1a9dOCNG+fftBgwbl5ua++eabQojbb7/9+++/79q168yZM9esWRMZGXn69On69et7FidCiKlTp44YMeLRRx/NysoKDw+fMmWKn0nz+/btKysru3r16rBhw1asWBEVFbVz505tNohPDz74YG5u7qZNm/yPKPvv//7vnj17tmnTpmnTph9//HFISOW37j/99NM999yjvFbKkpMnT1KfALbF+sIAAOMwMzA0NPSWW27ZtWvXsWPHlFvqTZs21alTR1kjKzIysrS0dMuWLREREcqd+ooVK4QQ27Zt0/bQpUuXVq1aLV++/Ny5c9euXdO216lTR3lx99135+fnCyFat2599uxZIcTZs2dbt27tlcnmzZtbtWp16NAhIUT//v3Pnz/frFmzitLOysrq1atXbGysEKJbt24tWrT45ptv/I/1SktL2717d0xMzJtvvjlo0KCK3jZp0qQ5c+b06NFjyZIl/fv3//LLL8PCwvzsVgjRsGFD7cCLioqEEI0aNfIfYjXUJ4AOrC8MADCObWYGBvz/lyZNmsTExMTExPTq1WvdunUTJ04sLS0dOnTo448/rr1nz549BQUFFe1hw4YNr7zyyqpVq5o2bTp37lw/ba1cuXLatGmbNm2qX7/+c8895/ktKWVpaekzzzxTaTGgaNWq1f79+5XXdevWbdq06ZUrV/yH1KtX7z//8z+HDRv2j3/8o6L6JC8vb9euXe+//74QYsGCBefOnVu1apX/gxJChIWFnTp1Snl96tSp0NDQSpcjsxrmxwMAAMBa4uPjV69eLYSIiYl57733iouLhRClpaV5eXnR0dFpaWnaTPFr1645HI7c3Fzly08++WTw4MF33XWX58MTn9q2bXvu3LmpU6cuW7asYcOGnt9yOBzR0dHKwxkhxIULF/xUREKIIUOGbNu2rbCwUAiRlZV16dKlHj16FBYWfvvtt+Xf3K9fv3//+9/K6++//7579+5CiNOnT3vNfRdC1K9f//z58xcvXlS+zMzMVJ7hHDhwQHny49O4ceNSU1OVw1+/fv2YMWMq/XMuVsPzE0AHxncBAIxTmx9r79u3b/Xq1RkZGatXrx4zZsz48eM/+OCDESNGTJ48ed++fV27du3YsaPD4Zg9e3bnzp0XL14cHR3dsWPHm2+++dlnn+3Ro8ef//znsWPHjh8/fuzYsQkJCUePHm3fvn1ISMjixYv79euXmppaUFCwf//+7OzsjIyMv/3tb926dbt48WJZWdmkSZN++OGHvn37rlixYunSpVeuXHn11VcXLVq0bNmy+Pj4Xr16tWzZ8sYbb1y0aJGf5Nu3b5+UlDRgwIAHH3zwcmI30gAAGWtJREFUm2++Wbt27Y033piWljZixIjPP//8gQce8Hxznz59XnzxxW7duu3Zs6dr165PPvmkEGLlypVLly5VHndo72zUqNErr7zSv3//6Ojob775pnnz5pMmTRJCKH/JJDU1VQjx7rvvbtmyRQjx1FNPDRs2rF+/fm3atElMTBw+fHi7du0OHjz40UcfGXC6DCaldLlc0njmtKIckdHs1GO0opedfsbsdCy0Qiu0Qiu/deZ8Jpujpo7l/PnzpaWlUsqrV69euXLF67uXLl3SXpeVlWmvi4qKlCj/ew4LCysuLlZ23rlz5927d5d/28WLF5X3ePnqq6+efPJJr41FRUXZ2dmeWxITE7/++mufCeTk5JSUlHhu6devX1FRUfl3FhYWHjp06OzZs9qWS5cuDRkyxPeBeSSTn59ffnuHDh38B1oBz08AAABgRTfddJPywvOpguaGG27QXjsc7kdPdevWrXTPOTk5p06dOnz4cKdOnY4fP37nnXfed9995d/mZ2b5oUOH3n777ebNmw8bNkxrt2XLltobVq1aFRoaWtEseWX1ZIWUMikp6bHHHvOZeb169ZSFyLTM58+fP3/+fP8HWLdu3VtvvVX78uzZs+vWrfMfYh3UJwAAAKhdwsPDP/zwQ6fT2aJFi3vvvXft2rU+SyA/4cpQKz+rAz/yyCNVnPjhcDjmzJlTxTffcsstS5cu9azHquK6665TyrmFCxfqCgwK6hNAB+afAACMU5vnn5hv1KhRo0aNCiy2adOmY8eO9f8eXbPSq/7mqjwdKq9JkyaVJmwd1CeADqwvDAAwDusLA4L1hQEAAABYB89PAB0Y3wUAMA6PHQBBfQLowvguAIBxGN8FCMZ3AQAAALAO6hMAAAAAVsH4LkAH5p8AAIzDsChAUJ8AujD/BABgHOafAILxXQAAAACsg/oEAAAAgFU4ysrKMjIygp1GjQkPD3e5XMHOArZ1KuRUVFiUXR6/C+EQXC8AfutMGA1rDofDVmOipLTN/yxhNoeU0pyR7iaNp3c4TLge7NRjtKKXnX7G7HQstEIrtEIrAOyB8V0AAAAArIL1uwAdWF8YAADAUNQngA6sLwwAAGAoxncBAAAAsArqEwAAAABWwfguQAfmnwAAABiK+gTQgfknAAAAhmJ8FwAAAACr4PkJoAPjuwAAAAxFfQLowPguAAAAQzG+CwAAAIBVUJ8AAAAAsArGdwE6MP8EAADAUNQngA7MPwEAADAU47sAAAAAWAX1CQAAAACrYHwXoAPzTwAAAAxFfQLowPwTAAAAQzG+CwAAAIBV8PwE0IHxXQAAAIaiPgF0YHwXAACAoRjfBQAAAMAqqE8AAAAAWAXjuwAdmH8CAABgKOoTQAfmnwAAABiK8V0AAAAArILnJ4AOjO8CAAAwVDDrk8LCwk8++eTQoUOtW7ceP358o0aNgpgMUBWM7wIAADBUMMd3xcTEFBQU/OlPf9q9e3ffvn2DmAkAAAAAKwjm85N77rlnyJAht99++8svvxwWFnblypWGDRsGMR8AAAAAwRXM+uTDDz9UXuzfv3/AgAEUJ7A+5p8AAAAYKsjrdx04cKBjx45vvfXW2rVrg5sJUBXa/BOj/7mOuExoJdjdCQD4NYfH779Gj67qRs/XycnGRlV9V0CgHGVlZRkZGcFqvqysrKCgIC0t7bXXXktJSWnRooXnd8PDw03IweVymdAKbMOcH0vT8PMP4LfOhNVEzOFw2GrNEin5LRgCJaV0uVzSeP5b6dq16wcffFD9VpQjMpoVeoxWaIVWaIVWaIVWzGnFHEII6XkbEx+vfaOSjZ6vV682NqpquzLnfgx2FbTxXT/99FOPHj2uXbsmhDh//vzJkye7du0arGQAAAAAWEHQ5sffeuut4eHhEyZMuPfee3fs2LF48eKOHTsGKxkAAAAAVhC0+iQ0NHTVqlWlpaVnzpyZN29esNIAAAAAYB1BXr+rTp06zZs3D24OAAAAACwiyPUJAAAAAGioTwAAAABYBfUJAAAAAKugPgEAAABgFUFbvwsAAACwDinlnj17OnTocP311/t/59GjRxcuXCiECAsLmz17tinZBcHJkyedTqcQ4rbbblNemIP6BAAAAEGWkZGxefNm5XWTJk26desWHh5ucg4LFixwOp2ZmZm33Xab/3fm5ORcvnx57ty59evXV7aUlpbu3r07NTXV6XRed517gNKFCxdee+21zMzMp59++g9/+IOffe7fv3/NmjUlJSWxsbE9evTwn0Bubu7GjRubNWs2cOBAbWN6evo///nPG2+8MS4urkWLFn7CfWZbfmOzZs2effZZIcSIESPMrE8Y3wUAAIAga926dX5+fnJycp8+fUJDQ2NiYpYuXVr18JMnT1Y/hxdeeKFBgwZVfHPjxo3btm175513CiEKCgoSEhLWr18/f/58KaX2ngMHDjz88MMDBw5MTk72X5zs3bv34YcfHjZsWFxc3JgxY/71r3/5eXNKSsqCBQtWrly5e/dubePChQuXLFnypz/96Xe/+11EREROTk5F4T6z9bkxNDS0bdu2bdu2rUJ/1CTqEwAAAARZaGhoy5YtGzRo0K5du9jY2BkzZqxcuVL77qVLl06fPu35/uLiYq0mOXz4cGJioud3s7Ozs7KytC/LysouXLgghPDaybVr13788Uc/WeXk5CiB/jVo0OCtt96aPn2650Yp5RNPPLFw4cLIyMhK9/DZZ58NHDjw97///f333z9s2LCvvvrKz5tjY2Nff/31Ll26aFuuXLny0ksvzZ49+4477hg0aFDv3r1XrFihK1ufG4OF+gQAAADWcuXKFeVPeJeUlEyePHnWrFnPP//8yJEjlV/tL1++fOzYsampqffee++RI0cmTZq0e/fuKVOmrFu37uTJk7179/74448TEhLGjh0rhDh06NADDzzQt2/fuLi4fv36RUZGKjtZu3bt0KFD165d27Fjx1GjRr399tueCWRnZw8dOvTNN98cOnToG2+8EcAhpKWlFRUVnTlz5rnnnnvzzTcLCgr8vPn+++//9NNPjxw5IqXct29fTEyMrrZ+/PHH4uLie++9V/kyPDz8yJEjAeRsEcw/AQAAgCXk5OSsWbPm2LFjP/zwg/L8ZMWKFcXFxe+++64Q4p577tmxY0fjxo0XLVrkcrlCQkK+++67kJCQCRMmfPnll8uXLxdC7N27NyIiYsaMGaNGjWrXrp0Qon379oMGDcrNzX3zzTeFELfffvv333/ftWvXmTNnrlmzJjIy8vTp0/Xr1588ebJnJlOnTh0xYsSjjz6alZUVHh4+ZcqUSifNe9m3b19ZWdnVq1eHDRu2YsWKqKionTt3ek5N8TRw4MCHH364e/fuYWFhU6ZM6dSpk6627r777ptuuumLL76Ii4sTQly6dOmOO+7QtQdLoT4BAACAJYSGht5yyy27du06duxYkyZNhBCbNm2qU6eOskZWZGRkaWnpli1bIiIiQkJChBDKKKZt27Zpe+jSpUurVq2WL19+7ty5a9euadvr1KmjvLj77rvz8/OFEK1btz579qwQ4uzZs61bt/bKZPPmza1atTp06JAQon///ufPn2/WrJmuY8nKyurVq1dsbKwQolu3bi1atPjmm28qGuv1zjvvNGzYMCcnZ9WqVXPnzr311luHDRtW9bbq1av3wQcfTJs2LTU1VUr52WefffDBB7qytRTqEwAAAFhCkyZNYmJiYmJievXqtW7duokTJ5aWlg4dOvTxxx/X3rNnzx4/Y6U2bNjwyiuvrFq1qmnTpnPnzvXT1sqVK6dNm7Zp06b69es/99xznt+SUpaWlj7zzDNhYWEBH0urVq3279+vvK5bt27Tpk2vXLlS0ZuXLFmyefPm+vXrT5o0qVGjRm+88Yau+kQIMXTo0CFDhvz8888HDhw4cuTI4MGDA8486Jh/AgAAAGuJj49fvXq1ECImJua9994rLi4WQpSWlubl5UVHR6elpWnzK65du+ZwOHJzc5UvP/nkk8GDB991112eD098atu27blz56ZOnbps2bKGDRt6fsvhcERHR2tTzC9cuOB/9ohPQ4YM2bZtW2FhoRAiKyvr0qVLPXr0KCws/Pbbb8u/+cYbb8zMzFReZ2ZmKs9qTp8+rWsaicPhyM7OnjFjhvbw5MCBA8ozot8W6hMAAAAE2b59+1avXn3gwAGlLBk/fvzVq1dHjBjRsWPHNm3adO3aNT4+/tFHH83Nze3cufPixYujo6MHDBgwduzYw4cP9+jRY/fu3WPHjt2yZcvYsWPfeeedSZMmffjhhyEhIYsXLz5w4EBqauqOHTv279+/adOmjIyMv/3tb2fOnMnMzCwrK5s0adIdd9wxYcKEa9euLVq06MqVK6+++mpxcfGyZct27drVq1evuLi4mTNnlpSU+M//3XffnTp1qhDiqaee2rRpkxCiffv2SUlJAwYMePHFF5944om1a9feeOONO3fu7Nu3786dO73Cly1bNmPGjOeee27cuHGbN29evHixEGLlypUPPPBA+UIrOzv76aef3rJly2effTZjxoyysjIhRFFR0ZIlS6ZNm5aSktKmTRvlnc8+++yYMWOqkm1FG4NDSulyuaTxzGlFOSKj2anHaIVWaIVWaIVWaMUKhBDS8zYmPl77RiUbPV+vXm1sVNV2VVP3Y+fPny8tLZVSXr169cqVK17fvXTpkva6rKxMe11UVKRE+d9zWFhYcXGxsvPOnTvv3r27/NsuXryovMfLV1999eSTT1blEIqKirKzsz23JCYmfv311+XfWVJScvTo0R9//NFzY79+/YqKiqrS0Hfffffpp596bbx06dKQIUOqEu5fhw4dqr+TqmP+CQAAAKzopptuUl6EhoaW/+4NN9ygvXY4HNrrunXrVrrnnJycU6dOHT58uFOnTsePH7/zzjvvu+++8m9r1KhRRXs4dOjQ22+/3bx5c/8TRerWrduyZUvty1WrVoWGhvqcJV+nTh3P6S5SyqSkpMcee6wqhyOE6NatW7du3Ty35OTkzJ8/f/78+VUJ9+ns2bPr1q0LODxg1CcAAACoXcLDwz/88EOn09miRYt777137dq