{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":1113,"title":"Create array of all Distances between two Sets of Points ","description":"This Challenge is a subsection of Martian Pranks based on Tim's efficient Distance calculation between sets of points.\r\nGiven Point Set vectors Start and Final determine the distance between each Start and each Final Point.\r\nInput: Start(m,2), Final(m,2)\r\nOutput: Distances (m,m)\r\nExample:\r\nInput: [0 0;0 1], [2 0;3 3]\r\nOutput: [2 4.24; 2.24 3.61]\r\nTestSuite will perform rounding\r\nHint: Tags","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: 261px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 130.5px; transform-origin: 407px 130.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 104.5px 8px; transform-origin: 104.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is a subsection 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: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMartian Pranks\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: 215.5px 8px; transform-origin: 215.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e based on Tim's efficient Distance calculation between sets of points.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 328.5px 8px; transform-origin: 328.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Point Set vectors Start and Final determine the distance between each Start and each Final Point.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 69.5px 8px; transform-origin: 69.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Start(m,2), Final(m,2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 26px 8px; transform-origin: 26px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 53px 8px; transform-origin: 53px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Distances (m,m)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 31.5px 8px; transform-origin: 31.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 75.5px 8px; transform-origin: 75.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput: [0 0;0 1], [2 0;3 3]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOutput: [2 4.24; 2.24 3.61]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 96.5px 8px; transform-origin: 96.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTestSuite will perform rounding\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 31px 8px; transform-origin: 31px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Tags\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d=xy_distance(Start,Final)\r\n d=zeros(size(Start,1));\r\n\r\nend","test_suite":" %%\r\n m=5;\r\n Start=rand(m,2);\r\n Final=rand(m,2);\r\n \r\n d=xy_distance(Start,Final);\r\n d=round(100*d)/100;\r\n \r\n d_expect=zeros(m);\r\n for i=1:m % 10\r\n  for j=1:m\r\n   dx=Start(i,1)-Final(j,1); % 14\r\n   dy=Start(i,2)-Final(j,2); % 14\r\n   d_expect(i,j)=hypot(dx,dy); % 14\r\n  end\r\n end\r\n \r\n d_expect=round(100*d_expect)/100;\r\n \r\n assert(isequal(d_expect,d))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":223089,"edited_at":"2022-12-31T12:41:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":"2022-12-31T12:41:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-12-11T04:52:10.000Z","updated_at":"2025-06-25T18:38:29.000Z","published_at":"2012-12-11T05:29:22.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is a subsection of\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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMartian Pranks\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e based on Tim's efficient Distance calculation between sets of points.\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 Point Set vectors Start and Final determine the distance between each Start and each Final Point.\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Start(m,2), Final(m,2)\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Distances (m,m)\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\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\u003eInput: [0 0;0 1], [2 0;3 3]\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\u003eOutput: [2 4.24; 2.24 3.61]\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\u003eTestSuite will perform rounding\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: Tags\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":58862,"title":"Given Hypotenuse points create two right triangles","description":"Given two points defining a hypotenuse create two right triangles of (h,5,R). Return the two (x,y) points that create the right triangles. I will elaborate on two geometric methods utilizing Matlab specific functions, rotation matrix, and translation matrix.\r\nGiven points [x1,y1] and [x2,y2] return  [x3 y3;x4 y4] such that distance(xy2,xy3)=distance(xy2,xy4)=5. h\u003e5\r\nThe below figure is created based upon h=distance([x1,y1],[x2,y2]), translating (x1,y1) to (0,0), and rotating (x2,y2) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,5] with R^2+5^2=h^2. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\r\nP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(d-Y)^2 = Y^2-d^2+2dY-Y^2=2dY-d^2 thus\r\nY=(R^2-P^2+h^2)/(2h)  and X=+/- (R^2-Y^2)^.5\r\nThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [x1 y1]\r\nA second method to find (X,Y) is theta=atan(5/R), X=Rsin(theta) and Y=Rcos(theta). The rotation and translation matrices are still required to return to the original coordinate system.\r\n\r\nIn this figure h represents distance from (x1,y1) to (x2,y2) and (x1,y1) has been translated to 0,0","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: 894.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 447.25px; transform-origin: 407px 447.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372px 8px; transform-origin: 372px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven two points defining a hypotenuse create two right triangles of (h,5,R). Return the two (x,y) points that create the right triangles. I will elaborate on two geometric methods utilizing Matlab specific functions, rotation matrix, and translation matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 332.5px 8px; transform-origin: 332.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven points [x1,y1] and [x2,y2] return  [x3 y3;x4 y4] such that distance(xy2,xy3)=distance(xy2,xy4)=5. h\u0026gt;5\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; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe below figure is created based upon h=distance([x1,y1],[x2,y2]), translating (x1,y1) to (0,0), and rotating (x2,y2) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,5] with R^2+5^2=h^2. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 358px 8px; transform-origin: 358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(d-Y)^2 = Y^2-d^2+2dY-Y^2=2dY-d^2 thus\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 143px 8px; transform-origin: 143px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eY=(R^2-P^2+h^2)/(2h)  and X=+/- (R^2-Y^2)^.5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 379px 8px; transform-origin: 379px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [x1 y1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.5px 8px; transform-origin: 383.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA second method to find (X,Y) is theta=atan(5/R), X=Rsin(theta) and Y=Rcos(theta). The rotation and translation matrices are still required to return to the original coordinate system.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 549.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 274.75px; text-align: left; transform-origin: 384px 274.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 416px;height: 544px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\" width=\"416\" height=\"544\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 302.5px 8px; transform-origin: 302.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this figure h represents distance from (x1,y1) to (x2,y2) and (x1,y1) has been translated to 0,0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xy = find_xy_RightTriangles(x1,y1,x2,y2)\r\n % The hypotenuse end points are (x1,y1) and (x2,y2) \r\n % A length 5 segment is attached to (x2,y2)\r\n % Complete the two possible right triangles\r\n % xy=[x3 y3;x4 y4]\r\n \r\n  h=norm([x2-x1 y2-y1]);\r\n \r\n  R2=h^2-25;\r\n  R=R2^0.5;\r\n  \r\n  %PRh mehtod\r\n  %y=\r\n  %x=\r\n  %xy=[-x y;x y];\r\n  \r\n  %Trig method\r\n  %theta=atan(?/R);\r\n  %y=\r\n  %x=\r\n  %xy=[-x y;x y];\r\n \r\n \r\n %Rotation Angle: atan2\r\n theta=atan2(x2-x1,y2-y1); % (X,Y) output radians Neg Left of vert, Pos Right of Vert\r\n \r\n %Rotation Matrix: [cos(t) -sin(t);sin(t) cos(t)]\r\n %Translation matrix: [x1 y1]\r\n %Check of (x2,y2) being regenerated from h, theta, and translation\r\n [x2y2]=[0 h]*[cos(theta) -sin(theta);sin(theta) cos(theta)]+[x1 y1]\r\n [x2 y2]\r\n \r\n %xy=\r\n \r\n \r\nend %find_xy_RightTriangles","test_suite":"%%\r\nvalid=1;\r\nx1=0;y1=0;x2=0;y2=13;\r\nxy = find_xy_RightTriangles(x1,y1,x2,y2)\r\nif sum(sum((xy-[x2 y2]).^2,2)-25)\u003e1e-6 % verify xy3,xy4 dist==5 from xy2\r\n valid=0;\r\nend\r\nh2=sum(([x1 y1]-[x2 y2]).^2);\r\nif sum(sum((xy-[x1 y1]).^2,2)+25-h2)\u003e1e-6 % Verify right triangles\r\n valid=0;\r\nend\r\nassert(valid)\r\n%%\r\nvalid=1;\r\nx1=0;y1=0;x2=0;y2=-13;\r\nxy = find_xy_RightTriangles(x1,y1,x2,y2)\r\nif sum(sum((xy-[x2 y2]).^2,2)-25)\u003e1e-6 % verify xy3,xy4 dist==5 from xy2\r\n valid=0;\r\nend\r\nh2=sum(([x1 y1]-[x2 y2]).^2);\r\nif sum(sum((xy-[x1 y1]).^2,2)+25-h2)\u003e1e-6 % Verify right triangles\r\n valid=0;\r\nend\r\nassert(valid)\r\n%%\r\nvalid=1;\r\nx1=5;y1=5;x2=5;y2=-8;\r\nxy = find_xy_RightTriangles(x1,y1,x2,y2)\r\nif sum(sum((xy-[x2 y2]).^2,2)-25)\u003e1e-6 % verify xy3,xy4 dist==5 from xy2\r\n valid=0;\r\nend\r\nh2=sum(([x1 y1]-[x2 y2]).^2);\r\nif sum(sum((xy-[x1 y1]).^2,2)+25-h2)\u003e1e-6 % Verify right triangles\r\n valid=0;\r\nend\r\nassert(valid)\r\n%%\r\nvalid=1;\r\nx1=0;y1=0;x2=0;y2=0;\r\nwhile norm([x2-x1 y2-y1])\u003c5.1\r\n x1=10*rand-5;y1=10*rand-5;x2=20*rand-10;y2=-20*rand+10;\r\n %fprintf('%.3f ',[x1 y1 x2 y2]);fprintf('\\n');\r\nend\r\nfprintf('%.3f ',[x1 y1 x2 y2]);fprintf('\\n');\r\nxy = find_xy_RightTriangles(x1,y1,x2,y2)\r\nif sum(sum((xy-[x2 y2]).^2,2)-25)\u003e1e-6 % verify xy3,xy4 dist==5 from xy2\r\n valid=0;\r\nend\r\nh2=sum(([x1 y1]-[x2 y2]).^2);\r\nif sum(sum((xy-[x1 y1]).^2,2)+25-h2)\u003e1e-6 % Verify right triangles\r\n valid=0;\r\nend\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-11T18:08:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-08-11T18:08:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-11T15:21:29.000Z","updated_at":"2024-11-18T01:49:13.000Z","published_at":"2023-08-11T17:36:27.000Z","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 two points defining a hypotenuse create two right triangles of (h,5,R). Return the two (x,y) points that create the right triangles. I will elaborate on two geometric methods utilizing Matlab specific functions, rotation matrix, and translation matrix.\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 points [x1,y1] and [x2,y2] return  [x3 y3;x4 y4] such that distance(xy2,xy3)=distance(xy2,xy4)=5. h\u0026gt;5\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 below figure is created based upon h=distance([x1,y1],[x2,y2]), translating (x1,y1) to (0,0), and rotating (x2,y2) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,5] with R^2+5^2=h^2. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\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\u003eP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(d-Y)^2 = Y^2-d^2+2dY-Y^2=2dY-d^2 thus\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\u003eY=(R^2-P^2+h^2)/(2h)  and X=+/- (R^2-Y^2)^.5\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 trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [x1 y1]\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\u003eA second method to find (X,Y) is theta=atan(5/R), X=Rsin(theta) and Y=Rcos(theta). The rotation and translation matrices are still required to return to the original coordinate system.\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=\\\"544\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"416\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eIn this figure h represents distance from (x1,y1) to (x2,y2) and (x1,y1) has been translated to 0,0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.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":59501,"title":"Compute the sum of distances from a point to the sides of an equilateral triangle","description":"Write a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the triangle. That is, for the triangle below, compute the sum . Input will consist of the point (x0,y0) and vectors x and y with the coordinates of the vertices of the triangle. