{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":60952,"title":"List even numbers whose Goldbach partition does not use the largest prime","description":"The strong Goldbach conjecture says that every even number greater than 2 can be expressed as a sum of two prime numbers—that is, they all have Goldbach partitions. Several Cody problems involve some form or variation of the Goldbach conjecture. Problems 60 and 56190 ask us to provide Goldbach partitions, and Problem 64 asks us to count Goldbach partitions for an even number. Problem 60739 restricts the Goldbach partitions to twin primes. Problem 44403 involves writing integers greater than 5 as the sum of three primes, and Problem 60949 involves writing integers greater than 2 as a sum of no more than two primes and the number 1. \r\nOne approach to finding Goldbach partitions of a target number is to start with the largest prime smaller than that number and determine whether the difference is prime. For example, 10 = 7 + 3, 14 = 11 + 3, and 16 = 13 + 3. However, that approach fails for numbers such as 18, 20, and 23 because in those cases, the difference between the numbers and the largest primes smaller than the numbers is 1, which is not prime.  \r\nWrite a function that takes an integer and lists even numbers smaller than or equal to that integer whose Goldbach partitions do not use the largest prime. In other words, for each number in the list, the difference between that number and the largest prime smaller than the number must not be prime (i.e., either 1 or composite).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 291px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 145.5px; transform-origin: 408px 145.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 63px; text-align: left; transform-origin: 385px 63px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe strong Goldbach conjecture says that every even number greater than 2 can be expressed as a sum of two prime numbers—that is, they all have \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eGoldbach partitions\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Several Cody problems involve some form or variation of the Goldbach conjecture. Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e60\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56190\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e56190\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ask us to provide Goldbach partitions, and Problem \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/64\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e64\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asks us to count Goldbach partitions for an even number. Problem \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60739\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e60739\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e restricts the Goldbach partitions to twin primes. Problem \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44403\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e44403\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves writing integers greater than 5 as the sum of three primes, and Problem \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60949\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e60949\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves writing integers greater than 2 as a sum of no more than two primes and the number 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 42px; text-align: left; transform-origin: 385px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne approach to finding Goldbach partitions of a target number is to start with the largest prime smaller than that number and determine whether the difference is prime. For example, 10 = 7 + 3, 14 = 11 + 3, and 16 = 13 + 3. However, that approach fails for numbers such as 18, 20, and 23 because in those cases, the difference between the numbers and the largest primes smaller than the numbers is 1, which is not prime. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes an integer and lists even numbers smaller than or equal to that integer whose Goldbach partitions do not use the largest prime. In other words, for each number in the list, the difference between that number and the largest prime smaller than the number must not be prime (i.e., either 1 or composite).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = goldbaching(x)\r\n  y = 1:x;\r\nend","test_suite":"%%\r\nx = 30;\r\ny = goldbaching(x);\r\ny_correct = [4 6 8 12 14 18 20 24 30];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = 100;\r\ny = goldbaching(x);\r\ny_correct = [4 6 8 12 14 18 20 24 30 32 38 42 44 48 54 60 62 68 72 74 80 84 90 98];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = 150;\r\ny = goldbaching(x);\r\ny_correct = [4 6 8 12 14 18 20 24 30 32 38 42 44 48 54 60 62 68 72 74 80 84 90 98 102 104 108 110 114 122 128 132 138 140 148 150];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = 800;\r\ny = goldbaching(x);\r\nlen_correct = 163;\r\nsum_correct = 61606;\r\nassert(isequal(length(y),len_correct))\r\nassert(isequal(sum(y),sum_correct))\r\n\r\n%%\r\nx = 4000;\r\ny = goldbaching(x);\r\nlen_correct = 774;\r\nsum_correct = 1523050;\r\nassert(isequal(length(y),len_correct))\r\nassert(isequal(sum(y),sum_correct))\r\n\r\n%%\r\nx = 25000;\r\ny = goldbaching(x);\r\nlen_correct = 4679;\r\nystr_correct = [21292 21298 21304 21308 21310 21314 21318 21320 21324 21332 21338 21342 21348 21356 21362 21368 21372 21374 21378 21380 21384 21392 21398 21402 21408 21416 21420 21428 21434 21442 21448];\r\nassert(isequal(length(y),len_correct))\r\nassert(isequal(y(3992:4022),ystr_correct))\r\n\r\n%%\r\nx = 53606;\r\ny = goldbaching(x);\r\nlen_correct = 10000;\r\nsum_correct = 267146550;\r\nsumsqrt_correct = 1539275.930840296;\r\nystr_correct = [48222 48230 48236 48240 48248 48256 48260 48268 48272 48280 48282 48290 48296 48300 48308 48312 48314 48322 48328 48334 48338 48342 48350 48354 48362 48368];\r\nassert(isequal(length(y),len_correct))\r\nassert(isequal(sum(y),sum_correct))\r\nassert(abs(sum(sqrt(y))-sumsqrt_correct)\u003c1e-7)\r\nassert(isequal(y(9000:9025),ystr_correct))\r\n\r\n%%\r\nx = 500000;\r\ny = goldbaching(x);\r\nL = [];\r\nfor p = [13 29 67 127 191]\r\n    L(end+1) = length(y(mod(y,p)==0));\r\nend\r\nlen_correct = 93640;\r\nsum_correct = 23440930328;\r\nystr_correct = [53606 80628 107348 134078 160826 187508 214172 240826 267582 294146 320760 347374 373862 400628 427150 453766 480518];\r\nL_correct = [7541 3219 1375 757 489];\r\nassert(isequal(length(y),len_correct))\r\nassert(isequal(sum(y),sum_correct))\r\nassert(isequal(y(10000:5000:90000),ystr_correct))\r\nassert(isequal(L,L_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-02T00:54:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-02T00:53:37.000Z","updated_at":"2025-10-02T12:04:26.000Z","published_at":"2025-07-02T00:54:19.000Z","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\u003eThe strong Goldbach conjecture says that every even number greater than 2 can be expressed as a sum of two prime numbers—that is, they all have \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGoldbach partitions\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Several Cody problems involve some form or variation of the Goldbach conjecture. Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e60\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56190\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e56190\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ask us to provide Goldbach partitions, and Problem \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/64\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e64\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks us to count Goldbach partitions for an even number. Problem \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60739\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e60739\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e restricts the Goldbach partitions to twin primes. Problem \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44403\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e44403\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves writing integers greater than 5 as the sum of three primes, and Problem \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60949\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e60949\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves writing integers greater than 2 as a sum of no more than two primes and the number 1. \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\u003eOne approach to finding Goldbach partitions of a target number is to start with the largest prime smaller than that number and determine whether the difference is prime. For example, 10 = 7 + 3, 14 = 11 + 3, and 16 = 13 + 3. However, that approach fails for numbers such as 18, 20, and 23 because in those cases, the difference between the numbers and the largest primes smaller than the numbers is 1, which is not prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes an integer and lists even numbers smaller than or equal to that integer whose Goldbach partitions do not use the largest prime. In other words, for each number in the list, the difference between that number and the largest prime smaller than the number must not be prime (i.e., either 1 or composite).\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":57810,"title":"List the two-bit primes","description":"Each year at Christmas, my father-in-law and his partner send me the Puzzle Mania section from the New York Times. This year’s edition had a puzzle by Mike Shenk called “Two Bits”, which asked solvers to find words whose first two letters could be shifted as a unit elsewhere in the word to form a new word. For example, the clue “??BID” had the answer RABID, with the accompanying word BRAID. The clue “??PREME” had the answer SUPREME, with the accompanying word PRESUME.\r\nIn a similar way, one can define two-bit primes: prime numbers whose first two digits can be shifted, as a unit, elsewhere in the number to form a new prime number. The first in the sequence is 113, with accompanying prime 311, followed by 131, with accompanying prime 113. Some two-bit primes can have multiple accompanying primes. For example, the two-bit prime 99611 has two accompanying primes: 69911 and 61991. Leading zeros are allowed: 1103 is a two-bit prime because 311 is also prime. \r\nRemember that the two-bit prime and its accompanying prime must differ. For example, the first two digits of 99991 can be moved one or two places to the right, but the resulting number (99991) is the same. Because 99199 is not prime, 99991 is not a two-bit prime. \r\nWrite a function to list the th two-bit and all its accompanying primes. ","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: 321px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 160.5px; transform-origin: 407px 160.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; 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: 313.108px 8px; transform-origin: 313.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach year at Christmas, my father-in-law and his partner send me the Puzzle Mania section from the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.8417px 8px; transform-origin: 52.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eNew York Times.\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: 17.1083px 8px; transform-origin: 17.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e This year’s edition had a puzzle by Mike Shenk called “Two Bits”, which asked solvers to find words whose first two letters could be shifted as a unit elsewhere in the word to form a new word. For example, the clue “??BID” had the answer RABID, with the accompanying word BRAID. The clue “??PREME” had the answer SUPREME, with the accompanying word PRESUME.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; 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: 381.058px 8px; transform-origin: 381.058px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a similar way, one can define two-bit primes: prime numbers whose first two digits can be shifted, as a unit, elsewhere in the number to form a new prime number. The first in the sequence is 113, with accompanying prime 311, followed by 131, with accompanying prime 113. Some two-bit primes can have multiple accompanying primes. For example, the two-bit prime 99611 has two accompanying primes: 69911 and 61991. Leading zeros are allowed: 1103 is a two-bit prime because 311 is also prime. \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: 379.875px 8px; transform-origin: 379.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemember that the two-bit prime and its accompanying prime must differ. For example, the first two digits of 99991 can be moved one or two places to the right, but the resulting number (99991) is the same. Because 99199 is not prime, 99991 is not a two-bit prime. \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: 80.375px 8px; transform-origin: 80.375px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 133.808px 8px; transform-origin: 133.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth two-bit and all its accompanying primes. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y,a] = twobitPrime(n)\r\n  y = isprime(n); a = primes(n);\r\nend","test_suite":"%%\r\nn = 1;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 113;\r\na_correct = 311;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 5;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 199;\r\na_correct = 919;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 31;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 977;\r\na_correct = 797;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 311;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 5119;\r\na_correct = 1951;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 500;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 7963;\r\na_correct = [6379 6793];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),sort(a_correct)))\r\n\r\n%%\r\nn = 873;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 13591;\r\na_correct = 59113;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 873;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 13591;\r\na_correct = 59113;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 1876;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 29009;\r\na_correct = [929 2909];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nn = 5277;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 86069;\r\na_correct = [6869 8669];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nn = 8153;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 134921;\r\na_correct = 492113;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 10003;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 168617;\r\na_correct = [861167 861617];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nn = 25000;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 433261;\r\na_correct = [324361 326143 343261];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nn = 39000;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 697877;\r\na_correct = [787697 787769];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\n[y,a] = twobitPrime(twobitPrime(54));\r\ny_correct = 19853;\r\na_correct = [81953 85193];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nfiletext = fileread('twobitPrime.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-19T00:22:09.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-19T00:21:05.000Z","updated_at":"2025-01-02T08:51:14.000Z","published_at":"2023-03-19T00:22:09.000Z","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\u003eEach year at Christmas, my father-in-law and his partner send me the Puzzle Mania section from the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNew York Times.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e This year’s edition had a puzzle by Mike Shenk called “Two Bits”, which asked solvers to find words whose first two letters could be shifted as a unit elsewhere in the word to form a new word. For example, the clue “??BID” had the answer RABID, with the accompanying word BRAID. The clue “??PREME” had the answer SUPREME, with the accompanying word PRESUME.\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\u003eIn a similar way, one can define two-bit primes: prime numbers whose first two digits can be shifted, as a unit, elsewhere in the number to form a new prime number. The first in the sequence is 113, with accompanying prime 311, followed by 131, with accompanying prime 113. Some two-bit primes can have multiple accompanying primes. For example, the two-bit prime 99611 has two accompanying primes: 69911 and 61991. Leading zeros are allowed: 1103 is a two-bit prime because 311 is also prime. \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\u003eRemember that the two-bit prime and its accompanying prime must differ. For example, the first two digits of 99991 can be moved one or two places to the right, but the resulting number (99991) is the same. Because 99199 is not prime, 99991 is not a two-bit prime. \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\u003eWrite a function to list the \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth two-bit and all its accompanying primes. \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":60958,"title":"Determine whether a number is a seesaw number","description":"Cody Problem 60957 dealt with balanced primes. In that case, balance was measured in terms of the average of primes around a given prime. \r\nThis problem involves a different sense of balance. Consider the input number  to be at the fulcrum of a massless seesaw (or teeter-totter). Then place the next  smaller numbers to the left and the next  larger numbers to the right. Each number creates a torque about the fulcrum equal to the product of the number and its distance from the fulcrum. In the example below with 14 at the fulcrum, the number 10 creates a torque of 140 units about the fulcrum. The number  is a seesaw number if  and  can be found to balance the seesaw; that is, the torque on the left balances the torque on the right.\r\nFor example, 14 is a seesaw number—as shown below—because the numbers 4 through 13 create a total torque of 385 units on the left and the numbers 15 through 20 create an opposing torque of 385 units on the right. \r\nWrite a function to determine whether the input number is a seesaw number. \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 523.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 261.9px; transform-origin: 408px 261.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60957-list-balanced-primes\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 60957\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e dealt with balanced primes. In that case, balance was measured in terms of the average of primes around a given prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 52.5px; text-align: left; transform-origin: 385px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem involves a different sense of balance. Consider the input number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to be at the fulcrum of a massless seesaw (or teeter-totter). Then place the next \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e smaller numbers to the left and the next \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e larger numbers to the right. Each number creates a torque about the fulcrum equal to the product of the number and its distance from the fulcrum. In the example below with 14 at the fulcrum, the number 10 creates a torque of 140 units about the fulcrum. The number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a seesaw number if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be found to balance the seesaw; that is, the torque on the left balances the torque on the right.\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: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, 14 is a seesaw number—as shown below—because the numbers 4 through 13 create a total torque of 385 units on the left and the numbers 15 through 20 create an opposing torque of 385 units on the right. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether the input number is a seesaw number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 247.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 123.9px; text-align: left; transform-origin: 385px 123.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"872\" height=\"242\" style=\"vertical-align: baseline;width: 872px;height: 242px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isSeesawNumber(x)\r\n  y = false;\r\nend","test_suite":"%% \r\nassert(isSeesawNumber(5))\r\n\r\n%% \r\nassert(~isSeesawNumber(8))\r\n\r\n%% \r\nassert(isSeesawNumber(14))\r\n\r\n%% \r\nassert(isSeesawNumber(50))\r\n\r\n%% \r\nassert(~isSeesawNumber(60))\r\n\r\n%% \r\nassert(~isSeesawNumber(84))\r\n\r\n%% \r\nassert(~isSeesawNumber(238))\r\n\r\n%% \r\nassert(isSeesawNumber(680))\r\n\r\n%% \r\nassert(isSeesawNumber(1001))\r\n\r\n%% \r\nassert(isSeesawNumber(1378))\r\n\r\n%% \r\nassert(isSeesawNumber(5182))\r\n\r\n%% \r\nassert(~isSeesawNumber(7276))\r\n\r\n%% \r\nassert(~isSeesawNumber(11648))\r\n\r\n%% \r\nassert(~isSeesawNumber(15102))\r\n\r\n%% \r\nassert(~isSeesawNumber(32586))\r\n\r\n%% \r\nassert(isSeesawNumber(40000))\r\n\r\n%%\r\nassert(isSeesawNumber(2*randi(2^15)+1))\r\n\r\n%%\r\na = NaN(1,10000); \r\nk = 0; x = 2; \r\nwhile any(isnan(a))\r\n    if isSeesawNumber(x)\r\n        k = k+1; \r\n        a(k) = x; \r\n    end\r\n    x = x+2;\r\nend\r\nd = diff(a); \r\nu = unique(d);\r\nh = hist(d,u);\r\nsuma_correct = 153539516;\r\nhist_correct = [6588 2370 673 250 83 23 8 4];\r\nassert(isequal(sum(a),suma_correct))\r\nassert(isequal(h,hist_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-16T02:59:05.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-16T02:58:01.000Z","updated_at":"2026-04-03T12:34:57.000Z","published_at":"2025-07-16T02:58:11.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60957-list-balanced-primes\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 60957\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e dealt with balanced primes. In that case, balance was measured in terms of the average of primes around a given prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem involves a different sense of balance. Consider the input number \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=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to be at the fulcrum of a massless seesaw (or teeter-totter). Then place the next \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e smaller numbers to the left and the next \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e larger numbers to the right. Each number creates a torque about the fulcrum equal to the product of the number and its distance from the fulcrum. In the example below with 14 at the fulcrum, the number 10 creates a torque of 140 units about the fulcrum. The number \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=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a seesaw number if \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be found to balance the seesaw; that is, the torque on the left balances the torque on the right.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, 14 is a seesaw number—as shown below—because the numbers 4 through 13 create a total torque of 385 units on the left and the numbers 15 through 20 create an opposing torque of 385 units on the right. \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\u003eWrite a function to determine whether the input number is a seesaw number. \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=\\\"242\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"872\\\"/\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\u003e\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":53990,"title":"Classify product/digit-sum sequences","description":"Cody Problem 53120 involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\r\nWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved Cody Problem 53120, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \r\nWrite a function to classify the product/digit-sum sequences given the first two terms  and . To encourage solvers to find the pattern, loops are banned, and to allow for large inputs,  and  are specified as strings. ","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: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 93px; transform-origin: 407.5px 93px; 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: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\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: 309.642px 7.66667px; transform-origin: 309.642px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 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: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 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: 383.883px 7.66667px; transform-origin: 383.883px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\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: 103.075px 7.66667px; transform-origin: 103.075px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \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: 384.5px 21px; text-align: left; transform-origin: 384.5px 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: 262.017px 7.66667px; transform-origin: 262.017px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\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 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\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: 93.35px 7.66667px; transform-origin: 93.35px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\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 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\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: 77.4px 7.66667px; transform-origin: 77.4px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are specified as strings. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = PDSseq(a,b)\r\n  c = [1 9 26 62 163];\r\n  y = c(a+b);\r\nend","test_suite":"%%\r\na = '1';\r\nb = '2';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7';\r\nb = '31';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '17';\r\nb = '28';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '51';\r\nb = '77';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '82';\r\nb = '262';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7021';\r\nb = '8878';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264';\r\nb = '412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8675308';\r\nb = '2941300';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '9142534264';\r\nb = '8424812653';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164';\r\nb = '8424812753';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '1352408463575';\r\nb = '9898989898985';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264534264534264534264';\r\nb = '412578412578412578412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '86753088675308867530886753088675308';\r\nb = '28413002941300294130029413002941300';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '914253426491425342649142534264914253463';\r\nb = '842481265384248126538424812653842481265324';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164842481275380314231648424812753';\r\nb = '84248127538031423164842481275380314231648424812756';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '43524084635758031423164842481275380314231648424812753';\r\nb = '98989898989858031423164842481275380614231648424812753';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = num2str(randi(835042)*57);\r\nb = char(randi(9,20,1)+48);\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = repelem('1',1,23);\r\na(randi(23)) = '4';\r\nb = num2str(10^randi(14));\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\nfiletext = fileread('PDSseq.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'system') || contains(filetext,'regexp') || contains(filetext,'java') || contains(filetext,'for') || contains(filetext,'while') || contains(filetext,'numpy'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2022-02-05T01:46:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-02-04T04:01:11.000Z","updated_at":"2026-01-15T18:05:52.000Z","published_at":"2022-02-04T04:04:20.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 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\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \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\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \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\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \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=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \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\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \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=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are specified as strings. \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":58977,"title":"Find the smallest number leading to a maximal product of two numbers that concatenate to another number","description":"Cody Problem 58971 involves the maximal product of numbers that concatenate to a number . For example, if , then the products are , , and , and the maximal product is 492. For , the maximal product is zero.\r\nThis problem seeks the smallest number leading to a given maximal product. If the product is 492, the smallest number is 682. Some products have no solution. For example, 13 is a product of both 113 and 131, but the maximal products are 33 and 31, respectively. \r\nWrite a function that takes a maximal product and returns the smallest number leading to that product. If the product has no corresponding number, return the empty set.  ","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: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 93px; transform-origin: 407px 93px; 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\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58971\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58971\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: 224.042px 8px; transform-origin: 224.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves the maximal product of numbers that concatenate to a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 52.1083px 8px; transform-origin: 52.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59\" height=\"18\" alt=\"n = 1234\" style=\"width: 59px; 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: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then the products are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"85\" height=\"18\" alt=\"1x234 = 234\" style=\"width: 85px; 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: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"85\" height=\"18\" alt=\"12x34 = 408\" style=\"width: 85px; 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: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"85\" height=\"18\" alt=\"123x4 = 492\" style=\"width: 85px; 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: 117.458px 8px; transform-origin: 117.458px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the maximal product is 492. For \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" alt=\"n \u003c 10\" style=\"width: 44px; 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: 15.55px 8px; transform-origin: 15.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the maximal product is zero.\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: 376.908px 8px; transform-origin: 376.908px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem seeks the smallest number leading to a given maximal product. If the product is 492, the smallest number is 682. Some products have no solution. For example, 13 is a product of both 113 and 131, but the maximal products are 33 and 31, respectively. \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: 382.983px 8px; transform-origin: 382.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a maximal product and returns the smallest number leading to that product. If the product has no corresponding number, return the empty set. \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\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = minWithMaxProd(n)\r\n  y = min(max(prod(n)));\r\nend","test_suite":"%%\r\nassert(isequal(minWithMaxProd(0),0))\r\n\r\n%%\r\nn = randi(9,1,randi(9));\r\ny = arrayfun(@minWithMaxProd,n);\r\nassert(all(isequal(y,n+10)));\r\n\r\n%%\r\nassert(isequal(minWithMaxProd(689),1353))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(943),1943))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(1615),1795))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(3196),3494))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(3252),4813))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(4077),4539))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(4710),5942))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(5986),7382))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(6386),10362))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(6545),7785))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(6960),8087))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(8200),10082))\r\n\r\n%%\r\nassert(isequal(minWithMaxProd(1e6),1250008))\r\n\r\n%%\r\nassert(isequal(minWithMaxProd(1e7-1),11111119))\r\n\r\n%%\r\nassert(isequal(minWithMaxProd(2122556450),3032223507))\r\n\r\n%%\r\nassert(isequal(minWithMaxProd(7777777777),10000177777))\r\n\r\n%%\r\nassert(isequal(minWithMaxProd(7199254740980),7254680599236))\r\n\r\n%%\r\np = primes(100000); \r\nlen = length(p);\r\na = zeros(1,len);\r\nfor k = 1:len\r\n    m = minWithMaxProd(p(k));\r\n    if ~isempty(m)\r\n        a(k) = m;\r\n    end\r\nend\r\nassert(isequal(length(find(a==0)),9257))\r\nassert(isequal(sum(a),40526242))\r\n\r\n%%\r\na = zeros(1,10000);\r\nfor k = 1:10000\r\n    m = minWithMaxProd(k);\r\n    if ~isempty(m)\r\n        a(k) = m;\r\n    end\r\nend\r\nassert(isequal(sum(a),39095445))\r\nassert(isequal(sum(diff(a)),12497))\r\nassert(isequal(a*(-1).^(1:10000)',6961479))\r\n\r\n%%\r\nfiletext = fileread('minWithMaxProd.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-17T16:21:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-16T05:27:31.000Z","updated_at":"2023-09-17T16:21:27.000Z","published_at":"2023-09-16T05:27:31.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58971\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58971\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves the maximal product of numbers that concatenate to a number \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, if \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=\\\"n = 1234\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 1234\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then the products are \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=\\\"1x234 = 234\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\\\\cdot234 = 234\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \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=\\\"12x34 = 408\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e12\\\\cdot34 = 408\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \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=\\\"123x4 = 492\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e123\\\\cdot4 = 492\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the maximal product is 492. For \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=\\\"n \u0026lt; 10\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026lt; 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the maximal product is zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem seeks the smallest number leading to a given maximal product. If the product is 492, the smallest number is 682. Some products have no solution. For example, 13 is a product of both 113 and 131, but the maximal products are 33 and 31, respectively. \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\u003eWrite a function that takes a maximal product and returns the smallest number leading to that product. If the product has no corresponding number, return the empty set. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\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":60991,"title":"Search for seesaw primes","description":"Cody Problem 60958 introduced seesaw numbers. A number  is a seesaw number if the next  smaller numbers can be placed on a seesaw to the left of  at the fulcrum and the  larger numbers can be placed to the right to make the net torque about the fulcrum zero. Recall that the torque is equal to the product of the number and its distance from the fulcrum. Let’s take torque leading to counterclockwise rotation as positive and torque leading to clockwise rotation as negative.\r\nThis problem deals with seesaw primes, which are like seesaw numbers except that they use primes instead of integers. The number 11 is not a seesaw prime because no values of  and  can be found to make the net torque zero. The minimum value of torque of 2 units occurs with one prime (7) to the left and one prime (13) to the right—i.e., . \r\nThe number 167 is a seesaw prime because with six primes on the left (137, 139, 149, 151, 157, 163) and five on the right (173, 179, 181, 191, 193) the torque on the left is 15,322 units, the torque on the right is -15,322 units, and the net torque is zero. \r\nSeesaw primes seem to be rare: 167 and 17,750,989 are the only ones smaller than 20,000,000. Although the envelope of the minimum torques increases, the dense cluster of points around zero on a plot with linear axes suggests suggests that other seesaw primes should be possible. A plot of the absolute value of the minimum torque  on semilog axes is less encouraging: for primes between 1 and 20 million, only thirteen have an absolute value of minimum torque less than 72 units.\r\nWrite a function to determine whether the input number is a seesaw prime. Also return the minimum torque, and  and , the number of primes on the left and right when the minimum torque occurs. At least one of  and  must be greater than zero. If the input is not prime, set , , and the minimum torque to NaN.\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1101.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 550.55px; transform-origin: 408px 550.55px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 42px; text-align: left; transform-origin: 385px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60958\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 60958\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e introduced seesaw numbers. A number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a seesaw number if the next \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e smaller numbers can be placed on a seesaw to the left of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the fulcrum and the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e larger numbers can be placed to the right to make the net torque about the fulcrum zero. Recall that the torque is equal to the product of the number and its distance from the fulcrum. Let’s take torque leading to counterclockwise rotation as positive and torque leading to clockwise rotation as negative.\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: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem deals with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eseesaw primes\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which are like seesaw numbers except that they use primes instead of integers. The number 11 is not a seesaw prime because no values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be found to make the net torque zero. The minimum value of torque of 2 units occurs with one prime (7) to the left and one prime (13) to the right—i.e., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"66\" height=\"18\" alt=\"m = n = 1\" style=\"width: 66px; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 167 is a seesaw prime because with six primes on the left (137, 139, 149, 151, 157, 163) and five on the right (173, 179, 181, 191, 193) the torque on the left is 15,322 units, the torque on the right is -15,322 units, and the net torque is zero. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 106.5px; 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: 385px 53.25px; text-align: left; transform-origin: 385px 53.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSeesaw primes seem to be rare: 167 and 17,750,989 are the only ones smaller than 20,000,000. Although the envelope of the minimum torques increases, the dense cluster of points around zero on a plot with linear axes suggests suggests that other seesaw primes should be possible. A plot of the absolute value of the minimum torque \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAAoCAYAAABerrI1AAAAAXNSR0IArs4c6QAABC5JREFUaEPtmGnIjWkYx3+vfJBlylZCKUnRFBLJPjP2kMEnS/ZtJkymmNA0sqeMGWlMjCXEB2vhw9gaTMYwHzTTkJ0kImGYkSVz/3Xdb0/HeZ3nuc95zpu3c76d53mu5X9f2/+6y6iCv7IqiIkSqPclqqVIlSJViSdQUfq1Ak4C9QJ9+xfoDvwRKJ+XWEWgRgJbgSvAbOfgUeAhUB3YAQwzq5uA8cBroD6wEJgG/A30AO7n5V2gcDZQerYB6AL0Bm5EdDcAfgFa27NRwLbIewE7BJyLgA10LVwsGyg5/jMwxxyMau/qInDMIvYA0P/zkQ9qA/uBdRlgwz0MkMwGqgUwHfjKAfsvQ6eALrNnithA4Enkm1rAD8DSDLABroWLJJlTNYBdwAAztwSYF246PckkoJq4GvsVaGaNoY9Lv8PpuRauOQmoXlZrkrljjeRquOn0JJOAWgzMNVcOWlt/lp5r4ZrjglID2Ad8YqbURJaHm01XMi6o5lZPjYCXblZ9ZIwjXe8CtccFNdgiJTOVyhbi4IwL6nubXdIZpUZxbBT9mzig6gBqDGIP+mVSozScbmd88wwwNGPA57QXB1SUsWejRjmNBHzQCTgCnLIu+yiJjjigPGOXXq0jYhT/JDFS7G9zgfKMfaw5thqYUWwnk9rLBSpz1dAetTuHETF17VR9XS12BD5z0f0d2AworbYAE+y9VpyGRowPOHYvKtbPMZfOQBtgInAPmGwMRrU2CbgA/GT65I/qvJx8vwuU3o1xXG9jBEQcUPpce5VqQjzxS7cBD3LOr7HOeQtY7953c2DOuu1anXWBE/rG7HSwne0S0N8Buu2+b+rA/maOi9WMAFYC201Guq55P7OB0knLkSFA24yoPHbP9tpa8V2W1cR/7oe11vqbFi3p1boiZxW5L4CZbjdbBAyPZICfiYrEVBv27YHjtnzetfGirqwaly51yFiRSprK0e91whoDz82gUss3HJFg7WE6Wa0ySindZ1w2BX4mjrYrBT2eAqx1Vws6pE+NWHvwb1G2XDUVCsyTX23An9tpq37UcPRfi2Rjo17anP1J1zWHtagqpf7KuBf51jbyF5a2Aqvt4UTU0TRA+ZVetfGxq4vTgHdWt1MixddtmOtqQJv017aj+TTT0PVbtd/jagI9jaZ5QvBBpO7KcaUByg/rPyOOeWdV2L5OZhnTV+1WM/BKLaWZUkq3ViLP0qc7k52WworShxYdpe8KOzQ1kje/NED52onmuq8JXyeyqys4te9VwCtzTmmpjqsU1TiYb/8VTR3Gj+a316frhJZ2OOUXQIUG5Ye1Wq7PdX9XqLTzdaL7DkVNxa6BLueeGgjdHSr9NHvUORUNzS0vK1yS2+Na+0V3hTfO2n2q6RfaXAomV+hIFcyxfBSVQOVzesWULUWqmKedj60qGan/AUU92ClcS2cwAAAAAElFTkSuQmCC\" width=\"26.5\" height=\"20\" alt=\"Tmin\" style=\"width: 26.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e on semilog axes is less encouraging: for primes between 1 and 20 million, only thirteen have an absolute value of minimum torque less than 72 units.\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: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether the input number is a seesaw prime. Also return the minimum torque, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the number of primes on the left and right when the minimum torque occurs. At least one of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e must be greater than zero. If the input is not prime, set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the minimum torque to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 166.9px; text-align: left; transform-origin: 385px 166.