1PksgP+GTJk0SQlT9780rHnnkkSquU+xwOObMmaN3UWNPt9xyy9KlSz0rN72uu+46pQhcuHBhwDsJAPUJAAAAap1Ro0aNGjUqsNimTZsqf/xRL131RnWKE1G150j+NWnSJLDDrCbmxwMAAACwCuoTAAAAAFZBfQIAAADAKqhPAAAAAFgF9QkAAAAAq6A+AQAAAGAV1CcAAAAArIL6BAAAAIBVUJ8AAAAAsArqEwAAAABW4SgrK8vIyAh2GjUmPDzc5XIFOwsAAGCSNm3aBDuFmuFwOIKdQk2SUgY7BfxWhSgXgwnX9pEjR8z5BLHNsdAKrdAKrdAKrdBKpa0Y3YRpuKEHFIzvAgAAAGAV1CcAAAAArIL6BAAAAIBVUJ8AAAAAsArqEwAAAABWQX0CAAAAwCqoTwAAAABYBfUJAAAAAKugPgEAAABgFdQnAAAAAKyC+gQAAACAVVCfAAAAALAK6hMAAAAAVkF9AgAAAMAqqE8AAAAAWAX1CQAAAACroD4BAAAAYBXUJwAAAACsgvoEwP9v7/5Cq6wfOI4/T26VDMxAh1RCUZ2RUrlsgfgnhhjBDNwEC4WELioRwrAb2cRCvAitIf0hMowkTkQXGasRgaAbufBCMincObLGtBmMEhqrkO3sdzHoIvdL9uec7/ecvV5X27n5fs7zuOF7O0cBAGKhTwAAgFjoEwAAIBb6BAAAiIU+AQAAYqFPAACAWOgTAAAgFvoEAACIhT4BAABioU8AAIBY6BMAACAW+gQAAIiFPgEAAGKhTwAAgFikhUIhn8+HnjFr6urqent7Q68AAEokk8mEngDMpqo0TZOSfG3ncrnSfAepmOfiFKc4xSlOcYpTbnhKsY8ASszruwAAgFjoEwAAIBb6BAAAiIU+AQAAYqFPAACAWOgTAAAgFvoEAACIhT4BAABioU8AAIBY6BMAACAW+gQAAIiFPgEAAGKhTwAAgFjoEwAAIBb6BAAAiIU+oRTq6upCT5g1nstc5orNZe7+VLliwPToEwAAIBb6BAAAiIU+AQAAYqFPAACAWOgTAAAgFvoEAACIhT4BAABioU8AAIBY6BMAACAW+gQAAIiFPgEAAGKhTwAAgFjoEwAAIBb6BAAAiEVV6AEAAFOQzWaTJNmyZUtVlb/GQAXy+xMAoJxs3br1ww8/XLp0aTabHR0dDT0HmGVV4+PjSZLkcrmiHjM6Orp8+fKiHvGPNE1LcxBTUkn3xXOZy1yxuczdn6piX7HvvvtuxYoVRT0CKL2qie8dmUym2Cf19vaW4JQ0TSeKq6hyuVwJnkslnVJJ98VzmSp/kqeqkq5YJZ3i7k9V8a5YNpu9ePHi7t27a2pqiv0DVqD0vHATACgnW7duDT0BKCLvPwEAAGKhTwAAgFjoEwAAIBb6BAAAiIU+AQAAYqFPAACAWOgTAAAgFvoEAACIhT4BAABioU8AAIBY6BMAACAW+gQAAIiFPgEAAGKhTwAAgFjoE0qht7c39IRZ47nMZa7YXObuT5UrBkyPPgEAAGKhTwAAgFjoE0rh4sWLX331VegVAADETp9QdL/99tuLL7745Zdfhh4yC77++uu2trZdu3aFHjJT58+fb21tPXjw4JkzZ0JvidqFCxcOHTr0r5fRT/oglWfSG10oFN59991nn332/fffDzUsWtdfsUKh8Nlnn+3du/fo0aPXrl0LuA0oI1WhB1DhRkdHn3vuuSeeeCL0kFnwyiuvFAqF1tbWhx9+OPSWGTl37lxLS8unn356+fLlbdu2ZbPZhoaG0KNidODAgZGRkaNHj9bX19fV1f3Hg1SeSW/08PDwli1bnnnmmWPHjoWdF6Hrr9j4+PjGjRvXrl27Y8eOjz76aMOGDSdPnkzTNPRSIHb6hOLatWvX9u3b8/l8f39/6C0z0tnZ+dNPP3V2duZyudBbZqqjo6OpqenRRx9dsGBBc3Nzd3e3PplUa2trkiSff/75DR+k8kx6o/fv39/Y2Lh9+/ZAo6J2/RX79ttve3p6vvjii+rq6j179hw5cqSrq+vxxx8PtxEoD17fRREdOXLktttua2lpCT1kFhw4cKClpeXgwYNvvPFGT09P6DkzUl9ff/z48VwuNz4+/sMPP2zYsCH0IigDIyMj77zzTkNDw759+/bv3z8wMBB6UewGBgbuueee6urqiU8zmUwF/HwHKAF9QrGcOXPmzTffXL9+/alTp/r6+gYHB0+dOhV61PSdP3/+0qVLq1evXrZsWUtLS1m/naapqWnTpk0NDQ3Nzc2bN29+8MEHQy+CMvDzzz/Pnz8/n883NTXV1NQ88sgjv/zyS+hRUXvggQe+//77K1euTHw6PDy8dOnSsJOAsuD1XRTLtWvXnnzyyY6OjiRJfvzxxz/++OP48eNr16696abyq+Lff/99eHj45ZdfXrhw4aJFi8bGxt56662NGzeG3jVNH3zwQU1Nza+//nro0KFXX3110aJFzc3NoUdB7AYHB++6667nn38+SZLHHnvs5MmTx44d27NnT+hd8aqvr9+7d29jY+Pq1av//PPPs2fPrly5MvQooAzoE4plzZo1a9asmfj49ddf7+/vb29vDztp2m6//fZbb711aGho4cKFSZLccccdIyMjoUdNX3t7+zfffDN//vynn376vvvuO3z4sD6BG6qtrR0aGvrn03L/PlAar732Wltb219//XX48OG777578eLFoRcBZaD8fpINpZem6aZNmyZ+F5QkyYkTJ5566qmwk2ZiwYIFfX19Ex/39fXV1taG3QNlYdmyZdXV1WfPnk2SZGxsrLu7u6mpKfSoMlBdXd3Z2dnd3d3W1hZ6C1Ae/P6EUli+fPmKFStCr5iR9vb2bdu2Xbp0aWBgoLa2dvfu3aEXTd/bb7+9Y8eOxsbG3t7eq1evfvzxx6EXRaqrqyubzQ4MDLS3t1+4cGHnzp3/70Eqz/U3+uabb/7kk0927ty5fv36c+fOvfTSS6tWrQo9MyKTfmkMDQ3t27fv77//7ujouOWWW0JvBMqDPqEUMplMJpMJvWJGlixZcuLEiaGhoStXrjz00EOh58zIypUre3p6+vv7L1++7N/6/A/r1q1bt27de++9d8MHqTyT3uhVq1adPn16cHBwyZIl8+bNC7UtTpNesa6urhdeeKHc/88ooMT0CUzB4sWLr169GnrFLJg3b9699947NjYWegiUmTRN77zzztArysbmzZtDTwDKj/efAAAAsdAnAABALNJCoZDP50PPmDWjo6NVVV60BgBzRbm/vxH4l6o0TZOSfG3ncjmnOMUpTnGKU5zilNk9pdhHACXm9V0AAEAs9AkAABALfQIAAMRCnwAAALHQJwAAQCz0CQAAEAt9AgAAxEKfAAAAsdAnAABALPQJAAAQC30CAADEQp8AAACx0CcAAEAs9AkAABALfQIAAMRCnwAAALHQJwAAQCz0CQAAEAt9AgAAxEKfAAAAsdAnAABALPQJAAAQC30CAADEQp8AAACx0CcAAEAs9AkAABALfQIAAMRCnwAAALHQJwAAQCz0CQAAEAt9AgAAxEKfAAAAsUgLhUI+nw89AwBgyu6///40TUOvAGbT/wBk2daYGBPosAAAAABJRU5ErkJggg==\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":60431,"title":"Calculating the Union Area of Overlapping Rectangles","description":"Calculate the area covered by a union of multiple rectangles. Each rectangle is represented by 4 integers: the first two integers denote the coordinates of the bottom-left corner, and the next two integers denote the coordinates of the top-right corner. The input is provided as a matrix where each row represents one rectangle.\r\nThe rectangles can overlap, meaning that simply summing up the areas of each rectangle will not yield the correct total area. Instead, the overlapping regions should be counted only once.