{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":60566,"title":"Given a Polyshape_01 (ps) Return its Perimeter, Area, and Centroid.","description":"Return the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\r\nReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\r\nReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. ","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: 104.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 52.3333px; transform-origin: 407.5px 52.3333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.6667px; 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: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; 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=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.3333px; 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: 384.5px 21.6667px; text-align: left; transform-origin: 384.5px 21.6667px; 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=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.6667px; 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: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; 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=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"%%\r\nfunction [P, A, Cx, Cy] = PolyShape_01(ps)\r\n    % Return the perimeter (P) of a polyshape object, which is the sum\r\n    % of the lengths of its boundaries.\r\n    \r\n    % Return the total area (A) of a polyshape object, which is the sum\r\n    % of the areas of the solid regions that make up the polyshape.\r\n    \r\n    % Return the x-coordinate (Cx) and the y-coordinate (Cy) of the\r\n    % centroid of a polyshape. \r\n end","test_suite":"%% Test 1\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),1313))\r\n    assert(isequal(round(A,4),134508.0227))\r\n    assert(isequal(round(Cx,4),17))\r\n    assert(isequal(round(Cy,4),47))\r\n\r\n    \r\n%% Test 2\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),1313))\r\n    assert(isequal(round(A,4),134508.0227))\r\n    assert(isequal(round(Cx,4),254))\r\n    assert(isequal(round(Cy,4),-1676))\r\n\r\n    \r\n%% Test 3\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),177.255))\r\n    assert(isequal(round(A,4),2451.4087))\r\n    assert(isequal(round(Cx,4),34.29 ))\r\n    assert(isequal(round(Cy,4),-226.26))\r\n\r\n    \r\n%% Test 4\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),206.155))\r\n    assert(isequal(round(A,4),2385.7031))\r\n    assert(isequal(round(Cx,4),34.0501))\r\n    assert(isequal(round(Cy,4),-226.4324))\r\n\r\n    \r\n%% Test 5\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),235.055))\r\n    assert(isequal(round(A,4),2319.9976))\r\n    assert(isequal(round(Cx,4),34.448))\r\n    assert(isequal(round(Cy,4),-226.6146))\r\n\r\n    \r\n%% Test 6\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,polyshape([20 30.1 40.1 45.1 50 45.2 40.2 30.2 27.2],[-235 -239 -239 -237 -235 -239 -241 -240.5 -240]));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),300.0489))\r\n    assert(isequal(round(A,4),2274.2476))\r\n    assert(isequal(round(Cx,4),34.4235))\r\n    assert(isequal(round(Cy,4),-226.367))\r\n    \r\n    \r\n    ","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":20795,"edited_by":20795,"edited_at":"2024-06-28T13:41:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-26T18:00:30.000Z","updated_at":"2026-03-18T15:16:22.000Z","published_at":"2024-06-26T18:18:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\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\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\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\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \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":43162,"title":"Translate German decimals to English decimals","description":"The string 'x = [2,5; 5,5; 4,3];' should return 'y = [2.5; 5.5; 4.3];'","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\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: 196.5px 8px; transform-origin: 196.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe string 'x = [2,5; 5,5; 4,3];' should return 'y = [2.5; 5.5; 4.3];'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = translate(x)\r\n  y = 'x in German';\r\nend","test_suite":"%%\r\nx = 'x = [2,5; 5,5; 4,3];';\r\ny_correct = 'y = [2.5; 5.5; 4.3];';\r\nassert(isequal(translate(x),y_correct))\r\n\r\n%%\r\nx = 'x = [2,25; 5,35; 4,13];';\r\ny_correct = 'y = [2.25; 5.35; 4.13];';\r\nassert(isequal(translate(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":57323,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":51,"test_suite_updated_at":"2021-08-12T17:40:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-07T15:05:46.000Z","updated_at":"2026-03-17T07:30:46.000Z","published_at":"2016-10-07T15:05:46.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe string 'x = [2,5; 5,5; 4,3];' should return 'y = [2.5; 5.5; 4.3];'\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":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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\" 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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vertically even-degree polynomial's graph by its mean over an interval","description":"Let p be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval [a, b], with a\u003cb.\r\nThe interval [a, b] is defined such that the endpoints a and b stand for the least and the greatest x-values of the equation p(x) = y_peak, the lowest and the largest real solutions, respectively. Here, y_peak stands for the highest local maximum of the polynomial p (see non-scale figures below). \r\nGiven p, return \r\nthe endpoints a and b if they exist. Otherwise, return a = '' and b = '' (see Hint 1);\r\nthe shifting constant, k, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\r\nHint 1. An n-degree polynomial has exactly n roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\r\nHint 2. To calculate the mean of a continuous function, use the integral definition.\r\ninput: p\r\noutput: [a, b, k]\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: 662.112px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 331.05px; transform-origin: 408px 331.056px; vertical-align: baseline; \"\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=\"\"\u003eLet \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; \"\u003ep\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 be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \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[a, b], \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=\"\"\u003ewith \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; \"\u003ea\u0026lt;b\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: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; 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=\"\"\u003eThe interval \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[a, b] \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=\"\"\u003eis defined such that the endpoints \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; \"\u003ea\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 \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; \"\u003eb\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 stand for the least and the greatest \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-values of the equation \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; \"\u003ep(x) = y_peak\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, the lowest and the largest real solutions, respectively. Here, \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_peak\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 stands for the highest local maximum of the polynomial \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; \"\u003ep \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(see non-scale figures 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=\"\"\u003eGiven \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; \"\u003ep\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, return \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=\"\"\u003ethe endpoints \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; \"\u003ea\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 and \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; \"\u003eb\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 if they exist. Otherwise, return \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; \"\u003ea = ''\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 and \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; \"\u003eb = '' \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(see Hint 1);\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=\"\"\u003ethe shifting constant, \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; \"\u003ek\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 the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; 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=\"\"\u003eHint 1. An \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-degree polynomial has exactly \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 roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\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=\"\"\u003eHint 2. To calculate the mean of a continuous function, use the integral definition.\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; \"\u003ep\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[a, b, k]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.8px; 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 132.4px; text-align: left; transform-origin: 384px 132.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"370\" height=\"259\" style=\"vertical-align: baseline;width: 370px;height: 259px\" 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LBIiFefy8/OLi4v7/vvv9+zZs3jx4sGDB/P7n8Viee+992xD3d69e3fo0IF/eZcuXdjKwo5Y5xF+ert27VhTDf/pN27cYAkxHTp0GDZsGP+qvn37Pvjgg3d88/DwcHboNxgM7MSwd+9e1iTAN2CeP3+eHbuDgoL4KWH8/PxYe4zJZPrll19EbztkyJDWVfbcuXOsGH379uWjyfbt23/11VcFBQVnz55lTWKRkZHnz59nLVXHjx9PSUl54YUXDh061IpP7NSpU2RkJBGVlZWxdzCbzXv27LFYLBzHPfHEEyqV/eF4rdvyvXr1at++Pf9UrVZv2rSpoKAgJyfHx8fnm2++Wbhw4YIFC5p6OcdxYWFhLOYgoh49erBNbTKZhF1jzJAhQ/g177//fhY/sRNtMxuEefTRR/kRcN7e3uy4TETnz5+vqqpq9UZrOT6rrKysLDY2lnXU/vjjj19//XUz+WQiAwcO9PPzY4/ZyYOIHnzwwfvvv5//FPagvLy8tra2trb2P//5D1vy8MMP81tPp9Oxl+Tn59+4cYPjuL///e8FBQWnT5/u1atXVlbW3/72t1mzZjXTltb8r9iuI0eOsH7M4cOH84UnQSBYUFBw7tw5IurVqxdrxCosLGQB69mzZ3Nzc9kWGDx4MBFdvnyZrdypU6fevXuzt+I4ju0/FouFtYcJifZVW67ZDs0T7uQajYbttM3v5G3fFBzHTZgwgQ3C2LdvX3V1Nd/1yXHc008/fe+99xIRa9QpKCj45z//WVBQsGHDhtjY2K1bt7aupnKDUcqu4OXlxdKjZs+eXVdXt3379qSkpMrKSnYtImq79vX1bfuRt9Wa//SysjJ29aBWq/njL3uV8GlTunXrNmzYsO3bt+fn5xsMhjFjxrDWZr4Bk4hqampY/w7LArZ9E/azF3508we4Zly4cIE9CAwMZL92uywWy5EjR5YtW3by5Mm23ycrIiJiw4YNJpNp3759zz33XFFREYtWu3Xr1kzI1bot37VrV9GSGzdufPjhh5999llL0mtEn6VSqdjhkohsJy1sS6aI6LX8U/4c0LqN1nL33XffvHnz5s+fzxIaWEctu9jt06ePXq/nO4xaWAv+R3TPPffw5zbef//7X7YB//vf/7IlfPK70K+//lpWVnbfffdVV1enp6d/+OGHohzMprTiGML/rPr06SMssI+PT2BgIAmaD1Uq1RNPPLFr1666urqMjIyRI0dmZWWx3enpp59mJ++amhrWwnHx4kW7m+7ixYu1tbXCH53tvmrLBduhea3YyR2yKfr169e/f/9jx4799NNPp0+f7tSpE4txg4ODhe+Zl5e3bNmynJwc11zWuhLaVJxlyZIlLPtar9cLT2+sHXLWrFns6R3TOzyJSqWKjo729vZm6WDHjx9n12QDBgz47W9/28I3EW0xb29v/vTpJHv37n3ppZdYT1BISMiSJUt27tzJkjZa4cEHHxw6dCgRHTt27Ny5c4cPH2btOnwHvwOJDqwmk2nevHlr1qwxmUxqtTo6Ojo1NXX16tWO/VBncMFGi4qK2rZt2+9//3sfHx/h8ry8vOnTpwuTeV2mtra2pqbGbDa//fbbSUlJV69e9fHxiYqKeu+99zZs2HC38zA5EN8f99NPP+Xm5rJUs7tKGOJjNd4dgwAZbgeHaMmm4LvOTSbTwYMHDx48ePnyZSIKDQ3lryVyc3NfeOGF/fv319fX63S6OXPm7Nmz55lnnnFJJZwObSrOMmLECJb/mJmZGRcXxzKbGIvF4qbTn7Rv316tVldWVpaXl1+5coXvMampqeGnnmve0KFDBw4ceOzYsZMnT3p5edXV1XEcFxMTwzebe3l5cRxnsVhCQ0NTUlLaPqajGT179mQPLl26xE7etuvU1tZ+8cUX7FJ74cKFL7/8MuuGv+eeVkb5fn5+v//97w8cOFBZWbl9+3Y2gMLb2zsiIsL24pvX9i1PRMePH2dZeDqdjiVLElEzw3MqKyuLior4LGyz2cwnsjj29HDlyhXhU7695ze/+Q0bL9a6jXa3+vTps3bt2rq6usLCwuzs7F27drFhxjdv3vzmm29YppQDcRzHX/GnpKSwHi5b+fn5LJsqICAgLS2NZR44/I4tfMdEXl4e61ZgT2/evFleXk7WjZedOnUaN25cXl7epUuXtm3bxpKHfve73/EJQ15eXqxqPXr0+Pe//22bqNcKfFaZU7eDwzlqU0RERHz88cfFxcU//vgja4BRq9VPPfUU/01t2bKFJTXHxMS888477IfT6sOU3HhINWTo4YcfZgnbly5deuWVVwwGAwucr1279tFHH6WmprLV7HZwONytW7cc8j733XcfO7tXVlay7C3m1KlTLRzJGRAQwI74Fy5cYLfG+O1vfytMvOjduzdLfCsoKOCHc5eWlrIZUwYNGnT06NGWF7j5IRu9e/dmVyTCzxJN/VJbW8vPVcDSaYno2rVrfM9RK0RERLB9Y/PmzSx04BOKm9L2LU9E169fZzthly5dWJM+EdlmnAh98803/AXf5cuXWcOSWq3u169fCz+0JfjcTCIym81ZWVns8cCBA/lW8VZstDviq7Z9+3Z+apba2to+ffrMnj37q6++SkhIEK3pQP7+/qyhiIiOHj3Kt7xu2LCB7X4JCQlms/nGjRssQAwMDGRbgIjOnz/v2ObYRx55hEXqhw8f5tOWiejQoUPnz58nov79+wu/9NGjR6vVaovFkpaWVlNTw3HcU089xQdePXr0YMkupaWlfL9SdXX19OnT7U4N0hKu2Q6Owh95HLUpHnjgAba3HDlyhPVLDhw4sG/fvvzH8VcsvXr1YmFKRUUF++48ACIVZ9FoNC+++CI7seXl5cXGxrJZeoYNG/b3v/+dXaP36dOnqQsph+jSpQu79jUajaWlpSaTqSVDRpuhVqsnTZrEKrV69WrW0pibm7t06dKWTyvCjx1gwsLChP2yGo2GDf24evVqYmJicXFxXV3d5s2bWaJ7aGhoS1J3+QvE3Nzc2traiooKux23Op2ODbm8evXqkiVLiouL6+vrs7Ozd+7cSUSdOnUaP378vffey1J9iWjr1q03btwoLS1NTk5mra+twx90Kisr2Z7AJxQ3xSFbng2CIKJTp04dPXrUbDbv3r1748aNzbxk9+7dH3zwQXV1dWlp6bvvvstmUmnht9ByrH+dBVIbNmzYs2cP3d7+/Dqt2Gh2qdVqFgoT0cmTJ81mc0VFxahRo9g1w6FDh1jvGBFdvHiRnRJYZrED6mlj/PjxLG38008/TU9Pr6+vLygoYN+Ij4/PpEmTVCpVu3btWP9mSUkJm1Hj2LFjK1ascGxJBg0axOp46dKlJUuWXLx4sb6+/uDBg8uWLaurq/Px8Zk5c6awIY3vj2OCg4NZLi0TEBAQHR3NcVxNTc3f/va3M2fO1NfXf/fddyzE7Nu3b0vyfkRcsx3ayPbI85vf/MYhm4LvOueXCKcRUqlUfDfQd999V1xcbDKZVq5caTtS0k0hUnEWjuPi4+NnzJjRVOu0RqNZvnw5f9B0hq5du7KxNlevXn3ssccGDRrU9u72p556asqUKURUVlYWHx8fHBw8ceLEurq6lleEn8uLbBowyXoempycnNGjR/ft23fFihVsErDExES+n6gZ/fv3Zz/pb7/9tn///hMnTmTtoiIqler1119nB+jDhw+PHj06ODh4xowZZWVlPj4+er2+T58+995779SpU1nuws6dO4cMGTJixIhdu3bxyTG2Y5HuSHTQUavVLelZaPuWHzJkCDssVlZWxsfH9+nTZ86cOTU1NawkFy9etB1sOXDgwFWrVg0YMIDVmoha/i203ODBg7du3frwww/37dv3f//3f9kcOWz78+u0bqPZxTdkrlmzpk+fPq+88oq3t/dbb72l0WgsFsv7778/aNAgNicpy9udMmUKm33L4Vi6ro+PT1VV1ZIlS4KDg9lAM47jFixYwH4FfDxdV1f35ptv9unTJyYm5vLly2xTXL9+vS1BM8/b2/uvf/0r+8TDhw+HhYUFBwfHxcUVFRX5+PgsXbpUtAX8/PxiYmL4X+64ceP4kXrM5MmT2e6al5c3YcKE4ODgP/7xjzdv3uzYseM777wjWrklXLMd2sjukcdRm4J1nbPHwkHvTExMDLsCPHbs2OjRowcNGpSWlubj48NfLbd9NICEEKk4kbe395IlS7788ssnn3ySD3h9fHz69++/ZMmSHTt28Ludk3Tq1Gn58uUPP/wwGxp9//3382MNWs3b2/svf/lLYmIiO0F27Njxf/7nfzZv3tzylFiVSsVHJ8IGTB6bh2b58uXsbov8p2zZsoVv9W3eqFGjkpKSWAm9vLzatWvXVGIQm3FL+Fnt27d/8sknt23bxg9Heuyxx9atW9evXz9256Z+/fqtXr16/fr17IJm7969tnM33RE/12dTG8FW27e8Wq1evXr19OnT2Yjc9u3bT548OTMzk52ELl26xE8zz3v11Vffe+89lmXl7+8/efLkTZs2tfBbaLlXXnll1apV/M01hw8fvnnzZn7781qx0ex67rnnXnvtNXZY9/Hx8fb2rqurGzhw4I4dO+bNm9ezZ0+2c/r7+w8fPnzt2rVvvfWW8FrWsaKior755puYmBiWBeLl5fXwww9//vnns2bNYsVQqVRvvPHGkiVLWIH9/f0fe+yxnTt3vvLKK0TEbhHgkJNQp06dUlNT165d+8gjj7DQnP8tvPTSS7ZXXMOGDWP7XkBAAD+wnMeCP+G7sf3n66+/bt1wLZdth7awe+Rx1KYICAhg7c1EFBoaKsolHzhw4GeffTZ8+HCW6tezZ8/ExMStW7eywog69dwOJ+FXazKZXn31VXY2FS6/du3atGnTbC9Vo6OjRWuCTJhMptmzZ7PzXDO5gcATbjG9Xv/SSy+1/X0cteWvXr363HPPselbZPVtOmqjAYB7kWzsT319/caNG3Nycthk3kIlJSVXrlzx9/fnJ+1hRE9BPtjMnkSkVqtb0a6rQIWFhex+PXc1ttOWora8ozYaALgXaSKV6urqFStWrFu3zm6LzpUrV8rLy5cuXTpjxgzXlw2at3DhQjbHeceOHdeuXTt48ODa2tqtW7eyESjsTqFSl1G+2IiA//73vykpKWzMQmhoaAu3mGK3fFs2GgB4AAkilby8vNdff/3kyZP9+/cvKCiwXeHs2bNEhCORPI0bN27Hjh03b94sKysTtYf5+/u/8sor7j4Rk1OdOXNm2rRp/LjKjh07zpgxo4U5EIrd8m3ZaADgAVydUWsymfR6fW5u7vz585OSkmwPNxaLJS8vr2PHjg6frxMcIjIyctu2bU8++WTnzp2F93mJiYnZunWrfHIa5Klr165s6icfH59HHnnkgw8+aHlKnWK3fFs2GgB4AFdn1JpMplWrVk2aNKlPnz4///zztGnTHn/8cWGerMlkmjlzZmlp6dixY7dv337p0iV/f/8JEybMmzfP4SMOAAAAQOZc3aaiVquXLl0qnCZB5Nq1axcvXiwsLPz0008HDBgwefLkzp07p6enR0dHs/kxAQAAQDlkd9+fiooKLy+vkSNHrlq1ig32qa+vT0lJWb58eXJyclM3gjEYDOx28AAAAOCORowYYXfSXtnN/BYSEnLgwIGNGzfyY5K9vLymTZs2ZMiQ3Nzcpu5icOjQIdtJq5TAYDCg4oqCiisNKq40Sq54Uy0OsmtTsSsgIECn0x07doy/jZmt0NBQ/nZiSoOKKw0qrjSouNIotuJ2ya5NhYiaupEem8vc9eUBAAAAqcguUlm+fPmgQYNSU1OFC0tLS3NzczF0GQAAQGlkF6lERESo1eotW7YUFhayJWxC27y8vLFjx7I7pQEAAIBCyC5PZejQoXPnzk1OTo6KihozZky7du1ycnKuXr06fPjwhIQElUp2BQYAAADnkd2Jn+O4WbNm9e3b97333svKyqqvr+/WrduSJUuef/55u+OTAQAAwINJGamEhITYncyN47iwsLCwsDDXF8ntPPHEE127dpW6FBJAxZUGFVcaVBx4sstTgbui2B0aFVcaVFxpUHHgIVIBAAAA+UKkAgAAAPKFSAUAAADkC5EKAAAAyBciFQAAAJAvRCoAAAAgX4hUAAAAQL4QqQAAAIB8yW42ffdmNFJEBE2fTomJUhfFHRiNDf9rtZSdTUR0C+uWLAAAIABJREFU4ULDwnvvpbNnrVbjH1ssd/1BaWmk1RIRabUNDwAAwE0gUnEoo5GMRtLrSa8nrRYhyx245s7YHCdewoKV8PCGB2FhFB7uipIAAMDdQ6TiUElJjY/5kCU8nMLDKS7OY6/mWXxmNNL06VIXpWVYI01amtVCPnwJCyOtFrELAChCRARlZze0NycmyvPQh0jFcYzGhi4Mkexsys5ubGXp2dNtzuhCfBdMdjbt39+whP3juWO9eHz4wiKYVvQxAQC4KXYwj4uTuhz2IVJxHK2WsrJo/37S6+2vwFpZiCg+viGAZVfwMoxh09IaUkbY+dtuBOYofAYJ/z970LOneJ3WYZtXFFQBAIDoAluuDf+IVByK7+hZv56MRnH/ghA7cbJdRIaX7/HxrviUwkJX/DCysqyesi0vbBZyahwGACBbwus3Gfd6I1JxAtbbR0SpqQ2NE021stDdhymsPSYsjJ1rfauriYj8/Khnz8aBM0TUrh2dPNnw2GikwsK7+xSLxU4iajNaF3BIEr/zrVlCwvAlO1sc3AAAeCThkVCuDSqESMXpWOpGYiIZjbR+fUPOSltYt9P4tum97h47zfNDZkjWYfhdEIYvrRuuxXENzWlunawDAEojw0Z9G4hUXIU1tLCzIOtxuHBB1v0ObBAvH45gJpJmsPYnFoYmJblx3jQAgPwgUpECGwRErb18dw30gLQOnzfNQhYPHp0OAOASiFTcjV5PRiN16EDXrxNRTXW1yttbpVLRvfdSbW3DOvypkQ2fwZlSEpgDEADAERCpuBvrE15NeTkRBQYGSlQaICKiwsLmkpD4kGXlSpo4EYEjAMBdwR0KAdqMJSFlZVFhYcOsxHYlJJBORzpdc8PXAQDAGiIVAMcRhSx2GY0UH++iex4BALg/RCoATsBCFouFCgvtDwK62xluAACUCpEKgDNptZSa2lwTCwAANAuRCoDz8U0sbCiQO0y1BAAgE4hUAFwoMRH9PgAAd0XKSMVkMsXFxS1cuND2T8XFxfPmzevXr19QUNCoUaM2bNhQV1fn+hICAACAtCSLVOrr6zdu3JiTk2P7p9OnT0dHR+/evXvo0KHR0dFms1mv1ycmJiJYAQAAUBppZn6rrq5esWLFunXrLDYd9nV1dR9++GFFRcWqVauioqKIqLKy8tVXX83IyIiKiho9erQU5QUAAABpSNCmkpeXFxsbu27duv79+/v6im8GXFBQYDAYQkNDw29PnxUQEJCQkODj47Nt2zbbyAbA83EcJSVJXQgAAGm4OlIxmUx6vT43N3f+/PlJSUne3t6iFc6cOVNWVjZs2DA/Pz9+oU6n02g0p06dun79umvLCyAPej3pdIhXAECBJGhTGThw4M6dO+fOnevj42P715KSEiLq16+fcKGPj09gYGBFRYXJZHJRKQFkguMaHhiNpNerQ0J8DQZJCwQAbi4igjiu4Z87XP+4OlJRq9VLly7t06dPUytcuHDBdqG/v3/Xrl1NJlNFRYUzSwcgd6qiIt+oKLc4uACATBmNjY/DwiQrRovJ7l7Kdgf4cBx3zz13CKqKioqKiopEC7t27eqwksmS2Wy2WCxms1nqgriagiqen6+aNUt8l2a9ntLSzB9/3OTdED2Ogr5xa6i41AVxNWdXXFVUJIxUzGYzuXwjs86TlpNdpGKbuUJEFovl1q1bzb/w0KFDsbGxooUrVqzo0qWLwwonPxUVFRzH1dTUSF0QV1NQxe+9lzZs8D10qMP8+SphLG40qh5/vDwhofJPf5KucK6joG/cGioudUFczdkVVxkMD/BPtNrLffvS5ctO+qxmvPDCC6IlRUVFCQkJdleWXaTSs2dP24VVVVUlJSVqtbp9+/ZNvTAmJqapSnqwgIAAIgoMDJS6IK6muIr36EGTJlFSkuj+QYErVwZu3UqpqR7fuKK4b/w2VFzqgria0yt+9mzjY622R48ezvqgZh04cEC0ZOXKlU2tLLvZ9Fmkcu7cOeHCmzdvlpeXt2/fXq1WS1QuABlITDT9/HNNaKjVQqORIiKQuQIALSLsSnaTKxzZRSq9e/e+//77DQZDdXU1v/D8+fNGo3HAgAEdOnSQsGwAkjNrNDW7dtm5MzMbxixKZwEAaIa9TgwZkl2kotFohgwZYjAYMjMz2TxvlZWVq1evvnXr1sSJEzl+xCaAkrE7HT7+uNVCNK4AQPOMRqvrGa1WqoLcFdnlqfj5+c2ZM+fYsWMLFiz4/PPPu3XrlpOTc/Xq1alTp4aKGr0BlEyrpW+/tc1cocREacoDAPInHJ+s1aL3p/WGDBmSnp4eFhb2008/ZWRkqFQqvV5vd0JbAKVjjSv84Qa3mwCAZuzfL3UJWkPKNpWQkJATJ07Y/ZNOp1u7dq2LywPglrRaysqy07gCACDihl0/JM82FQC4a4mJaFABgLvgJl0/hEgFAABAEUTptO4wjz6DSAUAAEAB3DOdlhCpAAAAKIIwndZ9klQIkQoAAIAiuOHstAwiFQAAAAUQ9v64T5IKIVIBUKi0NKlLAACuVVgodQlaCZEKgCLFx1NEhNSFAADXslga/qH3BwBkjd0/KzubdDqrBmEAAPlBpAKgMMLbfLKbGuIOzAAgY4hUABQmK8vqKYIVAJA3RCoAChMebnVTQyYigpKSpCkPAECzEKkAKA+7qaEoWNHrKT5emvIAADQNkQqAUmVl0fTpVkvS0jAgCADkBpEKgIKlpoqnWMjORrACALKCSAVA2VhPkBBGLwOAnCBSAVC88HAMCAIA2UKkAgC3BwQJGY0UH49gBQAkh0gFAIiISKsVj15mLSsAAJJCpAIAt9mOXrZYJCsMAAARIVIBADE+WEGYAgAyoJK6AAAgP6IEWwAA6aBNBQAAwENlZxPHWd2X1A0hUgEAAPBQ+/c3POA4902QR6QCAADgoYQTDYhu9eU+EKkAAAB4IqPRKlIJC5OsJG2DSAUAAMATie6JgTYVAAAAkBE+SYWItFrJitFmchylfO3atWnTpv3yyy+i5dHR0cuXL5ekSAAAAG7GI5JUSJ6RSklJyZUrV/z9/Tt06CBcLnoKAAAATRL2/sTFSVaMNpNjpHLlypXy8vKlS5fOmDFD6rIAwJ1wHKWm0vTpUpcDAASMRnGeituSY57K2bNniSgoKEjqggDAnbAZpeLjKS1N4pIAgJAwTNFq3br3R3aRisViycvL69ixo0ajkbosANAs4cSX8fFWneIAIC1PSaclGUYqVVVVly5dCggIyMjIGDVqVFBQUEhIyOLFi4uLi6UuGgBYS021ehoRgWAFQC48JZ2WZBipXLt27eLFi4WFhZ9++umAAQMmT57cuXPn9PT06OjoEydOSF06ABCYPl2cnoJgBUAOPGXON0Z2GbUVFRVeXl4jR45ctWoVG+xTX1+fkpKyfPny5OTklJQUtVpt94VbtmwxGAyiha+//nqXLl2cXmjp3Lhxg4iqq6ulLoiroeJSF+S2d94JqKxUb9nSuCQiovyrr6pHjHDs58iu4q6CiktdEFdzSMX9jh8PFDy93LcvXb7ctnI50pUrV5KTk0ULi4uLY2Ji7K4vu0glJCTkwIEDwiVeXl7Tpk3LzMzMzc09f/784MGD7b5wxIgRoaGhooW9e/d2VkHlob6+nogCAgKkLoiroeJSF0QgLY0iI+mVV/gFgc8+q9q+3bENznKsuEug4lIXxNUcUnGV8Lpdq5XbZgwICJg0aZJo4ZdfftnU+rKLVOwKCAjQ6XTHjh0rLS1tah2NRtNUOObBzGYzETXVzuTBUHGpC2Lt5Zdp82Zha7N63jxKTXVgsCLTijsfKi51QVzNMRU/dKjxcXi4DDej7fm6qKioqZVll6dCRCaTqba21nY5x3FeXl6uLw8A3FlWllVcYjRSfLxkhQFQOE+Z842RXaSyfPnyQYMGpVqPKSgtLc3NzcXQZQBZsw1WdDrJCgOgZIWFZLFIXQiHkV2kEhERoVart2zZUlhYyJZUV1evWLEiLy9v7NixOhz4AOTMNliJiJCsMAAKZ7GQxeLuQ5RJhnkqQ4cOnTt3bnJyclRU1JgxY9q1a5eTk3P16tXhw4cnJCSoVLIrMABYSU21mgUuO5siIigrS8oiAYA7k12bCsdxs2bNWrduXUhISFZWVkZGhkqlWrJkydq1azt16iR16QDgTrRaSk21mhOTBSsAAK0ixyYKjuPCwsLC3HymGgDl0mopK8sqSQVtKgDQWrJrUwEAT8CCFcaDMvsAwPUQqQCAc4SHU1YWwhQAaCNEKgDgNO4/6AAAJIdIBQAAAOQLkQoAAADIFyIVAAAAkC9EKgAAACBfiFQAAABAvhCpAAAAgHwhUgEAAAD5QqQCAAAA8oVIBQBkQHiTIABohYgI4jipC+EUiFQAQGocR0Yj7rcM0HpGI2VnExFxHHFcw2NPgUgFAKQjvArMzkawAtBKRqPVU8+6kQUiFQCQTmoqabWNT7OzKSlJssIAuK/9+xsfC39THgGRCgBIR6ulrCyrJXq9hzVcA7iC8FczfbpUpXASRCoAICnbYCUiAsEKwF3gk1SYsDDJSuIciFQAQGrh4aTXWy2Jj5emJAAeAL0/AACOl5hI06Y1PsVQIICWW7++8bFWi0gFAMA5Nm60GrCAoUAALSTs+vGsUT8MIhUAkA3boUBpaVKVBcBtCCOVuDjJiuE0iFQAQDa0WkpNtVoSH4/sWoDmiGZS8USIVABATsLDxUOB4uOVcCwGaCVhKK/VovcHAMD5REOBjEYMBQJokiid1hMhUgEA+UlMFGXX+kZFSVYYADkTtjh6YoMKIVIBAJnKyhIedmt27ZKuKAByZTRaRSoeN+cbg0gFAOSKz661WCQtB4BcCcMUD01SIdlGKsXFxfPmzevXr19QUNCoUaM2bNhQV1cndaEAwLXYRPsIUwCaIryjp4cmqZA8I5XTp09HR0fv3r176NCh0dHRZrNZr9cnJiYiWAFQHA+9RgRwPM/9saikLoBYXV3dhx9+WFFRsWrVqqioKCKqrKx89dVXMzIyoqKiRo8eLXUBAQAA5EE4pN9zZx6SXZtKQUGBwWAIDQ0Nvx0eBgQEJCQk+Pj4bNu2zYJ2YAAAAFue26Yiu0jlzJkzZWVlw4YN8/Pz4xfqdDqNRnPq1Knr169LWDYAAABwMdlFKiUlJUTUr18/4UIfH5/AwMCKigqTySRRuQAAAEACsstTuXDhgu1Cf3//rl27njp1qqKiwvVFajmjkdavp549afp0qYviJtgIO62WsrMbR9tduED33Uc//dS4gnBlxmxWq1RWey+f9s4esP979rRa4rmp8QAAHkt2kYrdAT4cx91zzx2afwwGg0ajES184oknHFayFvjlF5Ve70tESUk0fTqNHGkODa1x6ieyRibROVs+iopU7H/24MKFxmmKRPMV3T1xlVv4bnzUwrp0e/YkjcbpX5MDyfwbdx5UXOqCuBoqLnVBnKikpOTEiROihUVFRbYncUZ228Lb29t2ocViuXXrVvMvLC4u/vLLL0ULe/Xq1aVLF4cV7k7Wrg1gD4xGdt8SlUbjGxNj0mjqXnjB7IxPrKqqIiIvLy9nvHnLGY104UJDXFJe7vPLL17FxSo+QJEVPk4SpMmriNQajVmjMY8YUTNqVJ3ZbJbtTI8y+cZdDxWXuiCuhoq75uOiozsYDL4ajTkmxjRjRu3999/hVOsQ/v7+tufr4uJit4lUerL2emtVVVUlJSVqtbp9+/ZNvTAmJiYhIcGZRbsDo5G2bBEvLCpSrVwZSESLFpFWS9OnU1ycI/sgWN5xYGCgw96xaUYjabWUlkZEtH9/w5I2N43IBYurDAbflSuJbje9sF68xETpimXDld+4rKDiUhfE1VBx13ycry/R7VPVkCGuS134/PPPRUtWsoOvPTKNVM6dOxcZGckvvHnzZnl5efv27dVqtXRFuwOtlvR6ys5uckw7a2hh94hlUQsRhYXJa2SZsGtG2Fnj7IH6wuQSUcaJbeyq1ZLJZNJozOXlgaK5pFkIRYKKUKt6mtj67MvS6xt6i7RaBweaAAASsm5dlu/BTXaRSu/eve+//36DwRAXF8cPVD5//rzRaJwwYUKHDh2kLV7zEhMpMbEhrzYtrbmz4+3uoQYs2ZOFLGFhTsz95IvEn8Jd0DoiSmjVahvvotXqmpaXm4nI9qqjmbCPtQmx1F0+CGthBGY0NjQmsahl3Djq2lVebS1Kx3EUHW2nVRMAmuYudw2SXaSi0WiGDBly4MCBzMzMJ598kuO4ysrK1atX37p1a+LEiRzHSV3AO9NqG0IWIkpKaq6VhdfUWZOdxYOC6Le/bXxKRGFhDXtYTY2v2WzmW5r4gVM9ezaGIMKPcB5hOKLVUs+eDUvks+s3VR6+0ejChZZ+WR99RHQ7apk+XXYNY4rDDgsZGZSUhPgRoOX4RmiZk12k4ufnN2fOnGPHji1YsODzzz/v1q1bTk7O1atXp06dGhoaKnXp7hofsrCGlpacCIWEXRhN8G112VqHj0XodvMPySkcaQXblBQW1e3ff+fvi28bQ8giGeHVi16P7wCg5URtKrIlu0iFiIYMGZKenv7222/n5OQYDIZu3brp9frnn3/e7rAgd8E3tLA9Y/16IrLqAJIVPv7o3586d25Yopz5SPjOOGGUSc1+X6KQBeksrpOVRRERjU/j46mwULrSALgTYaQi5wif84w76bCcYWnH/rQa6/e528yJNhLljrDEEbanusUptry8nKQYF9CSqIVhIYvD+yKkqrjkmqt4UpLV9xEebnXbNjeHb1zqgriayypuNJJO1/g0K0viYKWZ87gc21SUhh8HJCQatMISUGw7g8xmM1nPESSMMzBPq8OxtjGiO6dO80O9wsMpLg7TFjtTYqJVR112NhJWAO6WnNtUEKnIlGi8blPKy02kyMsOORD26DUTsrBzKDt1Il5xltRUq8tDJKyAp+JbQtrcH+IuSSokwzsUArgdFrIUFlJhYcOAIFtGI8XHE8dRUpKHzJUnL1qtuMdHmLwC4DH4wwfHWaWT3z3hwB9EKgBKIQpZ7NLrSacjna5hghZwmPBw8UZHsAKex3HxhTAnUubtj4hUAByPD1mab2LR6SgpydVl82SJiVZHXNbrBuBJhPFF27qThe8k2zudMYhUAJzljk0sLOsW8YojZWVZxYbsDhcAnkE0OrQN8YWoDxq9PwBKJ2xisYV4xcFSU62eRkQgMwg8hONmvxe9EyIVACC6Ha9YLPa7hBCvOIxtwkp8vDQlAXAsxyWpuFE6LSFSAXA91r4i6qZg+HgFXRZtgoQV8EiOS4J1o3RaQqQCIJXw8IYUFrs3TYyIQLzSNqIZNzERHLg7xyWpkHXvj8zTaQmRCoC02DwgzcQr6LhoPRadWCxtnyMLQHoOTVJxr9wtRCoA0mPxit3+oLQ0JK+0Vng4YhTwHO+91/i4bakljot5XASRCoBcsP4g23xbJK8AAB092vg4Lq4t7+Re6bSESAVAbpoaz8w6g5555l4JygQA0hJ12ChmdloGkQqAHDUVr+zf79ehQyA6gwCUZf36xsdt7rBxr3RaQqQCIFv8fHG2ByXWGeReOXEA0HqOawZxu3RaQqQCIHMs2dZuZxAybQEUQTQ+uW1JKm6XTkuIVADcAj+5rQgybQE8n0ODC7dLpyVEKgBuJDGRdu2q0WjMwoUs0xaNKwAei423Z0Pu2xxcCC9sEKkAgOOFhtb8/LOpqcYVt+t+BoC7YLFQVpYD3w+RCgA4i91MW2SuAEDzHDojv+sgUgFwS01l2ur1NGWKBOUBAPkTNbu6RTotIVIBcGuscUXUhJuejjTbu8FxpNNJXQgAV3Dc7HEuhUgFwL1ptXbmiEOabUtxHNHt7QXg6dxx4A8hUgHwDImJdjLt9Hqcf5sl3DrZ2WiGAo8nbFNxl64fQqQC4DHYDQ5FR5/sbPQENS011eppRAS2FHgwN02nJUQqAJ7EbpoteoKaxLaXUHy8REUBcDp3nJ2WQaQC4GnQE3QXwsOtIjujEcEKeCphkop7kWOkcu3atfHjxwfZWLhwodRFA3APzfQEYXY4scREqy2VloY+IPBIjrvLoavJMVIpKSm5cuWKv7+/xlqHDh2kLhqA22imJwgnYjHbhBUEdODR3ChJhYhUUhfAjitXrpSXly9dunTGjBlSlwXAvSUmUliYVb8PC1ZSU2n6dMlKJTssrBNupvh4x05bDiAtUTqtGw1RJnm2qZw9e5aIgoKCpC4IgCew2xMUH498DGvh4VbbKDsbScjgSdw3nZZkGKlYLJa8vLyOHTtqNBqpywLgIViTgejYlJaGHFtrom2k16OfDDyGm875xsguUqmqqrp06VJAQEBGRsaoUaOCgoJCQkIWL15cXFwsddEA3Jtt2gpmWxFLTLR6inYn8BTum05LMoxUrl27dvHixcLCwk8//XTAgAGTJ0/u3Llzenp6dHT0iRMnpC4dgHuzHcDMhuUiWGkQHm6VXWs00tix0pUGlCo7mziu4Z+DCHt/3CudlmSYUVtRUeHl5TVy5MhVq1axwT719fUpKSnLly9PTk5OSUlRq9V2X7hly5YtW7aIFq5YsaJLly5OL7R0KioqOI6rrKyUuiCuhoq3+h169aIDB2jMmB78EpZj+89/lsfEyHd7uu4bf+yxTqGhvgZDw9PvvjMtXHg9IcHpn9sE7OpSF8TVKioqOqWk8E9rHn20ND29je9ZVKQyGh/gn/76a+nFizVtfM+2uHLlyoIFC0QLi4qKEpr4oXEWi8X5pWqrysrK6dOn5+fnb9y4cfDgwbYrrFy50m4lu3bt6pICSqa8vNxisShw/DYq3sb3KSpS2TalvPGGWdQ9JB8u/sZVwcHCi1BzXZ1rPtcWdnWpC+JqptzcwIce4p+a33hD3Gt797Kz6fHHGxomtFrKzze38Q3brqSkRLSEtTXYDVYka1MxmUyzZ8828BcuRKGhoU01mQQEBOh0umPHjpWWljb1hmzOFaeUVcZUKhX/v6Kg4m18H35YrjBYefttVXGxeG4RmXD1N56a2pBvbLGQpI3P2NWlLoir+VqfwlWRkdTmjfD9942PtVpZbNW7Ol/LLk+FiEwmU21tre1yjuO8vLxcXx4AT5WVRefPWy3BgKAGbJZ9d2hyBg/je+hQ4xMHjSd263RakjBSUavVmzZtKhDYtGmTWq1evnz5oEGDUq0v60pLS3NzczF0GcDhgoLEjSjZ2QhWiMhmHBCAawjDCgfNz+jW6bQkwzaViIgItVq9ZcuWwsJCtqS6unrFihV5eXljx47V6XTSFg/A80yfLh4QxEYvA4CriaaSdURYYTS6/c0hpO+sEhk6dOjcuXOTk5OjoqLGjBnTrl27nJycq1evDh8+PCEhQQ69awCeJzxcPJu80Ug6HaWmumVbMYC7Wr++8bGDun7cenZaRnZtKhzHzZo1a926dSEhIVlZWRkZGSqVasmSJWvXru3UqZPUpQPwWGzSfSFMtQLgak7o+nHr2WkZOTZRcBwXFhYW5o6daQDuTKulwkKr6IRNtWI7Ez8AOJ4Tun7I/dNpSYZtKgAgIa3WTo+PaDAzADiFE7p+iJwR/LgaIhUAsGL3doYIVgCczgmtH6JcWjft/UGkAgB2IFgBcClR109cnKPelafVIlIBAM+CYAXAdYQ/Lcd1/XhAOi0hUgGAZmRliccfIFgBcApRkoqDeEA6LSFSAYDmpaYiWAFwPsGPqub11x3yls4ZSyQBRCoAcAd2g5W0NEnKIjMcRxyHwA3aSrALmTWamtBQZ3wI2lQAwJPZBivx8YoPVjiu4QFamaCNwsPJYmF3xDQ77vZ2zulQkgAiFQBoEbvBinJP0KLRn/Hx0hQDPIzFUrNrl6PeTJSk674QqQBASyFnpZFWS3p941N26wEAuXLfrh9CpAIAdyU11eoETUoOVhITrQ7/aWlK3RAgRx6TTkuIVADgbiUmomXlttRUq6cREeJeIQCJeMAtlHmIVADgrqEbqAG79YAQ+oBAHjxjzjcGkQoAtAaClQbh4VaXq9nZlJQkWWEAbvOMOd8YRCoA0EoIVhqI7jug1ytyK4CMeFKSCiFSAYC2SE3FvYGIiCgx0eop+oBAUqJ0KbSpAICiZWXRxIlWS5Q4z0p4uFXCitFIERHSlQaUzpOSVAiRCgC03datVhdtCp1bBAkrIBseM+cbg0gFABxAlKphNJJOJ1lhJJOVZXVaQMIKyEBcnNQlaDNEKgDgGLbBihI7QEQzrCixcQkkJkqnRZsKAEAjUYJtdjY98YRkhZFGeLjVJL6FhZKVBJTKk+Z8YxCpAIDDaLXiNoVvv1VeywqbZf/2rXEBXMzD0mkJkQoAOJZWK25HUGJqqWjiWgAhlsbFcU56e0+a841BpAIADmY7xbxeT2lp0hQGQHaMxoYeGo4jjnNs2rWHzfnGIFIBAMcTTS9CypxkBcAuYRujaHB7m3nYnG8MIhUAcArbYEWh09cCCIkaPRw9htjzklQIkQoAOI9oHAwRRUSIr/kAlEU0gFh06yxHv71nkDJSMZlMcXFxCxcutP1TcXHxvHnz+vXrFxQUNGrUqA0bNtTV1bm+hADQRomJdu5iCKBc69c3PnZy34wHzPnGSBap1NfXb9y4MScnx/ZPp0+fjo6O3r1799ChQ6Ojo81ms16vT0xMRLAC4I5Ek6wodEY4ACLKznZq14/nzfnGNEQq1dXVeXl5LgsFqqur33333eXLl1ts5huoq6v78MMPKyoqVq1atWnTpuXLl3/33XejRo3KyMgwGAyuKR4AOFZWllV0kp2NYAUUSdig4oRJ2TxvzjemIVKprKycNWvW0KFDFy1adOzYsfr6eud9ZF5eXmxs7Lp16/r37+/r6yv6a0FBgcFgCA0NDb+9jQMCAhISEnx8fLZt22Yb2QCAW9i3Tzx9LSaaB2UxGq0G6zs6Q4U8NJ2W+Ei83z6eAAAgAElEQVTF19d30KBBdXV1W7ZsiYmJeeihh/72t78VFhY6PDIwmUx6vT43N3f+/PlJSUne3t6iFc6cOVNWVjZs2DA/Pz9+oU6n02g0p06dun79umPLAwAuI5q+Ni0Nk6yAkog6ZpyQReJ5c74xDZFKu3btVq9e/fPPP69fv/73v//9zZs309LSHnvssUcfffQf//hHUVGRA0OWgQMH7ty5c+7cuT4+PrZ/LSkpIaJ+/foJF/r4+AQGBlZUVJhMJkcVAwBczHZGOKVPsoI+MEURdf04utHDI+d8Y6wyar29vUePHr127VoWskyYMKG8vPz9998fM2ZMZGTkxx9/XFpa2sbPU6vVS5cu7dOnT1MrXLhwwXahv79/165dTSZTRUVFGwsAABLCJCuN2OSkCq288ojiiMREZ3yCkCe1qajsLmUhy+jRo+vq6nJzc7/88susrKxly5a9++67vXr1mj179rhx49RqtTMKZDerl+O4e+65wzAlu/m2TzzxRNeuXR1TMlkqLy+XugjSQMXd15Ah9Kc/qf7xj8YDSHw8bd9u0mjMzbzKAyouFNihQ8OjiIiaXbtqQkObWtPDKt5yHlZx348+4rMyzRqNacgQaqKCra747t2+RA0fotGYy8vl2wVRUlKyZ88e0UKWomp3/Tuc/q9evXrkyJFjx46x1hSLxXLu3Lk///nPjz766Mcff+yMsUK2mSvsc2/dutWKd/PsMAXATb35plmYTWg00qxZ9q+aPJKv9WWVatYsqUoCLmI0qj77rPGpc5o7vv++8Uf0wgvNxf2Su9tTs52jg8ViKS4u3rx581dffXXp0iUi4jhu4MCBcXFxjz/+OBHt2bPnn//857vvvltVVfXHP/7R7vtmZmbOnj1buCQlJSUyMvKOBerZs6ftwqqqqpKSErVa3b59+6ZeGBoampCQcMf390iBgYFSF0EaqLj7Sk21ag43GHyffdb3jncg9oCKExGNG0d6PT99r6qoKPDZZ5u//bKHVPzueUjFy8upqIh/ppox4471utuKG40knJ5s3DjfwEDx0FpZuavzdWObisViKSwsTE5OfvTRR8eMGfP+++9funRJp9MtWbLkP//5z9atW6OjowMCAgICAiZNmrRixQp/f/9vv/3W4aVnkcq5c+eEC2/evFleXt6+fXsndTkBgOtlZYnHLQtv3ObhEhPFlUfCigdbtqzxsaNvSciIklQ8aYgy8W0qpaWlcXFxv/zyC3varVu32NjYp59+unv37nZfptPpOnToUFtb29T7RkZGFhQUtKJAvXv3vv/++w0GQ1xcHD9Q+fz580ajccKECR34zl0AcH+pqaTTNT7V6ykszKMyAZsjqnxEhDh2A4+xZw9xXMNj50xxL5pJxcMilYY2FYvFUlVV1bFjx5kzZx44cODgwYNz5sxpKkwhorq6uueff/7tt992eIE0Gs2QIUMMBkNmZiYbGl1ZWbl69epbt25NnDiR479sAHB/tuOWFTQUyO6gbfBUFgtZLM64JSHjqTOpMA1tKgEBAZ999tkDDzzg5eXVkpd179795ZdfdkaB/Pz85syZc+zYsQULFnz++efdunXLycm5evXq1KlTm8oKBgD3xcYtCycWiYigwkJPuyi0j91smr/fNLsl0h2zdcB9FRY66Y2deTch6TW0qfj5+Wk0mhaGKc42ZMiQ9PT0sLCwn376KSMjQ6VS6fV6uxPaAoAHYOdrIQXNiGabsKKgbB1wDM9OUqGm5lNxjZCQkBMnTtj9k06nW7t2rYvLAwBSSUykkycpI6PhqbIaFxSdrQMOIJqm3/MilTvMpwIA4Bpbtii1ccFuto7oMhmgaaJp+j0PIhUAkAvRLQz1esVk19p2gDknERA8kjCsdcI0/dJDpAIAcqHooUCihJU9ezAUCFrCaPT8BjhEKgAgI7aNCwo6X4vmU0lLU0yYBq0nDFO0Ws9McEKkAgDyImpcYNm1SiHsALNYPPO0Aw4lTOfyyCQVQqQCADJkO9H+//6vMm5hyHeAWSxSFwXcj6dGtohUAECOUlOtLhD/8Q+1wSDrO645THg4whRoIeFtPokoLEyykjgVIhUAkCOtVjwUKCrKF2kbAEJKSFIhRCoAIFtson0hBWXXArSA6MaEngqRCgDIV3i41Q3dlJVdC3Annn1jQh4iFQCQtdRUpc5dC+7IhaG0QpJUCJEKAMifKLtWQXPXgnthsQPHEce55tN4HpykQohUAED+tFr68MMa4RIFzV0LbkSYSCW866RzKCRJhRCpAIBbCA2t+eqrcuESZNeCvIg6Y4QJVs6hkCQVQqQCAO4iPJymTWt8iuxakBfRZLFOvlWgKC6Ki3Pqp0kMkQoAuI2NG5FdC7JkNFJaWuNT5zdxiJJU0PsDACAXoungkF0LsiBqUBHtpk6gnCQVQqQCAO6FvzEOLyLC8+96bx/HoQNMFlzeoEJKSlIhRCoA4HbCw0mvt1qiuOxana5hHCw6wOTAtRkqpKSZVBhEKgDgfhITxQkrb74pWWFczWi0akRCB5jkRA0qzu+MUc5MKgwiFQBwS1lZVgfot99WzPnabgeYUiovP8IGPZc0qJBNI47HQ6QCAO5KlLaooPO17c0bFVR5ORFlqMyZ45rAQdim4vENKoRIBQDcl23jgoISVpCtIweiBpXnnnPBZ4p6/zw+SYUQqQCAWwsPt7qmVNZ0cKJsHaORIiMlK4wCZWeLR+C4pEFl/frGx0pIUiFEKgDg7kQJK6LTh4cTVX7vXiVFalJz+RwqjHD3VkKSCiFSAQAPoNyEFbKpPMYtu0ZamtVO5pJEWrIZn+yqj5UYIhUAcHuKTljRaqmw0GqJXm+V5gnOILwBoVbrgvsRMqJJDtGm4nQmkykuLm7hwoWi5deuXRs/fnyQDds1AQAYUYKpshJW7EZqCmpWkojFQhYLkU2zljOJJtFHpOJc9fX1GzduzMnJsf1TSUnJlStX/P39NdY6dOjg+nICgLuwnQ5OQd0gGLcsFYvFlUmtwq/UVe040lNJ8qnV1dUrVqxYt26dhQWk1q5cuVJeXr506dIZM2a4vmwA4L5SU0mna3yq11NYmCIGRxDdblYStixFRJC9Yyy4KaVNos+ToE0lLy8vNjZ23bp1/fv39/X1tV3h7NmzRBQUFOTyogGAe1N0wgoRJSZaXWiLJlwBN6e0SfR5ro5UTCaTXq/Pzc2dP39+UlKSt7e3aAWLxZKXl9exY0eNRuPisgGAB1B0wgoRpaY2nMEKC5UyMkQxREkqyiFBm8rAgQN37tw5d+5cHx8f279WVVVdunQpICAgIyNj1KhRQUFBISEhixcvLi4udn1RAcAdKTphhYiysqiwUFmnMmUQzTOnHK6OVNRq9dKlS/v06dPUCteuXbt48WJhYeGnn346YMCAyZMnd+7cOT09PTo6+sSJE64sKgC4L9FoDMXdbxhhisdRbJIKSZVR24yKigovL6+RI0euWrWKDfapr69PSUlZvnx5cnJySkqKWq22+8KioqKioiLRwq5duzq9xJIym80Wi8VsNktdEFdDxaUuiKvdbcU1GvruO3r88cZDXHw85ee733bDNy51QVytqYobjY07s0ZjHjWK3HfblJSU3NX6sotUQkJCDhw4IFzi5eU1bdq0zMzM3Nzc8+fPDx482O4LDx06FBsbK1q4YsWKLl26OKusMlBRUcFxXE1NjdQFcTVUXOqCuForKt63LyUkBKxcGcieGo00erQ5Pb3UOQV0FnzjUhfE1Zqq+MGDvyHqyB5rtXT58mWXF82RXnjhBdGSoqKihIQEuys7K1LJzMycPXu2cElKSkpka++eFRAQoNPpjh07Vlra5FEmJiamqUp6sICAACIKDAyUuiCuhopLXRBXa13F//UvKiig7dsbnhoMvuvW9XCvNFN841IXxNWaqvi+fY2P33pL1aNHD1eWyuFETRJEtHLlyqZWluNs+iaTqba21nY5x3FeXl6uLw8AuK9Vq6yeKi5hBTyCKElFaZwVqURGRhZYa2GDyvLlywcNGpRqnQ5XWlqam5uLocsAcLeUPsMKeIT16xsfK2omFUZ2bSoRERFqtXrLli2Ft++5xSa0zcvLGzt2rE44/SQAQAsofYYVaDXR/QClo9jxyYzsIpWhQ4fOnTu3oKAgKipq9uzZCxcujIiI2Lx58/DhwxMSElQq2aUAA4D8KX2GFWid9euJ40jqK2RR109cnGQlkYrsIhWO42bNmrVu3bqQkJCsrKyMjAyVSrVkyZK1a9d26tRJ6tIBgLtS+gwrTXGvBGNXys5uaIszGonjJCyIYifR50nZRBESEmJ3MjeO48LCwsIUNa8NADgZS1gR9vvEx9PtTmalYifg//s/cRwHRqNVQpNWS9nZUsUIoiQVBZJdmwoAgJMgYcUK306QlqbsDWGDhSnCpozp0yVsyhAWRIENKoRIBQAUxTZhRaF9QKJqZ2cjWGm0fr3V9pk+XcI+MiVPos9DpAIAyiLq6IiIUGSwEh4uHr2NYIXh01MYrVbarjGFj09mEKkAgLJghpUGdoMVqce5SMw2PUXqDB6Fj09mEKkAgOLYJqwgWGlgNJJOp8hWJiKjkf7nf+STnkIYn3wbIhUAUCJRwkpamkLPzhQeLh4BxQI3BW6O9evp228bn4aHSz6EG+OTGUQqAKBQtgkrspmS1LW0WiostBr/yoZFKSpYSUqSVXoKg/HJDCIVAFAoJKw0YsGK6Jo9IkIpU/mmpdkJU2QQGmB8MoNIBQCUKzwcs+wLZGWJz4d6veeHb2lpdrJoZRAXYHwyD5EKACia6Oys9Fn2s7Jo+nSrJZ49L5xtNrXUWbQ8jE/mIVIBAKUT5U16fCPCHaSmilM0PDh2E3Xx6PWSZ9HyMD6Zh0gFAJQOs+yLTZ9ulcJjsUhXFOfjayfpXLQiGJ8shEgFAMDOLPuKTlih26OXtVoPD1MYi4XCw+Uw2McuhXf9ECIVAAAmK8uqK0DpCStkb3CUB5NZTUU5vgqHSAUAoIHoolrpCSuEk6Q00PUjgkgFAKCBbcLKM89IVhhQLNEMhAgXEakAADQSJaxs3ar4PiBwOdGoH4UnqRAiFQAAEdtZ9hGsgCsdOuTLP0aYQohUAABEbBNJlT4OCFzIYPA1GBojFSVPTctDpAIAIBYebjVTa3Y2smtbDGFd2wgbVDA+mUGkAgBgh+jeL2lp6ANqAY4jvZ50OkpLk7gkbnsTAOFuJrqxgWIhUgEAsM82YUU0KAOscFzDA3YzHZ1OmvYVNsdwfLw7hpa4K6FdiFQAAOxjd9UVQh/QXTAaG9pXXBavGI2UlEQ6XePZng+e3ATuSmgXIhUAgCaJbqybnS19t4Z8FRbaObWyeIXjKCnJWduONUSwVhzhfDhuCHcltAuRCgBAc0Sz7Ltnr4JLsEFTWVn2z7F6fWOXkKO2IGtEiYigiAg7YZBtm5i8YWrapqikLgAAgNylplplZ8bHU2GhdKWROTZVGYshbKMH1sRCRFptK+8rxM7n+/eLT+xCWq2sbozcQsLaoOtHCG0qAAB3YDvLvnsOK3Eh1p5RWNhkd0wzcUZTWA6KTkfx8U2OxdJqSa+nwkK3C1PIJkkFeIhUAADuTDTLfnY2+oBaQKulxMSGeKXtTQSJic0NvnLnGIVsIjf3rISzSBCp3LhxIzk5+ZFHHgkKCurXr9+UKVMOHz5ssViE6xQXF8+bN69fv35BQUGjRo3asGFDXV2d64sKAMDDLPutxOKVrKyGkMWxzQWso4e9uTuf3oUxGLp+RFwdqRQXF8fExKxZs6Zdu3aTJ08eOnToTz/99NJLL+3evZtf5/Tp09HR0bt37x46dGh0dLTZbNbr9YmJiQhWAEBCtmkVGLR8d/gmlsJCSk0l6wvUu3sf1iHHAhTRJH3uSTiUG10/Ii7NqLVYLJ988klBQcGiRYtmz57t5eVFREePHn355ZffeeedgQMH9ujRo66u7sMPP6yoqFi1alVUVBQRVVZWvvrqqxkZGVFRUaNHj3ZlgQEAhNj5kU+9YDOcudX4EnlgDSGtkJrqqQ0Owva511+vIfJtclXlcWmbyq+//rp///7g4OBJkyaxMIWIHn744SeffLK4uPjs2bNEVFBQYDAYQkNDw2/viwEBAQkJCT4+Ptu2bbO0OgYHAHAEUcIKZtl3KdH8Np5CuAtpNObQ0BrJiiJLro5U7rnnnuDg4A4dOgiXd+zYkX985syZsrKyYcOG+fn58Qt1Op1Gozl16tT169ddV1wAAHswyz44lrDrR6MxS1cQmXJppNK/f//vvvtu9erVKlVjr1NlZWVWVlZAQECXLl2IqKSkhIj69esnfKGPj09gYGBFRYXJZHJlgQEAbCFhBRxINOpnyhQ0qIhJPErZYrF8/vnnx48fHzNmDItOLly4YLuav79/165dTSZTRUWFy8sIACDGpjfjZWdLczM+8ACiUT+4f7ItKeeotVgsW7ZsWbFiRVBQ0OLFi729vYnI7gAfjuPuuecOQdWWLVsMBoNo4euvv86aajzVjRs3iKi6ulrqgrgaKi51QVxNhhXftImiozsYDA2Zj3o9DR5cPmKEg0sow4q7hnIq/pe/dOLPxV271ly5coU8veJXrlxJTk4WLWRDg+2uL1mkUl9f/8knn/z973//7W9/+8EHH3Tv3p0tZ/GKiMViuXXrVvNvOGLEiNDQUNHC3r17O6S0slVfX09EAQEBUhfE1VBxqQviavKseGIiRUU1Pp03T33mjIMPqvKsuAsopOJGI+XkNO4ziYnk7+9Pnl7xgICASZMmiRZ++eWXTa3vrEglMzNz9uzZwiUpKSmRkZHssclkSkpKysjIGDRo0Pvvv9+tWzd+tZ49e9q+W1VVVUlJiVqtbt++fVOfqNFomgrHPJjZbCYitVotdUFcDRWXuiCuJs+KjxtnNWi5qEj11FPqVtzKphnyrLgLKKTi//lP42OtlsaN8y0vV5MCKm57vi4qKmpqZQnyVEpLS2fOnLlly5Zx48atW7dOGKbQ7Ujl3LlzwoU3b94sLy9v3769x395AOBebGfZR8IKtBzu9dMSzmpTiYyMLCgosF1eWVn5pz/96ciRIzNnzly0aJFtX0/v3r3vv/9+g8EQFxfHD1Q+f/680WicMGGCaHgzAIDksrKI4xqf6vUUFuaRs36Ag/3/9u49Lubs/wP4GRW1TSJautiaScqSculiNypCiSIkt1WotUuIrNj9UtaPjdZlQykq1veLbcuuuxUVxShWyK5cKqtpu1A0k6Kp+f3x2R3TTNl1mc9nmnk9H/vYR/OZM595fzTNvOec9zkHe/38S7T2qTQ2Nm7YsCEnJycsLGzFihWtlqSYmpra2dnxeLz09HRqnTeBQBATE9Pc3Ozt7c2Sfj8AAFAOmLQMb0A6TVHRpXffDVoram/cuHHs2DFCyN69ew8cOCBz7/r1652dnXV0dD7//PNr164tXbr0wIEDxsbG2dnZlZWV/v7+8gWzAADKwNWVnD1LRo7862ZJCXFzk01fAGRID/0gTXkFWjOVvLw8aum2yspK+XsbGv5a7sbOzu6HH374v//7v+zsbB6PZ2xsHBERMW3atFb7YAAAlMGIEcTV9eW35MxMkpmJjx9ok8zQz+zZjEWi/GjNVObPnz9//vx/05LD4ezevVvR8QAAvENJSYTDeXmT6lZBsgKtkqmlxevkFRheoxYAQGXIr7KPeUDQFukOFaQpr4ZMBQDgnXF1bbEaemYmqmuhFRj6eS3IVAAA3qWkpBZfkZOTW3wmARAM/bwmZCoAAO9YUlKLm25uLXahA5BOXrEl4T9CpgIA8I7JF6xgDAgkqHlhEi4ujEXSXiBTAQB491xdyZIlL29ilX2QkH4lYOjn30CmAgCgEFu2tPgQiohAwQpgBf03gUwFAEBRZD6HULACMivoo0jl30CmAgCgKK6ustW1KFhRc9g8+Q0gUwEAUKCAgBZjQChYUWcY+nkzyFQAABRLZk19FKyoLdTSvhlkKgAACoeCFSgpIcnJL2+iQuXfQ6YCAKBwKFgBmdwUy6j8e8hUAADoEBBAJk58eRMFK+pG+tft6oqhn9eATAUAgCZpaShYUVOopX0byFQAAOiDghX1hC0J3wYyFQAA+qBgRT1Jd6ggTXldyFQAAGiFFVbUjcyWhLNnMxZJO4VMBQCAbvIrrGAMSIVt3/7yZwz9vAFkKgAADJApWOFwUF2rmkpKSGrqy5uopX0DyFQAABjg6koyMlocQcGKSpKppcWCb28AmQoAADNkFtUoKSFubowFA4ogsy4txn3eDDIVAADGyBSsyJReQnuXmdmiAgm1tG8GmQoAAJNkJi27uSFZUR3SQz9Yl/aNIVMBAGCSuTkKVlSTTA8ZamnfGDIVAACGubqSiIiXN1Gwohqkl8nB5OS3gUwFAIB5a9ZgOTiVIrPRD6b8vA0GMpXa2tqoqCh7e3sul2ttbT116tTc3FyxWCxpUF1dPXbsWK6csLAw+qMFAKCHTMEK9i9s12QmJ2Po523Qnanw+fxJkybt2rWrc+fOfn5+gwYN+vXXXz/55JNTp05J2pSXl1dUVOjq6pq21LVrV5qjBQCgjXzBCqpr2ylMTn63NOl8MrFYvGfPnqKiouXLlwcHB2toaBBCrl69On/+/PXr1/fv379Xr16EkIqKiidPnqxatWru3Ll0hgcAwCyqYEW6ZiUkhH3zppCxgOCNYHLyu0Vrn8qjR4+ysrIsLS0nT55MpSmEkMGDB48bN47P5xcWFlJHqB+4XC6dsQEAKAOZgpXSUs2JE7swFg28EUxOfrfozlQ6dOhgaWkpM47TrVs3yc9isfjOnTvdunUzNTWlMzYAACUhvxwcqmvbEUxOfudoHf3p27fvmTNnZA4KBIKMjAw9Pb0ePXoQQurq6srKyvT09NLS0o4ePVpWVqarq+vl5RUSEmJiYkJntAAATElKIhzOy5sREcTFBV/N24etW1/+jMnJ7wTDs5TFYvGBAwfy8/OHDx9ubW1NCKmurn748GFxcfH+/fv79evn5+f3/vvv//DDD76+vtevX2c2WgAAerRaXStd+gDKqaSE/Pzzy5voUHknaO1TkSEWi1NTUzdv3szlcsPDw7W0tAghT58+1dDQ+Pjjj7/77jtqkKipqSk+Pj46OjoqKio+Pp7NZrd6Nh6PJz9gNGbMGEVfBbOEQiEhRFOTyd8jI3DhTAdCNzW88CFDyIoVmlFR2pIjgYHk6FF1qa5tp7/xwMCXn1CmpqLJkxuEr/kba6cX/lrKy8vlux5KS0vbqvpg7N+iqalpz549mzZt+uCDD3bu3CkZ2bGxsTl//rx0Sw0NjZkzZ6anpxcUFNy/f9/W1rbVE/L5/B9//FHmoIWFBTWopKrq6uoIIZLyZPWBC2c6ELqp54UvXkyuXev2yy8dqZuZmWTUKM20tBpmo6JHe/yNl5SQzMyXmcrHH4sEAsHrnqQ9Xvjr0tXVlf+85vP5dGcq6enpwcHB0kfi4+Pd3d2pn4VCYWRkZFpa2oABA3bs2GFsbPzqs+np6XE4nGvXrlVVVbXVZtKkSYsXL377yNsXHR0dQkiXLmo3NQAXznQgdFPbCz906ImnZzOP91fPCo+nHR9vpA5jCu3xN75q1cufzc3JwYPahBi97kna44W/gQMHDsgc2bZtW1uNGahTqaqqmjdvXmpqqoeHR2JionyaIhQKnz9/Lv9AFoul2mkmAIC82NgG6ZtYu1Y5YbU3xVFUpuLu7l7UEtWhIhAIli1blpeXN2/evK1bt8ovOxsdHT1gwICklstKV1VVFRQUYOoyAKghrF3bLsjsR6gO/V60obVPpbGxccOGDTk5OWFhYStWrKBKaGW4ubmx2ezU1NTi4mLqSH19/ebNm+/cuTN69GiO9Lw9AAD1ILPZMiEkMJCZSKBV8h0q5uZMxaKCaK2ovXHjxrFjxwghe/fulR+jWr9+vbOz86BBgxYuXBgVFeXp6Tl8+PDOnTtnZ2dXVlY6ODgsXrxYtcuhAQDasmZNiyXFSkrIiBHk3DkmQwIJdKgoFK0f/Hl5edT8q8rKSvl7GxoaCCEsFisoKMjKymr79u0ZGRlNTU3GxsYrV66cNm1aW/OTAQDUQUZGi3Ef6qbMwBDQDx0qikZrpjJ//vz58+f/YzMWi+Xi4uLi4kJDSAAA7YjM2rWZmSQ5mQQEMBYPkJa7/JibYz/Cd4/hNWoBAODfk6+uDQxEdS2TSkpalBBhP0JFQKYCANCeuLpiKpASQYcKDZCpAAC0M5gKpCRkOlTGj0eHikIgUwEAaH/WrGnxoVhSQtzcGAtGbclM+fH1ZS4UlYZMBQCgXcrIaJGsZGYSb2/GglFD8lN+0KGiIMhUAADaK5lk5ehRDAPRR/qfGmuoKBQyFQCAdqzl1iMkObnFF31QEOlV+AghAQFYQ0WBkKkAALRjmLdMv5ISLEpLK2QqAADtG+Yt00ymQwVpiqIhUwEAaPfk5y0jWVEQ+Q4VrBGsaMhUAABUwZo1sh+ZqK5VhMxMUlLy8qZMnRAoAjIVAAAVkZQku8iK9CZB8PZKSlrkf5iZTA9kKgAAqkNm3jJWhHu3UEjLCFr3UlYqPB7v8uXLTEfxthoaGggh2traTAdCN8Yv3NHR0cnJialnB3iFjIwWRSqZmcTNTbbkFt4AtXO1RHQ0OlRoor59KpcvX+bxeExH8ba0tbXVME0hTF+4aqS5oMJkiieoZAXehsy4j7k5GTyYuWjUjPr2qRBCnJycFi9ezHQUAADvmLk5KS5uUaSCnpW3tHdvi0LaNWuw1Bt91LdPBQBAhcmvCJeZidlAb0hmz2RXV8xMphUyFQAA1SS/IlxyMpKV1yY/7oOZyTRDpgIAoLKQrLw9bPHDOGQqKisuLo4rZ+DAgeHh4Xw+n+nolIJQKJw+fbqLi0tlZSXTsQAoSqvJivRsW3gF+Q4VzEymn1pX1BfvBXIAACAASURBVKqDYcOGmZiYSG7eunUrJSXl6tWrycnJ0sdpU1lZmZSUNH78+A8//JD+ZwdQT1SyIj39JyKCmJmh2OKfzZ378meM+zAFmYqKmzVrlru7u+SmWCyOi4vbtGlTSkrKkiVL6I8nLS3tf//739ixY+l/agB15upKkpJadA9QPyNZeYXISHLu3MubWJGWKRj9US8sFsvd3b179+6//vprXV0d0+EAAH0CAmS7BAIDWyxlBtJk5vugQ4VByFTUjr6+vo6OjkgkEovFhBA+nx8eHu7g4MDlci0sLNzc3Pbt29fY2Ej+LuNYtmxZYmKitbW1jY3NkSNHqONRUVH29vZcLtfGxmbt2rW1tbXUydPT07lc7tGjR7du3Uo1cHZ2PnLkSFNTEyEkLCxs48aNAoHAx8dn+vTpQqFQPjzq5AMGDOByuR4eHr/88ou/vz/VuNV4mpqajh8/7uXlZW1tTcUTFBRUXFwsHc+RI0fWrl1rbW1tYWExceLEvLw8mSctLCz09/e3tLS0trYOCQlBHQ+oqlaTFdSsyJPZhQBpCrMw+qN27t27V1VV5eDgoKurW1ZWNnfu3EePHk2ZMqV///4PHjw4dOhQZGRkp06dpk6dSrVPT0+/cePG6tWrKyoqbGxsBALBggULcnJynJ2dJ06ceP369ZSUlHv37u3YsUNPT496yNdff62jo7Nw4UJCSGJi4vLly7W0tDw9PWfMmNHc3Hzq1KlFixbZ2dnJLzIrFAoXLFhw8eJFb2/vYcOGXbhwISQkRCwWDxkyRNJGJp7ExMRNmzY5ODhQYaenp58+ffrPP//8/vvvu3btSj1k3bp1Ojo6K1euJITEx8fPmjVr+/btkkGx0tLSoKAgLy+vGTNm5OTkpKamlpWVJScnSy4HQJVQwz3Sw0AREaSkBJ/ELURGtljnLSAA4z5MQqbSQvtdcHr27H8eb25qaiooKFi7dm1zc7O3tzeLxbpy5UpFRcXWrVtdXFyoNiNHjpw5c2ZeXp4kU2loaPjqq68kDfbt25ednb18+fL58+ezWKwJEyY4ODiEhobu2bNHUvjC5XITEhKoT3onJ6eZM2eePXvW09Nz4MCBly9fPnv27Mcff2xjYyMfYUZGxqVLl5YvXx4UFMRisXx8fGxtbSNbfuOTjqempiYrK2vYsGHbt2/X0dEhhPj4+ERGRh4+fLi0tFSSqejr60sqiEeOHDl79uzY2FhHR0cWi0U1WL9+va+vLyFk3Lhx2trahw8fLikpaTVCABUgn6wkJ5OSEqxg+5fk5BaDYq6umO/DMGQqLUhPmm9f2sr3g4ODZY5oaGiEhoYOHTqUEOLt7e3t7S19b9euXd977z3pIz179uzbty/1c11dXXp6upGRkZeXl+RjftiwYYMGDcrKygr8+53P2dlZ0iFhaGhoaGhYWVlZV1enq6v7iksQiUSnT582MTEZP348dXIWi+Xp6fm///2vrXi6du26f/9+6XtZLFbPnj1lzjxr1izJRCdTU1NPT88DBw48fPjwgw8+IIQYGxtL9hpksViOjo779u2jOmxeES1AuyafrGC5fQrWeVNCyFRUnPQsZU1NzQEDBgwdOlRmfrJQKLx3715JSUleXt7FixdLS0vt7e0l9xoZGUlyl2fPnvH5fF1d3StXrty8eVPSprm5+dGjR5ISXU3Nl6+rjh07dunSRVIW8woNDQ3V1dVGRkbSwy46OjoGBgbSzaTjoTQ1NZWXl//+++9FRUXZ2dnXrl3r0KFFAZaxsbHMGWpqasrKyqhMpUOHDtIBa2lpvTpOANVArWAm3ZGMZEWmPIUQkpSEdd6Yx0CmwufzY2Jijh8/XldX161bt8mTJ3/22WedO3eWafPNN9+cOXPmxYsXxsbGwcHB06ZNw0fIG5CZpSyjpqZm9erVJ06cEIvFGhoaH3zwwcCBA6urq6XbSH/qi8VikUhUXFwcFhYmcyo9Pb3Hjx+/2+BbJRPP2bNnw8PDqZj19fVtbGxsbW2ls6hWsVgsDQ0NxQYKoPTk11lR82RFZhvCiAiUpygFujOV3377LTAw8NGjR/379+/Xr9+tW7fi4+PT09OlFyKj2lRXV9vb2xsbG2dnZ0dERNy+fTsyMlLRyUr77eV7g6xfLBbHxMScOXNm7dq1Pj4+bDabEFJZWXn16tW2HqKrq2tmZmZkZLR7926qvYyKiorXjuNv2traBgYGt27dEggEkpO/ePHiyZMnXbp0afUhd+/e/fLLL3v37r1hw4YPPviASj7i4uJkMhWZqO7du9elS5cePXq8cagAKqPVZIXDIUlJavchHRkpOy0Z5SlKgtZMRSQS7dq168mTJ1u2bKFqEcRicUJCQlRUlGQhssbGxtjY2KdPn3733Xeenp6EEGqySVpamqen57BhwxQaoVotglRXV3f79m1DQ0M3NzcqMxCLxTwer7y8/MmTJ8+fP5d/iK6u7qBBg+Li4i5cuED9dgghfD4/ICCgW7dusbGx//ikWlpaYrG4ublZ/i5NTc0xY8b88ssvR48epSpqCSE5OTn3798fPHhwq2f7448/qqqqZs2axfl7e/uamprMzMyGhoanT59Kmh09etTb25saVCotLT1//ryNjQ2Hw6HmTgOoOVdXUlxM/v4bIuTvQZCMDDVKVuTTFLXtWFJCtGYqNTU15eXldnZ2Li4ukpJJDw+PvXv35ubmCoVCNptdVFTE4/GcnJxc//4T0dPTW7x4cWBg4JEjR5ydnSWFnPCW2Gy2g4MDj8dbunTpxIkTCSHHjx+/fPmyWCx+9uwZtaSKvLlz5/7666+LFi3y9vZ2dXV9+PDhoUOHKioqli5dKplr8wpmZmZCofD777+vrq52cnKiJuxIuLm5DR06dNOmTYWFhdQs5fT0dPnJzBJWVlYmJiYJCQm1tbW2trYFBQWHDx+uqalpbGxsaGiQNMvNzZ06ders2bOFQmFsbCyLxVqyZImOjk6rC7oAqCFzcyIWEw6nxdiHmxtJSlKL72/Jya0s8obyFOVBa6ZiaGh46NAhmYMVFRU1NTUDBw6kPpB+//33x48fDxkyRPozjMPhmJqa3rp1q6amRqa+Et7Gp59+Sgj573//u3LlSl1dXRcXlxMnTsTFxfF4vJqamlYzDz09ve3bt8fGxv7888+HDx/u2LGjra3tpk2bpItwX8HR0XHChAk///zzpUuXDhw4QNW0SrDZ7JiYmK1bt6akpPz0009WVlbffvvt7t272zpbr169YmNjIyMjk5KSmpubP/jgg9DQUC6XO2/evIKCAkmBzoIFC+rq6tasWUMIcXZ2/uKLL/r06fPv/5UA1ERGBgkMbDEFMjCQPHig4oMgMpN9CFZPUUJi5rx48SIzM3PEiBH9+/e/cOECdTA2NpbD4Zw5c0a6pUAgmDZt2kcfffTgwYNWT7V169atW7e+1rO/wUOAfhUVFcOHD1+2bNmbPfzMmTMcDic2NvbdRsXgi6empqampoaRp2YWLpw2rq5iQlr85+pK5/P/hZ4LLy4Wm5u3uNiICEU/5z9Q25f6K95XGVtNPy4uzsrKiqqc3bNnj7OzM3X8wYMH8o11dXV79uwpFAqliw9A9SQkJHh4eNy9e1dy5PLly+Xl5b1792YwKgC1kpHRYiiE/F1j236Xm2oLVY4jsxatancgtVOMraciEon8/Pz++OOPvLy8uXPnLl++fNasWSwWq9XyCBaLJbNChrzU1NTU1FSZg5s3b25riscrZpQAU4YOHRofHz9v3rw5c+Z07979ypUrP/74I4fDkVmeThkIhcKHDx/S/7xPnz5lsVgCgYD+p2YWLpzOJ50zh+jqai9fbig5Qn2ob9nyZNIkmiJR9IWXlmr6+RmWlr78EJw0Sbh2bQ0Tf9YtqMNLnSptlDlYWlq6ePHiVtszlqlQm8IQQvLz84OCgr799tuBAwfa2Ni0Og9Z3MZsEWmOjo7yFym/XKkE0hQl1L9//507d0ZHR2/YsOHFixf6+vpTpkxZsmSJzHI7ykBbW9vIyIj+59XR0RGLxf+meFnF4MJpft4lS8iECSJLyxafEaGhXa5eZdOzmoNCL7ykhEyfrlla+vKIuTk5eFCbEAb+qGWow0vdyMhIZvFxQoh8X4OEojKV9PR0mXXc4+PjW12CzM7OburUqTt37szNzbWxsTEzM5NvU1dXV15ezmaz9fX123pGU1NTU1PTt48cmGVvby9fdv3G3N3di4qK3tXZpGlqakqvbEsb6kkZeWpm4cLpf+revUlxsWyN7f79mtnZJCND4VNjFHfhJSVk1KgWgz7UnGQleXWpyUv9tT6vGatTkdavXz9CCDXuQ2Uq9+7dk25ALf+lr6/f6mpjAACgCNRHuEzZSkkJ4XBIy51D2w0qePk0BXOSlZmiMhXqu6w0d3f3vLy84cOHh4SEiEQiSUuxWHz58mXy90hN7969u3fvzuPx6uvrJW3u379fUlLSr18/1e4QAwBQQmvWtLIMWkSEbDmq8qNKg6WZm5PiYqQpyo7WPhVzc3M2m33mzJkzZ85IDp49ezYtLY3L5VILcpiamtrZ2fF4vPT0dLFYTAgRCAQxMTHNzc3e3t5Y9g0AgH7UOrYyq4xQH/ztpXMlMlJ290EqTQHlR2umYmhoGBYW1qlTp0WLFk2cOHHVqlU+Pj6ffvopi8VatWoVte+Pjo7O559/rqent3Tp0hkzZoSFhY0aNSo7O9vX19fJyYnOaFVAfX39vn37xo4da2lpyeVyBw4cuGjRojt37kgapKenc7ncuLi4ts4QFhbm4uJSWVlJCBGLxfv37x8wYACXy/3kk08kOye/sbi4uH+zmyANhELh9OnTJVcKAPJaHQki7aFzhVrbTSbygACkKe0G3XUqI0aMOHz48JgxY+7du3fw4MGioiJfX9+ff/55xIgRkjZ2dnY//PCDi4vLr7/+mpaWpqmpGRERQcP2hCpGIBB8/vnnERERtbW1Pj4+/v7+5ubmJ0+e9Pb2Pnny5BucsKCgYNOmTRwOZ/PmzYsXL+7QocOhQ4fk67cBQIVRI0EywyXK3LlCza9OTm5xMCKiHe9Hq4YYqC7mcrnbt29/dRsOh/OKNdTh38jMzDx//vzSpUs/++wzapNhQsjvv/8eGBi4bdu2IUOGGBoavvoMhJDo6GjJzxUVFQKBYP78+dTehDdv3ly/fv1nn32moPgBQDlRI0EyW/oRQiIiSHKyEi2eVlJC9u6VDdLcXIkihH9JKeb+gCJcvHiRzWa7uLhI0hRCSN++fSdPnlxWVsbn89/stOjZAgDSRpltSQmJiJCdXMOIVkd8qK0Hkaa0O8hUVJaZmVlDQ0OJ3BtGWFjYjRs37OzsJEcaGhoSEhLs7e25XK6zs/ORI0eampokjV1cXEpKSqZPn04tkBMcHGxra5uYmOjj4yMQCDZu3CipNWlsbNy3b5+zszOXy7W2tg4JCZHOh8Ri8cWLF8eOHWthYWFjY/P111+/utJFKBRGRUVRZTEeHh6//PKLv7//9OnThUIhVVaybNmyxMREa2trGxubI0eOEELu3LkTFBQ0cOBALpdraWk5duzYkydPUnXZlZWVLi4uy5YtO3r0qJOTE5fLdXJy2rdvn8yayIWFhf7+/paWlvLxA4AMqnNFvnKFmgnM4ciOudCDylHkl/93dSUZGdh6sF1S8bVlXtub/WG97rbotDzLiBEjkpKSli5dmpKSMmHChI8++qhHjx6tTp6KjY3t2bPnwoULtbS09uzZExoaymKxxo8fL2mgpaW1aNEiW1vbXbt2ffrppwMHDjQzM/viiy++++47Dw8PDw8PU1PTxsbGNWvWHDx40MbGJiQkpKqqKjk5OSAgIDk5maqVPnXqVGhoaI8ePVavXk0ISUxMLC8vpzbQlicUChcsWHDx4kVvb+9hw4ZduHAhJCRELBYPGTJE0iY9Pf3GjRurV6+uqKiwsbEpKCgIDAx87733goKCzMzMCgoKUlJSQkNDu3btKqnFTk9Pz8rKGj9+vK2tbWpqakRExJ07dyL+fqMtLS0NCgry8vKaMWNGTk5OampqWVlZcnKynp7ea/3LA6gPc3OyZg2ZPVt2gTjyd8YQGUnfaEurwz0EIz7tHzKVlmQ2//6XXjdTeYNnef3qrz59+hw8ePCLL77IycnJzs4mhOjq6rq5uQUGBtrZ2UmnLB9++GFiYiK1Vs3gwYNnzpxJfZxLGmhpaTk5OQmFQqoBtdbwixcvYmNj+/TpM3r0aEJIVlZWamrqpEmT1q9fT40QOTs7BwUFbdy48dtvv62vr9+9e3evXr0kiYu7u3tAQEBbc20yMjIuXbq0fPnyoKAgFovl4+Nja2sb2bJgr6Gh4auvvnJxcaFubt26tWPHjvHx8VZWVoQQLy8vJyen4ODg/Px8Saby/Pnzb775hqqz8fLyWrVq1ZEjRyZOnEg9hBCyfv16X19fQsi4ceO0tbUPHz5cUlJiY2Pzuv/4AGqFmhaUmUkCA2XHfajxIKp+ZfZsRa1c0laOQrCwm0rA6A/t6Om2IYQQwuFwUlJSeDxedHT02LFjCSHHjh2bPHnyf/7zH+lRj5EjR0qW1DMxMbGwsCgrK6Pykn/v1KlTGhoafn5+kkIWW1tbV1fXK1eulJWVFRUV3b1718fHh0pTqCfy8fFp9VQikej06dMmJibjx4+nMioWi+Xp6WlpaSndrGfPnn379pXcXLJkSU5OjiTnIIQYGBjI9Nk4OTm5/t35q6Wl5efnJxKJ8vPzqSPGxsaSnIbFYjk6OgoEgoqKitf6dwBQW9RgUFJSK2mBpH6FmiL0rqpYSkpIcjJxcyMcTutdKRERWNhNFaBP5a3R0KHydgwNDX19fX19fcVi8e3bt8PDww8cOODo6CjpNZHZYOIft62WV1dXx+fzdXV179+/L91N0tTUJBAIampqqqqqhEKhtbW19KNkbko0NDRUV1cbGRlJD7vo6OgYGBhINzMyMnrvvfdkHltbW/vbb789ePDg8uXLPB5PZj/S7t276+joSG526dKFzWb//vvv1M0OHTpI/1OgdhjgDQQEkICA1vtXyN8pS0TEXyMyhLz2oAx1zsxMkpXV5vc+DPeoGGQqLb1BtdXrjsvQUtBF1ZZ+9NFHGzZskBxksVh9+/Zdt26d/PjOWxKLxSKR6PHjx6tWrZK/t6qq6l09kTSZjKq0tHTZsmV5eXmEkI4dO1pYWAwaNOjcuXP/eB5kJADvHNW/UlJCIiNbzyeolIWQv7IWc/O/3hrNzP7qAuneXVMkEj158jLdefCAZGbKVsPIo3IU9KOoEmQqLcnPumuPT0FI9+7ddXV1r127VlVVJbNuira2dqdOnd7txzObzTYzM3v48OGhQ4eMjY3lG9y8eVNPTy8/P196P22ZfSilIzQwMLh165ZAIJDsSUntUtmlS5dWH1JfX7927dqioqL4+Phhw4Z16tSJetILFy5IN3vy5Mnz58+pewkhFRUVT58+7d279+tfMQD8M8ms4L17SXJym4M+JSWkpEQ+BXm9/WipfhQXF8zuUUGoU1FNBgYG3t7ed+7c2bBhQ21treR4fX19YmLi06dPhw8f/pZPoaGhoampKdls8qOPPqqoqDh27Bg1K5gQIhAIPvnkk5EjRxYXF5ubm/fu3fvkyZOlpaXUvTU1NadPn271zJqammPGjOHz+UePHpWcLScn5/79+20FIxAICgsLLSwsnJycqESkqakpKytLptAkLy/vt99+o35ubGz8+eefO3fu7Ozs/Fb/EADwStT8oOLi1qc0v/3JAwJIRgYpLiZr1iBNUU3oU1FZM2bMKCgo+Omnn06cOGFvb9+rV6/Hjx9fvHjx2bNn06ZNk+7beDPdu3dns9knTpwwNTV1dHT08PC4dOlSVFRUTk7OxIkTa2trDx48WFhYuGLFCnNzcxaL9Z///CcoKGjq1KnUuiyvnqXs5uY2dOjQTZs2FRYWUrOU09PT22pMCDEwMLCzszt27NgXX3wxevTo2tra1NTU27dvs1gs6VIVgUAQEBAwZ84cMzOzvXv33rhxY8WKFX369Hn7PYwA4B9RKcuaNX9N1fk3QzmvOJWrK5k9G6mJWkCmorL09PS2bdvm5eWVkJCQl5eXk5PTsWNHW1vbTz/9VGbh2jdjaGhITUJeunTp5s2bJ0yY8J///MfKyio5OXnZsmUdOnSwtLSkFlyh5u/Y2dn997//Xb169bp16zQ0NEaNGhUcHLxx48ZWT85ms2NiYrZu3ZqSkvLTTz9ZWVl9++23r9hggdocis1mHzly5NSpU/r6+j4+Plu3bv3yyy+Li4slyYqDg8OECRO2bt1aVVVlYWEhHR4A0EaSshDy17jPhAkkNPSv4SFqMEjSUvL/AQOIgQHGd9QRS9K73q5t27aNELJ48WKFPgQYVFlZOWXKFHt7e+mtiF734SYmJvHx8ZLalzfG4IvnyZMnhJC26nVUGC6c6UDohgtnOhC6veJ9FXUqoIwSEhI8PDzu3r0rOXL58uXy8nJUvwIAqBuM/oAyGjp0aHx8/Lx58+bMmdO9e/crV678+OOPHA7H29ub6dAAAIBWyFRAGfXv33/nzp3R0dEbNmx48eKFvr7+lClTlixZ0rlzZ6ZDAwAAWiFTASVlb29/6NChd3W2999/Pysr612dDQAAaIM6FQAAAFBeat2nwuPxmA4B2iUejyfZyxAAABRKfTMVR0dHpkN4BxoaGgghr1gSTVUxe+FOTk6q8foBAFB+6pupODk5qcDXYrWdea+2Fw4AoG5QpwIAAADKC5kKAAAAKC9kKgAAAKC8kKkAAACA8kKmAgAAAMoLmQoAAAAoL2QqAAAAoLwYyFT4fH54eLiNjQ2Xy7W3t4+KiqqtrZVuUF1dPXbsWK6csLAw+qNVcuXl5UyHwAxcuLrBhasbXDhI0J2p/Pbbb76+vikpKVwu19/f39jYOD4+ftKkSXw+X9KmvLy8oqJCV1fXtKWuXbvSHK3yO3369N69e5mOggG4cHWDC1c3uHCQoHWNWpFItGvXridPnmzZsmX8+PEsFkssFickJERFRaWkpCxZsoRqVlFR8eTJk1WrVs2dO5fO8AAAAEDZ0NqnUlNTU15ebmdn5+LiwmKxCCEsFsvDw6Nnz565ublCoZBqVlhYSAjhcrl0xgYAAABKiNY+FUNDw0OHDskcrKioqKmpGThwILXbnFgsvnPnTrdu3UxNTemMDQAAAJQQk3N/Ghsbs7KywsPDNTQ0/P39NTU1CSF1dXVlZWV6enppaWnOzs5cLtfGxiY8PFy6kAUAAADUBGOZSlxcnJWVVWBgYHV19Z49e5ydnanj1dXVDx8+LC4u3r9/f79+/fz8/N5///0ffvjB19f3+vXrTEULAAAAjKB