{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":43021,"title":"How many figures currently exist?","description":"Return the number of figures that exist at any given time.","description_html":"\u003cp\u003eReturn the number of figures that exist at any given time.\u003c/p\u003e","function_template":"function y = numfig()\r\n    y = 0;\r\nend","test_suite":"%%\r\nassert(isequal(numfig(),0))\r\n\r\n%%\r\nclose all;\r\nfigure;\r\nassert(isequal(numfig(),1))\r\n\r\n%%\r\nclose all;\r\nfigure;\r\nfigure;\r\nassert(isequal(numfig(),2))\r\n\r\n%%\r\nclose all;\r\nfigure;\r\nfigure; plot(1,1);\r\nfigure; imagesc(magic(5));\r\nassert(isequal(numfig(),3))\r\n\r\n%%\r\nclose all;\r\nn = randi(20);\r\nfor ii=1:n\r\n    figure;\r\nend\r\nassert(isequal(numfig(),n))\r\n\r\n%%\r\nclose all;\r\nassert(isequal(numfig(),0))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-04T14:56:58.000Z","updated_at":"2026-03-02T15:03:36.000Z","published_at":"2016-10-04T14:56:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the number of figures that exist at any given time.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":537,"title":"Cody Computer Part 3 - Detect the graphic card used on Cody Computer","description":"In the Cody computer investigation party, you may have already solved :\r\nProblem 522. Cody Computer Part 1 - Guess the system font used by uipanel\r\nor\r\nProblem 536. Cody Computer Part 2 - Get the license number of Cody Computer\r\n*******************************************\r\nThis is the third problem to solve :\r\nYou have find the graphics card manufacturar used by the Cody Computer.\r\nExamples of manufacturar : NVidia, ATI, Zotac, ASUS ...","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; 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: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 231px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\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; text-align: left; white-space: pre-wrap; 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; \"\u003e\u003cspan style=\"\"\u003eIn the Cody computer investigation party, you may have already solved :\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; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 522. Cody Computer Part 1 - Guess the system font used by uipanel\u003c/span\u003e\u003c/span\u003e\u003c/a\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; text-align: left; white-space: pre-wrap; 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; \"\u003e\u003cspan style=\"\"\u003eor\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; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 536. Cody Computer Part 2 - Get the license number of Cody Computer\u003c/span\u003e\u003c/span\u003e\u003c/a\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; text-align: left; white-space: pre-wrap; 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; \"\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; text-align: left; white-space: pre-wrap; 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; \"\u003e\u003cspan style=\"\"\u003eThis is the third problem to solve :\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; text-align: left; white-space: pre-wrap; 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; \"\u003e\u003cspan style=\"\"\u003eYou have find the\u003c/span\u003e\u003c/span\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; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\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; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003egraphics card manufacturar\u003c/span\u003e\u003c/span\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; \"\u003e\u003cspan style=\"\"\u003e used by the Cody Computer.\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; text-align: left; white-space: pre-wrap; 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; \"\u003e\u003cspan style=\"\"\u003eExamples of manufacturar : NVidia, ATI, Zotac, ASUS ...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name\r\n  y = x;\r\nend","test_suite":"%% Which graphic card is used ?\r\n\r\nS = evalc('opengl info');\r\nS_lines = regexp(S, '  +', 'split');\r\nind = contains(S_lines, 'Vendor');\r\ny_correct = regexprep(S_lines{ind}, 'Vendor: ''([^''])+''.*', '$1');\r\nassert(isequal(your_fcn_name, y_correct))\r\n\r\n%% prevents cheating 14-June-2012\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'Brian Paul')))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":639,"edited_by":26769,"edited_at":"2023-02-24T22:26:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2023-02-24T22:26:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-30T08:32:22.000Z","updated_at":"2026-03-04T16:12:59.000Z","published_at":"2012-03-30T08:32:22.000Z","restored_at":null,"restored_by":null,"spam":null,"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\u003eIn the Cody computer investigation party, you may have already solved :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 522. Cody Computer Part 1 - Guess the system font used by uipanel\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\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\u003eor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 536. Cody Computer Part 2 - Get the license number of Cody Computer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\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\u003e*******************************************\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eThis is the third problem to solve :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eYou have find the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egraphics card manufacturar\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e used by the Cody Computer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eExamples of manufacturar : NVidia, ATI, Zotac, ASUS ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43276,"title":"Get Cody's screen size","description":"Return an object that helps this problem's test suite return Cody's screen size.","description_html":"\u003cp\u003eReturn an object that helps this problem's test suite return Cody's screen size.\u003c/p\u003e","function_template":"function y = getCody(x)\r\n  y = 0;\r\nend","test_suite":"%%\r\nCodys_screen_size = get(0,'screensize');\r\nCodys_screen_size = Codys_screen_size(3:4);\r\ny = getCody();\r\nassert(~isnumeric(y))\r\nsz = get(y,'screensize');\r\nsz = sz(3:4);\r\nassert(isequal(sz, Codys_screen_size))\r\ndisp(sz)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":57323,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-09T11:39:53.000Z","updated_at":"2026-01-22T15:33:44.000Z","published_at":"2016-10-09T11:39:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn an object that helps this problem's test suite return Cody's screen size.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61142,"title":"Shifting vertically a function's graph","description":"Given a real function, f, by n input-output pairs, consider a translation in the up-down direction given by an amount k.\r\nFor a real constant k, you may assume that the translation is given. However, if k = 'mean', you firstly must determine the real constant k such that the translated function has an average value of 0 over the given interval (see figure below).\r\nFind\r\ny_shifted, which is the 1×n vector that stands for the outputs of the translated function;\r\nv, which stands for either 'up' or 'down' if the function's graph is upward or downward shifted, respectively, and it stands for '' if the graph does not undergo a translation.\r\nHint. Calculate the mean of a piecewise linear discrete function, represented as an array of x and an array of y values. Be aware to the existence of calculus discrepancies whenever the function f will be continuous, but not piecewise linear.\r\ninput: (x, y, k)\r\noutput: [y_shifted, v]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 563.312px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 281.65px; transform-origin: 408px 281.656px; vertical-align: baseline; \"\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a real function, \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ef\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, by \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e input-output pairs, consider a translation in the up-down direction given by an amount \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a real constant \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, you may assume that the translation is given. However, if \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'mean', you firstly must determine the real constant \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that the translated function has an average value of \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the given interval (see figure below).\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_shifted,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e which is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vector that stands for the outputs of the translated function;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ev,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e which stands for either 'up' or 'down' if the function's graph is upward or downward shifted, respectively, and it stands for '' if the graph does not undergo a translation.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint. Calculate the mean of a piecewise linear discrete function, represented as an array of \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and an array of \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e values. Be aware to the existence of calculus discrepancies whenever the function \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ef\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be continuous, but not piecewise linear.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(x, y, k)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[y_shifted, v]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 259px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 129.5px; text-align: left; transform-origin: 384px 129.