\r\n\r\nExample:\r\nGiven the rectangles [ 4  8 11 10;  6  3  8 10; 16  8 19 11 ] the area covered by the union of these rectangles is 33.\r\n\r\n\r\n","description_html":"\u003cdiv 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; \"\u003e\u003cdiv style=\"block-size: 757.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 378.517px; transform-origin: 406.5px 378.517px; vertical-align: baseline; \"\u003e\u003cdiv 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: 383.5px 31.5px; text-align: left; transform-origin: 383.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 381.342px 7.81667px; transform-origin: 381.342px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the area covered by a union of multiple rectangles. Each rectangle is represented by 4 integers: the first two integers denote the coordinates of the bottom-left corner, and the next two integers denote the coordinates of the top-right corner. The input is provided as a matrix where each row represents one rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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: 383.5px 21px; text-align: left; transform-origin: 383.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 383.5px 7.81667px; transform-origin: 383.5px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe rectangles can overlap, meaning that simply summing up the areas of each rectangle will not yield the correct total area. Instead, the overlapping regions should be counted only once.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 0px 7.81667px; transform-origin: 0px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 33.5px 7.81667px; transform-origin: 33.5px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 367.383px 7.81667px; transform-origin: 367.383px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the rectangles [ 4  8 11 10;  6  3  8 10; 16  8 19 11 ] the area covered by the union of these rectangles is 33.