19EeaSCTy8/P7448/8vLy5s6du3z58lmzZrFYrKdPn2poaHz88cffffcdNdmnqakpPj4+Ojo6KioqPj6ezWa3ekIej0fvFSgF9bxqggtXP7hwdYMLVzc8Hs/JyanVu1hisZjmaGTk5+cHBQW9ePFi//79NjY2rbYRCAQBAQF37979/vvvbW1t5RvweLzLly8rOFIAAABQFEdHx1aTFUX1qaSnpwcHB0sfiY+Pd3d3l29pZ2c3derUnTt35ubmtpWp6OnpcTica9euVVVVtdrAycmprVwMAAAA2i+lWE2/X79+hJDGxkbqplAofP78uXwzFouloaFBa2QAAADAKEVlKu7u7kUtubu75+XlDR8+PCQkRCQSSVqKxWJq4KZnz56EkOjo6AEDBiQlJUmfraqqqqCgAFOXAQAA1A2tfSrm5uZsNvvMmTNnzpyRHDx79mxaWhq1BxAhxM3Njc1mp6amFhcXUw3q6+s3b958586d0aNHczgcOgMGAAAAZtFdUXvu3LnQ0NBnz57179+/b9++t27dKigoYLPZW7ZsGTFiBCFEsr6+lpbW8OHDO3funJ2dXVlZ6eDgEBMTY2hoSGe0AAAAwCwG5v4UFRVt3rw5Kyurrq5OV1fXw8NjwYIF5ubmkgZisfj8+fPbt2/Pz89vamoyNjaePXv2tGnT2pqfDAAAAKqK+VnKAAAAAG1Rirk/AAAAAK1CpgIAAADKC5kKAAAAKC/VyVRqa2ujoqLs7e25XK61tfXUqVNzc3PVqgpHKBTOnj07LCyM6UAU686dO/7+/paWlhYWFqNHjz558qRa/ZYJIenp6Y6Ojjdv3mQ6EDqIxeLc3NwpU6ZYWlpyudyPPvooKiqqtraW6bgUrqmp6fjx46NHj7awsLC0tJwyZYq6vaERQgQCgb+/v4uLS2VlJdOxKNzdu3cdHBy4cuLi4pgOTeH4fH54eLiNjQ21Xon837iKZCp8Pn/SpEm7du3q3Lmzn5/foEGDfv31108++eTUqVNMh0aTpqam77//Pjs7m+lAFCs9PX3SpEn5+flubm5jx44tLy9fuHBhQkKC+ryDFxcXR0VFNTQ0MB0IHag1C6ZNm3bz5k03NzdfX9/m5uZdu3YtXLhQIBAwHZ0CiUSir7/+etGiReXl5WPHjvXw8CgsLJw2bZpavdTFYnF8fHxubi7TgdCktLT08ePH+vr6pi3p6ekxHZpiFRQUTJs2LSUlhcvl+vn5de7cuZW/cXH719zcHBkZyeVyd+7cKRKJqINXrlwZMmSIs7PzH3/8wWx4NHj27Nm6deu4XC6Hw1m2bBnT4ShKdXX1hAkThgwZcu3aNepIaWmpu7u7g4NDYWEhs7HRIz8/f9iwYRwOZ8CAATdu3GA6HIUrLCx0cHCgFrymjjx79iw8PJzD4WzZsoXZ2BTqypUrNjY2U6dOra6upo5QL3U1eUOjnD9/3srKisPhDB8+vKKigulwFG737t1cLvfcuXNMB0KrZ8+eBQUFWVlZHTlypLm5WSwWv3jxYuXKlRwOZ//+/ZJmqtCn8ujRo6ysLEtLy8mTJ0s2Bho8ePC4fpOVXQAACsJJREFUceP4fH5hYSGz4SnanTt3pk+fnpiY2LdvX21tbabDUaAbN2789ttvXl5ekv20TUxMFi1a9OjRo3PnzjEbm6LV19fHx8fPnDnz+fPn6rNS84ULF6qqqmbNmiW5ZB0dnTlz5nTv3j03N1coFDIbnuLcvn1bW1vb39+/a9eu1BETE5MxY8aowxsapaqqasOGDX379qV2hVMHv//+e5cuXXr06MF0ILS6evVqVlaWv7//uHHjWCwWIURLS2vatGl6enrXr19vamqimqlIptKhQwdLS0vJXzWlW7duTIVEG6FQGBERUVBQEBoaGhkZqaWlxXRECpSXl9fY2Ojo6Ei9oCnW1tbdunW7cuVKq7taqoycnJxvvvnGxMRk//79AwcOZDocmpSXl3fv3r1v377SB3V1dTt16sRUSPSYMWNGbm7uhAkTJEdEIlFJSYm2tra+vj6DgdFDJBJt27atqqpq5cqVKj/2QREKhaWlpT169KD2v1Mf+fn5GhoaXl5e0u/qNjY2169f37hxo6TrQRUylb59+545cyYmJkZTU1NyUCAQZGRk6OnpqXyK2r9//+PHjy9cuLBjx45Mx6JY5eXlenp6MrtU6uvr6+joPH78WLVLN7S1tcPDww8fPmxpacl0LPT58ssvc3NzqR3BJK5evVpWVmZiYqKrq8tUYDSrqqr6+uuvT58+7ebm1r9/f6bDUbgzZ86kpaUFBwd/+OGHTMdCk9raWj6fr6enFxMTQ80LabWwVMWIxeKioqJu3br16NFj3759zs7ObV24ZlunaNfEYvGBAwfy8/PHjh1rbW3NdDgKxGazV61axXQUdKirq2u1/v+9994zMjL6888/VbtPxdnZ2dnZmekomMfn87/77jtdXd3JkydLfwlTVZWVlVOmTHn48CEhxNfXNyIiQkdHh+mgFIvP52/evNnZ2XnmzJmSzn+Vx+fzHz9+zOfzi4qKnJycOnXqlJ2dvWvXrqysrISE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B34qoqOj77zzTkLIjz/++OWXX9I7hU5p0KBB9DtC6EtHjRo1ZMgQk8kUHx8vfA5DfS0SIpXgatOmzezZs//zn//s2rVryZIlgwYNEj5/Dofj1VdfdQ91e/Xq1aFDB+HpXbp0oQ9mE7HBw/72a665hg7VCL/90qVLdEJMhw4dhg4dKjyrT58+N910U6svnpycTLv+goIC+sWwZ88eOiQgDGCePHmS9t1xcXFCSZg2bdrQ8Ri73f7DDz9wLzt48GBpf+yJEyfoYfTp00eIJtu1a7dly5aSkpLjx4/TIbHRo0efPHmSjlR98803a9aseeihhw4cOCDhN3bq1Gn06NGEkKqqKvoKTU1Nu3btcjgcJpPp7rvvNps9L8eTduZ79uzZrl074UeLxbJhw4aSkpL8/PyIiIiPP/44PT198eLF3p5uMpmSkpJozEEI6dGjBz3VdrudTY1RgwcPFh553XXX0fiJftH6OCHUbbfdJqyACw8Pp/0yIeTkyZO1tbWST5p4wqyyqqqqGTNm0ETtl19++eGHH/qYT8YZMGBAmzZt6G365UEIuemmm6677jrht9AbFy9ebGhoaGho+O9//0vvueWWW4SzFxsbS59SXFx86dIlk8n0l7/8paSk5Pvvv+/Zs2dubu4LL7wwd+5cH2NpvluxR4cOHaJ5zGHDhgkHT5hAsKSk5MSJE4SQnj170kGs0tJSGrAeP368sLCQnoFBgwYRQs6ePUsf3KlTp169etGXMplM9PPjcDjoeBiL+6y6U+Y8+MZ+yKOjo+mH1veHPPBTYTKZJkyYQBdh7N27t66uTkh9mkym++677+qrryaE0EGdkpKSv/3tbyUlJevXr58xY8ZHH30k7S/VGqxSVkJYWBidHjVv3rzGxsZt27ZlZmbW1NTQaxFu7DoyMjLwnlcy37+9qqqKXj1YLBah/6XPYn/05vrrrx86dOi2bduKi4sLCgruuOMOOtosDGASQurr62l+h84Cdn8R2uzZX+27g/Ph1KlT9Eb79u1pa/fI4XAcOnRo2bJlR48eDXyfrJSUlPXr19vt9r179z7wwANlZWU0Wr3++ut9hFzSznzXrl25ey5duvTaa6+9++67YqbXcL/LbDbT7pIQ4l60MJCZItxzhR+F7wBpJ028a6+9dsGCBYsWLaITGmiill7s9u7d22q1CgkjkX+F0Iiuuuoq4btN8PPPP9MT+PPPP9N7hMnvrB9//LGqquraa6+tq6vbtGnTa6+9xs3B9EZCHyI0q969e7MHHBER0b59e8IMH5rN5rvvvvuTTz5pbGzcvHnziBEjcnNz6cfpvvvuo1/e9fX1dITj9OnTHk/d6dOnGxoa2Ebn/ll1p8B58E3Ch1yWU9G3b99+/fodPnz466+//v777zt16kRj3Pj4ePY1i4qKli1blp+fr8xlrZIwphIsS5cupbOvrVYr+/VGxyHnzp1Lf2x1eoeemM3mSZMmhYeH0+lg33zzDb0m69+//w033CDyRbgzFh4eLnx9BsmePXtmzZpFM0EJCQlLly7dsWMHnbQhwU033TRkyBBCyOHDh0+cOHHw4EE6riMk+GXEdax2u33BggVvvPGG3W63WCyTJk3KyspavXq1vL80GBQ4aePGjdu6deuvf/3riIgI9v6ioqLU1FR2Mq9iGhoa6uvrm5qa/vznP2dmZlZUVERERIwbN+7VV19dv369v3WYZCTk477++uvCwkI61cyvCUNCrCZoNQjQ4HmQhZhTIaTO7Xb7/v379+/ff/bsWUJIYmKicC1RWFj40EMP7du3r7m5OTY29vHHH9+1a9dvfvMbRf6IoMOYSrAMHz6czn/cvXv37Nmz6cwmyuFwhGj5k3bt2lkslpqamosXL54/f17ImNTX1wul53wbMmTIgAEDDh8+fPTo0bCwsMbGRpPJNHnyZGHYPCwszGQyORyOxMTENWvWBL6mw4cbb7yR3jhz5gz98nZ/TENDw3vvvUcvtdPT0x977DGahr/qKolRfps2bX79619//vnnNTU127ZtowsowsPDU1JS3C++BYGfeULIN998Q2fhxcbG0smShBAfy3NqamrKysqEWdhNTU3CRBZ5vx7Onz/P/iiM9/zqV7+i68WknTR/9e7de+3atY2NjaWlpXl5eZ988gldZnz58uWPP/6YzpSSkclkEq7416xZQzNc7oqLi+lsqqioqOzsbDrzQPYdW4TERFFREU0r0B8vX7588eJF4jp42alTp7FjxxYVFZ05c2br1q108tDtt98uTBgKCwujf1qPHj3ef/9994l6EgizyoJ6HmQn16lISUl58803y8vLv/zySzoAY7FY7r33XuGdysnJoZOaJ0+e/NJLL9GGI7mb0hqd/BkadMstt9AJ22fOnJk/f35BQQENnC9cuPD6669nZWXRh3lMcMjuypUrsrzOtddeS7/da2pq6Owt6rvvvhO5kjMqKor2+KdOnaJbY9xwww3sxItevXrRiW8lJSXCcu7KykpaMWXgwIFfffWV+AP2vWSjV69e9IqE/V1c6ZeGhgahVgGdTksIuXDhgpA5kiAlJYV+NjZu3EhDB2FCsTeBn3lCyE8//UQ/hF26dKFD+oQQ9xknrI8//li44Dt79iwdWLJYLH379hX5S8UQ5mYSQpqamnJzc+ntAQMGCKPiEk5aq4Q/bdu2bUJploaGht69e8+bN2/Lli0LFy7kHimjtm3b0oEiQshXX30ljLyuX7+efvwWLlzY1NR06dIlGiC2b9+engFCyMmTJ+Udjr311ltppH7w4EFh2jIh5MCBAydPniSE9OvXj33TR40aZbFYHA5HdnZ2fX29yWS69957hcCrR48edLJLZWWlkFeqq6tLTU31WBpEDGXOg1yEnkeuU9GtWzf6aTl06BDNSw4YMKBPnz7CrxOuWHr27EnDlOrqavre6QAilWCJjo6eOXMm/WIrKiqaMWMGrdIzdOjQv/zlL/QavXfv3t4upGTRpUsXeu1rs9kqKyvtdruYJaM+WCyWKVOm0D9q9erVdKSxsLDw2WefFV9WRFg7QCUlJbF52ejoaLr0o6KiIiMjo7y8vLGxcePGjXSie2Jiopipu8IFYmFhYUNDQ3V1tcfEbWxsLF1yWVFRsXTp0vLy8ubm5ry8vB07dhBCOnXqNH78+KuvvppO9SWEfPTRR5cuXaqsrFy+fDkdfZVG6HRqamroJ0GYUOyNLGeeLoIghHz33XdfffVVU1PTzp073377bR9P2blz5z//+c+6urrKysqXX36ZVlIR+S6IR/PrNJBav379rl27yC/nX3iMhJPmkcVioaEwIeTo0aNNTU3V1dUjR46k1wwHDhyg2TFCyOnTp+lXAp1ZLMPf6Wb8+PF02vg777yzadOm5ubmkpIS+o5ERERMmTLFbDZfc801NL957tw5WlHj8OHDK1eulPdIBg4cSP/GM2fOLF269PTp083Nzfv371+2bFljY2NERMScOXPYgTQhH0fFx8fTubRUVFTUpEmTTCZTfX39Cy+8cOzYsebm5s8++4yGmH369BEz74ejzHkIkHvP86tf/UqWUyGkzoV72DJCZrNZSAN99tln5eXldrv9lVdecV8pGaIQqQSLyWRKS0t79NFHvY1OR0dHr1ixQug0g6Fr1650rU1FRcWdd945cODAwNPt995777Rp0wghVVVVaWlp8fHxEydObGxsFP+HCLW8iNsAJnGtQ5Ofnz9q1Kg+ffqsXLmSFgHLyMgQ8kQ+9OvXjzbpTz/9tF+/fhMnTqTjohyz2fzMM8/QDvrgwYOjRo2Kj49/9NFHq6qqIiIirFZr7969r7766unTp9O5Czt27Bg8ePDw4cM/+eQTYXKM+1qkVnGdjsViEZNZCPzMDx48mHaLNTU1aWlpvXv3fvzxx+vr6+mRnD592n2x5YABA1atWtW/f3/6VxNCxL8L4g0aNOijjz665ZZb+vTp86c//YnWyKHnX3iMtJPmkTCQ+cYbb/Tu3Xv+/Pnh4eEvvvhidHS0w+H4xz/+MXDgQFqTlM7bnTZtGq2+JTs6XTciIqK2tnbp0qXx8fF0oZnJZFq8eDFtBUI83djY+Pzzz/fu3Xvy5Mlnz56lp+Knn34KJGgWhIeH//GPf6S/8eDBg0lJSfHx8bNnzy4rK4uIiHj22We5M9CmTZvJkycLLXfs2LHCSj1q6tSp9ONaVFQ0YcKE+Pj43/72t5cvX+7YseNLL73EPVgMZc5DgDz2PHKdCpo6p7fZRe/U5MmT6RXg4cOHR40aNXDgwOzs7IiICOFqOfDVACpCpBJE4eHhS5cu/eCDD+655x4h4I2IiOjXr9/SpUu3b98ufOyCpFOnTitWrLjlllvo0ujrrrtOWGsgWXh4+B/+8IeMjAz6BdmxY8f/9//+38aNG8VPiTWbzUJ0wg5gCmgdmhUrVtDdFoXfkpOTI4z6+jZy5MjMzEx6hGFhYddcc423iUG04hb7u9q1a3fPPfds3bpVWI505513vvXWW3379qU7N/Xt23f16tXr1q2jFzR79uxxr93UKqHWp7eT4C7wM2+xWFavXp2amkpX5LZr127q1Km7d++mX0JnzpwRyswLnnjiiVdffZXOsmrbtu3UqVM3bNgg8l0Qb/78+atWrRI21xw2bNjGjRuF8y+QcNI8euCBB5566inarUdERISHhzc2Ng4YMGD79u0LFiy48cYb6Yezbdu2w4YNW7t27Ysvvshey8pr3LhxH3/88eTJk+kskLCwsFtuueXf//733Llz6WGYzebnnntu6dKl9IDbtm1755137tixY/78+YQQukWALF9CnTp1ysrKWrt27a233kpDc6EtzJo1y/2Ka+jQofSzFxUVJSwsF9Dgj301+vn58MMPpS3XUuw8BMJjzyPXqYiKiqLjzYSQxMREbi75gAED3n333WHDhtGpfjfeeGNGRsZHH31ED4ZL6oUck4pvrd1uf+KJJ+i3KXv/hQsXHn74YfdL1UmTJnGPBI2w2+3z5s2j33M+5gaCgD1jVqt11qxZgb+OXGe+oqLigQceoOVbNPVuynXSACC0qLb2p7m5+e23387Pz6fFvFnnzp07f/5827ZthaI9FPcjaAet7EkIsVgsEsZ1Dai0tJTu1+PX2k53hjrzcp00AAgt6kQqdXV1K1eufOuttzyO6Jw/f/7ixYvPPvvso48+qvyxgW/p6em0xnnHjh3Xrl07aNCghoaGjz76iK5AoTuFqn2M2kVXBPz8889r1qyhaxYSExNFnjHDnvlAThoA6IAKkUpRUdEzzzxz9OjRfv36lZSUuD/g+PHjhBD0RNo0duzY7du3X758uaqqihsPa9u27fz580O9EFNQHTt27OGHHxbWVXbs2PHRRx8VOQfCsGc+kJMGADqg9Ixau91utVoLCwsXLVqUmZnp3t04HI6ioqKOHTvKXq8TZDF69OitW7fec889nTt3Zvd5mTx58kcffaSdOQ3a1LVrV1r6KSIi4tZbb/3nP/8pfkqdYc98ICcNAHRA6Rm1drt91apVU6ZM6d2797fffvvwww/fdddd7DxZu90+Z86cysrKMWPGbNu27cyZM23btp0wYcKCBQtkX3EAAAAAGqf0mIrFYnn22WfZMgmcCxcunD59urS09J133unfv//UqVM7d+68adOmSZMm0fqYAAAAYBya2/enuro6LCxsxIgRq1atoot9mpub16xZs2LFiuXLl3vbCKagoIBuBw8AAAChaPjw4R6L9mqu8ltCQsLnn3/+9ttvC2uSw8LCHn744cGDBxcWFnrbxeDAgQPuRatAmpycnLKyMrWPQg/KyspycnLUPgqdKCgoQBuXC9q4XNDGZeRjxEFzYyoeRUVFxcbGHj58WNjGzF1iYqKwnRgEIicnZ+HChZjRHDja8PCxlBFOpizQxuWCNq4MzY2pEEK8baRHa5krfzwAAACgFs1FKitWrBg4cGBWVhZ7Z2VlZWFhIZYuAwAAGI3mIpWUlBSLxZKTk1NaWkrvoQVti4qKxowZQ3dKAwAAAIPQ3DyVIUOGPPnkk8uXLx83btwdd9xxzTXX5OfnV1RUDBs2bOHChWaz5g4YAAAAgkdzX/wmk2nu3Ll9+vR59dVXc3Nzm5ubr7/++qVLlz744IMe1ycDAACAjqkZqSQkJHgs5mYymZKSkpKSkpQ/JCCErFy5smvXrmofhR4MwjnZPAAAIABJREFUHjx45cqVah+FTtx99934WMoFbVwuaOPK0Nw8FVBdly5d1D4E/cDJlAu+WWWEj6WMcDIVgEgFAAAAtAuRCgAAAGgXIhUAAADQLkQqAAAAoF2IVAAAAEC7EKkAAACAdmmu8hsAAGWzkbw8MngweeUV0tRkaWxsatOGLFlC3nuPZGSofXAAoBREKgCgITQ62bev5QbDTPur7GxCCLFaSUwMSU4mSUkkNVX5wwQA5SBSMYTsbLJvHyGE2GwkI4MkJ6t8PADubDaybh2xWv14fHY2yc4mmZkkNRWjLKBReXkkM5PExJCYGHLjjQispUCkYgjr1jkvT2fPVvNIANz5G6O4P91qbfmHeAW0Zt8+Z/ebnIxIRQpEKoYQE+O8feqUaocB4C4z01eMQlM8hJC6uvrwcLPZbLbbyQcfeH4w4hUAXUKkYjg2m9pHAEAI8T6UIkxAEcIUQsjFi/WEkPbt27PPpQkgjtVK8vJIbm7QjhvAH2yXi8y7NIhUDIEdUwHQgrw8kpbGx800NMnIaP0TGxPTMnCSkeEh3MnLI7GxJCsLXwygPlwcBg71VAzhxhudt9FsQF02G8nMJCkpLh9FGnnk5pKsLP8Ca/rE0lI+WLHZSEqKhxEXABWxXTGIh0jFcBCpgIo8ZnxotEEXHksjBDqctDSSkiLxNQFkwUXkIAEiFUNgmwciFVALHU3hwpTkZJKbK8+CiORkUlrKZ3zy8hCsgJrQ5QYOkYohIJAH1dlsJC3NJR0TE0OsVpKbK+fnMyamJYXEQrACanGfiQUSIFIxBK55IMYHhdEwha05GxNDsrKCtZw4NZXPBCFYAS1ApCINIhUjQqQCSqKTW7kwJTc3uAtzaFKJRRcEASgJk1RkgUjFKDBVBVRBR1O4/lrejI83dNoKdzAYWQEIOYhUjALhPKiC3cmBKBimCL+OC1ZoHRcAZWBMRRaIVIwCBfVBedxKH4XDFOGXcsEK3dcQQAHobGWBSMWIkP0BBeTl8WGKv1Xd5EIjJBY3vRdAARhTkQyRilGgkYCS3GeEpKaqWdvefYItN8kXIBi41CdIg0jFKFBQHxTjHqZoYX/j5GS+6BwmrACEBEQqRoRIBYIqM9PlM5aaqn6YQmVkuIzrYCkQKAmb/kiGSMUosEoZlMHNV6XTU7SDq+OSl4ccEAQR1v7IApGKUaCRgAJo9RSB+1RWLeAiJ25XZwAZ4aMlC0QqRoGC+hBsXJhCCMnI0GKI7HEpEIDssOmPXBCpAIA8uCJvqany7JAcDMnJfA4oM1O1gwGDQKQiGSIVA8FUFQgem81D9RQt42rQWa2YsAIywyQVuSBSMShEKiAj9+kpGg9TKO4gMawC8kI3KxdEKgaCoB6ChFtBo26RN/G4CivIAYG82FL66H4DgUjFQLD1DwSD+4CKRqqniMFVWLFacR0MQYFIJRCIVAwK3THIJRTzPiwursI6IJAL5qnIBZGKgaCpgOy4vA+3piYkJCe7rFFCLTiQCy4I5YJIxUCw9Q/IK0Qn0rrjNnnGsArIDqX0A4FIxaAQqUDg1q1z+SCF0PQUd+zB22yYWgsyQPZHLohUDAT1VEBGXAEVLocScrj1SiivAoFDNysXRCoGgoL6IKPQXe/jDcqrgIxQSl9GiFQMBE0F5KKDibTuuHk2mFoLMkL3GwhEKsaCBBDIgh1vCN2JtO5SU13aCIZVQDJMUpERIhXjQqQC0mRnuww26CDvw2L/nLw8kp2t2pEAAIVIxVgQ2kOAuHUxMTGhPZHWHTe1FsMqIA3GVGSESMVYUFAfApSX59IF6ybvw+JWLGNYBSRABysjRCrGhewP+Isr9aaPibTuuL8LheBAAoypyAiRirGgwUAg1q1z+VFnM1RY2AwIAoRIRUaIVIwFBfUhEGypN24+h85wwypIAEEgUEo/QIhUjAuRCviFK/U2e7Z6h6IIbgoOhlXALxhTkREiFWNBPRWQhptYqtcZKixuWVN2NpoM+AGfFhkhUjEWhPYgDbcyWcczVFiorw/SoJS+vBCpGAu2/gEJ3AdUjNPzYlgFAmec9hIkiFQAoBXGHFChMKwCEmCSirwQqRgO22ywARu0ysgDKhSGVQDUhUgFAHzhBlR0v+THHTeGhGEVaBXGVOSFSMVw2CUbqPcMvhlwyY8790VAAL6ha5UXIhVDwzg2+MbmB405oEJhWAUkw5hK4BCpGA6aDYhkkF1+xOCGVdhavQDukP2RFyIVw0FBfRAJAyosblgFOSDwAV2rvBCpGBqaE3hjs7nsRzh0qHEHVChuWAXF9UEkbPoTOEQqhoOC+iBGXp7LmMoTT6h2JNrBjSphWAW8QfZHXohUDAfNBsRgB1SMPEOFxZ0H9hQBsHARKC9EKoaDgvrQKm5ARYWitHR5dFoaSUkhJhMxmdp36NC+QwfFj4PHDqtwZwmA4jpVRPmBM6t9AKAg2oAwqAKt4aq9KdfV0tkxGg4BUlNJZqbzq2jdOnwPAQQdxlSMITaWmEwkNpbExpLsbBTUBx9sNjUGVGw2kplJUlKI1arxDyV7QlBcH9xhkorsEKkYAwrTgmjcgAq74CUoaIwSG0us1pD42k9Ndfn6QRU44CBSkR0iFeOx2RC3gDfu5fOD/vvoOIo7mnayWkluLikttX/77cXDh4N8NGJhz0LwAZ2q7BCpGIP3wB6dLLC4am/BTf3QoRT3j2BqKo1OSG4uycig2zc3RUdr5/qUOy1YBATeaOYzG9oQqRiDa2FaNB7wiOZhBMnJQe5nuaEUmmrKzSVZWdqfp4ri+uANF+5D4BCpGI/NhoL64JHN5vJ5CHr5fIfDeTsmRv4Yhc4iD878XFSBAzFQoFYWakYqdrt99uzZ6enp7v9VXl6+YMGCvn37xsXFjRw5cv369Y2NjcofoX54L0yLSAUE3ICKEuMaDgeJiSFWKyktlfny02Qi5Jd5MEEIVlAFDrzBjFrZqRapNDc3v/322/n5+e7/9f3330+aNGnnzp1DhgyZNGlSU1OT1WrNyMhAsCIXFNQHd+osTiaEZGUF/ZcFJ1hBFTjwCJ2q7NSJVOrq6l5++eUVK1Y42OFfQgghjY2Nr732WnV19apVqzZs2LBixYrPPvts5MiRmzdvLigoUOVo9cD16jiG2Ngf0a6AqFjtLRi/yWYjY8a43BOEYIVbroxhFSBu3SnGVGShQqRSVFQ0Y8aMt956q1+/fpGRkdz/lpSUFBQUJCYmJv/Sf0VFRS1cuDAiImLr1q3ukQ1IgMYDHG5xctBrqARbTAzZtYuPgYITrAgwVQXcobOVhdKRit1ut1qthYWFixYtyszMDA8P5x5w7NixqqqqoUOHtmnTRrgzNjY2Ojr6u+++++mnn5Q9Xh1xTfkgAQQsbrVC0OfSKiM3N9jBCpe2QrACmKQSDCqMqQwYMGDHjh1PPvlkRESE+/+eO3eOENK3b1/2zoiIiPbt21dXV9vtdoWOUt8wqRZcsZmLmBgd9bC5ufwAkdzBCvvyqFcL6E6DQelIxWKxPPvss7179/b2gFOeyvu1bdu2a9eudru9uro6mEena65fPuxPqKhocOrvnBxUWVl8wZO0NBlfnh1/4mYlgwGx3al+In61aW4vZY8LfEwm01VXtRJU5eTkuE+5feaZZ7p06SLbwYWyDl26CHOC7IWFXbrUE9Jyx7Fj9WfPOtNqFRUVJpMpLCxM8WPUm4aGhqqqKrNZc62M84c/dBK6gujopj59Ks+eVfeIPLh06RIhpK6uTsqT583rsHNnpNA/2GxNo0ZVbtoky4H16UOiozuVlbWcwNdfr+/TR+tJarRxubi38ZqaKEIs9HaXLi5dKwjOnz+/fPly7s7y8vLJkyd7fLzm+lD3mSuEEIfDceXKFd9PHD58eGJiIndnr169ZDuyEGdmTmzk+fNssB8ebo6KihJ+tFgsFotF+9+v2mc2mxsaGthzq0E2G8nPd77XGRlEmwfc3NxMiPRja/rsM3LvvcKIhzk/v9PUqfWffCLLsT33XNP8+S3ncOPGyOefj9L4xTTauFzc2/j5885lIr16mbXZmlQXFRU1ZcoU7s4PPvjA2+M190m90VNJv9ra2nPnzlkslnbt2nl7YnR0tLdwDAghhAnazGZz377O5lRWZrZYLMKPv/rVr9CLycJsNtfX17PnVoMqK523Y2LInDlm4YpQU5qamgghAZ3MrCySkiLMIzDn51v++ldZcl2PPUbmz3f+eOiQZcCAwF81iNDG5eLexsvKnP8bHm62MPExsVp1l1uVzv37uow9d640V02fRionTpxg77x8+fLFixfbtWun8U5f07yX0McUMMOy2cgLLzh/lK2yiTYna9CC/SyrVa5DZb+AHnlElpeEkMR2p0lJrv+H0vpSaS5S6dWr13XXXVdQUMAmpE+ePGmz2fr379+hQwcVjy3kORwt/3JzsUoZiNsMUHkWJ9tsJC2NmEwt9ew1xT1YkWl2LRfkaTNUAwXw3SlWLctBc5FKdHT04MGDCwoKdu/eTeu81dTUrF69+sqVKxMnTjRpsO8LFa5rNdFkgARpo5/MTGfvrMEGm5zsEqzIFKdjGyAgHgvU4kJQDpqLVNq0afP4449HRUUtXrz4oYceSk9Pv+uuu/Lz8ydNmuQ+YRYk4yIVtCYDCsqASna2S/kz5Wry+4MNK+Qre82ewOxstCng9y3BBaJkmotUCCGDBw/etGlTUlLS119/vXnzZrPZbLVaPRa0BbmgVzUgri6tDBX0ad6HfdGsrIBfNDiysloyofLhTiASQAbUSqoHkYpUas79TkhIOHLkiMf/io2NXbt2rcLHYzQxMc52hUjFgNgMhQxjH1yYQgjJyNBu1xycA0tNdY4opaWF/vZJECBMUpGJFsdUQBloOEbG1aWVJ/XDvmJqqgG/qLnTiGEVo9m3z3kbHayMEKkYFwrqGxk7lzYmJuAxFZuNxMa6vKJm8z7BlJzs0qwwr9boMKYiE0QqQAiyPwbDzaWVYewjVKanBB9bWAVbKxsN25EmJ+MSUDaIVIwLIb5hcXNpAy2bmZ3t8oqyLXcOSVzYh2DFUFBMJUgQqRgXWy8RCXVDYbMSgfafNhufSTLwgArFBitIABnWjTciUpENIhXjQplaY+JSP4EOqLB13ghBmEJca6jn5aFxGQgikyBBpGJcaEjGJOdcWpuNr/Nm4LyPIDXVpXGxJxx0zGbzmf3hNwECPyBSMS6UqTUgLrQIaC5tCNV5Uxx7YjFVxZgQtMsIkQqAgXDxaECXee4riDBM9wsup4ZgxQg8pH5w/ScTRCqGxn6zYFKtEci5JSE3oBLohBe9Yc8tWxAMjMLDdoUgESIVQ0PbMRSZtyQsLXXum8PuTqwnAcwxwYaFRsOPqcTEuOwthd42AIhUDCY2lphMLf/y8lCm1lDk35KQEOJw8JVZ9YG2EatVcoiBDQuNxmsXKvdemAaESMXAXLtgXPPpnpxlVFg6G1Cx2YjJ5PwxgGEVFFYxFL5ALcgHkYrBuI6i6O9KGLyRuYyKjnHDTVwFXn+gsIqh4P0NHkQqBuNa7o0tU4tmpm/cgAqu+XzhlltLHQ9BYRXDYrtWCBwiFWiBPLq+cTvzQCusVuftAIZV2FONtcr6hgK1wYNIxWBcGxCak0Hk5cm66scIMjJkGQ/hTjWuB3QMw9LBg0jFYFzzPdy1NVqaXiH1IwU7l4eL9UTj1kVhXq1eoXhKUCFSMTAEJsYgZwV9Q5Fpmgkb8CABpFeIVIIKkYrBuG2gjDK1uselz7Hqxw9yDKtwoSGCFd1DmCI7RCoGg20JjYfbPBn8INOwCirr6x6m0wYVIhWDcWtDbB+KMrX6gzIqgZJjWAWV9XUPnWdQIVIxHrcEkJefQA+4CvqYS+s3OYZVUFlf9zCmElSIVIzNZkOj0rdgVdA3FLlnqyABpD+IVIIKkYrxuDYjlKnVMXlSPykpLvvgGJAcwypsZX0kgPQNBWplh0jFeLxv/YPeU2dkSP0IQwh0b2HDCnhYhYt2kADSGYypBBUiFWPDPBVdY1M/EmeoYOEQxQYaDoe0s8k+CSXgdAadZ1AhUjEe1+8blKnVKy71I6WCPhYOsTIyiMNBHA7JL4CtlfXKQ9k3mjOl/7A1ZcAQqRgPZqYYgwwV9NPSXF7C4NVtA/7zsbWyXnGpH37wEfNWAoZIxXhSU1suDR0OkptLUKZWpwLdPJkbUDF4mCITbK1sFJi3IitEKoB2pEMybJ7MzVAxeOpHJthaWZfYZect3SmGq2WFSAVcIhVUetAHruv0e0yF29UQBeNkgq2VjQjXggFDpAJoRzoUaN6GW98sZUwGPGPfDiSA9IHPtGJjZbkhUgFMsdWbQFM/Npsc03HBMy6NhgSQDmGSitwQqYALRCo6wIUZfneVXKSDGSpyQwJIZ9huk12LDnJBpAI+tiyE0MPNMJGS+uEKxmFARW5s7IcEkA7w3aaHGbYQEEQqgOJvusK9fX5f4WFAJfiwtbKeYFKKAhCpAOhKoDNM/vSnwJ4PoiABpBvl5Wb2x5gY1+AFLUgOiFSAENd+88CBSNWOAwITaOrHZiN79jh/xIBK0CABpEsophIkiFSAEIxY6kWgqR9uQAZ1aYMGCSDdKChoI9z20JGilL4cEKkAIa4NrKwsXLXjgMAEOheWbsInPB+CCVsr6xZWKcsNkQrwysrMrT8ItEe2urJ0TyhUexOPbpnrZxaHPcFIAIUutsNsaXTI/sgNkQoQ4pom4CaIQagINPXDwZiKGCkpxGRque3nwAgSQPrAd5hYCxQEiFSAhzGVEIUyKCpgB0a4Bd4iIAGkA2yHmZTklvpBpCIHRCpACD9PBZFK6MGWgupITQ1kwTESQDqADlMBiFSAkOxsLu5H2ws5Mqd+QDxuwbE/cxS4BBCClZDDdZUxMYQkJ7fM9HI4SGmpSselN4hUjCotrWUaoMlETp3CCGWo++c/nbeR+lFUYPNN2HeKLcIOoQgdaZAgUoGW63G2jWFyX2ix2cj77zt/