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 565.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 282.85px; transform-origin: 407px 282.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.433px 8px; transform-origin: 381.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the triangle. That is, for the triangle below, compute the sum \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"58.5\" height=\"18\" alt=\"a+b+c\" style=\"width: 58.5px; height: 18px;\"\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: 95.675px 8px; transform-origin: 95.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Input will consist of the point (\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: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex0\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey0\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: 42.3917px 8px; transform-origin: 42.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and vectors \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: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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: 15.5583px 8px; transform-origin: 15.5583px 8px; 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: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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: 0.241667px 8px; transform-origin: 0.241667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the coordinates of the vertices of the triangle. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 493.7px; 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 246.85px; text-align: left; transform-origin: 384px 246.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"495\" height=\"488\" style=\"vertical-align: baseline;width: 495px;height: 488px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABNUAAATDCAYAAABRWQOUAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxIAABcSAWef0lIAAAAHdElNRQfnDBwFFAFHyKGUAAAAJHRFWHRTb2Z0d2FyZQBNQVRMQUIsIFRoZSBNYXRoV29ya3MsIEluYy48WN0YAAAAInRFWHRDcmVhdGlvbiBUaW1lADI3LURlYy0yMDIzIDIzOjIwOjAxn9A1uwAAvSlJREFUeF7s3QuYZVV5J+7VoHhBiCYQI5n5t61hSJQEQcUbWnYeVLwlXocYowWoE2cCMqIzZETtbhUNExMzID6jEbE16JAoSiDKaEJT0bQKDqjMmMEgLXEw8RI1RgRR8F/fqbXp06v3qapTdS57n/2+z1MPaxWtrdB19t6//X3r2/CTRQkAAAAAWLV98l8BAAAAgFUSqgEAAADAkIRqAAAAADAkoRoAAAAADEmoBgAAAABDEqoBAAAAwJCEagAAAAAwJKEaAAAAAAxJqAYAAAAAQxKqAQAAAMCQhGoAAAAAMCShGgAAAAAMSagGAAAAAEMSqgEAAADAkIRqAAAAADAkoRoAAAAADEmoBgAAAABDEqoBAAAAwJCEagAAAAAwJKEaAAAAAAxJqAYAAAAAQxKqAQAAAMCQhGoAAAAAMCShGgAAAAAMSagGAAAAAEMSqgEAAADAkIRqAAAAADCkDT9ZlNdTc/XVV6dTTz0179bujDPOSMcdd1zeDe+aa65JZ599dt6t3imnnJKOOuqovAMAAABg1jUiVNu5c2c68cQT827t/ut//a/p13/91/NueB/4wAd6wdywzj333HTsscfmHQAAAACzbqbaP/fdd9+8WpurrroqrwAAAABgsEZUqn3rW99KV155Zd6tzre//e30+te/Pu9SevzjH5/e/va3593aPPe5z01f+MIXeuvnP//56WEPe1hvvZKHPvSh6b73vW/eAQAAADDrGhGqDev2229Pv/mbv5k+97nP9fYbN25MF110UbrXve7V26/FHXfckQ4//PDef3c477zz0jHHHNNbAwAAAEC/VrZ/xtlpVaC233779c40W0+gFq677ro7A7VoI33Uox7VWwMAAABAqXWhWgw1ePe73513Kb3yla9Mhx56aN6t3Ze//OW8Sun+97//us9nAwAAAGB2tSpUu+WWW9J/+S//Je9S+pVf+ZU0Pz+fd+tz9dVX51VKD37wg/MKAAAAAPbWqlAt2jz/8R//sbeOSrI3velNvfUo3HjjjXmV0pFHHplXAAAAALC31oRqX/3qV9O73vWuvFuazvkLv/ALebd+n/3sZ/Nqqf3zhhtuSGeeeWZ64hOfmB70oAelww47LB111FHp5JNPThdffHFvsAEAAAAA3dSa6Z+nnnpquuyyy3rr/fffP11++eXp3ve+d2+/Xl//+tfT4x73uLxL6VnPelZvmuhyHvjAB6a3vOUtvbANAAAAgG5pRaXa3/3d390ZqIUXv/jFIwvUwuc///m8WtIfqMV00Xvc4x57DS6IwQbPe97z9qhwAwAAAKAbWlGpFhM+L7nkkt76gAMOSH/913+d7nnPe/b2o3D22Wf3zmurRIAWAxCOP/74XitouP3229OnPvWpdM4556TPfe5zve+F+9znPunSSy9NBx10UP7O8FS7AQAAAG103XXX5VX3ND5U+9rXvpaOPfbYXqgVfud3fie97GUv661HJc5J+/jHP95bR2vpO9/5zt75aYO86lWvSh/84AfzbqlddD1DEyJU6/IfQhgXP1swHn62YDz8bMF4+NmC8en6z1fj2z/f97733RmoRQVZtFyO2mmnndarVHvjG9+Y3vrWty4bqIX4dTG8oBKDC7773e/mHQAAAACzrtGhWkzY/NCHPpR3Kf3qr/5qOvjgg/NudB7wgAf0quGe/exnp0c/+tH5u8s76aST8mqpNfTTn/503gEAAAAw6xodqkVQ9a1vfSvvUnruc5+bV9MXIVy/a6+9Nq8AAAAAmHWNDtX6J34eeOCB6bGPfWzeTV9MBL3LXe6Sdyn98z//c14BAAAAMOsaHar91V/9VV6l9IQnPCHts0+z/uf2h2pN+98GAAAAwPg0Ngn627/92z1aP+M8tXGI89CuvPLKtGPHjl5lXDUUYSXx62699da8S+mBD3xgXgEAAAAw6xobqv2v//W/8mpp6ufc3FzejVaEaS94wQvSS1/60nTqqaemz3zmM/nvLK/8dYceemheAQAAADDrGhuqXXXVVXmV0i//8i+nu971rnk3WkcccUReLbn88svzankXXXRRXi2d9/bIRz4y7wAAAACYdY0N1fqnaY6ztfLggw9OD3nIQ/IupQsvvDB99atfzbt6O3fuTJdccknepXTiiSc6Uw0AAACgQxqZBP3oRz9KN910U96l9PCHPzyvhve+970v/fZv//adX/1hXeW0007Lq5Ruu+229JKXvGRgsBbtoieffHLepbRx48b0ohe9KO+AJrnuuuvyChglP1swHn62YDz8bAHj0shQ7f/+3/+bV0t++qd/Oq+Gd/3116crrrjizq9vf/vb+e/s9ohHPKJ3rlpl165d6SlPeUp6wxvekD72sY/1grQPfehDvfAszl67+eabe79u//33T+ecc066293u1tsDAAAA0A2NDNW++c1v5tWSn//5n8+r8Xn1q1+dTjrppLxbqlh773vfm0455ZRekPa7v/u76ZOf/GT+uykddNBB6fzzz0+HHXZY/g4AAAAAXdHIUO3WW2/NqyWbNm3Kq/E6/fTT0wUXXLBsu+kBBxyQXvziF6ePfvSjew05AAAAAKAbNvxkUV4zJVHtps8fAAAAaJOu5xlGVgIAAADAkIRqAAAAADAkoRoAAAAADEmoBgAAAABDEqoBAAAAwJCEagAAAAAwJKEaAAAAAAxJqAYAAAAAQxKqAQAAAMCQhGoAAAAAMCShGgAAAAAMSagGAAAAAEMSqgEAAADAkIRqAAAAADAkoRoAAAAADEmoBgAAAABDEqoBAAAAwJCEagAAAAAwJKEaAAAAAAxJqAYAAAAAQxKqAQAAAMCQhGoAAAAAMCShGgAAAAAMSagGAAAAAEMSqgEAAADAkIRqAAAAADAkoRoAAAAADEmoBgAAAABDEqoBAAAAwJCEagAAAAAwJKEaAAAAAAxJqAYAAAAAQxKqAQAAAMCQhGoAAAAAMCShGgAAAAAMSagGAAAAAEMSqgEAAADAkIRqAAAAADAkoRoAAAAADEmoBgAAAABDEqoBAAAAwJCEagAAAAAwJKEaAAAAAAxJqAYAAAAAQxKqAQAAAMCQhGoAAAAAMCShGgAAAAAMSagGAAAAAEMSqgEAAADAkIRqAAAAADAkoRoAAAAADEmoBgAAAABDEqoBAAAAwJCEagAAAAAwJKEaAAAAAAxJqAYAAAAAQxKqAQAAAMCQhGoAAAAAMCShGgAAAAAMSagGAAAAAEMSqgEAAADAkIRqAAAAADAkoRoAAAAADEmoBgAAAABDEqoBAAAAwJCEagAAAAAwJKEaAAAAAAxJqAYAAAAwBl/5ytLXu9+d0tatKV1xRf4bzIQNP1mU10zJYYcdlq677rq8AwAAANqiCs6qwGxhYemvgwK0xz8+pR078qblup5nCNUaQKgGAAAAzRSBWfXX/uCsCtOGdf/7p7RrV960nFBNqDZ1QjUAAACYnioci9As1jfeuGeINkoq1WaHUK0BhGoAAAAwXlVl2WrbNMfl/PNTOuGEvGk5oZpQbeqEagAAALA+VbVZGZxVYdo4RUtniCq0jRt3r+P3PfHEpX0lWj+rX992QjWh2tQJ1QAAAGBlVTg2iTbNUgRh1VcEZ9U6wrNBNm/e839bVKhFpdqsEKoJ1aZOqAYAAABLIiTrD8qmEZzNzS3tIzCrvrcWGzbkRTZLrZ9BqCZUmzqhGgAAAF0RAVn11yoom3ab5nLVZmsVbZ/vfnfeZLOWwAjVhGpTJ1QDAABgllThWIRmsW56m+Y4bNq0Z0g4a62fQagmVJs6oRoAAABtE4FRf1A27TbN/r9OW1SozfKAgopQTag2dUI1AAAAmqaqsuoPymaxTXMcytbP+N+9Y0fezBChmlBt6oRqAAAATEMVjnW5TXMcZn1AQUWoJlSbOqEaAAAA41JVlmnTnIy61s9ZTV6EakK1qROqAQAAsFYRkFV/1aY5fV0YUFARqgnVpk6oBgAAwHKqkEabZrPFv4/Nm/Mmi7PUZvWflVBNqDZ1QjUAAAAiJOsPyrRptk85oCDMcuoiVBOqTZ1QDQAAoBvK4Eyb5mwpBxRs2ZLS1q15M4OEakK1qROqAQAAzIYqHIvQLNbaNLujbkDBrl1L/w5mlVBNqDZ1QjUAAID2qCrLtGnSL85S6/8zMMsDCipCNaHa1AnVAAAAmqUMzqbdplmFaTRX2foZgVoEa7NMqCZUmzqhGgAAwGRV4ViEZrHWpsl61LV+diFtEaoJ1aZOqAYAADB6VWVZFZRp02RcNm1a+rNV6ULrZxCqCdWmTqgGAACwNmVwpk2TSaurUtuxoxsBqlBNqDZ1QjUAAIB6VTimTZOmikAtgrVK/PmIUK0LhGpCtXT11VenU089Ne/W7owzzkjHHXdc3q2eUA0AAOiyqrJMmyZt1MUBBRWhmlAt7dy5M51Y1mquwX/9r/81/fqv/3rerZ5QDQAAmHVlcKZNk1lQ1/q5a1d3/mwJ1YRqIwvV/uAP/iA97WlPy7vVE6oBAABtV4Vj2jTpks2b9/wz3pUBBRWhmlAtfetb30pXXnll3q3Ot7/97fT6178+7+LD+vHp7W9/e94NR6gGAAC0QVVZVoUI2jTpsvhzH6Fav64MKKgI1YRqQ7v99tvTb/7mb6bPfe5zvf3GjRvTRRddlO51r3v19sMSqgEAAE1RBmfaNKFeOaAgdC1hEaoJ1Yb2pje9afEHZ+knZ7/99usFaoceemhvvxZCNQAAYFKqcCxCs2odwdkkq83iS5smbbdp055hc9daP4NQTag2lPL8tVe96lVpfn4+79ZGqAYAAIxSVVlWfWnThNHq+oCCilBNqLZqt9xySzruuOPSP/7jP/b2v/Irv5L+7M/+rLdeD6EaAAAwrCow06YJk1e2fnaxSi0I1YRqq/bmN785/fEf/3Fvve+++6Y///M/T7/wC7/Q26+HUA0AAChV4Zg2TWieDRvyIotALYK1rhGqCdVW5atf/Wp60pOe1BtSEF74whemM844o7deL6EaAAB0U1VZVn1p04Tmq2v97GqyIlQTqq3Kqaeemi677LLeev/990+XX355uve9793br5dQDQAAZlcVmGnThNlgQMFuQjWh2or+7u/+Lj3taU/Lu6WA7T/8h/+Qd+sXfwhXS/gGAADNUj1ca9OE2Rc/15s35022Y8ds/cwNk1EEoRrLeuUrX5kuueSS3vqAAw5If/3Xf53uec979vajoFINAACaraosq760aUI3lQMKQpdTFZVqQrVlfe1rX0vHHnvsnWep/c7v/E562cte1luPilANAACmrwrMtGkCgxhQsCehmlBtWeXEz4XFK+vBBx/c24+KUA0AAMavCse0aQJrUTegYNeupZ/lrhKqCdUGuuOOO9JjH/vY9K1vfau3f8ITnpDe+ta39tajJFQDAIDRqCrLqi9tmsCoxFlq/Z8lXR5QUBGqCdUG2rlzZzqxL4Z+xzvesXiBzFfIERKqAQDA6lWBmTZNYJK0fu5NqCZUG+i1r31tuvDCC3vrAw88MH3mM59J++yzT28/SkI1AADYrQrHtGkCTWFAQT2hmlBtoMc85jF3tn4++9nPTm984xt761ETqgEA0DVVZVn1pU0TaLJNm5Y+oypaP5cI1YRqtf72b/82PeMZz8i7lM4999zeFNBxEKoBADCLqsBsWm2aZXBWhWkAwzCgYDChmlCt1p/8yZ+k17/+9b11TP38/Oc/n+5617v29qMmVAMAoI2qcGxabZohwjJtmsA4la2f8TmzY0fedJxQTahW69RTT02XXXZZb/2QhzzkzrPVxkGoBgBAU1WVZdWXNk2gawwoGEyoJlSr9au/+qvppptu6q3HeZ5aEKoBADBNVWCmTRNgT3Wtn1KU3YRqQrW9/OhHP0qHH3543qX0e7/3e+mZz3xm3o2eUA0AgHGqwjFtmgDD2bx5z89KAwr2JFQTqu3l2muvTc95znPyLqV3vOMdaa56dTYGQjUAANarqiyrvrRpAqxPfH5GqNYvzlLz2babUE2otpfLL788/ft//+/zLqW/+Iu/SL/wC7+Qd6MnVAMAYDWqwKwKyrRpAoxPOaAgSFD2JFQTqu3lIx/5SHr5y1+edyl98Ytf7E0AHRehGgAAoQrHIjSr1to0AaZj06Y9X1ps2ZLS1q15Q49QTag2dUI1AIDuqCrLqi9tmgDNUzegYNeu3S8gWCJUE6pNnVANAGC2VIGZNk2AdjKgYHWEakK1qROqAQC0SxWOadMEmE0bNuRFFoFaBGvsSagmVJs6oRoAQPNUlWXV1zTbNAVnAJNT1/opOaknVBOqTZ1QDQBgOqrArL9NM4w7OIuArPqrNk2AZikHFGj9HEyoJlSbOqEaAMB4VA9F2jQBWI26KrUdO3x2DyJUE6pNnVANAGDtqmqz6kubJgBrFYFaBGuV+DyPUI16QjWh2tQJ1QAAllcFZto0ARgnAwqGI1QTqk2dUA0A6LoIzII2TQCmpa71c9cuL1GWI1QTqk2dUA0A6IKq2qz60qYJQJNs3rznNcmAgpUJ1YRqUydUAwBmRRWYVQ8l2jQBaIO4dsXUz34GFKxMqCZUmzqhGgDQFvHQESIkq9baNAFou3JAQZCWrEyoJlSbOqEaANAkVbVZ9aVNE4BZF1Vqca2raP1cHaGaUG3qhGoAwKRVgZk2TQC6zoCCtROqCdWmTqgGAIxa9ba9bNOswrRxqh5CtGkC0AZl62dcr+I8NVYmVBOqTZ1QDQBYiyogq760aQLA8DZsyIss2j6j/ZOVCdWEalMnVAMABqkCs0m3aYYyONOmCcCsqWv9lJKsnlBNqDZ1QjUA6K4IzII2TQCYPAMK1keoJlSbOqEaAMy2KiCrvrRpAsD0xXV48+a8yeIsNdfI1ROqCdWmTqgGAO1XBWZra9Nc/A/e6f75r6tXBmfaNAFgZeWAgiAhGY5QTag2dUI1AGi+CMzCaNs0406+/yCXeDW+97ixKhzTpgkAo2NAwfoJ1YRqUydUA4BmqAKy6mv8bZpbF7+2LS17Hp+2bFkK1QRnADA+dQMKdu3a/SKL1RGqCdWmTqgGAJNTBWZra9Ncnyoo232+2RWLN/S7D3O5/+Lf3BV39ADAWMVZav3XfgMK1kaoJlSbOqEaAIxOBGZhtG2aq1O93V5tm+YVi/8jN/edkCxUA4DJ0Po5GkI1odrUCdUAYDhVQFZ9tXWa5lcW/0dviln+fSJUi3ANABiPrVtT2tZ/+sIiycjaCNWEalMnVAOAvVWBWRWUTbNNMwKz6nujtqF4Vb5jx47F389BagAwLvE+K+4xKlo/106oJlSbOqEaAF1U3cy2oU1znKJSLSrWKkI1ABifugEFi5feqdwDzAKhmlBt6oRqAMyqKiCrvqbRphlf0w7OlhNnqsXZapUtW7akrdGXAgCMXARqEaxV4r4gQjXWRqgmVJs6oRoAbVYFZrPepjkuQjUAmBwDCkZLqCZUmzqhGgBNFoFZiNynWk+rTbNaN63abD0iQNvWd1pytH5GCygAMFp1rZ8xdLtNL+OaRqgmVJs6oRoA01YFZNWXNs3JEaoBwGRs3rznvY0BBesnVBOqTZ1QDYBJqAKz6mZSm2YzROtntIBW7r/4D2VXvDYHAEYm7nf6Lrc9BhSsn1BNqDZ1QjUARiECsxA3jdVam2bzCdUAYPzKAQVBGrJ+QjWh2tQJ1QBYrSogq760abbfVxb/BW7atCnvlkSoFuEaADAacamNe6aK1s/REKoJ1aZOqAZAvyowq4IybZqzb0MxiizOVIuz1QCA9TOgYHyEakK1qROqAXRL9ZZUmyaVqFSLirWKUA0ARseAgvERqgnVpk6oBjB7qoCs+tKmyXLiTLU4W61y/uKd/glxxw8ArFtREN4L1FxmR0OoJlSbOqEaQDtVgVmVhWjTZK3KUG3Lli1p69ateQcArFVd66cUZHSEakK1qROqATRTBGbVX/uDsypMG6cqHIuwTJvm7IsAbdu2bXkXb89P6FWrAQDrY0DBeAnVhGpTJ1QDmJ7qJitCs1hr02QaylAtzlOLc9UAgLWrq1KLy6t7rdERqgnVpk6oBjBeEZL1B2XaNGmaaP2MFtDK/Rf/gOyKsWQAwJpFoBbBWiXuv1xeR0uoJlSbOqEawPpU1WZlcFaFaeNUhWMRlmnTZK2EagAwegYUjJ9QTag2dUI1gJVV4ViEZrHWpsks+criH+ZNcehLnwjVIlwDAIZX1/oZ76tcWkdLqCZUmzqhGsCSCMn6gzJtmnTJhuJ1epypFmerAQDDiwLw/ntIAwrGQ6gmVJs6oRrQFRGYVX/tD86qMG2cqnAsMgptmjRRVKpFxVpFqAYAa6f1czKEakK1qROqAbOkygQiNIu1Nk1YnThTLc5Wq5y/ePd/grt/ABhaOaAgSD7GQ6gmVJs6oRrQNhGS9Qdl2jRh/cpQbcuWLWnr1q15BwCsVhxTWr3oDVo/x0eoJlSbOqEa0DTVTUgZnFVh2jhV4ViEZdo06ZII0LZt25Z38QBwQq9aDQBYPQMKJkuoJlSbOqEaMA1VOBahWay1acJ0laFanKcW56oBAKtXtn7G/aXL6fgI1YRqUydUA8alqizrrzYLkwzOtGnC6kTrZ7SAVu6/+MOyK16tAwCrZkDBZAnVhGpTJ1QD1qqqNiuDsypMG6cqHIuwTJsmrJ9QDQDWp671U+IxXkI1odrUCdWA5VThWIRmsdamCbPpK4s/2JviZOU+EapFuAYArMyAgskTqgnVpk6oBsTFvz8om0Zw1t+m2f9XYHI2FD0rcaZanK0GACwv7pv7Cr574iw1l9HxEqoJ1aZOqAazr3pj1h+UadMESlGpFhVrFaEaAKxOOaAgSDvGT6gmVJs6oRrMhuo5OEKzWGvTBIYVZ6rF2WqV888/P53gdGUAWFE5oGDLlpisnTeMjVBNqDZ1QjVojwjJ+oMybZrAKJWh2pbFJ4KtnggAYFl1Awpi1k/cOzNeQjWh2tQJ1aA5IiCr/lo912rTBCYlArRt27blXRywfEKvWg0AGCzOUut/yW1AweQI1YRqUydUg8mqwrG48MZamybQFGWoFuepxblqAMBgZetnBGpOT5gMoZpQbeqEajB6VWVZFZRp0wTaIFo/owW0cv/FD5Nd0b8CANSqa/2UckyOUE2oNnVCNRheBGTVX6ugTJsm0HZCNQAYzqZNe97/a/2cLKGaUG3qhGpQr7o4RmgWa22awKz7yuKH3KZ4OujjVg0A6tVVqcWpCe7ZJ0eo5k5t6oRqdFmEZP1BmTZNoMvqQrU4Uy3OVgMA9hSBWgRrlbhcOop0soRqQrWpE6ox68rgTJsmwGARqkW4VhGqAUA9AwqmT6gmVJs6oRptVz37adMEWL84Uy3OVqucv/iEcIInBADYQ13rZxxDGs8CTI5QTag2dUI12iBCsv6gTJsmwHiUodqWLVvS1q1b8w4ACDHXp/9ZxICC6RCqCdWmTqhGU5TB2bTbNKswDaBLIkDbtm1b3sVDwgm9ajUAYEk8r/QNy+4xoGA6hGpCtakTqjEpVTgWF6FYa9MEaJ4yVIvz1OJcNQBgSTmgIEg2pkOoJlSbOqEao1RVllVBmTZNgHaJ1s9oAa3cf/GDdVccEgMA9MSg7HjGqWj9nB6hmlBt6oRqDKsMzrRpAswOoRoADGZAQbMI1YRqUydUo1SFYxGaxVqbJkB3fGXxA39TvILv43YNAJaUrZ+q1KZLqOYubeqEat0UIVl/UKZNE4BQF6rFmWpxthoAdN2GDXmRRaAWwRrTIVQTqk2dUG12lcGZNk0AViNCtQjXKkI1AKhv/ZRoTJdQTag2dUK19qqed7RpAjBKcaZanK1WOf/889MJXsMD0HEGFDSPUE2oNnVCtWaLD+3+L22aAIxbGapt2bIlbd26Ne8AoHvistg3x6dnxw7PRtMmVBOqTZ1QbfqqwKx6ftGmCcA0RYC2bdu2vIs38Sf0qtUAoKvKAQVBmjF9QjWh2tQJ1cavCsciNKvWEZxNstosvrRpArAaZagW56nFuWoA0FUGFDSTUE2oNnVCtdGoKsuqL22aALRVtH5GC2jl/osXmV27duUdAHRL3YCCuCzGMxjTJVQTqk2dUG31qsBMmyYAs0yoBgC7xSWxv1jCgILmEKoJ1aZOqLZbFY7FB2a11qYJQNd8ZfEiuClGnPVxywZAV2n9bC6hmju0qevqH8IIyuJLmyYA7KkuVIsz1eJsNQDoEgMKmk2oJlSbui7+Iaz7YByFCMxCPHNo0wSgzSJUi3CtIlQDoIviHVPf5VDrZ8MI1YRqU9e1P4TxgVi8fB9KFZDFlzZNAGZVnKkWZ6tVzl98gjhBrwsAHWJAQfN1PVTbJ/8VJmY1H4BVSLZly9LXjh1LXxEBx4dorOPtxNatS28qBGoAzLr+qjUA6II4X7tf1YUETSFUYyrqynXjAzICs/7gLEKz+Iq/JzgDoEti4me/G+MQUgDokPLIoPn5vICGEKoxFXUhWXS4eAkPAEs2VoeDZirVAOiSujO4nYJA0wjVmIp4+V5XrVb2ywNAV5WVakI1ALpk+/a8yARqNJFQjampC9bieUGwBgB7h2oA0BXRxdQ3q6dH6ydNJFRjquqGDESZb/kBCgBdo1INgK4qq9SCM7ZpIqEaU6cNFABW5wpvnQDogPJyt2VLXkDDCNWYOm2gALC3qFTTAgpA10TnUlmc7Tw1mkqoRiNoAwWAvWkBBaBr6gYUeMdEU7UiVPu7v/u7tLCwkHbs2JGuvPLKdPvtt+e/wywZ1Abq+QEAlgjVAJh1ZWHF3FxeQANt+MmivG6Uf/iHf0h//Md/nD784Q+nm2++OX93yb777rv4gzWXXvayl6Vf+qVfyt9dv2uuuSadffbZebd6p5xySjrqqKPybniHHXZYuu666/Ku26I6rWz7jDcTdYEbAMy6Excviu+Oi2N2wuJF8XwXRQBmVN3zYDMTCypdzzMaWal26aWXpic/+cnpggsu2CtQC1Gpdvnll6dnPOMZ6T3veU/+7vp9+ctfTjt37hz669vf/nb+b2C9IkCLr37xwdr3PAEAnbFx48a8WqJSDYBZtm1bXmTlsyE0TeNCtYsvvji94hWvSLfccktvf5e73CU99alPTa95zWvSGWeckY477rhepVrlzDPPTJdccknerc9VV12VV0xTTHYpe+bjw9VzBABd40w1ALoiCinKy9z8fF5AQzWq/fP6669Pz3zmM9Ntt93W2x966KHp3HPP3estbZyxdtJJJ6VvfOMbvf2BBx7YO3Ptnve8Z2+/Vs997nPTF77whd76+c9/fnrYwx7WW6/koQ99aLrvfe+bd8PT/rm3urLfGGSwY0feAEAHXHHFFWnz5s15txSy7dq1K+8AYHbE819/h5Lnv3boep7RqFBtfn4+ffrTn+6tDznkkPTBD34w/fRP/3RvX/o//+f/pGc961l5F9VNW9Jv/uZv5t3w7rjjjnT44YffOQThvPPOS8ccc0xvPW5CtXrlh2qIY2SUAAPQFVGZtmnTprxb0tDjcAFgXTZsyIvMs187OFOtIeJfQhWohd/7vd8bGKiFBz/4wemRj3xk3qU9/rNrEb9/FahFe+mjHvWo3prp0QYKAHuL6jUAmCV1Z2hHpRo0XWNCtYsuuiivltopH/GIR+TdYNGi+fSnPz0df/zxq27VHCSGFFSitaL/3DamIwK1csBZBGplWygAzKq4JynPVZuWH/zgB+l73/te+v73v3/nUR0AMArbt+dFFhVqDbn8wbIaE6p94hOfyKuUfv3Xfz2vlvfEJz4xvfnNb06ve93r0gtf+ML83bW5+uqr82qpCo5miLcTZclvvKDfujVvAGDGTWtYwU033ZRe//rXp8c85jHp7ne/e9p///3TT/3UT6UDDjgg3e1ud+udZfuc5zynN7UdANYqLmtlEbYBBbRFI0K1H/3oR3tUivW3dU7KjTfemFcpHXnkkXlFE9S1gcabDG2gAHTRJEK1eGkZZ7m99rWvTTt37kw//OEP89/ZLSa1x/m30TXwlKc8pVfBBgDDiiN+Slo/aYtGhGr956Htt99+e0z7/OY3v5k+9KEPpVe/+tXp9NNPT1u3bk0f+9jHekHcKH32s5/Nq6U3wjfccEM688wze9VwD3rQg3qH7x111FHp5JNPThdffHFvsAGTEYGaNlAAuqqsVOt/ETgOZ5xxRvpP/+k/3XmvFUdiPO5xj+sNhIrOgJiW/oAHPKD39yof/ehH08tf/vK8A4DVK6vUDCegTRox/fMjH/nInTdiBx10UPqbv/mb9N3vfrf3ljTOWqsGCPQ78MADewFXTAxdr69//eu9m8VKTBXtP+OtzgMf+MD0lre8pRe2rZfpn6sTLZ/lW4yoYtMKCsAsixeK2/ougI9//OPTjh078m60vvCFL6Qjjjgi71J60pOelM4///x0v/vdL39nt8suu6x3H/aNb3yjt4/w7R/+4R/SwQcf3NsDwEpiQEFZLLFr196dSjSX6Z8N8M///M95lXpVYXFDFsHWn/3Zn9UGaiEOyn3jG9+YXvayl627auzzn/98Xi3pD9Sicu4e97jHXoMLol31ec973h4VboxX3WGV0QZqCBoAs2ySZ6rFC8PKv/pX/yp94AMfqA3UwnHHHbd4Hd59snTcs8WLUQBYrYWFvMii7VOgRps0olIt3sC+//3v762PPvroXsvnroinFz384Q/vndXxMz/zM71JU9EqGu2g/VOnYvpnDCtYq7PPPjude+65ebf0pjXevMZ/b3UjGzeKn/rUp9I555yTPve5z/W+F+5zn/v0DuiNCru1GqbaresVbfEcsWlT3mTxryj/cQGAmXPFFVekzZs3591SyFbdJ43ave997ztfdsbLy//yX/5Lbz1IvNiMgQXVmWvvfve7R9JFAEA3bNiQF1kc+6P9c/qG7cjrck7RiFAtzkuLqrR+USH2+7//+723oKWvfe1r6aSTTtrjhvI973lPesQjHpF3w4k20o9//OO9dUy2euc739k7P22QV73qVb2DeStRVfemN70p74an/XM42kAB6JKoTIuhAf3GefsWLzevuuqq3uCmQVVq/fqDuLiHetGLXtRbA8By6lo/p59OMCztnw0VIVVdoBYOOeSQ3vkeEYBV3va2t+XV8E477bRepVq8kX3rW9+6bKAW4tdFm2olBhfEGXBMRry5KKfBaAMFoEvG2QIaZ6LFNM+VArVbb701ffjDH+79FQCGVRZKqFCjjRoRqu2zz57/M+LN6NOe9rS8qxc3ev3tBfFGtW7c+2rEBKtjjz02PfvZz06PfvSj83eXF5VylWgN7Z9gynhFu6dpoAB0RXmmWhhnqFaKgU4xVOqCCy5I//k//+f0b//tv+0NbLrXve6VnvnMZ675/guA7oqCiPJS5vQA2qgRodrP/dzP5dWSeDu6Go997GPzainYuvLKK/Nu/CKE63fttdfmFZMQzxfR8tkvPpS1gAIwi2LiZ79xh2r/+3//714bZ7R2xn3aU5/61PRbv/VbvaM54siOG264YeAwKQBYSd+cmzuV3UjQBo0I1X7+538+r5b863/9r/Nqeb/8y7+cV0tuvvnmvBq/mAh6l7vcJe/2nGDKZGgDBaCrxhmqveY1r+ndY73rXe8aeH9z6KGH9qr2L7nkknTAAQfk7wLA6sR5av3KTiRoi0aEavEWtF/ZDjrIXe9617xaEhOoJqk/VFvt/2ZGRxsoAF1RtoDeeOONeTVar3/969Mb3vCGvFvyuMc9Lp1yyinpfe97X7r88st77Z5f+tKX0nnnnbficR0AUCoDtaBKjbZqRBIUZ6j1W23FWXmGx93vfve8Wr2qbXTHjh3psssuW3UrQ/y6/oN542wRJm9QG6hgDYBZsnHjxrxaMo5KtQjqtvWdGh3VaH/7t3+bFhYW0tlnn52e97znpc2bN/cmtPczqACAYZStn9GBVHN8KLRCI0K1Aw88cI+bxU9+8pN5tbydO3fm1ZJf/MVfzKvVizDtBS94QXrpS1+aTj311PSZz3wm/53llb8ubjyZjro20GgB1QYKwKwoK9XGEap96EMf2uPl4gc+8IEV762+//3vpx/96Ed5BwArK5/T5ubyAlqoMT2LT37yk/Mq9SZMxU3aSuLNaSVCuUMOOSTvVu+II47IqyXR1rAaF110UV4thYKPfOQj845J0wYKwKyrmwA6ap///Ofzauns2F/5lV/Ju8FiaEG/b3zjG3kFAHurGywXRRLQVo0J1Y4//vi077779ta33HJL+qM/+qPeepDrr78+/emf/mnepfTsZz87r4Zz8MEHp4c85CF5l9KFF16YvvrVr+ZdvaiQi4N5KyeeeKIz1aZMsAbALJtEpVr/WbG33Xbbim2d3/nOdxYfjvZ8OrrpppvyCgD2Vtf6CW3WmCQoqszm5+fzLqX3vve96S1veUve7SluJGPMe9Wi8LM/+7O9Fs46cajub//2b9/5de211+a/s9tpp52WV0s3kS95yUsGBmvRLnryySfn3VKFXPxvYfqiBbRsA41DMLWBAjCLRh2sHXvssXm1dHbsa1/72rzb2w033JCe8IQnpL//+7/P31miFRSAQeLZrLx09UUA0EobfrIor6cuBg9EsHbNNdfk76S0adOmXhVbvKGNG7xPf/rT6f3vf3/68Y9/nH9FVCidnx796Efn3Z5e97rXpQsuuCDvUnrHO96R5mqatmPSVQR5lTiEN37fo48+ujdl9Lvf/W669NJL9zjvbf/99+/9bznssMPyd9Ym/vPXXXdd3rEe8SG9+EdmD/Fyf9euvAGAltqwYUNeLYkXfY8f4bi0eLEY911f+9rX8ndS+vVf//X0whe+MP3Mz/xMb/9P//RP6S/+4i9690xVgPb//X//353h2m/8xm/07o0AoBRdRP2TP+MStngpo+W6nmc0KlQLP/jBD3pj21czrCCmff7+7/9+euITn5i/s7fVhmrhrLPOSu9617vybnkHHXRQetvb3rbXmWxrIVQbrfigLts+o6y4bA8FgDaJyZtX9JVfx0vFE0bcN/M3f/M3vQq0OIpjJRGmRUdADG96xSte0fveAx7wgPTlL3+5twaAfsW7od7zmfbP9ut6ntG4g8Duec97pvPOOy+deeaZvbeldeLstSc96Unp4osvXjZQG9bpp5/eC+Ae/vCH5+/s7YADDkgvfvGL00c/+tGRBGqMXnwwawMFYNaN41y1xzzmMemzn/1sOuaYY/J39hZh2hvf+MbeDXT8+qc97Wn57yy1hX7iE5/IOwBY0l+hVhlhsTVMTeMq1bpIpdroDWoDjfLi4qxnAGiFGIz07r6nkqhSi2o1AGi6zZv3LHLQSTQ7VKrBDIrgrPyQjqBt27a8AYCWieFI/cZRqQYAoxZhWtk1ZEABs0Koxswa1AZaV3oMAE0XQ5v6CdUAaIPt2/Oij9ZPZoVQjZkW1Wplu2dUq3kOAaBtylANANqgrFIznIBZIlRjpsXzx5YteZNFoFZOBwWAplOpBkDbRJdQebkqn8+gzYRqzLx4E1K+DYm3JdpAAWg7wRoATVa2fsZzmcJrZolQjU6ItyHaQAFos7r2T6EaAE1Wtn7OzeUFzAihGp0QzyF100C1gQLQJo8vTnYWqgHQVHWdQc5TY9YI1eiMeA6pawPdujVvAKBlhGoANFV0BvUTqDGLhGp0Sl0baPT5eyYBoA1MAAWgDeoGFMzP5wXMEKEanaINFIA227hxY14tWVhYyCsAaI7y8hTPYcUJBjAThGp0TnyYl2OctYEC0AYq1QBog/I8tfL5C2aFUI1OqhvlHG2g5XQaAGiSMlRzphoATVM3oECVGrNKqEYnaQMFoI2EagA0XRQr9KsraIBZIVSjs+raQOPZRBsoAG0iWAOgScrun7m5vIAZJFSj0+KtSVmKrA0UgKaqO1NNqAZAU9R1/sQzF8wqoRqdpg0UgLZ5fPE2SKgGQFOUxQkCNWadUI3Oi2BNGygAbSVUA6AJYkBBeUky9ZNZJ1SDRdpAAWiLuhZQAJi2hYW8yOL5yiWLWSdUg0XaQAFoi40bN+bVkoXyKQYApiAq1frNz+cFzDChGmSD2kAFawA0iUo1AJqmDNSC89ToAqEa9KlrA40WUG2gADRFGao5Uw2Aadu2LS8ygRpdIVSDPtpAAWg6oRoATRIFCOWlSOsnXSFUg4JgDYC2EawBMC0x4K1Udv/ArBKqQY24CJQXgjgnQBsoANNWd6aaUA2AaSnPUyvPqYZZJlSDGnXVakG1GgBN8PjizY9QDYBpMKCArhOqwQDaQAFoC6EaANNQtn5GoFZTUA0zS6gGy6ibBqoNFIBpq2sBBYBJK5+L5ubyAjpCqAYr0AYKQNNs3Lgxr5YsLCzkFQBMhtZPEKrBirSBAtA0KtUAmLZt2/IiE6jRRUI1WIVBbaB1b2cAYNzKUM2ZagBMUjwHlZee+fm8gA4RqsEq1bWBxtsZzzEATJpQDYBpKk8diAKEsggBukCoBqs0qA20LHsGgGkQrAEwKWXHjio1ukqoBkOINtDyrABtoABMWt2ZakI1ACah7tlHlRpdJVSDIW3ZslS11k8bKACTZlgBANOwfXteZFF04JJEVwnVYEhxwYhgrV8EaqaBAjBJZah2xRVX5BUAjEdcasrLjdZPukyoBmtQ1wYaF5etW/MGAMZMpRoAk1ZWqQWtn3SZUA3WqK4NNC4y2kABmISNGzfm1ZKFchQbAIxYWaVWFhpA1wjVYI0iUKubBqoNFIBJUKkGwCTFgIKygKA8Fge6RqgG6xClzuWFRBsoAJNQhmqmfwIwTgYUwN6EarBOdReTuOCUpdEAMEpCNQAmqXy+mZvLC+gwoRqsUzzTaAMFoAkEawCMQ7R+lpynBkI1GIm6NtB4rtEGCsC41J2pJlQDYBy2bcuLTKAGS4RqMCJxYSnHSWsDBWCcDCsAYNzieaZ8ZzM/nxfQcUI1GBFtoABMWhmqXeFNDgAjVg4oCGUxAXSVUA1GKJ5ttIECMCkq1QAYt/I8tbKQALpMqAYjpg0UgEnZuHFjXi1ZWFjIKwBYv7oBBarUYDehGoyYNlAAJkWlGgDjVLZ+RgGBSw/sJlSDMRjUBipYA2CUylDN9E8ARqnstpmbywugR6gGY1LXBhoXJW2gAIyKUA2AcakrCIhnHGA3oRqMSTznaAMFYNIEawCMQlkMIFCDvQnVYIwEawCMU92ZakI1ANYrBhSUl5PyeBtAqAZjFy2gZRtoXKS0gQIwCoYVADBq5TDpeJ5xuYG9CdVgzOqq1YJqNQBGoQzVrvDWBoB1iiKAfvPzeQHsQagGE1AXrGkDBWAUVKoBMEploBacpwb1hGowIXXTQLWBArBeGzduzKslC2XPDgAMYfv2vMgEajCYUA0mSBsoAADQVPHCv3zpr/UTBhOqwQRpAwVg1B5flEGb/gnAWpVVaqHstgF2E6rBhA1qA607uwAAhiVUA2Ctyiq1LVvyAqglVIMpqGsD3bZtqWoNAIZRN6hAsAbAsOIlf3n5cJ4aLE+oBlMwqA00gjUAGIZQDYBRqBtQYMA0LE+oBlMSF6nyzY82UADWoi5YA4BhlK2fc3N5AQwkVIMpijMKyucgbaAADKsM1a4on4wAYBl1L/a1fsLKhGowRfEMVB7+GYGaaaAADEOlGgDrUR5DI1CD1RGqwZTVtYFGgYE2UABWa+PGjXm1ZGFhIa8AYHl1Awrm5/MCWJZQDRpAGygAADAN5XuYxz9+6QtYmVANGiACtbppoNpAAViNxxdPP6Z/ArBaZYeMKjVYPaEaNEQ8D9W1gW7dmjcAsEpCNQBWo+7IGVVqsHpCNWiQujbQ7du1gQKwvLpBBYI1AFYSzxr94iW/2TewekI1aJBBbaCbN+cNANQQqgEwrLhMRGdMP62fMByhGjRMlFtHxVq/uOBpAwVgOXXBGgAMEoPRSlo/YThCNWigurLrKM0u3yQBQKUM1a5w0QBgGeVlojzfGViZUA0aKJ6LduzImyyq1UwDBWAQlWoArFYMKChPCSi7ZYCVCdWgoeLZSBsoAKu1cePGvFqysLCQVwCwp/ISEW2f3s3A8IRq0GBRgl2ea6ANFAAAWI+oVOtnQAGsjVANGizeFtVNA9UGCkDp8cVbGNM/AahTBmrBeWqwNkI1aDhtoAAAwKiUUz8FarB2QjVoAW2gAKykHFQQlWqq1QDoF88P5aVB6yesnVANWkAbKAArqZv+KVQDoF+8mC+VL++B1ROqQUsMagMVrAFQqQvWAKBSnqdWvrgHhiNUgxapawONEm5toACEMlS7wgUCgKxuQIEqNVgfoRq0iDZQAABgLcrWz3hhr8AZ1keoBi0jWANgkLm5ubxasrCwkFcAdF1ZvFxcMoA1EKpBC0WZdlmqHeXcunwAAIDS1q150Scq1YD1EapBC9VVqwXVagDd9vjijYvpnwCEutZPYP2EatBS2kABAICVREdL+Y5lfj4vgHURqkGL1U0D1QYK0F3l9M+oVFOtBtBt5fGadUfJAGsjVIOWG9QG6hkKoHvKUC0I1QC6LV6691OlBqMjVIOWG9QGum1b3gDQKXXBGgDdVAZqQZUajI5QDWbAoDbQuosoALOtDNWucCYAQGfVDSjw7gVGR6gGMyKq1coLZFSr6foBAIDuiXcq5XsVrZ8wWkI1mBERqG3ZkjdZBGqmgQJ0y9zcXO+v8Z6lV8QcJ1SrVgPonLJKLWj9hNESqq3C3/3d3y3ejy6kHTt2pCuvvDLdfvvt+e9As0Q5d3z1i+cobaAAHRBvUrZuTVsXn6J+srjdtfi1Y/Fra1wINm9OacOGlDZt6v0aAGZf+T6lfE4A1m/DTxblNX3+4R/+If3xH/9x+vCHP5xuvvnm/N0l++67b+8t8Mte9rL0S7/0S/m7a3fYYYel6667Lu9gfeKZKp6d+ts+o4ptx+KTlfMTAGZUBGXDTKiJC0L0AAnYAGZSvFQvO1Z27fI8wOh1Pc9QqVbj0ksvTU9+8pPTBRdcsFegFqJS7fLLL0/PeMYz0nve8578XWiGuFDWTQPVBgowg6o3KcOOfI7/XPxnonKt/y0MADPBgAKYDKFa4eKLL06veMUr0i233NLb3+Uud0lPfepT02te85p0xhlnpOOOO65XqVY588wz0yWXXJJ30AxxVkJdG6iCBIAZEh/sEYqV/T3DqEK59fx3ANA45cd6Pm4TGDHtn32uv/769MxnPjPddtttvf2hhx6azj333LRx48bevhJnrJ100knpG9/4Rm9/4IEH9s5cu+c979nbD0v7J+NQPSf1FyDE2yltoAAzID7cI1AbFRcIgJlR1/rpqZ9x0f7JnV7/+tffGagdcsghvdbOMlALEbb99//+3/Mupe9973u9s9egSeK5SBsowIwa9Yd59SYGgNYrTwQwoADGR6iWRbL66U9/Ou9S+r3f+7300z/903m3twc/+MHpkY98ZN6lPf6z0BTRBrplS95k2kABWi5KEMbRrhnBmnHRAK0WH+P9nSoh5tIA4yFUyy666KK8SumhD31oesQjHpF3gz3/+c9PT3/609Pxxx+fHvawh+XvQrPUHUoaB5c6PgegpYYdSjCMcf53AzB2Cwt5kcVzQLxoB8bDmWrZU57ylPTlL3+5t37d617XC8omxZlqjFsEaGVXT1xgY6w2AC1Sd1DOqMXZap7AAFppw4a8yOI4GO2fjJMz1Ug/+tGP7gzUQn9bJ8yCujbQKAvXBgrQMmUJwjhEOTMArVPXwe8dCYyXUG1R/3lo++233x7DCb75zW+mD33oQ+nVr351Ov3009PWrVvTxz72sV4QB20Sb6jKi6o2UICWKQ/KGYdJ/B4AjFz5TqTuGBhgtLR/LvrIRz6SXv7yl/fWBx10UPqbv/mb9N3vfje9+c1v7p21dvvtt/f+Xr8DDzwwnXzyyWl+BKc+av9kUuI5adOmvMm0gQK0SHyIjzv0cmEAaCWtn0xD1/MModqi97///b0KtPC4xz2ud6ZaDCG46aabet9bzpOe9KT0R3/0R2mffdZe9Bd/CFdL+MZ6xR/18hzqaA3VCgrQAuUT07i4PQRolThus2z/9FHOWg2TUQShWsdFoBbBWjj66KN7LZ+78hvahz/84b0Jnz/zMz+Tbrvttl6raLSDxroSQw0iiFsrlWpMUhQ4xEW3v+0zihLiTZYzFwAabhKVasHtIUCrlJeHqFCL+3sYN5VqQrXeeWl/9md/lndL4my13//930/HHXdc/s5uX/va19JJJ510Z/AW3vOe96RHPOIReTccoRqTpg0UoKVilPO4D8OMNywxARSAVqgbDB339c5TYxK6nmcYVDDAm970ptpALRxyyCHp/PPPT/vvv3/+Tkpve9vb8gqaLy6wddNAy4sxAB3kKQygVcrB0PFuxEc5TIZQbVF5HtqRRx6Znva0p+Vdvfvd7357DCm46qqr0g9/+MO8g+armwYaxQ+mgQI02AgGJK1k6+KF4AoXA4DWKM9Sm8ClAsiEaot+7ud+Lq+WPOUpT8mr5T32sY/Nq9SbEHrllVfmHTRfvL0qz1lQrQbQcBM4/HLb4sVg8+bNadOmTYsPasWTGgCNUvcxbeInTI5QbdHP//zP59WSf/2v/3VeLe+Xf/mX82rJzTffnFfQDoI1gJap698fof5ns68sXhBOXLwgRLhWTUkHoFnKqf4CNZgsodqie9/73nm1pGwHHeSud71rXi2544478graI4oeysKHeOOl8wegmSL46hvwNlLFs1lPhGvbFp/ahGsAzRL36/FCvJ/WT5gsodqiOEOt32orzsoz1O5+97vnFbRHXbVaUK0G0DxROXbitm1pHB/RX1m8GGxZ/Lr/gNOthWsAzbJ9e170mcApAUAfodqiAw88MG3cuDHvUvrkJz+ZV8vbuXNnXi35xV/8xbyCdtEGCtBsEWjFOWfVGWdRTDzSWGvLlnT/E05IJyx+7dixozfl/PEDnszKcC32AExeeZ7aGE8HAAYQqmVPfvKT8yqlj3zkI+n73/9+3g220De7OEK5Qw45JO+gfeqmgWoDBZi+CK2iQq2cyBmtml8ZxeE58RTWV3kWlWpVuBZfK4VrEfbF/z7hGsDkGFAAzSBUy44//vi077779ta33HJL+qM/+qPeepDrr78+/emf/mnepfTsZz87r6C9tIECNEsEaVERVgZqIQKv+8cH965dSyXHw4r/zOJ/R3+gVopALX6fXYu/RwRtdSJMiwq6Klyr+98KwGiVrZ/xEb2WSwGwPkK1LKrM5vtOdXzve9+b3vKWt+TdnuLm8UUvelG6/fbbe/uf/dmfTS94wQt6a2gzbaAAzVEFVaWoJNujgqwKx+IDfEBV2R7i10d1WoRxq/n1i+L3jJbQCNe2DOgv6g/XBgWBAIxG+RE7N5cXwERt+MmivO68GDwQwdo111yTv5N6N4VRxRY3kxGiffrTn07vf//7049//OP8K+Ie9vz06Ec/Ou+Gd9hhh6Xrrrsu72D64hmuvFDHs5qScoDJiLPKorWyFPcjEWwtK96GVB/i1VEVcXZshGkRosVf16kK0Or+N/aL/70Rwg2qcgNgeFFgXH78eqpnWrqeZwjVCj/4wQ/SKaecsqphBTHt8/d///fTE5/4xPydtRGq0TTxPLZpU95k8QwWhRAjeBYDYBlR6VVX5VW1YjbJMOFavLg0NRRg/eI+Pe7XK/Heouw2gUnpep6h/bNwz3veM5133nnpzDPP7FWp1Ymz1570pCeliy++eN2BGjRRBGflhTku3Cs8MwGwDhFQDQrUotqraYFaiLAsgrKqLTT2deL/W//EUADW5t3v3jNQC32nGAETplKtAVSq0VRxllpcuPtpAwUYvQjS6s5PC3ucn9ZwEZ7F/5cI0GI9iMo1gLUp78/j8tDAdy50iPZPodrUCdVoqngeime8/ueiKELQBgowOtE+GVMzSxE8xbmtbQnU+lXh2vbt22sr7ypVuBZnrg2qcgNgtw0b8iLzwptp0/4JMEA835RD3iJgMw0UYDSiUmtQoNamCrVS/O+PoCz+PywXDFZtoVGlF/8clqtuA+i6soMktPQyATNDqAYsK958lW+/ouhAxw7A+kSQVHfAfwRQcUbZrFRuVeFa/H8aNAU0wrSo2KvCteWq2wC6avv2vMjiI1WRL0yXUA1YUVSrlRfsuKgrKAAYXgRIbRtIMAoREkbVmnANYHjxcVh+JBpQANMnVANWFIFanNfQLwI1baAAw4mQKCZg1oVFETh14eD+/nAtQsRBqnAt/nnFGqDLyiq1oPUTpk+oBqxKXLTLZ594JtQGCrA6EaRFSFSqzk8bVL01q+L/d4SIK4VrUb0WVWvCNaDLyncxHbtkQGMJ1YBVqzu3Id6a1RRcANAnwqPlArW2DiQYhTJci32d/nCtCxV9AJV4nxBdIv2WeRcBTNCGnyzKa6ak6yNoaZcI0Mrnwnj+WXwWAqDGoPPTIkib1fPT1qM6V2379u299SARvs3PzwvYgJkX9979l5F40V0ezQLT0vU8Q6UaMJS6NtB45vFMA7CnCIQGBWrVREz2VlWuxT+fOHttUBVf/PON6alV5dpyARxAm5WXkbm5vACmTqVaA6hUo23iuSWGFPRf4KNaLd6YdbiDCeBOEfBE2FMngqKunZ+2XlXlWl1AWakq1+Kf7aAWUoC2idbPcjiYJ3iapOt5hlCtAYRqtFEEa+XzYjzDaAMFum65gQTLVV6xsggr41y1lcK1+GccAZt/1kDbxf12fyGu1k+aRvsnwBpEgKYNFGBP0YYoUBuf+OcYbaEx1GBQtV8Eb1HZFv8eVgrgAJosPr76A7UwP58XQCMI1YA1i+eZ8vnQNFCgqyLEiTO+ShGkRQgkUBudKqSsJoYOUoVr0YorXAPaJu6rSy4l0CxCNWDNolqtLD+Pt2nluQ8AsywqoyK4qQttDCQYrwjXojpwpXCt+ncU4VoEbQBtUH5cafuE5hGqAesSwVpdG6hgDeiCaiBBXaAWIU9UUzF+w4Rr0RJaTQwFaKq6/F+VGjSPUA1Yt7o20Hi+1GkDzLII0gZN+IzqNKHN5JXhWuzrRLgWrbrCNaCpytbPuN8e8JEGTJFQDVi3uMBrAwW6JIKYaCcsRYgTgZrz06arCtfi30VUCwrXJusHP/hB+t73vpduvfXW/B1gWOXL6bm5vAAaRagGjIRgDeiKaB80kKAdIkyrzrVbbvpqGa7FnuF85CMfSc95znPSPe95z7T//vunn/qpn0r3uMc9evv4/l/+5V/mXwmspO7+OSrVgObZ8JNFec2UHHbYYem6667LO2ivKkQr36zFGd2eMYG2q87jGjSQwPlp7RD//iJAq/v3WIkwLgK45VpIWfLVr341/eZv/mb65Cc/mb8z2G/8xm/0fk7ufve75+8AdeJkgf5sPwI1lxiaqut5hlCtAYRqzJK4ASiPGIrnkV278gaghSJQi3bPugqmCF60DrZPVZ223DTQKlybn59XgVjjxhtvTEcffXT6xje+kb+T0gEHHJCOPfbYXqXazTffnC677LL0L//yL/nvpvTUpz41XXrppXkHlOIjqaxUi/to+T5N1fU8Q/snMFJxwdcGCsySaiBBXaBmIEF7RWAWVVPLTQyNf+cRukWgGn8Glqtu66KnP/3pewRqr33ta9O3vvWtdNFFF/X+2f7pn/5p+trXvpZe+MIX5l+R0l/8xV+k8847L++A0sJCXmSR5wvUoLmEasDIRYl6+UI/3rp5FgHapgpUShHIGEgwG+LfZQSjy4VroapWjHBtueq2rrjgggvStddem3cpnXPOOb3Kv/322y9/Z8m97nWvtH379nTMMcfk76T0xje+Ma+AUvnxMj+fF0Ajaf9sAO2fzKIo6NAGCrRZnJ9WF55EkBaBGrOpqk6rG0bRL8K4aAvtaqXiYx/72DvPUXvkIx+ZPvWpT/XWg/zN3/zNHsFaBHKHH3543gEhLjlld4endZpO+yfAGESApg0UaKOqIkmg1k1l5Vrs68Sfk/6JoV3y/e9/f4/BBP/u3/27vBrsMY95TO+f0//4H/8j7dy5M/3iL/5i/jtAZfv2vMhM/ITmU6nWACrVmGXRNVW2fUbY5iYBaKIqUIu/lgwk6Kb4s1BNDK37c1HpUuXaRz7ykd7AgUr8c9m4cWPeAWsR98vlaQMm6NMGKtUAxqisVgvRUbPMcwnAVBhIQJ0Iy0444YTen4E4fH/QOXrx56a/cm25AK7t/umf/imvUtp3330FajACZZVaEKhB8wnVgLEa1Aa6wlE1ABNlIAErGTZciz9PcS7fLIZrMdGzcve73z2vgPUoOzuWmZsCNIhQDRi7aPUs2z3jqKKa44oAJi6Cj/gqRYgS52oJ1ChV4Vr8+Yh1nQjTqrA2/nxFJeSs+N73vpdXiw8T+3icgPWKe+Iyfx/w0QI0jKsgMBHxti2q1vppAwWmKUKP5QYSRGACy4ngNarWuhau/cIv/EJepXTrrbfmFbBWdQMKyvtmoJmEasBExI1BWcYegVpNcQjA2EXQMSjgiIEEUYUEq9UfrsWfn0GqcC3OXasLc9vinve8Z16l9KMf/WjVwdoNN9yQbrvttrwDKuWlaG4uL4DGE6oBExNv3coX+XET0eLnCqCFqoEEdYFahGkGErBWEa7Fn5+VwrUq1G1ruPbgBz84r5b85V/+ZV4t7yUveUm6293ulg488MD0+te/Pn8Xuq3uI0DrJ7SHUA2YKG2gwDRVlUKlCEMMJGBUynAt9nX6w7U2hbmHH354+rmf+7m8S+mSSy7Jq8G+//3vp4WFhd76X/7lX/YK5qCryuFdAjVoF6EaMFHxXFE3DVQbKDBuEVpEgFGKwCPCD4Eao1aFaxHYrhSuxcTQNoVr/+7f/bu8iuv6+elLX/pS3tX7gz/4g3T77bf31vvvv396ylOe0ltDl0WVWvlieX4+L4BWEKoBExfPrXVtoC16SQ+0TFSnRWhRMpCASegP1yKAGhTgluFa7JvqZS97WTrooIN66zhX7QlPeMLAYO3P/uzP9ggLX/GKV6S73/3ueQfdlYs37xQfDd7vQLts+MmivGZKDjvssHTdddflHXRDPCdEB1b/80K8wI+zwQe8yAcYWtVeN2ggQVuqgpg90Yq8ffv22j+blQjj5ufnU0wWHVTlNk2XXXZZevKTn5x3Kd31rndNz3/+89Nxxx3Xq0b7p3/6p/T+978//c//+T/zr0jpyCOPTDt37hSqwaING/Iii24O7Z+0TdfzDKFaAwjV6Kp4jiiPNopnBkUjwChEWFF3flqIaqEIKmDalgt+KxGoRXVbBGxNa1P+8z//8/Rbv/VbvXPSVnL00UenSy+9NB188MH5O9Bd0fpZnkgQ98BeLtM2Xc8ztH8CUxPPBeVwtKhcUzgCrNdKAwkEajRF9Wcy2pAH/bmM4K36M71SADdpv/Zrv5b+z//5P+mkk07qVarV+dmf/dn0xje+MX3qU58SqEG2fXteZPHjL1CD9lGp1gAq1eiyCNHq2kCj/N2ZEsBaREtn3flpVXjRxDY6qFQBWt2f4X7x53i589mA5or73k2b8iaLI1D8ONNG2j+FalMnVKPr6m4s4plXGygwrKjkqaviieAhAjVoi2HCtTgfUPUltEe0fUb7Zz9P5bSV9k+AKYsATRsosB4RQAwK1CJsEKjRNhGWRdVltIVGaDZIdSZbNTEUaL7yUiUTh/YSqgGNEDcTZcl7nDXRoGNjgIaKIC0ChbpALdrj4gvaqgzXBrUvR7gWVW3CNWi2qFCLl8f9lsnNgYYTqgGNEM8I5XNv3HCUU5EA+kWQZiABXVCFa/HnOoJi4Rq008JCXmTxUnnAjzPQAkI1oDHihkIbKLBaERgsF6g5wJ1ZFH++q5bm5QYVlOFa7IHpK89Sm5/PC6CVDCpoAIMKYLeqOq2/iyvCtqhi83wMVAwkgN2qc9XqfiYqEcbFz8dyLaTAeEWgVnZheBqn7QwqAGiQKkDrVwVtABEeGEgAe6qqM+PctUEtz/GzE9NEo3JtpQAOGI9ymK8TCqD9hGpA40SwVtcGKliDbotQwEACGCzCtfg5WGliaIRrEU4P+nkCRi9+1OJ+tp/WT2g/oRrQSPHmrmz3jJJ59/7QTfHgHwFAqarQMZAAdoufizhHbaVwrar8jJ+tCNqA8Ymp9iVHm0D7CdWARopqtbqiE9Vq0D3LDSRY7qB26LphwrVoCY1wLX49MHplbq24GmaDUA1orLpgTRsodEuEaTHBsBRBWgQFAjVYWRmuxb5OhGv9E0OB0agrBHX5gtkgVAMaTRsodFPVlmYgAYxOFa7Fz09UeQrXYDLK1s+4vx3w4we0zIafLMprpqTrI2hhJVGdVh6lFDciu3blDcyoL33pS+nv//7ve+v73Oc+6aEPfWhvPevigb7u/LQQVTYe8mE04mctguvti0/8yw0siPBtfn6+F2gPCuKAwTZsyIssOjEcBcqs6HqeoVINaLy4f9cGShedffbZ6QlPeELv63d/93fzd2fboIEEIaprBGowOhGQVZWfy51PWFWuRfVonL0We2B16i5bAjWYHUI1oBXi5kMbKMy2CMwGDSSIh37np8H4VOFanLs2aJpuhGkxJbQK15arbgOW1LV+ArNDqAa0RlmtFqJazQtzaL94QDeQAKYvQuyoWhOuwfrFC+DyPnWZQbxACwnVgNYY1AZa8xwOtEQ8nMeDeTygl6rKGWDy+sO1OMtwkCpci7btup9j6LKFhbzI4v1Q3M8Cs0OoBrRKvDSvawN1Hw/tUwVqdVUu8RAfD/TAdEW4Fq3ZK4Vr8fMcVWvCNdit/FGYn88LYGYI1YDWiefs8i1fVKuV5fVAc1UDCeJBvGQgATRPGa7Fvk5/uObnmC6ry5adZACzR6gGtE7cx5cvy+O5PM5Xgy75wQ9+kL73ve+lH//4x/k77VC1i5XiId1AAmi2KlyLn9WVwrU4J1G4RlfVDSgY8OMCtJhQDWiluDEpz0+ODjIdJ8y6r3/96+llL3tZ+umf/um0//77p5/6qZ9Kd73rXdOv/MqvpLPOOit9//vfz7+ymaKCJb5KBhJAu/SHa9GqPehntwzX6qpTYdbEPWl5soHWT5hNQjWgtaJarXzjpw2UWfaJT3wi/dIv/VI655xz0ne+85383SXXXntt+t3f/d102GGH9X5d08SD9KCBBPEwbiABtFOEa9VQkdWEa/E5IFxj1pVVasE7I5hNQjWgtSJQK88xj3t0baDMoi996UvpqU996p1h2hFHHJFe+MIXpt/6rd9Khx56aO974Wtf+1p60pOelD7zmc/k70xfPDxHddqggQQCNZgNVbi2XNVpf7g26HMB2q78Y112VwCzQ6gGtFrcs9e1gTq+hVnz93//9+lf/uVf0s/+7M+mj370o+lzn/tc2r59e3rve9/bC9ze9a53pbvd7W69X3vLLbek3/iN30i33XZbbz9N1UCCugfnePh21hLMnup8xAjXImirE+Fadb6icI1ZEgXZZSFmeRYwMDuEakDr1bWBRtl9eUMDbRdnqP3VX/1VOu644/J3douH0v/xP/5H3i09sL71rW/Nu+kwkAC6LX7WoyW0mhg6SPVZMSiAhzYxoAC6RagGtF7cqGgDpQvOOOOMdPjhh+fd3p7xjGekZz7zmXmX0jvf+c68mrwI+eKrFA/ZBhJAt8TPfVSlrhSuxcuAKlyrO38R2qDMhefm8gKYSUI1YCbE83l5nx43NTrLmBUx4fOUU07Ju8HinLXK3/7t3/ZaQyctHooHDSSIh2qgm4YJ1yKUryaGQlvUZcHOU4PZJlQDZkZdeX2U4OskYRY84hGPSPe6173ybrCnPOUpebXkmmuuyavxq6pM6tq3DCQAKmW4Fvs68ZkSQw2Ea7RFTKHvJ1CD2SdUA2ZG3JNrA2VWPeABD8ir5e23337pgAMOyLuUvvjFL+bVeBlIAAyrCtfiMyLOXhOu0WZRpRb3nf3m5/MCmFlCNWCm1LWBxg2Oe3Da7u53v3terayaAhr+8R//Ma/Gx0ACYD3isyKmhEblWoRrgz4zynAt9tAUCwt5kUVG7PIHs0+oBsycKLUvb2K0gdJ2++67b16tbJ99dl/eh/nPrUU82BpIAIxKhGsRxi/3+VGFaxHmx+ePcI0mKM9TW+bYQGCGCNWAmRNvBrWBMmt++MMf5tXKbrnllrxK6X73u19ejV480MaDbclAAmC9qkrX+CyJoK1OhGlRKRuVaxGu1bWfwyTUDSjwTgm6QagGzKQI1rSBMku+853v5NXyfvzjH6d/+Zd/ybuU/s2/+Td5NTrxIGsgATAJEa5FS2iEa8tNDK3a0Aed7QjjFB0R/SIHjntRYPYJ1YCZpQ2UWXLVVVfl1fLKh8lf/uVfzqvRiP/+QQ+t8eDrEHFgHCJci8+XlcK1KvSPz6kI2mASykvi3FxeADNPqAbMrHhDqA2UWfH//t//S//rf/2vvBvsggsuyKulh9AHPehBebd+Kw0kGNSiBTAqw4Rr0RJaDTWAcam7r3Q5hO4QqgEzLYK1ujZQwRptdNppp+VVvc985jN7VGa8+MUvzqv1W24ggQmfwKSV4Vrs60S41j8xFEatrFITqEG3CNWAmVfXBho3QDXda9Bof/3Xf53m5+fTHXfckb+zW7SH/tqv/VreLT1wnnrqqXm3PisNJBj0MAswblW4FuF+tKAL15ikeI8VL2v7LVNACcwgoRow8+L+WhsobXef+9yn99f3vOc9vZbOP/zDP0x//ud/ni688MJe0PaoRz0qfeMb3+j9mnvc4x7pfe97X7rXve7V26/VcgMJotXTQAKgKSJMqz6XIlwbVD1bhmuxh7VaWMiLLP7Yec8E3bLhJ4vymik57LDD0nXXXZd3wLjE28QySIsqtjJwg6Y4+eST07nnnttbRyvnPvvsk97xjnf09oNE+PbBD36w9uyzYUSQNui/Ix5YnZ8GNF20w2/fvr32xUAlwrgI4JZrIYVBNmzIiyzuKV0e6Zqu5xkq1YDOiLeH5YvrCNq0gdIWb3/729N/+2//LR100EH5O7vtu+++6bd+67fS5z//+bEFavHAaSAB0BZV5Vq0qQ/63IpKtWoIS5wbuVwAB/3iHrLk8gjdo1KtAVSqweREl8emTXmTxYvpxfttYFG0Q9Wdn1YFaio5gLaqWj/7B7rUqSrXDGBhOXE/2d89HIGa7ge6SKUaQIdEHlDe8MQNkfPVwEACYLbFZ1i0r1cTQwepqnXj3LWVAji6KQoa+wO1MD+fF0CnCNWAzok3idpAYTcDCYAuiXAtqnJXCtfiszFaQk0MpbR9e170UdgI3aT9swG0f8LkxdtFbaCw9NAYD4x1DCQAuqA6Vy2GGsR6kAjjYtqygI1yQEFks/5Y0FXaPwE6KAI0baB0XVSm1QVq8eBoIAHQFVXlWnzuLTcFNAK3aJFXudZtBhQA/YRqQGcNagN1fApdEA+EgyZ8RoWaA7qBrukP15b7HCzDteWq25g9Zetn3E8OyGGBDtD+2QDaP2F64j64rg00jpByg8SsGnR+WjxAOj8NYLeqLbTuM7MSYVx8fi5X5cbsKFs/o/NBpRpdpv0ToMPi3reuDbRmACK0XlRTGEgAsHrVZ2MMNViuci3Ct/h8jcEGywVwtFtd169ADbpNqAZ0XtwMlTdE2kCZNfHQF61KdQ97UV0RrU4A1IsKtCpcG3TepHBt9tW1fgLdJlQDWBRTm8qOjahWi6o1aLt4sBs04TMeEh24DbA61bmTEa7FC4lBqnAtPntjTfvFv8byvnB+Pi+AzhKqASyKQK28N44bJ9NAabvlBhJEoGYgAcDw4jM0Pl9XCteiei2q1oRr7bewkBdZXD5dQgGhGkBW1wYanRuKeGireJCLCXWlCNKWOx8IgNVZS7imOridykxUlRoQhGoAferaQOP8DG2gtEk8vEV1Wl1VhIEEAKNXhmuxrxOfz/GyQ7jWLnVFht5LAWHDTxbldSNcc8016eyzz8671TvllFPSUUcdlXdrM63fu+sjaKFpojqt7JaLGyc5BG1QBWrx11I86HmIAxi/+AyO8ywjQKv7PK5E+DY/P++zueHivrB/7kR0NpjvA0u6nmc0LlT7wAc+kM4444y8W71zzz03HXvssXm3NtP6vYVq0Dxxb1t2zUUVm3temiwe4OrOTwvOTwOYjqga3r59e+8zepAqXItq4kFVbkxH3cvWeNHqkgpLup5nNK7986qrrsqryZvm7w00S7yBLO9pow10mfthmKpq0lwpHs4EagDTU7XdL3eWZdUWGp/jcfbacgEckxX3fyWXVKDSuEq15z73uekLX/hCb/385z8/PexhD+utV/LQhz403fe+9827tZnW761SDZqp7s1kBG2L98TQKPEAVnd+Wjy8OT8NoFmqAG2laaARxkX1mpci07VpU/w7y5tFWj9hT9o/GxSq3XHHHenwww9Pt99+e29/3nnnpWOOOaa3Hrdp/t5CNWgubaA0WTyYDapoEKgBNFt8hkewVjeluV9UHJ9//vnCtSmI3HPxMruHeLmqQxd20/7ZIPEvogq19t133/SoRz2qt56Eaf7eQHPF28jyHlYbKE2wXKAWAwkEagDNFmFZ/8TQQeLzPtpCY2LoStVtjFbZ+ll3PAjQbY0K1b785S/n1dJFJsKtSZnm7w00V9w4lSX+0QJQvrWESYogLR6u6gK1CNNMkQNoj2HCtXiZEp//Pucno7zMzs3lBUDWqFDt6quvzquUHvzgB+fVZEzz9waaLYK18h43gjX3s0yDgQQAs6kM12JfJ8K1aBkVro1XXVFgVKoB9GtUqHbjjTfmVUpHHnlkXk3GNH9voPm0gdIEUaEQX6V48FpuqhwA7VGFa/GiJM5SE65NR3nUnUANqNOoQQVHHHFEuvXWW3vruID83M/9XHr/+9+fFhYW0v/7f/+vd+bZ/vvvnx796EenJzzhCenpT3962mef0eSC0/y9DSqAdojqtMX71j3EfW4cWAvjFtVpBhIAdE+EZ/H5v3379trrQCXCt5gWGlNDBwVxrE78Yy6LwuNS690V7M30z4aEal//+tfT4x73uLxL6VnPela66KKL8q7eAx/4wPSWt7yl9y9xPab5ewehGrRHvAiue3NZnrsGo1KdoVP3IBXtQaoTALojjgBYTbgWL1yWayFleVEUXrZ/NqcUBZql63lGY9o/P//5z+fVkv5Qa7/99kv3uMc99hoeEMMFnve856XPfvaz+TtrM83fG2iXujbQuK9d5t4W1iwemgwkAKASVWjx+R8t/7GuEy9jqvM3B72UYXlloOblKTBIYyrVzj777HTuuefmXeqFWFG+fPzxx9/5hiVaMD/1qU+lc845J33uc5/rfS/c5z73SZdeemk66KCD8neGM83fOwxT7aaiDaZPGyiTEA9Eg85Pi2MKnJ8GQBWgxdlqy6kq11w7VhaBWnn5jXs8RX90ybAdedo/G+Dkk09OH//4x3vrOLvsne98ZzrqqKN6+zqvetWr0gc/+MG8W2rZfNOb3pR3w5nm7x20f0L71N1waQNlVKICre4BKQK1qE4AgH6rDdfiOhLh2qAqN5bOUusv7nN/B8vrep7RmFDthhtu6H398z//c7rf/e7XGwiwkmc+85npi1/8Ym8d1WU7d+5M9773vXv7YUzz9w5CNWifqFaLUK3sqHCILetlIAEAazVMuBadOY4R2NuGDXmRRaAmg4TBhGoNCdXW4pJLLkmvfOUr8y6l//bf/ls67rjj8m68Rvl7C9WgnbSBMkoGEgAwKlW4FkMNYj2IcG1P8cI0uhH6GVAAy+t6ntGYQQVrceyxx+bVkmuvvTavxm+avzfQDBGgle0Acd9atoXCSpYbSBDnp3nYAWAYEZbFtSMqnJebAhqBW1S1xTXItWbvDgQVasBKWh2qxVTOu9zlLnmXeu2bkzLN3xtojrjZKts94w1nTTYCtaKSIFo+S/EAFA9Dzr0BYK36w7XlhtyU4dpy1W2zKu7fyv/bW7bkBcAArQ7VQn+wtc8+k/2/M83fG2iOusNrVauxGvHgMmjCZzwAmdIGwCjEdSVe0qw2XIuXPXF96lK4trCQF1n8IxpQ4Adwp0YkQbfffnu68sorex/yl112WW+/GvHrbr311rxL6YEPfGBerd40f29gNsQNlzZQhhUPLHUHSceDTkz4HNSqAwDrUYVrca1ZLlyrKqkHnfc5a8qz1Obn8wJgGY0I1eJD/QUveEF66Utfmk499dT0mc98Jv+d5ZW/7tBDD82r1Zvm7w3MjkFtoOUNGsSDyqAJn9WDDgCMW1UVHeHaoKMGuhKu1d2vDfhHArCHRoRqRxxxRF4tufzyy/NqeRdddFFepXTggQemRz7ykXm3etP8vYHZUtcGGoVIHeqcYAUrDSSILwCYpAjX4voT4VoMNRikCtfiOhbrWbJ9e15kAjVgtRoRqh188MHpIQ95SN6ldOGFF6avfvWreVdv586d6ZJLLsm7aLM6cU3nmk3z9wZmy6A20JoOPzoogrR4GClVlQIGEgAwTXE9irM+VwrXonotnn9mJVyL91zluy6tn8BqNSYJOu200/Iqpdtuuy295CUvGRhuxcPHySefnHcpbdy4Mb3oRS/Kuz29733vS7/9279959e1116b/85u4/q9ge6JXKTMRuJ+c8Ze6DKkeEhZLlAzkACAplhLuBa/vq3KKrXgsgys1oafLMrrqXvDG96Q3vve9+ZdSvvtt186/vjj09FHH53uete7pu9+97vp0ksvTZ/85Cfzr0hp//33T+9///vTYYcdlr+zp9e97nXpggsuyLuU3vGOd6S5ubm8220cv/dqxX/+uuuuyzug7aI6LfKT/rbPqGLbsWPpr3TLoPPTIkiLQA0Amqw6V2379u299SARxs3Pz7cuYNu0ac97tsgRW5wRwsR1Pc9oVKgWzjrrrPSud70r75Z30EEHpbe97W17nYvWb7WhWhj1771aQjWYPVGZdmIx/TPeespQuqN6g18XqEWrp/PTAGiTuK7FNS3CtbprW6UK1+JaF+smq7tf27XLS1AYRtfzjMYdBHb66af3QrCHP/zh+Tt7O+CAA9KLX/zi9NGPfnQkoVZlmr83MFvq2kDj/lMbaDfEg4eBBADMkgjIqinVcR0bdHRBXAO3bdvWq9SOqrXlqtumrW5AgUANGEbjKtW6SKUazKa4h9QG2j0RpA06P225hxAAaJvlqrIrcf2La19UrzXtGrhhQ15k8c6rfCkKLE+lGgBjEcFZWZAUAVvZZsDsWG4ggUANgFkT17eoXIuhBoOmWEfwFmeyxfVxpQBukuq6BwRqwLCEagBjFBlKeYMW95IOwJ098bAQ7S6lCNLiYUOgBsCsql4erTQxtArXBh2RMEnlJVugBqyFUA1gzOLeMqrW+sUZHv1tobRXvIGPB4S6h4Pq7BkA6III16Jqe6Vwrbp2RrgWQdukxW9Z3ofNz+cFwBCEagBjFoFaXRvo4r0kLbdcoBYPEwYSANBFw4Rr0RIa4Vr8+klZWMiLLIrJFZQDayFUA5iAuFEr7ykjWNMG2l4RpMVDQDwQlKI6bZIPBwDQRGW4Fvs6cS2NIxQmFa6VxXGq1IC1EqoBTEic1VHeS0Yb6JSPFGEN4oY/KtRK8bAQgZrz0wBgtypci2tkVHFPM1yr6zZ12QbWasNPFuU1U9L1EbTQJVHUtHifuIe4r9y1K29ovGhTqTv/JYI056cBwMoiPIuK7+3bt9ceoVCJ8G1+fr53RumgIG5Y8U6s/7eMl55Oa4C163qeoVINYILiflAbaDvFA0BUp9UFagYSAMDqRUBWXTuXq/CuKtfi+hsvtWK/HvEfLzM8rZ/AegjVACYs3oiW947aQJutCtQMJACA0aoqvePctQja6sR1OF5qVeHactVty9m2LS/6aP0E1kP7ZwNo/4TuiTel2kDbIW7c685PC8u9XQcAhlcFaFGhtpy4/saLrWGuw3HvFfdgFa2fsH7aPwGYuEFtoCeemDc0QvVWvBRtKwI1ABi9uMb2TwwdpHrpFUMN6o5mKMUv6Q/UwjL/9QCrIlQDmJK6NtDoZlhjRwMjFu0l8VWKIC1u9AVqADA+qw3XorItrtcrTQxdWMiLLC7j8ZITYD20fzaA9k/ornhjqg20Waqb87rzWiJIiwo1AGCyqrbQmBga60EijIuJoWXAtmFDXmTR9jngCDdgCNo/AZiaCNDKszziPlEb6HQsF6jFW3KBGgBMR1W5FtfiGBAU+zpxLY/z2Por1+q6QwVqwCioVGsAlWrQbVWIVuY4kd/oMJwcAwkAoD0iPItrd1Su1b0Mq0T49pWvzC+uIkVbCuIMKIDRUakGwFTVVasF1WqTYyABALRLXKNPOOGEOyvXBl2rl1pFY5JoXOeX2kbnI2MDGAGhGkAD1AVrVQUb4zVoIEHcrBtIAADNV4Vrcd2Odb24ni9Vqrm0A6MiVANoiLgHLG/y4gyQZToaWKeoTqsbwx9BWtyYAwDtES/EomqtPlxbKk/T9gmMklANoEG0gU5GtIJEoGYgAQDMnipcO//8eEG2ZfEr3louvblUpQaMklANoEG0gY5fBGkxEawuUIswrRzBDwC00/bt0e4Z1/Wll2VRvBb3WgCjIlQDaBhtoONjIAEAdEd57zQ3lxcAIyJUA2igQW2gvQFWrElUoBlIAADdUFd4PnCGAcAaCdUAGmhQG+i2mAjP0KI6bVvNPzwDCQBgNm3fnheZQA0YB6EaQEMNagOtGVbJAAYSAED3xL1SWd2/eNkHGDmhGkCDRbVaeaBuFFxpA13ZcgMJYiKYgQQAMJsWFvIii5eUBhQA4yBUA2iwuAEs36xGoGYa6PIiSFtuIMEJekAAYGaVVf3z83kBMGJCNYCGi/ynzICi+EobaL2oQDPhEwC6qe7+yKUfGBehGkALRLWaNtCVrTSQIII1AGB21Q0ocPkHxkWoBtACcTNYNw1UG+iS5QYSRKungQQAMPviNqC8FdD6CYyTUA2gJaJ1oa4NtOvn7a80kCC+AIDZV1apBa2fwDgJ1QBapK4NNG4gu9oGaiABAFAp36+5DQDGTagG0CLaQHdbbiBBVKcZSAAA3REDCsqXjOUEdYBRE6oBtExkReVNYtfaQFcaSCBQA4BuMaAAmAahGkAL1d0oxs1kzbFiM8VAAgCgTnlrMDeXFwBjJFQDaKEutoFGoGYgAQBQitbPkvPUgEkQqgG0VF0baARrs9gGWk34rGMgAQB0W3kihNsCYFKEagAtFjeN5fFhs9YGutxAggjUnJ8GAN1VN6Bgfj4vAMZMqAbQYrPeBmogAQCwnIWFvMji3sjtATApQjWAloubx1lrAzWQAABYjfI8tfKeCGCchGoAM2CW2kCXC9S2LN4pG0gAAIS6AQWq1IBJEqoBzIBZaQOtBhJEsFaK6rQ4Xw0AIMQLxH7xkjHuiQAmRagGMCMGtYG2JVgzkAAAGEZZ1D43lxcAEyJUA5ghdW2gccPZ9DbQE0880UACAGDV6l4axn0QwCQJ1QBmSNvaQKvz095dcyiKgQQAwCDlC0OBGjANQjWAGdOWYM1AAgBgLeJdXNzb9DP1E5gGoRrADIpuybJjMm5Am9IGaiABALBWCwt5kcU9jwEFwDQI1QBmUF21WmhCtVq0ehpIAACsVXlqxPx8XgBMmFANYEY1sQ00BhLEV8lAAgBgNWqOYXWeGjA1QjWAGVY3DXQabaDLDSSIIM1AAgBgNcph4QI1YJqEagAzblAbaM1xZmMRgVpUpw0aSCBQAwBWI24lyvsXrZ/ANAnVAGbcoDbQ8k3vOFQDCeoCNQMJAIBhbN+eF32cHAFMk1ANoAMGtYHWnUsyKgYSAACjVN63bNmSFwBTIlQD6IioVouqtX5RrTaONtCoQKsbSBCBmoEEAMCw6l4EOk8NmDahGkBHRKBWvtEdRxtoVKdtq/kvrSZ8AgAMq2z9jECtfFkIMGlCNYAOiRvQ8q3uqNpAqwmfBhIAAKNW3l7MzeUFwBQJ1QA6JqrVRt0GaiABADAudbcRWj+BJhCqAXRMBGp100BrjkBbFQMJAIBxqmv9BGgCoRpAB0XOVd6QRpHZsAVlBhIAAOMUR1SU1fTz83kBMGVCNYCOqmsDjTfBq20DNZAAABi3hYW8yOJ9nXd2QFMI1QA6aq1toAYSAACTUg5TUqUGNIlQDaDD4k1vVKz1W64NdLmBBOeff