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 0px 7.81667px; transform-origin: 0px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.033px; 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: 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rectangles_union(R)\r\n\r\nend","test_suite":"%% Example \r\nR =  [  4 8 11 10; 6 3 8 10; 16 8 19 11  ]\r\na = rectangles_union(R)\r\na_correct = 33\r\nassert(isequal(a,a_correct))\r\n\r\n%%  \r\nR =  [  4 8 11 10; 6 3 8 10; 16 8 19 11; 6 8 8 12  ]\r\na = rectangles_union(R)\r\na_correct = 37\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nR =  [  4 8 11 10; 4 8 6 12; 6 3 8 10; 16 8 19 11  ]\r\na = rectangles_union(R)\r\na_correct = 37\r\nassert(isequal(a,a_correct))\r\n\r\n%% Not overlapping\r\nR =  [  4 8 11 10; 16 8 19 11  ]\r\na = rectangles_union(R)\r\na_correct = 23\r\nassert(isequal(a,a_correct))\r\n\r\n%% Partial overlapping\r\nr = [ -3 -3 -1 -1 ];\r\nR =  [ r; r+1; r+2  ]\r\na = rectangles_union(R)\r\na_correct = 10\r\nassert(isequal(a,a_correct))\r\n\r\n%% Full Overlapping\r\nx1 = randi([10,20]);\r\ny1 = randi([10,20]);\r\na = randi([1,10]);\r\nb = randi([1,10]);\r\ns = a*b;\r\nR =  [  x1 y1 x1+a y1+b ; x1 y1 x1+a y1+b ]\r\na = rectangles_union(R)\r\na_correct = s\r\nassert(isequal(a,a_correct))\r\n\r\n%% Partial Overlapping\r\nx1 = randi([10,20]);\r\ny1 = randi([10,20]);\r\na = randi([1,10]);\r\nb = randi([1,10]);\r\nr1 = [x1 y1 x1+a y1+b];\r\nR =  [  r1 ; r1+1 ]\r\ns = 2*a*b-(a-1)*(b-1);\r\na = rectangles_union(R)\r\na_correct = s\r\nassert(isequal(a,a_correct))\r\n\r\n%% Partial Overlapping\r\na = randi([1,10]);\r\nb = randi([1,10]);\r\ns = a*b;\r\nR =  [  4, 8, 11, 10; 6, 3, 8, 10; 16, 8, 16+a, 8+b  ]\r\na = rectangles_union(R)\r\na_correct = 24 + s\r\nassert(isequal(a,a_correct))\r\n\r\n\r\n%% \r\nx1 = randi([10,20]);\r\ny1 = randi([10,20]);\r\nR = [x1 y1 x1 y1]\r\na = rectangles_union(R)\r\na_correct = 0\r\nassert(isequal(a,a_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":208445,"edited_by":223089,"edited_at":"2024-06-16T05:19:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-02T15:58:47.000Z","updated_at":"2024-06-16T05:19:18.000Z","published_at":"2024-06-02T15:58:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the area covered by a union of multiple rectangles. 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