RME2pbHBSlqaX09FCbiQxo6pIEwJHkQqRoVWpSNYFKkybkW3P5E+N/qFi4TQgsopykCkYlRs5USbjbj2mKdOKXw0EBCs+lEZd9L9nFeLFUChC12lMhCpgIdLclyjhxCs+tGErCznbT/n1WIFUOjCXoTKQKRiVOxIpc1GsFokZGHVjyZwQ//+ZHFQAi504aJOGYhUjIqL/10bHPrKEILUj1YEMK82gJosoBXYizB4EKlAC7dBFggNbFiJMEVNAcyrxQqgEMW+yZhRGzyIVAzMdV0y18wQrISEvDyXdwqpHzUlJ0seG0ECKBRhhx/FIFKBFmhmoYitFRYT48+Yis3m3FoP5BLA2AgSQKEOXWjwIFIxMLd1ySj+FnLYt4m7Lhf1TFqkGOQSQHl8JIBCDoqpKAaRChBCkOwJSdzevf6lftjL9pQUmY4IXIMVJIB0DZGKYhCpGJhb20Lxt9ASUOqH/SZE+X0Z0YCRblCXm+vXU5EACi3oJBWDSMXA3MrUsjDIon3SUz+Zmc7b/sU40JrUVOJwSHsq+z4gAaR9KPumGEQqQAjxsEkhaJ/E1A9X1Na/GAeCiFvmjKsFjcMbpBhEKgbmVkGFHWRBmlzjpA+LcCUgsLJZM7hlzuxbDBrX0nnSKer0H/pQ+SBSMTC3Cioo/hZCpKd+2BkQcXEYttYUJIBCCF/2DfVVggaRioHFxLTM+6P/YmLQskIFNyPWv9QP+8w//EG2YwI5cG8lLhg0q/WwBP2pfBCpgBPK1IYKdljEv9SP9GeCElJTUdYoJPFjKghTZIVIBVwgARQSpO/1g12CNI99W9iF6KApHsIS9JhBg0gFvEK70yYugcMtGPGFKxXnxzNBOWwCKDsbzVCjPLwvbH0VjKnICpEKuEDxN+3j5vEh9aMzSACFhFbCEkQqskKkAi569XLexsWcNnHxhlgooxI6kADSPrZ7HD3a7S5EKrJCpAIumprUPgLwSXodfC7wRBkVDUMCSPvYN6Wl28T7FDSIVMAFir9pnPTUD1tHLDkZqR8tw26F2seGJS2RpYe7QB5ajFQuXLgwfvz4ODfp6elqH5r+Ye2PxklP/WAubUhhgxUkgDTIQ/eIHjNotBipnDt37vz5823bto121aFDB7UPTf+4K200PU2RnvqhVf6E25ikonlcAgg0xUPZNxSoDSaz2gfgwfnz5y9evPjss88++uijah8LgIZwM/b8TuDQYCUlRbYDAr+YTCQ5meTminlsaipJS3P+mJ2N8FJDuJYYE0OIzfURiFRkpcUxlePHjxNC4uLi1D4Qg8IKSc3idiWUSNw3JcgmO7tlyzpCSF6e+IFKrAAKJVj4E0yai1QcDkdRUVHHjh2jo6PVPhaDio52rv9BSRXtwFSTUMUVSBG9RTL7FiMBpCls4Mh2mBAkmotUamtrz5w5ExUVtXnz5pEjR8bFxSUkJCxZsqS8vFztQzOK7t2dDQ/zVLSDey+QCwglkrZI5t5iBCvawTbGlg6TDV4wpiI3zUUqFy5cOH36dGlp6TvvvNO/f/+pU6d27tx506ZNkyZNOnLkiNpHZwi4RNAmdtUPlhiHGG4ETHRWFQkgbWIjFXSYCtDcjNrq6uqwsLARI0asWrWKLvZpbm5es2bNihUrli9fvmbNGovF4vGJOTk5OTk53J0rV67s0qVL0A9aX371q8uEtJzk3bubTp8+q+7xhK6GhoYLFy7I9Wq7d3cTGuwtt9hPn/5JrlcOCdXV1SaTqaamRu0DkaRnz27R0eayMvpT/euvV/bsKeZ5EyZE5uV1orezs8kLL5yW5XDOnj3b3NwcFhYmy6sZUH19J0Ii6e2oqKrTp38ijzxCHnnE+YjT8rxTenX+/PnFixdzd5aVlS1cuNDj400OYe2ihtXU1KSmphYXF7/99tuDBg1yf8Arr7zi8Y/s2rWrIgcYwsx//jOxWuntpocfJllZH3zw44MPOs9bYyOuGCSqr6//8ccfZZlxlZdH7rrLeV3x2WdNRhtWuXjxosPhCN1SBea5c9n8TVNjo8gnhofL/76XlZV17drVbNbclWqoYN+Uf//73JQp16l4MCHq3Llz3D10rMFjsBIan9SoqKjY2NjDhw9XVlZ6ewytuaLkUekEU7fBnJ9PzOYRI1z60LIyM7Ku0pjN5rCwMFm+D/7zH+ftmBgyenRotFwZ0dMYwl+uWVlspGLOzxeZw4uJceYa3n3X3LLFTGDoxzKET6aquBljN97owJmUwK/va83NUyGE2O32hoYG9/tNJhOGK4MLE2i1ip3YgLm0oYoN+dlpRz5JmowLQcRNUsE8FQVoLlJZsWLFwIEDs7Ky2DsrKysLCwuxdDkoPA2YsG0PJVVUx61Pxo4ioYotKiw66ODeblxNgAFpLlJJSUmxWCw5OTmlpaX0nrq6upUrVxYVFY0ZMyY2Nlbdw9MhLlKx2dzvA3Vxe/0YbYaKfkhadsxVY8GVg+pQTEV5motUhgwZ8uSTT5aUlIwbN27evHnp6ekpKSkbN24cNmzYwoULkQ4MCrdtCdk7sDZSdeyXE8KU0CZp2THWKmsWu/k8BI/mIhWTyTR37ty33norISEhNzd38+bNZrN56dKla9eu7dSpk9pHZwA2G0Hz0xKUptUVSXVnud0KkQBSF9seMfysDM1FKoQQk8mUlJT0/vvvFxcXl5SU5Ofnz50711sZFZABe8l26hTB1j9awnWLGFMJbUgA6QsiFWVoMVIBNbllf3ABpy5ukopY2DBZs9hgBQmgEIQxFeUhUgEPrc3TLFtQAZf6YdeOtP40un8v3cIXtINLAIlrXVwCCNTCvV2IVJSBSAVcp6Vg7Y+WcDvJi0394KJPy7h3UdwbhN0KNQKRiioQqYCrX77kkBfXgldfdd72o0+UmDECpaSmEoej5Z8/TxIgAaQFaFuKQaQCnle+ohGqzmYj7J6bYlf9SMwYgYJcK1uKJGnZEMiMjRHRSSoGkQq0XvwNF3Cq4MaZxRbRx2IhneLeSYx0qg6RimIQqQAhxKXNmcvLCRqhBrABoh/xBlI/+sV+DERvHARywhwwVSBSAZ65rIx4mGULSpNSmhapH11DAkhTaCcZuXEjVtgFGyIVIIS4fBOGl5Vx/4lxZuVJ3JUQqR9d4zKAuIRQnvuYSkuHSSsCoI5RcCBSAR4dU+G+49AnKkziroRI/egd+65mZqp2GMbU+hJlNLrgQKQChBBCsrKEZZM//e1vBC1Obeylm9i5tEj9GAAbs+L6QV20k4w8cIC/C+SGSAW8QkkVtSD1A96wH4a8PAQriuIqMXqAzV2DA5EKeIXLA7VIDDnY1A/CFJ3CboUq8lhMxcxO7EOnGRyIVMArlFRRi5SQgxuHEVsnDkIPdivUDnNZmdltCQLIDpEKeIXLA1XIEHIg9aNr3G6FSAAppvXCAWh3wYFIBbxCSRVVSNyVMC3NeRvdpa5xM6yRAFIF7R6R+lEGIhUQBb2hYtilp2K7PqR+DAa7Faqi9Rm1EByIVMArXJkrT2LIERPj3JgXqR8D4BJAoACbzdPQMnYsVAQiFfDK08aFEFwSdyUUOByktFSugwFF0SKnbBbPO+6DgWBFeR4uBxCpBA0iFfCFbXqIVBTw2WfO2xgZMYrsbOfGMaKnyLIfj+Ji2Y8JeJ5TP9ixUBGIVEAsRCoK+OIL523MNjEKSVNk2RLEL70k49GAZ63neVD2LWgQqYAvqNygpLw8XKEZlf9TZLEzlyZgkq0iEKmAL2h6SuIu2pD9MRBJNVKwW6GSPBdTQYSoCEQq4As7nImFysEmZVdC0AdJCSA2lkXzDDY2JmkJLFvfWxnkgUgFfMGMWsVI3JUQdMP/BBD7IfG8hhZk4vn0cqkfRCpBg0gFfEEuXDHYCNno/E8AYbdCtbQ0z+Tk+rq60//7n7oHYwSIVICRkkJMph433GAODxdKNKArVAY2Qja6gBNHnOInAAAgAElEQVRAmPMePK1MnEUdoyBDpAIM7J6sElTDB0ICTQBht8LgQSladSFSAYanJoiLNgVI3JUQdMb/IvnYrRCMoCVSqaurKyoqamxsVPdoQGWedk/GBYQCpOxKCPojqUg+ditUgOclyqCUlkilpqZm7ty5Q4YMefrppw8fPtzc3KzuYYH6folUsFA52JD6ASd23x9JCSAINpSiVV5LpBIZGTlw4MDGxsacnJzJkyfffPPNL7zwQmlpqYPuzgoG4WlRMhYqBxt3VnHFZmh33OG8jQSQZqB4tLpaIpVrrrlm9erV33777bp16379619fvnw5Ozv7zjvvvO222/7617+WlZUhZDEET4uSsVA52Ngr5+Rk9IPGJikBxDZSdhEZyAIF3lTnMqM2PDx81KhRa9eupSHLhAkTLl68+I9//OOOO+4YPXr0m2++WVlZqdaBgoowrBJUUlLgaWnEZHJuwAt64v8kdjZjiASQ7FDgTXWe1/7QkIWOsuTk5Dz44IN1dXXLli1LTEwcM2bMBx98YLfbFT5QUEhr5VMQqchLSmlam835dWQyYccXvfE/7sDeC0GFXQhV18oq5YqKikOHDh0+fJiOpjgcjhMnTvz+97+/7bbb3nzzTawV0iEsVFYWO1Yvdn0yFy2i8L7OCHGHw0FEp92xW2HwnDql9hEYntn9LofDUV5evnHjxi1btpw5c4YQYjKZBgwYMHv27LvuuosQsmvXrr/97W8vv/xybW3tb3/7W6UPGYKK7fCuXHG/D+QlZVdC7Lmse/7PC0xOdo6/5OWRjAx5D8jQsERZdc5IxeFw2Gy2TZs2bdmypaKigt4ZGxs7ffr0KVOmdOjQQXjklClTevToMXfu3E8//RSRip7t308eeYRgoXLQSNyVEHsug5ukJJdIxWbDBUZQYImyKloilcrKytmzZ//www/0x+uvv37GjBn33Xdf9+7dPT4tNja2Q4cODQ0NCh0mKIbt8LBQOcik7EqYl4c9l8FdairJzHQ2z7w8BLGywRJl1bVEKg6Ho7a2tmPHjvfff/+sWbO6d+9u8rmsoLGx8cEHHxw8eLAiBwkq+aWBui9URnOVBTdJRRSkfsALNgG0bx8iFXlgibIWtEQqUVFR7777brdu3cLCwsQ8rXv37o899lgwDwxUIuKbD5GKLLjUj9iJBUj9gBfseGh2NsnKUvNgdANLlLWgZe1PmzZtoqOjRYYpoGdcQ0QCKGik7EoocWILGIKkonHQCs/dnc1GCxpFtmmj8PEYE/ZSBjeeSqqw36NYsycLKbsSSlnTDAaC3Qplx3Z3znbKxC892A0QIDgQqYBPv/R8GFORl8RdCbFcEnzCboWy89zmmE6wKTpauaMxKkQqwDv9+edNjY1c1Sl2bR4ilcBJ2ZUQey5Da7BbYVA5u0EMLCsLkQr4Dd1f4KTsSihlTTMYDnYrlJfnJcrMpUb98OHKHY1RIVIBUbhrNQyrBEhKGkfKmmYwHOxWKCOvS5TRAyoLkQpIgXYaCIm7EkpZ0wyGg4sKGXldosz8R11ionIHZFSIVEAsTKqVS6C7EiL1Az6xTRUJoEB4XaKMHlBZiFRALCxUlouU4m1S1jSDQbFNFbPKAuF5ibIrzFNRACIVkAJXFJJJLN6Wm+tcjYXUD/jEfqjoboUgDZYoawQiFRCL7f7Q90kW6AoehwOpHyMymVr+iZglm5rqsXwjBMS5RBndn+IQqYAU6Pskwwoe8FtKivO2uNKzbDSLYrWSeV6izOSEMKaiDEQqIBbWFAQOK3hACv9XHnPFatFaJRC1RBl7bykCkQpIhL5PAqzgASn8Lz2LYrWBE7NEGZSBSAX8gIXKAcIKHpDI/5XH2K0wQF5PGtv34WpDEYhUwA9IfgcCqR+Qjo07JCWAIBAu1xW4SlMcIhXwA4YBAoHUD0jHzYcQ8WXJJYAQrPir1SXKhKBPVAgiFfADu6MyOj5/YdUPSMftYylu4gkGQQPheeIs+y64zF6BIEKkAq1hSjhwwwAYBPWLlF0JAQT+xx3YrVAyXxXzaQ1Gh4OUlip5SEaGSAW8SEtrqTRFnPUDcP0gGVcqFGsbwW9c3OF/AggrgMRDrlZTEKmACEyrRe1LadhrYHR8IIWkBBB2K5QGA8aagkgFvPBSPB+Zb2mk7EoIwPG/+bHPQAJIPDF7E4JiEKmACF7GVEAkibsSAnD8X3ns/5ohIASzyjQGkQp44aXKG5b/SMCt+kHHBxL5v/IYuxVKg1llmoJIBbzwss4HYyoSSLk+S0lpmc4MwPK/9Cwytv7ytfAH1IBIBcT5peFiobK/pJSmFZ5Dl19h8AoE/ieA/F8zBC4wCKo6RCrgnZcEEAaT/cJtHC9qUAp1MMEbdkzF4RDzDElrhgyNW6IMqkOkAt6xlxLMVHgvd4NnUkrTsmP0ycm4pgMXQuUx0ZAA8gtXUwBUh0gFxPEyZIyRZN8k7kqIhQcgKy5lhGbrG9qf1mg0UikvL1+wYEHfvn3j4uJGjhy5fv36xsZGtQ/KeLxcTbC9HkaSfSsvNwu3xa76wZpmkBu3ZujAgUh1jiMEsasdQS1ajFS+//77SZMm7dy5c8iQIZMmTWpqarJarRkZGQhWlMa2Uea708v0FfDglVc6CLfFDiNjTTMEARusFBS0Ue04NI+7UkD2Rws0F6k0Nja+9tpr1dXVq1at2rBhw4oVKz777LORI0du3ry5oKBA7aMzGC8hCZb/iFRWZi4ocF68IvUDKmLH5nJyLOodSIhBE9QCzUUqJSUlBQUFiYmJyb98QKKiohYuXBgREbF161aHP5PIIFDeQxIsJRCjrCzg1A+7wBQgAFwC6J13zJ4fZ3hY+KNBmotUjh07VlVVNXTo0DZtnOOTsbGx0dHR33333U8//aTisRmdl2EVLP/xJjPTeVtKl4fUD8gKK4DEwMIfDdJcpHLu3DlCSN++fdk7IyIi2rdvX11dbbfbVTouoxIxJwXZH4+4wRGxIUdamvM2ukmQFVcCDjzy2mzz8loqMZpMJDZW4aMyOM1FKqc8XaG3bdu2a9eudru9urpa+UMyNC+DJ142WgYn7rSIWsEjcU0zgChcAgh5W/9gsEU9mktVelzgYzKZrrqqlaCqrKysrKyMu7Nr166yHZlhNDc3NzU10dv089EkvCm/3M9+cvLySJPzfmixb5/zFEVHN40cSVo9SWYmummKjiZinmMYTU1NDocDn7QAxcQ4P2X/+lfTyJFqHow25eU5W+6IEc5PnJmJ7JpGjKBts+kXih5i6KPJE/E0F6mEh4e73+lwOK5cueL7iQcOHJgxYwZ358qVK7t06SLbwRlDRUUFISQsLIwQQl54gbzwAjl7lnvMnXcSQnoIPx46VBkdjbbqYufOToS0LPyZNq3+7NnWp1h1WrrUuVIoJuas22k3surqapPJVF9fr/aBhLYnnoh8+ulO9PY775hfeum0usejNTYbYXu2tm0rz55t6dk61dcLzbO+vv6ns2cJIQ0NDT/99JPZrLlvUu176KGHuHvKysoWLlzo8cGaO783eqqzU1tbe+7cOYvF0q5dO29PnDx5src/EvzVrVu3VtteTIwzwXH8eLfbbgv2QYUSm42wa+rvucfSo0dr60Jdn2N+9NEePXr4eLjRREVFEULat2+v9oGEtvR08vTTzh+bm3sgj8E6edJ5OyaG3HZbN+fPzDCA5Z57LD16EELq6+uvvvpqNFUJPv/8c+6eV155xduDNTdPhUYqJ06cYO+8fPnyxYsX27VrZ7GgDACEAK5ylNj1ySx8gUBwsJ8stsogEB9zUWw2zMhTkeYilV69el133XUFBQV1dXXCnSdPnrTZbP379+/QoYOP54KSsOLRB/YLYO1acc/BroSgiOefd962WlU7DG3yWkyFC1PQPJWluUglOjp68ODBBQUFu3fvpnXeampqVq9efeXKlYkTJ5pMJrUPEFpg+Y833AoeOuGndRkZzg1y0Q9C0PTs6fIjGi9LVNk3jHcqTnPzVNq0afP4448fPnx48eLF//73v6+//vr8/PyKiorp06cnJiaqfXTgGZY7sgLdtweFmMFfwiVcaWmr36PJyS6TzNatw3J4J697g2KJsqo0N6ZCCBk8ePCmTZuSkpK+/vrrzZs3m81mq9WamZnpcVkQqIWrzYArMwHb2Q0fjrUqEGRsFTJxFw3sxxKXGQJfU8XY/8OQp+K0GKkQQmJjY9euXfvDDz+UlJTk5+fPmjULYYoGYfcfd1zqZ8qUGtUOBQzC/yljiYkukQouMygu9eNrngooS6ORCoQETKp1x6Z+oqObMKYCQcdmKbKzxXynTp5cwxZAwmUG5SvDw55VUQWnQU6IVEA6pGvdsZ3+iBGohgfBl5oqYXiTvczAWmXK644/WKKsNkQqIB1bpQ8bnhG31A83lQcgWPwf3mTHBZAAosSOm2CeiuIQqYB0mFTLkVLwDSBwXAJIBEkDMXrma9xE1NplCCJEKhAQdHYsdhQdYQooh7toEBesYJ4Zi4tGXNovliirDZEKyObUKbWPQFVc6mf2bNWOBIwoJcV52/8EkLiZuHomdjotIhU1IFKBgLBXHgbv6ZD6ATXNmuW8jQSQ/7xOpyWIVNSHSAUC4n9+XLe40rQAiuISQP6vAEICSMCuFSCEkNzclp0uHA4U9FUFIhUQwWYjJpPzH4P7SjbysAr71YDeDFTg/y7JSABRXOoWVxpag0gFRPAejyDHQbHjSUj9gDrYAFl0Aohl2ASQr+m0oAGIVEAc7wltpLqJ6xXsLbeodxxgZJJGONlgxbAJIMP+4aECkQqI4308FKlubuj4ySdVOxIwNLpLskDcdQMSQARTZjUPkQqIwzZf13iE7emM2c1JXPWTkuJx6g+AdP5fNyABRLBTsuYhUgFxxF1oGLObk7LqhxuHMeaJA9lJGiExeAKIa4vYf1CDEKmAON73+DF4TX2umxO76gfVVyAYhBopdEmtuMAZCSAW2qIGIVIBcXx2eUaeVCsx5ED1FQiS0lLicPj1DIMngDBJRfsQqYA43Dew62WXkSfVStnrR+I4DECwGDkBhF19tA+RCogmbqGyoUjc6wfVG0BjjJwA8lVHH7QBkQqI5j0e8T6JReckpn4yM12eBqA2I+8BhOm02odIBUTzvlDZsJNqZUj94CIOtMGYOVyus8KFgzYhUgHRMKnWlQypH4KLONAKYyaAuEwsIhVtQqQCorE5HrdghL0gM0hr55bviB0cYS9Xk5MxpgIaYeQEEGWQjisUIVIB0dh27HbBdcMNztvitnENeRJzOEj9gFaxn0eDtGJ2zhjfHG02kp1txJBNexCpgGg+FyrHxjpvG2FSrfTUD+bvgVaxn8e8PEMkgFppjmlpzl0vQD2IVMAf3keHjTapVmLqR+LTAJTAJYB0P6zSynRalITTDEQq4A9a/pL+42ITg02qlSH143YCAVTHfpitVrWOQiFclQE+GkFJOM1ApAKyMc4qx7w8pH5An7gPs74vOVrZ0wJTyjQDkQrIhlvlqGPctZbYTgy7EoLmJScbKwEkQHPUMkQqIBvuokSvU1XoggCBHzkcKXXiAJTGfqR1fMnR+hAnRkA1A5EKyIb78tXruLHN5hKE+dGD5ea2TPEh4jNGAPIRd/XA7Zip44Ys8DDEieK1WoJIBeTEtvZTp1Q7jKDiCjBIGRxxODCmAsqhi2xNJvFBhxEKq7QyXxbFa7UEkQrIyWdxOD3Apj0QYtLSnLdFT3Rnh/z0mgBqpSFj4Y+WIFIBOel+Ui13oYUcDmidpDbJzb7SZVtuZRYKiqloCSIVkJPu67+xqR8MCUMIkBp06LvoQOuzUBCpaAkiFZCZjuu/cakfbuIhgEZJCjq4BJDOrjq4SiqtFFPBwh+1IVIBmen4Ugz1UCAkSZp1wo3F6Oyqg2vLPCz80RhEKiAzHU9VaaWiJYA2SQ062Ofp7KqD5eGSAwt/NAaRCshMr/XfuNRPVpZqRwLgN0l1Z/WaAGq95hsW/mgMIhWQmV7rv7We2AbQLEl1Z7nK+ux08pDWSs030B5EKiA//Q0ao4wKhDZu3ED08Aj7UddNMrf1ERO0do1BpALy0994AxepoIwKhBjX4ZGonByRz9Pl1sqtxyHCxhcOB9b4aQEiFfCfzeasz20yuV+f3Xij87Y+rsO4Miq4yoLQw3xqIw8cEP8knVXWb32SCmgPIhXwX2tjJjqr/4YyKqAHzHdyZEGBuaxM5PP0XVkfVx0hAZEKSNJafTc91X/jSi9wcRhAaEhNldYsdVZZH7UGQhEiFZCktfpueqr/Jrlrixw3rscNN8h9OABSSW2WbLAS6gkgTJYNRYhUQJLWvrF1U/9NeupHeCadzRPqI0ugA1yzFJ2XZZ+XlxfC+VxMjQ9RiFRAktYmzepmxJgbUPHjIgy190FrmGbZ1NgofoSQSxyFbmEVVFIJUYhUQBIRTVwHCSCbzSXG8q9fQz4cNMjhIA7H6f/9z9/n6aOwCmrPhihEKiCJiJr5bNcWuqkP9i/zY6wY64VAX7iPcIgmgDBJJUQhUgGpWltHwCaIbLaQ7NrS0py3ucISfsAoM4Q+7lMcigkgVFIJXYhUQCq23zp1yv3/pS6K1IqAJt+xMQ5GmUEX2GGVUNywEJNUQhciFZCK/QL20mmF9FQVbp6JH2VUsMAA9Ij7ag+5YRWu0jSEEEQqIJWIhcihu1bZZiNWq/NH/y6/uGs3lIoDvZC0JbNWsO0SAyqhBZEKyMTTsEroltXnDtW/YRHm2q0pOlqW4wHQAm5ebQgFK9xUOUxSCS2IVEAq7qrESxgSolNV2IFi/+bSuqZ+7JMny3dQACrjpneEUL1a6YWRQAMQqUAAdDpVJaAlxq7noW74cDmOCEAr2PHFEKpXi/XJIQ2RCgRARBgSilNVuJl3kgu+1ScmIvsDOhOK9WrFznFPS2vZ+wI0BpEKBIANQ7xcW3FTVbSfAAqoLi33ZCTDQY9Cbl4t1zl5bdTC40ym0AjBDAORCsjB4SC5ud7+k70C035im9uux7+5tGJ7RIAQFnLzatkBX19hCgrDaRUiFQhAairdRsT3o0Lr+zqgmXfsk6UXtQXQutCaVytlkgoar5YgUoGgk7rVvAry8gLbrkd63ggglHDzarWc1RU7VsKVQQItQaQCQRdCZfUDmktLWjaqbRlkwugxhBZ/WibXqLU8rMLlc702auyzrGGIVEAJIbFWWc79jx0OjKlAaKCrXUwmf8ONUNkGiEvJeoV1zBqGSAWUEBIJIG5ABUXwQf/YfKWfM2O5BqLNtTJ+7MGF6bQahkgFlKD9BFBAi5MBQlRgVQTYvbG0eQUiNvXDHTqyPxqDSAUUovHFAlyPFlDqByCEBDDfhGsmGmzXYlM/3HRaRCoag0gFFMKOp2qtCLfNRtLSnD8mJ6OnAsPg5pv4iR2UYYdYtMCP1A+m02obIhVQiJYTQNzB+FftDSCkBZYA0nIVOD9qI2E6rbYhUgHlaDMBZLOhYBsYWwAJIC4C0NS8Wj/CD3aMF9NptQeRCihHmwkgORcnA4SiwBJA7LO5mekq8iP1Y7NppTMCLxCpgHK0mQAKtNobQKgLLAHEDUNqZLjUj9QPN50WXYD2aDFSuXDhwvjx4+PcpKenq31oECit9WhcIfCsLNWOBEBNgVWc1WBxfT9SP5hOq3lajFTOnTt3/vz5tm3bRrvq0KGD2ocGgdJaAggDKgCEyLACiP2KV322ih+pH4LptCFAi5HK+fPnL168+Nvf/vZzV88995zahwaB0lQCKDsbM1QACCGBJoCIa/NRfVgloB3RQXu0GKkcP36cEBIXF6f2gUBQsL0GW8VEYdySH5TPB6MLLAGUmqqhpu3fKElurnNvUVyvaJLmIhWHw1FUVNSxY8fo6Gi1jwX8IexzZjL5Tupwc0HUWimAGSoALgJLABHXJIuKi4C4SAVNWwc0F6nU1taeOXMmKipq8+bNI0eOjIuLS0hIWLJkSXl5udqHBj75k9RRfV6t+4CKlPFhLcwbBJBLwAkgblhFrdkq7O9F3kcfNBepXLhw4fTp06Wlpe+8807//v2nTp3auXPnTZs2TZo06ciRI2ofHXg3dqzzNjuX3hPVVwrIM6Cybp1zGAlABwK+hlC9tgrXtJHM0Qez2gfAq66uDgsLGzFixKpVq+hin+bm5jVr1qxYsWL58uVr1qyxWCwen1hQUOCeMLr77ruDfsS68/PPP9vtdrPZv8+GedCgyF9uN+3eXW+3+3jwlCkkM9Mi5Ij+9a+moUPr/T9SicrKzJmZwsGSkSObhg71fbwemMvKIpluuH7Jkqbnn+ceU19fX1tba/f3pcETehr9/ViCR97auHnatEjhez472756tb+vPHQoGTkyMj+/5ZXT0siUKYp+/jMznV8Q0dFSmrZf0MalOXfunPvQQ1lZmbdZH5pr9gkJCZ9//jl7T1hY2MMPP7x79+7CwsKTJ08OGjTI4xPLy8s/+OAD7s6ePXt26dIlWMeqU3a7vW3btmFhYX49q019vfDlby4rq/vhh6bu3X08fuHCpkWL2tPb77xjXriwrnv3JimH67+dO9vYbM5I5Xe/s9fU1Pn7IubCwkjmx/rExLqaGu4xDQ0NP//8c43b/SBBbW0tIcTfjyV45LWN33dft/nzL27ZUjd8OCGESPro/u53Tfn57YUfrVbyu98p1ARsNpKX54xUpk2rD3brQxuXpm3btu7f1+Xl5d4iFZPD4Qj+UXlgt9vnzZtXUFAg3JOYmOhjyCQ9PX3z5s1r1qwZPXq0+/++8sorhJCFCxcG6WgN5fTp0926dZNy8comQbKyWl1Lwz48NVWhiW82G4mNdf6YnExycyW9UEqKc5TZy6vU19dXVlb26NFD0i8AFxcvXiSEtG/fvtVHQqukt3Fx2MZBCCktVaigWmamcz/nmBhSWhr034g2LiMf3+Oam6dCCLHb7Q0NDe73m0wmXFFpGtsbnTrV6sPZSEaxfDa7eDImRmp45F9hKQBj4WaHKLNi2WZzhikEc2n1RbVIxWKxbNiwoYSxYcMGi8WyYsWKgQMHZrl+gVRWVhYWFmLpstaxfYOI6rPK7xfPzbZLTpZ6qce+CiqxALhKTnZpE8rMmud+BS4f9ERzYyopKSkWiyUnJ6f0l5G7urq6lStXFhUVjRkzJpYduAetYUvli4g7FN4v3maTaUCFuJXABABXWVkuLUOBYRW2UXKbJkKo01ykMmTIkCeffLKkpGTcuHHz5s1LT09PSUnZuHHjsGHDFi5ciJn/msYNLYgYVuFKRQX1wmvdOpcjkr58kTtQrIME8IRbsRzUYAWNUt80F6mYTKa5c+e+9dZbCQkJubm5mzdvNpvNS5cuXbt2badOndQ+OmiNn5v6cNsABa8vc89hS8/YcKkfXLsBeMIVguO22ZKR+3ApGqXOaC5SIYSYTKakpKT333+/uLi4pKQkPz9/7ty53tYEgbawPURr9d8odn6+zRaUHJB7RxbQJRdSPwDicAnWIGV4163jlxqBzmgxUoEQ5udUFYoNb6xWMVkj/3AdGXep5x+MMgOIFhPjMpaZlyd/sIIlP0aASAVkxY0xiAs6grqmMS/PpSOTeUAF/SKATxkZ/KWIvDkgOYdLQasQqYCsuG9ucX1ScjJ/4SVXX2azkZQU548yFIPybzt5AODLInJ14QLBzX3xY8lPXh626wohiFRAbmxXIaL+G5WRIf/UWvflBoHWPeFiKFRsABCHvRQhMk1Y4aa1+Vd3gM6io9uLslczoEmIVEBubMThz5QTtpeRZWqt+/SUQEeGT5503kbqB0A0LgeUlydDeBBQ3QEMjoYURCogt6ws4nC0/POntho3chtgPjs7m5+eEui+QjYbmTPH+SPq0gL4IzeXD1YCKUvNNXC/6w6wnQu7DgA0CYXUQEOysly2D0xJ4Xs3kdiNygghMTFStyFkxcQQh8OZ25a1dysoKDhw4ICML6g/9fX1hJDIyMhWH2lAw4cPT0xMVPsoWsc18LQ0cuqUlJHO7OzAJtJyY72oNaB5GFMBDaHBAMvfyXc0bcQlxblJMAGhY0VyF+s+cOAAu684uIuMjESY4pFCYa7JFPj0MfdrBqvV71d1n39WWupnc+SKNyJS0TyMqYDmpKa6DAuLH1mx2ci6dXyYkpUVhESNDEM0vMTERI/bnQOoiR2+yM4OPOpPTiZZWS6hRnY2sdnENimbjXCbv3HtXRQUbww1GFMBzXGPLVJSWk9p0ystrtuyWjGfBCAAXPuRY3lxaio/aSwvjzz4YOvz77OzPYQpgU6Tx3TaUIBIBbQoK4vvQNLSSGys53iFxiixsfyYrgy9GACwwQo7GhHYS3KDKO+9R2JjSVqa53glO5ukpHgoOiClgXNlpjGdNhQg+wMalZvLT1KhEUlmpkvP6bFMHF3pg4slABkkJTkvEWh7k6NpJSe3tHFWdjbJziYxMa23cfeBGbHYUAi1BkIEIhXQrtxc8utf89de3DYf7uisPWSfAeSRmkoyM51f8OvWyfXtnpxMSkv5hA4R0cZjYwMoOsDunIpuIkQg+wOatncvsVrF9ic041Naiv5Hc15//fU4NzfffPOSJUvKy8vVPjpNsNvtM2bMSEpKqqioUPtY3LBDHIFUQXFDl/uJnxVL23hJSQC/EjXfQhAiFdC6jAxSWtpKvCLEKJiYomWjRo2azrjhhhvef//91NRUtYKVioqK5cuXf//996r89lDCtStZgxXCtHEf5GnjmKQSmpD9gdCQkUEyMkhmJsnPJ01NzvuvuorccQcClNAwc+bM0f+/vXuPiyl/HwB+phoazaDU6mZrJlG+RrFNDb+hWqFEqXWZXLZYtSyVyn1RWS+trEvIpUhil7SxGxEioyTlEnIJXXY1bTUpNZOGps7vj7M7xpQoNefM9Lxf+4c+c+bM0+yczjPP5+bkJP0RRdH9+/dv3RTymugAACAASURBVLo1KSlp2bJlio/n1KlTv/322+TJkxX/0srHweHdPZ7H6/I5ddjqbdg1fu0a0tLy7iENDYTD6aJrXG7UPdRUlARkKkCZQEaiSkgkkpOT0+HDh+/cudPQ0KClpYV3RODDvL3f3ea7YmGVD+neaxxWUlFO0PsDAMBNv379KBSKRCJBURRBED6fv3r1altbWwaDYWZm5ujomJCQ0NTUhPw3jCMkJCQuLs7CwoLJZKakpGDtW7ZsYbFYDAaDyWRu3Lixvr4eO3l6ejqDwThz5szOnTuxAzgcTkpKSnNzM4Igy5cvj4yMFAqF7u7us2fPFolErcPDTj5ixAgGg+Hs7Hzx4kUul4sd3GY8zc3Nqamprq6uFhYWWDy+vr4lJSWy8aSkpGzcuNHCwsLMzMzDwyMvL0/uRQsLC7lcrrm5uYWFhb+/P1HG8cgVUTqy+SiByNZU4HuP8oCaCgAE9fm7SePF3v5Ty+rPnz8XCAS2trZaWlrl5eXfffdddXX1jBkzhg8f/tdffyUmJoaHh/fu3XvWrFnY8enp6ffv39+wYUNlZSWTyRQKhUuWLLl+/TqHw/Hw8Lh3715SUtLz58+jo6NpNBr2lJ9++olCoSxduhRBkLi4uBUrVpDJZBcXlzlz5rS0tKSlpQUEBFhbW7deql8kEi1ZsiQ7O9vNzW3s2LGZmZn+/v4oitrY2EiPkYsnLi5u69attra2WNjp6ekXLlz4559/jh49qq2tjT1l06ZNFAplzZo1CILExMTMmzdvz5490k6xsrIyX19fV1fXOXPmXL9+PTk5uby8PD4+Xvrr4CkkBNm27d9/OzrK73xBfHJznaGmojwgUwGAoDqzTDgxhIV9PFNpbm4uKCjYuHFjS0uLm5sbiUS6detWZWXlzp077f8b5zh+/Pi