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"367\" height=\"259\" style=\"vertical-align: middle;width: 367px;height: 259px\" 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dv/+/WfPnrVo0aKhP6L1TvoBo4P+EqjHzZs3+/btS4sL1LqynZ2do6OjHR0dCSHPnj3TfhTABPTo0aNPnz6EkDt37ly/fv3EiROEEEtLS39/fy1H+ms+Y9bW1s1aMiCTySIiInbs2CGTyXg8XlBQUHx8/ObNmxv3aFwuNygoyNLSsrKy8sSJE4WFhbS7om3btnW/UzbuWmqJ7ezZs9OmTaPzmj09PZctW3by5Ek65mLIdPWk8Xg8DodTWVkZFxen1t9jpP7+++/Kykrd/oiCkUJ/CdTD0dGxc+fOxcXFRUVFJ06ccHd3V33fffbsmTb92waI6Xym3cuMJ0+eaBOwbGxsJkyYQGcsHjt2jHbF9+zZk4YVQgiHw2FCRlxcnJalLo3z4osvduzY8f79+1Kp9NGjR3S6ZU1Xrlyhg01CoTAxMZH26zRls5UePXoIhcLbt2+LxeKkpKTs7GxCyEsvvdS5c+c67tXEZ54Q8uzZs/3799PimoULF86aNYvD4chkMuaDe015eXn0rY7elMvl9OfW1tZWh1mwvLy8pKSE6XuoqqqiWzup9t417klT5ePjExsbu2LFiuTk5KtXrx44cMDwF9mzsLCgz3Pd3TPnz5/X7Y8oGCP0l0A9WrVq5evrS/9N+4TpkvOVlZUZGRnvv/8+XX6gY8eO9VbY6oSuYhAzLJ2RkcEsol9ZWal9VaG3t3enTp0IId9++y0dRhk6dCjTFW9ra8tklMuXLzODBXv27KGrMkRGRmpf//LPP//UcTKPx2Mm06heS22pleLiYvrsMYtNEUK0KTOpjb29PZ0UUlBQsGXLFrVpv7Vp+jP/7Nmzv/76i/6bTnolhPz11191VFbfvHnzxo0bzM0LFy7QDOTm5tayZUstr1uvJ0+e0Fpx6u7duzR2tG/fnhm0atyTpmratGnt27efPXs2/WHbu3ev6rJAappp3mtDOTs7CwQCQkhhYSGTR8vLy0NDQ+nCLcePHyeE6PxHFIwRcgnUb9KkSXT6XlVV1Y4dOwYMGODi4tKtW7exY8fSfYA5HM6ECROYOYw6x+PxaAIghFy7dk2hUJSUlDRxXlvfvn179epFCLl9+/batWtLS0tlMtmmTZu0f3d0cnIaPHgwc7Nt27b+/v6qJ4wcOZI+J3v37v3222+rqqpycnK++uorQoiVldXEiRPr/aTO/HUuKiqSSCS0pkbjmRMmTKAzkePj4+m1iouLd+zYQYt0hg4d6uTkRCtfCCE3bty4fPmyQqE4deoUbU+jDRo0iMfjKZVKOouTmfZbh6Y/8y1atGDm5Rw9erS0tLSwsHD9+vU0HWokk8mioqJu3bpVVVV16tSp+Ph4ovWr0CCbN29OSUmhu1quXr2avl70+WfOacSTVpO3t/eECRMIIQUFBV9++aX2GZcVfD4/KCiIw+HI5fIPP/yQvhBnzpyhvSPdunWjk06a40cUjA5yCdTP0dHxs88+U/3DqorD4bz99tuhoaHN2gb6TkYI2bFjh7u7++zZs5tYbGxnZxcVFUXfy48cOeLt7d2rV6/t27drv7AVXV6MGRoYOHCgWs0Is+5LWVnZsmXL3NzcaBUJh8OZP3++j49PvZfg8/m0OFYul0+dOrV79+579+7VeGbPnj0//PBDW1vbiooKeq2+ffseOXKEEOLj4zNv3jxa+0D/+kul0rCwMHd393fffVcul9N3gvv37zeitJKZZ0P16dOH1pvUoenPfIsWLYKDg+nKIidPnvT29h4wYEBSUhIzVpKZmal2l06dOpWWlo4aNcrNze3dd9+VSqXavwra69Spk6Wl5dtvv+3m5jZ48GA6/YV5/pnTGvGk1UR/71xcXAghx44du3z5si6+g2Y0efLkKVOmEEJu375NX4j333+/oqKibdu2a9asoQm+OX5Eweggl4BWevbseeLEiWXLlnXv3p1ZYK1du3ajR4/+/vvvly1b1tzFipMmTZo7dy59M7OysqIzB5v4mN7e3l9//fVrr71mZWVlYWHRt2/fr7/++t1339X+Ebp160ZXj6UZpeYn74CAgB9++GHChAm0nIRe5Ztvvqm5zKhGNjY2q1evHjJkCH3OW7VqVcd3HRAQcPToUdVreXh4REdH79ixg3b483i8zZs3h4aG0sqUVq1aTZ48OTk5mRlWYBb7156Njc3QoUPpv2t7Empq+jM/ePDg3bt3e3h4cDgc+p1u3rw5MTGRWS9EbTZo586dv/7668mTJ1tZWXE4nK5du27ZskXLV0F7nTt3TkxMnDx5Mn0J2rZtO2/evC+++EKt0KZxT1pNjo6O7777Lp1b88UXXxj4VtuWlpYfffTRrl27+vfvT3+ebW1tJ0+eTLMpPac5fkTB6HD0XOT9119/TZ06teanmaCgoHpX8ATQg+TkZFrWKxKJ4uLiUIVYr+Tk5HfeeUepVLq7u3/11VeNHs5rjmeeqZI1tFdTV08agOnRdz3Ow4cPHz16ZGtra2dnp3pc7SYAW5gPnQ4ODtiAtF5KpfL06dP04432y6hrZD7PvA6fNADTo+9c8ujRo6dPny5fvvztt9/W86UBVF2/fn3q1Kl00ac333xz6dKl1tbWEomETrLjcDjar0Rinp49e2ZlZfXTTz/R3X3peuFaLqNuts98o580APOh71xCF+aic7UAWCQUCr29venWJF999ZXanH8/Pz+14hpQ88EHHxw6dIi5OXr0aNW5nHUw52e+0U8agPnQ67xXpVJ5+/bttm3b1lbZAaA3PB5v+/bt0dHRL730EjNqYGVl1b1799jY2C1bthjOXATD5OnpST/oOzg4vPPOO8uXL9dy7rM5P/ONftIAzIde573KZLIZM2YUFhYOGzbs+PHjBQUFtra2o0aNioiIoGuZAwAAgDnTay75888/X3/99QcPHtja2g4cONDOzi49PT03N9fe3j4uLk771QsAAADAJOl1fklJSYmFhcUrr7yyadMmWoBTVVUVFxcXGxu7fv362qr4xGJxHduXAwAAgIEbMGCAxq2ka9Lr/BJPT8+ffvrpq6++YqqCLSwspk6d6u3tnZGRQTeSqOnixYtYS8dwHDx4EC+H4Th48GBeXh7brQBCCMnLyzt48CDbrYBqeDkMSoP6F9jfT5iutP3HH38wO3jVJBKJIiMj9dkqqI1YLJ44cSLdmANYd/DgwcjISEwkNwR5eXkhISH4S2UgaGTHy2GM9L0OvUwme/bsWc3jdDFpPTcGAAAADIpec0lsbGyvXr3oTp6MwsLCjIwMFA8DAACAXnOJv78/j8c7ePBgbm4uPVJeXr5hw4bbt28PGzaM7psKAAAAZkuv80v69Onz3nvvrV+/PiAg4NVXX23ZsuX58+cfP3788ssvR0ZGNm5HTQAAADAZeo0CHA4nPDy8W7duW7ZsSUlJqaqq6tSp07Jly15//XUTXuERAAAAtKTvLgoOh+Pr6+vr66vn64KuLFmypGvXrmy3Aqpt2LDBwcGB7VYAIYQ4ODhs2LCB7VZANS8vL1dXV7ZbAY2BoRNomA4dOrDdBPgPXg6DgpfDcDg4ONA9q8Ho6LtOGAAAAKA2yCUAAABgKJBLAAAAwFAglwAAAIChQC4BAAAAQ4FcAgAAAIYCuQQAAAAMBdYvAQAwcWKx+OLFi2y3Qq/kcrlCocBK4s1kwIABIpGomR4c/SUAACbu4sWLYrGY7VbolbW1NUJJM2numIv+EgAA0ycSiSIjI9luBUD90F8CAAAAhgK5BAAAAAwFcgkAAAAYCuQSAAAwBVVVVefOnZsyZYqHh4eLi4unp2d4ePgff/yhVCrruJdMJgsJCQkJCZHJZPVe4vr1615eXtu3b296a5OTk11cXJKTk5v+UE23fft2w2mMeeUSiYRwONX/xcQQiYTtBgEAgC4UFxe/9dZbM2bMePLkydy5czdv3jx16tTr169PnDhxxYoV5eXlbDcQtGVG9TgSCQkL++9mdDSJjiahoSQqiggErLUKAACaqLy8fMmSJRcvXly5cuW0adMsLCwIIaNGjZo7d+6GDRt2797dokWLlStXcjicmvfl8Xj79u3T8kKenp5Xr17VZdOhBjPqL0lMJKmp6gcTEohQSIRCDV8CAACjkJqampaWFh4eHhoaSkMJZWNjM3/+/MGDB3///fe///47iy0E7ZlLLpFISHR0XV/19ydCIUlI0FuLAABABxQKxcmTJ1u2bDl69OiaPSI2NjaTJ08uKytLSUkhhCQnJ3t5eZ08eXLcuHGurq5Tp07Nz89Xm1+Snp4+fvx4V1dXDw+PmJiYQ4cOMXMvVOeX0Akix48f//zzz/v37+/i4uLj43Ps2LGqqir6OFVVVSdPnhw1apTqfJfc3FxtvimlUpmUlDR48GAXF5devXrt3Lnz888/9/Lyun79OiFk+/btvr6+ycnJPj4+bm5uCxcurKioyM/PX7p06csvv+zi4uLq6urv779nz57KykqiMocmOTl5xIgR9DHXr1+vNqWmtLT0ww8/9PT0dHV1HTly5C+//FL31JxmYhbjODR2MAQC4uenIYLQgZ6YmOrBHQAAMHylpaU5OTlOTk4ODg4aT3B3d3dwcLh27VpZWRkhRC6XR0VFvfbaa6+//rpcLm/VqpXqycnJye+9916HDh1WrVpFCNm9e3fdozwfffSRjY3Ne++9R09etGiRpaVlQEAAvfnJJ5+8/PLLMTExLVq0SE5OPn369IMHD7766is7O7u6v6ldu3atW7euZ8+ea9euLSws3LFjh1Qqtba2Zk549OjR8uXLJ06c2KFDB3t7+ydPnrz99ttPnjyZNGlSz5497927d+DAAXrdKVOm0LvcuHFjwYIFQ4YMmTVrVkpKSlxc3M2bN7du3cosjLts2TIPD48VK1bIZLJt27bNmjUrPj6+b9++dTdV58wil6hNcaWxIyqKJCZq6EShPSsJCUgnAGDKVD+tGZfp00lo6H83FQpFWVlZ69atVUdwVFlbW3O5XKlUqlAoCCGVlZU9e/aMiYmxsbEhhKj2GUil0m3btjk7OyckJDg6OhJCRo4cOX369MzMzNoa4+LisnPnTj6fTwgRiURTp049e/ZsQEBAcXFxWlraoEGDtmzZQi8UGBgYExNz+PDhvLy8unPJ/fv39+zZ88orr2zdupU+8muvvRYWFiaXy5lzKioqRo4cuWjRItpFdOzYsUePHn3++ee+vr70hMGDB0+dOjU9PZ3JJTKZbMmSJeHh4RwOJzAw0MPDIzY2NiUlZcyYMfSEYcOGbdiwwdLSkhDStWvXmTNnpqenI5foXkLCc10jfn7VaUMgqE4nMTEkIUG9NgfpBABMm/FOqvPza+ojiEQimhXUZGZm3rp1a+7cuTSUEELs7e2Dg4Oja58H4OPjQ6MDPdne3v7x48dlZWV2dnZ79+5VPZPD4dTWo6Pm8uXLBQUFUVFRzCN37949ICDg8OHDapdmxq3Gjh07duxY1a/a2dm9+OKLqkfc3NzGjx9P78LhcEaNGrV3795ffvmFySUjR46koYSe3L59+7t372rTYN0y8fklajU4AgGJj1c/JyqK5OaS+HgNVTk0naCoGADAYHE4HC6X+88//9R2At1bmM/nc7nVH8W7dOmi8cySkhK5XN61a1fVg506darj6sxjEkKsrKxat26tUCiYaRlVVVX5+fnJyclxcXHTpk3bunWrNt/Rw4cPeTxehw4dmCM1Mw2Px7O3t1e7o0wmu3LlypEjRz744IMpU6bk5eWpfrVNmzaqaYzH47Vq1erevXtMjxETSuj39cIL7CQEU84laqGEkLpKgkNDSW4uyc3VnMSjo4lQiHQCAGBw7Ozsunfvnp2dnZ+fr/GE3NzcJ0+e9OrVy9bWlh5RfQNuJkqlMjk5ecCAAYMGDZo5c+a2bdsIIV5eXrp6fA6Ho5obiouLIyIivLy8goKCFi1aJBaLe/furc2OylwuV2P5NItMeRxHrTA4NPS5IUmNBAKSkkIkkurBHTV0yRPa6dL0jkQAABbV7Dw2FmofL7lc7qhRo86cOXPgwIGai5SUl5d//fXXLVq08NdiQk2rVq2sra3v3r07ZMgQ5uCjR48a0cg7d+588MEHXbt2Xbt2befOnencl+3bt9OCmro5ODjIZLJHjx55enpq0wylUrl58+YzZ858+OGHgYGBNI48fvz48uXLqqc9ffq0oqKCuVlUVPTkyRMvGp9pHQAAIABJREFULy8mrhkIk80laoXBGkdwakNPrmNirL9/9fSUeoMOAIBhMqU/X0OGDJkwYcK+ffucnZ2ZddUIIeXl5Rs2bDh79uz06dP79OlT7+N4eHh079794MGDY8aMoVNMpFLp8ePHG9GkP//8s7Cw8M033xQKhfRIcXFxamqqXC4vKSmp+759+/bt1KnTnj17BgwYQKeY5OXl/fTTT7WdX1ZWlpmZaW9v7+/vT0OJUqkUi8UPHz58+vTps2fP6GnZ2dkXLlygs0lod05JScmIESMa8d01K9PMJTULgxvxyYAmj+nTa00nKCoGADAElpaWy5YtKy0t/eijj7777rtx48Y5OjreunXr+PHjeXl5wcHBTN1K3fh8/uzZs997772QkJC33nqLELJ79+7GrWHfrVs3R0fHnTt3lpaWenl5ZWRkHD58uLi4uLKyUrWsRiOartatWzd16tSQkJDCwsLExMQ62s/j8V5++WWxWDx//vzx48cTQk6ePHnx4kWlUvn333/TJUwIIZWVlYsWLfrtt9/69et3/Pjxs2fPTpkyZeDAgY347pqVac4vqVkY3OhhF5pOcnM1L8tGe2WwXCwAALv4fP7GjRt37drF5/M3bNgQERGRmJjo7u7+/fffr169WmP1jUaDBw/evXu3ra3thx9+GBsbO2TIkKVLlzaiPc7Oztu2bXN3d4+Pj587d+6pU6fmzZu3d+9ePp+fkZFR793feuutzz77rKioaNmyZYmJiTNnzgwJCanj/HfeeWfu3LnZ2dnLli1bvXp1y5Ytf/jhh8DAwPv37xcXFzNN+vjjjy9evBgZGXnz5s1Vq1atXLlSD1NtGorDympuDbJx40ZCSGRkpJbnJySo1+Bot7yeVjQWFVOhoUY8Xqu9Bw8e8Pl8baZTgR7cv3+/Y8eOqhUBwBaFQvHgwQNnZ2e2G6JBQ/+Kgqrt27dv27Zt7969qrM99G/hwoXp6enfffdd+/btG3pfmUw2c+bM/Pz8xt1dTSN+nBp0F1PrL6lZGJySosvHr6OomG61AwAARurx48cBAQGxsbHMJ3apVJqamtqmTZt27drprRnXr1/39fU9cOAAcyQvL++PP/5wdHRUW5LEJJnUx6wGFQY3BS3toZdTHcGRSIhQiGodAACj1KZNm759++7YsePBgwd+fn5///33vn37MjIyli5d2rFjR701QygUCgSC1atXZ2Zm9uvX78mTJ7t373706NGyZcvMoa/apHJJIwqDm4J2xqSmPjfHlk65jY7GZFgAACPD5XKXLl3K5/OPHj16+PBhCwuLHj16fPXVV//73//02QwejxcbG/vpp58eOXIkMTHRysqqd+/eO3fudHd312cz2GI6uaQphcFN4edHcnOJv/9zk06io0lqqo6HkAAAoLnxeLwlS5YsWbKE3WbY29uvW7du3bp1Onk0Ho9X9+6DBsVE5pfopDC40ejUWrWxm9RU1OkAAAA0jInkEh0WBjdaSop6LTFNSzXXjQUAAACNTCGXqO0YTFccYUVUlIaxm7Aw9dm4AAAAoJHR55LmLgxuKDrdRK23BiXEAADNqry8fM+ePSNHjnRzc3Nxcendu/fcuXNv377NnJCcnOzi4rJ9+/baHmHhwoW+vr6PHz8mhCiVyr179/bq1cvFxWXatGllZWVNbN727du9vLy02RynuclkspCQEOY7NUDGnUv0VhjcIDQb1RzTwXQTAIDmIJVK33333ejo6NLS0sDAwODgYIFAkJSUNHbs2KSkpEY8YEZGxieffCIUCjds2BAZGfnCCy8cOHDAiKaOGjXjrsfRc2Fwg0RFEV9flBADADS71NTUn376af78+bNnz2Y27bt161ZYWNjGjRv79etnb29f74PExsYy/3706JFUKp01a1ZAQAAh5Pr162vWrJk9e3YztR9UGXF/CVuFwdqjYzpq/TfR0USL3bYBAEBbv/zyC4/H8/X1ZUIJIaR79+4TJ04sKCjIz89v3MMa4N4x5sBYcwm7hcHaQwkxAEBz69Kli1wul9TYumzhwoXXrl3z9vZmjsjl8p07d/bv39/FxcXHx+fYsWNVVVXMyb6+vhKJJCQkZObMmYSQmTNnenl57d69OzAwUCqVfvzxx8wckcrKyj179vj4+Li4uHh4eERERKimH6VS+csvv4wcOdLV1dXT0/Ojjz6qe4aKTCZbv349nc4yYsSIH3/8MTg4OCQkRCaT0ekgCxYs2L17t4eHh6en57Fjxwght2/fDg8P7927t4uLi5ub28iRI5OSkujy+Y8fP/b19V2wYMHx48dFIpGLi4tIJNqzZw+zsTCVlZUVHBzs5uZWs/3sMtZxHEMoDNZeSgqJiXmud4fmqvh4Axp4AgDz0rg1DBr6N0svV3nttdfi4+Pnz5//3XffjRs3buDAgR06dOBwODXP3LZtm4ODw3vvvWdpafnll1/OmzePw+GMGTOGOcHS0nLu3LleXl47dux45513evfu3aVLl8WLF2/atGnEiBEjRoxwcnKqrKyMiorav3+/p6dnREREYWFhQkJCaGhoQkKCo6MjIYTuHtyhQ4dVq1YRQnbv3v3w4UNra2uNjZfJZHPmzPnll1/Gjh07aNCgn3/+OSIiQqlU9uvXjzknOTn52rVrq1atevTokaenZ0ZGRlhY2IsvvhgeHt6lS5eMjIzvvvtu3rx5dnZ2IpGIuUtaWtqYMWO8vLwOHjwYHR19+/bt6H/fh/Ly8sLDw0eNGvXGG29cuHDh4MGDBQUFCQkJfD6/Qc98czDKXGI4hcHaqzndhBASFkbS0gy0pwcATFzjFjBoaC5pxFUa/jfR3d19//79ixcvvnDhwvnz5wkhtra2/v7+YWFh3t7eqgGlR48eu3fvtrOzI4T07dt36tSp9M2bOcHS0lIkEslkMnrCkCFDCCEVFRXbtm1zd3cfNmwYISQtLe3gwYMTJkxYs2YNHevx8fEJDw//+OOPP/300/Ly8l27djk7OzMxZciQIaGhobXVv6SkpPz666+LFi0KDw/ncDiBgYFeXl4xMTGq58jl8hUrVvj6+tKbn3/+uZWVVVxcXLdu3Qgho0aNEolEM2fOvHLlCpNLnj17tm7dOjo/ZtSoUcuXLz927Nj48ePpXQgha9asCQoKIoSMHj3a2tr68OHDEomE3T2TKeMbxzG0wmDt1VZCjOkmAGCa9NMlQwghRCgUfvfdd2KxODY2duTIkYSQEydOTJw4ceXKlarjF4MHD6ahhBDi6Ojo6upaUFBAU4j2Tp06ZWFhMXnyZGYCipeXl5+f32+//VZQUJCTk3Pnzp3AwEAaSuiFAgMDNT6UQqE4ffq0o6PjmDFjaH7icDgBAQFubm6qpzk4OHTv3p25+f7771+4cIFJGISQNm3aqPXHiEQiv3/fbywtLSdPnqxQKK5cuUKPdOrUiUkwHA5nwIABUqn00aNHDXoemomR9ZcYZmGw9miKUhvTodNNsAsxABg6PXSWNI29vX1QUFBQUJBSqczMzFy6dOk333wzYMAApkeEy33uXe+FFxr84bysrCw/P9/W1jY7O1u1C6SqqkoqlRYXFxcWFspkMg8PD9V7qd1kyOXyv/76q2PHjqoDKDY2Nm3atFE9rWPHji+++KLafUtLS2/evHnv3r2LFy+KxWKpVKr61Xbt2tnY2DA3W7duzePxbt26RW++8MILqk+FQc3wNbJcYsiFwdqLiiJdujz3C4sSYgDQt0Z8EmroCItePmzRGaADBw5cu3Ytc5DD4XTv3n316tU1R2qaSKlUKhSKoqKi5cuX1/xqYWGhri6kSi0/5eXlLViwID09nRBiZWXl6urap0+fc+fO1fs4BpU/asNmLqmsrFy+fPmPP/64d+9ebca0DL8wWHt0oi52IQYA1ujhb41e/py1a9fO1tb2jz/+KCwsVFunxNraukWLFrp9M+bxeF26dLl///6BAwc6depU84Tr16/z+fwrV67QuSnU3bt3NT6atbV1mzZtbty4IZVKeTwePVhRUfH06dPWrVtrvEt5efmHH36Yk5MTFxc3aNCgFi1a0Iv+/PPPqqc9ffr02bNn9KuEkEePHpWUlHTt2rXh37G+sTm/5Pjx44cOHdLyZGMpDNYeHdNBCTEAQFO0adNm7Nixt2/fXrt2bWlpKXO8vLx89+7dJSUlr776ahMvYWFhweVyFQoFvTlw4MBHjx6dOHGC1uUSQqRS6bRp0wYPHpybmysQCLp27ZqUlJSXl0e/WlxcfPr0aY2PzOVyhw8fnp+ff/z4cebRLly4kJ2dXVtjpFJpVlaWq6urSCSisaOqqiotLU1tgkh6evrNmzfpvysrK48ePdqyZUsfH58mPRF6wVp/ye3bt9evX8+8DPUyrsJgLWmcbkITWM3IAgAAGr3xxhsZGRlHjhz54Ycf+vfv7+zsXFRU9Msvv/z999+vv/66ar9F47Rr147H4/3www9OTk4DBgwYMWLEr7/+un79+gsXLowfP760tHT//v1ZWVlLliwRCAQcDmflypXh4eFTpkyh66DUXSfs7+//v//975NPPsnKyqJ1wsnJybWdTAhp06aNt7f3iRMnFi9ePGzYsNLS0oMHD2ZmZnI4HNUpJlKpNDQ09K233urSpUtiYuK1a9eWLFni7u7e9L1+mhs7/SXl5eWxsbF2dnYvv/yyNucbY2Gw9jTuQuzvj12IAQC0wufzN27cuHXr1h49eqSnp+/fvz8tLa1Hjx47d+6MiYlp+jiOvb19eHh4Xl7e/PnzL168aGlpuXLlylWrVv35558LFiz46KOPCCGbNm16++23aU2Nt7f3119/7ezsvHr16rVr1/bq1YsuZKIRj8fbvHnzm2+++eOPPy5YsODWrVuffvqpavWNGi6XGx0dHRwc/PPPP8+fP/+zzz7r3bv3qVOnBgwYkJuby0STl19+edmyZd98882CBQvKyspUm2fgONr3WOjQzp07P/vss02bNp06derMmTN1zy/ZuHHj++9HMjdpH4MR1eBoiZYaqY3g+PkZ3HSTBw8e8Pl8ZhwU2HX//v2OHTuqlRgAKxQKxYMHD5ydndluiAYbN24khERGRtZ7JhiCx48fT5o0qX///qpb9jT07o6OjnFxcc3xt7oRP04NugsL/SVXrlyJi4sLCgrya9RAhXEVBmtP4y7EmG4CAGDadu7cOWLEiDt37jBHLl68+PDhQ6OYo9oc9J1LpFLphg0b7O3tIyMjG/Ehz0gLg7UXFaU+n5dON3l+6T8AADAR//vf/4qKimbMmJGYmHjy5MmYmJjly5cLhcKxY8ey3TR26LX7V6lUfvPNN7/99tuOHTu02XVaDZeb5+19cOPG6pvDhw93cHDQcRMNwLhxxNubjBnDy8v779WhJcSHDz9lsWFUaWlpVVUVMy8d2FVSUmJjY4NxHEOgUChKSkoMYXuRmuRyeR3zKIFdPXv2/OKLL2JjY9euXVtRUdGqVatJkya9//77LVu2ZLtptZLL5U+fan4/evjwYc3iI7FYzCwvWy+9/jm7cuXK1q1bg4ODG1qqNHr0wYyMCaNHX1Q9aJKhhBIISFKSPCKCpzqCk5pKPD15mzfLUKcDDA6HnSliUJNSqTSKSYVggPr373/gwAFdPVr79u3T0tJ09WgN1fS3Zv3lkuLi4g8//NDFxSUiIqKhv71DhuQdP04ImdA8TTNErVtrKCHOy+OOH9+a3RLi8vJyzHs1HFKp1M7ODv0lhkChUMjl8trWwmIXOktAt6ytrev4UW/iDGv9/TnLy8vLycmRSqV9+/ZV+1JgYCCfz9dy1VezonEXYn9/Ehpq9MvKAYA+icVitpsAJqJBgzKNoL9cYmdnN2HCBLlcrnpQLBbn5+f7+/t36tSJ2eMRVNFdiNVKiBMSiERicCXEAGCYBgwYwHYT9I12X6FntzmIRKJm/YnSXy5xcnKqubDMwoULi4qK5syZg56SOmAXYgBoCpFI1KwfcA2QTCaTSqUdO3ZkuyHQYGzujwMNghJiAAAwecglxiQ0lOTmqi8rFx2tPgEFAADASLGcS2JjY69evYpBHO1hF2IAADBh6C8xPhpXrKdjOogmAABg1JBLjBV2IQYAANODXGLEaAmx2phOQgKmmwAAgLFCLjFu2IUYAABMCXKJKUAJMQAAmAbkEhOBEmIAADAByCWmAyXEAABg7JBLTApKiAEAwKghl5gglBADAICRQi4xTSghBgAAY4RcYrLomE5o6HMHMd0EAAAMGXKJiYuPRwkxAAAYDeQS04cSYgAAMBbIJWYBJcQAAGAUkEvMBUqIAQDA8CGXmJfaSogx3QQAAAwBconZ0VhCjOkmAABgCJBLzBFKiAEAwDAhl5gvlBADAIChQS4xayghBgAAg4JcYu5QQgwAAIYDuQRQQgwAAIYCuQSqoYQYAABYh1wC/0EJMQAAsAu5BJ6DEmIAAGARcglogBJiAABgBXIJaFZbCXFQkB07DQIAADPAZbsBYLjomE5Y2HMjOGKxtacn8fOrjiy+vurzUQAAABoNuQTqQqNJTMxzVcQSCUlI0HCmQFCdUXx9q28CAAA0CHIJ1C8qivj61lOVI5EQiUR9bizCCgAANAhyCWiFlhCrjenUS5uwQh8cAACAIJeA9uiYzvffF/72G9/GxpqmjUYUD9cbVrp0+e/fAABgVpBLoGFeeUUxYoSCxyNRUdVHaM6QSMi9e5ozhzbqCCv0P4QVAABzgFwCTaVx1ohEQgghqak6CCs1L0dIdUEQwgoAgIlBLoFmQdOD2rqxugorhKgXBKmGFYLqZQAAo4VcAvpTb1ih/9BtWFGdY4uwAgBg4JBLgGVqYUVt2kpaGiGEpKZqHtOpGz0f1csAAEYEuQQMlGp60GFYIVhqBQDAgCGXgDHRJqyQ5qlexlIrAAB6gFwCRq+OsILqZQAA44JcAqYJ1csAAMYIuQTMCKqXAQAMHHIJmDtWqpcRVgAANEIuAdCguauX1cIKQUEQAAAhBLkEoEFQvQwA0KyQSwCaisXq5Zdesh43rnGtBgAwRPrOJUqlMj09/ZNPPrly5co///zj6uoaGRk5YsQICwsLPbcEoFnpq3rZnhASHf3fJQAAjJq+c0l8fPzatWstLCz8/f1btmx5/vz5iIiI4ODgmJgYS0tLPTcGQM+aqXo5OpokJJD4eEyhBQCjp9dccv/+/fj4+M6dO+/atUsoFBJCpFLpnDlzTpw4MWHChL59++qzMQAGQifVyxIJ8fcnfn4kJaVZGgkAoB96zSX37t2rrKwcN24cDSWEED6fHxQUdP78+fT0dOQSAEbjqpdTUwmHg2EdADBies0lPj4+YrFY7eDdu3cJIQ4ODvpsCYAxqlm9/OuvDxYvtj9//rlfZAzrAIDxeoHFa0ul0m3btiUmJvbq1euVV15hsSUARsrJSZGSQqKj1Y/TYZ2wMBaaBADQFOzkEplMFhIS4uXl9cknn7z00ku7d++2t7dnpSUAJiAqiuTmakgnCQlEKCQxMSw0CQCgcdhZv6SioqJz586dO3dOT0+/dOnSpEmTNm7c2LNnz9rOrzn6QwgZPnw4Rn/0r7S0tKqqSqFQsN0QIISQkpISGxsbLpfbujWJjCSBgWT2bGux2Jo5QSKpHtbZtk0uEslZbKrJUygUJSUlfD6f7YYAIYTIZLKysjIbGxu2G2J2Hj58ePr0abWDYrFYJBJp+Qjs9Je0adNm3bp169atS05OXrp0qUQiWbNmjUwma9CDIJQAcDgcpVLJ3BQISFKSXOOwTkCAdc3joENKpZLD4bDdCgCWNf2tmeX1XjkczpQpU5KSkrKysv78888ePXpoPE0kEkVGRuq5baBReXk5n8/n8XhsNwQIIUQqldrZ2XG5z/0iR0WR6dNJYqL6yM7Gja2PHiWhoajWaRYKhUIul7du3ZrthgAhhHC5XAsLC7wcrGji+zWb816pli1bCoVChUJRVVXFdlsATIRAUD3pRG0ZNzqsIxQ2ZgcfAAA90Gsu2bx5c+/evY8cOaJ68MmTJzdv3uTxeK1atdJnYwBMnkCgeT6sRIL5sABgoPSaS7y9vcvLy7du3Zqfn0+PVFZWbt++/fbt26+++mqnTp302RgAM0E7TmquZUI7ThIS9N8iAIBa6XV+iUgkmjZt2pdffjlixIiBAwfy+fzz588/fvzYy8srIiJCbYwcAHRFICApKSQ1lYSFPTeCI5GQsDCSmEji4zVs3AMAoH967S+xtLRcsmTJtm3bXFxczp07d+jQIS6Xu2zZsq+++gqdJQDNzc9P87BOaiqGdQDAUOi7i8LCwmLYsGHDhg3T83UBgKLVOmFh6nvrYPV6ADAE7NfjAICe0WGdlBQN1Tr+/sTfH9U6AMAa5BIAM4VhHQAwQMglAGat7modtbEeAIDmhlwCYO6YYR01zLAOAIDeIJcAACF1DutwOBjWAQA9QS4BgGrM6vUY1gEAtiCXAMBz6LCOxtXr/f1JWBgLTQIA84FcAgAa0I6TmukkIQHVOgDQjJBLAECz2oZ1mE2JMawDADqHXAIAdal7WAcdJwCgW8glAFC/2oZ1aMcJ0gkA6ApyCQBohRnWqbl6PU0nWL0eAJoOuQQAGkAg0NxxIpGg4wQAdAC5BAAajHachIaqH8ewDgA0EXIJADSGQEDi4zVvShwdjU2JAaCRkEsAoPGwKTEA6BZyCQA0FVavBwBdQS4BAB1gNiWuOaxDNyXGsA4AaAO5BAB0BsM6ANBEyCUAoGMY1gGARkMuAQDdY4Z11DDDOgAAGiGXAEBzqWNYh8PBsA4AaIBcAgDNqLZNiQmGdQBAE+QSAGh2dW9KHBbGQpMAwDAhlwCAntS2KXFCAqp1AKAacgkA6E9twzrMpsQY1gEwc8glAKBvdQ/roOMEwJwhlwAAO2ob1sGmxADmDLkEAFjDDOto3JQYwzoAZgi5BABYJhBo7jjBsA6AGUIuAQCDQDtOQkPVj2NYB8CsIJcAgKEQCEh8vOZNiaOjsSkxgFlALgEAw4JNiQHMGXIJABgirF4PYJ6QSwDAQDGbEtcc1qGbEmNYB8D0IJcAgEHDsA6AWUEuAQAjgGEdADOBXAIAxoEZ1lGDYR0AU4JcAgDGxM+PKJUY1gEwWcglAGB8MKwDYKqQSwDAKNFhnfh49eN0WCcsjI02AUCTIZcAgBELDdVcrZOQgGEdAKOEXAIAxo3ZlFhtWAebEgMYI+QSADAFdFgHmxIDGDvkEgAwHbTjpGY6wabEAMYCuQQATAozrKNxU2IM6wAYOBZyye3bt2fMmOHh4eHi4tK7d++lS5fm5+frvxkAYMIEAs0dJxjWATBw+s4lSUlJY8eOTUtL69Onz+TJk9u0afPtt9+GhoYimgCAztGOk9BQ9eMY1gEwWHrNJYWFhZs3b+bz+fv379+3b9+6det+/PHHRYsW5eTkfPzxxwqFQp+NAQBzIBCQ+HjNmxLTdILV6wEMil5zSUZGRlZW1qhRo/r06UOPWFhYTJkypVu3bleuXPnrr7/02RgAMB+1bUoskaDjBMCw6DWXFBQUtGzZ0tvbm8PhMAetrKxatmypz2YAgHmqe/X6hAT9twgA1Ok1l7zxxht//PHHuHHjVA9mZWXdvHnT0dHxxRdf1GdjAMAMMZsS1xzWCQvDpsQA7GO5TlgqlW7cuLGsrGzixIk8Ho/dxgCAmahtWAebEgPokERCEhKIvz9ZscJJ+3txm69B9ZLJZFFRUefPnw8ODh4zZkwdZ4rF4poHhw8f7uDg0NCLch49auXhQaKjZRMmKJwa8EwBVVpaWlVVhUnKBqKkpMTGxobLZfMX2XhFRpLAQDJ7trVYbK16PDqaJCSQbdvkIpFc+0dTKBQlJSV8Pl/XzYTGkMlkZWVlNjY2bDfE7OTlcY8efXr3rtPzA6MTCNmo5SOw1l9SXFw8Z86cI0eOjBs3bvny5ZaWlg19hEaEEu7q1a08PAghJDqa5+lpHRCATlswahwOR6lUst0KIyYQkKQkeVKSev6QSEhAgHVAgLX2fyGUSqXqzDkA8yGREImErF7NDQiw9vTkrVjh1JTZWux8zLpz505ERMSdO3dmzJixaNGiekOJSCSKjIxs6lUlEvLpp6oHrMVi6969q5eHrLnEAWhSXl7O5/Mx6GYgpFKpnZ0d+kuaaMQIolSSmBj1kR2x2Lp3b+voaBIVVf+DKBQKuVzeunXr5mkjNAyXy7WwsMDL0awkEpKaStLSdDxnnIU/Z+fPn583b55UKl2xYsW0adMsLCz0cVW6ymNtX0IoATB7UVFk+nQSFqa+UD0d1omP11DIA2BuaNdIWhpJTdVqSweBgPj5kSdPDmp/CX3nkitXrsybN6+iouKLL7547bXX9HfhxEQM2QBA3Wi1TkICCQt77jj9XOPnR1JSWGoZAKsa1DUiEBCBgEyfXh1KCCEbN+Zpfy295pL8/PxFixYRQnbv3t23b1/9XTgh4bn+Wfq3JzGx+iCG5wFARWgo8fP77y8Eg1brhIZqNawDYOyYLEL/US+aQqZPb2rPol5zyXfffZednW1lZfX++++rTRDr1KnT5s2b7e3tdX9Vui4Bg4YSOqckKgoVgQBQE/0LUXNYh65ej2EdMGE0hSQmNiCL+PoSPz/1NYEaTX+5RCaTXbp0iRBSUVFRc5e+5iorUAslhJCoqOeePHzwAYBa0E8xNefD0mEdLefDAhi+hs5gFQhIaGh1HNE5/eUSHo+3b98+vV2umlrkCw3FFFcAaBDacVJzWId2nGBYB4wUnXJJ3yQb1DXS3O+iJl1eSLtcGXRfUQCABmKGddQWqlcd1vHxYa15ANprxAxWZqRGP0w3l6gVBuswlHA41X1Y+JQEYE4EApKbW8ewDvett9hpGEDdGlfcq4euEY1MN5fQPyHM7Fo6w15XmE9JSCcAZoZ2nMTEqH/cjI4mu3Z1nDGDdOmC4WIwCE0s7mWL6eYSSqms7t4WC3ShAAAgAElEQVTQVXpQLSNCOgEwS7T7lVbrqA7r5OVxaVdKWFj19HoaUPTZBw5mjq3iXh0y9VxCCFEqdbmimkCg/mgoHAQwS3RT4prDOhT9O6E2w43WUiKmgM6xXtyrQ2aQSwjR5ROfm0tSU9U/JZF/R5jj49GBC2BWalu9via65zuDmVHYpQv7PedgjJiukdRUrT59N2txrw6ZRy7RLfopSSLRMMIcFkbS0lD1A2BW6DInCoVi6VL55cs8bT6wkn+nIjInY9wHtCSRGGJxrw4hlzQWHWGOilL/oJSQQFJTSW4uaw0DAJZERhY7O/OISvmDWvioA8Z9oA6GX9yrQ8glTaNxPUiJhAiFmG4CYLaYNwaKWcCKEG0/5hKM+5g94yru1SHkEl2IiiK+vs8tl4J1qgHgX3SMhv4xoP+nH3/v3WtYTFHreqHTBQjGfUyLkRb36hByiY7QSSdqi0FGR5PUVOyMDgBqmEjBxJSGjvsQTStaY9zHSJlAca8OIZfoDl3Jzd//uR8rhBIAqI/auA/5d24j0cW4D0GHiqEypeJeHUIu0TXV6SbNsUMyAJgBZjFIjPuYGFMt7tUh5JJmQKebmM8PEQA0s9rGfUgDO1TUxn2MumrDuJh8ca8OIZc0D/yWA0CzUR2jYZJKI8Z91BZQwbiPbplVca8OGXMukUhIWBgmcAAA1Bz3aVCJKall3AcTaRvKbIt7dciYcwntFKMb6WEmBwDAv5gP300c99E4kRYxpSYU9+pQdS4pLy+/f/++UCi0tLRkt0HaSkh4bqRUKMQSqwAAGmkc92niRFosnE+fkMREFPfqWHUukUql4eHhf/3114gRI0JCQnr16mVhYcFuy+pC96Zh0EVXAQBAO7VNpG1QTCFmuXA+inubW3Uusba27tWr15kzZw4ePHjw4EEejzdx4sQ333xTIBBw6ECJQVHbzjcqCi84AECj1Rz3ITpdON/Y35VR3KtP1bmkZcuWmzdvrqysFIvFiYmJ58+fT0hISEhIaN++/aRJk6ZMmeLo6GgoAYVujMcIDTWF+UJhYdiFGAAMRHMsnG+M4z4o7mUFR6lpxigNKN9+++2ZM2cqKioIIUKhMDg4eNy4cfb29npu4saNGwkhkZGRhPy7JR6DLrFq7GjgM5Lv5cGDB3w+n8fjsd0QIISQ+/fvd+zYkcs15gnspkKhUDx48MDZ2ZnthuiD6sL5WnYh1NSs4z4ymUwqlXbs2LGhd0Rxb3N47n28Ppr/nFlaWg4aNGjQoEGVlZUZGRnff/99SkrK2rVr161b5+rqOnPmzBEjRrDwzkQLgxkCgUn1MWAXYgAwEia2YTKKew1KPR+zHj9+nJ6e/scffxQWFhJClErl3bt3Fy9eHBMTM3fu3NDQUL3W76hNNAoNNYW3cNXRMexCDABGyEjHfVDca5g05BKlUpmfn3/gwIHDhw8XFBQQQjgcTs+ePadPnz506FBCyOnTpz/77LN169aVlZW9//77emqpWmEws4qQscMuxABgcpq+YXIz1fuguNfw/ZdLlEqlRCL59ttvDx8+/PjxY3qQTiuZOHGinZ0dc+bEiROdnZ3Dw8N//PFHPeUSiYQcOfLfTVMqDNa4C3FqKsZ0AMBksL5hcuOKe9E1worqXFJYWDh9+vTMzEx6s1OnTiEhIYGBgY6OjhrvJhQK7ezsnj17pp9WDti+ncjl/902vcJg1V2IKTqmEx+PAUwAMD3NvWFyv35EIiGnT6O41/hU5xKlUllWVta2bdvx48dPmzat3qrgysrK119/3dvbWy+NJCLVUGIahcE10V2I/f2fOxgWRtLSTGp6LwBADc2wYTKPkPqLMzCD1QBV5xI+n//111937NhRy2VeHR0dZ82a1ZwNq4WJ1eCo8fMjubkkLOy538KEBCKRmM64FQBAfXSyYXK9D46uEcNUnUtsbGycnJzYbUr9TDuUUHTqjNqYDqabAIB5a/qGyegaMRbGsRyT2NpaJJebSGGwNqKiSJcuzy3WghJiAIB/ablhMop7jZHm9V4NSvU6cU+fmt1bMs0iavO12H69sN6rQcF6r4bDrNZ7NXyZmfJWrYobsd4rNIcGrff6QjM3RnfMLZSQf8d0EPIBABrIyUnBdhOgkYwnl5gnGk2YuSZsd5YAAAA0K+QSYxAVRVJSEEoAAMDkIZcYCYzmAACAGUAuAQAAAEOBXAIAAACGArkEAAAADAVyCQAAABgK5BIAAAAwFMglJkp1DXsAAAAjgVxiohISiL8/240AAABoGOQSU8ThEPLvLsRN3BEcAABAj5BLTA4NJRTd+S8mhr3WAAAANAByicnJzSUCwXNHoqMxpgMAAEaBzVySkZHRv3//5ORkFttggjTuQowxHQAAMAas5ZLi4uL169cXFRWx1QBTprYLMUXHdBBNAADAgLGTS/Ly8t56660LFy6wcnVzQXchVuPvjxJiAAAwWPrOJVVVVceOHRs3btzdu3d79Oih56ubHT8/kpurPqaDEmIAADBU+s4lN2/eXLlypYWFxY4dO0aPHq3nq5sjjWM6mG4CAAAGSd+5xMLCYtq0aWfOnBk4cKCeL23WoqJIfPxzR1BCDAAAhkffuaRHjx4LFixo2bKlnq8LJDRUcwkxAACAweCy3QCtiMXimgeHDx/u4OCg/8YYsdatyeHD1rNnW//7fD4tLiZPnzboMUpLS6uqqhQKRTO0DxqspKTExsaGyzWOX2TTplAoSkpK+Hw+2w0BQgiRyWRlZWU2NjZsN8TsPHz48PTp02oHxWKxSCTS8hGMeF01hJLGEAjkSUnoJjEZHA5HqVSy3QoghBClUslRXW0ZwCw1/a3ZOD5miUSiyMhItlthQqKiiK8v8fNr3fC7lpeX8/l8Ho+n+1ZBw0mlUjs7O/SXGAKFQiGXy1u3bsRvFegel8u1sLDAy8GKJr5fG3F/CTSJWvEwAACAAUAuAQAAAEOBXAIAAACGArkEAAAADAVyCQAAABgKNnPJrFmzcnJyhgwZwmIbAAAAwHCgvwS0g12IAQCg+WHZA9ACXS1KIiEpKWw3BQAATBn6S6A+zBKWqalEKOReuMBqawAAwJQhl0CdEhKeuymR2E+aZL1uHUlNZaU5AABg2jCOA3UKDSV+fsTfn0gkzDHu//0f+b//I4RU707s51f9D19fLCMLAABNgVwC9REISEoKCQvT0EdCw4panwohBDvJAQBAo2AcB7RAowl2IQYAgGaGXAJai4oiSqVcJKoetdGtmBiSmoppKwAAZg7jONAwxYcO8fl8Ho9HJBIikZC0NEJIdZ5oSqpQ7YwRCIhAUD1VpUuX//4NAACmDrkEGks1PURFVR+kYaWJ6IOopRx6OfofwgoAgIlCLgGdormhoZglUupQM/Fgdi0AgMnB/BIwANHR6PwAAACC/hIwCFFR1SNBtEckNZXcu1f9Dx3OhBUK/xv9wVIrAAAGCbkEDAkdAwoNrb6pNm2FmWPbuFksdUxbYcJK48ahAABAR5BLwBhonGOrE/WGFd1eDgAA6oRcAlCDalhBLgEA0CPkEjAPqakkPp7cu6e5gwQAAAwDcgmYh5qzXFXn2NYWVhpRiszhPLedIZZaAQBoCOQSMFdqc2wptbDSOBq3M8TeywAAWkAuAVChMazoRB1hJTdX95cDADBOyCUA7Gn6mv0AAKYFuQRAp3JzdbDUSt1iYrDUCgCYKuQSAJ2qYzvDZth7uaOT0wuffUYmTmz8owEAGBLkEoDmV0dYaVpvCjcvj0yaRAQCEhqKpVYAwARg3z4AltCkopM5thIJiY4mQiHWZQEAY4dcAmBsaiswlkiIvz+JidFrYwAAdAq5BMDYpKQQpZLk5pLcXNmCBepfpR0nSCcAYJyQSwCMk0BABILiyEjFnTvqhTkY1gEAo4VcAmDkBAKSm6tapFMNwzoAYISQSwBMQlSU5nRCO04AAIwEcgmAqRAISFQUSUnRMKwDAGAkkEsATIufn3rHSSN2RQYAYAlyCYAposM6fn4IJQBgXJBLAEyUQEBSUthuBABAwyCXAAAAgKFALgEAAABDgVwCAAAAhgK5BAAAAAwFcgkAqMDq9QDAKuQSAPgXh1O9er2/P9tNAQAzhVwCADWkpmJTYgBgBXIJABBCiHofCTYlBgA2IJcAACGEkJQUbEoMAKxDLgGAf9W9KTHSCQA0P+QSAFBBNyWme+uowrAOAOgFcgkA1ED31sGwDgDoHQu5JD8/PyIiwsPDw8XFxcfHZ8+ePZWVlfpvBgDUA8M6AKB3+s4lN2/eDAoKOnXqVJ8+fYKCghQKRXR0dFRUFKIJgCGiwzopKUQgeO44HdYBANA1veaSysrKbdu2lZSUbNq0ad++fbGxsWfOnPHx8Tl06JBYLNZnSwCgAfz8NHScKJXsNAYATJpec0lOTo5YLBaJRH7/Tqnj8/mRkZFWVlbHjh1T4s8cgCHTOB8WAECn9JpLbt26VVRU1K9fPxsbG+agUCh0cnK6ceNGcXGxPhsDAA1G58OmpKCzBACaiV5zycOHDwkhHh4eqgetrKxat25dUlIik8n02RgAaCR0mQBAs9FrLrl3717Ng7a2tg4ODjKZrKSkRJ+NAQAAAEPD1efFNBbdcDicF16oJx5pnBU7fPhwBwcH3bQMtFZaWlpVVaVQKNhuCBBCSElJiY2NDZer119k0EihUJSUlPD5fLYbAoQQIpPJysrKVOcMgH48fPjw9OnTagfp1FItH0Gv/SWWlpY1DyqVyn/++acRj4ZQAsDhcDBh3EAolUoOh8N2KwBY1vS3Zr1+zOrSpUvNg2VlZQ8fPuTxeK1atartjiKRKDIysjmbBtoqLy/n8/k8Ho/thgAhhEilUjs7OyPoL0lNNflZKQqFQi6Xt27dmu2GACGEcLlcCwsLvBysaOL7tV77S2guuXv3rurBioqKp0+ftmrVCm91AKaJwyH+/sTfn+12AIAR0Gsu6dq1a7t27cRicXl5OXMwOztbIpG89NJLdnZ2+mwMAOhVairhcLB6PQDUTa+5xMnJydvbWywWJycn00FxqVS6efPmf/75Z+zYsRiaBTBBar/X2JQYAOqk11xiY2Pz7rvv8vn8+fPnv/HGGwsXLhw6dOj58+eDgoK0n6kLAMaktk2Jw8JYaAwAGDx979vn7e397bff+vr6/v7774cOHeJyudHR0TExMRpLdQDA6NW2KXFCAjYlBoCaWJjGLxQKd+3apf/rAgA76KbE06eTsLDnRnDopsQJCSQ+3uSrdQBAS/ruLwEAM0X31qltWAcdJwBACEEuAQC9qm1Yh86HRToBMHvIJQCgX3RYJzeXCATPHafDOkIhO60CAMOAXAIAbBAINHecSCT6bwsAGA7kEgBgD+04CQ397wi2+wEwb8glAMAqgYDEx5OUFPVhHQAwSwa/3RcAmAM/P5Kby3YjAIB96C8BAAAAQ4Fc8v/t3X9M1Pcdx/HPeQeK5ajVXn+InQesk7FupU6UrKagwSpRN+rMxJoqrGC6tjgxcTabHepcOtpujWFatUY0+xGrrmtcLGl0BVaSorRTGKVD2kHdHVIVrnCHP+DO2x9fdtLjhwfC9/M57vn4Y7EfDbznxw+8+PwEAACqIJcAAABVkEsAAIAqyCUAgta8ebIrADDCyCUAglZZmTAYuL0eGEvIJQCCk8HQ8wvt9vreLxUDCFrkEgBByBdKNNqjxNnZkqoBMGLIJQCCUL9v6xw4wKPEQLAjlwAIQr5HiVNTv9Lue5SYZR0gOJFLAAQtq1WUlvb/KPG8eUycAMGIXAIgyGkTJ33TiTZxQjoBggq5BEDw8y3r+D1K7FvWaWqSUheAoSKXABgrrNb+J06amkRMjIR6AAwduQTA2KJNnGRlya4DwHCQSwCMOVarKC4WpaU3l3W8Xpn1AAgYuQTAGJWa2rOsQygBgge5BMCYVlAguwIAQ0AuAQAAqiCXAAAAVZBLAACAKsglAABAFeQSAPgqg4Hb6wFZyCUA0IvBIITgUWJgyJqaxIEDIjv7Nj+MaUSKAYCxQAslGu1R4qwsUVwsryBAbdrLUwcPirKymzn+9oYM8yUA8H9939Y5cIBHiQF/vqmRmBgREyO2bBnByUVyCQD8n/a2TmrqVxp9jxKzrINQ1tQkysrE1q1i3jwREyOys8WBA/3/yd7zjkPHOg4A9GK1itJSsXWr/9yJtqyzZQsXyCK0aHGkvHzAFNKb1SpSU0VKyu18QnIJAPRRUCDWrBEHD/qnky1bxIEDIiuLdIJQERNz6z+jxZE1a/znGoeFdRwA6I/V2rOs43uUWMOyDiCEsFp7doU3NorGRlFcPCKhRJBLAGAwVmvPo8R+tGUd9sMi1FitYssWUVrak0WysvyD+20jlwDArWgTJ1lZ/u198wow9vimRrxe0dgoCgpGamqkX+wvAYAAWK2iuFisWSOys3vubBBCeL0ySwKGRNvB2jdeD073f+TMlwBAwFJT+1/WAdTU93Cv8pgvAYAh0k7rjPSyOjBiBjncazAoPs9HLgGAoRteKCkrG9WFeYQ0XxbRfhG0yCUAoJd584T4/2UPVqtISSGm4HZpKUR7oeaWtH97aiOXAIC+tLdFfKzWnu8W06f35BUgQDExN3dhD0I7UBMkOZhcAgBSNTV9ZeJdyyXaoYkg+UYCaRobB3yMxncl/FAP4MgmM5fU1tZmZ2e/9NJLaWlpEssAAD1oizi3pP346zvyo/YWRajFN/cWzIlWWi5xOByFhYWtra2yCgAAXZWW9mSOgweFEKKsLKg3J0IhQTs10i85ucRms+Xl5VVXV0v57AAgh7ZGo735p/2vtoLz+efEFIimpuHsLiotDd6pkX7pnUs8Hs/x48e3bdt2/fr1hISEuro6nQsAAIVoGxJFr5jS1NRz1HN4pz0NBs77BBOtow8evNndQ125G3NdrHcuqaure/HFFydMmLBnz56amhpyCQDc5NsfcDsGOu8j2EirjCEd7g0xeucSo9G4evXq3NzcqKiompoanT87AIScvlMvvkkaYoqefPeelZUFdLg3VOmdSxISEhISEnT+pAAQEgY6MuqnqekrT/xYraKxcXQKguhZpglw/xC31wTL/SWVlZV9GxcuXHjffffpX0yI6+jo