76BBADAyNRNJ1elBjSJUA2g4+Jstbo20DI3iyBtuYEEJzg1GAAYoboBBeU9C8A0CdUAOm41baBRgWbCJwAwKfFyr3zBp/UTaBqhGgC1baARrEU350oDCSJYAwAYpbJKLXiHBzSNUA2Anmip2PNm9Stp27b6gQTR6mkgAQAwLuXth1MmgCYSqgHQs3cbaLR77h2oxUCC+AIAGIcYUBAV8/3KinqAJhCqAXCnCNZ237TuWYlmIAEAMAkGFABtIVQDYA+720Dj7rUK1u6ftmw5v3eOGgDAOJWtn3NzeQHQMEI1APawZxtohGgRrO1K27YJ1ACA8YrWz5IieaCphGoA7GXPNtClMC3ONjnxxN4SAGAsyoHjAjWgyYRqANTa3Qa6W7Rj1AwDBQBYt7jHKAcUzM/nBUADCdUAqLVnG+gS1WoAwLiUAwqC41yBJhOqATCQYA0AmJTyPLXyHgSgaYRqACwr3hCXb4njplcbKAAwKnUDClSpAU0nVANgWXXVakG1GgAwKmXrZ5ztGvcgAE0mVANgRdpAAYBxKivg5+byAqDBhGoArErdNFBtoADAetW9pIv7DoCmE6oBsGraQAGAUStf0AnUgLYQqgGwatpAAYBRiqr3uJfot2VLXgA0nFANgKEMagOtm9oFALCchYW8yOIew4ACoC2EagAMra4NdNu2vd80AwAsp3wpNz+fFwAtIFQDYGiD2kAjWAMAWI26KnfnqQFtIlQDYE3ipre88dUGCgCsVvkyTqAGtI1QDYA1i4OEy3NPtIECACuJiZ/l/YLWT6BthGoArFkEauWErrhBNg0UAFjO9u150acchATQdEI1ANalrg003j5v3Zo3AACFuFfoV76kA2gDoRoA61bXBhpvoLWBAgClOH+1vEdwnhrQRkI1ANZt0DRQbaAAQKls/YxArXw5B9AGQjUARiLOQSlbN7SBAgClsvVzbi4vAFpGqAbAyNS9adYGCgBUovWzpPUTaCuhGgAjM6gNdPPmvAEAOm3btrzIBGpAmwnVABipujbQCNa0gQJAt9UNKJifzwuAFtrwk0V5zaJrrrkmnX322Xm3eqeccko66qij8m44hx12WLruuuvyDqD9qiEF/WemVFVsEboBAN0T9wb97Z9xT7BjR94ArdT1PEOoVvjABz6QzjjjjLxbvXPPPTcde+yxeTccoRowiyJY27Qpb7II1nbtyhsAoFM2bMiLLF62af+Edut6nqH9s3DVVVflFQDrEQGaNlAAINQNKFC9DrSdSrXCc5/73PSFL3yht37+85+fHvawh/XWK3noQx+a7nvf++bdcFSqAbNKGygAEGJoUf/9QFSolcONgPbR/ilUu9Mdd9yRDj/88HT77bf39uedd1465phjeutxEqoBs0wbKAB0W929QJyl5gUbtJ/2T+4UfxCqQG3fffdNj3rUo3prANZuUBtoVLABALNv27a86CNQA2aBUK3Pl7/85byKh8D794I1ANYvWjzKm+doAelvAwEAZlN5vTecAJgVQrU+V199dV6l9OAHPzivAFiv6hy1fqrVAGD2xYCCuOb3KyvYAdpKqNbnxhtvzKuUjjzyyLwCYBQEawDQPQsLeZFF5XrcEwDMAqFan89+9rN5tdT+ecMNN6QzzzwzPfGJT0wPetCDegfwHXXUUenkk09OF198cW+wAQCrFzfSZRtovMHWBgoAsymu8/3m5/MCYAaY/pl9/etfT4973OPyLqVnPetZ6aKLLsq7eg984APTW97yll7Yth6mfwJdUjcBLN5YmwYKALMlArWyIt3TJ8yWrucZQrXsYx/7WDrllFPybk/77bdfb2jBbbfddud00Mr++++f3vGOd6SHPexh+TvDGyaUE74Bs6DuJjsOLS7bQwGA9oqXaP3nqbnWQzsMWzgkVCOdffbZ6dxzz8271AvR5ufn0/HHH99rBQ0RqH3qU59K55xzTvrc5z7X+164z33uky699NJ00EEH5e8MR6Ua0EWbN+/d9rljhxH7ADAL4hof1/p+rvMwe7qeZzhTLfvSl76UV0vVZ3/yJ3+STj/99DsDtRBB2zHHHJMuvPDC9OxnPzt/N6XvfOc76Q/+4A/yDoDVqHtTbWgBAMyG7dvzoo9ADZg1KtWyGEoQX//8z/+c7ne/+6VHP/rR+e8M9sxnPjN98Ytf7K0jcNu5c2e6973v3dsPQ6Ua0FXaQAFgNm3YkBdZXNvjGg/MFpVq9DzgAQ9Ixx57bK8CbTWBWjjppJPyaqk19NOf/nTeAbAacXNdNw20nBQGALRH3XVclRowi4Rq6xAhXL9rr702rwBYrbqqtG3b9jzYGABoj7L1M16i9Z2qAzAzhGrrcI973CPd5S53ybvUax0FYDhxk10GaxGoRbAGALRPOYhobi4vAGaMUG2d+kO1ffbxjxNgLeINdnnOijZQAGifrVvzoo+z1IBZJQVaFOehXXnllWnHjh3psssu6+1XI37drbfemncpPfCBD8wrAIa1ZcverSHaQAGgXepaPwFmlVBtUYRpL3jBC9JLX/rSdOqpp6bPfOYz+e8sr/x1hx56aF4BMKwI1CJY6xeBWjkdFABopqgwL1+Gldd2gFkiVFt0xBFH5NWSyy+/PK+Wd9FFF+VVSgceeGB65CMfmXcArEVdG2icy6INFACab2EhL7KY+GlAATDLhGqLDj744PSQhzwk71K68MIL01e/+tW8q7dz5850ySWX5F1UUpzoTDWAEdAGCgDtVL4Em5/PC4AZJQXKTjvttLxK6bbbbksveclLBgZr0S568skn511KGzduTC960YvyDoD1GDQNVBsoADRXXVV5VKoBzDKhWvaIRzyid65aZdeuXekpT3lKesMb3pA+9rGP9YK0D33oQ73wLM5eu/nmm3u/bv/990/nnHNOutvd7tbbA7B+cRNe1wZaN1EMAJi+ugEFWj+BWbfhJ4vymkVnnXVWete73pV3yzvooIPS2972tr3OZBvWYYcdlq677rq8AyBEddrmzXu2fcbN+Y4dbtIBoEnixVdcs/vF9VqlGsy+rucZKtUKp59+errgggvSwx/+8PydvR1wwAHpxS9+cfroRz+67kANgHqD2kDLm3YAYLrKKrUgUAO6QKVaA6hUAxgsWj5jUEG/GGagFRQAmmHTpj0ry6P1s3wxBswmlWoA0GB1Z7LEG/FoNQEApisGFPQHaiFefgF0gVANgEarzlHrFzfvpoECwPQZUAB0mVANgMaLm/PyrXcEa1pAAWC6ysrxubm8AOgAoRoArRBvvstDj7WBAsD0ROtnKa7XAF0hVAOgFQZNA9UGCgDTUQ4SEqgBXSNUA6A1tIECQDPUDSiYn88LgI4QqgHQKtpAAWD6FhbyIosXX+X1GWDWCdUAaBVtoAAwfeV5amUlOUAXCNUAaJ1BbaCCNQAYv7oBBarUgC4SqgHQSnVtoNECqg0UAMYrjl3oF9fkeOEF0DVCNQBaSRsoAExH+QJrbi4vADpGqAZAawnWAGCy6q6xUakG0EVCNQBaLVpAyzbQOOtFGygAjF55fRWoAV0mVAOg1eqq1YJqNQAYrXhpFRXh/Uz9BLpMqAZA62kDBYDxW1jIiywqxQ0oALpMqAbATKibBqoNFABGJ66r/ebn8wKgo4RqAMyMQW2gZasKADCcMlALzlMDuk6oBsDMGNQGum1b3gAAa1JeSwVqAEI1AGbMoDbQujfsAMDK4iiFsupb6yeAUA2AGRTVauXByfGGXRsoAAxv+/a86FO+wALoIqEaADMnArVyxL9poACwNmW1d3mNBegqoRoAMynaQMvzXqJ9RRsoAKyeAQUAgwnVAJhZ8SZdGygArF3Z+hmBWnltBegqoRoAM2vQNFBtoACwOlHl3W9uLi8AEKoBMNviIOW6NtCtW/MGAKhVd63U+gmwm1ANgJlX1wYa7SzaQAFgsLrWTwB2E6oBMPO0gQLAcGJAQfnyaX4+LwDoEaoB0AnRBhoVa/20gQJAvYWFvMjiOhpfAOwmVAOgM+omlkVrS3kIMwB0XVSq9VOlBrA3oRoAnaENFABWVgZqQZUawN6EagB0Sl0baARr2kABYEndgIKy0hsAoRoAHRQPB+Ubd22gALB0LSyvh1o/AeoJ1QDoHG2gAFCvrFILWj8B6gnVAOikCNa0gQLAnsoqtajuBqCeUA2AztIGCgC7xYCCeMHUr3wBBcBuQjUAOksbKADsZkABwHCEagB02qA2UMEaAF1TVmrPzeUFALWEagB0Xl0baN30MwCYVdH6WXKeGsDyhGoAdJ42UAC6btu2vMgEagArE6oBwCLBGgBdFZXZ5YCC+fm8AGAgoRoAZNECWraBRjuMNlAAZlk5oCCU10MA9iZUA4CsrlotqFYDYJaV56nVXQsB2JtQDQD6aAMFoEvqBhSoUgNYHaEaABTqpoFqAwVgFpWtn3ENjBdMAKxMqAYANbSBAtAF5Qujubm8AGBFQjUAqKENFIBZV3dNi0o1AFZHqAYAAwxqA607fwYA2qasUhOoAQxHqAYAy6hrA922balqDQDaKl4QldeyLVvyAoBVEaoBwDIGtYFGsAYAbbWwkBdZVGYbUAAwHKEaAKwg2mHKlhhtoAC0WXkNm5/PCwBWTagGAKsQLTHlG3xtoAC0Ud1LIeepAQxPqAYAqxCBWnnWjGmgALRReYSBQA1gbYRqALBKdW2gMTlt69a8AYCGi+tWWWWt9RNgbYRqADCEujbQ7du1gQLQDnHNKsWQAgCGJ1QDgCEMmgaqDRSANohKtX7l0QYArJ5QDQCGFG/0y4cQbaAANF0MKCgrq52nBrB2QjUAWIN4CKlrAy0rAACgKcrWz7prGQCrJ1QDgDXQBgpA25Qvfubm8gKANRGqAcAa1bWBRrCmDRSAponWz5LWT4D1EaoBwDrEA0k5NU0bKABNs21bXmQCNYD1E6oBwDpoAwWg6eoGFMzP5wUAayZUA4B1imBNGygATbWwkBdZVFiXVdYADE+oBgAjoA0UgKYqz1NTpQYwGkI1ABgBbaAANFHdgAJVagCjIVQDgBEZ1AYqWANgWqJqul9UVsf1CoD1E6oBwAjVtYFGC6g2UAAmLV7slNcfrZ8AoyNUA4AR0gYKQFNs25YXfbR+AoyOUA0ARkywBkATlFVqUU0NwOgI1QBgDKISoKwGiMOitYECMAlxzYkXOv3Kcz8BWB+hGgCMQV21WlCtBsAkLCzkRRYvegwoABgtoRoAjIk2UACmJSrV+hlQADB6QjUAGKO6aaDaQAEYpzJQC85TAxg9oRoAjJk2UAAmqZz6KVADGA+hGgCMmTZQACYlKqHLAQVaPwHGQ6gGABMwqA20rkUHANZq+/a86FNefwAYDaEaAExIXRtotOiUFQUAsFbly5q6aw8AoyFUA4AJGdQGWp59AwBrUVf9rEoNYHyEagAwQdEGWh4YrQ0UgFEoWz/jehMvdAAYD6EaAEzYli17P+RoAwVgvWJIQb+5ubwAYCyEagAwYRGoRbDWzzRQANZj69a86FNWRgMwWkI1AJiCujbQqDDQBgrAWtS1fgIwXkI1AJgSbaAAjEK8kCmvHWVFNACjJ1QDgCkZNA1UGygAw1hYyIssJn4aUAAwfkI1AJiiePCpawOtOxsHAOqURwfMz+cFAGMlVAOAKatrA42zcbSBArCSurM444UNAOMnVAOAKRvUBrp5c94AwAB1Awq0fgJMhlANABogqgrKQ6UjWNMGCsAgcVxAfPXT+gkwOUI1AGiIuuqCqEAoH5gAIJRVakHrJ8DkCNUAoCEiUNuxI28y00ABGKR86VIOvgFgvIRqANAgEaxpAwVgJTGgoBxoU14/ABiv1oVqP/zhD9POnTt7X9dff33+LgDMjqg0KNt3tIEC0M+AAoDp2/CTRXndCq973evSBRdc0Fs/4xnPSGeddVZvPQrXXHNNOvvss/Nu9U455ZR01FFH5d3wDjvssHTdddflHQAsVR9s2pQ3WTws7dqVNwB02oYNeZHFFGntn8CkdT3PaFWl2ic+8Yk7A7Vx+PKXv3xnFdwwX9/+9rfzfwMAjIY2UAAGidbPkkANYPJaE6pFcHX66afn3XhcddVVeQUA06cNFIA627blRSZQA5iO1rR//of/8B/SX/3VX+XdklG3fz73uc9NX/jCF3rr5z//+elhD3tYb72Shz70oem+971v3g1P+ycAg2gDBaBfVKmVU6FjcnT5EgZgErqeZ7QiVLvwwgvTa1/72rzbbZSh2h133JEOP/zwdPvtt/f25513XjrmmGN663ETqgGwnGj5rKtKiPNzAOiWCNT62z+9aAGmyZlqDXfjjTemN73pTb31gQcemI488sjeetTiD0EVqO27777pUY96VG8NANNW1wYaD1TaQAG6pzxPrTx/E4DJaXSoFtVjr3zlK9Mtt9zS25955pnpoIMO6q1HLYYUVO5///v3gjUAaIKoQqirSivbfwCYbXUDCrR9AkxPo0O1c845584zzqLV84lPfGJvPQ5XX311XqX04Ac/OK8AoBnqgrU4b02wBtAdMaymX1Qyx/UBgOlobKh2zTXXpLe97W299SGHHJJe85rX9NbjEm2mlXG1mALAemgDBeiueJFSft7PzeUFAFPRyFDtBz/4QXrFK16Rd6k3jOBe97pX3o3HZz/72bxaav+84YYbeu2mUR33oAc9qHf43lFHHZVOPvnkdPHFF/daUwFg0rSBAnRTObAmxMsWAKankaHatsUrxk033dRbn3TSSenoo4/urcfl61//err11lvzLqVLLrkkPfnJT07vec97ehVs1QCDm2++OX384x9P//k//+f0tKc9zcROACZOGyhAN5VVagI1gOlrXKh22WWXpQ9/+MO99aGHHtobVDBun//85/NqyUUXXZRXKe23337pHve4x16DC2KwwfOe97w9KtwAYBK0gQJ0S3zGxwuUfqZ+Akzfhp8syuup++Y3v5me/vSnp+985zvpLne5Sy9ci2CtX7RfRrVYiOEF0Rq6XmeffXY699xz8y71ArT5+fl0/PHH91pBQ1SrfepTn+oNT/jc5z7X+164z33uky699NJ1TSWN1tLVUh0HQIiHq02b8iaLS9aOHQ6tBpg1UY3cP/kzXqzE5z3AOAyTUYQu5xSNCtUiyPr0pz/dW0eF2kte8pLeut84QrX+/879998/vfOd7+ydnzbIq171qvTBD34w71J61rOeld70pjfl3fDiD6ywDIBhxQNW2fYZVWx1564B0F4bNuRFFp/z2j+BJuh6ntGY9s/t27ffGajF9M26QG1cTjvttF6l2hvf+Mb01re+ddlALcSvi+EFlRhc8N3vfjfvAGAyBrWB9lczANBudZ/pAjWAZmhEqHb99denN7/5zb11VIr94R/+YW89KQ94wAPSsccem5797GenRz/60fm7y4sBCpVoDa0CQQCYpKhWKNs9Y0JcefYOAO1UTv0UqAE0x9RDtR/96Efp5S9/ebrtttt6+zPOOCMdcsghvXWTRQjX79prr80rAJicCNTKw6pNAwWYDTGApnxJMj+fFwBM3dTPVHv7299+Z2VaTNl82tOe1lsPsnPnznTTTTf11hs3bkxHH310bx3iTLZysME4PfjBD04//vGPe+vnPve56Q1veENvPSxnqgGwXuUh1sGZOwDtVvfZ3pwTsQHkGVMP1V73utelCy64IO/W5x3veEeam5vLu/E74ogj0q233tpbx6TQ+P+yFkI1ANYrKhk2b96zosE0UIB2KwcURGXy1q15A9AABhV0XJyHduWVVy4+dOxIl112WW+/GvHrqkAtPPCBD8wrAJi8CM7KqZ/aQAHay4ACgOabeqXa1VdfnW644Ya8W1lUtX3xi1/srWNK6HOe85zeOjzmMY9J97vf/fJudf7yL/8y/c7v/E7exQPJ+asaVhBtqCf2Pams9j9XR6UaAKNS1yqksgGgfaL6OM5Uq0SgVr48AZg27Z9TDtWGdfLJJ6ePf/zjvfUznvGMdNZZZ/XWa/XNb34zHXPMMXmX0gte8IL06le/Ou8Ge+UrX5kuueSS3vrAAw9Mn/nMZ9I++6yt8E+oBsCoaAMFmA1l66dzMoEm0v7ZcQcffHB6yEMekncpXXjhhemrX/1q3tWLKrUqUAtRsbbWQA0ARkkbKED71VUXC9QAmmfmk6D3ve996bd/+7fv/Lr22mvz39nttNNOy6uUbrvttvSSl7xkYLAWZ69FtVwlJpC+6EUvyjsAmL7HP36p5bNftBBpAQVoh+3b8yITqAE008yHatdff/3ig8QVd359+9vfzn9nt0c84hG9ts/Krl270lOe8pT0hje8IX3sYx/rBWkf+tCHeuHZS1/60nTzzTf3ft3++++fzjnnnHS3u92ttweApogHsLLdMx7S+s/nAaB54lzM/hb+MD+fFwA0ip7FLM5RO+mkk/JuqWLtve99bzrllFN6Qdrv/u7vpk9+8pP576Z00EEH9YYTRP8wADSNNlCAdlpYyIssqo/jC4DmEar1Of3003vTRR/+8Ifn7+ztgAMOSC9+8YvTRz/60XTEEUfk7wJA89S1gUawpg0UoLnKCc6q1ACaq3XTP2eR6Z8AjEtVndbf9llVsal8AGiWCNTKiuJdu0xvBprL9E8AYGZpAwVoj7oBBQI1gOYSqgHAjIsHMm2gAM0WFcXlMBmtnwDNJlQDgA6Iaoey3dM0UIDmKKvUgjZ9gGYTqgFAB2gDBWi28iVHvAwBoNmEagDQEYPaQAVrANMVAwri87hf+XkNQPMI1QCgQ+raQOvO8QFgcgwoAGgnoRoAdIg2UIDmKV9szM3lBQCNJlQDgI4RrAE0R7R+lpynBtAOQjUA6KBoAS3bQOPBThsowGRt25YXmUANoD2EagDQQXXVakG1GsDkxIuMckDB/HxeANB4QjUA6ChtoADTVQ4oiM/lsooYgOYSqgFAh9VNA9UGCjAZ5XlqW7bkBQCtIFQDgI7TBgoweXUDClSpAbSLUA0AOk4bKMDkla2fUTkcn8cAtIdQDQAY2AZaV0kBwPqVbfZzc3kBQGsI1QCAnro20G3b9p5MB8D61FUCx8sNANpFqAYA9AxqA41gDYDRKavUBGoA7SRUAwDuFA925cOdNlCA0YnP07IC2NRPgHYSqgEAe4iHu/KwbG2gAKOxsJAXWZxnaUABQDsJ1QCAPcTDXVk1YRoowGiUlb/z83kBQOsI1QCAvdS1gcYZQFu35g0AQ6trpXeeGkB7CdUAgFp1baDbt2sDBVircvCLQA2g3YRqAECtQdNAtYECDC+qfcuXElo/AdpNqAYADBQHaJfnq2kDBRheVPqW4jMWgPYSqgEAy4r2pLo20AjXAFid8jOzfGEBQPsI1QCAZWkDBVifGFBQtn46Tw2g/YRqAMCK6tpA4wFRGyjAysrWz7oKYADaR6gGAKxKPASW5/9oAwVYWfk5OTeXFwC0mlANAFgVbaAAw4vWz5LWT4DZIFQDAFYtgjVtoACrt21bXmQCNYDZIVQDAIaiDRRgdeoGFMzP5wUArSdUAwCGog0UYHUWFvIiixcS5UsJANpLqAYADG1QG6hgDWC38jw1VWoAs0WoBgCsSV0baLSAagMFqB9QoEoNYLYI1QCANdEGCjBYnDXZL15ExOcmALNDqAYArJlgDWBv8TlYVu1q/QSYPUI1AGBd6g7ejrYnbaBAV23blhd9tH4CzB6hGgCwLnXVakG1GtBV5UuFaP0EYPYI1QCAddMGCrAkKnXj869fOS0ZgNkgVAMARqJuGqg2UKBrFhbyIovPRQMKAGaTUA0AGBltoEDXxcuEfgYUAMwuoRoAMDLaQIEuKwO14Dw1gNklVAMARmpQG2jdwybALCmnfgrUAGabUA0AGLm6NtB42CwP7waYFXF+ZPkZp/UTYLYJ1QCAkRvUBlpWcQDMiu3b86JPWbULwGwRqgEAYxFtT2XrkzZQYFaVn211FbsAzBahGgAwNlu2LFWt9dMGCsyaupcFqtQAZp9QDQAYmwjUIljrZxooMGvK1s+o0i1fKAAwe4RqAMBY1bWBxoHe2kCBWRGfaf3m5vICgJkmVAMAxk4bKDCrtm7Niz7liwQAZpNQDQAYu0HTQLWBAm1X1/oJQDcI1QCAiYhDu+vaQOuqPADaINrYy4rb8hxJAGaXUA0AmJi6NtCo8tAGCrTRwkJeZPHywIACgO4QqgEAEzOoDXTz5rwBaJFy4Mr8fF4A0AlCNQBgoqKSo2yPimBNGyjQJnUTjOPzDYDuEKoBABMXZ6vVtYHGGWsAbVA3oEDrJ0C3CNUAgImLB88dO/ImMw0UaIt4AVC+BND6CdA9QjUAYCoiWNMGCrRRWaUWtH4CdI9QDQCYmmiXKh9EtYECTVd+RsVnGQDdI1QDAKZm0DRQbaBAU8WAgvic6ldW3QLQDUI1AGCqBrWBCtaAJjKgAICKUA0AmLq6NtC6g8ABpq38XJqbywsAOkeoBgBMnTZQoA2i9bPkPDWA7hKqAQCNIFgDmm7btrzIBGoA3SZUAwAaI1pAyzbQqAzRBgpMW92Agvn5vACgk4RqAEBj1FWrBdVqwLQtLORFFp9X5UsAALpFqAYANIo2UKCJyvPUyqnFAHSPUA0AaJy6aaDaQIFpqRtQoEoNAKEaANBI2kCBpti+PS+yCP6jqhaAbhOqAQCNpA0UaIL43CmrZOfm8gKAThOqAQCNpQ0UmLZt2/KiT3w2AYBQDQBotEFtoFE9AjBuZYgvUAOgIlQDABptUBtoXfUIwChFZWwZ4Jv6CUBFqAYANN6gNtC6iXwAo7KwkBdZfA4ZUABARagGALRCVKuVD7NRraYNFBiXMrifn88LAFgkVAMAWiECtbLtKgI100CBcairhHWeGgD9hGoAQGvEA235UBuHiGsDBUatPLdRoAZASagGALRKVKtpAwXGKcL68jNF6ycAJaEaANAqg6aBagMFRmX79rzoUw5LAQChGgDQOvFwW9cGunVr3gCsQ9lSXp7nCABBqAYAtFJdG2hUl2gDBdbDgAIAVkuoBgC0kjZQYBzK1s8I1MoAHwCCUA0AaK1oAy3bsrSBAusRnyH95ubyAgAKQjUAoNXqqkii0qR8MAZYSV0gr/UTgEGEagBAq2kDBUalrvUTAAYRqgEArVfXBhrBmjZQYLViQEE56GR+Pi8AoIZQDQCYCVFREuFaP22gwGotLORFFp8n5WcKAPQTqgEAM0EbKLAeUanWT5UaACsRqgEAMyOCNW2gwLDKQC2oUgNgJUI1AGCmaAMFhlU3oKCcKgwAJaEaADBTtIECw4jAvQzdtX4CsBpCtSH98Ic/TDt37ux9XX/99fm7AECTDGoDFawBpbJKLWj9BGA1hGpDOuussxZvyE/sff3xH/9x/i4A0DR1baB1FSlAt5WfCfHZAQCrIVQbwic+8Yl0wQUX5B0A0GTaQIGVxICC+FzoV1a5AsAgQrVV+va3v51OP/30vAMA2kCwBizHgAIA1kOotkqvfvWr0z/90z/lHQDQFtECWraBRnWKNlCg/ByYm8sLAFgFodoqXHjhhemv/uqv8g4AaJO6arWgWg26LcL1kvPUABiGUG0FN954Y3rTm97UWx944IHpyCOP7K0BgPbQBgqUtm3Li0ygBsCwhGrLuOOOO9IrX/nKdMstt/T2Z555ZjrooIN6awCgXeqmgWoDhW6Kn/tyQMH8fF4AwCoJ1ZZxzjnnpC984Qu99TOe8Yz0xCc+sbcGANpJGygQygEFUc1ahu4AsBKh2gDXXHNNetvb3tZbH3LIIek1r3lNbw0AtJc2UCCU56lt2ZIXADAEoVqNH/zgB+kVr3hF3qV01llnpXvd6155BwC02aA20LpDy4HZU/ezrkoNgLUQqtXYtm1buummm3rrk046KR199NG9NQAwG6JaLarW+sWh5eUZS8DsKVs/I2gvPw8AYDU2/GRRXrPosssuS6eeempvfeihh6aLL7447bvvvr19OPnkk9PHP/7x3jrOWYsqtvU67LDD8mpl1113XV4BAOsR1Spl22c8XNeduwbMjg0b8iKLn3mTPwF2GyajCF3OKYRqfb75zW+mpz/96ek73/lOustd7pI+/OEP94K1fuMK1YRlADB5EaqVrWAesGF21f3MexoCWLuu5xnaP/u88pWv7AVq4T/+x/+4V6AGAMyWOJxcGyh0xxVX5EUmQAdgPYRq2fbt29OnP/3p3vrII49ML3nJS3prAGB2RaBWTv0zDRRmU1SolYG5qZ8ArIdQbdH111+f3vzmN/fW+++/f/rDP/zD3hoAmH1RqVJWq0Q1y9ateQPMhIWFvMhi4qcBBQCsR+dDtR/96Efp5S9/ebrtttt6+zPOOCMdcsghvTUA0A11baAxIVAbKMyO8iy1+fm8AIA16vyggre//e13Vqbd4x73SE972tN660F27tyZbrrppt5648aN6eijj+6tw/zilXkt57AZVAAA0xfVaZs3500WlSw7duQN0Fp1034NKABYv67nGZ0P1V73utelCy64IO/W5x3veEeam5vLu9UTqgFAM0TLZwwq6BdVbFpBod02bdqz8jRavmPSLwDrY/onAAA98aBd1wZaTgwE2iN+fstWbq2fAIxC5yvVrr766nTDDTfk3cqiqu2LX/xibx1TQp/znOf01uExj3lMut/97pd3q6dSDQCao64NNIK2XbvyBmiVaPssz1PT+gkwGto/Ox6qDevkk09OH//4x3vrZzzjGemss87qrddDqAYAzaINFGZH2frpZxlgdLR/AgCwh2gDjSEF/bSBQvtEhVrZ+hk/3wAwCkI1AIBCtHuWh5jHg3k5PRBotgjD+9WdmwgAayVUAwCoEQ/e0SbWL4I1bWPQHmV16RoG9QPAQEI1AIABtIFCe5XDCYLWTwBGSagGADCANlBor3LYiEANgFETqg3prW99a2+yRXyNYvInANBsg9pABWvQXHUDCubn8wIARkSoBgCwgro20GgB1QYKzbSwkBdZ/PyWP8MAsF5CNQCAFWgDhXYpz1NTpQbAOAjVAABWQbAG7VA3oECVGgDjIFQDAFiluhayeIDXBgrNERN6+0X7doTiADBqQjUAgFWqq1YLqtWgGaJ6tAy5tX4CMC5CNQCAIWgDhebati0v+mj9BGBchGoAAEOqmwaqDRSmr/wZjJ9VABgXoRoAwBpoA4VmiWA7qkb7bdmSFwAwBkI1AIA10AYKzbKwkBdZVJMaUADAOAnVAADWaFAbaHwBk1X+3BlQAMC4CdUAANahrg00Dksv29CA8akLsp2nBsC4CdUAANZhUBto3RRCYDzKnzeBGgCTIFQDAFineIAvH+K1gcJkxMTPsjJU6ycAkyBUAwAYgZgyWB6Krg0Uxm/79rzoU551CADjIFQDABiBCNQiWOtnGiiMX1kRWnfOIQCMg1ANAGBE6tpAozVNGyiMR93Plio1ACZFqAYAMELaQGFyytbPCLXLnz8AGBehGgDACA2aBqoNFEYvKkH7zc3lBQBMgFANAGDEov2sPF8tHv63bs0bYN3qfp7K9msAGCehGgDAGNS1oUWrmjZQGI261k8AmCShGgDAGAxqA928OW+ANYsBBWVAXVaHAsC4CdUAAMakrg00ggBtoLA+Cwt5kcXPmgEFAEyaUA0AYIwGtYGWB6wDqxeVav3m5/MCACZIqAYAMEYRqO3YkTeZaaCwdmWgFqJSDQAmTagGADBmEaxpA4XRqBtQoPUTgGkQqgEATEA8+JfVNNpAYTjx81L+zGj9BGBahGoAABMQlTR100C1gcLqlVVqQesnANMiVAMAmJBBbaCCNVidskotKkABYFqEagAAE1TXBlrX0gbsKQYURAjdrwypAWCShGoAABOkDRTWxoACAJpGqAYAMGGCNRheWc05N5cXADAlQjUAgCmIFtCyDTTa27SBwt7iZ6PkPDUApk2oBgAwBXXVakG1Guxt27a8yARqADSBUA0AYEq0gcLK6gYUzM/nBQBMkVANAGCK6qaBagOF3RYW8iKLMLr8mQGAaRCqAQBMmTZQGKw8T23LlrwAgCkTqgEATJk2UKhXN6BAlRoATSFUAwBogEFtoHWhAnTF9u3/f3t3AmV3Wd4P/A0JwRBQNuOBtqd/sIJAWxaBQkwdcljFpUJoo2WZylIMxIOFyGYLCS1yOOZQFJSGAJpaBIQSlhTwgMShNA3UgiHAYbEKJ5WdYEFWWf55fvNOuPObeydzZ73L53POnDzv706YJHMv997vPM/75iKLx0mE0ADQCIRqAAANotoYaJx6WN6kHdpB3O/Lewt2dOQCABqAUA0AoEHUGgONYA3aTbX7fXSqAUCjEKoBADSQCA3KwYExUNpRuUtNoAZAoxGqAQA0mDjdsLxvlDFQ2kmEyOX7u1M/AWg0QjUAgAYTgVo5QIiAwWmgtIuurlxkcYiHAwoAaDRCNQCABlRtDDTG4YyB0g7K9/POzlwAQAMRqgEANChjoLSjasGx/dQAaERCNQCABlXrNFBjoLSy8qmfAjUAGpVQDQCggcVeUtXGQOfOzQtoIXHfLndiGv0EoFEJ1QAAGly1MdBFi4yB0nrifl0WwTIANCKhGgBAg6s1Bjp9el5Aiyjvp1Y+BRcAGolQDQCgCUS3TjlgiGDNGCitwgEFADQboRoAQJOIgKHaGGjsQwXNrjz6We3+DgCNRKgGANAkImBYujQvMqeB0irK4XBHRy4AoEEJ1QAAmkgEa8ZAaTXV7r9GPwFodEI1AIAmE2FD+UREY6A0s2qjnwDQ6IRqAABNptZpoMZAaUZxQEHcfyt1duYCABqYUA0AoAkZA6VVdHXlIosuzHInJgA0IqEaAECTMgZKK4hOtUq61ABoFkI1AIAmZQyUZlcO1IIuNQCahVANAKCJ1RoDFazRDKodUBD3aQBoBkI1AIAmV20MNEZAjYHSyKrdR41+AtBMhGoAAE3OGCjNqNylFox+AtBMhGoAAC1AsEazKXepRcclADQToRoAQIuILp9yp09sBG8MlEYT98sIfSuV9wYEgEYnVAMAaBHVutWCbjUajQMKAGgFQjUAgBZiDJRmUO6e7OjIBQA0EaEaAECLqXYaqDFQGkXcF8vspwZAMxKqAQC0oFpjoOV9rGC0zZuXi0ygBkCzEqoBALSgWmOg5UADRlN0S5aD3c7OXABAkxGqAQC0qFpjoNXG72A0lA8oiPC3fB8FgGYhVAMAaGHRrVY+VTG61YyBMhbKge5ZZ+UCAJqQUA0AoIVFoFYOLpwGylio1iGpSw2AZiZUAwBocTEGWt4MPva2MgbKaCqPfsZ9stxFCQDNRKgGANAGolvNGChjKYLcSh0duQCAJiVUAwBoAxGoVTsN1Bgoo6Ha/azcPQkAzUaoBgDQJmL/qmpjoHPn5gWMkHKXmkANgFYgVAMAaCPVxkBjrytjoIyU2LuvfP9y6icArUCoBgDQRoyBMtq6unKRRcekAwoAaAVCNQCANhOhRrlTyBgoI6V8ymxnZy4AoMkJ1QAA2lDsaVVtDLS89xUMRTlQC/ZTA6BVCNUAANqQMVBGw7x5ucgEagC0EqEaAECbqjYGGsGaMVCGQ3Q9lg8oMPoJQCsRqgEAtLHoHIpwrZIxUIZD3I/Kyvc1AGhmQjUAgDZmDJSRUg5my12RANDshGoAAG0ugjVjoAynOKCgPPppPzUAWo1QDQAAY6AMq/LoZ9y/yqfNAkCzE6oBAGAMlGFVDmM7OnIBAC1EqAYAQKHWGKhgjXrE6GeZ0U8AWpFQDQCAtaqNgUbXkTFQBmrevFxkAjUAWpVQDQCAtYyBMhTVDijo7MwFALQYoRoAAL0I1hisrq5cZNH1WO58BIBW0fCh2mOPPbbmybkrLV26NN17773pnXfeybcAADBSqoUh0YVkDJT+lPdT06UGQCsb9+4auW4Yzz//fFq4cGG65ppr0iuvvJKvdpswYUI66KCD0jHHHJO22267fHV43Hfffelb3/pWXg3cl7/85bTrrrvmVf3i7/HII4/kFQBAY4jutK23zossuth++cu8gAoRqJW7GeO+EvcZAFpTu+cZDReqLVu2LJ100knpxRdfzFdqizBr9uzZeTV01157bfra176WVwP37W9/O+277755VT+hGgDQqKoFJbHxfHk8FKZP793J6H4C0PraPc9oqPHPFStWpFmzZvUK1Pbee+90xhlnpK9//etp5syZafPNN8+3pHThhRem+fPn59XQ/dd//VeuAAAI1U4DNQZKWXQ1lu8TRj8BaHUN06n29ttvpwMOOCCtWrWqWEd4dvHFF6eddtqpWPd49dVX04knnpjuvPPOfCWl6667Lu244455NXh//ud/nu6///6iPuyww9Juu+1W1OvysY99LH3oQx/Kq/rpVAMAGpkxUNYluhnL+6k13iYzAAw3458NEqpdffXV6cwzz8yrlK688sqa+5S98cYb6cADD0xPPvlksf7MZz4z5I61OADhD//wD4twL1x22WVp2rRpRT3ShGoAQKMzBkp/InSN8LWH+wZAezD+2SBuvvnmXKU0derUfjf+32CDDdKMGTPyKqXbbrstV4MXd4KeQG38+PFpr732KmoAAGqPgZa7k2g/cR+oDNTCWWflAgBaWMOEai+99FIRZoX99tuv+LU/22yzTa5Sev3119cGYoP1P//zP7mKcYb/t/bPAgBAt2qdR/Pm9Q1UaC9dXbnIInx14icA7aBhQrXFixenBx54IF1//fVp//33z1drixHQHhGAjRs3Lq8G5957781VGpb92QAAWk0EJeVgLQK1CNZoX+VuRQcUANAuGur0z/XWWy9tv/32aYsttshXaqscF40Z3vi9Q/HEE0/kKqVddtklVwAAVIox0PioZAy0fVX7vpfvHwDQqhoqVBuom266qdfpn4cffniuBu+nP/1prrrHP3/xi1+kc845p+ia22GHHYrgLvZ5mz17drrhhhuKgw0AANpR7JdVHu8zBtqeyl2KAjUA2klThWqPr3mldvrpp6c5c+bkKynts88+vQ4tGIxnnnmm2JetR4R2n/zkJ9M///M/Fx1sPfu1vfLKK8WhCKecckr69Kc/7cROAKAtRaBW3og+ArXy6aC0tp/8pG+QavQTgHbS8KFaBFzHHXdc2nPPPdMBBxyQrrvuunxLSkcccUS66KKL8mrwVqxYkatulV9j4sSJadKkSX0OLoiDDb7whS/06nADAGgX1cZAI2SZOzcvaHmLFuWiQvmEWABoZePeXSPXDenUU08tDi8oi5HMCNsOPPDAfGXwvvWtb6Vvf/vbedV98EFnZ2eaOXNmMQoaolvtP//zP9OFF16YfvaznxXXwqabbpqWLFkyoH3gaonR0oHSHQcANIroUpo+vXe3Urx0Wrq073gorad8TlgcYmH8E6D51ZNRhHbOKRo+VIs9zGIEc6uttkqrV69ODz744NpxzLDtttumBQsWFLcPVnyNGOsMkydPTpdeemmxf1otZ5xxRvrXf/3XvErpkEMOSeeee25e1S/usMIyAKAZRXdaBGuVolspgjVaVxxQUB73/eUvhakA7abd84yGD9XKIlhbuHBhuvzyy/OVlKZMmVIcHrDZZpvlK/WJQwni4//+7//SlltumaZOnZpvqe3ggw9ODz30UFFHZ9uyZcvSJptsUqzrJVQDAJpZjHyWN6yPPdeMgrauCFIjUO0RHWrRqQZAe2n3PKPpTv+M4CxGQuNkzh7PPvtsmj9/fl7Vb5tttkn77rtvceDBQAK1cNRRR+WqezR0+fLleQUA0F4iUCl3KMV+W5WhC62l/L3t6MgFALSRpgvVehx66KFp2rRpeZWKTrU33ngjr0ZehHCVVq5cmSsAgPYSgVq5S8lpoK2rWgeivdQAaEdNG6qFOEigx1tvvTWq3WJxIuiECRPyKhWjowAA7Sr2UYuRz0oRrBkBbT3lUz8FagC0q6YO1eKQgkovv/xyrkZHZai23npN/U8JADBkEa5EuFbJGGhriQMKKk97DeUwFQDaRUMkQc8991xaunRpWrx4cTrzzDPz1XWbOHFirroNJtiK/dDuueee4uvfeuutvU4W7U983uuvv55XKX34wx/OFQBAezIG2vq6unKRRYjqxE8A2lVDhGorVqxIX/rSl9Jpp52Wrr766mI9EA8//HCuuk2ePDlXAxdh2hFHHFF8/RNPPDHdfffd+Zb+lT/vIx/5SK4AANpXBCzGQFtXdKpV6uzMBQC0oYYI1fbcc880fvz4vEppyZIluerfLbfckqvuUczKgwsGaqeddspVtzvuuCNX/bvuuutyldL73//+4u8AAIAx0FZVDtRC+fsMAO2kIUK1jTbaKO211155ldJVV12VVq1alVfVxcjmjTfemFcpzZgxo1cwN1Af/OAH084775xXqeiUW9fXXrZsWbrpppvyKkYavmhPNQCAzBhoa6p2QIHRTwDaWcMkQXPmzMlVSm+++WY6/vjj01NPPZWv9HbXXXcVt/fYeOON0wknnJBXvf3gBz9Ixx133NqPlStX5lvec9JJJ+Wq+2sfe+yxNYO1GBedPXt2XqX0+7//++noo4/OKwAAQq0xUMFac4ouw3KnodFPANrduHfXyPWYW7BgQTr//PPzKqVJkyalQw89tBitXH/99dPq1auL0dAI1XpEd9oll1xSc/Tz7LPPTldccUVepeJzOzo68uo9//AP/5C+//3v51X3IQgzZ85Me+yxR/G1f/3rX/f52rGH25VXXpm22267fGVw4vc/8sgjeQUA0Bp6QrTKMKani83YYHOJ72N5/LNx3kUAMFbaPc9oqFAtXHzxxemCCy7Iq/5tuummRQg3derUfKWvgYZq4bzzzkuXX355XvVviy22SN/5znf67Mk2GEI1AKBVRbC29dZ5kUWw9stf5gVNIb6H8b3sEaOf5RFfANpPu+cZDbcR2KxZs9K1117b78b/0SF25JFHpptvvrnfQK1ep556ahHA7b777vlKXzFqeswxxxSHJAxHoAYA0Mrsr9b8okOtMlAL5dFeAGhHDdep1o50qgEArazaGGhYutQYaDOYPr33906XGgA9dKoBAMAIqtatFnSrNYdyGFpjJxUAaDtCNQAARpwx0OZUPpwgRKcaACBUAwBglEQYUx73jNCm3AlF45g3LxeZQA0A3iNUAwBg1BgDbR7VDijo7MwFACBUAwBg9BgDbR5dXbnI4nvnYAkAeI9QDQCAUVVrDLTa/l2MnfL346yzcgEAFIRqAACMumpjoLF/V3nckLFRLeDUpQYAvQnVAAAYdbXGQMsb4zM2Fi3KRRbdhfE9AwDeI1QDAGBMRFBTPk3SGOjYi3CzfCJrR0cuAIC1hGoAAIyZ2Ker3AFlDHRsVesWLIefAIBQDQCAMRSBWnkDfKeBjq1yl5pADQCqE6oBADCmqo2BRrBjDHT0xb95uUvQqZ8AUJ1QDQCAMWcMtDF0deUiixM/HVAAANUJ1QAAGHMR3FQ7DdQY6Ogqdwd2duYCAOhDqAYAQEOIrqhqY6Bz5+YFI6rauK391ACgNqEaAAANo9oY6KJFxkBHQ/nUT4EaAPRPqAYAQMOoNQY6fXpeMCKiI7AcXBr9BID+CdUAAGgoMQZaPnEyAh9joCMnugHL4vsAANQmVAMAoOHE6GG1MdDoqGL4lfdTK4eaAEBfQjUAABpOBGpLl+ZF5jTQkeGAAgAYHKEaAAANKYI1Y6Ajrzz6Wa1LEADoS6gGAEDDioCnvLeXMdDhVf637OjIBQDQL6EaAAANq9ZpoMZAh0e1rj+jnwAwMEI1AAAamjHQkVNt9BMAGBihGgAADc8Y6PCLAwoinKzU2ZkLAGCdhGoAADQ8Y6DDr6srF1mEluXgEgCoTagGAEBTqDUGKlgbnOhUq6RLDQDqI1QDAKBpVBsDjXDIGGh9yoFa0KUGAPURqgEA0DSqjYEG3Wr1qXZAQfzbAgADJ1QDAKCp2F9taKKrr9zZZ/QTAOonVAMAoOkYAx28cpdaMPoJAPUTqgEA0JSMgQ5OOXiMgBIAqJ9QDQCApmQMtH7RzRf/RpXKJ6oCAAMjVAMAoGkZA62PAwoAYPgI1QAAaGq1xkDLHVn0DRs7OnIBANRNqAYAQFOrNQY6b15eUIgOvjL7qQHA4AnVAABoerXGQKsFSe2qHDIK1ABgaIRqAAC0hOhWK+8PFkGSMdDusc/yv0NnZy4AgEERqgEA0BIiUCufZBlBktNA+x5QEP9W5c4+AKA+QjUAAFpGjDSWxxqjS6vdx0DLf/9y+AgA1E+oBgBAS4nAyBjoe6oFirrUAGDohGoAALSUWqeBtusYaHn0Mzr5yqEjAFA/oRoAAC0nOrGqjYHOnZsXbST+3pU6OnIBAAyJUA0AgJZUbQw0urbaaQy0WndeOWwEAAZHqAYAQEsyBtq3S02gBgDDR6gGAEDLijHQ8kmX7TIGGgcUlLvynPoJAMNHqAYAQEurtjF/jIGWu7haTVdXLrIIGB1QAADDR6gGAEBLa9cx0OhUq9TZmQsAYFgI1QAAaHnVxkAjWGvVMdByoBbspwYAw0uoBgBAW4hQKcK1Sq06BjpvXi4ygRoADD+hGgAAbaFdxkAjJCwfUGD0EwCGn1ANAIC2EcFaq4+BRvddWblDDwAYOqEaAABtpdXHQMt/j3KICAAMD6EaAABtpZXHQOOAgvLop/3UAGBkCNUAAGg7tcZAmz1YK49+RqAWf1cAYPgJ1QAAaEvVxkBjdLKZx0DLf/aOjlwAAMNOqAYAQFtqtTHQGP0sM/oJACNHqAYAQNtqpWBt3rxcZAI1ABhZQjUAANpajICWx0Cj66uZxkCrHVDQ2ZkLAGBECNUAAGhr1brVQjN1q3V15SKrFhQCAMNLqAYAQNtr9jHQ8n5qutQAYOQJ1QAAYI1qp4E2wxhotQMKdKkBwMgTqgEAQNaMY6CLFuUii3AwOu8AgJElVAMAgKzZxkDjz1bupDP6CQCjQ6gGAAAVao2BVhuzHGvz5uWigtFPABgdQjUAACipNgYaAVZ0hjWScpdaBIIAwOgQqgEAQEmtMdBqnWFjJTrnyiHfWWflAgAYcUI1AACoIrq+yp1fjTQG2tWViyzGPh1QAACjR6gGAAA1ROdXOahqlDHQcrjngAIAGF1CNQAAqCECtfJIZQRqY30aaLVuOfupAcDoEqoBAEA/qo2BxgEBc+fmxRgo7+0mUAOA0SdUAwCAdag2Brpo0diMgUagV/66Rj8BYPQJ1QAAYB1qnQY6FmOgEeaVxSEFAMDoEqoBAMAARHBV3l9tLMZAy/uplcM+AGB0CNUAAGCAYu+yamOgEa6NhmoHFOhSA4CxIVQDAIABGusx0PLoZ7WQDwAYHUI1AACoQ7Ux0AjWRmMMtNwR19GRCwBg1AnVAACgTtEhVh67HOkx0GqhXfw5AICxIVQDAIA6jcUYaLXRTwBg7AjVAABgECJYG60x0DigIP7blcpfGwAYXUI1AAAYpNEaA+3qykUWX9MBBQAwtoRqAAAwSKM1BhqdapU6O3MBAIwZoRoAAAxBrTHQ4QrWyoFaKHfHAQCjT6gGAABDVG0MNEZAh2MMtNoBBUY/AWDsCdUAAGCIRmoMtFowZ/QTABqDUA0AAIbBSARr5S61YPQTABqDUA0AAIZJBF7l0Cv2RBvsGGj598XoJwDQGIRqAAAwTKp1q4XBdKtFGBedbpXKByIAAGNHqAYAAMNouMZAHVAAAI1NqAYAAMOs2mmg9Y6Blj+3oyMXAEBDEKoBAMAIGMoYaARwZfZTA4DGIlRbh8ceeyx1dXWlpUuXpnvvvTe98847+RYAAKhtKGOg8+blIhOoAUDjGffuGrkme/7559PChQvTNddck1555ZV8tduECRPSQQcdlI455pi03Xbb5atDE/+dRx55JK8AAGgl06f3HeWMsK1WUBZdauXgbenSvuOkADDW2j3P0KlWsmzZsvTpT396zYuZ7/UJ1MJbb72VbrzxxvTZz342XXTRRfkq0IiGK/gGevPYgvpUGwONTrTyyZ49j62uruKXtaLjTaAGg+d5CxgpQrUKK1asSLNmzUovvvhivhIvYPZOZ5xxRvr617+eZs6cmTbffPN8S0oXXnhhmj9/fl4BAEBftcZAyyOePcr7qZ11Vi4AgIYiVMvefvvtdPLJJ6fXX3+9WEd49sMf/jAtWLAgdXZ2phkzZqSzzz473X777ekTn/hE8TkhxkQffPDBvAIAgL5i1LM87hnhWTlAK6+DLjUAaExCtezaa69Nq1atyqtUjHbutNNOefWeDTfcsLhtq622ylfiJ49VevoBAKBCdJxF11ql8hjookW5yCKIK/8eAKAxCNWym2++OVcpTZ06Ne2666551dcGG2xQdK71uO2223IFAADVRThWHuWsPA30t7/9nT4HGnR05AIAaDhCteyll15K48ePL+r99tuv+LU/22yzTa5SMTIa46MAANCfamOgEaTF2OcLL3w5X3lP+XMBgMYhVMsWL16cHnjggXT99den/fffP1+t7Y033shVKsK4cePG5RUAANRWawz0tdf2yKtuAjUAaGxCtQrrrbde2n777dMWW2yRr9RWOS4aRzTH7wUAgHWpdRpojH9WcuonADQ2SdAg3HTTTenOO+/Mq5QOP/zwXAEAwLrFiZ79daLF7Q4oAIDGJlSrw+OPP55OP/30NGfOnHwlpX322afXoQUAADAQ1cZAe3R25gIAaFjj3l0j11QRXWlLlixJK1asSC+++GK+2u2II45IZ5xxxpBHP2N8FACA9vPqq3uk//3f7+fVe7bd1utDAJrDI488kqv2I1Rbh1NPPbU4vKBshx12SMcdd1w68MAD8xUAAKjf3LkpdXV1d67F3mrxEdcAgMYmVFuH2bNnpyeeeCJttdVWafXq1enBBx9Mb7/9dr41foq4bVqwYEFxOwAA1CtCNPunAUDzEarVKYK1hQsXpssvvzxfSWnKlCnphhtuSJtttlm+AgAAAEArc1BBnSI4i5HQc845J19J6dlnn03z58/PKwAAAABanU61ITj66KPTXXfdVdQTJkxI9957b9pggw2KNQAAAACtS6faEMycOTNXKb311ltp+fLleQUAAABAKxOqDUEcUlDp5ZdfzhUAAAAArUyotsZzzz2Xli5dmhYvXpzOPPPMfHXdJk6cmKtu663nnxMAAACgHUiB1lixYkX60pe+lE477bR09dVXF+uBePjhh3PVbfLkybkCAAAAoJUJ1dbYc8890/jx4/MqpSVLluSqf7fcckuuug8qmDZtWl4BAAAA0MqEamtstNFGaa+99sqrlK666qq0atWqvKrunnvuSTfeeGNepTRjxoxewRwAAAAArUuols2ZMydXKb355pvp+OOPT0899VS+0ttdd91V3N5j4403TieccEJeAQAAANDqxr27Rq7b3oIFC9L555+fVylNmjQpHXroocV46Prrr59Wr15djIZGqNYjutMuueQSo58AAAAAbUSoVnLxxRenCy64IK/6t+mmmxYh3NSpU/MVAAAAANqBUK2KlStXpvnz56fly5fnK73FKZ+xh9qsWbPSZpttlq8CAAAA0C6EagAAAABQJwcVAAAAAECdhGoAAAAAUCehGgAAAADUSagGAAAAAHUSqgEAAABAnYRqAAAAAFCnce+ukWsazDvvvJPuuOOOou7o6Ejrr79+UQP9+/Wvf51WrlyZ3nrrrTRhwoS0yy67pI022ijfCgwHz1EwvJ555pn06KOPFs9d6623Xvq93/u9tM022+RbgcF67LHH0pNPPlk8b33gAx9IO++8c/EYA4bXG2+8kf77v/+7qKdMmZL+4A/+oKhbnVCtgS1cuDDNnz+/qO++++60ySabFDVQ3ZIlS9Jll12WHnrooXzlPR/72MfS8ccfn6ZNm5avAEPhOQqG7vnnn0/f/e530/XXX1/UZZMnT06f/exn09FHH12EbMDAxOMpnqeuueaa9Morr+Sr3eIHrgcddFA65phj0nbbbZevAkN19tlnpyuuuKKoP/e5z6XzzjuvqFudUK1BPfjgg+nzn/98evPNN4u1NyxQ29tvv51OPfXUdNNNN+UrtR122GHpzDPPzCtgMDxHwdBFp+cpp5ySXn755XyltokTJxZvVg4++OB8Bahl2bJl6aSTTkovvvhivlLbl7/85TR79uy8Agbr3//934ugukc7hWrj566RaxrE448/nv7qr/4q/eY3v8lXUjr22GPT+973vrwCKsWbkspAbeutt06HHHJIOvTQQ9MHP/jB9PTTT6fXXnutuC3GQl9//fX08Y9/vFgD9fEcBUO3dOnSNGvWrLXBdNh9992L7pkZM2akbbfdthhP+9WvflXcFj88uv3229Pv/u7vpu233764BvS1YsWK4o195XPU3nvvnf7yL/8yffKTn0xbbLFFr9eF99xzTzGyNnXq1GIN1G/16tXpqKOOWvu4Ch/96EfTfvvtl1etTadag7nvvvvSCSeckF544YV8pZsuAKguRj5PPvnkvErFC6lYV+6V8eqrr6Y5c+akH//4x/lKSldddVWx1xowcJ6jYOheeumltP/++6/took3+d/85jfTbrvtVqwrxWMuumh6RkOjY+1HP/pR2mqrrYo18J4Inw844IC0atWqYr355puniy++OO20007Fuke8LjzxxBPTnXfema+kdN1116Udd9wxr4B6xBY7le+zQjt1qtmhsYH8y7/8SzryyCP7vFkBqosNZ88///y8SunAAw9MX/3qV/tsPrvhhhumCy+8sNiYtsc3vvGNXAED4TkKhkc8lnoCtfHjx6dLL720aqAW4oc/3/ve94rPC9HZdvnllxc10Nu11167NlALF110UZ9ALcTrwritMpyOvQ2B+l199dV9ArV2I1RrAD//+c+LluS///u/XzsGYIwG1u0//uM/1o7GhOhGqyXekFROu8fJNPHYA/rnOQqG1y233JKrlD7zmc+sc5zzIx/5SPqzP/uzvErptttuyxVQ6eabb85VKsY5d91117zqa4MNNihGrXt4XEH9nnjiiXTuuecW9fvf//62nQISqo2xM844I33qU59ae/RsiG6anjsnUFvlG5M43XNdJ6PFG5d4c9Kj8sUX0JfnKBhev/3tb9Ojjz6aVynts88+uepf5X5PsR9UdGoDvcVodU9X50D2ctpmm21ylYr9dmN8FBiYeB6KhoaefdTOOeecYjuDdiRUG2Nx8lOP2Ccj5vuvvPLKNGXKlHwVqGX58uW56h6RGYjKEdDYnBaozXMUDK/YGy32mYkwLfZv+sAHPpBv6d/666+fq27e/ENfixcvTg888EC6/vrri30L1yUOKOgRYdy4cePyCliX2Frn/vvvL+p4XhvIY65VCdUaRLT/x8azsclfeT8ooK/4aX/l6Ge1PTOqidPVesQJUcC6eY6C4bHlllsWGzd/5zvfKTZG/5M/+ZN8S/8eeeSRXHUH3OWQDegWz1ExmTCQjpnKiYXtttvO8xsMUByiE89jIfYm/Lu/+7uiblf+zzHGYpY/Rtjmz5/vJCeoQ/wkstJGG22Uq/7FvH+P2B+q8uhnoDfPUTD2YsTmpptuyqveHdfA4MRjqvL0z8MPPzxXQH/i9NyTTz45r1Lxg6KBvg9rVUK1MRYnFVbO8wMD03NyWo8//uM/zlX/4sSnSitXrswVUOY5CsbeVVdd1etEw8pDC4D6PP744+n000/vdbhVjGNXHloA1DZv3ry100JHHXVU2mOPPYq6nQnVgKYUG8pWmjRpUq76V3lQQdCpBkCj+sUvflF0ivb48Ic/nA455JC8AgYiutKOO+64tOeee6YDDjigGL3uccQRR6SLLroor4D+3HrrrcWehSHeU1WG0+1MqAY0pdhTrVLPaU/r8r73vS9XANC4nnvuufTFL34xvfLKK8U6nufi5F37PkF97rrrrvSTn/ykz5TDDjvskHbbbTePKRiAeE6aO3duUU+YMCH94z/+44Dff7U6/wcB2lo5nAOAsRZvXg477LD09NNP5yspnXXWWQM+lAd4TwTT2267bdp7772L7UJ6goCHHnqoONU6DuN58skni2tAddGV1hNMf+UrX+kz/dPOhGpAW3OCGgCN5Iknnkh/8Rd/UfzaI974z5w5M6+AesR4Z4yALliwIF1zzTVF51rsBdXj0UcfLR5fq1evzleASosWLUrLly8v6l122SUde+yxRU03odow+MEPfpDOPvvsdX7ce++9+XcAQ1UOw+J0tIF46623cgUAjSVeK37hC1/o1TUTgdrxxx+fV8BQbbbZZunUU09N55xzTr6S0rPPPttr/0Kg289//vO1j43Jkyen888/v6h5j1BtGHR1daUrrrhinR+x2SwwPMp7o73xxhu56t/DDz+cq272WAOgEdxwww2ps7MzvfDCC/lKKt70C9RgZBx66KFp2rRpedX9GBzo60loB7FNzt/8zd+kN998s1h/7WtfS1tttVVR8x6hGtCUNtlkk1x1G2ho3bPhc48/+qM/yhUAjI3oAjjllFPWvnGJH/j80z/9U/GmHxg5lWPVMc3QM+IGpHT55ZcX49Fh0qRJ6b777kt/+7d/W/Mj9insUf7cxx57LN/SeoRqwyBOjpk6deo6Pz70oQ/l3wEMVTkMi7b9gXjppZdyldLEiRPThhtumFcAMLrefvvtYrxz4cKF+UpKW2yxRbG1yPTp0/MVYKTEAQaVXn755VwBzzzzTK5Seu2114o9Cfv7+NWvfpU/u3t/0MrbWvkwEKHaMIgXQ9/97nfX+fGnf/qn+XcAQxV7qk2ZMiWvUnr88cdz1b+VK1fmKqUdd9wxVwAwumLM7Jhjjkm33nprvtL9g9rrr7/e8xPUKU7MXbp0aVq8eHE688wz89V1ix+wVlpvPW+PgfqMe3eNXNNAfvrTnxZHqfe4++67+4y7Qbs76aST0r/9278V9X777Vec7rQun//854t25HDkkUcWewMA9fEcBUMTh+vE6WlxCmGPT3ziE+mb3/ymDmoYhNtvvz2dcMIJeZXSD3/4w7TTTjvlVW133HFHmjVrVl6ldMkll6SOjo68gvYWh+fUsy987CPfMwIap4RWbmHw8Y9/PG255ZZ51VqEag3KGxZYtyVLlqSTTz65qCdMmFA8TjbaaKNiXc2qVavSvvvum1fd/+Pfbbfd8goYKM9RMDTRSXP11VfnVUqf+tSnnKgGQ/Cb3/wm7bHHHsVIdRjoD06/+tWvphtvvLGo47Xk/fffn8aPH1+sgfrMnj073XbbbUX9uc99Lp133nlF3er0twJN64ADDkibbrppUcfmshdccEFR1/KNb3wjVyltvfXWAjUARl2MqFUGanvvvbdADYYofqi611575VVKV111VfHD1P7cc889awO1MGPGDIEaUDehGtC0Yl+1o48+Oq9S+v73v1/sX1hN/KTkRz/6UV6l9JWvfCVXADA6Yuzz7LPPzqvuzpiDDz44LVu2rK6Pnm4c4D1z5szJVSpO0j3++OPTU089la/0FqPXcXuPjTfeuNf4KMBAGf9sUEZrYGDiDUochx7t+j2i/T9m+OMx8/TTTxcdAQ8++GC+1ZgNDJXnKBicG264IZ1yyil5NXixN6i916CvBQsW9HqNN2nSpOI14Z577ln8MHb16tXF9iGV+xlGd1rspTZt2rR8BRgM458ATShOaYoXUB/96Efzle52/njT8td//dfFvjWVgVq8YDr33HPzCgBGz49//ONcASPhuOOO6zWN8NprrxWTDNGFFq8LTzvttF6BWmwjcumllwrUgEETqgFNb7PNNitOeYoXTNG+X83mm29eBG2XXXZZ2mCDDfJVABg9zz77bK6AkRKneV577bVFd1otkydPLg4zuPnmm9PUqVPzVYD6Gf8EWkqMgy5fvjy98MILxX4aEydOTL/zO7+Tdt5556KrDQCA9vD888+nn/3sZ+nll18u9iKMH6xOmTIl7b777l4XAsNCqAYAAAAAdRLPAwAAAECdhGoAAAAAUCehGgAAAADUSagGAAAAAHUSqgEAAABAnYRqAAAAAFAnoRoAAAAA1EmoBgAAAAB1EqoBAAAAQJ2EagAAAABQJ6EaAAAAANRJqAYAAAAAdRKqAQAAAECdhGoAAAAAUCehGgAAAADUSagGAAAAAHUSqgEAAABAnYRqAAAAAFAnoRoAAAAA1EmoBgAAAAB1EqoBAAAAQJ2EagAAAABQJ6EaAAAAANRJqAYAAAAAdRKqAQAAAECdhGoAAAAAUCehGgAAAADUSagGAAAAAHUSqgEAAABAnYRqAAAAAFAnoRoAAAAA1EmoBgAAAAB1EqoBAAAAQJ2EagAAAABQJ6EaAAAAANRJqAYAAAAAdRKqAQAAAECdhGoAAAAAUCehGgAAAADUSagGAAAAAHUSqgEAAABAnYRqAAAAAFAnoRoAAAAA1EmoBgAAAAB1EqoBAAAAQJ2EagAAAABQJ6EaAAAAANRJqAYAAAAAdRKqAQAAAECdhGoAAAAAUCehGgAAAADUJaX/Dy15wHUcCl8fAAAAAElFTkSuQmCC\" alt=\"equilateral triangle with distances from a point\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d = sumdist(x,y,x0,y0)\r\n%  x,y = coordinates of the triangle's vertices\r\n%  x0,y0 = coordinates of the point in the interior of the triangle\r\n  d = sum(hypot(x-x0,y-y0));\r\nend","test_suite":"%%\r\nx = [1 6.215999461960969 2.397622843553612];\r\ny = [2 3.397622843553612 7.215999461960969];\r\nx0 = 2.1;\r\ny0 = 3.2;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 4.676537180435970;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [1   4.284147809382832  3.404163056034262];\r\ny = [-2 -2.879984753348571  0.404163056034262];\r\nx0 = 3;\r\ny0 = -1;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 2.944486372867091;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [1   1.292541480647668  0.910019578262454];\r\ny = [-2 -1.727200655975001 -1.610251974085906];\r\nx0 = 1.1;\r\ny0 = -1.8;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 0.346410161513776;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [-4  0.854101966249685 -4.627170779605921];\r\ny = [-8 -4.473288486245162 -2.032868627790361];\r\nx0 = -2;\r\ny0 = -4;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 5.196152422706631;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nxr = 100*rand; yr = 100*rand; s  = 100*rand;\r\nx = xr+s*[-4  0.854101966249685 -4.627170779605921];\r\ny = yr+s*[-8 -4.473288486245162 -2.032868627790361];\r\nx0 = mean(x);\r\ny0 = mean(y);\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 5.196152422706631*s;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [0 0.819152044288992 -0.087155742747658];\r\ny = [0 0.573576436351046  0.996194698091746];\r\nx0 = 0.2;\r\ny0 = 0.4;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 0.866025403784439;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nfiletext = fileread('sumdist.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-12-28T05:22:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-28T05:22:00.000Z","updated_at":"2023-12-28T05:22:29.000Z","published_at":"2023-12-28T05:22:07.000Z","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\u003eWrite a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the triangle. That is, for the triangle below, compute the sum \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a+b+c\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea+b+c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Input will consist of the point (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex0\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) and vectors \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the coordinates of the vertices of the triangle. \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=\\\"488\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"495\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"equilateral triangle with distances from a point\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":1113,"title":"Create array of all Distances between two Sets of Points ","description":"This Challenge is a subsection of Martian Pranks based on Tim's efficient Distance calculation between sets of points.\r\nGiven Point Set vectors Start and Final determine the distance between each Start and each Final Point.\r\nInput: Start(m,2), Final(m,2)\r\nOutput: Distances (m,m)\r\nExample:\r\nInput: [0 0;0 1], [2 0;3 3]\r\nOutput: [2 4.24; 2.24 3.61]\r\nTestSuite will perform rounding\r\nHint: Tags","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: 261px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 130.5px; transform-origin: 407px 130.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 104.5px 8px; transform-origin: 104.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is a subsection 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: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMartian Pranks\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: 215.5px 8px; transform-origin: 215.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e based on Tim's efficient Distance calculation between sets of points.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 328.5px 8px; transform-origin: 328.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Point Set vectors Start and Final determine the distance between each Start and each Final Point.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 69.5px 8px; transform-origin: 69.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Start(m,2), Final(m,2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 26px 8px; transform-origin: 26px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\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: 53px 8px; transform-origin: 53px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Distances (m,m)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 31.5px 8px; transform-origin: 31.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 75.5px 8px; transform-origin: 75.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput: [0 0;0 1], [2 0;3 3]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOutput: [2 4.24; 2.24 3.61]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 96.5px 8px; transform-origin: 96.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTestSuite will perform rounding\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 31px 8px; transform-origin: 31px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Tags\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d=xy_distance(Start,Final)\r\n d=zeros(size(Start,1));\r\n\r\nend","test_suite":" %%\r\n m=5;\r\n Start=rand(m,2);\r\n Final=rand(m,2);\r\n \r\n d=xy_distance(Start,Final);\r\n d=round(100*d)/100;\r\n \r\n d_expect=zeros(m);\r\n for i=1:m % 10\r\n  for j=1:m\r\n   dx=Start(i,1)-Final(j,1); % 14\r\n   dy=Start(i,2)-Final(j,2); % 14\r\n   d_expect(i,j)=hypot(dx,dy); % 14\r\n  end\r\n end\r\n \r\n d_expect=round(100*d_expect)/100;\r\n \r\n assert(isequal(d_expect,d))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":223089,"edited_at":"2022-12-31T12:41:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":"2022-12-31T12:41:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-12-11T04:52:10.000Z","updated_at":"2025-06-25T18:38:29.000Z","published_at":"2012-12-11T05:29:22.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is a subsection of\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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMartian Pranks\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e based on Tim's efficient Distance calculation between sets of points.\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 Point Set vectors Start and Final determine the distance between each Start and each Final Point.\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Start(m,2), Final(m,2)\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Distances (m,m)\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\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\u003eInput: [0 0;0 1], [2 0;3 3]\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\u003eOutput: [2 4.24; 2.24 3.61]\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\u003eTestSuite will perform rounding\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: Tags\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":58862,"title":"Given Hypotenuse points create two right triangles","description":"Given two points defining a hypotenuse create two right triangles of (h,5,R). Return the two (x,y) points that create the right triangles. I will elaborate on two geometric methods utilizing Matlab specific functions, rotation matrix, and translation matrix.\r\nGiven points [x1,y1] and [x2,y2] return  [x3 y3;x4 y4] such that distance(xy2,xy3)=distance(xy2,xy4)=5. h\u003e5\r\nThe below figure is created based upon h=distance([x1,y1],[x2,y2]), translating (x1,y1) to (0,0), and rotating (x2,y2) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,5] with R^2+5^2=h^2. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\r\nP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(d-Y)^2 = Y^2-d^2+2dY-Y^2=2dY-d^2 thus\r\nY=(R^2-P^2+h^2)/(2h)  and X=+/- (R^2-Y^2)^.5\r\nThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [x1 y1]\r\nA second method to find (X,Y) is theta=atan(5/R), X=Rsin(theta) and Y=Rcos(theta). The rotation and translation matrices are still required to return to the original coordinate system.\r\n\r\nIn this figure h represents distance from (x1,y1) to (x2,y2) and (x1,y1) has been translated to 0,0","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: 894.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 447.25px; transform-origin: 407px 447.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372px 8px; transform-origin: 372px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven two points defining a hypotenuse create two right triangles of (h,5,R). Return the two (x,y) points that create the right triangles. I will elaborate on two geometric methods utilizing Matlab specific functions, rotation matrix, and translation matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 332.5px 8px; transform-origin: 332.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven points [x1,y1] and [x2,y2] return  [x3 y3;x4 y4] such that distance(xy2,xy3)=distance(xy2,xy4)=5. h\u0026gt;5\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; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe below figure is created based upon h=distance([x1,y1],[x2,y2]), translating (x1,y1) to (0,0), and rotating (x2,y2) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,5] with R^2+5^2=h^2. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 358px 8px; transform-origin: 358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(d-Y)^2 = Y^2-d^2+2dY-Y^2=2dY-d^2 thus\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 143px 8px; transform-origin: 143px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eY=(R^2-P^2+h^2)/(2h)  and X=+/- (R^2-Y^2)^.5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 379px 8px; transform-origin: 379px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [x1 y1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.5px 8px; transform-origin: 383.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA second method to find (X,Y) is theta=atan(5/R), X=Rsin(theta) and Y=Rcos(theta). The rotation and translation matrices are still required to return to the original coordinate system.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 549.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 274.75px; text-align: left; transform-origin: 384px 274.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 416px;height: 544px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\" width=\"416\" height=\"544\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 302.5px 8px; transform-origin: 302.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this figure h represents distance from (x1,y1) to (x2,y2) and (x1,y1) has been translated to 0,0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xy = find_xy_RightTriangles(x1,y1,x2,y2)\r\n % The hypotenuse end points are (x1,y1) and (x2,y2) \r\n % A length 5 segment is attached to (x2,y2)\r\n % Complete the two possible right triangles\r\n % xy=[x3 y3;x4 y4]\r\n \r\n  h=norm([x2-x1 y2-y1]);\r\n \r\n  R2=h^2-25;\r\n  R=R2^0.5;\r\n  \r\n  %PRh mehtod\r\n  %y=\r\n  %x=\r\n  %xy=[-x y;x y];\r\n  \r\n  %Trig method\r\n  %theta=atan(?/R);\r\n  %y=\r\n  %x=\r\n  %xy=[-x y;x y];\r\n \r\n \r\n %Rotation Angle: atan2\r\n theta=atan2(x2-x1,y2-y1); % (X,Y) output radians Neg Left of vert, Pos Right of Vert\r\n \r\n %Rotation Matrix: [cos(t) -sin(t);sin(t) cos(t)]\r\n %Translation matrix: [x1 y1]\r\n %Check of (x2,y2) being regenerated from h, theta, and translation\r\n [x2y2]=[0 h]*[cos(theta) -sin(theta);sin(theta) cos(theta)]+[x1 y1]\r\n [x2 y2]\r\n \r\n %xy=\r\n \r\n \r\nend %find_xy_RightTriangles","test_suite":"%%\r\nvalid=1;\r\nx1=0;y1=0;x2=0;y2=13;\r\nxy = find_xy_RightTriangles(x1,y1,x2,y2)\r\nif sum(sum((xy-[x2 y2]).^2,2)-25)\u003e1e-6 % verify xy3,xy4 dist==5 from xy2\r\n valid=0;\r\nend\r\nh2=sum(([x1 y1]-[x2 y2]).^2);\r\nif sum(sum((xy-[x1 y1]).^2,2)+25-h2)\u003e1e-6 % Verify right triangles\r\n valid=0;\r\nend\r\nassert(valid)\r\n%%\r\nvalid=1;\r\nx1=0;y1=0;x2=0;y2=-13;\r\nxy = find_xy_RightTriangles(x1,y1,x2,y2)\r\nif sum(sum((xy-[x2 y2]).^2,2)-25)\u003e1e-6 % verify xy3,xy4 dist==5 from xy2\r\n valid=0;\r\nend\r\nh2=sum(([x1 y1]-[x2 y2]).^2);\r\nif sum(sum((xy-[x1 y1]).^2,2)+25-h2)\u003e1e-6 % Verify right triangles\r\n valid=0;\r\nend\r\nassert(valid)\r\n%%\r\nvalid=1;\r\nx1=5;y1=5;x2=5;y2=-8;\r\nxy = find_xy_RightTriangles(x1,y1,x2,y2)\r\nif sum(sum((xy-[x2 y2]).^2,2)-25)\u003e1e-6 % verify xy3,xy4 dist==5 from xy2\r\n valid=0;\r\nend\r\nh2=sum(([x1 y1]-[x2 y2]).^2);\r\nif sum(sum((xy-[x1 y1]).^2,2)+25-h2)\u003e1e-6 % Verify right triangles\r\n valid=0;\r\nend\r\nassert(valid)\r\n%%\r\nvalid=1;\r\nx1=0;y1=0;x2=0;y2=0;\r\nwhile norm([x2-x1 y2-y1])\u003c5.1\r\n x1=10*rand-5;y1=10*rand-5;x2=20*rand-10;y2=-20*rand+10;\r\n %fprintf('%.3f ',[x1 y1 x2 y2]);fprintf('\\n');\r\nend\r\nfprintf('%.3f ',[x1 y1 x2 y2]);fprintf('\\n');\r\nxy = find_xy_RightTriangles(x1,y1,x2,y2)\r\nif sum(sum((xy-[x2 y2]).^2,2)-25)\u003e1e-6 % verify xy3,xy4 dist==5 from xy2\r\n valid=0;\r\nend\r\nh2=sum(([x1 y1]-[x2 y2]).^2);\r\nif sum(sum((xy-[x1 y1]).^2,2)+25-h2)\u003e1e-6 % Verify right triangles\r\n valid=0;\r\nend\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-11T18:08:31.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2023-08-11T18:08:31.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-11T15:21:29.000Z","updated_at":"2024-11-18T01:49:13.000Z","published_at":"2023-08-11T17:36:27.000Z","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 two points defining a hypotenuse create two right triangles of (h,5,R). Return the two (x,y) points that create the right triangles. I will elaborate on two geometric methods utilizing Matlab specific functions, rotation matrix, and translation matrix.\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 points [x1,y1] and [x2,y2] return  [x3 y3;x4 y4] such that distance(xy2,xy3)=distance(xy2,xy4)=5. h\u0026gt;5\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 below figure is created based upon h=distance([x1,y1],[x2,y2]), translating (x1,y1) to (0,0), and rotating (x2,y2) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,5] with R^2+5^2=h^2. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\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\u003eP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(d-Y)^2 = Y^2-d^2+2dY-Y^2=2dY-d^2 thus\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\u003eY=(R^2-P^2+h^2)/(2h)  and X=+/- (R^2-Y^2)^.5\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 trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [x1 y1]\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\u003eA second method to find (X,Y) is theta=atan(5/R), X=Rsin(theta) and Y=Rcos(theta). The rotation and translation matrices are still required to return to the original coordinate system.\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=\\\"544\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"416\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eIn this figure h represents distance from (x1,y1) to (x2,y2) and (x1,y1) has been translated to 0,0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.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":59501,"title":"Compute the sum of distances from a point to the sides of an equilateral triangle","description":"Write a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the triangle. That is, for the triangle below, compute the sum . Input will consist of the point (x0,y0) and vectors x and y with the coordinates of the vertices of the triangle. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 565.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 282.85px; transform-origin: 407px 282.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.433px 8px; transform-origin: 381.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the triangle. That is, for the triangle below, compute the sum \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"58.5\" height=\"18\" alt=\"a+b+c\" style=\"width: 58.5px; height: 18px;\"\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: 95.675px 8px; transform-origin: 95.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Input will consist of the point (\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: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex0\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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey0\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: 42.3917px 8px; transform-origin: 42.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) and vectors \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: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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: 15.5583px 8px; transform-origin: 15.5583px 8px; 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: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\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: 0.241667px 8px; transform-origin: 0.241667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the coordinates of the vertices of the triangle. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 493.7px; 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 246.85px; text-align: left; transform-origin: 384px 246.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"495\" height=\"488\" style=\"vertical-align: baseline;width: 495px;height: 488px\" src=\"data:image/png;base64,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\" alt=\"equilateral triangle with distances from a point\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d = sumdist(x,y,x0,y0)\r\n%  x,y = coordinates of the triangle's vertices\r\n%  x0,y0 = coordinates of the point in the interior of the triangle\r\n  d = sum(hypot(x-x0,y-y0));\r\nend","test_suite":"%%\r\nx = [1 6.215999461960969 2.397622843553612];\r\ny = [2 3.397622843553612 7.215999461960969];\r\nx0 = 2.1;\r\ny0 = 3.2;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 4.676537180435970;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [1   4.284147809382832  3.404163056034262];\r\ny = [-2 -2.879984753348571  0.404163056034262];\r\nx0 = 3;\r\ny0 = -1;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 2.944486372867091;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [1   1.292541480647668  0.910019578262454];\r\ny = [-2 -1.727200655975001 -1.610251974085906];\r\nx0 = 1.1;\r\ny0 = -1.8;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 0.346410161513776;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [-4  0.854101966249685 -4.627170779605921];\r\ny = [-8 -4.473288486245162 -2.032868627790361];\r\nx0 = -2;\r\ny0 = -4;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 5.196152422706631;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nxr = 100*rand; yr = 100*rand; s  = 100*rand;\r\nx = xr+s*[-4  0.854101966249685 -4.627170779605921];\r\ny = yr+s*[-8 -4.473288486245162 -2.032868627790361];\r\nx0 = mean(x);\r\ny0 = mean(y);\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 5.196152422706631*s;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nx = [0 0.819152044288992 -0.087155742747658];\r\ny = [0 0.573576436351046  0.996194698091746];\r\nx0 = 0.2;\r\ny0 = 0.4;\r\nd = sumdist(x,y,x0,y0);\r\nd_correct = 0.866025403784439;\r\nassert(abs(d-d_correct)/d_correct \u003c 1e-8)\r\n\r\n%%\r\nfiletext = fileread('sumdist.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-12-28T05:22:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-28T05:22:00.000Z","updated_at":"2023-12-28T05:22:29.000Z","published_at":"2023-12-28T05:22:07.000Z","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\u003eWrite a function to compute the sum of the (shortest) distances from a point inside an equilateral triangle to the sides of the triangle. That is, for the triangle below, compute the sum \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a+b+c\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea+b+c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Input will consist of the point (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex0\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) and vectors \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with the coordinates of the vertices of the triangle. \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=\\\"488\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"495\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"equilateral triangle with distances from a point\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.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\"}]}"}],"term":"tag:\"hypot\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"hypot\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"hypot\"","","\"","hypot","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f3d9834dca8\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f3d9834da28\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f3d98348348\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f3d9834e9c8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f3d9834e4c8\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f3d9834e2e8\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f3d9834e068\u003e":"tag:\"hypot\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f3d9834e068\u003e":"tag:\"hypot\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"cody-search","password":"78X075ddcV44","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"hypot\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"hypot\"","","\"","hypot","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f3d9834dca8\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f3d9834da28\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f3d98348348\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f3d9834e9c8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f3d9834e4c8\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f3d9834e2e8\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f3d9834e068\u003e":"tag:\"hypot\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f3d9834e068\u003e":"tag:\"hypot\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":1113,"difficulty_rating":"easy"},{"id":58862,"difficulty_rating":"medium"},{"id":59501,"difficulty_rating":"medium"}]}}