5c+fm5eVJMxWxWLxu3TrpAQkJCVlZWStWrFi0aBGJRJo2bZqtrW1QUNChQ4ekA18YDEZsbCx2p2ez2XPnzr18+bKLi8vIkSNv3rx5+fLl//u//2Myma0jzMjIuHHjxooVK3x9fUkkkru7u5WVVfj7+aNsPLW1tTweb+zYsXv27KFQKAiCuLu7h4eHnz59uqysTJqp9OvXLz4+3sjICPsFvb299+3bZ2dnR/pv88vNmzd7enoiCDJlyhRNTc3Tp0+Xlpa2GaGiTZnyLlNBkK5aWEVxHBzebTIK2/0oFej9Ad2PROqS7c2AsvPz85NOUTY3N/fw8CgqKgoICBg9ejSCIG5ubnfv3rWXmY6hra3dp08f2TPo6+tbWlpi/25oaEhPTzcwMHB1dZXe5seOHTtq1Cgej1dXV4e1cDgcaUFCT09PT0+vqqqqoaGh/VAlEsmFCxeMjIymTp2KnZxEIrm4uJibm38oHm1t7WPHjh06dAhLU7Cn6Ovry5153rx5WJqCIIixsbGLi0tpaemLFy+wFkNDQ+muyCQSyc7OTigUVlZWth+tgshtzNlF69UqGrbJ6H9dckApQE0FdCe57c06v1qTwmE7oSldfZvYxo4dK71Ja2hojBgxYvTo0dIWjEgkev78eWlpaV5eXnZ2dllZGYvFkj5qYGAgzV1ev37N5/O1tLRu3br14MED6TEtLS3V1dXSXERD491fuV69evXv3186LKYdYrG4pqbGwMBAttuFQqHo6OjIHiYbD6a5ubmiouLx48fFxcVZWVl3795VU3vvC6GhoaHcGWpra8vLy7/88ksEQdTU1GQDJpPJ7cepaIoaVwuALMhUQHfy8ZHfNVVZNgzEvi9KC8V4fANTlreqNROTttvlZinLqa2t3bBhw7lz51AUVVdX//LLL0eOHFlTUyN7jOxdH0VRiURSUlKyfPlyuVPRaLSXL192/hf4ZHLxXL58efXq1VjM/fr1YzKZVlZWsllUm0gkkrq6evcG2lXkrujwcGX6+gGUFmQqoJt18zIM3UJuNW+cOuN71C0ARdHdu3dfunRp48aN7u7uVCoVQZCqqqrbt29/6ClaWlomJiYGBgYHDx7EjpfzOZ0mmpqaOjo6Dx8+FAqF0pO/ffv21atX/fv3b/Mpz549+/HHHwcPHhwREfHll19iycf+/fvlMhW5qJ4/f96/f/+BAwd2OlRF8/F5t/Jbj/qMAvzAOBXQzby93/27q5e27C5yMzBlfwXQPRoaGp48eaKnp+fo6IhlBiiK5uTkVFRUvHr16s2bN62foqWlNWrUqPz8/MzMTGkjn8+fMGECl8utra396IuSyWQURVtkVxn7j4aGxqRJk/h8/pkzZ6RdRdevXy8qKvrQ2f7++2+BQMDhcOh0Opam1NbWXr16VSwWSwfNIAhy5swZoVCI/busrOzatWtMJpPeevMbwsIm92KjPQBQCKipAMUqLVWCjm3Z+R1yowhB96BSqba2tjk5OcHBwR4eHgiCpKam3rx5E0XR169fY0uqtPbdd9/duXMnICDAzc3NwcHhxYsXiYmJlZWVwcHB0rk27TAxMRGJREePHq2pqWGz2dKRsBhHR8fRo0dv3bq1sLAQm6Wcnp7eejKz1NChQ42MjGJjY+vr662srAoKCk6fPl1bW9vU1CQWi6WH5ebmzpo1y9vbWyQS7du3j0QiLVu2jEKhtLmgCxFhW/UAoEBQUwHdzMfnvdSk9fbtRCO3MwgsD6Uo33//fUBAQFFR0Zo1azZt2tS3b99z5865u7u/ePHiQwUSGo22Z8+ehQsX3rhxIzAwcNeuXfr6+gkJCc7Ozp/yinZ2dtOmTfvzzz/XrVsnEAjkHqVSqbt37543b97FixdDQkIeP368bds26Uyf1gYNGrRv374hQ4YcPnw4ICAgLS0tKCjo2LFjNBqtoKBAetiSJUvYbHZoaOjWrVutra1//fVXa2vrT4kWgB6L9NEx8EohKioKQZDAwEC8A1EFL168MDAwkJ2A8Lnmz3/X7+PjQ/S+bdloP28srVgsFggEgwYN+uiR8AFWClVVVTNmzGCxWL/88ksnnp6enu7n57dy5cpFixZ1YVSd+PB0/TXeU336NQ4+qp1PMtRUQPeT3bCU4ENVSkvfixD6fXqw2NhYZ2fnZ8+eSVtu3rxZUVExePBgHKMCoAeCTAV0P7n5PkTuAJLbahXG0vZgo0ePfvny5cKFC48cOZKamhoeHr527Vo6ne7m5oZ3aAD0LJCpAIWQHapC2KUtS0vfi83cHGoqPdnw4cP37t2rr68fERHh7+//xx9/zJgx4+TJk3JLtwEAuhv0UwKFCA1VgsVq5cbSrl2LWySAGFgsVmJiYledzcnJqbi4uKvOBkDPATUVoBBK0QEEk5MBAIB4IFMBikLwvc2uXoXJyQAAQECQqQBFIfhitbIFFVNTKKh0ucbGxoSEhMmTJ5ubmzMYjJEjRwYEBDx9+lR6QHp6OoPB2L9//4fOsHz5cnt7+6qqKgRBUBQ9duzYiBEjGAzGt99++9G9kT9q//79n7JHjwKIRKLZs2dLf1MAAGQqQFGI3AEEq711M6FQ+MMPP4SFhdXX17u7u3O5XFNT0/Pnz7u5uZ0/f74TJywoKNi6dSudTt++fXtgYKCamlpiYuJvv/3W5ZEDJXb1KkIi/bvPKFBmMKIWKJDsboVHjhCobiFXUFGKbRSVytWrV69duxYcHLx48WLpvsGPHz+eP39+VFSUjY2Nnp7eR08iu95aZWWlUChctGiRi4sLgiAPHjzYvHnz4sWLuyl+oJSkvcwkEuLggGRk4BoN6DyoqQAFknYAoSixpv/IBkOc/EmFZGdnU6lUe3t7aZqCIIilpeX06dPLy8v5fH7nTksmk7soQKByYBVHFQKZClAgHx/ibsGKBWZqSqwUSlWYmJiIxeJSuU2qEWT58uX379+X3fhGLBbHxsayWCwGg8HhcFJSUpqbm6UH29vbl5aWzp4928/PD0EQPz8/KyuruLg4d3d3oVAYGRkpHWvS1NSUkJDA4XAYDIaFhYW/v79sPoSiaHZ29uTJk83MzJhM5k8//dT+SBeRSLRlyxZsWIyzs/PFixe5XO7s2bNFIhE2rCQkJCQuLs7CwoLJZKakpCAI8vTpU19f35EjRzIYDHNz88mTJ58/fx7bvaSqqsre3j4kJOTMmTNsNpvBYLDZ7ISEBLmNGAsLC7lcrrm5eev4iYtEerceAb7kPmyyK2UDZQO9PwDI+IxdfkA7vv7668OHDwcHByclJU2bNm3MmDEDBw4ktTWAYN++ffr6+kuXLiWTyYcOHQoKCiKRSFOnTpUeQCaTAwICrKysDhw48P33348cOdLExGTlypW7du1ydnZ2dnY2NjZuamoKDQ09ceIEk8n09/cXCATx8fE+Pj7x8fFGRkYIgmDbBw4cOHDDhg0IgsTFxVVUVHxon2SRSLRkyZLs7Gw3NzdsU2V/f38URW1sbKTHpKen379/f8OGDZWVlUwms6CgYP78+X369PH19TUxMSkoKEhKSgoKCtLW1maz2dKn8Hi8qVOnWllZJScnh4WFPX36NCwsDHu0rKzM19fX1dV1zpw5169fT05OLi8vj4+Pp9FoXfO/pGvJ7pZFkAWTYNEBFQKZCgBE1bnvph29SSjkVYYMGXLixImVK1dev349KysLQRAtLS1HR8f58+dbW1vLpizDhg2Li4vT1tZGEOSrr76aO3cudjuXHkAmk9lstkgkwg5wcnJCEOTt27fYPsYTJ05EEITH4yUnJ3/zzTebN2/Geog4HI6vr29kZOS2bdsaGxsPHjw4aNAgaeLi5OTk4+Pzobk2GRkZN27cWLFiha+vL4lEcnd3t7KyCpe9ESKIWCxet26d/X9f3Hfu3NmrV6+YmJihQ4ciCOLq6spms/38/PLz86WZyps3b37++WdsnI2rq+vatWtTUlI8PDywpyAIsnnzZk9PTwRBpkyZoqmpefr06dLSUiaT2aF3XkFCQ9/rapk/H+dkRW6MPKQpSg4yFQCIqnNzuTt6h+jEq3Sq8kSn05OSkgQCQWZm5pUrV3g83tmzZ1NTU728vEJDQ6UjTsaPH4+lKQiCGBkZmZmZlZeXi0QiKpX66a+Vlpamrq4+c+ZM6WmtrKwcHByys7PLy8tra2ufPXvm5+eHpSnYC7m7u8fGxrY+lUQiuXDhgpGR0dSpU7GMikQiubi4yM0z0tfXt7S0lP64bNmyZcuWyR6go6MjV7Nhs9kO/91ByWTyzJkzU1NT8/PzsUzF0NBQmtOQSCQ7O7uEhASsYPPp74PiYOPQZcsqoaHv7aGhYND1o1ogUwGgB3N07MyzPuMOpKen5+np6enpiaLokydPVq9effz4cTs7O2nVREPjvT9KamodHkvX0NDA5/O1tLSKiopkyyTNzc1CobC2tlYgEIhEIgsLC9lnyf0oJRaLa2pqDAwMZLtdKBSKjo6O7GEGBgZ9+vSRe259ff2jR4/++uuvmzdv5uTkCIVC2Ud1dXUpFIr0x/79+1Op1MePH2M/qqmpyb4VSjB2WK6sEh6OZ1kFun5UC2QqAKiQjt4bFLKqDTa2dMyYMREREdJGEolkaWm5adOm1v07nwlFUYlE8vLly7Vt7dwkEAi66oVkyWVUZWVlISEheXl5CIL06tXLzMxs1KhRV65c+eh5lCAj+RDilFXkun5gR3TlB5kKAET13+DKDujoSjCdeImO09XV1dLSunv3rkAgkFs3RVNTs3fv3l17e6ZSqSYmJi9evEhMTGxz3+MHDx7QaLT8/HxsjAvm+fPnbZ5NU1NTR0fn4cOHQqFQ2gP19u3bV69e9e/fv82nNDY2bty4sbi4OCYmZuzYsb1798ZeNDMzU/awV69evXnzBnsUQZDKysq6urrBgwd3/DcmjMOHCVFWkd2sA5ZHUgmQqQBAVApYKlchq/Hq6Oi4ublFRkZGRESEhYX17dsXa29sbIyLi6urqxs3btxnvoS6urqGhoZEIsF+HDNmTHJy8tmzZ7ExsAiCCIXCJUuW8Pn8gwcPmpqaDh48+Pz581wu19jYGEGQ2traCxcutHlmDQ2NSZMmXbx48cyZM9KzXb9+vaio6KuvvmrzKUKhsLCw0MzMjM1mY4lIc3Mzj8cTCoWVlZXSw/Ly8h49ejRy5EgEQZqamv7888++fftyOJzPfCtwhntZpbT0vfwb+n1UAmQqAIBuN2fOnIKCgj/++OPcuXMsFmvQoEEvX77Mzs5+/fq1l5eXbG2jc3R1dalU6rlz54yNje3s7JydnW/cuLFly5br1697eHjU19efOHGisLBw1apVpqamJBJp/fr1vr6+s2bNwtZlaX+WsqOj4+jRo7du3VpYWIjNUk5PT//QwQiC6OjoWFtbnz17duXKlRMnTqyvr09OTn7y5AmJRJIdqiIUCn18fBYsWGBiYnLkyJH79++vWrVqyJAhn7+HEZ5wL6vIdWhC149KgJXfAADdjkajRUVFRUdHDxs2LC8v78SJEzweb9iwYbGxseHh4Z/f+6Onp+fr61tWVhYcHHzz5k0ymbx+/foNGzb8/fffISEhP/30E4Igu3bt+u6777CiiLW19a+//jpo0KBNmzZFRESMGDECW1ilTVQqdffu3fPmzbt48WJISMjjx4+3bdsmO9NHjoaGRlhYGJfLzczMDA4O3rFjx8iRI9PS0uzs7EpKSqTJiq2t7Zo1a44fPx4SEtLQ0CAbnnKTLWnExyt6hy/Zrh8YS6sqSCgxFwztoKioKARBAgMD8Q5EFbx48cLAwEBuCgboBLFYLBAIBg0a9NEj4QOsXKqqqmbMmMFisWS3Iuro042MjGJiYjo0+7pNnfjwdPs1LptvTZqEpKV11wvJuXr1velsGRndnal8+jUOPqqdTzLUVAAAoD2xsbHOzs7Pnj2Ttty8ebOiokK5R792K9myyoULiiuryG01CgUVVQHfmwEAoD2jR4+OiYlZuHDhggULdHV1b9269fvvv9PpdDc3N7xDIypsbRXp8muOjorY7UtucrJCRosDxYCaCuhJCLJ3GlAqw4cP37t3r76+fkREhL+//x9//DFjxoyTJ0+2OQUa/EtuIK0CLj3ZSUYwOVm1QE0FEAaJhJSUdOOcRmwX+Ph4gm7mDAiMxWIlJiZ21dm++OILHo/XVWcjKGw0q7TIER+PeHt3e3cMdmmTSNDvo2KgpgIIgET6dwje+7u+daXS0nff6kgkhE7vrhcCAGDkyioKyx5QlBCbOYOuA5kKwFtQ0Lt/d9+cxqtX3zszVIYB6G6mpu+G1kIhE3wG6P0BeAsMRHbufPdjeHjXf/eSLaggCGJqSsDRdjk5OXiHAJRSTk6OdNdlwgkNJeC1BpQO1FQA3mS/eCEIcvXqe2tcfj65NAXp+DZ+3c/Ozo64NxtiEIvFYrEY7yiIiM1m29nZ4R0FAN0IaiqAAOTmNM6f35W9M0eOyPf7EG+0HZvNhkylfa9evUIQ5EObAgIAVBjUVAAxdNOcxvj49wo2pqYELKgAAABoB2QqgBjkdujokqG1rYenZGR87jkBAAAoFmQqgDDkqh2fOWO5tPS9HUAQBIcN6AEAAHw2yFQAYch1zchtNtYhWDVFOvAFQZCwMJiZDAAAyggyFUAkcsNdO5esYNUU2c4jBweYKgkAAEoKMhVAMHJ9QB1NVrA0RbaaAqNoAVAZspc26DEgUwEEY2qKlJS81/LpycrVqwidLp+mdOteQgAARTpy5N+dN0BPApkKIJ7Wk3Q+cR6Q3EIpMNkHAGVRWoqEh7dXMsHKpdiiA5Cs9DCQqQBCcnB4L8mQq7K0Q7q9CFRTAFAWpaUInY6EhSF0ehv5Cpaj0OnvfWOBTUZ7EshUAFHJJisdSjhQFPHx6UByAwDAl2zageUrcv/JVVVNTWEqX48Cq+kDAnNw6OQWrDCEFgBl0ebKSe10A7UeygZUHdRUAAAA4Cc0FCkpeW/Xiw/BdjOFNKXngUwFAAAArkxNP5KvSHMUWBipR8IzUxGJRN7e3suXL2/9EJ/P9/f3t7CwYDAYHA4nISGhqalJ8RH2TJWVlXiHoCIqKirwDkF1wJvZhQh6jWP5CooiKIpkZLz7D0UJm6PAx1IxcMtUmpubjx49mpWV1fqhR48eeXp6pqWljRo1ytPTUyKRhIWFhYaGQrKiGMHBwXD5dYmKioo5c+bgHYWKuHDhwpEjR/COQkUowTWObVkqt3Ep8cA1rhj4jKhtbGzcvn17XFwc2mq8ZFNT0759++rq6nbt2uXi4oIgiFAoXLJkyalTp1xcXMaOHYtHvAAAAADABw41ladPn86ePTsuLs7S0lJTU1Pu0eLi4pycHDab7fBfKk2j0QIDA3v16pWSktI6swEAAACAClN0piISicLCwgoKCoKCgsLDw8lkstwBjx8/fvnypY2NDYVCkTbS6XRjY+OHDx/W1tYqNl4AAAAA4AmHmsrw4cNTU1OXLl3aq1ev1o9ivacWFhayjb169erfv39dXZ1IJFJQlAAAAAAgAEWPU6FSqWvXrm3ngL/++qt1o5aWlr6+/sOHD+vq6rotNAAAAAAQDuHWqG1zgg+JRFJT+0j5Jycnp3si6nHKysqSk5PxjkIVlJWVlZWVRUVF4R2IKoALvAvBNd5V4BrvQtgQ1TYfIlym0nrkCoIgKIq2tLS08yw7O7tui6jHCQwMxDsEFWFsbAxvZlf50J8w0AnwsewqcI13ITab/aFbeXdlKunp6X5+frItMTExTk5OH32iiYlJ68aGhoaKigoqldqvX782n8Vms+EPGQAAAKB6CLeaPpapPH/+XLbx7du3r1696tevH5VKxSkuAAAAAOCgu2oqTk5OxcXFnXji4MGDdXV1c3JyvL29pROVi4qKSktLXV1dtbW1uzRMAAAAABAa4WoqxsbG1tbWOTk56enp2DpvQqFw9+7dLS0tbm5uJBIJ7wABAAAAoDiEG1FLoVB++OGHu3fvBgcHHz9+3NDQMCsrq6qqisvlwkgUAAAAoKchXE0FQRBra+uTJ0/a29vfuXPn1KlTGhoaYWFhbS5oCwAAAADVRoKddAAAAABAWESsqQAAAAAAYCBTAQAAAABxQaYCAAAAAOJSzUzlzJkzQ4cO3b9/P96BKKv6+votW7awWCwGg2FhYTFr1qzc3FwY0vTpnj59yuVyzc3NzczMJk6ceP78eXj3OgdF0dzc3BkzZpibmzMYjDFjxmzZsqW+vh7vuJSeUCjkcrn29vZVVVV4x6KU+Hz+6tWrmUwmg8FgsVjwsew02WvczMzM0dExJSWlublZ9hgVzFRKSkq2bNnS5k6H4FPw+fxvvvnmwIEDffv2nTlz5qhRo+7cufPtt9+mpaXhHZpySE9P/+abb/Lz8x0dHSdPnlxRUbF06dLY2FhIVjoKRdHY2FgvL68HDx44Ojp6enq2tLQcOHBg6dKlQqEQ7+iUGIqiMTExubm5eAeirAoKCry8vJKSkhgMxsyZM/v27Qsfy05LTEycM2cOdo17eHgIhcJly5atX7/+vZs4qlpev37t6+tLp9PpdPq+ffvwDkf5tLS0hIeHMxiMvXv3SiQSrPHWrVs2NjYcDufvv//GNzziq6mpmTZtmo2Nzd27d7GWsrIyJycnW1vbwsJCfGNTOoWFhba2ttiC11jL69evV69eTafTd+zYgW9sSu3atWtDhw6l0+njxo2rrKzEOxwlg91lhg4dmpKS0tLSgqLo27dv16xZQ6fTjx07hnd0Sqa8vNzBwUH2D2ZNTc2sWbOYTOatW7ekh6laTeXUqVNZWVkeHh54B6KsqqureTyeubn59OnT1dXVscavvvpqypQpfD6/sLAQ3/CI7/79+48ePXJ1dbWyssJajIyMAgICqqurr1y5gm9sSiczM1MgEMybN49Op2MtFAplwYIFurq6ubm5IpEI3/CUlEAgiIiIsLS0/N///od3LErp9u3bPB6Py+VOmTIFWzadTCZ7eXnRaLR79+7JdVuA9lVXV9fU1IwdO1b6B1NbW9vBwUEkEuXn50sPU6lMpaCgYOfOnZ6enp+yaTNoU3V1tZqamrm5udwWSwMGDMArJOWSl5fX1NRkZ2cnu/ODhYXFgAEDbt269ebNGxxjUzoVFRW6urqWlpayjVpaWr1798YrJGUnkUiioqIEAsGaNWtoNBre4Sil/Px8dXV1V1dX2WucyWTeu3cvMjJS+gUPfAp1dXUNDY2amhqxWCxtxL6EyN50VCdTEQqFkZGRAwYM+OGHH2A1206ztLS8dOnS7t27NTTe7bQgFAozMjJoNNrAgQNxjE0pVFRU0Gg0Y2Nj2cZ+/fpRKJSXL1/KXo3go3788cfc3FwWiyXbePv27fLyciMjIy0tLbwCU16XLl06deqUn5/fsGHD8I5FKaEoWlxcPGDAgIEDByYkJHA4HBhR+znMzc0nTZqUmZm5d+9ekUjU3NyclpZ29OjRIUOG2NraSg8j3L4/nYOi6PHjx2/dunXgwAFDQ8NHjx7hHZHqwN7b/Pz8yZMnW1hY4B0OoTU0NLQ5k6JPnz4GBgb//PMP1FQ+E5/P37Vrl5aW1vTp02G/0o7i8/nbt2/ncDhz586FTorOaWhoqKioaGpq2rBhQ05ODovFYrPZWVlZBw4cePjwYXR0NFSqOoRMJq9fv37AgAEHDhyIjo7GGidOnLh+/XpDQ0PpYSqSqdy7dy82NpbL5XI4HLxjUSkoiiYnJ2/fvp3BYKxevRqKVe1DUVQikbT5kJqa6tQv8SIQCEJCQoqLi1etWiX7fQt8iqampujo6Pr6+uXLl1MoFBjl8zmqqqqam5tPnDhhbW2NIEhjY+PGjRsTExMPHTq0bNkyvKNTJs3NzSdPnoyPj9fU1LS3t+/du3dWVtalS5doNFpoaCiVSsUOU4W/nkKh8Oeff9bT01u8eDF8zepCzc3NsbGxa9asMTIy2rt3r5GREd4RER2JRJLtNZPV0tKi4GBUTElJibe3d15enr+///z58+FK76i0tLRTp04FBAQMGTIEXuQr8wAABnBJREFU71hUgb+/P5amIAhCoVAWL15sYGDA4/Hq6urwDUy5XLx4cfPmzdbW1jweb/fu3b/88ktGRsbMmTOTk5MPHDiA/reyg5JlKvv372fIsLKyun//fkxMzKNHj0JDQ/X09PAOUJm0fjMfPHggfVQkEq1evXrLli3Dhw8/evSoubk5jqEqCy0trS+++KJ1++vXr//55x8dHR0YCto52dnZXC63uLg4NDQ0MDAQansdha0yNWHChJkzZ+Idi3LDvo2QyWQGgyHbrqOjY2JiUlNTAz28n04ikaSmpqqrqwcEBEjncFAolODg4CFDhly+fLm2thZrVPreH7FYfPv2bZFI5OXlJfdQZGRkZGTkypUrFy1ahEtsyksgEPj7++fm5rq4uGzatEluHhBoh6mpqVAorKysZDKZ0sa6urrGxsYBAwZoamriGJsywvof161b17t37z179owfPx6qKZ1QVFRUXl5eXl6empoq9xCbzR40aFBSUlKbSTaQo6WlZWRkJJFIWi8uCnXTjhKLxTU1NWQyWe4PI4VC0dHR4fP50s50JctUFi1aJJd2vHnzxtHR0dTUVLaRz+dnZmZaWVlZWloOHTpUoSEqj9ZvJkYoFIaEhOTl5S1cuHDFihXw/bVDrK2tyWRyVlaW7D314cOH1dXVNjY2UFPpqLS0tHXr1n3xxRd79+4dPnw43uEoK319fS6XK9vS1NR07dq1xsZGJyengQMHQg796ezs7BITE3k8noODg/Qa5/P5RUVF5ubmffr0wTc8JaKpqamjo4PlK7LtjY2NNTU1Ghoa776WKHpFOoW4dOkSrFHbOdhii3Jr1IJPV1VV5eLiYmNjI11gEdao7bS7d+/a2NjIrlELuopQKPTy8oI1ajuhrKxs/PjxNjY2mZmZWAu2dDKDwYA1ajsqJSWFwWDMnTu3pqYGa3n79u2OHTsYDEZ4eDi2BDCKokpWUwHd7f79+2fPnkUQ5MiRI8ePH5d7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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [a, b, k] = Vshift(p)\r\n  a = x;\r\n  b = x;\r\n  k = x;\r\nend","test_suite":"%%\r\np = [0.25 -1 -2 0 0];\r\na_correct = 2*(1-sqrt(3));\r\nb_correct = 2*(1+sqrt(3));\r\nk_correct = 64/5;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\np = [0.25 -2 1.5 10 0];\r\na_correct = 2-3*sqrt(2);\r\nb_correct = 2+3*sqrt(2);\r\nk_correct = -3.2;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\nfiletext = fileread('Vshift.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [1 0 0 0 -1];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [1 -8.5 14 34 -72 0 -17.5];\r\na_correct = -2.094230059318471;\r\nb_correct = 4.727773843365965;\r\nk_correct = 29.244170120692807;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-09T14:11:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-03T12:06:01.000Z","updated_at":"2026-03-25T12:52:10.000Z","published_at":"2026-01-09T14:11:42.000Z","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\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b], \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u0026lt;b\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\u003eThe interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eis defined such that the endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stand for the least and the greatest \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-values of the equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x) = y_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the lowest and the largest real solutions, respectively. Here, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the highest local maximum of the polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see non-scale figures 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\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \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:t\u003ethe endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they exist. Otherwise, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea = ''\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb = '' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see Hint 1);\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:t\u003ethe shifting 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, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\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 1. An \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-degree polynomial has exactly \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 roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\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 2. To calculate the mean of a continuous function, use the integral definition.\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\u003ep\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[a, b, 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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"370\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Vertical shift\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" 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\",\"relationship\":null},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":519,"title":"Pig Latin to English Translator","description":"Pig latin is a faux-language based off of English. The rules are as follows (excerpted from the \u003chttp://en.wikipedia.org/wiki/Pig_Latin Wikipedia entry for Pig Latin\u003e):\r\n\r\n1. In words that begin with consonant sounds, the initial consonant or consonant cluster is moved to the end of the word, and \"ay\" is added, as in the following examples:\r\n\r\n    * happy → appy-hay\r\n    * question → estion-quay\r\n\r\n2. In words that begin with vowels, the syllable \"ay\" is simply added to the end of the word.\r\n\r\n    * another → another-ay\r\n    * about → about-ay\r\n\r\nA hyphen is sometimes used to facilitate translation back into English. Ayspray, for instance, is ambiguous, but ay-spray means \"spray\" whereas ays-pray means \"prays.\"\r\n\r\nGiven a string in Pig Latin (may be multiple words), produce the English version.","description_html":"\u003cp\u003ePig latin is a faux-language based off of English. The rules are as follows (excerpted from the \u003ca href=\"http://en.wikipedia.org/wiki/Pig_Latin\"\u003eWikipedia entry for Pig Latin\u003c/a\u003e):\u003c/p\u003e\u003cp\u003e1. In words that begin with consonant sounds, the initial consonant or consonant cluster is moved to the end of the word, and \"ay\" is added, as in the following examples:\u003c/p\u003e\u003cpre\u003e    * happy → appy-hay\r\n    * question → estion-quay\u003c/pre\u003e\u003cp\u003e2. In words that begin with vowels, the syllable \"ay\" is simply added to the end of the word.