8Hg8brdbdiEQQoj29vaIiAiTKTgG8tjmdrvb29vNZrPMIhwO3yLOhFOnJvT3lbMfTU1ffvnlqNalP5fL1dnZGRERIbGGSfn5/TxP04d72jT3tGnuRx91z50rUlNFkPdFS0vLu+++69dYWVmZnJwc4EcI4i9nhBLAYDB4ud9CDV6v1xDgdMWoslq1uZBrQlwTwmSzmWy2CadODfLz+pcOh54FhpDBQ4nVKlJT3Y8+6lq+XKd6dHH735pHJZe4XK61a9f2nuRITk7eu3dvZGTk8D5gcnLyT3/60xGqDrfl6tWrZrN52F2JkeV0Ou+66y7mS1TgdruvXbs2adIk2YV81aRJ4qGHxKJF/ud9xM0LVIZT87x5il/eZTKZjEaj5O7wev1X1rQ9yNpj1KmpQgiTEIr9ixkBt/n9mi9nABAyep/N8SWVYeg9+8LF+bek/Z2vWcNfTiBGJZdERkb++c9/Ho2PDAAYSbe/0dLv4nzBg8m9FBfzFuNQMV8CABiKW26j6fcCldLS0axp1Pgd7h3qdq4xcTG8zsglAIChKC4e2sX52qaW4DKkw70YUeQSAMBQDHRxfrBfF+abGgngcC9Gj8xc8swzzzzzzDMSCwAA3Ba/i/NH8MHkrVvF9OkjcCv/4Hy5KsBqY2K4g260MV8CABghAz2YPIxtFr6NtKN33ic7O6CpkT6HezGqyCUAgFHje4tn2EbvvE8A955xuFd/5BIAgGIGP/IzyIPJ2iTNsGkfJyWFqRGJyCUAAMVs2TLk8z5lZUM+xOu7j1Wb1OG2FTWQSwAAiikoGOTi/JFUXMwVI6ohlwAAVNXvxfkjct5HQyhRD7kEABA8rFb/8z6+g74YE8glAICg5ZtQuc0dr1DGONkFAAAA9CCXAAAAVZBLAACAKsglAABAFeQSAACgCnIJAABQBbkEAACoglwCAABUQS4BAACqIJcAAABVkEsAAIAqyCUAAEAV5BIAAKAKcgkAAFAFuQQAAKiCXAIAAFRBLgEAAKoglwAAAFWQSwAAgCrIJQAAQBXkEgAAoApyCQAAUAW5BAAAqIJcAgAAVEEuAQAAqiCXAAAAVZBLAACAKsglAABAFeQSAACgCnIJAABQBbkEAACoglwCAABUQS4BAACqIJcAAABVkEsAAIAqyCUAAEAV5BIAAKAKcgkAAFCFhFxy7ty5nJyc+Pj42NjYRx555IUXXrDb7fqXgeH54osvZJeAm+gOdbS0tMguATfRHcFL71xSUlLy/e9/v7y8fObMmT/60Y8mT558+PDhrKwsokmwKCwsfPfdd2VXgR4bNmzg6686Vq1aJbsE9Kiurt6wYYPsKjAcJj0/2aVLl4qKisxm8+7du7/73e8KITwez969e1999dWXX375t7/9rcmkaz0AAEApus6X1NbW1tfXL168eObMmVqL0WhcsWLFjBkzzp4929bWpmcxAABANbrmkubm5qioqMTERIPB4GsMDw+PiorSswwAAKAmXddNVq1a1Xf9tb6+vq6u7qGHHpo4caKexQAAANVIPifsdDp37NjR2dm5fPnyyMhIucUAAAC5ZO4zdblcBQUFFRUVmZmZS5cuHeRPVlZW6lYVBme32ysrK202m+xCIIQQNpvtL3/5i+wq0MNms+3YsUN2FRBCiMrKSrvdTncoorKyMjk5OcA/bPB6vaNazUAcDsf69evff//9jIyMbdu2DTJZUllZeerUKT1rAwAAI2jOnDkBRpNRySUul2vt2rW9JzmSk5P37t3rCx8NDQ15eXkNDQ1PP/30xo0bw8LCRrwGAAAQdCSs41RUVOTn5zudzs2bN69evdpoNOpfAwAAUJDe6zhnz57Nzc3t6up67bXX5s+fr+enBgAAitN1vsRut2/cuFEIsX//fu2+VwAAAB9dc8mRI0c+++yz8PDw9evX975aTQgxderUoqIii8WiZz0AAEAp+uUSl8t1+vRpIURXV1ffV/oMBmkngwAAgCJIAwAAQBWS73sFAADwIZcAAABVkEsAAIAqlM4l586dy8zMfPDBB+Pi4h5//PGSkhJ2w8jS0NAwe/bs2D52794tu7TQUltbm5SUdPLkSb92j8dz7NixuXPnxsbGxsfH5+TkNDY2SqkwdAzUF3/605/6jpSHH374X//6l5Q6x7Zz587l5OTEx8fHxsY+8sgjL7zwgt+5CoaGnm7ZHYGMDpnv9g3u5MmT+fn53d3d8+bNGz9+fHl5+fPPP79p06bc3Fy/M8bQgc1ma21tvfPOO81mc+92v//EqHI4HIWFha2trX7tbrd7+/btf/jDHywWy7Jly5qbm8vLy6urq994443ExEQppY55A/WFEKK2ttZgMFgslvDwcF+j2Ww2mdT9ehukSkpK8vPzPR5PUlLS1772taqqqsOHD3/00UcHDhyIjo4WDA193bI7RICjw6uktra2jIyMWbNmnTlzRmux2WxpaWmzZ8+ur6+XW1to2rdvX2xs7HvvvSe7kND13//+NyMjIyYmJiYm5sSJE71/q7Ky8tvf/vZTTz3V0dGhtbzzzjszZszIzc29cuWKjGLHuEH6wuVyPfXUU/Pnz7948aKs8kLExYsX09PTZ82a9eGHH2otbrd7165dsbGx69at6+7u9jI0dBRIdwQ4OhRdx6mpqamrq1u8ePHDDz+stURHR69bt+7y5cvvvfee3NpC0yeffDJp0qR7771XdiGhSJuIzsjI+PTTTxMSEvx+1+v1lpSUXL9+/emnn/ZNXy1YsGDhwoWnTp369NNPda93LBu8L4QQnZ2dn3/+eXR09MSJE/UvL6TU1tbW19cvXrx45syZWovRaFyxYsWMGTPOnj3b1tbG0NDTLbtDBDw6FM0lVVVV3d3dc+bM6b1kEx8fP2XKlA8//PD69esSawtBLpfLZrPde++99913n+xaQlFdXd2LL75oNBr37NmzZMkSv9/t6Oiorq6+5557HnzwQV+jyWSaPXu20+msqanRt9gxbvC+EEJcuHDB4XDExcXdcccd+pcXUpqbm6OiohITE3t/mwgPD4+KitJ+zdDQ0y27QwQ8OhTNJS0tLWazedq0ab0b77zzzoiIiNbW1mvXrskqLDR1dHTY7Xaz2VxUVJSUlBQbG5uUlFRYWNjR0SG7tJBgNBpXr1594sSJ733ve31/9/r1621tbQ888EDv8S+E0Ca3Lly4oFOVoWHwvhBCNDc3u1yuGzduaLv/tD37x48f93g8Opc65q1aterMmTMZGRm9G+vr6+vq6rSfyBkaerpld4iAR4eK+7A6OzsvXrzYt33ixIn333//hQsXmC/Rmd1ub21ttdvt//nPf5KTk8ePH19RUbFnz57y8vI33njDt6EJoyQhIaHfJQPN5cuXXS5X33aLxRIZGdnS0jKapYWcwftCCPHxxx8LIf74xz/GxcVlZGS0tbX94x//WLdu3cqVKwsKCsLCwvSqNBQ5nc4dO3Z0dnYuX748MjLy/PnzDA2J/LpDBDw6VMwl2n6Zfn9r3DhFJ3jGtvb29vHjx//gBz/45S9/GRERIYS4evXqtm3b3nzzzd///ve/+tWvOGggkcfj6Xe8jBs3jpNrOvN4PB0dHZGRkb/+9a+XLFmi/f03NjauXbv2yJEjjz76aHp6uuwaxyyXy1VQUFBRUZGZmbl06VLB0JCq3+4IcHSo+G3eYDAM9H3uxo0bOhcDIURaWtqZM2deeuklLZQIISIiIp599tno6OiKiop+J7egG6PR2O94uXHjhpf7fvRlNBq3bdtWU1OzdOlS33e+mJiYdevWud1u7eSO3ArHKofD8dxzz7399tsZGRk///nPtZ+8GRqyDGdY75EAAAWgSURBVNQdAY4OFXPJHXfccc899/Rtv3LlyoULFyZPnjx+/Hj9q4Kfu+6664EHHujo6Oj3Cgfo5u6779bmSP1cunTJ5XKxVVkFVqtVWzjo7OyUXcsY1NDQsHLlyoqKipycnMLCQt9wYGhIMVB3DKTv6FAxlwghrFar0+n84osveje2t7dfvXp1ypQpEyZMkFVYyHI6nd3d3X3bTSaT0WjUvx74aPuu7Hb7lStXerdrw+f++++XVFeI8ng87e3t/f44bjKZWD4YcRUVFU8++WRTU9PmzZs3bdrUewcPQ0N/g3SHCHh0KJpLEhMTw8LCKioqev8f+Pjjjy9fvjxr1izmS/Tkdruff/75xMTE8vLy3u12u72hoYHDw9JFRkZ+85vfbGlp+eSTT3yNbrf7gw8+MJvN3/nOdyTWFmrOnz//2GOPZWRk+O2pPHPmjNPp5PDwiDt79mx+fn5XV9euXbuys7P9fkZiaOhs8O4IfHQomktmzJgRFxd3/Pjxf/7zn1qL3W7fuXOnxWKZP3++3NpCjclkWrhwoRDi4MGDDodDa3Q4HNu3b29ra3viiScmT54stUCI+fPnGwyGffv2+TroxIkTJ0+enDNnzte//nW5tYWUqVOnzpo16/z582+//bbv6ONHH31UVFQ0ZcqUH/7wh3LLG2PsdvvGjRuFEPv37x/o+wJDQze37I7AR4eixygsFkteXl5+fv6qVasee+wx7X2czs7OTZs29b4hB/pYtGjRihUrDh06lJKSkpKSIoQoLy93uVwZGRkrV66UXR1EcnLysmXLDh06lJ6ePnfu3Obm5qqqqkmTJj377LO+rcrQgclk+tnPflZXV/fKK68cPXo0KSnp/PnzVVVVRqNx+/bt3/rWt2QXOKYcOXLks88+Cw8PX79+vd8C2dSpU4uKiiwWC0NDN4F0R4CjQ9FcIoRIT0+/++67X3755dLS0hs3bsTFxeXn5y9atIgFWv2FhYVt3bo1KSnp9ddff+edd4QQcXFxP/nJT5YsWcJ9DCrQOig+Pn7v3r1vvfVWeHh4SkrKL37xi5iYGNmlhZzo6Og333xz9+7df/3rXw8fPqz1RV5enu9JDYwIl8t1+vRpIURXV5ffi7VCCIPBoO0BYGjoI8DuCHB0GDguBQAAFKHo/hIAABCCyCUAAEAV5BIAAKAKcgkAAFAFuQQAAKiCXAIAAFRBLgEAAKoglwAAAFWQSwAAgCrIJQAAQBXkEgAAoApyCQAAUAW5BAAAqIJcAgAAVEEuAaA3p9OZmZkZGxu7efNmt9vta3/rrbfi4uIWLFhgt9sllgdAInIJAL2ZzeZNmzaZzeajR49+8MEHWqPNZtu5c2dYWNiGDRuio6PlVghAFnIJAAkSExNXr17d1dW1c+dOp9PZ3d29Y8eOxsbGZcuWpaWlya4OgDQm2QUACEUGg+HHP/5xRUVFVVXVsWPHoqKijh07FhcX99xzz4WFhcmuDoA0Bq/XK7sGACHq/fffz83NjYyMHDduXEdHx2uvvZaeni67KAAysY4DQJq5c+c++eSTbW1tly9fXr58+YIFC2RXBEAycgkAaQwGQ1JSUlhYmMFgmD59usnEyjIQ6sglAKS5dOlSUVGR2+02Go379u07d+6c7IoASEYuASCH1+t9/fXX//3vfz/xxBNZWVmXLl169dVXr169KrsuADKRSwDIcfr06aNHj1oslrVr1+bm5sbHx//9738vKSmRXRcAmcglACRwOBy/+c1vOjs7c3JyvvGNb1gslry8PJPJ9Lvf/a6xsVF2dQCkIZcA0JvX6z106FB1dXVSUlJmZqbWmJaW9vjjjzc3N+/atau7u1tuhQBkIZcA0Ft1dfX+/fsjIyPz8/PNZrPWGBYWlpeXZ7FY/va3v508eVJuhQBk4V41AACgCuZLAACAKv4H9DYYEujzABcAAAAASUVORK5CYII=\" alt=\"Vertical shift\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y_shifted, v] = v_shifting(x, y, k)\r\n  y_shifted = x;\r\n  v = x;\r\nend","test_suite":"%%\r\nx  = [0 1 2 5 10 15 20 25];\r\ny = [4 4.6 4.4 3.4 3.1 1.8 1.4 2];\r\nk = 'mean';\r\ny_correct = [1.38   1.98   1.78   0.78   0.48  -0.82  -1.22  -0.62];\r\nv_correct = 'down';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n\r\n%% \r\nx  = [0 1 2 5 10 15 20 25];\r\ny = [5 4.6 4.4 3.4 3.1 1.8 1.4 0.9];\r\nk = 'mean'; \r\ny_correct = [2.47  2.07  1.87  0.87  0.57 -0.73 -1.13 -1.63];\r\nv_correct = 'down';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n\r\n%%\r\nfiletext = fileread('v_shifting.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = -pi:pi/6:pi;\r\ny = (sin(x)).^2;\r\nk = - 1;\r\ny_correct = -(cos(x)).^2;\r\nv_correct = 'down';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n\r\n%%\r\nx = -5*pi/12:pi/12:5*pi/12;\r\ny = (tan(x)).^2;\r\nk = 1;\r\ny_correct = (sec(x)).^2;\r\nv_correct = 'up';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n\r\n\r\n%%\r\nx = -5:5;\r\ny = atan(x);\r\nk = 'mean';\r\ny_correct = atan(x);\r\nv_correct = '';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-29T14:41:30.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-20T13:44:19.000Z","updated_at":"2026-03-24T16:04:22.000Z","published_at":"2025-12-29T14:41:30.000Z","restored_at":null,"restored_by":null,"spam":null,"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\u003eGiven a real function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e input-output pairs, consider a translation in the up-down direction given by an amount \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eFor a real constant \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, you may assume that the translation is given. However, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'mean', you firstly must determine the real constant \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that the translated function has an average value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the given interval (see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eFind\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_shifted,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e which is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector that stands for the outputs of the translated function;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e which stands for either 'up' or 'down' if the function's graph is upward or downward shifted, respectively, and it stands for '' if the graph does not undergo a translation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eHint. Calculate the mean of a piecewise linear discrete function, represented as an array of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and an array of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e values. Be aware to the existence of calculus discrepancies whenever the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be continuous, but not piecewise linear.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(x, y, k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[y_shifted, v]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"367\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Vertical shift\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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YAxis does this Graphic object belong to?","description":"Your function gets a graphic object in an Axes that has 2 YAxis. Can you determine which YAxis does this object belong to?\r\nI provided my reference answer to prove the solvability of the problem, but Size 159 is definitely not optimal.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 25.5px; transform-origin: 408px 25.5px; vertical-align: baseline; \"\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: 385px 10.5px; text-align: left; transform-origin: 385px 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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour function gets a graphic object in an Axes that has 2 YAxis. Can you determine which YAxis does this object belong to?\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: 385px 10.5px; text-align: left; transform-origin: 385px 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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eI provided my reference answer to prove the solvability of the problem, but Size 159 is definitely not optimal.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function YAxis=GetYAxis(GObject)\r\nYAxis=GObject.Parent.YAxis\r\nend","test_suite":"%%\r\nNumTrials=100;\r\nQA=gobjects(2,NumTrials);\r\nDirections=[\"left\",\"right\"];\r\nAx=gca;\r\nfor A=1:NumTrials\r\n    Random=randi([1,2],1);\r\n    yyaxis(Directions(Random));\r\n    QA(1,A)=scatter(A,A);\r\n    hold on;\r\n    QA(2,A)=Ax.YAxis(Random);\r\nend\r\nassert(~contains(fileread('GetYAxis.m'),'evalin'),'evalin is not allowed');\r\nfor A=1:NumTrials\r\n    assert(isequal(GetYAxis(QA(1,A)),QA(2,A)),sprintf('Incorrect YAxis for Scatter %u',A));\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":362068,"edited_by":362068,"edited_at":"2025-08-01T10:41:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2025-08-01T10:37:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-08-01T04:35:44.000Z","updated_at":"2025-10-22T13:29:59.000Z","published_at":"2025-08-01T04:35:44.000Z","restored_at":null,"restored_by":null,"spam":null,"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\u003eYour function gets a graphic object in an Axes that has 2 YAxis. Can you determine which YAxis does this object belong to?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eI provided my reference answer to prove the solvability of the problem, but Size 159 is definitely not optimal.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":43021,"title":"How many figures currently exist?","description":"Return the number of figures that exist at any given time.","description_html":"\u003cp\u003eReturn the number of figures that exist at any given time.\u003c/p\u003e","function_template":"function y = numfig()\r\n    y = 0;\r\nend","test_suite":"%%\r\nassert(isequal(numfig(),0))\r\n\r\n%%\r\nclose all;\r\nfigure;\r\nassert(isequal(numfig(),1))\r\n\r\n%%\r\nclose all;\r\nfigure;\r\nfigure;\r\nassert(isequal(numfig(),2))\r\n\r\n%%\r\nclose all;\r\nfigure;\r\nfigure; plot(1,1);\r\nfigure; imagesc(magic(5));\r\nassert(isequal(numfig(),3))\r\n\r\n%%\r\nclose all;\r\nn = randi(20);\r\nfor ii=1:n\r\n    figure;\r\nend\r\nassert(isequal(numfig(),n))\r\n\r\n%%\r\nclose all;\r\nassert(isequal(numfig(),0))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-04T14:56:58.000Z","updated_at":"2026-03-02T15:03:36.000Z","published_at":"2016-10-04T14:56:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the number of figures that exist at any given time.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":537,"title":"Cody Computer Part 3 - Detect the graphic card used on Cody Computer","description":"In the Cody computer investigation party, you may have already solved :\r\nProblem 522. Cody Computer Part 1 - Guess the system font used by uipanel\r\nor\r\nProblem 536. Cody Computer Part 2 - Get the license number of Cody Computer\r\n*******************************************\r\nThis is the third problem to solve :\r\nYou have find the graphics card manufacturar used by the Cody Computer.\r\nExamples of manufacturar : NVidia, ATI, Zotac, ASUS ...","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; 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: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 231px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\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; text-align: left; white-space: pre-wrap; 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; \"\u003e\u003cspan style=\"\"\u003eIn the Cody computer investigation party, you may have already solved :\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; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 522. Cody Computer Part 1 - Guess the system font used by uipanel\u003c/span\u003e\u003c/span\u003e\u003c/a\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; text-align: left; white-space: pre-wrap; 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; \"\u003e\u003cspan style=\"\"\u003eor\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; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 536. Cody Computer Part 2 - Get the license number of Cody Computer\u003c/span\u003e\u003c/span\u003e\u003c/a\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; text-align: left; white-space: pre-wrap; 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; \"\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; text-align: left; white-space: pre-wrap; 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; \"\u003e\u003cspan style=\"\"\u003eThis is the third problem to solve :\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; text-align: left; white-space: pre-wrap; 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; \"\u003e\u003cspan style=\"\"\u003eYou have find the\u003c/span\u003e\u003c/span\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; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\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; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003egraphics card manufacturar\u003c/span\u003e\u003c/span\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; \"\u003e\u003cspan style=\"\"\u003e used by the Cody Computer.\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; text-align: left; white-space: pre-wrap; 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; \"\u003e\u003cspan style=\"\"\u003eExamples of manufacturar : NVidia, ATI, Zotac, ASUS ...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name\r\n  y = x;\r\nend","test_suite":"%% Which graphic card is used ?\r\n\r\nS = evalc('opengl info');\r\nS_lines = regexp(S, '  +', 'split');\r\nind = contains(S_lines, 'Vendor');\r\ny_correct = regexprep(S_lines{ind}, 'Vendor: ''([^''])+''.*', '$1');\r\nassert(isequal(your_fcn_name, y_correct))\r\n\r\n%% prevents cheating 14-June-2012\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'Brian Paul')))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":639,"edited_by":26769,"edited_at":"2023-02-24T22:26:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2023-02-24T22:26:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-03-30T08:32:22.000Z","updated_at":"2026-03-04T16:12:59.000Z","published_at":"2012-03-30T08:32:22.000Z","restored_at":null,"restored_by":null,"spam":null,"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\u003eIn the Cody computer investigation party, you may have already solved :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 522. Cody Computer Part 1 - Guess the system font used by uipanel\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\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\u003eor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 536. Cody Computer Part 2 - Get the license number of Cody Computer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\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\u003e*******************************************\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eThis is the third problem to solve :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eYou have find the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egraphics card manufacturar\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e used by the Cody Computer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eExamples of manufacturar : NVidia, ATI, Zotac, ASUS ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43276,"title":"Get Cody's screen size","description":"Return an object that helps this problem's test suite return Cody's screen size.","description_html":"\u003cp\u003eReturn an object that helps this problem's test suite return Cody's screen size.\u003c/p\u003e","function_template":"function y = getCody(x)\r\n  y = 0;\r\nend","test_suite":"%%\r\nCodys_screen_size = get(0,'screensize');\r\nCodys_screen_size = Codys_screen_size(3:4);\r\ny = getCody();\r\nassert(~isnumeric(y))\r\nsz = get(y,'screensize');\r\nsz = sz(3:4);\r\nassert(isequal(sz, Codys_screen_size))\r\ndisp(sz)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":57323,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-09T11:39:53.000Z","updated_at":"2026-01-22T15:33:44.000Z","published_at":"2016-10-09T11:39:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn an object that helps this problem's test suite return Cody's screen size.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61142,"title":"Shifting vertically a function's graph","description":"Given a real function, f, by n input-output pairs, consider a translation in the up-down direction given by an amount k.\r\nFor a real constant k, you may assume that the translation is given. However, if k = 'mean', you firstly must determine the real constant k such that the translated function has an average value of 0 over the given interval (see figure below).\r\nFind\r\ny_shifted, which is the 1×n vector that stands for the outputs of the translated function;\r\nv, which stands for either 'up' or 'down' if the function's graph is upward or downward shifted, respectively, and it stands for '' if the graph does not undergo a translation.\r\nHint. Calculate the mean of a piecewise linear discrete function, represented as an array of x and an array of y values. Be aware to the existence of calculus discrepancies whenever the function f will be continuous, but not piecewise linear.\r\ninput: (x, y, k)\r\noutput: [y_shifted, v]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 563.312px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 281.65px; transform-origin: 408px 281.656px; vertical-align: baseline; \"\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a real function, \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ef\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, by \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e input-output pairs, consider a translation in the up-down direction given by an amount \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a real constant \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, you may assume that the translation is given. However, if \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'mean', you firstly must determine the real constant \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that the translated function has an average value of \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the given interval (see figure below).\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_shifted,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e which is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vector that stands for the outputs of the translated function;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ev,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e which stands for either 'up' or 'down' if the function's graph is upward or downward shifted, respectively, and it stands for '' if the graph does not undergo a translation.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint. Calculate the mean of a piecewise linear discrete function, represented as an array of \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and an array of \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e values. Be aware to the existence of calculus discrepancies whenever the function \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ef\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be continuous, but not piecewise linear.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(x, y, k)\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[y_shifted, v]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 259px; 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 129.5px; text-align: left; transform-origin: 384px 129.