\u003c/p\u003e\u003cpre\u003e    * another → another-ay\r\n    * about → about-ay\u003c/pre\u003e\u003cp\u003eA hyphen is sometimes used to facilitate translation back into English. Ayspray, for instance, is ambiguous, but ay-spray means \"spray\" whereas ays-pray means \"prays.\"\u003c/p\u003e\u003cp\u003eGiven a string in Pig Latin (may be multiple words), produce the English version.\u003c/p\u003e","function_template":"function e = piglatin2english( p )\r\n  e = p;\r\nend","test_suite":"%%\r\nstr1 = 'estion-quay';\r\nstr2 = 'question';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))\r\n\r\n%%\r\nstr1 = 'another-ay';\r\nstr2 = 'another';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))\r\n\r\n%%\r\nstr1 = 'ix-nay';\r\nstr2 = 'nix';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))\r\n\r\n%%\r\nstr1 = 'another-ay one-ay ites-bay e-thay ust-day';\r\nstr2 = 'another one bites the dust';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))\r\n\r\n%%\r\nstr1 = 'ow-hay uch-may ood-way ould-way a-ay oodchuck-way uck-chay if-ay a-ay oodchuck-way ould-cay uck-chay ood-way';\r\nstr2 = 'how much wood would a woodchuck chuck if a woodchuck could chuck wood';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))\r\n\r\n%%\r\nstr1 = 'eter-pay iper-pay icked-pay a-ay eck-pay of-ay ickle-pay eppers-pay';\r\nstr2 = 'peter piper picked a peck of pickle peppers';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))\r\n\r\n%%\r\nstr1 = 'our-fay ore-scay';\r\nstr2 = 'four score';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":166,"test_suite_updated_at":"2016-12-12T17:58:46.000Z","rescore_all_solutions":false,"group_id":14,"created_at":"2012-03-22T15:04:46.000Z","updated_at":"2026-03-15T01:34:17.000Z","published_at":"2012-03-22T15:05:17.000Z","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\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"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\\n\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\u003ePig latin is a faux-language based off of English. The rules are as follows (excerpted from the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Pig_Latin\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia entry for Pig Latin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1. In words that begin with consonant sounds, the initial consonant or consonant cluster is moved to the end of the word, and \\\"ay\\\" is added, as in the following examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    * happy → appy-hay\\n    * question → estion-quay]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2. In words that begin with vowels, the syllable \\\"ay\\\" is simply added to the end of the word.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    * another → another-ay\\n    * about → about-ay]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hyphen is sometimes used to facilitate translation back into English. Ayspray, for instance, is ambiguous, but ay-spray means \\\"spray\\\" whereas ays-pray means \\\"prays.\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a string in Pig Latin (may be multiple words), produce the English version.\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":61145,"title":"Translating even-degree polynomial by its vertex to the origin","description":"Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\r\nFind \r\nd (d\u003e0) the shifting distance of the above translation;\r\nv the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\r\nh the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\r\nHint. Compare to the Problem 61143.\r\ninput: p\r\noutput: [d, v, h]\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: 315.188px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 157.587px; transform-origin: 408px 157.594px; vertical-align: baseline; \"\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=\"\"\u003eLet \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; \"\u003ep\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 be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\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: 102.188px; 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 51.0875px; transform-origin: 391px 51.0938px; 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; \"\u003ed (d\u0026gt;0)\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 the shifting distance of the above translation;\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 the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\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; \"\u003eh\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 the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\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=\"\"\u003eHint. Compare to the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61143-translating-parabola-by-its-vertex-to-the-origin\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 61143\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 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; \"\u003ep\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[d, v, h]\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=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [d, v, h] = shift_vertex(p)\r\n  d = x;\r\n  v = x;\r\n  h = x;\r\nend","test_suite":"%%\r\np = [1 0 0 0 -1];\r\nd_correct = 1;\r\nv_correct = 'up';\r\nh_correct = '';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isequal(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [1/4 -1/3 -2.5 -3 16.25];\r\nd_correct = 5;\r\nv_correct = 'up';\r\nh_correct = 'left';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [0.25 -1 0.5 -3 15.25];\r\nd_correct = 5;\r\nv_correct = 'down';\r\nh_correct = 'left';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\nfiletext = fileread('shift_vertex.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [3 -20 12 96 54];\r\nd_correct = 5*sqrt(2);\r\nv_correct = 'up';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\ntolerance = 1e-13;\r\nassert(abs(d-d_correct)\u003ctolerance)\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\nd_correct = 2;\r\nv_correct = '';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\ntolerance = 1e-13;\r\nassert(abs(d-d_correct)\u003ctolerance)\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [-0.5 -2.4 3 22 -4.5 -54 -25.4];\r\nd_correct = 5*sqrt(2);\r\nv_correct = 'down';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-04T13:00:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-26T17:29:02.000Z","updated_at":"2026-03-26T10:19:33.000Z","published_at":"2026-01-04T13:00:23.000Z","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\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\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\u003ed (d\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the shifting distance of the above translation;\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 the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' 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=\\\"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\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' 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. Compare to the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61143-translating-parabola-by-its-vertex-to-the-origin\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 61143\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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: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\u003ep\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[d, v, h]\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\u003e\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":60566,"title":"Given a Polyshape_01 (ps) Return its Perimeter, Area, and Centroid.","description":"Return the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\r\nReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\r\nReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. ","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: 104.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 52.3333px; transform-origin: 407.5px 52.3333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.6667px; 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: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; 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=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.3333px; 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: 384.5px 21.6667px; text-align: left; transform-origin: 384.5px 21.6667px; 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=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.6667px; 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: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; 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=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"%%\r\nfunction [P, A, Cx, Cy] = PolyShape_01(ps)\r\n    % Return the perimeter (P) of a polyshape object, which is the sum\r\n    % of the lengths of its boundaries.\r\n    \r\n    % Return the total area (A) of a polyshape object, which is the sum\r\n    % of the areas of the solid regions that make up the polyshape.\r\n    \r\n    % Return the x-coordinate (Cx) and the y-coordinate (Cy) of the\r\n    % centroid of a polyshape. \r\n end","test_suite":"%% Test 1\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),1313))\r\n    assert(isequal(round(A,4),134508.0227))\r\n    assert(isequal(round(Cx,4),17))\r\n    assert(isequal(round(Cy,4),47))\r\n\r\n    \r\n%% Test 2\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),1313))\r\n    assert(isequal(round(A,4),134508.0227))\r\n    assert(isequal(round(Cx,4),254))\r\n    assert(isequal(round(Cy,4),-1676))\r\n\r\n    \r\n%% Test 3\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),177.255))\r\n    assert(isequal(round(A,4),2451.4087))\r\n    assert(isequal(round(Cx,4),34.29 ))\r\n    assert(isequal(round(Cy,4),-226.26))\r\n\r\n    \r\n%% Test 4\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),206.155))\r\n    assert(isequal(round(A,4),2385.7031))\r\n    assert(isequal(round(Cx,4),34.0501))\r\n    assert(isequal(round(Cy,4),-226.4324))\r\n\r\n    \r\n%% Test 5\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),235.055))\r\n    assert(isequal(round(A,4),2319.9976))\r\n    assert(isequal(round(Cx,4),34.448))\r\n    assert(isequal(round(Cy,4),-226.6146))\r\n\r\n    \r\n%% Test 6\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,polyshape([20 30.1 40.1 45.1 50 45.2 40.2 30.2 27.2],[-235 -239 -239 -237 -235 -239 -241 -240.5 -240]));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),300.0489))\r\n    assert(isequal(round(A,4),2274.2476))\r\n    assert(isequal(round(Cx,4),34.4235))\r\n    assert(isequal(round(Cy,4),-226.367))\r\n    \r\n    \r\n    ","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":20795,"edited_by":20795,"edited_at":"2024-06-28T13:41:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-26T18:00:30.000Z","updated_at":"2026-03-18T15:16:22.000Z","published_at":"2024-06-26T18:18:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\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\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\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\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \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":43162,"title":"Translate German decimals to English decimals","description":"The string 'x = [2,5; 5,5; 4,3];' should return 'y = [2.5; 5.5; 4.3];'","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\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: 196.5px 8px; transform-origin: 196.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe string 'x = [2,5; 5,5; 4,3];' should return 'y = [2.5; 5.5; 4.3];'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = translate(x)\r\n  y = 'x in German';\r\nend","test_suite":"%%\r\nx = 'x = [2,5; 5,5; 4,3];';\r\ny_correct = 'y = [2.5; 5.5; 4.3];';\r\nassert(isequal(translate(x),y_correct))\r\n\r\n%%\r\nx = 'x = [2,25; 5,35; 4,13];';\r\ny_correct = 'y = [2.25; 5.35; 4.13];';\r\nassert(isequal(translate(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":57323,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":51,"test_suite_updated_at":"2021-08-12T17:40:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-07T15:05:46.000Z","updated_at":"2026-03-17T07:30:46.000Z","published_at":"2016-10-07T15:05:46.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe string 'x = [2,5; 5,5; 4,3];' should return 'y = [2.5; 5.5; 4.3];'\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":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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\" 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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vertically even-degree polynomial's graph by its mean over an interval","description":"Let p be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval [a, b], with a\u003cb.\r\nThe interval [a, b] is defined such that the endpoints a and b stand for the least and the greatest x-values of the equation p(x) = y_peak, the lowest and the largest real solutions, respectively. Here, y_peak stands for the highest local maximum of the polynomial p (see non-scale figures below). \r\nGiven p, return \r\nthe endpoints a and b if they exist. Otherwise, return a = '' and b = '' (see Hint 1);\r\nthe shifting constant, k, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\r\nHint 1. An n-degree polynomial has exactly n roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\r\nHint 2. To calculate the mean of a continuous function, use the integral definition.\r\ninput: p\r\noutput: [a, b, k]\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: 662.112px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 331.05px; transform-origin: 408px 331.056px; vertical-align: baseline; \"\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=\"\"\u003eLet \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; \"\u003ep\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 be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \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[a, b], \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=\"\"\u003ewith \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; \"\u003ea\u0026lt;b\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: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; 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=\"\"\u003eThe interval \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[a, b] \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=\"\"\u003eis defined such that the endpoints \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; \"\u003ea\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 \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; \"\u003eb\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 stand for the least and the greatest \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-values of the equation \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; \"\u003ep(x) = y_peak\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, the lowest and the largest real solutions, respectively. Here, \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_peak\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 stands for the highest local maximum of the polynomial \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; \"\u003ep \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(see non-scale figures 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=\"\"\u003eGiven \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; \"\u003ep\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, return \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=\"\"\u003ethe endpoints \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; \"\u003ea\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 and \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; \"\u003eb\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 if they exist. Otherwise, return \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; \"\u003ea = ''\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 and \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; \"\u003eb = '' \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(see Hint 1);\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=\"\"\u003ethe shifting constant, \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; \"\u003ek\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 the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; 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=\"\"\u003eHint 1. An \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-degree polynomial has exactly \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 roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\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=\"\"\u003eHint 2. To calculate the mean of a continuous function, use the integral definition.