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg 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dv/+/WfPnrVo0aKhP6L1TvoBo4P+EqjHzZs3+/btS4sL1LqynZ2do6OjHR0dCSHPnj3TfhTABPTo0aNPnz6EkDt37ly/fv3EiROEEEtLS39/fy1H+ms+Y9bW1s1aMiCTySIiInbs2CGTyXg8XlBQUHx8/ObNmxv3aFwuNygoyNLSsrKy8sSJE4WFhbS7om3btnW/UzbuWmqJ7ezZs9OmTaPzmj09PZctW3by5Ek65mLIdPWk8Xg8DodTWVkZFxen1t9jpP7+++/Kykrd/oiCkUJ/CdTD0dGxc+fOxcXFRUVFJ06ccHd3V33fffbsmTb92waI6Xym3cuMJ0+eaBOwbGxsJkyYQGcsHjt2jHbF9+zZk4YVQgiHw2FCRlxcnJalLo3z4osvduzY8f79+1Kp9NGjR3S6ZU1Xrlyhg01CoTAxMZH26zRls5UePXoIhcLbt2+LxeKkpKTs7GxCyEsvvdS5c+c67tXEZ54Q8uzZs/3799PimoULF86aNYvD4chkMuaDe015eXn0rY7elMvl9OfW1tZWh1mwvLy8pKSE6XuoqqqiWzup9t417klT5ePjExsbu2LFiuTk5KtXrx44cMDwF9mzsLCgz3Pd3TPnz5/X7Y8oGCP0l0A9WrVq5evrS/9N+4TpkvOVlZUZGRnvv/8+XX6gY8eO9VbY6oSuYhAzLJ2RkcEsol9ZWal9VaG3t3enTp0IId9++y0dRhk6dCjTFW9ra8tklMuXLzODBXv27KGrMkRGRmpf//LPP//UcTKPx2Mm06heS22pleLiYvrsMYtNEUK0KTOpjb29PZ0UUlBQsGXLFrVpv7Vp+jP/7Nmzv/76i/6bTnolhPz11191VFbfvHnzxo0bzM0LFy7QDOTm5tayZUstr1uvJ0+e0Fpx6u7duzR2tG/fnhm0atyTpmratGnt27efPXs2/WHbu3ev6rJAappp3mtDOTs7CwQCQkhhYSGTR8vLy0NDQ+nCLcePHyeE6PxHFIwRcgnUb9KkSXT6XlVV1Y4dOwYMGODi4tKtW7exY8fSfYA5HM6ECROYOYw6x+PxaAIghFy7dk2hUJSUlDRxXlvfvn179epFCLl9+/batWtLS0tlMtmmTZu0f3d0cnIaPHgwc7Nt27b+/v6qJ4wcOZI+J3v37v3222+rqqpycnK++uorQoiVldXEiRPr/aTO/HUuKiqSSCS0pkbjmRMmTKAzkePj4+m1iouLd+zYQYt0hg4d6uTkRCtfCCE3bty4fPmyQqE4deoUbU+jDRo0iMfjKZVKOouTmfZbh6Y/8y1atGDm5Rw9erS0tLSwsHD9+vU0HWokk8mioqJu3bpVVVV16tSp+Ph4ovWr0CCbN29OSUmhu1quXr2avl70+WfOacSTVpO3t/eECRMIIQUFBV9++aX2GZcVfD4/KCiIw+HI5fIPP/yQvhBnzpyhvSPdunWjk06a40cUjA5yCdTP0dHxs88+U/3DqorD4bz99tuhoaHN2gb6TkYI2bFjh7u7++zZs5tYbGxnZxcVFUXfy48cOeLt7d2rV6/t27drv7AVXV6MGRoYOHCgWs0Is+5LWVnZsmXL3NzcaBUJh8OZP3++j49PvZfg8/m0OFYul0+dOrV79+579+7VeGbPnj0//PBDW1vbiooKeq2+ffseOXKEEOLj4zNv3jxa+0D/+kul0rCwMHd393fffVcul9N3gvv37zeitJKZZ0P16dOH1pvUoenPfIsWLYKDg+nKIidPnvT29h4wYEBSUhIzVpKZmal2l06dOpWWlo4aNcrNze3dd9+VSqXavwra69Spk6Wl5dtvv+3m5jZ48GA6/YV5/pnTGvGk1UR/71xcXAghx44du3z5si6+g2Y0efLkKVOmEEJu375NX4j333+/oqKibdu2a9asoQm+OX5Eweggl4BWevbseeLEiWXLlnXv3p1ZYK1du3ajR4/+/vvvly1b1tzFipMmTZo7dy59M7OysqIzB5v4mN7e3l9//fVrr71mZWVlYWHRt2/fr7/++t1339X+Ebp160ZXj6UZpeYn74CAgB9++GHChAm0nIRe5Ztvvqm5zKhGNjY2q1evHjJkCH3OW7VqVcd3HRAQcPToUdVreXh4REdH79ixg3b483i8zZs3h4aG0sqUVq1aTZ48OTk5mRlWYBb7156Njc3QoUPpv2t7Empq+jM/ePDg3bt3e3h4cDgc+p1u3rw5MTGRWS9EbTZo586dv/7668mTJ1tZWXE4nK5du27ZskXLV0F7nTt3TkxMnDx5Mn0J2rZtO2/evC+++EKt0KZxT1pNjo6O7777Lp1b88UXXxj4VtuWlpYfffTRrl27+vfvT3+ebW1tJ0+eTLMpPac5fkTB6HD0XOT9119/TZ06teanmaCgoHpX8ATQg+TkZFrWKxKJ4uLiUIVYr+Tk5HfeeUepVLq7u3/11VeNHs5rjmeeqZI1tFdTV08agOnRdz3Ow4cPHz16ZGtra2dnp3pc7SYAW5gPnQ4ODtiAtF5KpfL06dP04432y6hrZD7PvA6fNADTo+9c8ujRo6dPny5fvvztt9/W86UBVF2/fn3q1Kl00ac333xz6dKl1tbWEomETrLjcDjar0Rinp49e2ZlZfXTTz/R3X3peuFaLqNuts98o580APOh71xCF+aic7UAWCQUCr29venWJF999ZXanH8/Pz+14hpQ88EHHxw6dIi5OXr0aNW5nHUw52e+0U8agPnQ67xXpVJ5+/bttm3b1lbZAaA3PB5v+/bt0dHRL730EjNqYGVl1b1799jY2C1bthjOXATD5OnpST/oOzg4vPPOO8uXL9dy7rM5P/ONftIAzIde573KZLIZM2YUFhYOGzbs+PHjBQUFtra2o0aNioiIoGuZAwAAgDnTay75888/X3/99QcPHtja2g4cONDOzi49PT03N9fe3j4uLk771QsAAADAJOl1fklJSYmFhcUrr7yyadMmWoBTVVUVFxcXGxu7fv362qr4xGJxHduXAwAAgIEbMGCAxq2ka9Lr/BJPT8+ffvrpq6++YqqCLSwspk6d6u3tnZGRQTeSqOnixYtYS8dwHDx4EC+H4Th48GBeXh7brQBCCMnLyzt48CDbrYBqeDkMSoP6F9jfT5iutP3HH38wO3jVJBKJIiMj9dkqqI1YLJ44cSLdmANYd/DgwcjISEwkNwR5eXkhISH4S2UgaGTHy2GM9L0OvUwme/bsWc3jdDFpPTcGAAAADIpec0lsbGyvXr3oTp6MwsLCjIwMFA8DAACAXnOJv78/j8c7ePBgbm4uPVJeXr5hw4bbt28PGzaM7psKAAAAZkuv80v69Onz3nvvrV+/PiAg4NVXX23ZsuX58+cfP3788ssvR0ZGNm5HTQAAADAZeo0CHA4nPDy8W7duW7ZsSUlJqaqq6tSp07Jly15//XUTXuERAAAAtKTvLgoOh+Pr6+vr66vn64KuLFmypGvXrmy3Aqpt2LDBwcGB7VYAIYQ4ODhs2LCB7VZANS8vL1dXV7ZbAY2BoRNomA4dOrDdBPgPXg6DgpfDcDg4ONA9q8Ho6LtOGAAAAKA2yCUAAABgKJBLAAAAwFAglwAAAIChQC4BAAAAQ4FcAgAAAIYCuQQAAAAMBdYvAQAwcWKx+OLFi2y3Qq/kcrlCocBK4s1kwIABIpGomR4c/SUAACbu4sWLYrGY7VbolbW1NUJJM2numIv+EgAA0ycSiSIjI9luBUD90F8CAAAAhgK5BAAAAAwFcgkAAAAYCuQSAAAwBVVVVefOnZsyZYqHh4eLi4unp2d4ePgff/yhVCrruJdMJgsJCQkJCZHJZPVe4vr1615eXtu3b296a5OTk11cXJKTk5v+UE23fft2w2mMeeUSiYRwONX/xcQQiYTtBgEAgC4UFxe/9dZbM2bMePLkydy5czdv3jx16tTr169PnDhxxYoV5eXlbDcQtGVG9TgSCQkL++9mdDSJjiahoSQqiggErLUKAACaqLy8fMmSJRcvXly5cuW0adMsLCwIIaNGjZo7d+6GDRt2797dokWLlStXcjicmvfl8Xj79u3T8kKenp5Xr17VZdOhBjPqL0lMJKmp6gcTEohQSIRCDV8CAACjkJqampaWFh4eHhoaSkMJZWNjM3/+/MGDB3///fe///47iy0E7ZlLLpFISHR0XV/19ydCIUlI0FuLAABABxQKxcmTJ1u2bDl69OiaPSI2NjaTJ08uKytLSUkhhCQnJ3t5eZ08eXLcuHGurq5Tp07Nz89Xm1+Snp4+fvx4V1dXDw+PmJiYQ4cOMXMvVOeX0Akix48f//zzz/v37+/i4uLj43Ps2LGqqir6OFVVVSdPnhw1apTqfJfc3FxtvimlUpmUlDR48GAXF5devXrt3Lnz888/9/Lyun79OiFk+/btvr6+ycnJPj4+bm5uCxcurKioyM/PX7p06csvv+zi4uLq6urv779nz57KykqiMocmOTl5xIgR9DHXr1+vNqWmtLT0ww8/9PT0dHV1HTly5C+//FL31JxmYhbjODR2MAQC4uenIYLQgZ6YmOrBHQAAMHylpaU5OTlOTk4ODg4aT3B3d3dwcLh27VpZWRkhRC6XR0VFvfbaa6+//rpcLm/VqpXqycnJye+9916HDh1WrVpFCNm9e3fdozwfffSRjY3Ne++9R09etGiRpaVlQEAAvfnJJ5+8/PLLMTExLVq0SE5OPn369IMHD7766is7O7u6v6ldu3atW7euZ8+ea9euLSws3LFjh1Qqtba2Zk549OjR8uXLJ06c2KFDB3t7+ydPnrz99ttPnjyZNGlSz5497927d+DAAXrdKVOm0LvcuHFjwYIFQ4YMmTVrVkpKSlxc3M2bN7du3cosjLts2TIPD48VK1bIZLJt27bNmjUrPj6+b9++dTdV58wil6hNcaWxIyqKJCZq6EShPSsJCUgnAGDKVD+tGZfp00lo6H83FQpFWVlZ69atVUdwVFlbW3O5XKlUqlAoCCGVlZU9e/aMiYmxsbEhhKj2GUil0m3btjk7OyckJDg6OhJCRo4cOX369MzMzNoa4+LisnPnTj6fTwgRiURTp049e/ZsQEBAcXFxWlraoEGDtmzZQi8UGBgYExNz+PDhvLy8unPJ/fv39+zZ88orr2zdupU+8muvvRYWFiaXy5lzKioqRo4cuWjRItpFdOzYsUePHn3++ee+vr70hMGDB0+dOjU9PZ3JJTKZbMmSJeHh4RwOJzAw0MPDIzY2NiUlZcyYMfSEYcOGbdiwwdLSkhDStWvXmTNnpqenI5foXkLCc10jfn7VaUMgqE4nMTEkIUG9NgfpBABMm/FOqvPza+ojiEQimhXUZGZm3rp1a+7cuTSUEELs7e2Dg4Oja58H4OPjQ6MDPdne3v7x48dlZWV2dnZ79+5VPZPD4dTWo6Pm8uXLBQUFUVFRzCN37949ICDg8OHDapdmxq3Gjh07duxY1a/a2dm9+OKLqkfc3NzGjx9P78LhcEaNGrV3795ffvmFySUjR46koYSe3L59+7t372rTYN0y8fklajU4AgGJj1c/JyqK5OaS+HgNVTk0naCoGADAYHE4HC6X+88//9R2At1bmM/nc7nVH8W7dOmi8cySkhK5XN61a1fVg506darj6sxjEkKsrKxat26tUCiYaRlVVVX5+fnJyclxcXHTpk3bunWrNt/Rw4cPeTxehw4dmCM1Mw2Px7O3t1e7o0wmu3LlypEjRz744IMpU6bk5eWpfrVNmzaqaYzH47Vq1erevXtMjxETSuj39cIL7CQEU84laqGEkLpKgkNDSW4uyc3VnMSjo4lQiHQCAGBw7Ozsunfvnp2dnZ+fr/GE3NzcJ0+e9OrVy9bWlh5RfQNuJkqlMjk5ecCAAYMGDZo5c+a2bdsIIV5eXrp6fA6Ho5obiouLIyIivLy8goKCFi1aJBaLe/furc2OylwuV2P5NItMeRxHrTA4NPS5IUmNBAKSkkIkkurBHTV0yRPa6dL0jkQAABbV7Dw2FmofL7lc7qhRo86cOXPgwIGai5SUl5d//fXXLVq08NdiQk2rVq2sra3v3r07ZMgQ5uCjR48a0cg7d+588MEHXbt2Xbt2befOnencl+3bt9OCmro5ODjIZLJHjx55enpq0wylUrl58+YzZ858+OGHgYGBNI48fvz48uXLqqc9ffq0oqKCuVlUVPTkyRMvGp9pHQAAIABJREFULy8mrhkIk80laoXBGkdwakNPrmNirL9/9fSUeoMOAIBhMqU/X0OGDJkwYcK+ffucnZ2ZddUIIeXl5Rs2bDh79uz06dP79OlT7+N4eHh079794MGDY8aMoVNMpFLp8ePHG9GkP//8s7Cw8M033xQKhfRIcXFxamqqXC4vKSmp+759+/bt1KnTnj17BgwYQKeY5OXl/fTTT7WdX1ZWlpmZaW9v7+/vT0OJUqkUi8UPHz58+vTps2fP6GnZ2dkXLlygs0lod05JScmIESMa8d01K9PMJTULgxvxyYAmj+nTa00nKCoGADAElpaWy5YtKy0t/eijj7777rtx48Y5OjreunXr+PHjeXl5wcHBTN1K3fh8/uzZs997772QkJC33nqLELJ79+7GrWHfrVs3R0fHnTt3lpaWenl5ZWRkHD58uLi4uLKyUrWsRiOartatWzd16tSQkJDCwsLExMQ62s/j8V5++WWxWDx//vzx48cTQk6ePHnx4kWlUvn333/TJUwIIZWVlYsWLfrtt9/69et3/Pjxs2fPTpkyZeDAgY347pqVac4vqVkY3OhhF5pOcnM1L8tGe2WwXCwAALv4fP7GjRt37drF5/M3bNgQERGRmJjo7u7+/fffr169WmP1jUaDBw/evXu3ra3thx9+GBsbO2TIkKVLlzaiPc7Oztu2bXN3d4+Pj587d+6pU6fmzZu3d+9ePp+fkZFR793feuutzz77rKioaNmyZYmJiTNnzgwJCanj/HfeeWfu3LnZ2dnLli1bvXp1y5Ytf/jhh8DAwPv37xcXFzNN+vjjjy9evBgZGXnz5s1Vq1atXLlSD1NtGorDympuDbJx40ZCSGRkpJbnJySo1+Bot7yeVjQWFVOhoUY8Xqu9Bw8e8Pl8baZTgR7cv3+/Y8eOqhUBwBaFQvHgwQNnZ2e2G6JBQ/+Kgqrt27dv27Zt7969qrM99G/hwoXp6enfffdd+/btG3pfmUw2c+bM/Pz8xt1dTSN+nBp0F1PrL6lZGJySosvHr6OomG61AwAARurx48cBAQGxsbHMJ3apVJqamtqmTZt27drprRnXr1/39fU9cOAAcyQvL++PP/5wdHRUW5LEJJnUx6wGFQY3BS3toZdTHcGRSIhQiGodAACj1KZNm759++7YsePBgwd+fn5///33vn37MjIyli5d2rFjR701QygUCgSC1atXZ2Zm9uvX78mTJ7t373706NGyZcvMoa/apHJJIwqDm4J2xqSmPjfHlk65jY7GZFgAACPD5XKXLl3K5/OPHj16+PBhCwuLHj16fPXVV//73//02QwejxcbG/vpp58eOXIkMTHRysqqd+/eO3fudHd312cz2GI6uaQphcFN4edHcnOJv/9zk06io0lqqo6HkAAAoLnxeLwlS5YsWbKE3WbY29uvW7du3bp1Onk0Ho9X9+6DBsVE5pfopDC40ejUWrWxm9RU1OkAAAA0jInkEh0WBjdaSop6LTFNSzXXjQUAAACNTCGXqO0YTFccYUVUlIaxm7Aw9dm4AAAAoJHR55LmLgxuKDrdRK23BiXEAADNqry8fM+ePSNHjnRzc3Nxcendu/fcuXNv377NnJCcnOzi4rJ9+/baHmHhwoW+vr6PHz8mhCiVyr179/bq1cvFxWXatGllZWVNbN727du9vLy02RynuclkspCQEOY7NUDGnUv0VhjcIDQb1RzTwXQTAIDmIJVK33333ejo6NLS0sDAwODgYIFAkJSUNHbs2KSkpEY8YEZGxieffCIUCjds2BAZGfnCCy8cOHDAiKaOGjXjrsfRc2Fwg0RFEV9flBADADS71NTUn376af78+bNnz2Y27bt161ZYWNjGjRv79etnb29f74PExsYy/3706JFUKp01a1ZAQAAh5Pr162vWrJk9e3YztR9UGXF/CVuFwdqjYzpq/TfR0USL3bYBAEBbv/zyC4/H8/X1ZUIJIaR79+4TJ04sKCjIz89v3MMa4N4x5sBYcwm7hcHaQwkxAEBz69Kli1wul9TYumzhwoXXrl3z9vZmjsjl8p07d/bv39/FxcXHx+fYsWNVVVXMyb6+vhKJJCQkZObMmYSQmTNnenl57d69OzAwUCqVfvzxx8wckcrKyj179vj4+Li4uHh4eERERKimH6VS+csvv4wcOdLV1dXT0/Ojjz6qe4aKTCZbv349nc4yYsSIH3/8MTg4OCQkRCaT0ekgCxYs2L17t4eHh6en57Fjxwght2/fDg8P7927t4uLi5ub28iRI5OSkujy+Y8fP/b19V2wYMHx48dFIpGLi4tIJNqzZw+zsTCVlZUVHBzs5uZWs/3sMtZxHEMoDNZeSgqJiXmud4fmqvh4Axp4AgDz0rg1DBr6N0svV3nttdfi4+Pnz5//3XffjRs3buDAgR06dOBwODXP3LZtm4ODw3vvvWdpafnll1/OmzePw+GMGTOGOcHS0nLu3LleXl47dux45513evfu3aVLl8WLF2/atGnEiBEjRoxwcnKqrKyMiorav3+/p6dnREREYWFhQkJCaGhoQkKCo6MjIYTuHtyhQ4dVq1YRQnbv3v3w4UNra2uNjZfJZHPmzPnll1/Gjh07aNCgn3/+OSIiQqlU9uvXjzknOTn52rVrq1atevTokaenZ0ZGRlhY2IsvvhgeHt6lS5eMjIzvvvtu3rx5dnZ2IpGIuUtaWtqYMWO8vLwOHjwYHR19+/bt6H/fh/Ly8sLDw0eNGvXGG29cuHDh4MGDBQUFCQkJfD6/Qc98czDKXGI4hcHaqzndhBASFkbS0gy0pwcATFzjFjBoaC5pxFUa/jfR3d19//79ixcvvnDhwvnz5wkhtra2/v7+YWFh3t7eqgGlR48eu3fvtrOzI4T07dt36tSp9M2bOcHS0lIkEslkMnrCkCFDCCEVFRXbtm1zd3cfNmwYISQtLe3gwYMTJkxYs2YNHevx8fEJDw//+OOPP/300/Ly8l27djk7OzMxZciQIaGhobXVv6SkpPz666+LFi0KDw/ncDiBgYFeXl4xMTGq58jl8hUrVvj6+tKbn3/+uZWVVVxcXLdu3Qgho0aNEolEM2fOvHLlCpNLnj17tm7dOjo/ZtSoUcuXLz927Nj48ePpXQgha9asCQoKIoSMHj3a2tr68OHDEomE3T2TKeMbxzG0wmDt1VZCjOkmAGCa9NMlQwghRCgUfvfdd2KxODY2duTIkYSQEydOTJw4ceXKlarjF4MHD6ahhBDi6Ojo6upaUFBAU4j2Tp06ZWFhMXnyZGYCipeXl5+f32+//VZQUJCTk3Pnzp3AwEAaSuiFAgMDNT6UQqE4ffq0o6PjmDFjaH7icDgBAQFubm6qpzk4OHTv3p25+f7771+4cIFJGISQNm3aqPXHiEQiv3/fbywtLSdPnqxQKK5cuUKPdOrUiUkwHA5nwIABUqn00aNHDXoemomR9ZcYZmGw9miKUhvTodNNsAsxABg6PXSWNI29vX1QUFBQUJBSqczMzFy6dOk333wzYMAApkeEy33uXe+FFxr84bysrCw/P9/W1jY7O1u1C6SqqkoqlRYXFxcWFspkMg8PD9V7qd1kyOXyv/76q2PHjqoDKDY2Nm3atFE9rWPHji+++KLafUtLS2/evHnv3r2LFy+KxWKpVKr61Xbt2tnY2DA3W7duzePxbt26RW++8MILqk+FQc3wNbJcYsiFwdqLiiJdujz3C4sSYgDQt0Z8EmroCItePmzRGaADBw5cu3Ytc5DD4XTv3n316tU1R2qaSKlUKhSKoqKi5cuX1/xqYWGhri6kSi0/5eXlLViwID09nRBiZWXl6urap0+fc+fO1fs4BpU/asNmLqmsrFy+fPmPP/64d+9ebca0DL8wWHt0oi52IQYA1ujhb41e/py1a9fO1tb2jz/+KCwsVFunxNraukWLFrp9M+bxeF26dLl///6BAwc6depU84Tr16/z+fwrV67QuSnU3bt3NT6atbV1mzZtbty4IZVKeTwePVhRUfH06dPWrVtrvEt5efmHH36Yk5MTFxc3aNCgFi1a0Iv+/PPPqqc9ffr02bNn9KuEkEePHpWUlHTt2rXh37G+sTm/5Pjx44cOHdLyZGMpDNYeHdNBCTEAQFO0adNm7Nixt2/fXrt2bWlpKXO8vLx89+7dJSUlr776ahMvYWFhweVyFQoFvTlw4MBHjx6dOHGC1uUSQqRS6bRp0wYPHpybmysQCLp27ZqUlJSXl0e/WlxcfPr0aY2PzOVyhw8fnp+ff/z4cebRLly4kJ2dXVtjpFJpVlaWq6urSCSisaOqqiotLU1tgkh6evrNmzfpvysrK48ePdqyZUsfH58mPRF6wVp/ye3bt9evX8+8DPUyrsJgLWmcbkITWM3IAgAAGr3xxhsZGRlHjhz54Ycf+vfv7+zsXFRU9Msvv/z999+vv/66ar9F47Rr147H4/3www9OTk4DBgwYMWLEr7/+un79+gsXLowfP760tHT//v1ZWVlLliwRCAQcDmflypXh4eFTpkyh66DUXSfs7+//v//975NPPsnKyqJ1wsnJybWdTAhp06aNt7f3iRMnFi9ePGzYsNLS0oMHD2ZmZnI4HNUpJlKpNDQ09K233urSpUtiYuK1a9eWLFni7u7e9L1+mhs7/SXl5eWxsbF2dnYvv/yyNucbY2Gw9jTuQuzvj12IAQC0wufzN27cuHXr1h49eqSnp+/fvz8tLa1Hjx47d+6MiYlp+jiOvb19eHh4Xl7e/PnzL168aGlpuXLlylWrVv35558LFiz46KOPCCGbNm16++23aU2Nt7f3119/7ezsvHr16rVr1/bq1YsuZKIRj8fbvHnzm2+++eOPPy5YsODWrVuffvqpavWNGi6XGx0dHRwc/PPPP8+fP/+zzz7r3bv3qVOnBgwYkJuby0STl19+edmyZd98882CBQvKyspUm2fgONr3WOjQzp07P/vss02bNp06derMmTN1zy/ZuHHj++9HMjdpH4MR1eBoiZYaqY3g+PkZ3HSTBw8e8Pl8ZhwU2HX//v2OHTuqlRgAKxQKxYMHD5ydndluiAYbN24khERGRtZ7JhiCx48fT5o0qX///qpb9jT07o6OjnFxcc3xt7oRP04NugsL/SVXrlyJi4sLCgrya9RAhXEVBmtP4y7EmG4CAGDadu7cOWLEiDt37jBHLl68+PDhQ6OYo9oc9J1LpFLphg0b7O3tIyMjG/Ehz0gLg7UXFaU+n5dON3l+6T8AADAR//vf/4qKimbMmJGYmHjy5MmYmJjly5cLhcKxY8ey3TR26LX7V6lUfvPNN7/99tuOHTu02XVaDZeb5+19cOPG6pvDhw93cHDQcRMNwLhxxNubjBnDy8v779WhJcSHDz9lsWFUaWlpVVUVMy8d2FVSUmJjY4NxHEOgUChKSkoMYXuRmuRyeR3zKIFdPXv2/OKLL2JjY9euXVtRUdGqVatJkya9//77LVu2ZLtptZLL5U+fan4/evjwYc3iI7FYzCwvWy+9/jm7cuXK1q1bg4ODG1qqNHr0wYyMCaNHX1Q9aJKhhBIISFKSPCKCpzqCk5pKPD15mzfLUKcDDA6HnSliUJNSqTSKSYVggPr373/gwAFdPVr79u3T0tJ09WgN1fS3Zv3lkuLi4g8//NDFxSUiIqKhv71DhuQdP04ImdA8TTNErVtrKCHOy+OOH9+a3RLi8vJyzHs1HFKp1M7ODv0lhkChUMjl8trWwmIXOktAt6ytrev4UW/iDGv9/TnLy8vLycmRSqV9+/ZV+1JgYCCfz9dy1VezonEXYn9/Ehpq9MvKAYA+icVitpsAJqJBgzKNoL9cYmdnN2HCBLlcrnpQLBbn5+f7+/t36tSJ2eMRVNFdiNVKiBMSiERicCXEAGCYBgwYwHYT9I12X6FntzmIRKJm/YnSXy5xcnKqubDMwoULi4qK5syZg56SOmAXYgBoCpFI1KwfcA2QTCaTSqUdO3ZkuyHQYGzujwMNghJiAAAwecglxiQ0lOTmqi8rFx2tPgEFAADASLGcS2JjY69evYpBHO1hF2IAADBh6C8xPhpXrKdjOogmAABg1JBLjBV2IQYAANODXGLEaAmx2phOQgKmmwAAgLFCLjFu2IUYAABMCXKJKUAJMQAAmAbkEhOBEmIAADAByCWmAyXEAABg7JBLTApKiAEAwKghl5gglBADAICRQi4xTSghBgAAY4RcYrLomE5o6HMHMd0EAAAMGXKJiYuPRwkxAAAYDeQS04cSYgAAMBbIJWYBJcQAAGAUkEvMBUqIAQDA8CGXmJfaSogx3QQAAAwBconZ0VhCjOkmAABgCJBLzBFKiAEAwDAhl5gvlBADAIChQS4xayghBgAAg4JcYu5QQgwAAIYDuQRQQgwAAIYCuQSqoYQYAABYh1wC/0EJMQAAsAu5BJ6DEmIAAGARcglogBJiAABgBXIJaFZbCXFQkB07DQIAADPAZbsBYLjomE5Y2HMjOGKxtacn8fOrjiy+vurzUQAAABoNuQTqQqNJTMxzVcQSCUlI0HCmQFCdUXx9q28CAAA0CHIJ1C8qivj61lOVI5EQiUR9bizCCgAANAhyCWiFlhCrjenUS5uwQh8cAACAIJeA9uiYzvffF/72G9/GxpqmjUYUD9cbVrp0+e/fAABgVpBLoGFeeUUxYoSCxyNRUdVHaM6QSMi9e5ozhzbqCCv0P4QVAABzgFwCTaVx1ohEQgghqak6CCs1L0dIdUEQwgoAgIlBLoFmQdOD2rqxugorhKgXBKmGFYLqZQAAo4VcAvpTb1ih/9BtWFGdY4uwAgBg4JBLgGVqYUVt2kpaGiGEpKZqHtOpGz0f1csAAEYEuQQMlGp60GFYIVhqBQDAgCGXgDHRJqyQ5qlexlIrAAB6gFwCRq+OsILqZQAA44JcAqYJ1csAAMYIuQTMCKqXAQAMHHIJmDtWqpcRVgAANEIuAdCguauX1cIKQUEQAAAhBLkEoEFQvQwA0KyQSwCaisXq5Zdesh43rnGtBgAwRPrOJUqlMj09/ZNPPrly5co///zj6uoaGRk5YsQICwsLPbcEoFnpq3rZnhASHf3fJQAAjJq+c0l8fPzatWstLCz8/f1btmx5/vz5iIiI4ODgmJgYS0tLPTcGQM+aqXo5OpokJJD4eEyhBQCjp9dccv/+/fj4+M6dO+/atUsoFBJCpFLpnDlzTpw4MWHChL59++qzMQAGQifVyxIJ8fcnfn4kJaVZGgkAoB96zSX37t2rrKwcN24cDSWEED6fHxQUdP78+fT0dOQSAEbjqpdTUwmHg2EdADBies0lPj4+YrFY7eDdu3cJIQ4ODvpsCYAxqlm9/OuvDxYvtj9//rlfZAzrAIDxeoHFa0ul0m3btiUmJvbq1euVV15hsSUARsrJSZGSQqKj1Y/TYZ2wMBaaBADQFOzkEplMFhIS4uXl9cknn7z00ku7d++2t7dnpSUAJiAqiuTmakgnCQlEKCQxMSw0CQCgcdhZv6SioqJz586dO3dOT0+/dOnSpEmTNm7c2LNnz9rOrzn6QwgZPnw4Rn/0r7S0tKqqSqFQsN0QIISQkpISGxsbLpfbujWJjCSBgWT2bGux2Jo5QSKpHtbZtk0uEslZbKrJUygUJSUlfD6f7YYAIYTIZLKysjIbGxu2G2J2Hj58ePr0abWDYrFYJBJp+Qjs9Je0adNm3bp169atS05OXrp0qUQiWbNmjUwma9CDIJQAcDgcpVLJ3BQISFKSXOOwTkCAdc3joENKpZLD4bDdCgCWNf2tmeX1XjkczpQpU5KSkrKysv78888ePXpoPE0kEkVGRuq5baBReXk5n8/n8XhsNwQIIUQqldrZ2XG5z/0iR0WR6dNJYqL6yM7Gja2PHiWhoajWaRYKhUIul7du3ZrthgAhhHC5XAsLC7wcrGji+zWb816pli1bCoVChUJRVVXFdlsATIRAUD3pRG0ZNzqsIxQ2ZgcfAAA90Gsu2bx5c+/evY8cOaJ68MmTJzdv3uTxeK1atdJnYwBMnkCgeT6sRIL5sABgoPSaS7y9vcvLy7du3Zqfn0+PVFZWbt++/fbt26+++mqnTp302RgAM0E7TmquZUI7ThIS9N8iAIBa6XV+iUgkmjZt2pdffjlixIiBAwfy+fzz588/fvzYy8srIiJCbYwcAHRFICApKSQ1lYSFPTeCI5GQsDCSmEji4zVs3AMAoH967S+xtLRcsmTJtm3bXFxczp07d+jQIS6Xu2zZsq+++gqdJQDNzc9P87BOaiqGdQDAUOi7i8LCwmLYsGHDhg3T83UBgKLVOmFh6nvrYPV6ADAE7NfjAICe0WGdlBQN1Tr+/sTfH9U6AMAa5BIAM4VhHQAwQMglAGat7modtbEeAIDmhlwCYO6YYR01zLAOAIDeIJcAACF1DutwOBjWAQA9QS4BgGrM6vUY1gEAtiCXAMBz6LCOxtXr/f1JWBgLTQIA84FcAgAa0I6TmukkIQHVOgDQjJBLAECz2oZ1mE2JMawDADqHXAIAdal7WAcdJwCgW8glAFC/2oZ1aMcJ0gkA6ApyCQBohRnWqbl6PU0nWL0eAJoOuQQAGkAg0NxxIpGg4wQAdAC5BAAajHachIaqH8ewDgA0EXIJADSGQEDi4zVvShwdjU2JAaCRkEsAoPGwKTEA6BZyCQA0FVavBwBdQS4BAB1gNiWuOaxDNyXGsA4AaAO5BAB0BsM6ANBEyCUAoGMY1gGARkMuAQDdY4Z11DDDOgAAGiGXAEBzqWNYh8PBsA4AaIBcAgDNqLZNiQmGdQBAE+QSAGh2dW9KHBbGQpMAwDAhlwCAntS2KXFCAqp1AKAacgkA6E9twzrMpsQY1gEwc8glAKBvdQ/roOMEwJwhlwAAO2ob1sGmxADmDLkEAFjDDOto3JQYwzoAZgi5BABYJhBo7jjBsA6AGUIuAQCDQDtOQkPVj2NYB8CsIJcAgKEQCEh8vOZNiaOjsSkxgFlALgEAw4JNiQHMGXIJABgirF4PYJ6QSwDAQDGbEtcc1qGbEmNYB8D0IJcAgEHDsA6AWUEuAQAjgGEdADOBXAIAxoEZ1lGDYR0AU4JcAgDGxM+PKJUY1gEwWcglAGB8MKwDYKqQSwDAKNFhnfh49eN0WCcsjI02AUCTIZcAgBELDdVcrZOQgGEdAKOEXAIAxo3ZlFhtWAebEgMYI+QSADAFdFgHmxIDGDvkEgAwHbTjpGY6wabEAMYCuQQATAozrKNxU2IM6wAYOBZyye3bt2fMmOHh4eHi4tK7d++lS5fm5+frvxkAYMIEAs0dJxjWATBw+s4lSUlJY8eOTUtL69Onz+TJk9u0afPtt9+GhoYimgCAztGOk9BQ9eMY1gEwWHrNJYWFhZs3b+bz+fv379+3b9+6det+/PHHRYsW5eTkfPzxxwqFQp+NAQBzIBCQ+HjNmxLTdILV6wEMil5zSUZGRlZW1qhRo/r06UOPWFhYTJkypVu3bleuXPnrr7/02RgAMB+1bUoskaDjBMCw6DWXFBQUtGzZ0tvbm8PhMAetrKxatmypz2YAgHmqe/X6hAT9twgA1Ok1l7zxxht//PHHuHHjVA9mZWXdvHnT0dHxxRdf1GdjAMAMMZsS1xzWCQvDpsQA7GO5TlgqlW7cuLGsrGzixIk8Ho/dxgCAmahtWAebEgPokERCEhKIvz9ZscJJ+3txm69B9ZLJZFFRUefPnw8ODh4zZkwdZ4rF4poHhw8f7uDg0NCLch49auXhQaKjZRMmKJwa8EwBVVpaWlVVhUnKBqKkpMTGxobLZfMX2XhFRpLAQDJ7trVYbK16PDqaJCSQbdvkIpFc+0dTKBQlJSV8Pl/XzYTGkMlkZWVlNjY2bDfE7OTlcY8efXr3rtPzA6MTCNmo5SOw1l9SXFw8Z86cI0eOjBs3bvny5ZaWlg19hEaEEu7q1a08PAghJDqa5+lpHRCATlswahwOR6lUst0KIyYQkKQkeVKSev6QSEhAgHVAgLX2fyGUSqXqzDkA8yGREImErF7NDQiw9vTkrVjh1JTZWux8zLpz505ERMSdO3dmzJixaNGiekOJSCSKjIxs6lUlEvLpp6oHrMVi6969q5eHrLnEAWhSXl7O5/Mx6GYgpFKpnZ0d+kuaaMQIolSSmBj1kR2x2Lp3b+voaBIVVf+DKBQKuVzeunXr5mkjNAyXy7WwsMDL0awkEpKaStLSdDxnnIU/Z+fPn583b55UKl2xYsW0adMsLCz0cVW6ymNtX0IoATB7UVFk+nQSFqa+UD0d1omP11DIA2BuaNdIWhpJTdVqSweBgPj5kSdPDmp/CX3nkitXrsybN6+iouKLL7547bXX9HfhxEQM2QBA3Wi1TkICCQt77jj9XOPnR1JSWGoZAKsa1DUiEBCBgEyfXh1KCCEbN+Zpfy295pL8/PxFixYRQnbv3t23b1/9XTgh4bn+Wfq3JzGx+iCG5wFARWgo8fP77y8Eg1brhIZqNawDYOyYLEL/US+aQqZPb2rPol5zyXfffZednW1lZfX++++rTRDr1KnT5s2b7e3tdX9Vui4Bg4YSOqckKgoVgQBQE/0LUXNYh65ej2EdMGE0hSQmNiCL+PoSPz/1NYEaTX+5RCaTXbp0iRBSUVFRc5e+5iorUAslhJCoqOeePHzwAYBa0E8xNefD0mEdLefDAhi+hs5gFQhIaGh1HNE5/eUSHo+3b98+vV2umlrkCw3FFFcAaBDacVJzWId2nGBYB4wUnXJJ3yQb1DXS3O+iJl1eSLtcGXRfUQCABmKGddQWqlcd1vHxYa15ANprxAxWZqRGP0w3l6gVBuswlHA41X1Y+JQEYE4EApKbW8ewDvett9hpGEDdGlfcq4euEY1MN5fQPyHM7Fo6w15XmE9JSCcAZoZ2nMTEqH/cjI4mu3Z1nDGDdOmC4WIwCE0s7mWL6eYSSqms7t4WC3ShAAAgAElEQVTQVXpQLSNCOgEwS7T7lVbrqA7r5OVxaVdKWFj19HoaUPTZBw5mjq3iXh0y9VxCCFEqdbmimkCg/mgoHAQwS3RT4prDOhT9O6E2w43WUiKmgM6xXtyrQ2aQSwjR5ROfm0tSU9U/JZF/R5jj49GBC2BWalu9via65zuDmVHYpQv7PedgjJiukdRUrT59N2txrw6ZRy7RLfopSSLRMMIcFkbS0lD1A2BW6DInCoVi6VL55cs8bT6wkn+nIjInY9wHtCSRGGJxrw4hlzQWHWGOilL/oJSQQFJTSW4uaw0DAJZERhY7O/OISvmDWvioA8Z9oA6GX9yrQ8glTaNxPUiJhAiFmG4CYLaYNwaKWcCKEG0/5hKM+5g94yru1SHkEl2IiiK+vs8tl4J1qgHgX3SMhv4xoP+nH3/v3WtYTFHreqHTBQjGfUyLkRb36hByiY7QSSdqi0FGR5PUVOyMDgBqmEjBxJSGjvsQTStaY9zHSJlAca8OIZfoDl3Jzd//uR8rhBIAqI/auA/5d24j0cW4D0GHiqEypeJeHUIu0TXV6SbNsUMyAJgBZjFIjPuYGFMt7tUh5JJmQKebmM8PEQA0s9rGfUgDO1TUxn2MumrDuJh8ca8OIZc0D/yWA0CzUR2jYZJKI8Z91BZQwbiPbplVca8OGXMukUhIWBgmcAAA1Bz3aVCJKall3AcTaRvKbIt7dciYcwntFKMb6WEmBwDAv5gP300c99E4kRYxpSYU9+pQdS4pLy+/f/++UCi0tLRkt0HaSkh4bqRUKMQSqwAAGmkc92niRFosnE+fkMREFPfqWHUukUql4eHhf/3114gRI0JCQnr16mVhYcFuy+pC96Zh0EVXAQBAO7VNpG1QTCFmuXA+inubW3Uusba27tWr15kzZw4ePHjw4EEejzdx4sQ333xTIBBw6ECJQVHbzjcqCi84AECj1Rz3ITpdON/Y35VR3KtP1bmkZcuWmzdvrqysFIvFiYmJ58+fT0hISEhIaN++/aRJk6ZMmeLo6GgoAYVujMcIDTWF+UJhYdiFGAAMRHMsnG+M4z4o7mUFR6lpxigNKN9+++2ZM2cqKioIIUKhMDg4eNy4cfb29npu4saNGwkhkZGRhPy7JR6DLrFq7GjgM5Lv5cGDB3w+n8fjsd0QIISQ+/fvd+zYkcs15gnspkKhUDx48MDZ2ZnthuiD6sL5WnYh1NSs4z4ymUwqlXbs2LGhd0Rxb3N47n28Ppr/nFlaWg4aNGjQoEGVlZUZGRnff/99SkrK2rVr161b5+rqOnPmzBEjRrDwzkQLgxkCgUn1MWAXYgAwEia2YTKKew1KPR+zHj9+nJ6e/scffxQWFhJClErl3bt3Fy9eHBMTM3fu3NDQUL3W76hNNAoNNYW3cNXRMexCDABGyEjHfVDca5g05BKlUpmfn3/gwIHDhw8XFBQQQjgcTs+ePadPnz506FBCyOnTpz/77LN169aVlZW9//77emqpWmEws4qQscMuxABgcpq+YXIz1fuguNfw/ZdLlEqlRCL59ttvDx8+/PjxY3qQTiuZOHGinZ0dc+bEiROdnZ3Dw8N//PFHPeUSiYQcOfLfTVMqDNa4C3FqKsZ0AMBksL5hcuOKe9E1worqXFJYWDh9+vTMzEx6s1OnTiEhIYGBgY6OjhrvJhQK7ezsnj17pp9WDti+ncjl/902vcJg1V2IKTqmEx+PAUwAMD3NvWFyv35EIiGnT6O41/hU5xKlUllWVta2bdvx48dPmzat3qrgysrK119/3dvbWy+NJCLVUGIahcE10V2I/f2fOxgWRtLSTGp6LwBADc2wYTKPkPqLMzCD1QBV5xI+n//111937NhRy2VeHR0dZ82a1ZwNq4WJ1eCo8fMjubkkLOy538KEBCKRmM64FQBAfXSyYXK9D46uEcNUnUtsbGycnJzYbUr9TDuUUHTqjNqYDqabAIB5a/qGyegaMRbGsRyT2NpaJJebSGGwNqKiSJcuzy3WghJiAIB/ablhMop7jZHm9V4NSvU6cU+fmt1bMs0iavO12H69sN6rQcF6r4bDrNZ7NXyZmfJWrYobsd4rNIcGrff6QjM3RnfMLZSQf8d0EPIBABrIyUnBdhOgkYwnl5gnGk2YuSZsd5YAAAA0K+QSYxAVRVJSEEoAAMDkIZcYCYzmAACAGUAuAQAAAEOBXAIAAACGArkEAAAADAVyCQAAABgK5BIAAAAwFMglJkp1DXsAAAAjgVxiohISiL8/240AAABoGOQSU8ThEPLvLsRN3BEcAABAj5BLTA4NJRTd+S8mhr3WAAAANAByicnJzSUCwXNHoqMxpgMAAEaBzVySkZHRv3//5ORkFttggjTuQowxHQAAMAas5ZLi4uL169cXFRWx1QBTprYLMUXHdBBNAADAgLGTS/Ly8t56660LFy6wcnVzQXchVuPvjxJiAAAwWPrOJVVVVceOHRs3btzdu3d79Oih56ubHT8/kpurPqaDEmIAADBU+s4lN2/eXLlypYWFxY4dO0aPHq3nq5sjjWM6mG4CAAAGSd+5xMLCYtq0aWfOnBk4cKCeL23WoqJIfPxzR1BCDAAAhkffuaRHjx4LFixo2bKlnq8LJDRUcwkxAACAweCy3QCtiMXimgeHDx/u4OCg/8YYsdatyeHD1rNnW//7fD4tLiZPnzboMUpLS6uqqhQKRTO0DxqspKTExsaGyzWOX2TTplAoSkpK+Hw+2w0BQgiRyWRlZWU2NjZsN8TsPHz48PTp02oHxWKxSCTS8hGMeF01hJLGEAjkSUnoJjEZHA5HqVSy3QoghBClUslRXW0ZwCw1/a3ZOD5miUSiyMhItlthQqKiiK8v8fNr3fC7lpeX8/l8Ho+n+1ZBw0mlUjs7O/SXGAKFQiGXy1u3bsRvFegel8u1sLDAy8GKJr5fG3F/CTSJWvEwAACAAUAuAQAAAEOBXAIAAACGArkEAAAADAVyCQAAABgKNnPJrFmzcnJyhgwZwmIbAAAAwHCgvwS0g12IAQCg+WHZA9ACXS1KIiEpKWw3BQAATBn6S6A+zBKWqalEKOReuMBqawAAwJQhl0CdEhKeuymR2E+aZL1uHUlNZaU5AABg2jCOA3UKDSV+fsTfn0gkzDHu//0f+b//I4RU707s51f9D19fLCMLAABNgVwC9REISEoKCQvT0EdCw4panwohBDvJAQBAo2AcB7RAowl2IQYAgGaGXAJai4oiSqVcJKoetdGtmBiSmoppKwAAZg7jONAwxYcO8fl8Ho9HJBIikZC0NEJIdZ5oSqpQ7YwRCIhAUD1VpUuX//4NAACmDrkEGks1PURFVR+kYaWJ6IOopRx6OfofwgoAgIlCLgGdormhoZglUupQM/Fgdi0AgMnB/BIwANHR6PwAAACC/hIwCFFR1SNBtEckNZXcu1f9Dx3OhBUK/xv9wVIrAAAGCbkEDAkdAwoNrb6pNm2FmWPbuFksdUxbYcJK48ahAABAR5BLwBhonGOrE/WGFd1eDgAA6oRcAlCDalhBLgEA0CPkEjAPqakkPp7cu6e5gwQAAAwDcgmYh5qzXFXn2NYWVhpRiszhPLedIZZaAQBoCOQSMFdqc2wptbDSOBq3M8TeywAAWkAuAVChMazoRB1hJTdX95cDADBOyCUA7Gn6mv0AAKYFuQRAp3JzdbDUSt1iYrDUCgCYKuQSAJ2qYzvDZth7uaOT0wuffUYmTmz8owEAGBLkEoDmV0dYaVpvCjcvj0yaRAQCEhqKpVYAwARg3z4AltCkopM5thIJiY4mQiHWZQEAY4dcAmBsaiswlkiIvz+JidFrYwAAdAq5BMDYpKQQpZLk5pLcXNmCBepfpR0nSCcAYJyQSwCMk0BABILiyEjFnTvqhTkY1gEAo4VcAmDkBAKSm6tapFMNwzoAYISQSwBMQlSU5nRCO04AAIwEcgmAqRAISFQUSUnRMKwDAGAkkEsATIufn3rHSSN2RQYAYAlyCYAposM6fn4IJQBgXJBLAEyUQEBSUthuBABAwyCXAAAAgKFALgEAAABDgVwCAAAAhgK5BAAAAAwFcgkAqMDq9QDAKuQSAPgXh1O9er2/P9tNAQAzhVwCADWkpmJTYgBgBXIJABBCiHofCTYlBgA2IJcAACGEkJQUbEoMAKxDLgGAf9W9KTHSCQA0P+QSAFBBNyWme+uowrAOAOgFcgkA1ED31sGwDgDoHQu5JD8/PyIiwsPDw8XFxcfHZ8+ePZWVlfpvBgDUA8M6AKB3+s4lN2/eDAoKOnXqVJ8+fYKCghQKRXR0dFRUFKIJgCGiwzopKUQgeO44HdYBANA1veaSysrKbdu2lZSUbNq0ad++fbGxsWfOnPHx8Tl06JBYLNZnSwCgAfz8NHScKJXsNAYATJpec0lOTo5YLBaJRH7/Tqnj8/mRkZFWVlbHjh1T4s8cgCHTOB8WAECn9JpLbt26VVRU1K9fPxsbG+agUCh0cnK6ceNGcXGxPhsDAA1G58OmpKCzBACaiV5zycOHDwkhHh4eqgetrKxat25dUlIik8n02RgAaCR0mQBAs9FrLrl3717Ng7a2tg4ODjKZrKSkRJ+NAQAAAEPD1efFNBbdcDicF16oJx5pnBU7fPhwBwcH3bQMtFZaWlpVVaVQKNhuCBBCSElJiY2NDZer119k0EihUJSUlPD5fLYbAoQQIpPJysrKVOcMgH48fPjw9OnTagfp1FItH0Gv/SWWlpY1DyqVyn/++acRj4ZQAsDhcDBh3EAolUoOh8N2KwBY1vS3Zr1+zOrSpUvNg2VlZQ8fPuTxeK1atartjiKRKDIysjmbBtoqLy/n8/k8Ho/thgAhhEilUjs7OyPoL0lNNflZKQqFQi6Xt27dmu2GACGEcLlcCwsLvBysaOL7tV77S2guuXv3rurBioqKp0+ftmrVCm91AKaJwyH+/sTfn+12AIAR0Gsu6dq1a7t27cRicXl5OXMwOztbIpG89NJLdnZ2+mwMAOhVairhcLB6PQDUTa+5xMnJydvbWywWJycn00FxqVS6efPmf/75Z+zYsRiaBTBBar/X2JQYAOqk11xiY2Pz7rvv8vn8+fPnv/HGGwsXLhw6dOj58+eDgoK0n6kLAMaktk2Jw8JYaAwAGDx979vn7e397bff+vr6/v7774cOHeJyudHR0TExMRpLdQDA6NW2KXFCAjYlBoCaWJjGLxQKd+3apf/rAgA76KbE06eTsLDnRnDopsQJCSQ+3uSrdQBAS/ruLwEAM0X31qltWAcdJwBACEEuAQC9qm1Yh86HRToBMHvIJQCgX3RYJzeXCATPHafDOkIhO60CAMOAXAIAbBAINHecSCT6bwsAGA7kEgBgD+04CQ397wi2+wEwb8glAMAqgYDEx5OUFPVhHQAwSwa/3RcAmAM/P5Kby3YjAIB96C8BAAAAQ4Fc8v/t3X9M1Pcdx/HPeQeK5ajVXn+InQesk7FupU6UrKagwSpRN+rMxJoqrGC6tjgxcTabHepcOtpujWFatUY0+xGrrmtcLGl0BVaSorRTGKVD2kHdHVIVrnCHP+DO2x9fdtLjhwfC9/M57vn4Y7EfDbznxw+8+PwEAACqIJcAAABVkEsAAIAqyCUAgta8ebIrADDCyCUAglZZmTAYuL0eGEvIJQCCk8HQ8wvt9vreLxUDCFrkEgBByBdKNNqjxNnZkqoBMGLIJQCCUL9v6xw4wKPEQLAjlwAIQr5HiVNTv9Lue5SYZR0gOJFLAAQtq1WUlvb/KPG8eUycAMGIXAIgyGkTJ33TiTZxQjoBggq5BEDw8y3r+D1K7FvWaWqSUheAoSKXABgrrNb+J06amkRMjIR6AAwduQTA2KJNnGRlya4DwHCQSwCMOVarKC4WpaU3l3W8Xpn1AAgYuQTAGJWa2rOsQygBgge5BMCYVlAguwIAQ0AuAQAAqiCXAAAAVZBLAACAKsglAABAFeQSAPgqg4Hb6wFZyCUA0IvBIITgUWJgyJqaxIEDIjv7Nj+MaUSKAYCxQAslGu1R4qwsUVwsryBAbdrLUwcPirKymzn+9oYM8yUA8H9939Y5cIBHiQF/vqmRmBgREyO2bBnByUVyCQD8n/a2TmrqVxp9jxKzrINQ1tQkysrE1q1i3jwREyOys8WBA/3/yd7zjkPHOg4A9GK1itJSsXWr/9yJtqyzZQsXyCK0aHGkvHzAFNKb1SpSU0VKyu18QnIJAPRRUCDWrBEHD/qnky1bxIEDIiuLdIJQERNz6z+jxZE1a/znGoeFdRwA6I/V2rOs43uUWMOyDiCEsFp7doU3NorGRlFcPCKhRJBLAGAwVmvPo8R+tGUd9sMi1FitYssWUVrak0WysvyD+20jlwDArWgTJ1lZ/u198wow9vimRrxe0dgoCgpGamqkX+wvAYAAWK2iuFisWSOys3vubBBCeL0ySwKGRNvB2jdeD073f+TMlwBAwFJT+1/WAdTU93Cv8pgvAYAh0k7rjPSyOjBiBjncazAoPs9HLgGAoRteKCkrG9WFeYQ0XxbRfhG0yCUAoJd584T4/2UPVqtISSGm4HZpKUR7oeaWtH97aiOXAIC+tLdFfKzWnu8W06f35BUgQDExN3dhD0I7UBMkOZhcAgBSNTV9ZeJdyyXaoYkg+UYCaRobB3yMxncl/FAP4MgmM5fU1tZmZ2e/9NJLaWlpEssAAD1oizi3pP346zvyo/YWRajFN/cWzIlWWi5xOByFhYWtra2yCgAAXZWW9mSOgweFEKKsLKg3J0IhQTs10i85ucRms+Xl5VVXV0v57AAgh7ZGo735p/2vtoLz+efEFIimpuHsLiotDd6pkX7pnUs8Hs/x48e3bdt2/fr1hISEuro6nQsAAIVoGxJFr5jS1NRz1HN4pz0NBs77BBOtow8evNndQ125G3NdrHcuqaure/HFFydMmLBnz56amhpyCQDc5NsfcDsGOu8j2EirjCEd7g0xeucSo9G4evXq3NzcqKiompoanT87AIScvlMvvkkaYoqefPeelZUFdLg3VOmdSxISEhISEnT+pAAQEgY6MuqnqekrT/xYraKxcXQKguhZpglw/xC31wTL/SWVlZV9GxcuXHjffffpX0yI6+jo8Hg8brdbdiEQQoj29vaIiAiTKTgG8tjmdrvb29vNZrPMIhwO3yLOhFOnJvT3lbMfTU1ffvnlqNalP5fL1dnZGRERIbGGSfn5/TxP04d72jT3tGnuRx91z50rUlNFkPdFS0vLu+++69dYWVmZnJwc4EcI4i9nhBLAYDB4ud9CDV6v1xDgdMWoslq1uZBrQlwTwmSzmWy2CadODfLz+pcOh54FhpDBQ4nVKlJT3Y8+6lq+XKd6dHH735pHJZe4XK61a9f2nuRITk7eu3dvZGTk8D5gcnLyT3/60xGqDrfl6tWrZrN52F2JkeV0Ou+66y7mS1TgdruvXbs2adIk2YV81aRJ4qGHxKJF/ud9xM0LVIZT87x5il/eZTKZjEaj5O7wev1X1rQ9yNpj1KmpQgiTEIr9ixkBt/n9mi9nABAyep/N8SWVYeg9+8LF+bek/Z2vWcNfTiBGJZdERkb++c9/Ho2PDAAYSbe/0dLv4nzBg8m9FBfzFuNQMV8CABiKW26j6fcCldLS0axp1Pgd7h3qdq4xcTG8zsglAIChKC4e2sX52qaW4DKkw70YUeQSAMBQDHRxfrBfF+abGgngcC9Gj8xc8swzzzzzzDMSCwAA3Ba/i/NH8MHkrVvF9OkjcCv/4Hy5KsBqY2K4g260MV8CABghAz2YPIxtFr6NtKN33ic7O6CpkT6HezGqyCUAgFHje4tn2EbvvE8A955xuFd/5BIAgGIGP/IzyIPJ2iTNsGkfJyWFqRGJyCUAAMVs2TLk8z5lZUM+xOu7j1Wb1OG2FTWQSwAAiikoGOTi/JFUXMwVI6ohlwAAVNXvxfkjct5HQyhRD7kEABA8rFb/8z6+g74YE8glAICg5ZtQuc0dr1DGONkFAAAA9CCXAAAAVZBLAACAKsglAABAFeQSAACgCnIJAABQBbkEAACoglwCAABUQS4BAACqIJcAAABVkEsAAIAqyCUAAEAV5BIAAKAKcgkAAFAFuQQAAKiCXAIAAFRBLgEAAKoglwAAAFWQSwAAgCrIJQAAQBXkEgAAoApyCQAAUAW5BAAAqIJcAgAAVEEuAQAAqiCXAAAAVZBLAACAKsglAABAFeQSAACgCnIJAABQBbkEAACoglwCAABUQS4BAACqIJcAAABVkEsAAIAqyCUAAEAV5BIAAKAKcgkAAFCFhFxy7ty5nJyc+Pj42NjYRx555IUXXrDb7fqXgeH54osvZJeAm+gOdbS0tMguATfRHcFL71xSUlLy/e9/v7y8fObMmT/60Y8mT558+PDhrKwsokmwKCwsfPfdd2VXgR4bNmzg6686Vq1aJbsE9Kiurt6wYYPsKjAcJj0/2aVLl4qKisxm8+7du7/73e8KITwez969e1999dWXX375t7/9rcmkaz0AAEApus6X1NbW1tfXL168eObMmVqL0WhcsWLFjBkzzp4929bWpmcxAABANbrmkubm5qioqMTERIPB4GsMDw+PiorSswwAAKAmXddNVq1a1Xf9tb6+vq6u7qGHHpo4caKexQAAANVIPifsdDp37NjR2dm5fPnyyMhIucUAAAC5ZO4zdblcBQUFFRUVmZmZS5cuHeRPVlZW6lYVBme32ysrK202m+xCIIQQNpvtL3/5i+wq0MNms+3YsUN2FRBCiMrKSrvdTncoorKyMjk5OcA/bPB6vaNazUAcDsf69evff//9jIyMbdu2DTJZUllZeerUKT1rAwAAI2jOnDkBRpNRySUul2vt2rW9JzmSk5P37t3rCx8NDQ15eXkNDQ1PP/30xo0bw8LCRrwGAAAQdCSs41RUVOTn5zudzs2bN69evdpoNOpfAwAAUJDe6zhnz57Nzc3t6up67bXX5s+fr+enBgAAitN1vsRut2/cuFEIsX//fu2+VwAAAB9dc8mRI0c+++yz8PDw9evX975aTQgxderUoqIii8WiZz0AAEAp+uUSl8t1+vRpIURXV1ffV/oMBmkngwAAgCJIAwAAQBWS73sFAADwIZcAAABVkEsAAIAqlM4l586dy8zMfPDBB+Pi4h5//PGSkhJ2w8jS0NAwe/bs2D52794tu7TQUltbm5SUdPLkSb92j8dz7NixuXPnxsbGxsfH5+TkNDY2SqkwdAzUF3/605/6jpSHH374X//6l5Q6x7Zz587l5OTEx8fHxsY+8sgjL7zwgt+5CoaGnm7ZHYGMDpnv9g3u5MmT+fn53d3d8+bNGz9+fHl5+fPPP79p06bc3Fy/M8bQgc1ma21tvfPOO81mc+92v//EqHI4HIWFha2trX7tbrd7+/btf/jDHywWy7Jly5qbm8vLy6urq994443ExEQppY55A/WFEKK2ttZgMFgslvDwcF+j2Ww2mdT9ehukSkpK8vPzPR5PUlLS1772taqqqsOHD3/00UcHDhyIjo4WDA193bI7RICjw6uktra2jIyMWbNmnTlzRmux2WxpaWmzZ8+ur6+XW1to2rdvX2xs7HvvvSe7kND13//+NyMjIyYmJiYm5sSJE71/q7Ky8tvf/vZTTz3V0dGhtbzzzjszZszIzc29cuWKjGLHuEH6wuVyPfXUU/Pnz7948aKs8kLExYsX09PTZ82a9eGHH2otbrd7165dsbGx69at6+7u9jI0dBRIdwQ4OhRdx6mpqamrq1u8ePHDDz+stURHR69bt+7y5cvvvfee3NpC0yeffDJp0qR7771XdiGhSJuIzsjI+PTTTxMSEvx+1+v1lpSUXL9+/emnn/ZNXy1YsGDhwoWnTp369NNPda93LBu8L4QQnZ2dn3/+eXR09MSJE/UvL6TU1tbW19cvXrx45syZWovRaFyxYsWMGTPOnj3b1tbG0NDTLbtDBDw6FM0lVVVV3d3dc+bM6b1kEx8fP2XKlA8//PD69esSawtBLpfLZrPde++99913n+xaQlFdXd2LL75oNBr37NmzZMkSv9/t6Oiorq6+5557HnzwQV+jyWSaPXu20+msqanRt9gxbvC+EEJcuHDB4XDExcXdcccd+pcXUpqbm6OiohITE3t/mwgPD4+KitJ+zdDQ0y27QwQ8OhTNJS0tLWazedq0ab0b77zzzoiIiNbW1mvXrskqLDR1dHTY7Xaz2VxUVJSUlBQbG5uUlFRYWNjR0SG7tJBgNBpXr1594sSJ733ve31/9/r1621tbQ888EDv8S+E0Ca3Lly4oFOVoWHwvhBCNDc3u1yuGzduaLv/tD37x48f93g8Opc65q1aterMmTMZGRm9G+vr6+vq6rSfyBkaerpld4iAR4eK+7A6OzsvXrzYt33ixIn333//hQsXmC/Rmd1ub21ttdvt//nPf5KTk8ePH19RUbFnz57y8vI33njDt6EJoyQhIaHfJQPN5cuXXS5X33aLxRIZGdnS0jKapYWcwftCCPHxxx8LIf74xz/GxcVlZGS0tbX94x//WLdu3cqVKwsKCsLCwvSqNBQ5nc4dO3Z0dnYuX748MjLy/PnzDA2J/LpDBDw6VMwl2n6Zfn9r3DhFJ3jGtvb29vHjx//gBz/45S9/GRERIYS4evXqtm3b3nzzzd///ve/+tWvOGggkcfj6Xe8jBs3jpNrOvN4PB0dHZGRkb/+9a+XLFmi/f03NjauXbv2yJEjjz76aHp6uuwaxyyXy1VQUFBRUZGZmbl06VLB0JCq3+4IcHSo+G3eYDAM9H3uxo0bOhcDIURaWtqZM2deeuklLZQIISIiIp599tno6OiKiop+J7egG6PR2O94uXHjhpf7fvRlNBq3bdtWU1OzdOlS33e+mJiYdevWud1u7eSO3ArHKofD8dxzz7399tsZGRk///nPtZ+8GRqyDGdY75EAAAWgSURBVNQdAY4OFXPJHXfccc899/Rtv3LlyoULFyZPnjx+/Hj9q4Kfu+6664EHHujo6Oj3Cgfo5u6779bmSP1cunTJ5XKxVVkFVqtVWzjo7OyUXcsY1NDQsHLlyoqKipycnMLCQt9wYGhIMVB3DKTv6FAxlwghrFar0+n84osveje2t7dfvXp1ypQpEyZMkFVYyHI6nd3d3X3bTSaT0WjUvx74aPuu7Hb7lStXerdrw+f++++XVFeI8ng87e3t/f44bjKZWD4YcRUVFU8++WRTU9PmzZs3bdrUewcPQ0N/g3SHCHh0KJpLEhMTw8LCKioqev8f+Pjjjy9fvjxr1izmS/Tkdruff/75xMTE8vLy3u12u72hoYHDw9JFRkZ+85vfbGlp+eSTT3yNbrf7gw8+MJvN3/nOdyTWFmrOnz//2GOPZWRk+O2pPHPmjNPp5PDwiDt79mx+fn5XV9euXbuys7P9fkZiaOhs8O4IfHQomktmzJgRFxd3/Pjxf/7zn1qL3W7fuXOnxWKZP3++3NpCjclkWrhwoRDi4MGDDodDa3Q4HNu3b29ra3viiScmT54stUCI+fPnGwyGffv2+TroxIkTJ0+enDNnzte//nW5tYWUqVOnzpo16/z582+//bbv6ONHH31UVFQ0ZcqUH/7wh3LLG2PsdvvGjRuFEPv37x/o+wJDQze37I7AR4eixygsFkteXl5+fv6qVasee+wx7X2czs7OTZs29b4hB/pYtGjRihUrDh06lJKSkpKSIoQoLy93uVwZGRkrV66UXR1EcnLysmXLDh06lJ6ePnfu3Obm5qqqqkmTJj377LO+rcrQgclk+tnPflZXV/fKK68cPXo0KSnp/PnzVVVVRqNx+/bt3/rWt2QXOKYcOXLks88+Cw8PX79+vd8C2dSpU4uKiiwWC0NDN4F0R4CjQ9FcIoRIT0+/++67X3755dLS0hs3bsTFxeXn5y9atIgFWv2FhYVt3bo1KSnp9ddff+edd4QQcXFxP/nJT5YsWcJ9DCrQOig+Pn7v3r1vvfVWeHh4SkrKL37xi5iYGNmlhZzo6Og333xz9+7df/3rXw8fPqz1RV5enu9JDYwIl8t1+vRpIURXV5ffi7VCCIPBoO0BYGjoI8DuCHB0GDguBQAAFKHo/hIAABCCyCUAAEAV5BIAAKAKcgkAAFAFuQQAAKiCXAIAAFRBLgEAAKoglwAAAFWQSwAAgCrIJQAAQBXkEgAAoApyCQAAUAW5BAAAqIJcAgAAVEEuAaA3p9OZmZkZGxu7efNmt9vta3/rrbfi4uIWLFhgt9sllgdAInIJAL2ZzeZNmzaZzeajR49+8MEHWqPNZtu5c2dYWNiGDRuio6PlVghAFnIJAAkSExNXr17d1dW1c+dOp9PZ3d29Y8eOxsbGZcuWpaWlya4OgDQm2QUACEUGg+HHP/5xRUVFVVXVsWPHoqKijh07FhcX99xzz4WFhcmuDoA0Bq/XK7sGACHq/fffz83NjYyMHDduXEdHx2uvvZaeni67KAAysY4DQJq5c+c++eSTbW1tly9fXr58+YIFC2RXBEAycgkAaQwGQ1JSUlhYmMFgmD59usnEyjIQ6sglAKS5dOlSUVGR2+02Go379u07d+6c7IoASEYuASCH1+t9/fXX//3vfz/xxBNZWVmXLl169dVXr169KrsuADKRSwDIcfr06aNHj1oslrVr1+bm5sbHx//9738vKSmRXRcAmcglACRwOBy/+c1vOjs7c3JyvvGNb1gslry8PJPJ9Lvf/a6xsVF2dQCkIZcA0JvX6z106FB1dXVSUlJmZqbWmJaW9vjjjzc3N+/atau7u1tuhQBkIZcA0Ft1dfX+/fsjIyPz8/PNZrPWGBYWlpeXZ7FY/va3v508eVJuhQBk4V41AACgCuZLAACAKv4H9DYYEujzABcAAAAASUVORK5CYII=\" alt=\"Vertical shift\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y_shifted, v] = v_shifting(x, y, k)\r\n  y_shifted = x;\r\n  v = x;\r\nend","test_suite":"%%\r\nx  = [0 1 2 5 10 15 20 25];\r\ny = [4 4.6 4.4 3.4 3.1 1.8 1.4 2];\r\nk = 'mean';\r\ny_correct = [1.38   1.98   1.78   0.78   0.48  -0.82  -1.22  -0.62];\r\nv_correct = 'down';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n\r\n%% \r\nx  = [0 1 2 5 10 15 20 25];\r\ny = [5 4.6 4.4 3.4 3.1 1.8 1.4 0.9];\r\nk = 'mean'; \r\ny_correct = [2.47  2.07  1.87  0.87  0.57 -0.73 -1.13 -1.63];\r\nv_correct = 'down';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n\r\n%%\r\nfiletext = fileread('v_shifting.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = -pi:pi/6:pi;\r\ny = (sin(x)).^2;\r\nk = - 1;\r\ny_correct = -(cos(x)).^2;\r\nv_correct = 'down';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n\r\n%%\r\nx = -5*pi/12:pi/12:5*pi/12;\r\ny = (tan(x)).^2;\r\nk = 1;\r\ny_correct = (sec(x)).^2;\r\nv_correct = 'up';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n\r\n\r\n%%\r\nx = -5:5;\r\ny = atan(x);\r\nk = 'mean';\r\ny_correct = atan(x);\r\nv_correct = '';\r\n[y_shifted, v] = v_shifting(x,y,k);\r\nassert(all(isapprox(y_shifted, y_correct), 'all'))\r\nassert(strcmp(v, v_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-29T14:41:30.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-20T13:44:19.000Z","updated_at":"2026-03-24T16:04:22.000Z","published_at":"2025-12-29T14:41:30.000Z","restored_at":null,"restored_by":null,"spam":null,"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\u003eGiven a real function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e input-output pairs, consider a translation in the up-down direction given by an amount \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eFor a real constant \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, you may assume that the translation is given. However, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'mean', you firstly must determine the real constant \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that the translated function has an average value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the given interval (see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eFind\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_shifted,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e which is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector that stands for the outputs of the translated function;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e which stands for either 'up' or 'down' if the function's graph is upward or downward shifted, respectively, and it stands for '' if the graph does not undergo a translation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eHint. Calculate the mean of a piecewise linear discrete function, represented as an array of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and an array of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e values. Be aware to the existence of calculus discrepancies whenever the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be continuous, but not piecewise linear.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(x, y, k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[y_shifted, v]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"367\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Vertical shift\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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YAxis does this Graphic object belong to?","description":"Your function gets a graphic object in an Axes that has 2 YAxis. Can you determine which YAxis does this object belong to?\r\nI provided my reference answer to prove the solvability of the problem, but Size 159 is definitely not optimal.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 25.5px; transform-origin: 408px 25.5px; vertical-align: baseline; \"\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: 385px 10.5px; text-align: left; transform-origin: 385px 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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour function gets a graphic object in an Axes that has 2 YAxis. Can you determine which YAxis does this object belong to?\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: 385px 10.5px; text-align: left; transform-origin: 385px 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 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eI provided my reference answer to prove the solvability of the problem, but Size 159 is definitely not optimal.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function YAxis=GetYAxis(GObject)\r\nYAxis=GObject.Parent.YAxis\r\nend","test_suite":"%%\r\nNumTrials=100;\r\nQA=gobjects(2,NumTrials);\r\nDirections=[\"left\",\"right\"];\r\nAx=gca;\r\nfor A=1:NumTrials\r\n    Random=randi([1,2],1);\r\n    yyaxis(Directions(Random));\r\n    QA(1,A)=scatter(A,A);\r\n    hold on;\r\n    QA(2,A)=Ax.YAxis(Random);\r\nend\r\nassert(~contains(fileread('GetYAxis.m'),'evalin'),'evalin is not allowed');\r\nfor A=1:NumTrials\r\n    assert(isequal(GetYAxis(QA(1,A)),QA(2,A)),sprintf('Incorrect YAxis for Scatter %u',A));\r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":362068,"edited_by":362068,"edited_at":"2025-08-01T10:41:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2025-08-01T10:37:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-08-01T04:35:44.000Z","updated_at":"2025-10-22T13:29:59.000Z","published_at":"2025-08-01T04:35:44.000Z","restored_at":null,"restored_by":null,"spam":null,"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\u003eYour function gets a graphic object in an Axes that has 2 YAxis. 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