\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; \"\u003ep\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[a, b, k]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.8px; 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 132.4px; text-align: left; transform-origin: 384px 132.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"370\" height=\"259\" style=\"vertical-align: baseline;width: 370px;height: 259px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [a, b, k] = Vshift(p)\r\n  a = x;\r\n  b = x;\r\n  k = x;\r\nend","test_suite":"%%\r\np = [0.25 -1 -2 0 0];\r\na_correct = 2*(1-sqrt(3));\r\nb_correct = 2*(1+sqrt(3));\r\nk_correct = 64/5;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\np = [0.25 -2 1.5 10 0];\r\na_correct = 2-3*sqrt(2);\r\nb_correct = 2+3*sqrt(2);\r\nk_correct = -3.2;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n\r\n%%\r\nfiletext = fileread('Vshift.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [1 0 0 0 -1];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\noutput_correct = ['', '', ''];\r\nassert(isequal(Vshift(p), output_correct))\r\n\r\n%%\r\np = [1 -8.5 14 34 -72 0 -17.5];\r\na_correct = -2.094230059318471;\r\nb_correct = 4.727773843365965;\r\nk_correct = 29.244170120692807;\r\n[a, b, k] = Vshift(p);\r\ntolerance = 1e-13;\r\nassert(abs(a - a_correct) \u003c tolerance)\r\nassert(abs(b - b_correct) \u003c tolerance)\r\nassert(abs(k - k_correct) \u003c tolerance)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-09T14:11:42.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-03T12:06:01.000Z","updated_at":"2026-03-25T12:52:10.000Z","published_at":"2026-01-09T14:11:42.000Z","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\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial with positive leading coefficient. Consider its vertical translation by shifting its graph by its average value over a specified interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b], \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewith \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u0026lt;b\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\u003eThe interval \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[a, b] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eis defined such that the endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stand for the least and the greatest \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-values of the equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep(x) = y_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the lowest and the largest real solutions, respectively. Here, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_peak\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the highest local maximum of the polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see non-scale figures 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\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return \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:t\u003ethe endpoints \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they exist. Otherwise, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea = ''\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb = '' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see Hint 1);\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:t\u003ethe shifting 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, which stands for the above vertical translation (see Hint 2). Return k = '' if the interval is empty.\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 1. An \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-degree polynomial has exactly \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 roots (counting multiplicity) in the complex number system. An odd-degree polynomial always has at least one real root. Therefore, a real polynomial of even degree always has at least one vertex, but might not have local maxima.\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 2. To calculate the mean of a continuous function, use the integral definition.\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\u003ep\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[a, b, 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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"370\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Vertical shift\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" 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\",\"relationship\":null},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":519,"title":"Pig Latin to English Translator","description":"Pig latin is a faux-language based off of English. The rules are as follows (excerpted from the \u003chttp://en.wikipedia.org/wiki/Pig_Latin Wikipedia entry for Pig Latin\u003e):\r\n\r\n1. In words that begin with consonant sounds, the initial consonant or consonant cluster is moved to the end of the word, and \"ay\" is added, as in the following examples:\r\n\r\n    * happy → appy-hay\r\n    * question → estion-quay\r\n\r\n2. In words that begin with vowels, the syllable \"ay\" is simply added to the end of the word.\r\n\r\n    * another → another-ay\r\n    * about → about-ay\r\n\r\nA hyphen is sometimes used to facilitate translation back into English. Ayspray, for instance, is ambiguous, but ay-spray means \"spray\" whereas ays-pray means \"prays.\"\r\n\r\nGiven a string in Pig Latin (may be multiple words), produce the English version.","description_html":"\u003cp\u003ePig latin is a faux-language based off of English. The rules are as follows (excerpted from the \u003ca href=\"http://en.wikipedia.org/wiki/Pig_Latin\"\u003eWikipedia entry for Pig Latin\u003c/a\u003e):\u003c/p\u003e\u003cp\u003e1. In words that begin with consonant sounds, the initial consonant or consonant cluster is moved to the end of the word, and \"ay\" is added, as in the following examples:\u003c/p\u003e\u003cpre\u003e    * happy → appy-hay\r\n    * question → estion-quay\u003c/pre\u003e\u003cp\u003e2. In words that begin with vowels, the syllable \"ay\" is simply added to the end of the word.\u003c/p\u003e\u003cpre\u003e    * another → another-ay\r\n    * about → about-ay\u003c/pre\u003e\u003cp\u003eA hyphen is sometimes used to facilitate translation back into English. Ayspray, for instance, is ambiguous, but ay-spray means \"spray\" whereas ays-pray means \"prays.\"\u003c/p\u003e\u003cp\u003eGiven a string in Pig Latin (may be multiple words), produce the English version.\u003c/p\u003e","function_template":"function e = piglatin2english( p )\r\n  e = p;\r\nend","test_suite":"%%\r\nstr1 = 'estion-quay';\r\nstr2 = 'question';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))\r\n\r\n%%\r\nstr1 = 'another-ay';\r\nstr2 = 'another';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))\r\n\r\n%%\r\nstr1 = 'ix-nay';\r\nstr2 = 'nix';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))\r\n\r\n%%\r\nstr1 = 'another-ay one-ay ites-bay e-thay ust-day';\r\nstr2 = 'another one bites the dust';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))\r\n\r\n%%\r\nstr1 = 'ow-hay uch-may ood-way ould-way a-ay oodchuck-way uck-chay if-ay a-ay oodchuck-way ould-cay uck-chay ood-way';\r\nstr2 = 'how much wood would a woodchuck chuck if a woodchuck could chuck wood';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))\r\n\r\n%%\r\nstr1 = 'eter-pay iper-pay icked-pay a-ay eck-pay of-ay ickle-pay eppers-pay';\r\nstr2 = 'peter piper picked a peck of pickle peppers';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))\r\n\r\n%%\r\nstr1 = 'our-fay ore-scay';\r\nstr2 = 'four score';\r\nstr1_f = piglatin2english(str1);\r\nassert(strcmp(str1_f,str2))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":166,"test_suite_updated_at":"2016-12-12T17:58:46.000Z","rescore_all_solutions":false,"group_id":14,"created_at":"2012-03-22T15:04:46.000Z","updated_at":"2026-03-15T01:34:17.000Z","published_at":"2012-03-22T15:05:17.000Z","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\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"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\\n\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\u003ePig latin is a faux-language based off of English. The rules are as follows (excerpted from the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Pig_Latin\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia entry for Pig Latin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1. In words that begin with consonant sounds, the initial consonant or consonant cluster is moved to the end of the word, and \\\"ay\\\" is added, as in the following examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    * happy → appy-hay\\n    * question → estion-quay]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2. In words that begin with vowels, the syllable \\\"ay\\\" is simply added to the end of the word.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    * another → another-ay\\n    * about → about-ay]]\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA hyphen is sometimes used to facilitate translation back into English. Ayspray, for instance, is ambiguous, but ay-spray means \\\"spray\\\" whereas ays-pray means \\\"prays.\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a string in Pig Latin (may be multiple words), produce the English version.\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":61145,"title":"Translating even-degree polynomial by its vertex to the origin","description":"Let p be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\r\nFind \r\nd (d\u003e0) the shifting distance of the above translation;\r\nv the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\r\nh the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\r\nHint. Compare to the Problem 61143.\r\ninput: p\r\noutput: [d, v, h]\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: 315.188px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 157.587px; transform-origin: 408px 157.594px; vertical-align: baseline; \"\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=\"\"\u003eLet \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; \"\u003ep\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 be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\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: 102.188px; 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 51.0875px; transform-origin: 391px 51.0938px; 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; \"\u003ed (d\u0026gt;0)\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 the shifting distance of the above translation;\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 the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' if the graph does not undergo a translation;\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; \"\u003eh\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 the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' if the graph does not undergo a translation.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\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=\"\"\u003eHint. Compare to the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61143-translating-parabola-by-its-vertex-to-the-origin\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 61143\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 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; \"\u003ep\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[d, v, h]\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=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [d, v, h] = shift_vertex(p)\r\n  d = x;\r\n  v = x;\r\n  h = x;\r\nend","test_suite":"%%\r\np = [1 0 0 0 -1];\r\nd_correct = 1;\r\nv_correct = 'up';\r\nh_correct = '';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isequal(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [1/4 -1/3 -2.5 -3 16.25];\r\nd_correct = 5;\r\nv_correct = 'up';\r\nh_correct = 'left';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [0.25 -1 0.5 -3 15.25];\r\nd_correct = 5;\r\nv_correct = 'down';\r\nh_correct = 'left';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\nfiletext = fileread('shift_vertex.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\np = [3 -20 12 96 54];\r\nd_correct = 5*sqrt(2);\r\nv_correct = 'up';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\ntolerance = 1e-13;\r\nassert(abs(d-d_correct)\u003ctolerance)\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [0.5 3 7.5 11 11 8 4];\r\nd_correct = 2;\r\nv_correct = '';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\ntolerance = 1e-13;\r\nassert(abs(d-d_correct)\u003ctolerance)\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n\r\n%%\r\np = [-0.5 -2.4 3 22 -4.5 -54 -25.4];\r\nd_correct = 5*sqrt(2);\r\nv_correct = 'down';\r\nh_correct = 'right';\r\n[d, v, h] = shift_vertex(p);\r\nassert(isapprox(d, d_correct))\r\nassert(strcmp(v, v_correct))\r\nassert(strcmp(h, h_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-04T13:00:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-26T17:29:02.000Z","updated_at":"2026-03-26T10:19:33.000Z","published_at":"2026-01-04T13:00:23.000Z","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\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be an even-degree polynomial such that has a unique vertex (single global extremum). Consider its translation by shifting its vertex to the origin.\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\u003ed (d\u0026gt;0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the shifting distance of the above translation;\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 the vertical shift, which stands for 'up' and 'down' if the polynomial's graph is upward or downward shifted, respectively, or simply '' 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=\\\"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\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the horizontal shift, which stands for 'right' and 'left' if the polynomial's graph is shifted to the right and to the left, respectively, or simply '' 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. 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