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA2sAAAKQCAIAAACO9XWpAAAACXBIWXMAABcSAAAXEgFnn9JSAAAAB3RJTUUH6QgOCzITSKsmVgAAACR0RVh0U29mdHdhcmUATUFUTEFCLCBUaGUgTWF0aFdvcmtzLCBJbmMuPFjdGAAAACJ0RVh0Q3JlYXRpb24gVGltZQAxNC1BdWctMjAyNSAwNjo1MDoxObM5dFcAACAASURBVHic7L17dBv1mf//YOciJ/1yNOIWpT9Oxig0DbSb02CxhYVjOcuxt1s4W5J2MZQie3tJSS/ZtvRAoa1ttgRaWloKhHJgNxblYpY20G6hsU8hUmGBoHAnyVIyeNyUOAWqUUmDJokJvz8e6eOPZ0ajkTSyZfv9+oPjSKPPfGZkrLeey/s56r333iMAAAAAAAA80zDVGwAAAAAAANMMKEgAAAAAAFAeUJAAAAAAAKA8oCABAAAAAEB5QEECAAAAAIDygIIEAAAAAADlAQUJAAAAAADKAwoSAAAAAACUBxQkAAAAAAAoDyhIAAAAAABQHnOmegOgXnj22WdfeumlPXv2rFix4rTTTlu8ePFU7wgAAAAAdcpRmIsNstns+vXrn3rqKfFIY2PjV77ylUsvvXQKdwUAAACAugVZbEAsH08//fQ777xz27Zt1113XTAY/MlPfnLPPfdM9dYAAAAAUI8gBjnbee655zo7OxctWrRly5ampiZ+8PHHH//sZz97/PHHP/bYY1O7PQAAAADUIYhBznb+9Kc/EdFpp50m5CMRnXXWWXPmzHnjjTcOHz48dVsDAAAAQJ0CBTnbYeG4b98++cFsNjs2NtbY2NjY2DhF+wIAAABA/QIFOdtpa2tbtGjRM88888tf/pIfeffdd6+++moiOu+88xoa8BsCAAAAACuogwS0Z8+e9evX79ix44Mf/OCJJ5740ksv7du377zzzrv66qsXLFgw1bsDAAAAQN0BP0hApmkec8wxRPTqq6++9tprhw4dampqOu6446Z6XwAAAACoUxCDnO3s2LHjoosuMk3zsssu+7d/+7fGxsY9e/Zce+21jzzyyKmnnnrffffNnTt3qvcIAAAAgPoCCnL6kc1mV69efdppp11//fUuh/3qV7965JFHuNVaVdVVq1ade+659sM+85nPPP3001//+tfXrl0rP37BBRc8//zzV1111SWXXOLv/gEAAAAw3UEWe/px+eWXv/766yeffHKxAzKZzNq1a1988UXxyI4dOx566KGBgYGNGzceffTR8sHPPPMMEV144YWWRS6++OLnn3/+6aefhoIEAAAAgAV02k4zLr/88mQy6XLAkSNHPve5z7F8vOSSS2699dZbbrll9erVRJROp7/0pS9ZDn733XeJ6H3ve59lHX4EfpAAAAAAsIMY5LQhm81+4xvfePzxx90PSyQSO3bsIKKbbrqpvb2dHzznnHOWL19+zTXXPP3007/4xS8++clP8uMNDQ3HH3/8G2+88cILL3zkIx+R19m9ezcRBYNB/68EAAAAANMcxCCnB1u2bDnvvPNYPi5cuNDlyDvvvJOIzjrrLCEfmUsuuSQajRJRIpGQH+fw5HXXXXfw4EHx4J49e/7zP/+TiC644ALfrgEAAAAAMwXEIKcB3d3dTzzxBBE1NTX19PRs2bKlWCL7ueee27t3LxF94hOfsD+7Zs2adDr9hz/84bXXXjvppJP4wXXr1j3xxBPPP//8xz/+8U996lMnnnjijh077rvvvv3793/mM59ZuXJlra4KAAAAANMWxCBrzt69e+XwXjFee+21Yk9xQnnVqlUPP/zw+eef77LISy+9xD+cdtpp9mdXrFjBP3Cam5k/f34ikfjMZz4zOjp6ww03fO1rX7vjjjvmzZt35ZVXfvvb3y65bQAAAADMQhCDrDkbN2587bXX7rjjDpf5LqlUat26dQ8++KBjh3VbW9uaNWuE/nOBpWFjY+PixYvtz6qqyj+k0+nzzjtPPL5gwYJvf/vbV1555bPPPnvgwIHFixe7NHoDAAAAACAGWXO+853vNDY2fu5zn3vnnXccD3jsscfWrVt34403FtNtV199tRf5SES5XI6IiknVhoaGQCBARI47aWhoaGlpaW1thXwEAAAAgDtQkDVn/vz5d9xxRzER+dhjj33xi1+88cYbzznnnOrPxeny+fPnFzuAB8yYpln9uQAAAAAwa4GCnAyKiUh/5aPg+OOPL/bUnDmoWwAAAABAtUBBThJ2EVkj+UhE2WzW3wUBAAAAAGSgICcPWURu2bKFax/9lY8NDQ1UyGU7cujQISJqbGz08aQAAAAAmG1AQU4qLCIPHDiwfv36733ve75HH5uamqhIowzD4tLdkxwAAAAAwB0oyMnmf//3f3fv3n3qqafed999LlKvMtjEJ5fLHTlyxP7swYMHx8bGiAjd1gAAAACoBijISeXRRx/98pe/fOONN957770LFy7s7u72V0R+6EMf4h9eeOEF+7M82IYkY0gAAAAAgAqAgpw8fve7333lK1/56U9/es4558yfP//mm28++uiju7u73377bb9OceaZZ3KN45NPPml/9vnnnyeiOXPmnHXWWX6dEQAAAACzECjISeJ3v/vd+vXr5dYZISI///nP+yUijz766DPOOIOI7r77bktH9ltvvXXPPfcQ0bnnnsuukAAAAAAAlQEFORn87ne/++pXv2rvvK6FiLzsssuI6K233lq7du2bb77JD+7Zs+ezn/3s22+/PW/evHXr1vlyIgAAAADMWmamv3Q2m129evVpp512/fXXl/XCPXv2bNu2rdizRx111Jo1a8rdzKOPPrp+/fqbb7551apV9mdZRH75y1/+/Oc/v2nTJpfZ2R5Zvnz5lVdeuWHDhueffz4Wi7W0tBw5cuSZZ5559913iWjDhg1Lliyp8hQAAAAAmOXMTAV5+eWXv/766xV0HD/wwAO33HJLsWfnzZtXgYLcs2fPzTff3NbWVuwAFpHXXnvtG2+84UuPSzweP+64466//vq9e/c+9dRT/GBzc/NVV1119tlnV78+AAAAAGY5R7333ntTvQefufzyyx988EEiisVit912W1mv/epXvzo4ONjY2OjouT137txnn33Wn11OCjt27Pjzn/9MRO9///uXLVs21dsBAAAAwAxhRsUgs9nsN77xjccff7ziFdgEZ/Xq1d/73vf829eUceqpp5566qlTvQsAAAAAzDRmTifNli1bzjvvPJaPlc1cOXjw4L59+4joox/9qM+bAwAAAACYQcwQBdnd3b1+/fo33nijqanpuuuui0ajFSwiSgYjkYivuwMAAAAAmFHMEAW5e/duIlq1atXDDz98/vnnV7bIyMgIEc2ZMwclgwAAAAAALsyQOsi2trY1a9asWLGimkVefPFFIlqxYoVpmg8++OD27dsPHDiwcOHC5cuXr1mzJhQK+bRZAAAAAIDpzQxRkFdffXX1i7z66qtE9NZbb7W2tsr+3g899NAtt9zS09NTcXQTAAAAAGAmMUMUZPUcOXKEFeTIyMicOXM+/vGPn3TSSfv379+5c+fTTz+dy+WuuOKKAwcOXHzxxV5WQx4cAAAAmA288sorU72FqQEKMs9LL73EU1tOPvnkW2+99cQTTxRPPfbYY+vXrz9w4MC111579tlne5zpMmt/pWY5y5Ytw1s/a8G7P2vBWz9rmc0BoxnSSVM9J5544s9+9rMf/OAH/f39snwkorPPPvvKK68korGxsXvuuWeKNggAAAAAUC9AQeYJhUJtbW3/8i//cuyxx9qfXb16dSAQIKInnnhi0rcGAAAAAFBfQEF6oqGh4fTTTyeiP/7xj1O9FwAAAACAKQYK0isNDQ1EdNRRR031RgAAAAAAphh00uRJpVJbt249dOjQhg0bHA/Ys2cPEXlsowEAAAAAmMEgBpnnN7/5zb333vvLX/6SJ9NY2LNnj6ZpRMS5bACKgX7M2Qze/VkL3nowC4GCzPOxj32Mf7j99tvtz1577bVE1NjYeOGFF07qtgAAAAAA6o/ZqCCHhoZWrly5cuXK73//++LBVatWnXLKKUR0//33//CHPzxy5Ag/ns1m169f/8gjjxBRd3f3SSedNCV7BgAAAACoH2ZjHeTY2NiBAweI6ODBg/LjP/vZzy688MLXX3/99ttvv+uuu84444x33nln+/btY2NjRNTR0fHNb35zanYMAAAAAFBPzEYFWYwTTjhh8+bNN99887333pvL5R599FF+fPHixV/4wheQvwYAAAAAYI567733pnoPMxBMuAIAAABmPLP543421kECAAAAAIBqgIIEAAAAAADlAQUJAAAAAADKAwoSAAAAAACUBxQkAAAAAAAoDyhIAAAAAABQHlCQAAAAAACgPKAgAQAAAABAeUBBAgAAAACA8oCCBAAAAAAA5QEFCQAAAAAAygMKEgAAAAAAlAcUJAAAAAAAKA8oSAAAAAAAUB5QkAAAAAAAoDygIAEAAAAAQHlAQQIAAAAAgPKAggQAAAAAAOUBBQkAAAAAAMoDChIAAAAAAJQHFCQAAAAAACgPKEgAAAAAAFAeUJAAAAAAAKA8oCABAAAAAEB5QEECAAAAAIDygIIEAAAAAADlAQUJAAAAAADKAwoSAAAAAACUBxQkAAAAAAAoDyhIAAAAAABQHlCQAAAAAACgPKAgAQAAAABAeUBBAgAAAACA8oCCBAAAAAAA5QEFCQAAAAAAygMKEgAAAAAAlAcUJAAAAAAAKA8oSAAAAAAAUB5QkAAAAAAAoDygIAEAAAAAQHlAQQIAAAAAgPKAggQAAAAAAOUBBQkAAAAAAMoDChIAAAAAAJQHFCQAAAAAACgPKEgAAAAAAFAec6Z6AwAAAAAAPqNnzL6hYSJqjQS7ouGp3s4MBAoSAAAAADONvqHh/vQoESU1Qw0FYhHFl2WTmqFnTB8XnL5AQQIAAABgJqNnTIr4sE5SM/oGh5NaVg0FetqbZ3loE3WQAAAAAJhptEaCaijAwULfApC7s0ktS0R6xkxpWV/WnL4gBgkAAACAmUZXNKyGAnrGjEUUNRTwZU2WpHrGJKIlij9rTl+gIAEAAAAwA4lFFF+S1wJOW6e07BIl0NvR7OfS0xAoSAAAAAAAT3RFw7O8/FGAOkgAAAAAzHY4Nw28gxgkAAAAAGYv3GFNRGqoaVPn8qnezrQBChIAAAAA0wM9YyY1gwolib6QSO/jDmvVMPvTo0hSewQKEgAAAADTA/YJV0OBlJb1PV6IRHZZQEECAAAAYBqQ1AwOQOoZU1dyPBum+mXj0UV6Jqcbpo/OkbMBKEgAAAAATANUpUlV8naMaqhJDQV4bmGVeedYRFE7m4jIL9vIWQIUJAAAAACmAWoo0NPRrKb3LVECsaXB7oFdIiRZpTujR+1YEK8QmkRQkAAAAACYLohEM2e0WdKlNEPPhGst7FiwqkogDktIIoIfJAAAAACmHZzRHv9njeWjEKxJLYuJ2AxikAAAAADwGT1jiiLFWsg7NRSIR8NqqImI4tFFvq8PSgIFCQAAAACfYdsdIhoxzBrZdE/mgMFYRIm3hFOaQUStkeDknLTOgYJ0I5vNrl69+rTTTrv++uunei8AAADA9EDPmHomxz9z/tcXl5ypbWTp7WiehGrLaQQUpBuXX37566+/fvLJJ0/1RgAAAIBpgxoKqKEm0rIk9b5USX96NJEeJaLWiFJl53XFQD7KQEEW5fLLL08mk1O9CwAAAGD60dPevEQJkE/jB/WMmUiP8uxB3TBrVFsJygIK0oFsNvuNb3zj8ccfn+qNAAAAANMSNRTwMVIo60W5BRtMIVCQVrZs2XLNNde88cYbRLRw4cIDBw5M9Y4AAACA2U68EMtsjSgIQNYDUJAT6O7ufuKJJ4ioqampp6dny5YtSGQDAAAAU05XNMz1lJCPdQIcxSewe/duIlq1atXDDz98/vnnT/V2AAAAAH/gRuZpjRoKQD7WD4hBTqCtrW3NmjUrVqyY6o0AAAAA/pDUjL7BYd0wYxGlRtaMUwtPx/al4xt4BwpyAldffbVfSy1btszyyCuvvOLX4gAAAEAxLIoqkd7HXcxJMvrTo9NiprOeMZOaoYYCJXVh7+BwYvsoEcVbwr707ri4V9o/2WczUJC1AnoRAADA5OO7opp8RNBUVQJ61HSRvHrGTGkGJ+gT20erdPmRg7U97c32peyf7LNZU0JBAgAAADMEWVGlNINnqMSji/RMjoXRtAhAJndn89aPGVMNNbns2V+XH3He/szoEsVPN6IZCRQkAAAAMJOJRZTYOkXPmNOlDYU7ZlgHLymlC+PRsBpqIqLWSND7BaJ0snqgIAEAAIAZghoKCN/E+MSU7nSRj0TUFQ1zMNU9ACkOLjewWizR3xUNjximnsl5OS+AggQAAABmDhUoqjqkt6OZqCZJ5KRmJLaPikS/fBY1FNjUuXwaBWunFvhBAgAAAGAGktSM3sHh/vSo/KCqNLlXTEI+egQxSAAAAADMNLixOqlluaRSZKstif6p2+C0BwoSAAAAADMNPWOKhu4RY8I8npmR6J9ykMUGAAAAwExDHoFYsqEbVABikAAAAACYevrTo9zF4kuAkF3BU1oWzo41AgoSAAAAAFNMf3q0b2hY9EEXE5Fl+TgiW11ToCABAACAWpHUDD1jxiJK3Xb48g69TKCuKXrGZIcd8YOd7oFdrCBlH0cvE7Q5uhlbGhTH8KuoIFV7B4fZftJxmCFwBArSjdtuu22qtwAAADOfpGYkd2f9Sl/WDyKuFosEN3WeUofSRN4hdfg8o8VLvFAoOTGHRq5ftKyWtA1s1DNm98BObrjuaW92/P1h/3A9Y6a0oNrZZHkVnzHvEImUdzlAQQIAAJhKZNcVKp6+nI6ktCwrnqSWTWpGV6juLk3eYevurC8KkhfsT4/y3JdYRNnUubzYwX1DwyKs2NPe7FIHyT6OIjzJvy1JzRAN1ykt6/jCEaMQ3TRMfheSmqEbZuFVhhoKi2UtXduO2COasxMoSAAAAFNJcne2pAiYpogW4GJxtSnH9x32p0cT6VGhz4goSUZSMxzFliWs2Nux0mVl9nHkEdjx6CJ52+4TtMevUclfoxoKCDGqhppiESUWCeqGqSqB1kiw5AVy1DalBanD/dgZDhQkAACAqSS2NJjYnk8mzjDXFVbDI4bZGpmyeJV7KpkztrxDX7Q7qyv5EVUJqEqT48FyWJGloTv2zhi54brY/u3vQiyi6FFTDTXxq9RQYFPnKSWLKRlL1LbknmcwUJAAAACmEhYBPtq41AP96dF68JFxbD2x4OMOLfMD+d1sjQTl6KY8ddoxrFguJRuu1dCEd0G8NXJuXQ0FPNYYtEaCoveoPuPKkwYUJAAAgClmxghHJqkZcihuqkSkY+tJrU8qrjoWCdrLH1nRqkqgp6OZo32TbLhj8Qyq4K3pioZ5yA1Hba+twSanC1CQAAAAgJ/IfjReOjNqhGPrSU0RBYXkNHK6Pz3KilbPmGp635Sk9WXPIPmt6R0cHjFMjzFjNGszUJAAAACAn6ihQCwS5O7ykp0ZNd1G9Tnics/ovaBwSogtDaY061vDbeMiMT3DIuK1AwoSAAAA8JNYRKEOaq0Dh8vJH8riUlDYFQ2ntGySDFUJTI6itSPeGou7eEkzc2AHChIAAADwmVhEqc8g3NSyqXO53EkzJdjfGmEJFIsEY0unLGY87YCCBAAAAGYpYppfPLpociRvHfYvs6FPPYx2nF5AQQIAAACzkaRmiGl+VGr84MwmFlEoMtWbmG5AQQIAAACzHT2Tm+ot1At6xuxPj5Z0WU9qRjGn9FkCFCQAAAAwAdYQRDRdZh8nNSOR3qdncq0RxbvXDFcEFlpbatVwIxy8OVlc/YLsvENEPe3NtciJ9w0N87tfrKlcz5g8zltVAu8c8wHfNzBdgIIEAAAAJiA0REoLqp1NdVi6ZyGR3scb1g2zLNW7qXM5x9JqdI2+m6uPZ96JiMhuWl49IhyrZ8yEk29lUjPydztjHv3/fdT3DUwXGqZ6AwAAAEAdoWfMcQ1hmLoxDdK71eSgYxGldhK5pLk6qzEevVjugrUgqRm6tM9iN1bcscMLjpm1BkBQkAAAAMA4aijALtxEpCrTozm3NaKwJY13F6HeweG2jc+Kwdk1gs3V+Qe7uXp/erR7YFf3wK6+wWGP2+CxN3yxtXBrT6T3yVN8HJP7XdEwb4OIxpqO6R7YWdN7WLcgiw0AAABMoKe9eYkSoOkzsLu3o5mNDD3KR/cubD1j6kbOF+nMDt7xIkY5KS3Lci2pZVt3Z72cUYy9SaRH+eW1mzEYbynqx76pc3l/ejSpZQ8vOMb75mcYUJAAAADABNSQp/nIdUVZCkZOvFoStUnN6Bsc1g0zFlHkVhWPHcrOGytilMMynQqe3h4XVEMB0kg3TB5OSL4OquZhOeX2JM1OoCABAACAMqh1L/AkIAYMEpGcqO0dHBZ9Kv2Z0SXKuJLuT4/2DQ1T8Q7lCuDFRwyTO7W9v1CeQ+jx+P70KG/b/S3jMgAvg3O6omFuEpr80ZF1AhQkAAAA4BW5F1gWWHZE0M79sKmCu7BJCl7K8pGRVZTog8mrN5/8tyu7M7Glwb6h/M9eRLxoru+Khh3bt/vTo4n0KBHFo2EX1yE9Y/JNS2lZOXY7Tb9IVAkUJAAAAOCVks3FAhG04xRtHYapLHHEEcOUm0gsTTlLFGl4dB3U/PFmiCilZd3vbffALpaPVGj9thyvZ8xEejSpZfmflmeTmsEHcI+2PeqZ1IykZtTDPZlkoCABAAAAr3ATLosJ915gOWg3GTurmtZIkNVSLBKM2zKzvR35lH1N3X98h+Wd+CdrQd6/cMHUjZzs4FOwAs1HGXWjtv5B0xcoSAAAAMArohe4ZC1gaySoZ3K6YU4XSyCWjHqmqCd5/YRR5Wk6xXR8MdmX1LI0OMzvy6bOUwpqMiC6wkUwsiRqKPDnV1+Mt3dMi/fXd4567733pnoPM5Bly5a98sorU70LAAAAU0khpFdHQTvRUDLVG/EBl+GTXNPJ0xr1jJkq+IRbZCWHky2lnx4jjmoosPXSlR1nrJi1H/eIQQIAAKgJXhpaZzYuRjZTgvAPj7eE67C5xwv96VERJe1Pj3Lrj2X4pOh2Yi24qfMUIupZGuwe2EUTNaL3cCOTz3qPv3w2GokLoCABAAD4T+/gcErLm8XUT/ZzNsMVgYXuE4NokhSkj18kRLc4S0bR+pPUsknN6AqFxRnFS5Jatm9omMdz2591pCsaFjeKEVHbeHQRy1BeJ1WmAJ1hQEECAADwGc4bFmtuBTWCdY+XJLUY21hTLBY51S8oJKNumEnNkA3JSfLp1DM57gfiDLVoxC6GJXMdjy6KRxe1bXxOPiYeXZQXkS1hSYzmDi84pvrrmqZAQQIAAPAfubkV6Ww9Y7LsKHegi3d4lkxSy8YiQepwGFHDM2YS6VE11FSYvJJ3N/R9S3y9snTzpRh0XDIqAZJcGPWMKUKD+QMKw81LRhxjkeDWdSubr3lCHJlI7xPWRSQZG3FYXTdM77WSMxsoSAAAAD6jhgLxljC3MrTWUx/JVCHklI8DXSwkd+ebiF3GNFump/Cu1FAgpWUdfbYrpj89WjLyVxZCzIlHZAdHx+N54o47sUiQO+vlF/ZnJuxcVQI97fnZOeXWTc5soCABAAD4T29HM4uVKuVjNSME5a6LkkdyTZtIVvqLPL/Ex4Eu8pqpggzyOGNaGCXqGVNXcv7GiWWvdTVUybcIPWPqRo7tG/OPGBOqG72swD/w76Gjoo1Hw2oowCeyPBWLBHnudrwwosYyhEbPmEkt27TiErtF+SwBChIAAEBNqF6ReB8haEfuuqCOcftoO5aRJLVQkK0RhWvyqvGGZDHteB/6hoZ5/xz99SJoVKVJmCCqofzNscw5rBhhTq6GAps6l3tZUEhGoYZ9CfipoUA8uii522GpWCTI6W9ZGlLhHsaWBlt3Z8UwIT1jtkYUsSW+ND1j5o75QAIKEgAAAJgEvDdYeB8haEdu1FXT+1glOJ5RHkliERN+Uf1AF+FcIxYUT8ljV1TF6/hENRTo6WhW0/uWKIHY0iBJXj897c1VSiIeLe3uhcmSkYgS6X18FaoSqEA1Whx2xIO8mp4xua7R/sKklrXPm+mKhkWtaiyicKlocnc2pRlqqEkOZ6IUEgoSAABAnklwwHafQWzB+whBO7JocG/pEANOiKi1ZlbbVWoyWUxbvHjkaCKVH/pNFXLZwsKmyqAaSy7HUeBcV0D5msL8ecWzXrpeWiOK3ObPhYxttz4rH6aGAj3tzZxlpiL5ay9n5NaZcVGrZbui4Xh0kez1M/edv8SjfpaQTiOgIAEAABAVmnl1w0wooz0dzTUaW2KZQexefud9hKAdjtKNGGZrJOjedUFEPe3NrVpwaoe1uNdixpYGE9tlK2xDHMO1eqKNxntZXiK9Lx9OM8x4y/hLqvH6ES3hIubKD6a0rF0yVkBsabC3g9Wh0Tc0zLY+soAmIi4VsDTEyHCEkpwS5f3pUd5tayQoB32lxSfo9aa//KEr+qlqrmj6AgUJAACASGrm1TNmsWbe6olFFG7TJiIvDRZqKCCcostFpHr1jMlzkIudsZqz+IIcmtUzudg6By8eIVx0W0JftrZOaVmPClJO2XMim3O17PVTGSLyx4Y+CWXUnimuGNFmroYCpJE4iyrFm/lbR396NJWv6QzyWy+LRTY2IqLugZ12Ecl93BZTcaY1Esz7BBWqTvf/4S++XNp0BAoSAADABDw281ZMb0cz65VJC/j51RheO7yEZkU7TiyiqMp4mDCpGbIWdKz5cyTOPSKGyXn8WESpbFANBzJFlFG+ipLakeO+ZVn/sAORWNx+CqELY4XKB4vm5lvEIUzHUxTbdiI9yoaa/Ou0RAnce+dDRDd43/xMAgoSAAAAEVFvRzOn7bx3Y1TM5CeL8yWeHpx9pgRLLaaj0i3WjiOCx0QUK8exvCsajkUU3chVcE84575ECUyoFCwTLlgk11JFoQL5LCnNSGy3yjuL4BP7cdmYY/RR7CreEuZKTeeVtSznwZcogX0rLpErCmYVUJAAAACIJn6K1+eHond/R/sL+4aG9YyZ2O7VXKYWuBd9bupcXtJMx1EdcsyYFy/XUM7WYAAAIABJREFUedFLvJl3xc0xHIFbogQcawTLJRZRuqJhyzgZkkLFqhLQjQmBxpJq1cuu5M07decoXGrZf80oFfLglmU5AprUsnTiGX2Dw2pnUa+oGQwUJAAAACKilJYV9jfl1kHW2pGbbP6OZZ1FXJqeMZMVlXgmNSOR3qdnchWPeObGXiJy7FLi8c1s91ju9ng/3PzhS/BYXCwROVQxeo449rQ3O0bySqIqgU2dp7DXT/fALi+pcHLVjvIcQg4fiiE3rRGlKxpOTRhLkyPpC1VJzZrUsknNmNo62ikBChIAAADRRBfosgIq+a7Y8aBOTRSk7O8YL3OsS8lLK2lRKbctu7dss82hxcBctkZX0/vsL+coKRWCgo574A04ei11Vapr5cV5exVnpWORoBpqEnoxFglyJ1NSM2QV2BUN84WooQA7NLVGgnomJ5+Ux8DkA6uWPutQQFUC8omIiFPh8i+hjHAIT+7Ocm9+VzTMg7D1jDli5GO3ZV21VZLOvgAkQUECAABguqJh/kCtJpRVI0duIlqiBAom1cFyP7Ddo3T2mTT29T1el3BEUpWAHGt0VDbcR6xncq0RZWTc0tw5kMYhWCJKRXyYYc1uOFS4J1RcfpVFT3szDVGSDFUJxAv3mbvvWR/zMa2RIKt5fi+6ouGUlhWhTVlAy29EPnZomBw15BNRwfdb3oYlJBlvCbOWld8OIUyTmtE7OEyFMYbkGHa1EYsore1BPWP++D/v6en8tzos+ZgEoCABAADkUUOBEcNMadmynBEnx5Gb+0gq7oapMkrHfdBUuNhihxVzRGKRxNJKWKP3DQ2LuCbLVtbHjuunCiE3Npop9w5MMAzfPmGkSskssygEtEQZZUQJJl+dKGbg4K4c3usbGrYMZmQLxvGllIBjwahovu4bGh4xzE2dyzlumtIM7s6WPX3y8WYl0BpRLEMg8zl6SbLbazqTmsGp7WKBSXGB9371zq7oVS53bwYDBQkAANMSv0YYCyyWhHo0L5i8BPwmx5G7Rh3irH4Kk2+K9kHHlgb1jFnxHrhRxnE8t54xW9uD8egi+0AgVn6y3aOqBGQrHx6WTUQ97c0u8wOFWnV81sv+1VA+/icHFMefypgjhslzEQtZbMUS3GV4GywByVYCQROHdHNA12nPOSLqioZ7B4eFZI9FlE2dp8hN1o4lp6IgweUOcGLasppM3+CwHq38l2Fm4L+CPHjw4Ojo6P79+w8fPrxy5Up+8M033zzuuON8PxcAAMxORE4zFlGqz2kysiWhGBnMNWQ85tjltVPuyF0lLBAd5Z0gFlFKFl92RcMjhqlncmwZyDeQKyPtwUuuzqRCXFMNBSzrdw/sEt6HVCg0bJWS+HJ5JQcmOSdOhcnU4jCLU2NZyBIqpRlb160cMUxZhPEGLL38LJeLralncqLF29bmnGMZau/RFohQt9yHznUO43bfSiCR3tc3OMwe6VIKu0RBgmi6cjGM5P9B3NeZ8fipIF999dW1a9e+/vrr4pFf/OIXH/7wh3O53FlnnbV48eK777578eLFPp4RAABmJ1XmNB2Rk9GyXbNIGlZ/Che4m9uvbuIK8HIPS8Z91VBA3KjugV16Jsc1kZyn3tS5nGOKHKxlkWePOzIitysEliUhq2fMRHqfeFbPmDzHjwWf/JZZFpe7QFwupEhXShMR9bQ3W3pfrIcpAZbjQs9ZSGpZfWAXOcX/klqWBoftLxHEIkF2pCepwlVkxuPRRWw2RCJBn3cXz89XdFlZwD37JX3O+4aGMysucTdpmsH4piB/+tOf3nLLLY5Pvf3220S0d+/etra2G2+88Z/+6Z/8OikAAMxO5ECLS6SnXIQloSXT50t/DNefLVEC9oim8Gvkj3xL4Zq/iCaScqWqaJf2Evdl/ScPTUmSwUWBeU0ZNdnQu1hc03KLhGxKakZyd9ZSy2hH9J5ToZeFDWtaI0psabCkRU7RpmbbwEP7UJmuaJhz00uUgItic928W1t068RorqXClb8I2UsYRU7c0tnNgdtkYUohP26Zr+Oop/OPnHjG7LTyIb8U5M033yzk4/HHH79o0aLh4eH9+/fzI/v37z/66KNZR65fv/7JJ58MhUK+nBcAAGYGcluuF/0kPshby29Mdkf+bBayoPr+GD1j9hVK1uwRTTnkOVLL5KCeMbmyjTVBWVI1UfC7qTjum9LG+2zEZLxiiAHiemEWdt/gcB8NezSdscQ1ezuaeWJhXkgVEYjuslIteFVy5Sg/yP5HrZEg2yHx4yIgKrN13UcS6X1e7CH5zhQLAdp/Q9hrUw01cTFoUjMsKebWSDCR3me/daoS4DhxVzTM/0/pGTOljUcfRTuOS1eN90HkMwwfFGQmk7npppv459///vcnnHACEbW0tIgDli5dmk6nb7zxxo0bNxLRxRdf/PDDD1d/XgAAmDH0p0dlu0HHDySLyqxpz0osoiR3S90bVYtUuchSz+Qsib/Y0mBKC7KwE63KtUBoC+7hLWsMdLGErCPcfC2rqHhLOC9uMiYVmV7NFZOsp1kSTXjKXd4V7mcsogjnI8sbJ+t4+YV5o0ol0NPeLPe12DUlVzf2p0c5oinsM8enyIQCCSflxwfEo4v43Xe5kMJWx8PeFvNFImL/HQ5mjxeDatmkxt3uSiyiiJvPkx5TRZLp+dMpBQvPCDnuv1zDyNmADwpyw4YN/MNzzz23YMGCYoetX79+7969Dz74oKZphw8fnjt3bvWnBgCAmUFJO0DypjJrRPVOgTHpQ10028rPUge17s7W+rom+guWl/1n9UO2LGoxNnUu57HRJCktIQ3FP9l+nL8biOBofolSkkVEyIiIc9zcAd03NJzYPppQRi0h7b4hhxDmeCWlYco6deu6j+RfVRCdXKEoJ4L5596OZhHhc+8viUUUPWraDRc5myxn3sU6wqZHqvjMyQ3d8p75Z90we9qbhUbnO8O+5VyQao+D6obZPbCzp6OZXy7fHLGgXU+rocCfX30xHv2IyyXPYHxQkE8++SQR/eM//qOLfGS+853vPPjgg0T05ptvoqUGAAAE4uNN9TDUrmQ4yhc4LsifuL6oOv5QL6YR3X0Wq0eUP8ZbwsL+pqwVYhEltq68HfZ2NOuZCSE6kU2mQkrdMve52DsrxxRZNaqhQErL6pkcS1JRDpvUjPw3jYypG+aIYfa0N+tGLrl7vLbPMWHN5YOFn/N6lIj6aLyvxSJA2UwxNTFrHIsoupIjong0zDskSXbbo7MMG0JxN5VdFMpnlKUkByOdL6fgG9qfHu1O7xJ7Ey3wlgvRM2ax5h5+Vp6OIwpMf/fQQ7HIF2lW4oOC5ALHr3zlKyWPfN/73jdnzpyxsTHTnO098AAAIOPelssISacqAdGL6hf2jCcLJr8avYlIDQVq2iLjjjBE7IqGa91XLsNpVuHpGI8u4iwwm/6UTIwKbaRnTHb2jkWUeHRR3+BwYrskrQpCjQohXvGq/syoiO3Jsoxje9IknmBPe3P3wM78AYbZPbCLp7m4p+/z6iokJgZNaDNiSyM26BYPxqOLLFFAPWP2p0d7O5r5sF6nXmwxk0a8MKllrVHbwmqi56k1EpRdgWKFA+RlxSOl6gQK7WsFNd+fHm36wMfRi105R44cIaKGhgYvB4+NjVV/RgAAmHLYfcYyXUMgSvu929OUtBuMRRS1s8k+c7l6eLfkNBW6zse18VSSklNqRACSJjYp1whul+ZoK89flnaSo1K9xjITXmuYesbknm6nkxamAtpyxF7kEdOat7zJezSmNKN7wCxpakMFgcvjp/NVlRNdwVNa1sXz3EJXNGyZExOLBHn2oz1L7nhd+UtWchYbAfvLLY3kxWDFP2HxjElEY03H6EYOCrJC/t//+3+GYdx222033HCD+5Fvvvkm/xAIzMZ7DQCYMVgGaVhEZO/gcH5oh5bVMzkfC/s40sNpysqG+9mRXampZnNfaoG4zyktqHa6qep8+KrQL+Lv5z3XMhJRIr2P8obYeTHXPbDL2stSZOaymBzofiLyIATlTCtXEDoKVj1jch5fPCs3IItFXNSVPfiX0oy+oWHOgHOeXcyk6c+MchNY3rldsb5WhNVZdFrOJSzu3a/daZMTAqgcxZQvgSOmJUVksQPm5P7io53W9MIHBXnSSSc988wzDz30UEkF+bWvfY1/QBEkAGBaIxdj1dR9xo6wTkxpQeqo9xhhTRFFe7phlowD9XQ0q+l9JBkhVQMHMvWMOWKYFt9vC47hQAvsvB2Phi3z/RyRs64ljuSu5KVB3cn9kQdwq6EA23cnC05DMiVjpV3R8BIlMGKY/F+WWaLtxiIx+RQpLbip85R4NCwrQjWUtzV17BZn7MqYc/quGrfJ0vPO7VPyrto2Put+jUVWttZEzkJ8UJA/+tGPYrEYEZ1zzjlDQ0PF0tnXX399Op0mojPPPLP6kwIAwBSihgKxSFH3mdjSYGJ7/kOleidFC0K8JrVs6+5s9QpS+A6qSiA+fQKQVKatejWdOiItKyzBPQbD2Fu72MFd0TAHLPWM2doe7IqG5Yo9x85fLuxz7ESxH6lncn1Dw4ntAbYTtzbBGKbYW2U+NXrG1JWcPIPHfoD9Wrjreeu6lZarKLRg5yyJZst9UEOBnvZmYRjp6Lwj4IJR+RH7ROzKmtImoZWt/vFBQYbD4VWrVj366KN79uxZvnz5Jz7xiUsvvZSfOnjw4Jtvvvn73//++uuvN4z8l0VhHgkAANMUd/cZMb+OP8j9PbU8CNiv4IfoYJjkaIpe6XgYRji2xJaWsFW3FD6yjHB/d3hvqbwBeI6KJ6Ad4RnWPe3Nm0LL2zY+6yjRZDUj7MqZvFhsDxKRJTCphgJqaBF37heLaG69dKXckd03NGy/P7rr4GmP6IbZOzjMVRzCT8AufO3N1Ed941HLUv3p0a5oWCS4OdAYlyyQhBm7XhjDbb8zsge7GgoUC2f6yFjTMd0Du+S527MHf2bS3Hrrreeff/7OnTuJ6MEHH2TLHiL69Kc/bTnyzjvvfN/73ufLSQEAYApxj2mVbIupjPG5zBHyd4T0lGTiuD+6gvEwjMfm7u6BXWw0rYaa4tFFet6Y3YxFJlRPcvsLFXomyq26k5PLYkZL98BOOazLqkgNNTkGJu3lEHrG7IqG9RaT7XK4sVrP5DZ1nrJ13crugV3FIpE8eltINy5M9HI5vHN2TFRDActwSzt6xkxsHxVdJq0RJR4KWISpl/PqGTORHuWs+qbOU7j9KN4S5jqB1kiQaNzQe8Qw+XirVFUC/F1CTMdJeZuC7YjHaoHDC47pT48u8WDCNfPwbS72Aw888MMf/vD2228vdsCxxx67efNmnlgDAAAzhnFVV/sTcVurqgR6yplJww3L9mnUdnoHh/kDexL6adjjhgoRJj1TensVIOZT6xlTdFSI1G3f0DDb6/CowwrWF76A3JXCw1qWKOMdJMT2OgU9qhumGnLoI+G+EyHXdGkqIFtItm18VqygGzndyBUbOc3qauu6lWLADJdbWLYtAnXyTkS7dFco3J8e9TgPfXzbrglod3TD7Bsa3tS5XDgKceiUg8E80UdEHx2NkLiuQw3lzTK7ouHuAZM8vK2y1+Z4th156lL4piCJ6LLLLvva1772wgsv/Md//Mdf//rXgwcPNjQ0LFy48PTTT//iF7+I7hkAwMyD41tEJGqzakdy9/hUZe8VkN0Du+QBHi5H9qdHOQPoPbPMbciVqWe5Idc+paZ6OKZoCexZVBer2HK1gpgEI9qHxR1QQ4GURvlOfCIi0g1zU+cprVqwu9DO0p8Z7WlvtsQ4uQ7Vfi6x/9aIIl6S3J1NuW7bPm7HsaGH+2AS28X0P0VoKf7F9hg+dPxnfswMlVhEtq5MktG28VnLSBjxX1l2y/KRK5J5Kb4WUePhODrS0T+S17dfjhfUkP/+rNMCPxUkETU2Nq5cufKBBx7wd1kAAHBH+C9OZkGSiG8RUSI9Omk+OB4rIDldK+JDXBjnsklRYeaxvUC0lVhMpD2ihgIl+6OTmpFI79MzObtRpTscr7W3A3vpjLbv03JYvCVcLKCbsnU0582DtAlhP24Hkcv4XO4566HejuZUIZgqK1R5n9w9wy6kHE52v7T+9GhPe/PwVWfyL0ksonQP7HJxrLQ3teSLAQp5ecutFmFUVRpaaFlTHmCtF8zJ7aeILQ2OGM4BRd6q6Aofr/50siWn4m96xRWTtR6nVLf4rCABAGDyEcEz/oCZtL/mEz/qau4JxzV/7JziRU7J8pEmlpo5Hi+NFQl6iakItcQe1xUI6JIfvaIOj+NSXk7BoUfRTlF9LpI7WhKFbQgVaD9Sz5j2tK9oeZZ34t6jLQu1pGYkbzW2Xrqy5HcGVQls6lzORvecQ/eSROagHf9q9Q4Ou1c98rjC8ey8EuCsN1vquFgR6Rmz59LmuLGob+JYbbJFhUVAkQpFmfpEx3iWyI6FqsJZqbByUUUobqbHXw/392vWAgUJAAAVwj44IvY5CWcsq92kmJrpCjnrMI6rJXdnK/Aqr1EjjjwFpG9o2HGuichWu/syOiLaseW5f7Lw4ll/ouO+d3A4sX2Ue0fsYde+oWGRTiUpA8vtIOMnVQIcILQoPBZPsUiQx0nLurPt1mdjEYUT2eKG2C+Ht1dWJV9ZRais28b/aZhcX0vFp10z/KulhgLJSDZZCKAK6Skun2OZ4lVJzZBnPgmBvkQJ2PWcl7ky4kQ9Hc3E309cTZHGrzSTc7mZdj+vWYIPCvL73//+yy+/7P34hoaGRCJR/XkBAICJRZRUJJskQ1Uc3BkZ9yGEFcNdDj4u6CNy5ZzAXSh4zMeJtmV2NGytLosnR/UshZWtkfEOXJEVjUcXsWSsoGPaDv9K8K+HSIDyU/k8uxSvEtWHXN4n9swNNPpEmSiuS6zMOHp3U77JJqAbZiI9arER5WvvaW9m2ZpI77PUF6qhQDwatrcnyxQLSQo/9tjSYN+Q272yOkoWGrE5UrhECRQ9RSYnNN8Eb8jCNwRWdYn0PksePKUZvYP53w3R4u0x3ewSghW/YB51pxzQ5fmKopDgmD/8piu6yssiMw8fFOS2bdt27Njh/fjGxsbqT+rIr371q0ceeeRPf/oTEamqumrVqnPPPbesFfbs2bNt27Zizx511FFr1qypdpcAAL9RQ4FNncuTmlFsYLQlxeaviJxyuPdFt3Vb9xbUDwe0iO1Oypd6emFqnwjXiRLDeEvY+7BjR4QptBiCJxdW9nY0W+Yj96dHvUebSIoyOr6KNVBKM9jg2vLCnvYJDe8TihaUQFIzYpRvoLYUJso9MXI5oDty7LCYSOL9cOhObveORRSOArq0HrvLKdETVhZ8dSUzvLphtm18zt7sHIsoPXxFS4OxiMJjIWV4mKHL5u3IrTk8K5InGcorsIcl/5p5mQNk2YD8m3C46RiPG5t5zJAsdiaTWbt27Ysvvige2bFjx0MPPTQwMLBx48ajjz7a4zoPPPDALbfcUuzZefPmQUECULe4u0OLD4BJHkI4CYh6R3tqNVawNanYckgWFvGWcG9Hs9A3nJytRj5yaaaQQSmNRGGlmDVXblbacvymzuVs1uOyByJKakZrJCiUEFfg2csuRetPf3pUN8yEMmpJvFIhHOgu5ipANPyKThp54jMXUcSjixxT+Y7ROL46DsEW8zz3SMn3qFhNqp7J8TcQ4X9eweIyPe3Ncpc6f8/p6WjWCyagJKlSNtJ3D9zakUPIaiiw/w9/8f7aGYYPCvLHP/5xsafee++9w4cPb9u27b/+679ef/11Itq8efOpp55a/Ulljhw58rnPfY7joJdccskZZ5xx5MiRRx55ZPPmzel0+ktf+tLPf/5zj0vt3r2biBobGx0DpXPnzvVx2wCASSO2NJjSig4hnNbI3RvsTcMykT8y2Um7LPNIOY8sN5sTkSiYE4rE0S2l8muRivwqyE13RcM8xU4WQ32Dw/FoWH6kWBcFK6qUlnWxw+Qsf+/g8PgmnYQXp6G7ouFCj3OwGn0mn12f2F8vroiHOnJpgZNQc76Z/PZVKR/LRb4b/I67d+F4Rw0FHIY3ZkxR2is3fYtvkvytwNFgsiSxiPLEnQ8R3VDlzqcpPijIJUuWuB9w8sknX3zxxQ888MAVV1yxevXqbdu2BYN+/gVPJBIsH2+66ab29nZ+8Jxzzlm+fPk111zz9NNP/+IXv/jkJz/pZakXXniBiFavXv29733Pxx0CAKYW9yGE0wtLsl4NBeTx0EIpykPt1PQ+zg+WtAoXpuXCItsezeL0bsmiUj674+lEBSFH8gqnLvvzWw6tsfmfPf/LASe5iI31tKxaxH3rioa7omGuaxQpV7l7nZ9yD2Pb5a9ua5qx5HO9jD9RlaIejVzGECPF3STSQlnFAH7BfULjLe1KQDdyKS1r37bHkTATXlLE/ZGbn+xPsdN+xUkJNRTQM7l9Ky4RX9tmG5OXxT7//POTyeSWLVv+9V//dWjItVi3TO68804iOuuss4R8ZC655JKhoaF0Op1IJLwoyIMHD+7bt4+IPvrRj/q4PQBAPTADPNuKhRXl8dCOL5QmneRc3HxIMi3vz4yyZ5Dw99ENUwzo6yrlzihy37o0rlDePxEVG+7nnVhE2XTVcp6Ax1IgtjRoD/hNaM4wTD1jchuKJOCaWITxnRFRTP5nQhnlu+0Y/yuGvAc9Y7Ict0fImHhL2NHi0bpgEZHNsr5G7fA+wvK9b1BywTRMYbRugcc/eiwh5Wt3HGNY7BfMUlArR9bt22b/IPvvlZ4x6cQz+gaH5fGYs4dJrYO88sort2zZMjIy8re//c2v6djPPffc3r17iegTn/iE/dk1a9ak0+k//OEPr7322kknneS+1FNPPcU/RCI1GGcLAADVIT7z9IkzaVSn8dDcWsHmeZVFm9RQoG/ceKVp67qVHl8oD3rhXl3R7zyh2bm4HiJbfI6KSIGJPc5GPLqop6O5tdCpbfnIZx3cPbDLHrzsHthpb7kQ1Xv6wC5HQ2y7Wo0VaiTsSrG3o1kM2RNdybGIwi3MJb0bXWJynKjVM6bcuj6ZcC0jd0EV79cJ9nQ0q0qTfeSMI7ph6uVEB7lxu6yXyKhKvpndaggfCrCbvSjMLbLVHBRkbQmFQvzDG2+84ZeCfOmll/iH0047zf7sihUr+IcdO3aUVJAjIyNENGfOnGXLlvmyNwAA8Av+gPR+PPenc75YTK5rdQ1AElFXNMzaiw3ShWayWEva+3K4epI7YywirD8z6jFCxs3dRBOnAmZMS3uEwBpGUgIiWd/b0ZzUDH1ifEs2BhIPclC2b8i5glC+CofHHdLTTWzrbdFSXEJqKRtl8ynWpsVuiFhkU+dyYWdjR9yxCmou+fZWIz15JGNrREkWj6TyDZFHWbqjZzw1acnCuqpmIN6e1JwkSBRmL7m8POl5yuhMYlIVZC6X/xt05MgRv9bkCsjGxkbHuduqqvIP6XT6vPPOc1+KW7lXrFhhmuaDDz64ffv2AwcOLFy4cPny5WvWrBHyFwAwOcg+LzPMf6cC+qXoiPdqTv587e1o5gR3yQ85WXcWkzXCvCYWUbhzhR93+fzO1yAuDSa2W8sBJ3pKK9wXbNnSiJH/aHeJw3E9KEteIXBLihXRWeVlfIvDy5WARVj0p0cLQ1OspZBcQDnBDdEwuwd2cWmg3OdBUnhSSMNi2V4LFaio6t0JOJ/rfup8C3k7Oaq0Yi9xP6DcWkkXea1nTMfR5F6augrf7mbd36hJVZBcsEhECxYs8GtNVqXFFmxoaAgEAqZpvvPOOyWXevXVV4norbfeam1tffvtt8XjDz300C233NLT03P++ed735g9kPnKK694fzkAQAzN043xsWaiXq1OvvGLWSa13o+c6Iy3eJogIlPW9nhxbqZJpEd54o6IMopIWH+mPGtGLkVlnaSGApw3tHw899uCPXL8zyVcRxPKPU0eU+6uO9kamrU4l1GW1ZDLL9dtLRqOBYssUKyyshA5i9u+D7BxkiymLcpb5MHtZode6GlvFtc7aS01LCK5JNSXkxYrW3R5E11CuV7EYjEmYahpHTJJCvLIkSP333//TTfdxP90jBdWxsGDB4lo/vz5xQ6YO3euaZqmWeLX4siRI6wgR0ZG5syZ8/GPf/ykk07av3//zp07n3766Vwud8UVVxw4cODiiy/2uDHoRQDKondwmMcDCodq+1A+0SmsKgHqmLz518UQ/byxSLDW++EeYb5F7O8opsJUX4Al63K5UZqIuDhMfOhW9hEr5K88pXBT53I5AEke3MKFXhfBP0vN4vgVGWbzNU9wTpwDS5ZzsU2geMu4TLMsS23dMF2StjKFa3e+dXK9qXgktjRYMnrKB7jnju2vIqKe9uauaLh7YJd3uSyciYptwyPyNxB/ETtxi4UbZqoGdaJcKOL7svWPDwrys5/9rMtMmnfffffw4cMif01EF1xwQfUntXD88ccXe2rOHE/X+NJLL7377rtEdPLJJ996660nnniieOqxxx5bv379gQMHrr322rPPPrukexEAoFz606P5CI2WJSK2xebADDvL5KehFDqFLa0kU4VwIUlq2UnYj5igqGdM0S/sOKC5LPSM2XZrPtYlsnjyGDfv9LRbR8iIU/QNDstjndVQIJHel9ydLdmDbFmHN7mp8xTdyLloET6SF8+H6GyNtH2Dw3rUFPUAjp4y8qVxo0YxzVpy2xa46LPY7cqXnxbJL8t7KOsGimE/3O3k/YV6JicHPsUe7JuvwIXHFxxjtPZjPDZ3lwUHjH1ftv7xQUEahmEYXn8RP/jBD1599dXVn9RCNlvtt4oTTzzxZz/72dtvv/0P//APxx57rPzU2WeffeWVV1511VVjY2P33HPPt771rSrPBQCwY/+L3xUNxyKKPCXZS8vqZCICD2xlzG7b1S9ryYyLid4i3KgbOcl8O+ex56AYspmmN2X7AAAgAElEQVSzfG/Lvc9d0TAP+Wi79Vn7ay3DoKv8LOe4nccdFjuM98OdNKJ6shhcJOexC8TjrorZN8Yi+ZoNH09H+bbiRUSU1Az7/ED3/7M48C9ch9yOLOe3sUb/OwulOzl/K2bemCuP+KAg582bN2/ePJcDGhoa5s2bpyjKt771rba2turPaFmcCrlsRw4dOkQehnGHQiGXva1evfo//uM/TNN84oknKt0pAKAobD3DToHyzBhLDy9ncoU7zFTsdAJianOhk8DoClVrVy7mHXNmnCYqPP5QzKdx8x+TZRjR6dKEa86DV9mEO7ET1uhPj3bZmkJ8gT35WOTZqwYrRjd42F1ODZXoEa6mSK4Yxe48v6fJUt403hUSx1m577t7YJdjuSeHn4stmH+LS8lH+WCXbXMRQiyitEaCvkyjqWAbZVFXX1zrBx8U5MDAQPWLVExTUxMRuTTKsLhcuHBhNWdpaGg4/fTTf//73//xj3+sZh0AgCM85iRuLKJSPR/1IBwFHttjXbA3Bon+Ic6Myx9dfUPDQkH2tDe3FsaouK/P7S/6RLe8WESpbIybBV5HJDRTWrZYs4vYuZcGW8djetqbW7Ug55orGMRn6T4R5RB5sVvdrXC/Lrm3gz0p3W/CkkLhposWL8u1R3zjsoyplCm5qyq6TMZvOBXG/PDXgNrJR39x2WTTX/4Qj35kMjdTP0xqL3Yt4KacXC535MgRjkfKHDx4cGxsjIhOPvnkKk/Eix911FFVrgPAbIYFjTyUTzAthmrIWCrJSo5psaNnzO6BnVxxyM0NNDEzzspywhxh4XEtzXqxL5vUjJSW1TM5S7uJwHuM0KJULFIpv9vCAUuUgEWgsGDitm41FBARVpczOn5aJ7WsY3LcO+NxXJsFT/XEIsqSlgAHpO1qcuINbKJSaiyxfTSlGa0RpTUS5DfRsSrA+/YS20djS4OJ9D6XIUCWx4sNYqkAlowxac9JzfBl5TqBh5LPQqa9gvzQhz7EP7zwwgsf+Yj1e4BIOgtjyGKkUqmtW7ceOnRow4YNjgfs2bOHPAwBBwAUQ+6klttgpymyNzLbKJa7QrKQQeboHStI1oWcqedHNnWeYhmmF4sExQBDueSLj6kyMW3bpHWpTZ3LExPmWY/LaP4OICRUVzTc095sqWStQL3xcJ1yL4rHw9hf5ZDArTpHyQUYjnOZLXhxsSkURVTSzFRswbaNz5X3EsO5lYfvarn+QUuUQOvEL0LTIvTohbGmY7oHds6AP2gVMO0V5JlnntnY2Pjuu+8++eSTdgX5/PPPE9GcOXPOOuss93V+85vf/PrXvyaitWvX2mXinj17NE0jotNPP923rQMgUWUzxLSg3jqpq4THnRER2yVWtoKQCLIbiEg49g4OCyNMQVc0vEQJ6Bmzd/cwW/pRYSKwd41VsTRhscsXnihYiwsS8tDCgh+TvH95JrKXTVKhfdhxppzLVbDBOBHFSoXrONhWVuGm3dqmRpJoCmVWsSty1I7uv05qKJDYPhpvCVcwL6f+ObzgmMmxYqhDfFCQ3//+919++eUqF/nud79bWaL56KOPPuOMMx5//PG77777oosuCgbHa/Dfeuute+65h4jOPffcuXPnuq/zsY99jBXk7bff/r3vfc/y7LXXXktEjY2NF154YQWbBMAFjszR9J+8wjGwEcOMRxc5/jGtt07qsnDMv3vPXAu3S/nmcG5X9FlbjueUaGJ7QM66qqGAnsnZc5HJgm+2I5bbzlbYLP4qeEfsro0uVnxiV/x77iIg2N1G1sHxlrAQ0KxZy5DIUj6dhYvLlXrxtZFfPmkW3HVIufJRvKQs1yEwLfBBQW7bts3FD3ISuOyyyx5//PG33npr7dq1N99883HHHUdEe/bs+fKXv/z222/Pmzdv3bp18vFDQ0NXXHEFEV1wwQWXX345P7hq1apTTjll586d999/fzAY/PrXv86Fj9lstqen55FHHiGi7u7uksO1ASiXRHqfmLzifVpdHSIyrXomp3Y6VDpaPLFrsYcahXL7C4NxK8u/JzVDdruUX15Mg6bGB1JPCPm4xLpcPsXZWDu2NMgaLqllxyWpawcuk4/SFZdNJTWosF63PyX0h26b2pLSDDUUoAhRoWHIEgBzCUDKWlNEvh0P9qJKuVC1ZAVnTSkZ55uq72bT9Duhv0zfv9vVMO2z2ES0fPnyK6+8csOGDc8//3wsFmtpaTly5MgzzzzDDuEbNmywZKXHxsYOHDhANg+gn/3sZxdeeOHrr79+++2333XXXWecccY777yzfft27sXp6Oj45je/OYmXBcA0Y3zciGHqRs5RyQlPbN9hizu2ZanSYdvO+HzFjNm6O8syzp5flndCRBxu9JLfFB3TRFTusBA7ltZXDv2qoUByd1ZykRzfEs95cxOg0TCnzh3tr91hTe9i1u2iCGW/xu6BXS5dIC5rloU9zZqv7FQC/P3HLwVZQT5XvijxP5dUMDDZMm6qnMPrEDUUKPYXb2bjg4LcvHkzEbW0tOzfv5+IPv3pT3/uc58LBoPz588/cuRILpd74403/v3f/51nBq5Zs2bt2rX2RarsUInH48cdd9z111+/d+/ep556ih9sbm6+6qqrzj77bI+LnHDCCZs3b7755pvvvffeXC736KOP8uOLFy/+whe+gPw1qBHx6CJut4wVRvROU3jiiJ4xVSXgb3Nifzrf4upyf5K78+N9VcNkV0K/zq5P9JoWljopzXmSYSK9j3eS1Aw2u6GCkJLdLvmjtz89Kiad8CdQ98CuKj+KROGg0CgcQC3W46x78ySKLQ0Wc8B2RA0FWiOK44BK7+JDN8z+9GjeHLEisVKW0FFDTerEGxWLKKLwIGEbgV0xVSrROtFt1W+j3spaKpPF+W+JkdrsqY456r333qt+lVNPPXVsbOzv/u7v7rvvPrulDrN169YvfvGLRHTLLbecc8451Z+0nlm2bBnmYgPviHbaqd6IM2w97SXDzlLPl0nN8tk5QiZb3tjpHtgl0qybOpdXoCBFHafdrlwsbgnv2U8kDHrs64toFne9UPkNrXa4onHEMGWBtXXdR4SKZYoNNfZIV74G0XAPg1noaW/mYdP25G9ZukEYUFdwr/h3hogqnsXMhkqbOpf3Dg7LlXyO0copFEOICFaPmp8LX3bXP1sxoJOmEm6++eaxsbGmpqb777/f5bC2trbLLrvshz/84WWXXcYt0gAApm61I0kNEPwB6d7r41fkj8N+LEaTu7OiTk5Y3tiRQ7mV/SnvL3QWCyNGnlbSGlHi0UXcK81SjNVMLBJ0dLVsjSiOn0DiKtw/n0RDCbnNLAnQxEaT7oFd3E0ciwQtQVNuvrEbejsqHpZrNFHdFlOfWy9dSUR9Q8OOAcIRw2zb+Kyj8itL6FTZ5pwoLp29qC49YybJsHeCy9HKWCTY09Fcrl2Ov/CI7SncwAyA3+sKftn0jJlEL3ZlcL9zT09PySO7urp++MMf5nK5P//5zyeccEL1pwYA1BqhePSMOSJV0ckmf74jmnJGDLM1EhTqRx54aCEWUdTOpmp2NTKxRlB0HHOHk5DOvR3NvB97HaQQUtWEo/g+c/63mILkqBjHhqnQ001ErHctulbPmPGWsGqY/ZlRFr6s6lx2uHXdSiJqvuYJOTpuP75vaDgeXdTT3tx/jYN2qUXDsovmc7zn7pfpvarSfiRrdO4xouIxTt8Dk8W6miooUQV2Kr6Hs3M0tg8K8q9//SsR/f3f/33JI+fOnTtv3rxDhw7t378fChKAaqi1hhMICx41FOA4HBvT6IYZbwnXwn5Iz5iibC6pGaxRStZBiq1WfF4x/0NVArGI0qcNi/1YjnTcRllz9tyjXyW1F49+4eR+31De5Jnh4GVPe7NlmnaqEJXkMK2uOKfqRKCUeHZL4Qf7wXqGJWmutQ5CL6o0KHxyEHWrkzxbRQ01LVEcXLF8ufYK+nsqM3sHMwMfFOScOXPGxsb++te/8oBBF955551Dhw4RUUl3RgCAC2K4C8eianou2bOQ9aJw7ONRab6r2LwXtJYlIhZzumKq0bKlYX96NKVliYijmLxPF+XN5ZvszVlMw/HL85G/pUGeAc3D4rxvLBYJxqPhlJatLGVGRIntE6y87Z/fI0aTrKhSkn0PFfSlPAlaHtbMWey+oWFp6kxRfZAsdKlPDi4N3VVKqAqChR677KvYlAM1taKs4K0s6zd/BsPT4eu5HqkW+KAgQ6HQ3r17161bt3XrVvcjf/CDH/APixZVMr8BAMAIC8kkGf72HTtSzLPQ955rQU97M4chezqauwd2sUcPD1b2uIKeMUUDB0+co478g+7Km4UU130KVcFK1NLRnNge2HrpSkvPikdSWrbcV8kSx12XJLUsTZQCchsQp7nl5miLR3prJCgPUaw4D1ssoFWfPR8l91NvXcN1Au7JbMa5b7osurq6iGjv3r1XX321y2H33XffvffeS0Qf/OAH58+fX/15AQCO8DS82sUq4oVW66SW1Y1xIcJ5VbknuuQ+uXfb/hQHwHTDbNv4XH96NKll7XNQLFjWSWqG7H2Y1LLJ3VnWlNxo4hg7KRZV6k+Pskej5VluIil5pRaSWtblVY4q2Rf5wnboXdFw78TZMHx/RAQl4TRypuxzFX8J12WWu2CtKXmNkErABa6WnupdTDY+xCDj8fgNN9xgmubdd9+9ZcuWr3zlK6tWrWI/yMOHD+/fv3/nzp3f/e53X3/9dT7+7rvvrv6kAMxmeAozl6BZooNJzeACOP5zVovwZFc0nNKy3PnbNzgsxs+IaBx3/hI5eCUKxNS+rmjYElxkeef9A1uMheQSsdjSIMca7UeK5LgFFrI8Y1oekeJ+Xi4EpIqCasUOLtYfzZ227qdwnxzDm+TiB5dcsGU8dMXxQvcMbx0OuPMymwcAIOPPTJrf/va3bW1tRPSXv/ylt7e3t7e32JF33333+973Pl9OCsCshQ1rHMtuHL1v2JOPfBq9LXe6yONnpPaXLJUq0xTe1EnNiBuL5AtRlfEaPlZFbM0dW+rciC1y+qwOU5pU0hcKxFvCwuIxqRnC8UfPmN3pXeRHJ4SqBOLRcCyitN36rIsEsagxufRQ4PjyeEu4Kxp2d/OORYKbOk9xUWYVGt1JI7kdni3oXYtN5nSEfyv8EtBgtsHfQGYb/ijIxYsXv/jii52dnTt37ix2zPvf//7NmzcHg0XNOAAAZVEs3Wn3vhEVgbpRdBZfWeeVg3liNdkHUZRpsvhzWmS8V8bluljyupSo96dHLRlhWZbxMDoi0o1c7+AwP6sqgaRmeM/yl8wgcyTYcoz9VTxYeVxyhZpcxJmgK5pveI9Hw+7Dqd2TaDzZpeTpLLj7eMtPFXPBFHurcx1mj7+Kxyd/MwBMC3ybiz1//vwHHnggm80+/PDDd9111/79+w8fPtzQ0LBgwYJYLPb5z38e9j0A+IJs0WcnL5g8eN/4tRnRytPb0SzatO2wB5AaauIZcexfSEStESdXxYK0Ypc1F/koe9YwqjKe801q2e6BnbyaxzYUx2t0P4A3yS3eQoXEIorcap2fDS2VZtrDXY62QZs6l7NqjEWUlNPIZvEqbjmq5kKqeUlKM4rJxOlbHwb5CDwiDyadPfigIH/zm9/09vZ2dnauW7cuGAxedNFFF110UfXLAgDseMlH24VjPB+HM+Mt4ZpaSPZ0NHP+miOLrYXxMEnNyJfxaXkHbJ4D5riI/LFtl0TyjGzHYjvdMHukCc5lpVbtg1u8IKZgy3qRJD9FKh7iGt+20xmTmtF8zRPk9LVBzPorHDnef90VDceji7qdpl1XGQss9nL3qkfoMDDjQRa7Qn70ox/t37//9ttv//SnP71gwYLqFwQA6IXBdLIclB1qiEjPjI+fZu/DJUrAcSZ1VzQciyhlOZDzvJNiKW9hvs3VlnphFnYsosTWKUKEOY5Odo+TUaFTJ0kGFbSvQAQdeWXHORB6xqxmvtymzuWWasJi0UE5oSx731DBRLPtVusoPAuOpZAy7lWSxV6bN0KaaCpO8sTCKublVPZCf6n/nDiYbXipSJl5+KAg33rrLSKaN29eOFx3Bg0ATEf0jMk9GV5GUZPUf01EI4bpGNsra16LmIWd2B7oaW+2BzVZkvJ5hXgS+8xH4Ca6DBYThY5w6lbYgIvxfSMFzaRnzGJz5KqB6yYTEz2GLBNc1FCALdZd1tEzue6Bne5TUmKR4NZ1Kx0T8V5w052GKUaZW14yY4QXRCQAU44PCnL+/PmHDh3iYTMAgOoRLom6NIqaiNRQoFVqW3GM8PlCcndWzMIWDd0W1FCAtPFTlxwLy3OcydXiR4YP4/YXf81fXEa3JbVs98CuretWyiMKLUHTeEtYjgTLuDgBFevqrcU4PqEUZ6rGmqnXBaY1s60IknxRkJdeeikPm7nnnntQAQmARxzz1IysxpZMLK/p7WjWM2Ga+NcqFlESSr46cIkf5Tj2WdiOxCIKqzG579sFd+0ozH1SefGac8/wOm6bPMiLYq6QDLdp93Q064U6QotYdJGzxWooOZhqb6Nu2/hsudc4k+iKhssy/qxbEBAF/D1wtolIHxTkZz/72bGxsRtuuKGvr2/btm1XXHHFCSec0NDgw7QbAGYwnP91zFO3RoL8yeqYenZ8ZFPnKcX0aLmwhuNPxHhL2CWHLs4r0s1iBXlydMnT6YVhg9V8DMciQR6BWPJIPZOzVDFOfNZMaVmiYGWhwWKNJvY2GvcoZp1Qa0PEurrYipkZVwGqATNpKuS73/3uyy+/fOKJJ+7Zs2fLli1btmwhooULFxYTkUcddVQ6na7+vABMI5KakUjvI6LWSDClZTnARnm9Ysg9MSQ58nj3blRDga6QV+3o3nYjRsuooQCbeLMidLQHUkOBGFl32FcYmjdihFUlb2HI15LUDFVp0o0cT5GhUo6D3tENU7Yid4ErAVy0WrlDcXyk3rRITSe11G7wJgCTDHqxK+Tll1/esWOH5cEDBw4UO76xsbH6kwJQ/7BXIhHFlgaFqLJ/aqqhJsfuaV/OPmKYrZGgvFpSM0QZn2PbjaXsj6ddO7b1cCKew4di/IyeMSXXw5wY09I3lM9a1mJ4Cc+e8RgDcDGtZCZfxrmUZk4t9bkrAEA94IOCXLBgQVNTk/fjkeAGswTRp8xz9izPiswvD7mu3dn1TC42se1GVnj2mTGtEYUP4NmJvYPDoi0jsX1URCLZmVJEEJNk9KdHeSkRCLToj8J+/NdnsYI7ZjwaFta+8ZawY81iNaqoYqknQp497c2WCddqyG1yIACg/mmtpc9u3eKDgrzrrruqXwSA6Q7LIxHtE40yjMhxiGpr9xLD6nEcXU1S2w0RJbVsPGNSZMILezuaY0uDifS+JUogqRmxpcHE9vEW40QhhmrpR+anKjCmqb7yjwe3UCG8ml9WCSS2+58kbc27C5UtIvXxMd/W5ut6y1wDAMqFC35mG75NNQRgNtM9sIv1osjz5ttvM1xQ2CTPprO3ntQCDiXqGVNVAqoyniVgSyDWQMVMIpO7s1wImNKC8WhYHtanGyYH9uy6pwJdZZGPJdUkW3Bbzi6N/95nGcztO1Wq0qSWRV643rqFAKievsHh2LpZF4aEggSgWuTGC7ktJh5dxFY4HJgU4UnvLS9eTs0NOjxsWn6qt6NZzEexyETWuBwv5JdbXiuMu5NalkcUiuZl350LXf5pQQ0F1FBTPBpOaVm5tZk3r2fMktNuqgfSp3pwDwGYGfivIPfu3fvMM8/cddddR44caWxs/Od//uczzzxzyZIlc+fO9f1cANQDlhZgNRSQO6+r74kphp4xRYNOUjPsw2Psp+4dHBa9NdxQ0p8e1TM5l2/PeXtqLVtZ6MhHOxjhiWOxqOSGIT2TQ3gPAAAmDT8V5MMPP/zd7353//798oPPPZcfUBuLxW677TYfTwdAnaCGAvFoWA01UaEtRhjiWLpYvOPFnFY3clJPjJlIj7qfq3dwmBPQSc1IRbJy94YUQ80WM7KpTAXGW8IjhoMboh1ZoXKxoKMilKtLmQom1tjVMFKrAICKmZ3NcL4pyMsuu+x//ud/XA5IJpPLli178sknQ6GQXycFoE5QQwGioPBxLNbF4gWeSU1ErYX+4mJwr7Rcoeh+rhFJblJkvGNaN8y2jc/VQkJxnSUHZUsubpN0zpNjqt+kKKb0d1kAwKyl1nXt9Yk/CvKaa64R8nHx4sUXXXRRW1vb/PnzDx8+vHfv3uuvv/7//u//+NnW1taXXnrJl5MCUCf0Dg5zg0VKy27qXM6tKrIhTlmriXYQ3SjtKB6PLhLijNu9eaY2W4WLwTa8SGskKNwoZVvKkjOUxYRD98Mc6R7YFYsEy31VT3tzqmYpaSS7AQD+MglF2HWIDwoyk8nceeed/PN///d/r1ixQn72pJNOOuuss44cORKPx59++ulDhw79+Mc//trXvlb9eQHwCz1j9g0N65lcybCfI6mChkuSwfaKbIjDSq7KjVmsdizEIsrWS1d2D+zUDTMeDYvsORc7cq8MKz9VCXCevQLiLWEq2FWIystiyLFMR1dIL1i8kAAAANQbPijIDRs28A+//e1vTzrpJMdjGhoafv7zn7e1te3du7e/vx8KEtQV/elRFl5JzXl2nzsi3yr75sQiirv4s8NtLlRIs8YiiuNOxLCZJUqgt6M5qRns2iN7Mcrt4eP/rTT2NmKYor6zpBz0JR1cQWkjAABMFaiDrJBt27YR0Qc+8IFi8lFw9913t7W1mab51ltvHXvssdWfGgDfqUAAcSqZiOJOY6Y90p8e5VElnHTe1HlKsaX606MssPiA1ESlWMFVlJyz0p8enao50QAAUP9gLnaFZLNZkiKRLixevJh/+Nvf/gYFCeqH2NIgDx5UlYDjaIF8oWERSZfcnZUPs7/Wi6zMm+YQ6RlzSYuz0beeMXUjJ0ytOe5YcmV3eKReyTYax2dFiBT6EgAwy/H4p34m4Vsvtsdp142Nje++++7Y2Jhf5wWgemIRRe1s0o2cqjRZ/gToGbN7YCdxX0tE4el5lgPEmGPZTpzpHRxOaYYaarI7flv3sDTYN5T/OaUZvYPEowWpYH/IwtF3oVbxgoXGmtlYPw4AABZmm3wkXxTkwoULDx06dNddd1177bXuR2az2XfffZeIFixYUP15AfCRYvP9+qXpz9woUxhwnHde5N5nxzWTmpEXl1qWCnYPjlNkWGhKL8wmtawQlL5QpVlPfkjjxA7uJIm7ESxm3wgAADMe1EFWSDgcNgxj8+bNJRXkNddcwz8cd9xx1Z8XgJrSnx5NpEctfxf6Boe5baUrGuZ45Ih0gBqaEMJ0VGxyL3MsonBbjIhi1ghHB8RykeUjWXquC1MQAQBgFsL2urMtDOkp9ezOT37yE/7hU5/6lMth9913369//WsiOvnkkzHhEPhO7+Bw28Znuwd2+TVAL5EeTWpZsVosEmRTm4JDjcHdM2LCnhoKcMOyWEGUNlIh26tnTKHk+tOjbRufbbv1WbmHukbIF1IZ9pfLleMVLB6LONSbAgDAdISryad6F5ONDzHIJUuWnHLKKTt37nzxxRc//OEPf/Ob3zz33HPF4Jl33nnnzTffXLt27fBwvuS/v7+/+pMCICPak0nLsseNj4vz3wW2iuweMC3GPdxNwv6LHFPUjRwnfOU2l6SWbdv4rCUQOK3TvlVuflpfOwAAyKAXu3IeeOCBZcuWEdGhQ4euueYazlbPmzfv0KFDliOvu+46dGED3ykWA+MixYosHvNzZUQcMaUZRM0iyhiPLso7dYfGBatIfMciir3FBJoJAADAjMG3XuxXXnnlggsueP7558UjFvnY1NR0xx13tLS0+HVGAASOdjxJzRBDWfSMyTpP9Kyooaae9maXvAPPlZHT4nrGLDalkGeoJAptN2JWNQAAgBkPOmmq5b777vvzn/980003PfHEE2+//fbY2FhDQ0NTU9PixYs3bNhw8skn+3guAGQc7XiSu7P/P3vvH+RIXef/v5iBtcOvSkfADRa1HXoXblc5FDfUoXDppXCmRKxSwHNEisyUd/JD/N4vPZDVm4w/8Cy8sxRcUEtnggpzn7VQOKxi9oRNTkQxywLi/kCmmZ5bIau1pFOckObHLt8/XulX3ulf6SSdmczk9fiDyiTd7353ZpY88/rxfJHDIva7NJqjATAZ7XbnAWGk3ng6md2cLHq5heMBhfnqommxGyLDMMwgM5idNFEqSAB4y1ve8qUvfSnaNZkBAXUbusZ0cLrbjgcDkzioMKPGQXDtDtiDkpCmdizMlMoUuTQq9Qw45sTR35FVI8MwDINwJ02HPP/88/iARs74UalUnn322VtuueU///M/u78us5pA425MBEyOpNotW6RFxH/DmirDKBiz+7CxGp8ZTycLtvNiRmgHxhJGAEB1iKsVdbOgx/Olg069yBWNDMMwjADHIDvh+uuv37Nnzzve8Y6WuvDAgQMf+9jHAODFF1888cQTu780s2oo6CY1mkzM7kMxh+3PIVfwnP5Csq9ge3pPjqQyehxsi+zc3MKiaRmVWsPRUFCHBb1a2PZ4JDfIMAzDrFa4F7vnPPPMM/jA3aPNDBQY0nMkrEWHahR8hmlp6+PupPZMqVzUqyCMdWmYcgvTX3JzC+6x0UpCGk/UA5y5uYXOrLztgX6hTuxyGAzDMAzT5zjGSQwInSjIp556qq3nkZ///Od33HEHPpakgXujGaKgmziXRVPjRtoaTydJTRpyzVFiWJiv5ksHRYtH8vrGpTRVzjR7U6ONDjbN0JNKQlISMcOs4eLYWOMYstIWmiqHabjW7PrLji/EMAzD9DkUFlnujSwpnSjIa6655tChQ44nn3jiicsvvzzM6SeeeOLxxx/fwXWZ1UFhvmrrvyp+b8NRgYosTY6m0IsbXRUVWRJjhCgiDbNGvglGxYYJ2IgAACAASURBVJqplAu6OTmSIklnmFZubkFbH3foNpwiE9XEmpB+PdjH0/0VGYZhmL5lMLPYnUw13L59ezeXvPPOO7s5nVnpiE3T62QJBaVRsQp6tTBfBYDxdHJ6bNP02MaMKpPgo/HT6MjoHj9NFt9GxZrasTAxu0+8qGPG4FLCAUiGYZjVDfdih+XUU0+9//776ccbbrgBO2mCfXyGh4djsVgy2UmPLbMiKOimaMfoB6atF00Lc9O5uaZSxYJuko7U1oNox1PQzXzpINg91BQF1NR4Ua/mSzVRq7FuYxiGYZYG9oNsA097cPYMH1gw7FfQTUWWsulkSy8escN6PJ1EU2602pmY3Ys57vyu8vTYxsnRVNaukpyY3YeVi9g6TSsU9Crb6zAMwzDLyKDJR4ikF3tqaqr7RZgVTUE3bW1nKYkYeS6GCUkaZmN+dEE3xRrHwnw1N5oyZMswayQfgQdMMwzDMP0E+sENmoiMQEGeddZZ3S/CrHREzxpqhUH/xeB/VIX5KkrDmUp5nSyJPc5TOxaKtqbkrDTDMAzTtwyafIQl9oNkVitY2kiG3mjWAwAzlXJGjZP/oojn1zXRfwfhcCPDMAzT5wxmLzYrSCYacqMpgBQAbNm2m2SfWyNSNwwWTdIIQYQDjQzDMMxKhLPYDNM2aLKIDjszpbLY45Ld3OiqwdS2GFOkETIMwzAMs6IZNPkIrCAZEQwH4khAo2IZZq1lK8xMqTy1Y8GoWJoanxxNiZ6LSkJaNC30ZWwaPM0wDMMwqwjupGEGC6NiFXSThlNPzO4jBUl2OQ53HtHxEdtfinoVdWFBr8LcghiADD+4hWEYhmFWLoosDZp8BFaQg4lRsSZm94I9cw9HAtLEP1H2ie484uzBfOkgyk0xrMhdLwzDMMwAwjFIZpWDvt8AYFRqpPaMipUvlYv+4s+o1Aq6OTG7D8WiUbEM+zHDMAzDMNyLzaxypnYskCm3iGOmC+asRZW5Zdvj4vEsHxmGYRhmwBla7g0w0VPQTUwx46gYEnxGpTH9RVPjSkIaTyfdUXejUlsnS1TRyLlphmEYhglA7AEYHDgGudqghhiEuqQ1Vc6oMtZqjKeT2fRaRY7NlMoYe3eUM7JqZBiGYZjwDFoRJESrIOfn5++4447FxcXDhw8HHDY8PLx9+/YIr8sQGH10ZJkLejUzX9VUOTeaUhISljzaJjuD+LWJYRiGYaKFO2k65KGHHrr22mtDHjw8PBzJRRkRtG80KpYiSw5dKPoyuvUlwzAMwzBMu0SgIP/4xz+Gl49M5KA1D9k3uhPQ7MvIMAzDMD1l0AKQEImCvOaaa/DBSSedNDMzc/zxxx99NJdXRgZa8BiVWkaVc6MptAEHu2OaRsLQwcu5V4ZhGIZhBoMIpN6BAwcA4LjjjvvlL3/Z/WoMglpQSUhkwWOY1qJpocmOkpDypTJwozTDMAzDLDdYPzZoYcgIFGStVgOACy64oPul+oR77733wQcf/MMf/gAAiqJceOGFl1xyyVJuYKZURoGYUWWy4BGT0eL4aYZhGIZhlhHDHDj5CJEoyGOPPfbFF19873vf2/1Sy06lUrn66qt/+9vf0jN79uz52c9+Njs7u23bthNPPLF3l6b0tKbKlJjmECPDMAzDMH3IUW+88UaXS1xxxRWPPfbYhg0b7r///kj2tFwcOXLk8ssv37NnDwBcddVV55133pEjRx588MF77rkHAM4999wf/OAHIZc688wzn3766bauvmXbbkxPc3CRYRiGYVYQSkLaee05gxaGjCAG+c1vfvM973nPM888Uy6Xk8lk9wsuF/l8HuXjrbfeOjIygk9edNFFGzdu/PKXv/yb3/zmxz/+8eWXX97NJWioYFGvGpWakohhkhqNvoFbYRiGYRiGWQlEEIMEgLvuumtqagoAvvOd72Qyme4XXBa2bNny/PPPn3/++d/73vccL1155ZWlUumMM874r//6rzBLuWOQM6VyUa+yHSPDMAzDrDI4Btk5V1xxRSwWu/HGGz/xiU8MDw/Lshxg6DM0NLRz585Irhshjz/++PPPPw8AH/zgB92vXnbZZaVS6fe///2zzz57+umnh1yz3kNdsfK7yiwcGYZhGIZZNUSjIG+77bZbb70VHx8+fPjQoUMBB/fnTJqnnnoKH7zrXe9yv3r22Wfjgz179gQryIJu5ksHD5z3j6kvP8KqkWEYhmGYVclQ90s8/vjjJB9XLlgBOTw8fOqpp7pfVRQFH5RKpeB18qWDM6Vy7c1nsHxkGIZhGGa1EkEM8jOf+Qw+0DQtl8slEok3velN3S+7xKCr5bHHHuv56tDQkCRJlmW9/PLLAYuQIw/DMAzDMMwqJoIYJOas3/rWt377299OJpMrUT4CwCuvvAIAAZs/5phjAMCygiKLSkLSVDnyvTEMwzAMw/QVESjI1157DQA+9rGPdb/UsnPKKaf4vRRy2PfkSGpyJHXigV9pajy6fTEMwzAMw/QREWSxTzjhBNM0V2jo0UG12u0MGCUh5UZTd/9/d+78f1uNimWYtcJ8taib5PjIMAzDMAyz0okgBnnuuecCwPe///3ul1pGhoaGwM5le/Lqq69Cm43kmNTOjaZ2XnfOwtZ3j6dXsN06wzAMwzAMEYGC/OpXvwoAzz333M9//vPuV1suYrEYAAQ0yqC4PO644zq+RDa9VlPjSkIS/4svDZoNKcMwDMMwK5oIstixWOz222+/9tprP/nJT374wx/+1Kc+dfLJJ2NIbwWBJj61Wu3IkSPuzb/yyiuvv/46AGzYsKHjS2iqrIzFDLOmyDEAUBKSOKJGU+WCbuZL5YLebSadYRiGYRimp0SgIG+66aY9e/a8+c1vfuGFF7Zv3759+3YAkCTpqKOO8jx+aGho9+7d3V83Wt7+9rfjgyeffPKd73yn49VHHnkEH5AxZGcoCUkMN2qqDGrj1fFEEoQZ2QzDMAzDMP1JBApy//79+/fvdzwZ4HrTnzNp3v3udw8PDx8+fPhXv/qVW0E+8cQTAHD00Ueff/75Pd0G1koaFUtJSKgjlYRU1Ks4IJFhGIZhmD5kAKvRounFPuGEE8If7xebXF5OPPHE88477+GHH/7Rj350xRVXxOMNL55Dhw7dddddAHDJJZegK2RPcTfckMfkOlkCAJyyrSQkRZaURMyo1DjxzTAMwzDLCH4uL/culpSj3njjjeXeQ7+wb9++D37wgwDwjne847bbbjv55JMB4MCBA9dff/3+/fvXrFlz//33r1u3LsxSZ5555tNPP92jfWI8ktzLt2zbzQqSYRiGYZYLTY1Pj20aNAUZQQxy1bBx48abbrrp5ptvfuKJJzRN27x585EjRx577LHDhw8DwM033xxSPvYaR5BSScTApSBJX+KURS6sZBiGYZgeYZiD+CHLCrKJbDZ78skn33LLLc8///yvf/1rfDKVSm3duvWCCy5Y3r35kU2vdVRJamo8m05qqozFlIZZAwCjYk3tWGApyTAMwzCRM2gBSOAsdo/oaRbbzcTsPow1AoCmytn0Ws/x3BOz+7gjh2EYhmGiRUlIC1vfvdy7WGoiiEF+9atf/d3vfhf++KGhoXw+3/11GWJ6bCNKw+CxN9iIwzAMwzBMhCiyNICdNBEoyEcffXTPnj3hj+9PN5+VTpiRidr6eFGPB7TdYNabaiiNSo3NKRmGYRgmGK6DZFY5OBRny+27PUXheDqZUeOoIMmWEgAmZvdyrzfDMAzDBDBoAUiIREF+/etf93vpjTfeeO211x599NHvf//7zz33HADcc889b3vb27q/KNMxGGwHHJAjS6gOlYSUUeOuLm8JADKqzJFIhmEYhmFEIlCQLT1uNmzYcOWVV/7kJz+58cYbL7300kcffVT062aWjJlSuahXC3oV89QYcUQFaVR8NWJuNLVoWjOVrlpw6MsZK1GGYRhmlcF1kL3lQx/6UKFQeOCBB/7mb/5mx44dS3ZdBjEqVr5UrkccZWl6bCMAzJTKVPsY8KefUeMF3STxZ+e4G7Nw8Jl1soQzGN0FlEbFGk8nqWGcYRiGYVYNhjlw8hGWuA7ypptueuCBBxYXF//85z8ff/zxS3lpxjBrYqkv1TsqCakwX9XWxz0NgJDxdDJfKiuyZJhWdnMyN5oCgNzcAspETY1n02upBQfVZEE3C/PVqR0LtAgbCTEMwzCrFY5B9pZEIoEP/vSnP7GCXGI0VdZUuQAmAGRUmf7Q8fmWp++87hyqnsRncqMpjF9q6+NTcwuGaSmyZKQtVJCKHCvqC45FJkdSi6bFg7wZhmGY1YQykGZ5S6oga7UaPjhy5MhSXpdB0DaSzHraxf3tCsXijJ0cNyqWkohhtjpfOujpbjA9thGn44hpcVqcqyQZhmGYFQdnsXvOnXfeiQ+OPfbYpbwuQ4SxjewADEYCwDpZys0t5HeVA7SgQz4qCSm7OamtjwNAvnSQk90MwzDMyoI7aXrIkSNHtm/ffuutt+KPp5566tJcl1kCxtNJo2ItmtY6WRpPJ0W/SU2NZ1QZM9cUnhTlI47wJl1rVCxHbJJhGIZh+hx2FO+Qj3/84wEzaQ4fPvzaa69R/hoAPvKRj3R/UaavwN4awES27TepqfHpsU2UnqYvZ6IhJR1ApwfLR8qb9+Y+GIZhGKZtFDnIz2S1EoGCNE3TNMO6tPzFX/zFF77whe4vyvQnYse3WBfifuD+saCbi2ZTahsAxIS4psbRhAhYRDIMwzB9AzqTDJqIjEBBrlmzZs2aNQEHDA0NrVmzRpblz372s1u2bOn+ikzfosgxCjGiBHQzOZrKzFcBAGsfEaNiTc0tYEeOpsYnR1OaKhsVqygktbN2snvdQHa9MQzDMP0JxyA7ZHZ2tvtFmNWBkpBQINJwbTee/kEOu0pFjkF91qKMz2c3N8oltfXxoh5H/yAAcHgDUVsPgfWXXF7JMAzD9AKOQTJMBAQYTGKjjKedkBi8VBIx0XUSQ5XiKZoqK2Mxw6yh0JzasYCdOvhfx+Sb8XRyemxjQTcnZvdBK8Mgt/pkGIZhmJYMmnwEVpDMkoE2kGhISYNtCApegstyyFOPimMYqTgSxZ8xW2seqFgr6Kamygtb343iMl86CAAYlWwMdZQlNFpHockwDMMwTABRKsj5+fk77rhjcXHx8OHDAYcNDw9v3749wusyKwL08QEArG4ESDkOCDkdJwDUlBlVLuhViiYW9GpmvoorGxWrqFfXyRLqV2zHwZndeDqGSDkMyTAMw7QFZ7E75KGHHrr22mtDHjw8PBzJRZmVhfhPS0nEenQV9DMH+x9zPb6YwHJJc2rHgqgOi7oJAJOjKXHG4+RIKm9P2WEYhmEYxpMIFOQf//jH8PKRGVhQnBX1KgBMjjgDkFFBvdv1aksV0Occms0mSWUCgFI6KMY+x9PJ8XRyYnafUakZpqWpMj7wC0ySTuXIJcMwzGDCvdgdcs011+CDk046aWZm5vjjjz/6aC6vZDwYF8bP9AglEQO9CgCKLGXTa0VpqCQkTY1jgluRpeARAlhbiQWUADBTKudLZQDIqHJRNx0RSk2NAw/1ZhiGGVR4Jk2HHDhwAACOO+64X/7yl92vxjBtMVMqGxVLWx9HqZdNr8XnM2pcU2WsdETZqqkyjAI5DU3M7iuAqchSRo37LY6elHg8ad+CHgfbuhLs0OZ4OjmdTopZco5KMgzDDAg8F7tDcGLhBRdc0P1SDNMWWPVoVKyiHofRei8OxR0nZvdh705Rr2JMUXx1emwj5bv91sdcNgCgwzk+qamykbawlFO0mRxPJ5WEhI3eRqXGlZQMwzCDw6DJR4hEQR577LEvvvjie9/73u6XYphgjIo1UyovmlZGjY+nk4t2eWJBr2YrFqiNI2dKZZJ3BTA9vx0G/4MXV3DUSmqqjCHJ3NxCUTeVRAxjn6RQJ2b3QSuf8zAveaKp8YC6TIZhGGaJ4Sx2h2zYsOGxxx674447Lrnkku5XY5gA0FESAIxKTVPldbKE8ktT46IcxOhjI6HcaY2zW6WhqyVal0+OpHKjKbctEQBk1LhjCk52c3LRtNzjvDuoocRSzvDHMwzDML2Gs9id8M1vfvM973nPM888Uy6Xk8ne9kkwAw7mlAFHSJm13GiqriDtOkiwjSfF5DIVR7YFBhoLuolNOfjkTKlcV4GCr6Sb8XQyXyqLulBbH1fkmJjdHk8nsU98ascCuFLewYFJyr8rstRxuhz/Z8exTIZhmC7hXuwOOemkkyYnJ6empjRN+853vpPJZLpfk2E8wTHZRsVSZAlHGrqbu8UBiTjSsLNrKQkpTK0kCONtSMUaFQuNzemYqbkFJRETMx3U62NUao728OzmZMjpON2kTgbwGzPDMEwv4Cx251xxxRWxWOzGG2/8xCc+MTw8LMtygKHP0NDQzp07I7kuM2jkbPdvTZX91I+SkLLpJHa6dBZ9dKwm/qitjxf1uGFaiizhwO6ZUhlbsDU1DqMAAFNzCwCgJGJoHoQnFvSqGGjEZfFc2rOmyoZZw7sLJR+7Dh/2IgDJTegMwzCDQDQK8rbbbrv11lvx8eHDhw8dOhRwMM+kYbohjKNk74wnNVVWxmKGWVPkGKrAol4VxycumhaqRsW0NFV299OgRXlGldFRCJ9HSyAl3Rifg13keArWUAIAThXvqT7DHbrrNcPD8pFhmAFkALM6ESjIxx9/nOQjw6x6aEwiNoaLUk9JSIt2LsOoWAUwHSdmNyfF0klquNHUOEY060cKiXhNlekUDKlOzO6j3Hov5Bpm1d0rY9MPuxQxDMM4UOTB0o5IBAryM5/5DD7QNC2XyyUSiTe96U3dL8swfQ41hmMVI4YVlYTUNA5RaOhBByJxBft4y5GUx6Q2ajWMR2KFpSM62NSp02zx03GXjDj70QGaFhm2fmUYhmGIQQtAQiQKEnPWb33rW7/97W93vxrD9C2OJAU1hgNANp0cTydRfmVUOQOwaFpKIqaYFoYYHSMWCRze7QmKS6Ni5ZvdKEnAaWocyz2xKWdidi+9hL044oyctvAUoAHDexiGYQaZeovngInICBTka6+9BgAf+9jHul+KYfoW0Twc9ZzYGI7PTO1YaPKhTEio5MQ27fB4ij+MVuJLGSHBDcJMcABYNC18yahYi6aFnkThE9D1aeCVRrxTSUhFvZov1QIkaZ/30PT59hiGWbmwm0+HnHDCCaZpcuaaWcUUdBPHJ4JeRTWGjuLkRqkkJIcPJdgSsLOeHtGNUgz+YbM2UtRNo5Kk5hsQRNI6WXJc2qhYBd0s6lXHJj1xd9IYFUsUlJ4EL9scvu2tkvOp45RxOlFPL80wDDMgRKAgzz333Lm5ue9///tXXnll96sxTB/i0IUoJR2O4mL7CyoY6rkJeQmxxRvdKFEXivFL8Spgy7KCbk7NLWCIUVPjGXvoooiSkMYTSWwARy3Ya0dxTLKTGMWOcmo8ch8c4ahG9zpKQsqo8XWyVP8mwDAMw3RHBAryq1/96tzc3HPPPffzn//8oosu6n5Bhuk3xtPJol7F3uqA8dbkQ5lR445JOcGgBESbycnRVGO+zny1qJtTsJC1/YnwKmD3RGOTTWG+ShlqJRHzm5QDdflbo8eeAhdjn122e4uRUSS/C8dReqwWVfYHZahnvp46hDRVbhlM7R7OmDPMQMGO4h0Si8Vuv/32a6+99pOf/OSHP/zhT33qUyeffPLQ0FD3KzNM/0ARQZJ6ov8OEsaHMje3sGhajvglSUCjYmXmq6ggG6lzACURo5VRzoJeLehVpXQQKyMp6hnc76IkJLFc0lPlGJVadnP9Wtr6uFGx8qVymBpKUTa5e7qDhzR2r7dwSmQGAE3a3fg93wtYPjIMs+qJQEHedNNNe/bsefOb3/zCCy9s3759+/btACBJ0lFHHeV5/NDQ0O7du7u/LsMsMSjsHI7iLREz0TOlMopC1HwkClsuJfZ9i3FEDBbiOkW9ioO23VdX5FhBN7GhZ3IkhVWSfs3aBb2K36enxzZiq7iSkJTSwZY248srm/zy4wzDML2G/SA7ZP/+/fv373c8aVm+nyU8k4ZZ0YSvbjQqFnZnQ71TLwa2zHJE3dAJCHu9SQJqqozNH4pcz1wLG6jHEclI0h3+FK8Ods56ciQ1nm64mhsVy7MusD5lx46GKnIsm15rVGr1cTv2ZB0AoKxxgN+4Z0oXTTTb8icXp0S64bAfwzDMUhJNL/YJJ5wQ/ni/2CTDrDLE7mxsvgFbTjmG0ABAbjQF4KxfxNS5O95JccSApDnOy3H0ABX1qngKzhnPl8oAkFHlRdNyBxrRxqjJrlyWqA8dm9CzVFI5t+BuiPHJlQcJPs3OxQv1ndJKrzTioT4Ms1pZ6f936owIFGQ+n+9+EYZZfbhDlZoanxxNofAK2WTjeZiSkALaZQCgoJtFH9eeLdt2i66W4+lkPdCYkAAgo8bR8UdT5XoRZKMWU8JMTUaVoT5csYauRo1NjjaCrGJ0czyd9HQICrgFfKNIjy67D2WXV+kfrzju8mGYyEGLjP75Z740RKAgGYbxRFPl7OYkBfCUhJRR5YAhNBGC2gsfk1pteNnYGXA6gE4ct4fruJupFVmaHtuEx+fm6hMdRVcjjFYCQDadpOgmprnb3r9pTczuC3niEhg9YuC2mybuSLqFIqFPtsEwzEqHFSTD9BDMTaObN3TqLt4Bmirn5XrLTnZzvfARm7vxALE1xw1pShLBAJBNJwO+Ybs7xzVVNipWBmA8nZyY3SvsLS5OAPOy/o5TZ3rLO8U0ek9VEXa4F1d49plDjwzTO5RE2N7K1QQrSIbpOejmvcRXnBxNZearYsc3teaAnYkOQ240ZVTqVpT0pLY+XtTjfq5G4OrjaZyoxqfHNqHm09bHJ2b3QbO40dR4Np30cxd3y6BoVZGnzML6Ub9X6cTJkVRI26O2rh4VLB8ZpncEfydfrbStINPpNPZZ33vvvaeffjoAjI2N7dmzJ/wKQ0NDTz75ZLvXZRimLVAvOp70nHPTEnQvcizucDWiaGVBrxZ0E3YAhQaLujk5mlJKBwEgo8ZJT+fmPLyEwO5MJ9sj96DInkJXFFu/WzoZ1VuLuqum11TZkGvcasMwKxGug2zNa6+99uqrr4rPvPrqq45ngmE3H4ZZRlpqx5lSGbuzs+mkpsoYSnQMywEvV6PcaCo3BwW96hiirSRinnK22Ow0hC3qWGqZG02Np5OGWcP4HzkHaarcZc4ajcc9u86xYJSeD6/ksHjUTxCHZ6ZUHrRPIIZZNQzgP962FaQsy5IkOZ6R5TbiGTyuhmH6FvcEGlRU4rCcABaFIBzOxQaAbHqt54XcP4q1RHWFqtaLR3FuuKbKubkFrOZs104S7GnjRsUS6zLFPTh6ZRwRUFSf7tk2GTUelZ95xxpUnEXJMMwSw24+odi5c6fjme9973sRbYZhmGXGMGvd/K8QjcexPnJ6bFPAl3LPCwXUEqGgRJcifGZyNDUJkC8dpAhlGP20ZdtuCB1fdMncGmbhHc+jpkSbTE+H9mC6L3/EKkxjthZ+HdT3LDoZJhJoEuxAwZ00DMM0wHJGDPJlVBlncKPvY5hGcnd9ZNCRckM52W6ULWKcNEAcH+fsxDquM1MqL5pWgCpq11LHMTjHMC3PjmxyrMSYa7u03FLL+T1GxSMp77cUhXvXdTeHLXhEEMMMFIscg2QYhsmNprC9GsUZpn3Dl/iEn/o4PbYJdQ/5jYsiFVWR2EsefFHceUE3SUt1IHHc4cCMKovRzeBSxahy2eI20I9pPJ1MffmRgFPa/QDDG+k4AIltQwErjKeTFI0GgGw66TmEnWFWB11+H1uhsIJkGMaJo96xRxXiNFmnPkHHtLBrG68+taNuWl7Uq9NjG/EUPL6omxlV9pzKky8dpMUxookiJqPK2CcevCWHxFFkKYx/UCOwJ3fSju0uYXRcYtG0tty+O3iRkF04Yty3Gz0XZiglKu/6KPY5Z/EowzArnSgV5IEDB2ZnZ3ft2vXaa68FHDY8PLx9+/YIr8swTABib/WSWZqHBIUI5aapXwdHiuMxBd2cmN1Hc8A9B4h7oiSk3Og5wmDx1JZtu0lEamo8o8rBZYsFvSqKTj+LSpozZFRqNAEy4BSwyxCNSi2jytr6oEYcd39PwJEtj+km79yyWYca6sUKy3yprCQkvxmbDLM64Cx25xw4cODDH/6waYbK4LCbD8MsJWJvtabKS2k5gXMOxTHcIiRtRYq6CZBS5BhFy0QJtWhaFI8UoULAdbKEM280VUa5LF5XDBAapjW5Pp4bTc2UykW9igpVWx+fmltoS2YZFcuQa1gBSetj7I0mACEosFBxZtNrC/NVo1Ir6uZK+ezBaenNPk0ebp31t8J+vqBXjdl93cvHlsWgDLOMcBa7Q44cOXLRRRd1vw7DMJHT9AEfhVJBoRZGiTbmHDaP4SZI2opLGaY1UyqPp5NoQu5K73o3a1PKGx0l0ffHc+duxptDs8pYPX4WJutt32kVmo9UEk2mP1jLqK2Pk4KcKZUb4c/6+9PI/Ia5KBKmpVronglV+Oh3mK2VW+TB3e9zy/FCpK0DtoeR6Zabbwk3ADG9YKV8D4yWCBTkN77xDXr8D//wDxdffLEkSWz6yDD9AJYDonbMbg4abB0G9GI0KtZ4OukZC/QjeOSXZwkgmpBPzO6joBeVNrpPp/UN03LLx5lS2dEMhPY3nvaWwsicuuZWZClr96R3ZgOkUdWmWn+mqFfdLTsYEG1LvGJlQkE33aFTvMeiXiVJF1KbirWSDr1VsMVu9yLMc3pkwPEhm81bX3cgP+mZXsNTDTvknnvuwQePP/74scce2/2CDMNECM13aWuSoSdUzYZ1isELthzDnU0nQajMo+mI4rLTYxszapxCaOP1U8zCfBUAtPVxjIYqiRhFOh27ItWrqXGcuwgAjvk6njh60unSU3ML7UYKsZQTiuSKWAAAIABJREFUP2MyquyeiENul5oqK2lpy7b2gm2aKsMoZOari6aFHdDoW0TZ+Vanx0H4RdCDemjWJUwjF2Fh/IyiKqNc4nJM7EnnqOeqpzMnr5VOBAqyWq0CwKZNm1g+Mkx/Et5hp9U6daGmyJJjUrYnwWO4x9NJzOeiqsOeEveR7u6ffOmg3aYd166TAWByJIVC030wqV4sfBxPtwjEiml692Y0Vdaua4qMhkEs5fQUE9nNyaJendphYrwzm06KIhVT1Z5BOCoVNSqWtj6OwlrQgmGV6ORoqrDtcdfiNbf090tJ01R08ckVKvuiQklI6KWq2TM5IbpgKsMsOxEoSExYb926tfulGIbpZ2g+IY5mCXNKcKjPNvQJ1VuNOHPWFQv1MaaevS7RpHqDtx0mTY+yzE8eYYs3AITPRNdble3AIQBkmu3WMWKKwUUQxojjjc+Uyn5Wi+jF2FJ+4YbduWm0kQ82abfvWs6Npgp63NE0Q06fvSNCnRo5+AtV7FqIyZGUeyQmw6xcIlCQxx9/vGVZ999//+bNm7tfjWGYvsWdI156HDnrlkJ2ciS1TpYWTSubXtvy4JZpeqNiUcUhBinXyRL1xCgJSbBMqnd507l+OswxKccwLcNOuwOAkogZFQtU2HndObm5hakdCyj1cEi3kpAm/DudJ0dTU62MGPEq7kXG00l8x6bHNrpjro4+mIxaT/dPjqQmZveJtxx89S7phbFA5JKU4sQTs3sdrWPBF+pnccw44DrIDrn44ovvvPPO//7v/87lct2vxjAMEwzmrKFVgBMh3/IwtEzTi+O8FVnCOCU2WWNQUEyjO7q8A4KFTZewD8ioMvZ0F3QTlSgKsoJeVRJSNr1WkWMTs3udLuiJetxRSUiF+er02KbgYTaGaRVcgTEUhfT2To6koDn9qshSdnMSI2pYcFmsO3o2PkeXQP2E8YpvV4f1btuNkl9ZghDenCtFPqJ/lnu33Pa+6olAQf7Lv/zLnXfeeejQoR//+MeXX3559wsyDMMEEJCz7pKWaXrRqJJq58lRPBhNladgAZpFHo6x8dMK+VI9uukuu8yXDlJeG4SAqJKQinp1plI2KhYaUgZLKL+w6NSOBaoEVRKSoyMHA6X0o1+qundRNLKHbNnW04c6rN1OrH6D/oDxR89fwVL6zvYDg9njH4GCPOaYY+68886rrrpq69atv/vd766//vqTTjqp+2UZhmGWGM80PdqVL5pWRo2jUWVmvgpeLT4B1Ju4K022SpiFx8iimEdGeaQkpEUzBq4oDp7rEG1GxVq3uT62R0yda+vji2bYqTaOBafmFpSxeuWow+4upABq6fLYjcSkqtDOTl9GVtaeHSHGyZGUaCYQ8BscqACkwo7inXHTTTft2bPnlFNO+dOf/nT33XfffffdACBJ0lFHHeV5/NDQ0O7dLWa8MgzD9BqHSaQfmH0GgIJuYliug2JQo2LRB+qiaYmJdVxtciRFwycxAY2O626n8XpXjetjG6OGAJBR46KDTEaNt2yF8d6zaRlmzTBr2OLdMW7zcPHVznKdK0uEESErIPsKnCwP9p6xs6rxqs+NuJ9f3VOFPA3LVj0RKMj9+/fv37/f8aRl+f7z6N1Uw3vvvffBBx/8wx/+AACKolx44YWXXHJJWyscOHDg0Ucf9Xv1qKOOuuyyy7rdJcMwvYT8wwNihJilRaeVyZFUsI5cFGYVYlNLZ5B48vRoHLe9wRU5Zpg1cWD3zuvOIc9wTY3jRETPT2J0I8+NnlO0x+RgaNNxg6KMC7AK0lTZfqOCG7F9VwCA7OakIwgq5kCXTFIse1cKbSCq4Tq9RnzH0LoV/7pWqxtRl38h6B07aESgIE844YQTTjgh/PF+scluqFQqV1999W9/+1t6Zs+ePT/72c9mZ2e3bdt24oknhlznJz/5ybe+9S2/V9esWcMKkmH6mYJuouLBzwO/HpqZUrn+QahX18m+rTYoRrG4EJujO25FRzmLFt+e0ha1WkE3sTvE8Sp6hmftoYiY/qZKR/GTD4ccokZpVKo1fzQ6Wr8d16KSSvTiad36Y1pZH99s1PHifkRz+HXNDSWOUGW04rJjcRCV9KSO7A4qCpYFxx8P/jHkd3X+Vjg8B/qNbvbm6R07CESgIPP5fPeLdMORI0f+9m//ds+ePQBw1VVXnXfeeUeOHHnwwQfvueeeUqn0yU9+8gc/+EHIpebn5wFgeHjYM1B6zDHHRLhthmEipzBfpY9qTLcV5qvB8Ug/qHUahWNmJN6ZMTvuAe2ExtO+oyALdnTHqFhKIpbdnMzvKqPBOB7g6NfBO9LWx0X3nMmRFD4v2kkG4/5cNyrW9NaNuKVFs0UhIzQCus5jyA9oPJHERcTDMPTrCGhRyZ1RsbKbk+6OE/dm/LYXlfJT5NZa1q8ZOewlljs+2hKq1g3/d8UMAhEoyGUnn8+jfLz11ltHRkbwyYsuumjjxo1f/vKXf/Ob34RvEn/yyScB4NJLL/3Sl77Uuw0zDNMjtPXxoh5HvxsAwMwvPnb47KC+1FTZT1zS6OqCXp30P6wlNEHHqNSoMcUTUUngLEpo1dPa3BsuaevjBd3EAko8oIMqQyUh5eYWlISUL5VFYeQpdPBJT1Uh+gGh/MWgaV3imzV0KRIb0sV1qKyTwLAlua+HuZHu5U7Idw9HkAfUmwYrXXwT2r3okoHfUsI0i/S/Gu4F+G9w0NrPYXUoyDvvvBMAzj//fJKPyFVXXbVjx45SqZTP58MoyFdeeeXgwYMA8Fd/9Vc92irDMJ5gttRzqmFb0IRosWEZDQtRkOXmFrCrGicuBlyOktfdzIQ0HBN0zJrfUthDbcg1JRFDU6HgixoVj1Ex7pndGVWmnLh7HrffymIVpvi858FChV9TKA53iDFgDAmjpkSnoS32EEW0Yfcc1uIKjtYyajw3WndWD9hVwPOR4NBJeNfTYxvFjbnxDFXSjxlVxqhzH/rCUFw/+DAcbrla5+4MpjgOZsUryMcff/z5558HgA9+8IPuVy+77LJSqfT73//+2WefPf3004OX+vWvf40PVLXTUnmGYdqHZgkW9XhwlC4M1CuNrdNi8wpdCFNywWFFLI4kE58wl54plR0VUThBRzEto2I5mrhxYo1RqdEYm+mxjeEjGVM7FkgOYr92RpUXTavgnEzYyOCL+W7Hx6FTEnVkwY1d5KhisVKT5vcgnh0kqO/DpEcL9iCi8XR9Bnf3H+qelpwBy06OpDAIKspB1MdgD6D3O9f9qxHVNtmzd3k73S/SMVSYuyoJflcHMAAJHSjIdDqNfdb33nsvarKxsTFMIodkaGgIk8WR8NRTT+GDd73rXe5Xzz77bHywZ8+elgpycXERAI4++ugzzzwzqu0xDNOSRfokNq2CbrbrFk5hRYfOwyF7RaFXZlH4yA/zKRt+mA0ATMzuQ4WU3ZwUT5we24hSzxHvbM4118czhvwcEkObGMPDFWZKZUdgsmjLrAARrKnx6bFN2McDdlgxuzkJtnVLSEWSL5V3XneOMhZDMVTUnQ3jAetk00nHwX75d3QXUhKxSVXW1scdItUN5r49o6pKQpoe2+ge7ROQiXZMMBdOqeXmFsbTyYnKPs9zQ8Z0u2fntedsuX13yMUjj6t1ttpKD+9lOy1xWem0rSBfe+21V199VXzm1VdfdTwTTLRuPiheh4eHTz31VPeriqLgg1Kp9IEPfCB4KWzlPvvssy3L+ulPf7pr166XXnrpuOOO27hx42WXXZZIJCLcNsMwRCNfLLfd0kh5QzJrFF91zBUkZ0RNjUfrviHmlIu6aVSSohZ0qzdnDtQ/u+2JIgwHV4Tmbur4LjQP+MYns+m1OMYG3yVqCsbxiTihsaCb+dJBUY67h2L7vgmmNTG7Dy8RLAg0NZ5NJ7HOUpElvFxRr2IQF/xL7gyzMZd8PJ2kogXwydEr9nhGz9hYdnMS34qMKocpPQz44lHQqwW92usErqbGJ0dTfpPQUfcrCckxnbwlyy7gVrR8BLtmdwDbsdtWkLIsS5LkeEaW23jjhoaG2r1oALVaDQCOPfZYv2tJkmRZ1ssvv9xyqWeeeQYADh06lMlkXnzxRXr+Zz/72be+9a3JyckPfehDEe2aYZgGudFU3S5nvfcswQDaMmsct23tui+4dCPmYVvehZKQMqqMFW+dWZRPjqQwNe+QwiiaMUWOfSeojQpgZtT49NgmEFprHb1EKB/xJQqLZtNrQ1oAGv5WNaJGGU8n6/PEVRn7fnCIDo07BwBHczdaAuGvWMj81mZK5bqObM7ROy6Nn+60N1pNfAcWTcuhfbvssPbeSacWRZoaz6jyeLouEGkKubiaIkv4x1AMfYmQBY5LScdydhnHcIf5n8+qpG0FuXPnTscz3/ve9yLaTCe88sorAPCmN73J74BjjjnGsqwAh3PkyJEjqCAXFxePPvro97///aeffvr//d//7d279ze/+U2tVrvxxhtfeumlK6+8MuTG3Knwp59+OuS5DDNodNzpLJo1igM/AhpWOtxiIJhKxknZNFw7mNxoCj/vw8tH0oWoJAKS7BR8nZi1QDBcpLcFZatRsbAnWgMZB+GgWJyplDNqnMoJ6EMd5QvgwO521JWordfJjf4ko2QV9Cro1YJuKmMSdTs5qhLBS+XgUOypHQui51HjTmUczyMbFSs3v0BJ//oBct1daNGsFwCgqBVbYZRETEnE3JoYQ30kzcXng98QNFd3j6kMcy4INRX0y603itnTHQt61ZjdNz220XGz0Mr13RMsrl16TdaZYZBYcNzWWX7Ht/uO9ZUKXzJWfCcNcsopp/i9dPTRoe7xqaeeOnz4MABs2LDh9ttvP+200+ilX/ziF3//93//0ksvfeUrX7ngggvWrVsXZkHWiwyzBGjr43VXbdPCGBjOBsyocltVjN3jyJiHoa3QI5ml449h7q6gmyg3sV/HfTlaE9Oj3ovYFpsE3SnFBbGJOGQieGrHQn5XGTfTaFQXojjuGdwzlbLY8Q32r1sModH+M2qcUoozpbI7NilWduJ8SFx8plQu2r0+mP42vOZ6GxXLLR+RyZGUmMimbeBtetZi0pp4sF/VqWFaGHClW8Am98nRlKMSNF866OUSH/OchBSAkoi5lSj0PuXdmWYNGf92vuSjVjFFAMsa11wRrBIFWa12+zs+7bTT7rjjjhdffPE973nPSSedJL50wQUX3HTTTVu3bn399dfvuuuuz372s11ei2GYSMBZfyQjxG5Ww+xJqnq5mCmV88J4GGwJMsyaIvu2roudPRhgcyN6Xmbmq9r6+KKZxMRuw8rRttgEVyEgmZznRlO4H2yspj373Y77815T47iZ8XQyo8Yd51JnDwCMp5NTO5zdM6iZMvYitHnPfK4YEFUSMSUhTczuE6+IZZp0Xbfy81QViiw5tK8i10ObRn3gkMfMnuYOHg/FRpA2pTpXT3XrKaTWufbmBzabF/Sq369vxQXbAjbspw7pfyZEvRDC/0865Nu7yuh3BXn48OHrrrvO/fxZZ511/fXXg11ViblsT7DLp2X7TiKR2LJli9+rl1566Re/+EXLsh555JGQO2cYptdg5m65d9FzHCbhKBknZvdiG8rkaMozuBjQ2UNQXIqKBTG1LR6sqbKRrotyxWckI60AaqNOIJtemy8dRFXUMiFYsAd5YziT1hSrJymd7VZaRsUSvTAXTQulm1/gjdLxWDPqsBnC5Hj4qlawk57OXHkiVq8TmPcWZFQb0HgTvLZKwn1idp/DA6jlxmgRxTUByPMwbDYPuax7nx2c2CfrtyR4mnmw+l+ttK0gy+UI3J6SybC5niNHjhQKhYADYrEYAAQ0yqC4PO6449rYn4uhoaFzzz33f/7nf/73f/+3m3UYhokQJSFhmgk/gzVVzqhxLNGjNttlB9OjSkeTFWkF+lDHij1SJEbFysxXyf8SFVvd3CdEZw9uadG0xGnd7oOxWyU45OmGApm4DUwKY6jGMbbbebMuhWRUrInZvRlVDuigF+sycUTkeDqZG01RYjqjypR9zm5OBtyvO7DX8maVRMwdOi3opjHbujMdADxrALB7BprT3x2oKBzLOTG71+9V7Isv6NWAZnMHYiFmmI21pf80u6HKYVAf8vTOCLbS9M2D2/flnmU/CLStIN/3vvdh+3PHDA8P793r/afsZmhoSNM09/NnnXUWPkATn1qtduTIEXeX9yuvvPL6668DwIYNGzreMO0EAI466qgu12EYJiocE2iwJQJVS/8Y/KL1N37SiMWLqCwBoGW2XVPlvFw2bJtGTZUL8x7NMTQ+EU8J09kT3I7jOLLjtxRPFG0+KTJHs7/FIKsnaJeT39UUnsQST8qwN61v/7jzunPoMalJMS6rqTJ2xnTTeW1UatTU5bmNAPAdwKuLK+Ati890FofDkGrw20vmUGHAItG8IB8p9+13PD3GoG+r9WPoru/w6aTVeqEmjYo1OZIKqFV1I+6Es9j9yPDw8Le//e2AA97+9rfjgyeffPKd73yn41VKOpMxpB/FYnHnzp2vvvrqzTff7HnAgQMHACBkGw3DMEuD2wqnf7QjCHaM2H4B0JBrNFSmqMe164IUpJKQpsc2iXN0yH0mI3jxOMYndtDZ0zscmXHUo6SDAWByNJWxf6y3RvlEKMUf/bSIQ+8Gh5egXsdZD6qhysSUfSvV1aiNw8Zw6vVpS4xiLabfqw5J6reTAKXlKI7EhDsVOaCLZ+it1t06scBUscd+auvjYhOSKIXFNz9MJh0ACrq5ZdvuydGUp09nZwrPE9HXCewKivDrr7iS0MjpSkG+9a1v9TNiDCDaMN673/3u4eHhw4cP/+pXv3IryCeeeAIAjj766PPPPz94nfvvv/++++4DgKuvvtotEw8cOKDrOgCce+65kW2dYZjVjiLH6DMJI4KI4ZiX3WqYoZKQKIZnVKyCjuaOTf0xLW2xHVV3PcJxL9iUYFRqSiI2OZISav5MjPfgrnZedw59E8DPdQDIlxpd9u3uAQDE5mWwHZfqAUvTwqwujZTEjeVGUwCp3NxCYceC4oopeiIKNboKZo1D7tyo1MSGsJD3SO/k5EhK7LJyvOo+CwtnybeorfcW+5mKukne7+Pp5ORIqiBUT7pbfNrNRNf/KuYWQqaG/X5NitzCgHOdLImSsWNFqKnxkB5eq4y2FaSYKX7uuedOO+20rVu3/vVf/3W0k2bCc+KJJ5533nkPP/zwj370oyuuuCIeb1TJHDp06K677gKASy655Jhjjgle533vex8qyO9+97tf+tKXHK9+5StfAYDh4eGPfvSjEd8AwzCrF/zAVkoH1zX3oCjCUBny7g4DpvbwQ9HhW6TYQ5mNipUvHXSEZuvd3KalqXI2vbYXRaKeYhFLEgEAhPGSwZBcpndsplTGGkqS3S07qLDpJF8qo3DHS2uqjIWzYn7Z/f7bxZoehYliP5Nf47NRsSZKew17UnZLXRJ+KnfzZmQct6MkpKLdhyTuQVPjjmXFXz3NFm95IeGKcXHKJSpFz1pP8bGmypmReFszcpCCayqmH97yMSFNjqbypYMB2XmxbaslQa5AiVifVF0vMW0ryN27dz/77LP/+I//uH//fgA4cODANddcAwCpVOqWW26h8sSl5NOf/vTDDz986NChq6+++rbbbjv55JNxY9dff/2LL764Zs0aRzf3jh07brzxRgD4yEc+csMNN+CTF1544aZNm/bu3bt9+/Z4PP5P//RPqJWr1erk5OSDDz4IABMTEy2HazMMw4j4jZyhoTJt5ZrFYA+F08K06VCh4UylvK796ZFuDMFGEQC09XF6LIpFvw9dqj7EXU3M7gvQteLd4XVRELeMuRqVuoM35bUdjcYYjHS4h/r5IIqe1e6YH2kR0QhGU+MUBsP0MRrrYF9RB1FAvFBWsOQUW2TEDLL7zRF/74rggY8v+Y1kpMz19Ngmx8TtlnFTTY2jxVKExYvhlxIrgz2hqgP6BU2Opqi4wvGGBFyUOrfC7Go10UkW+/TTT7/33nsBYM+ePf/8z/+8sLAAAAsLC5dffjkAbNq06etf/3rLusMI2bhx40033XTzzTc/8cQTmqZt3rz5yJEjjz32GDqE33zzzY6s9Ouvv/7SSy+BywPojjvu+OhHP/rcc89997vf/eEPf3jeeee9/PLLu3btwl6c0dHRz3zmM0t2UwzDrG7Cd7E4znI8Qx9sOFq6AKYiSz3NqVHTd0aVaRp1UY+LaXoCSzYLukkz9wisPqyHVO1wbMurU/IUM8Wkk2iGiqfCQDWprY87Ct3weVThGM8jzYHPOCYH+skIGtXj0G0ODyZH4YEY0vOETIJonezmJP3ZGBXLPSPbT2AZaPyekACgqFdxFrlQROtrk25UrOmxjePppFGx2h0YU5+oaYv4+g5lKTi/343cpCJUvwix3ybB/naBb29uro0R5yFbplYfXdVBvu1tb3vggQewBvFf//Vfn3vuOQDYu3fv6OjomjVrzj333C9+8YvYK91rstnsySeffMsttzz//PO//vWv8clUKrV169YLLrgg5CJvectb7rnnnttuu+3uu++u1WoPPfQQPn/qqad+4hOf4Pw1wzDLjqbKOBZZVBUkvLCDFbyEJlpkYxY7wBMnDBTaaTJbMa2sHRUTxWLdfkg3PZ2AxB5hGg8TchtiJQDN2saNuXOm2O2BzfuGS3VhODAvl2lCIHrc4JCY+t1tTjoaLxorq7KSkByzYaBZCRl153aTflkF3cRbhuYOZUWuK1cMNBoVa8vtu923n5tbCG4cxnceVSbtgR6LjVm5uQWUjxRJdRq225vvwH61oaFljwk6BCk/bIgOWJBuOUAru18KOFh8XJivoiWqtj6e39WOA1F3/6ZWKBH0Yg8PD59//vkPPfRQrVZ78MEH//3f//35559/9dVXH3744S1btsRisfe+972f/vSn3/KWt3R/rQAuvvjiiy++uMsj4/H45z73uc997nORbo1hGCYyMHQ0MbsPGrGTWiPA42/9SD5HM6XyRGkfAERYEIm6BzWWWyx6XoUa1cGeI9dul8/kSArTwRRLc5jFkKUiWSZhUYE7OuUIIxmmlS+VseM4o8rT6Yb1j3iukpAmR1J1ZSnkx3GyTlGvNh0sS4rcCNPmSwcpOCe6VaMWp2E2qOocUgbHUbrfEAzv4SlYnJeb946loWjGmyIliiJvy7bHPU8RB/wEFgXWm6/xTRC92d0RUzolm07iHRV1E+cAgVfElzLOfn8qbmsnmtjpJ17FbSya1pZtu+vlwpuTfpl994nib3ZwiNLNJxaLXXLJJZdccsmf//zn++677/bbb//Tn/5Uq9Xuu+++++6778QTT7z00kv/7u/+zjEzkGEYhumY+me5GupIwGymnWw1KrVgIyFPMmrcqNTwU7YA9Zgc6b9gSWpULIp+iRO3MerT7k7EFnXH87QrTErOlMozlTIGC7PptcG5Y3DVUGrr456aiZzJRWGqqXFsJCq6Mtqi1hev5fgRtR2WCoiB3sZE8nlvJVTQq1Rtibo2IJ6HIUlHK8nUnHOaH/ak5+YWqDxUSUjZzUkqYPC8HSUh4fEUZIXAKYJCcLSKVkqOBe1LxyYFZ3jHVt2/IApOA0A+4dFVQ+7lAJBRZRLTITPg9iJtf/lZHfTED/L444+/4oorrrjiimq1evfdd//whz88dOjQiy++ODMzMzMzc8opp/ziF7/oxXUZhmEGhIwaRykmdupgOhJNIv0+0gyzJkbL2kocIzSiRpSAYRyVqZFcNAukFabmFpSxRvCSDsjNLeDUnJBlo5j5FQftUMJXU+PTY5uwEoA62Yu6ibWGlMJ2b9uoWAUwHSE0sZJVvJ2CXsXYlWMOHopCCtDib7DeNO2qC8yXDrpl7jpZmimVxZ50N+J8yJZJWLw1bDPCsKW4ZwwiivWmlObGmC7GWT3luCjB7Wecew7ILBu2f35wRltcyh2pdZjs1F2Hmn+D9I+loJvkqdQu7RZgrBp66ygej8evvfbaa6+99o9//OPXvvY1tMt54YUXenpRhmGYVQ9+7BkVi+IfM6Uyigb8sPfTW6g4C2CCEDhsF3IOIhHgN4FahMQr9m3g2GjhVYtCdCiFG8/bH88hRaTjsKLgnl3QzfFEEkWwfe/1nnHDrGGAli6Kp2tqHMsc3fKC6hrJH56edygVkqHGbG16bBO1z2Pw1ag0JnGTSnNfztHl7dingzZq+FSZOsTBDr9hsFZT5YnZfWItIwbqJmb3YU+PkpDWyY1p2n4Xrb9RXuWV9BZhXFMs8C26tKlfbzVFOulrVUaNK/aEKqqs2HntOWL3FdW2gg7F0OZBXndXxb+rzk5fufRWQWJl5H/8x39gkw3DMAwTFZoqi8nr8A2h2NoC4XqfDdujxx3XHE8n3V7WwYj+6hSEq4tRu0yQzMYd28jvKhd1M9v+rB1quMGErP2k1HyMpCQkUCnfWp8kROl1wz/I2vC8FHbbtLJtbV3Xkbo5nkiK5ZuUM8WDKY7Y+NEFJugNwR+0JZSxdYyRxOangiuaODW3UFCrjkgq/WqKupmbqw8Q0lQZaw39DHRQPVMdhdfe6rdDbUP4JxFwO/W4o6ChM2o8m147NbdQ71IyLVSleIMAMD22KaPK+KtE+egIineGkuh85ueKpicKslar7dy582tf+5pDOEqSpGkaWTAyDMMwUaGtjxf1ONaQtawpDN9AQ9G1RdNymNGAIM7ESdMBFzXSFlXpKfZsQ8Uecl3QzeKOqiPdSc0TdnIz1q6CROtNjLGFvPH6YSpAfdRhFbUvRV5BqB+YCnR+MZpNE7E+EpO/mE/HZ+gwUcqgysGCAbH4rzPJgvOm8TE2Y+FoGZrNKObiDdvnSNy5kog1ed/YirMAJr63jlpJcc+NCKt3o3TNnfTPqLI4gNF5O7I0PbaJQu/1LvL5Krn5gBC1pR8xWK7IUm40NVOmVFnOAAAgAElEQVQqi6FTR1jdsZmA8TZKFAarK5EoFaSfcFyzZs3555//+c9/fmmcfRiGYQYQTZWVsRjqkqgiIoYwfZHihfQjCMVtYg46AMe0brGIU2zxURISBsyy6aSSkDLz1TBVfX4ogdabweFYcVdo8UOePhStDAhP0iLiY0Oukbs7NJtEimWgmhrHbwL4LuXm6nFQ7JhG05mAAKQ4QYfulIyvG7pQlgq6SbJpciSlrY+Lbcvj6aT4N+B5U7hzscRWkSX8XU/tWBAlYHZzUlsfd4QqUfDhYHQ6Eh9gvHxqbsGdr8caDMykY+Vry8k34kVpMKPfHYHQfBYQ4I+98PvJ6z4SfN3VSgQK0k84Hn300eeee+4XvvCF0047rfurMAzDMMH49SZ3s6Dn9MWZUpmiOyQ+jHAt4X449MfkaIqaThQ5JgSTouxawCYbaHbq9tsV2D3FYv2ApspCar4eiwoehSIKO7Q0yqbX0ikLW9+NUxxRaeGUyOmxjbnRFAlKPFJ004TmxhTFHjnjF8CjzLu4wuRICt+EfOIgTt/RVJlMRmdK5YJQiClWLmbsbwLkgFMvOU0n8XTUkZrdtkLeN9RsTlFVscsKG1zypYNKIuaW6fQ3gL+ULds8XDOpHcddFIHfAdz9N2L9a4C3EdjfKD57452KPO53zOqmcwXpJxyHh4f/8i//8t/+7d+WciwNwzAM0wto+qKYGafyR9RMGFTDXpAOBu0gjhYfR1DQMZO6s0sQFE+lXg2/LLwixyh/nfGJU06OpjB+RqWiAUMCHRgVC2WifblGIrURCLRHyASkSsfTyWx6LckdCuCJI8Wx79hvBTQtwsd4IthqVbHnAJGDT72Ly3bZxGLZek+3nQQv6lW6HA5UpM5oJSFR5PWof36IbgGXwr5+PMUvyIrtTa3e3aZQqGiNhDebm1sIjh8H1ycAQL5UfuGM90/M7u2gPHcV0LaC9BOOAHDGGWd84xvf4MnRDMMwqwbPFDAFJhGqUwzw9EEpowSO8Cbh4jhGSUiToymldBAAuh/YiAHUkIFMJSFNj20SJ7i4cY8+F6v9MFIFAKK3togYJjRMa6ZUdvsd5m0h6GcCn02vzZcOOk5xzC0UU+R5V5TUYXjuvlklIWXUOFVMKgkJO7Ix600mjkIauobKkm4HO1pEsSUOD0x9+REsDMW6TyUhTe0IUnjUZ40H+xVNKglpplR2TKdEpS7GJtFTCbxy2bSO46X6gse+ueAK0g8IbSvI8847r1ZrKnNWVfUb3/jGhg0botsVwzAM0xX44Y3tI5FHR1DG1dOX6+P0se3n6SOKNgxbosuje2/hVVpLjIplmDVw1TiKbSvj6STmozP+MS13bUDLTnb0pERjcPTucbSJOPbZuJYsLZqWO+pWsL1mCro5PbbRjvzVPBextx1r/rFRwOo5gHFyNNXyDybfXLwIAGi65J4EgxtwmBxRdw6tT185DNvHG2+KymHdXe24Mv4FFvS6SSfeHcbLxfoK1O6iUw91cIuC3k76S2LHEo3JATtoWmiux3Vvz/NNW8V0VQf5ta997ayzzjrqqKMAYHFxMfyJ69at6+a6DMMwTDD04W1UalSfFxUOPYejugNMv0XRVpiv0icx9nDg+GlD8LbsHqq9U2TJSFuiJCKZS5aHba1MpZNYI+h32KJZlzVup8CAxt6CXh1PxALMZTDrjW00jbLRhGRULId8xwpL8e7wDRd9fESwDQWPwd8mJqnFMZWO2DNgB9WusqMEk75OFH10MzX0kKNT04LNzTQIhXLFSgnytMf/5kvlydEUORJgv5F4XSyLHE8nt9y+29neVLE0Vc7vapjGUwM+2N3W+PdJwUuHAPW809VNVwry05/+dAdnDQ8P7927t5vrMgzDMME0dUl31+PSkvFWRWCi9aPDvAZFAAaEcGZMJCKSOkUMlwEQPm7L3EekKFjYOCSaeHUSRphNFqs8s5ubRvw5XBKNSi1gZiAxIzhxGsKQa8KRlZ4plfOlsp8DuUNOzVTKmES2O5kkAJgcTYkileodxXVoEDmWK2zZ5qEgxbPwd+HooXZ3kQOAkogV9So1UKOIdDZTm5bDkQBDvxiwpP4ktI53XFEMpdv7bDRRTdqaFV2QHKfTcMtBo7eO4gzDMMyygM7JRsXqB7M6apKgOkga6Gd3HFsQ0WwPtG/EyKunWgo294kcyiZjlWe998jubinoVWf5oGllE1JutCkhi9Ou7TpC70pQd5XexOxewLak9XHPmSsO8Sq+Y2Jsrx6HKx3EmCuKbyUhubPhaBKJlY7iMBvHRcWuLE2Vm9qkZCmbTmZUebFelVijCkuyeae2J4e7pFGxcnMLudEU/glNzO6jykv6DuMeBY41lJoqT5SahCxtSVPjRsXKzS/gX69DRlee3JkbvdB9m4NA2wry7W9/+8svv9zNJYeHh7s5nWEYhmkJ+uRB3xT4u6OA1MxbmO/KKFtEzNLiBz9E1HyTL5Wx/A57eoxKLevfHK2pMvppU8UeQm8C1tXl5hYKLmFHITq0iMeJKajJxG4YbX08v6vFJBW7dLI6tcP3GEcVpmPKS/ORNRAmRs54ZcPF+KK79BM9Pt3JZRFqGMfTFTlmmLX6sKLb6wsqiZiSkHD0JX4PcewEv0WgZMQg9Dq54TnluDuUpFu2mYpP/QD9jqgDfdFMosvS5Ehq9LwJgK1+t7O6aVtB/vCHP+zFPhiGYZho6efMWoRpZQeUeaRpdVNzC8pYzE+bkr2L34I4uwUAsASQGlmCyY2mcOJ2SGjONRrQAHbqjEJmvkqmOXZbcT2Uu/Pac7Bt2TFOui1EzYSTEh0GQPWJLy4zIyUhoXTD4kIQBh5in4rjQhi9y+8qT80tiJWpuDKZpaNCxfAhCD6dlDvW1DjaZ9LlxBtHX3HXkMkaBk3pd03TDptW0KuaGg+YPYNaU1sfR5PLfvhitrxwFpthGIbpivBTtj2JMK2syDFNlbGMj6JNfvNyxG4bv8BYbs7RTdzU/myYtW4krziIEh3UMd7WCDQ2dyw5fIjIfjJfOmiYTeP4xtPJgDJKauUhTQa2fATXFw+cweN+ngSu6NCEPUaeIcyMGsfNi6/iiWiWTjfeVEW6q4zpbDGiqalybr6pk5oeB7TvKEIYEuyiArfFUr1fx7Q8pWRBr8LcQj5xMKCJanBgBckwDMN0Ds2nCe5NXhqUhDQ5ksqocQDAxguwG0HcNHXblA56akHR4VKMw9GoPZpt3cFuse1DVI3B6zQ0saDDHBMCwe4xJ2NFKigUCvtkAKCuak83bLs1u0bKEsfDiM84BG5uNDWeTk7M7qVQnyjy8kLrD+aFsacK2+HFdcjFHey2Ho+3bn0cU/M4OQa7+3HmzaJpQWM2pow3TsWUCL4nWBggBiMBoIhWPpvrOtIzqa2Y9YJL98YGClaQDMMwTOeQMihAY+zyMkL2jZoqr5Ol4OR4gG8OQh0Y2GVMoiFfOkizrTNqnLp/yOA65PvQVuknNY60PAslqejihBHTgj07h+J8nsNdxMgrRjfH00nqm6FnPHeYTScxJa2pcnZsbb50kOoRHQcbFYv62R3DwXER73JM0zIqlmifjiaOUG+7qYlTlDRVnpjdB3rVLois3yl+xwC7rBPFMcYv3cMePfYQaJ4/OLCCZBiGYTpH9Ajsq8qwlsnx8XSyqFcNuQb+3TaOph9yhBGvQo/JrBt1nuPqorGiH9gC4ufp7W5pB4CMGseGZYy3AUA27TWesVlQouQ1hMmEYDcMOU40aCi2/VtGNWYIdp6OTVILFwAocow6YNz4+SKRJbv7FE2VDbNGSW3DtAqNmekWNoz7/d6xL1vcMxVgYIO8XwbcuU5CIg06yLCCZBiGYTqnaT7NctsGtUuYlgjSalQ2l99VN6Z2DJs2KpbfgEfRWcYvPEnrY9DOUwbhuTOl8kypjF32DsXmiWe3kHsbfmbjmio7xFx+V5k6bPAAVFRKQsJSVLouJbWbF4yLEwgd1pVIbjTlNsXU1Dhm5x23RrinImXTa+uuSQnnm+/o1xF7eoxKo64Ue4DEzVC304DDCpJhGIYJBYobaBYfHcwb7CvCx01FI3TwUp/UngzNUoZSxqRIPNcXyxwDkqQ4FMcQDNiD33+KLIpZeM9lmyZH2+lyrAhcJzudF8UHM5VywzFebngPiZFLat8hJUfOnZ5BU0cPEwizB7HaFW+Kkt1+v0fs+MlWLMcbRUod6i7xSQxak0fmVCO0Wcum12JxQv09ETxNX37zGQFv/uqGFSTDMAzTGown+aVoVyKegjgAcbIOJrIdqkVTZSNddx/0TaQmnMG2xumCAWRAknTR1kxuA3Z3U7xRsfJNCWgPrQaoMnfZAbaElN2cJL1Y1M2ibjqsfDQ17qhTFFt80FjRMbsFy1LR3hx3GDDKyKhYtB/alRj5o3NxwDrqdYyMYkuNKHnHfZw7qV8HhF8luVGS3WZBrxa2PU6rTY6ksJAUKxZiZ7zfbzTRqocVJMMwDNOagm5Sgq+omzMlqU+8yjsGR4eHF8RiGaKfYvBURX4G4+7D3P44bsS53uL7H3Jgtydip4smhCpproxhWuihSL3YFEGkvwpxQZpYTdBAwqJu5hMHce62uzAUl12H3uaCOZGfKKcnt2xrjLp2tG8vmha9IWKrUzadREHv1uv4KxNz9xTprFsOzddtxmtvPmNqbgFGO3ezWrmwgmQYhhksOjMyFD/pDdOamN0X4RjrpQczy2AL4pDu3x1Xv4U0GKeWjpZ7cPSYG/VZf87GFNGBKKPKhllDVUTNOqjYQExbCxpX9L8Ue27A1sqUC0Z9jMdn7GlADho1AHoVAPK7nDWU1Ljt6JFfF6LuUOzocl23BnbIGSOy9LUhYNncaIpMy903oggDFQt61c8NanXDCpJhGGaA6NjIEI+nYXGAbbBdj7FeLkTTwYDM8tKDw/pAsGl0OAR59pg3lWM2N6bkRlNGpX4izWvBNmqs9hPrHR0ykey1xWpXLHAkCUuaLJtO0l+U22fRjbuG0l1niaDqDY4Tk/ClUdqUu8+oMhaDiu3k6FWObpR+a06PbSQLTNwDGgnhM2KUdDBhBckwDDNAUPbNYWQYBgw7TczuwyyhInc7xnoZsdsyYhDF4OyoKOimGPeqm9r4OwSJ4MBuAMi4LB7pR+dMHaF3B7wkGlYQOiLWmP3H1Yr2zGijYhX1qmPwN/ksgq0CPRH34EfLOLEYvkV9PAlAypvS8eJF8c9YU2W/oUqkm8Wenhm7gye7OakkYj8q/u49Z6n98ye0lLCCZBiGYdoAHZujGmO9jIg1ixhXA8HOsE9wlJ8GqKgwTfHkVoMHF8BsaVHufolkaH2YtR07dDvp0JbExpTOMExry7bdWUGhOhqGDLOG0UEsNsUKS883hPrl8V62bNtNU7npXHCUbXjZoWMw+Off/JfpL2/vq7+ZJYMVJMMwzACBY9/wg7azqr6WTt3LCAW92hWCFFcTuy6WHmzgyO8qoycO2D3IUWXbcQK1UbHqXpJevuItQRlqVCxFlqbHNmFGO7hUsbkpO55RZfojbLhC2unvgBVw1qLof4k91/lSudEbrlfRehMAdl53Dp4uupbmRlPkBAmCHxAWaGLHD6pJSspr6+OiAkZtihs49oXfD6Z8BICj3njjjeXewyrkzDPPfPrpp5d7FwzDMN60tNHuK0LulvyGAGA8nQwvBAu6SdYzS98e5Fa9DoNDak/un/goqu3wzfiiFRTad4tLYSvP5Eh9wCDVUEKr1HYwaBsJAJ5jfrAyMqPKfu0yuCWxLZ1y2eLzg/xxzzFIhmGYgaNPhEhLQrphI4ZZd5aB5oK/lmA8qV7cmWgxeDBaqMwRhPCne3hMcHjPc7pgT2k3eq0kpOmxTZ7um467EyeMA4Aix7CAMrgpxxNyBfc0/izqVcO0jF1lBZ2DfMZwE9n0Wpok3rcx+CWGFSTDMAzTp4Rxwya6aa/G4k7owq+nMzpWvfYp1sTsXlwBna4j3l8zjo4TjJ4CQHBHM0JJ85DQgqiqUQ425goGprwJsbk7XyqLFZ/iTEVUt5giFxdfNK3c3ALpRfzrMkxrplTmqYbACpJhGIbpT5pGnvhP+SPQ+xAVJ9o9hg/LLVdxJ4U/RePG8BR0kxS22ArdGcHtRI4p0mL0FAKnckcCNnevkyWyOgK7LBIEM0ujYuHAGLe4LNht4w6zSQAwzJro71jvv66U6zWRCcl2vnR2nfNUQ4ZhGIbpO0hU2c4prZPLi414nlWYr/ZJqzjG6nAANPl4U/8Khj+D59D4Ieoedyt0uwS0E9Fob7CNdRzR00gqa21zco+yRQS9LfFCubmGPZAiSzimHNCiXI+TuHQjNsTUdaGwlKbGJ0dSwlDsxtxtx1uN1qp/PPuqidl9bVmrrhpYQTIMwzB9iuiGHeZ4Gl2tqXEcXR055KcdMPzaQb50kEwElYRUmK9i90ZRj+M0vI7Dn9i7jbq5ywAkDekBL0UoVgjQpdEPCAAy7cy39DNfFFtV8Jfo+bbQhUjS4TcNTZVBrR8znkji+wwARd0kN03HUvQMRVKVhGSY1sTsXuE2639I5KiPM8SLulkvnTz2zTOltq1VVwesIBmGYZj+pa3QDuUW27KnIahxJ+vfvDJTKmOAivKbLZd1FDgu2k0bBb2arVikezojkuQ7VQRSFanbk9x2F4rRFOnpsY2U9Q55IUqFO6o2Rf0Kdg1i8FKYWfaT8oIVZTxrJ7hxkDeglJcl0UtIfB+oKz+bTor95jQiyKg0td0MYPQRYQXJMAzDrB46DsVhs4VY2OepDMREecjuYKeP9zxdwjk8ZlnAJhXqVvZzdvRsCW/r3Z4plUmx5ZubURwxTiUhkU4NIIx6bsQm1cYXDMOsoeU4zpAs+AzUFnfoaOUhYi/8XktnBrOxhhUkwzAMwzQR0LjTQaIcfbzBTt2i7umfoT4F3WwIIzWaoKYnTWnx5mZ5McbZcVVo+G3QTnKjKYAUNZXjTG18ydHYNFMqi53gVBxpwBmw0gxWo4IVJMMwDLPyiPwzG8vpUEAENO5gnzJe3TFYr+6z7ZVAdzzTb4aCnmWCfgWLHYNVm0XdxOGBjleDbS97imMgZMsbx4E3FISeKZXDF8WuJlhBMgzDMCuJ3NwCzsQLYzPe3srNwUI/xKYNgsbhFPW4MraktuR+4LgXv75mAgsKUdjhEBcAyM0t5HfVB89EOOYRY35RrdYjPH/7NA60oFfDeEsNAqwgGYZhmBVDbm6h4bRiWpGnOzsLuc2Uyg1rG9NCf8EId9XZlqZ2LHiOY3HjFnZFu2CxAO05a65K8G3Mpteio3jD30eWfvmU/p6z1B41/vc5rCAZhmGYFUNR6NjtKxpdILKkyO1NxOkFlGMN3/EjoiRi4NNfMmiInUYg/KKzm5Pj6eQFP5yc/vL2Zf/CsCywgmQYhmFWDKKycZSvLSOaKmtqHD1i2jJH7B2iXWIH+8E6RSwV6JM3ebkQ3dSVhES/aG19XElIx77w+374dS8LrCAZhmGYFQN1YLQs71tKlIQ0PbbJMGvQg/l+5GHe1i1jx09hvtqZNWb/qPMASNX19Cri+ugrjmn9gRWOxFFvvPHGcu9hFXLmmWc+/fTTy70LhmEYpluWRqYEQKWfOBu6p8IuuA25My3bI9D+3TCtaHt9PEHbSGwhd7w5g/xxzzFIhmEYhvEGZx8vjUzxw+lh3t0MmwBa9l/TPB6jUnOYGRHuIeA9oqhXsfm9AOaM7U8uDhyP8ForooV86WEFyTAMwwwEAZEkP/Klg26ZssSgw3bdw7yXAciW/deLYr+5j5Z1DAFfmlQ4RohRAYsDx8kqPPxvnAkPK0iGYRhm9VPQTZQX2IizgvREbjSFCmnZa+9IyyqyrzQUh4D3NGKaTa/Fa1Gvj3vg+NTcAn4BMCq1PjHpXE2wgmQYhmFWP6KjjahyghFlyjJW/vX00lToOTmaUuwEtKdARC2LaWI/NZZNJ2kIeE+3ramydp0sjiZqCFy7D50OZg/wXsAKkmEYhln9jKeTRb1aABMAsqGVjVumLAu96+bBzK8iS1i22DI021IU0tTHpRHc4nviHjiuJGKKLWc5ABk53IvdEwa5OYthGKZviXzW8xLQu6bjgm5OzO5Deaqp8Z3XnRPh4m5wyuI6WUKV2dNriReFXgZxB/njnmOQDMMwzKCwsrQj4tl0vOIo6CZOWcQfox1oHsAKfbtWBEPLvQGGYRiGYUIRbeiObMM1Ne7I7KP1YyG6GZLicMVFrkpcFXAMkmEYhmH6F3fTcVTMlMrUVER+ikW9ik8W9KqSkCZHUpGE8XDwI66ZUePdLwi2+6OSkDjQuCywgmQYhmGY/qV33TyUHzdMa6ZUVhJSvlQu2GPHAcCoWEW9Gok+w8GPBd2MyiQS7c2p83ol1iesdFhBMgzDMEy/szTTn92uN+vkyK6rJKTxRGTBwqJexbS4UbEK81VWkEsPK0iGYRhmpbLsPjvdY1QsLDdc+lSsOz+uqTIaHimypCRi2De9xLsKSUaNF3STYpAAgD92tuGCbhbmq5wQbwtWkAzDMMzKg+YvK4nYck2sDgkaynhaEhoVa2rHAmaQjYq1ZB3KiDs/Pj22ETezNCG9bsyVUOpRHSQN9S7q1Xb/HnD6OdZoArdvh4YVJMMwDLPyoPnLimn1s8cNDWvW1Pj02CaHiDTMGqooo2IVdRNgSRUk4thSJO8k6fuMKvvJ4onZfXjvHTfriGe1HOodtNt5ux40urrPQYAVJMMwDLOCQZuYvk1nk7IxTMswa45NKnJMkSV75ExsebbYA0jfY2GlOztc0M2C/c7ko/gCoCRiOPFcab9wk6YgKgkpwrrPVQ8rSIZhGGblgTV8hmkZFSu/q1zUTXeErx8QlY0iN2lEDNRh8lRT5cmRZQhA9ggyCcLfDgQmlyORztn0WnxAIw1dW7IMs+b5EupXnJezxIUEKxpWkAzDMMzKQ1NlZSw2MbuXYpAzpXIffvxPjqTWyRIOaxYFrlGxsPYOABRZ8lNXK3EMIwBkVBmjj2QkXgBTjBNrqpzdnCzqOKZ8bfdX1ALNMrHSESdDTo6klISEXpLobY7CkZPX7cIKkmEYhlmRKAkpo8p1EWY35PYbSsI3rCVa53hm4alSMLs52YfiOIDcaEpbHwcAUSU7bjA3mlqyuk+M9QLATKWcUeNGycLiVHxVSUjaeu/IJRMAK0iGYRhmpTKeTi6aFnZsrKwYEmau0Ton49OmTZWCRd00Ksn+lMh+1AXZKCilgxBRoLF78D2k4lSkHihVl29bKxNWkC2oVquXXnrpu971rltuuWW598IwDMM0oSR887/9D1rngH/7MzXZQO8dxXtEcHJ5yUD9it80NFUu6lWwR+8oCUmReaRNJ7CCbMENN9zw3HPPbdiwYbk3wjAMw6w2AuKmSkLKppPYZRLVIOmBBYUsVkMWdVNJxCZHUoumlU2vNSqWp1Un0xJWkEHccMMNhUJhuXfBMAzDDCLj6eTKSs33OVQNqZjW9NjGetyRk9edMrTcG+hTqtXqxz/+8Z/+9KfLvRGGYRiGYSJGrINkOoMVpAcPPPDABz7wgYcffhgAjjvuuOXeDsMwDMMw3ZJR45oaxx4mDu52D2exnUxMTDzyyCMAEIvFJicnH3jgAU5kMwzDMEyELIvP5Xg6qamyn6840y6sIJ3Mz88DwIUXXvj5z3/+1FNPfeCBB5Z7RwzDMAzTCTmhcaR/mkVmSuWpHQsAoKnyErfS961v6EqEFaSTLVu2XHbZZWefffZyb4RhGIZhOmemVK77ZvfZvL58qUyDamaiGIrNLAusIJ184QtfWO4tMAzDMEy30ERBAFg0+6hxhGaFQyufy4JuFuarADCeXmGG6oMAK8heceaZZzqeefrpp5dlJwzDMMwAMp5OFnXTMC1FlvpkJAzi8Pf2O0wcHb5oWv1gHe/+ZB9kWEH2CtaLDMMwzDKiJKTpsU2GWVPkWMsAXkE386WDqOp6ne8OOajGMGs0Otyo1Hq6pZC4P9kHWVOygmQYhmGY1Un4xpF86SCOWDRMq6ib2T4wM1fkGM11xNk8TF8xQAry8OHD1113nfv5s8466/rrr1/6/TAMwzBMv4HVk4ZpFZe7/0ZJSJOjqYxdB7lc22D+//buPiyKcv/j+A0LCFFcQg968PgDNVFULhWFwCMJZNmDHBHqeEzSSJNSL+mUiVlWehAkO3n5mIqpaEWmmT3YwRKDMFPARL0oUzGIfEKDvbBlF2KX3x9zzv748STDDsyy+379Nc3sznydu9HP3nPPPa2xowRpMpmY2REAgObGDehZWqnP+e8DLqWVhu2Vl6X+SxVDZDvvd0MVdpQgHR0dw8PDm68PCAjo8loAALAi0mzbS7/8OaekyvwEd2mlwaoe4oZVsaMEqdFoNm3apHYVAABYI18v121/95cm0Mktqcop0fp6uY4b0FPtumCl7ChBAgCAtkk3jnNKeo47r/X1cmUAIlpDggQAAP8PAxBxU45qFwAAAIBuhgQJAAAAeUiQAAAAkIdxkDfB49sAAABN0AcJAAAAeeiDBAAAatpecDm3RCuEmBHUm2fAuwsSJAAAUE1ppSGj4LL0QsXSSn34HBJk98BdbAAAoJrSKn1po3cnmt+pCCtHHyQAAFDNf96CI6qEEOMGePp6uapdEdqFBAkAANQkvY9bCMEgyG6EBAkAAFRGdux2GAcJAAAAeUiQAAAAkIcECQAAAHlIkAAAAJCHJ2kAAOg6rx/4ObekytfLjfevoFsjQQIA0EVySqoyCi+XVhpEiVbwADK6M+5iAwDQRXjhitWiaeSiDxIAgC4SPsAzd4A2R1T5erqOG9BT7XIghNQxXHCltFLv6+U2bkDPJ4P+pHZF3QMJEgCALuLr5Sq9f8XX043X91mJnPPa7QWXhRCiRFtaqX8y6E+llQbpHTmkyTaQIAEA6FIMfyaHd50AABzvSURBVLQqZVX/7/51TknV0gM/55Rofb1cSysNr0/op1ZhVo4ECQAA7NeMoN5Sj6MQYtwAz9JKQ06JVghRWmloEi7RGAkSAADYr/ABnl8/G1hapZeWc0qqpN5HIYSPJyMNWkWCBAAAds3Xy9U8LDV8gOdrD/TLLdH6eLoyDrINJEgAAID/82TQn8iON8V8kAAAAJCHBAkAAAB5SJAAAACQhwQJAAAAeUiQAAAAkIcECQAAAHlIkAAAwN7llFSZ30yD9mA+SAAAYNdeP/BzRuFlIcSM0X/iRdjtRB8kAACwX6WVhtySqtJKg3lB7Yq6BxIkAAAA5OEuNgAAsF++Xq4z/vsOwxlBfzK/IBttI0ECAAC7xouwO4C72AAAAJCHBAkAAAB5SJAAAACQhwQJAAAAeUiQAAAAkIcECQAAAHlIkAAAAJCHBAkAAAB5SJAAAACQhwQJAAAAeUiQAAAAkIcECQAAAHlIkAAAAJCHBAkAAAB5SJAAAACQhwQJAAAAeUiQAAAAkIcECQAAAHlIkAAAAJCHBAkAAAB5SJAAAACQhwQJAAAAeUiQAAAAkIcECQAAAHlIkAAAAJCHBAkAAAB5SJAAAACQhwQJAAAAeUiQAAAAkIcECQAAAHlIkAAAAJDHSe0COoVWq42JiRk1atTKlStlfbG8vPzYsWOtbXVwcIiNjbW4OgAAgO7NNhNkUlLSxYsXBw4cKPeLH3/88fr161vb6uLiQoIEAACwwbvYSUlJOTk5Hfvu+fPnhRAajcalJc7OzkoWCls0aNAgtUuAamh9u0XTww7ZVB+kVqt94YUXDh8+3OE9nDx5UggRExOTnJysXF0AAAA2xXb6ILOysqKioqT46O7u3oE91NbWXrlyRQgREhKicHEAAAA2xEYSZHx8fGJiYkVFhZub24oVK4KCgjqwk6NHj0oLAwYMULQ6AAAAm2IjCVIavxgZGfnFF19Mnjy5YzspKysTQjg5OTGiBQAAoA02Mg4yIiIiNjZ2+PDhluzk1KlTQojhw4cbDIZ9+/YVFhbqdDp3d3d/f//Y2FgvLy+FigUAAOjebCRBLlu2zPKdnDt3Tghx/fr1cePGVVdXm9fv379//fr1r732mqzeTToy7RZNb89ofbtF08Pe2EiCtJzJZJISZFlZmZOT0yOPPNK/f/8bN2788MMP+fn5er1+0aJFOp0uLi6uPXv76aefOrleAAAA1ZAg/+P06dNGo1EIMXDgwLfffrtv377mTXl5eYmJiTqdLjU1NSwszMfHR70yAQAA1GcjT9JYrm/fvhs3bnzjjTe2b9/eOD4KIcLCwhYvXiyEqK+vf//991UqEAAAwFpYex+k0WicM2dO8/UBAQHz5s1T8EBeXl4RERGtbY2JifnnP/9pMBiOHDmi4EEBAAC6I2tPkCaTqcOvKFSQo6NjcHDwN99888svv6hdCwAAgMqsPUE6OjqGh4c3Xx8QEND1lQghHBwcuvi4AAAA1sbaE6RGo9m0aVMXHCg3N/frr7+uq6tLSUlp8QPl5eVCCB6jAQAA4Ema//j8888zMzM/+ugj6c00TZSXl5eUlAghgoODu7w0AAAA60KC/I+HHnpIWkhPT2++NTU1VQih0WimTp3apWUBAABYH3tMkF9++WVgYGBgYGBaWpp5ZWRk5JAhQ4QQu3fvfvPNN00mk7Req9UmJiZmZ2cLIeLj4/v3769KzQAAANbD2sdBdob6+nqdTieEqK2tbbx+48aNU6dOvXjxYnp6+rvvvhsaGlpTU1NYWFhfXy+EmDBhwosvvqhOxQAAANbEHhNka3r16rV3795169ZlZmbq9fpDhw5J6729vWfPns39awAAAIlDQ0OD2jUAAACgO7HHcZAAAACwBAkSAAAA8pAgAQAAIA8JEgAAAPKQIAEAACAPCRIAAADyMB+kkj755JPs7Oxff/1VCOHr6xsZGTlx4kS1i4ICLG/Z8vLyY8eOtbbVwcEhNjbW0iqhNq1WGxMTM2rUqJUrV6pdC5TU4ZblwrdVWq32448/PnHixK+//trQ0NCnTx8/P79HH33U29tb7dK6DvNBKqOysjIhIeHUqVNN1gcFBW3YsMHDw0OVqmA5pVp2zZo169evb22ri4vL6dOnO14lrENCQkJOTk54ePimTZvUrgVK6nDLcuHbpM8++2zJkiV6vb7Jeicnp6SkpOnTp6tSVdejD1IBJpNp1qxZxcXFQojp06eHhoaaTKbs7Oy9e/cWFBTMnTt3586dateIjlCwZc+fPy+E0Gg0Go2m+VZnZ2cFy4YqkpKScnJy1K4CyrOkZbnwbc/BgwcXLFgghPD09IyLixs6dKgQ4syZMzt37vztt9+WL1/u7OxsJy+xI0EqICMjQwoZa9eufeCBB6SV48eP9/f3X758eX5+/p49ex599FFVa0RHKNiyJ0+eFELExMQkJyd3XsFQhVarfeGFFw4fPqx2IVCY5S3LhW9jjEbj0qVLhRDe3t4ffvjhnXfeKa2PiIiYMmXK3//+97KysrS0tAkTJnh5ealaaVfgSRoF7NixQwgxduxYc8iQTJ8+PSgoSAiRkZGhTmWwjFItW1tbe+XKFSFESEhIJ5QJNWVlZUVFRUkhw93dXe1yoBjLW5YL3/bk5uZWVFQIIZ5//nlzfJR4eXktWrRICKHX6/Py8tSpr2uRIC114sSJS5cuCSGio6Obb5VGSZ89e/bChQtdXRkso2DLHj16VFoYMGCAojVCZfHx8YmJiRUVFW5ubitWrJB+V8AGKNKyXPi257vvvpMWHnzwweZb//KXv0gLx48f77qa1EOCtJR5HPSoUaOabx0+fLi0IN0MRTeiYMuWlZUJIZycnAYNGqRcgVCfNMotMjLyiy++mDx5strlQDGKtCwXvu2Ji4vbvHnz6tWrWxzDqtPppIUePXp0bV3qYBykpaQAodFoWnyG39fXV1ooKCiIiorqysJgIQVbVnqUe/jw4QaDYd++fYWFhTqdzt3d3d/fPzY21h6Gy9iqiIiI2NhY888J2AxFWpYL3/b4+Pj4+Pi0tvXAgQPSQov9DraHBGkp6Xn+W265pcWtjo6Orq6uBoOhpqama+uCpRRs2XPnzgkhrl+/Pm7cuOrqavP6/fv3r1+//rXXXqP7qptatmyZ2iWgUyjSslz4dqWmpmbz5s1CiNtuuy0iIkLtcroCCdJStbW1os0ua2dnZ4PBYDAYurAoKECpljWZTNI/JGVlZU5OTo888kj//v1v3Ljxww8/5Ofn6/X6RYsW6XS6uLg4ZesHoCIufHuzcOFCaej8c889x11syHDXXXe1tsnJiZPcjVnesqdPnzYajUKIgQMHvv3223379jVvysvLS0xM1Ol0qampYWFhbdwcAdC9cOHblVdeeeWrr74SQtx3333286uAJ2mUodVq1S4BncLylu3bt+/GjRvfeOON7du3N/5XRAgRFha2ePFiIUR9ff37779v4YEAWA8ufDthNBqff/753bt3CyFCQkJWrVqldkVdhwRpKUdHR/HfO54tqqurE0K0+EICWDOlWtbLyysiImLSpEl33HFH860xMTGurq5CiCNHjlhULgBrwoVvD6qrq5966qn9+/cLIcaOHbt582Y7uX8tIUFays3NTQjRxuMUUgRhquFup2ta1tHRMTg4WAjxyy+/WLIfAN0IF74NKC8v/9vf/ibN+hkdHZ2enm5X8VEwDtJy0lQver3eZDJJvVaN1dbW1tfXCyEGDhyoQnGwQJe1rLRzBwcHC/cDoBvhwu/WCgsL582bV1VVJYR47rnnnn32WbUrUgEJ0lLDhg2TFk6ePDly5MgmW813KMzTB6K7UKplc3Nzv/7667q6upSUlBY/UF5eLoRgND1gS7jwbdiRI0fmzJmj1+tdXV1TU1MffvhhtStSB3exLTVmzBhpJJz5ZUeNFRUVCSGcnJzGjh3b1ZXBMkq17Oeff56ZmfnRRx9JL6hoory8vKSkRAgh3dICYBu48G3VTz/9NG/ePL1e7+HhsW3bNruNj4IEaTkPD4/Q0FAhxHvvvdfkud3r169Lz9lNnDixxTcgwZop1bIPPfSQtJCent58a2pqqhBCo9FMnTpVkbIBWAMufJtUW1s7d+5cnU7n4uKyZcuWwMBAtStSEwlSAQsWLBBCXL9+PSEh4dq1a9LK8vLymTNnVldXu7i4zJkzR9UC0UFyW/bLL78MDAwMDAxMS0szr4yMjBwyZIgQYvfu3W+++abJZJLWa7XaxMTE7OxsIUR8fHz//v275g8FQFlc+PbjnXfekYYfjB49+ty5c3taUVhYqHalXYFxkArw9/dfvHhxSkpKUVFReHj46NGjTSbT8ePHpelkU1JSGOnSTclt2fr6ep1OJ5rNAbRx48apU6devHgxPT393XffDQ0NrampKSwslJ7FmTBhwosvvtiFfywASuLCtx+ZmZnSwpEjR9qYiemxxx4bPXp0VxWlGhKkMmbMmHHnnXeuXLny0qVL0rP9Qoh+/fq9/PLLYWFh6tYGSyjSsr169dq7d++6desyMzP1ev2hQ4ek9d7e3rNnz+Y2FmCTuPBtjF6vr6ioULsKK+LQ0NCgdg02pbi4+OrVq0KIPn36DBo0SO1yoBhFWtZoNBYWFt64ccPR0fF//ud/7r77bkVrBGCNuPBhk0iQAAAAkIcnaQAAACAPCRIAAADykCABAAAgDwkSAAAA8pAgAQAAIA8JEgAAAPKQIAEAACAPCRIAAADykCABAAAgDwkSAAAA8pAgAQAAIA8JEgAAAPKQIAEAACAPCRIAAADyOKldAAAAgDU6fPiw0WhsbauXl1dAQEBX1mNVHBoaGtSuAQAAwOoEBgbqdLrWtoaHh2/atKkr67Eq9EECAAC0YMKECbW1tc3XZ2VlGY3GIUOGdH1J1oM+SAA3kZaWtmvXrta2uri4eHt7//nPfw4ICHjkkUe8vb3l7j8yMlKr1bq7u+fl5VlWKdolLCxMp9NxwoGO2bBhw+rVq0NCQjIyMtSuRU30QQK4idra2jbu4+h0uqqqquLi4gMHDqxateqZZ56ZP3++rP3X1NS0sX8oTqfTccKBjvn+++9Xr159++23/+tf/1K7FpWRIAG0V58+fQYOHNhkpcFg+OGHH6qrq4UQRqNx/fr1dXV1CxYsUKNAAOhERqNx0aJFQoikpKQ77rhD7XJURoIE0F7h4eGvvvpqi5uuXr26fPnyAwcOCCHS09OjoqIGDRrUzt2mpaX98ccfGo1GsUIBoBNs3bq1rKxs5MiRkyZNUrsW9TEfJAAF9OrVa82aNUOHDpX+c+fOne3/7rhx48aPHx8REdE5pQGAAmpqajZv3iyEeOmll9SuxSqQIAEoZtasWdJCYWGhupUAgLJ27txZXV0dHBw8fPhwtWuxCtzFBqAY88CgiooK88rk5GSDwTBy5MjY2NgdO3bs2LHj2rVrAQEBjz32mHQnKDU1VafTubq6vvLKK+ZvSSulb12+fPmdd97Jycm5evWqs7NzSEhIXFzcmDFjpE+eP39+69at3377bWVlpYeHx5gxY5566il/f//Wijx9+nRmZmZRUdGlS5eEEP369RszZsy0adPkPkXeuMJr165t37798OHDpaWlDg4OgwcPvu+++6ZOnXrrrbc2/srrr79eX1/v7u7eYh/Gjz/++N577wkhQkJCJk6c2AWnQghx4cKFrVu35uXlVVZWenl5BQUFPf7444GBgW18RdYJvGnrA93FBx98IISYPXu22oVYC2bzAXATy5Ytk5LNtGnTWhsHKTly5Eh8fLwQ4rbbbjN3Q0pT8kZHRw8ePHjFihXmD/fp0+fQoUNCiJCQkKqqKnd39++//968VVoZHR09YcKE559/Xq/XNznWwoULZ86c+dFHHy1ZsqTJSyM0Gs2aNWvGjx/f5Ct6vf7VV1/99NNPm1fu5OS0cOHCGTNm3Oxk/B9zhVFRUc8999yNGzeafOCuu+7atm3b3XffbV4TEBBQV1fn6el59OjR5js8ePDg3LlzRbPzrPipkFrE3d09OTk5KSmprq6uyQ7/+te/Jicn9+jRo8n6DpzAm7Y+oCytVhsTEzNq1KiVK1e28bFPPvkkOzv7119/FUL4+vpGRkY2/tnWnPSXW+/evXNzcxWuuNuiDxKAYn766SdpofldntLS0s8++0wIodFoHBwc6uvrY2JibrrDM2fOfP755/X19aNGjRozZoxGo8nLyzt+/LgQQppK44033tBoNA8++GBgYGBFRcWBAwfKy8uNRuNLL70UFhbWOAMZjcann366oKBACOHp6Tl58mRp1GZhYeG+ffv0en1KSkpNTc2zzz4r64989uzZuXPnGgyGwYMHh4SE+Pr6Hj9+/MCBA3V1dRUVFfPnz//iiy9k7bALToWktrb2H//4hxAiODh40qRJt95664kTJ3bt2qXX6z/99NOGhoY333yz8ectOYEda32gA5KSki5evNh81gizysrKhISEU6dOmdcUFxfv37//gw8+2LBhg4eHR4vfysrKEkJERUUpXnA31gAAbVq6dKmfn5+fn9/SpUvb+FhFRUVoaKj0ya1bt5rXjxw50u+/MjIyjEZjQ0NDQUHBL7/8In3gnnvu8fPzGzlyZOO9SSv9/Pz8/f3379/feNP8+fPNOwwNDT179qx5k8FgiI6Oljb9+9//bvyttWvXSuunTJny22+/Nd5UWloaHh4ubT116lQ7T4u5Qj8/v927dzfeVFJSYt767bffmtcPGzbMz8/vnnvuaXGHX331VYvnWfFT0bhFtm/f3uRUjB07Vtr0zTffNN7UsRN409YHFLRw4ULpf7bZs2e3+AGj0Th58mTpM8nJydnZ2V999dWiRYukNXFxca3t+d577/Xz8ysoKOi02rsfnqQBYBGj0fjjjz+mp6dPmjTpt99+E0L07t378ccfb/7J6dOnT58+3dHRUQgxevTovn37tmf/06ZNe/jhhxuvaXyr9NVXX23c2dCjR4+nnnpKWj558qR5fU1NjfT6Wg8Pj40bN3p5eTXeoY+Pz4YNG6Tlt956qz1VNfbkk08++uijjdf079/fXGRRUZHcHbZGkVPR2GOPPdbkvrOPj495nmTpsVOJ5SewY60PtJNWq505c+a+ffva/lhGRkZxcbEQYu3atS+//HJkZOT48eNTU1NffvllIUR+fv6ePXuaf+vq1atXrlxxcXFpe4iwveEuNoD2eu+996QBkW1wdXVdtWpV83umQogm6aedoqOjm6wx3yJ3cXF54IEHmmz19PSUFhoPTMzOzpZG+02ZMqVnz57Nj+Lv7z9ixIiioqJjx45VV1e3dierRU3io2Tw4MHSwpUrV9q/q7YpcioaS0hIaL4yODh48ODBZ86cyc/P12q10umy/AR2rPWB9sjKylq+fLn0AJ+7u3sbr1zasWOHEGLs2LFNrpfp06d/+eWXBQUFGRkZza9o6TfYiBEjpJ9AkHAuAChmxIgRH374YYs/0zUaTQemwNBoNM0fJTbPPT5w4MDmf6G3+Ff8N998Iy200YUgdeAZjcYTJ07IqrDFEVfmDG0ymdq/t7YPpMipMOvbt29rHYHmljI/DmXhCexY6wPtER8fn5iYWFFR4ebmtmLFiqCgoNY+eeLECWkCgeY/xoQQsbGxQoizZ89euHChyaaff/5ZCCF3ugabRx8kgPby8fEZNmxYk5WOjo6urq5BQUEBAQH9+/dv7buurq4d+Pnu4uLSxrfuvPPOdu7n999/lxYWLFjg4uLS4mcMBoO0IL2hsZ1cXV3b/2FLKHUqzMy9pM0NHz58165dolHnpYUnsGOtD3tw6dKl22+/vcW7Fo1duHChtb9ezp8/L4SIjIxcsmSJt7e39MhLi06fPi0tjBo1qvlW84+c4uLiJscqKysTQvTu3bvtIu0NCRJAe40dO7bt2Xza0FrsaJtSscMcbnQ6XRt3uCS1tbWKHFRZiiewNlrEyek//zSY5way8AR2rPVhDzZs2HDhwoUtW7bccsstrX0mNzd3zpw5+/bta7G/PyIiIjY2tj2d3NIISI1G02Jvoq+vr7RQUFDQ5JnrlJSUlJSUm+7f3pAgAdg+c/xavny5s7Nz2x8eMWJE51ekviYzRzZmvvNuvkvOCUQnWbJkyaxZs2bNmtVaiMzLy5szZ87q1atbm6Bn2bJl7TyWNJdqa1FVup1iMBhqamrauUM7R4IEYPvc3NykhUGDBgUEBKhbTGvq6+u78nDmG9PNlZaWSgu33XabtNAtTiC6ox49emzZsqW1EJmXl/fMM8+sXr26+QsCOkDqHW/jjrmzs7PBYDD3uKNtDEwBYPvMj4yYB0I19+OPP+bn5//xxx+dV4bUk9da59/Fixc779DNtfHucvMMROZeHys5gbBJUojUaDSzZs1q3P+nbHw0u+uuu1rbZB6/gfYgQQKwfffff7+0kJmZ2eIHTCZTYmLiE088MWzYsNZmT7Sc1JOn0+laDJHZ2dmddNwWGQyGI0eONF9/6dIl6cUzAwYM8PHxkVZayQmErWoeIjspPgohtFqtsju0WyRIALYvMDBQevT47NmzTV7WJ1m7dq30uOWQIUM6b94ZaSoco9HYfFrNjz/+WHpFYVd6/fXXmzw3Lb0FUQq4cXFx5vVWcgJhwxqHyKysLGnso7LxUboJ0MajctKkp+bhv2gbCRKAXUhJSZFuUaWnpycmJp47d05af/ny5WXLlkmvVNFoNB1+2Lw9IiMjpYW0tLRNmzZdvXrVZDKdPHnypZdeWrRo0e233955h25RWVnZ448/br6dXVxc/MQTTxw9elQIMWLEiCYvFrKGEwjbJoVInU6XmJiYnJyseO+jdBOgjQdlpHDp7u6u7HFtFbf8AdiFoUOHrlu37oUXXtDpdFlZWVlZWU5OTk5OTuZR805OTmlpaSNHjuy8GmJiYvbs2XPixIn6+vq33nqr8QsA3d3d16xZM23atM47ehPh4eFarbaoqGjatGlOTk6Ojo5SB4wQYujQoW+//XaTz1vDCYTN+/bbb8+fPz906NBdu3bdf//9bUzx0wHSJD56vd5kMjWfHqu2tlZ6mq21h77RBH2QAOxFRETEJ598EhUVJfWl1dfXS+lHo9Hce++9e/funThxYqcW4OjouG3btlmzZjWZhzw4OHjPnj2jR4/u1KM34ezsvG3btilTpmg0mvr6eik+urm5Pf3005mZmU3efC1R/QTCth06dGjevHmrV6/OzMx0d3ePj49XdmId8wsRWhyqax4WbJ4YEm1zaGhoULsGAOhSRqPx2LFj0nQ2PXr0CAoKUraroz0FfPfdd7///ruLi8vQoUN79erVlUdvorq6+vjx47W1tbfeemtoaGh7BoGpfgJhew4ePJiYmGge+1hbWztv3rzq6ur09HRZ76lPSEjIyckJDw/ftGlTk03V1dUhISFGozExMXHOnDlNtq5atWrjxo1OTk5FRUU3nfQUggQJAADU1SQ+SjoWIttIkEKImTNnHj58+I477ti/f3/Pnj3N669fv/7QQw9VV1dHR0enpaVZ+MexE9zFBgAAqjl48OD8+fObP3ndo0ePdevWeXh4PP3007LeVt+GBQsWCCGuX7+ekJBw7do1aWV5efnMmTOrq6tdXFya902iNSRIAACgjkOHDiUmJq5bt67FJ68bh0hFxkT6+/svXrxYCFFUVBQeHj5jxownnnhiwoQJZ86cEUKkpKSY50DFTZEgAQCAOsrLy9etW2ee6Ko5KUT6+/tXVFQocsQZM2asWrXK29u7vr7+6NGj+fn5RqOxX79+W7ZsiYqKUuQQdoJxkAAAwO4UFxdfvXpVCNGnT59BgwapXU73Q4IEAACAPNzFBgAAgDwkSAAAAMhDggQAAIA8JEgAAADIQ4IEAACAPP8LM+6yr8FduG8AAAAASUVORK5CYII=\" alt=\"Minimum torque vs. prime on linear scales\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 166.9px; text-align: left; transform-origin: 385px 166.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA2sAAAKQCAIAAACO9XWpAAAACXBIWXMAABcSAAAXEgFnn9JSAAAAB3RJTUUH6QgOCzIVociDYwAAACR0RVh0U29mdHdhcmUATUFUTEFCLCBUaGUgTWF0aFdvcmtzLCBJbmMuPFjdGAAAACJ0RVh0Q3JlYXRpb24gVGltZQAxNC1BdWctMjAyNSAwNjo1MDoyMZbPr6YAACAASURBVHic7N1/fJNlnu//Dy2FpAinCT+Wtl8PKYWpwCijUDyyeAg9LrgeOSugI6NCYdVF0B53RlxcWOXHCIvDjq6Di3p2lBZFy6IwzOgMMAqpyyA0/BQr8iMStpYCYpKBGRtaWr5/XO3NTdqkudOGtLlfzz/2Ee7czX21jNs313V9PleXy5cvCwAAABC1lEQPAAAAAJ0MCRIAAADGkCABAABgDAkSAAAAxpAgAQAAYAwJEgAAAMaQIAEAAGAMCRIAAADGkCABAABgDAkSAAAAxpAgAQAAYAwJEgAAAMaQIAEAAGAMCRIAAADGkCABAABgDAkSAAAAxpAgAQAAYAwJEgAAAMaQIAEAAGAMCRIAAADGkCABAABgDAkSAAAAxpAgAQAAYAwJEgAAAMaQIAEAAGAMCRIAAADGkCABAABgDAkSAAAAxpAgAQAAYAwJEgAAAMaQIAEAAGAMCRIAAADGkCABAABgTNdED6BDWLVq1X//7//97rvvbvHdioqKvXv3/td//dfw4cP/8i//0m63X+PhAQAAdChdLl++nOgxJNi6deuee+65++677/nnnw95q76+ft68eb/5zW+0K1ar9fnnnw+XNQEAAMzA7KvYH3zwwXPPPRfu3Z/+9Ke/+c1vbrrpptWrV3/00UcLFiy4fPnyU089tW/fvms5SAAAgA7FvAny4sWLL7zwwlNPPRXuhq+++urdd9/t06fPG2+8MXr06Ouvv3769OkrVqwQkZ/97GfXcKQAAAAdi0kT5P79+//6r//6zTffzMrKevDBB1u8Z9OmTSLywx/+sFevXtrF8ePH5+Tk7N+//6uvvrpGYwUAAOhgTJogDx8+fPr06UceeeTDDz8cOnRoi/d89tlnInLTTTeFXB8+fLiI7N+/P96DBAAA6JhMWos9atSojz76KCsrK8I9Bw8eFJEbbrgh5Pr3vvc9Edm/f/+UKVPiN0IAAIAOy6QJctCgQa3eEwwGRaRfv34h1/v06aO9CwAAYEImXcWORn19vYikpqaGXFdXGhoaEjAmAACADoAEaRgdNAEAgMl1jlXsQCAwefLkESNGqGY64WzatOnjjz/++uuvRcThcBQUFLSl9XfXrl0vXbpUX18fMg156dIlEUlLS4v5kwEAADq1zpEg582bV1VVNXjw4HA3+Hy+WbNmqepppaKi4sMPPywtLV21apW+HU/07Hb72bNnT548OXDgQP31//qv/1LvxvCZAAAASaATrGLPmzfP5XJFuKGhoeGRRx5R8XH69Omvvvrqv/3bv02ePFlE3G73448/HttzVdee5n0f1RX1LgAAgAl16AQZCAQefvjhX/3qV5FvKykpqaioEJGVK1cuWLCgoKDgjjvu+Od//ucFCxaISHl5+XvvvRfD00eMGCEiu3bt0l9saGjYvXu39i4AAIAJddwEuXnz5okTJ+7YsUNEevToEeHONWvWiMiYMWPGjx+vvz59+vT8/HwRKSkpiWEAf/M3f9OtW7d169YdPnxYu/jyyy/7/f6CgoK+ffu2+gkrm1RVVcUwAAAA0AGVl5drv+ITPZaE6aD7IGfOnLlz504RsVqtCxcu3Lx5c7iF7P379586dUpE7rnnnubvTpkyxe12Hz169KuvvgrZztgqu93+9NNPL126dNq0aTNmzHA4HFu3bt2yZUuvXr2effbZaD7hlVdeCXkBAACSSVFRUaKHkBgdNEEeP35cRAoKCp599tmsrKzNmzeHu/PQoUPqRYvLytpuxYqKCqMJUkSmT5+elpb28ssva//IGDp06IoVKyIfZqO3bds2EcnOzjb6aHRqeXl5R44cSfQokAD81ZsWf/Wmoi0tFhQUJHYkCdRBE+S4ceOmTJkSTbWK2gGZmpraYqpzOBzqhdvtnjhxYoufcO+99957773hPv9HP/rR/ffff+DAgQsXLjgcjgEDBkQzfs20adNEpKioaNKkSYa+EAAAdExVVVXPPPNMokeRYB00QS5ZsiTKO2tqakQkPT29xXdTUlIsFkswGPzuu+9iHkxKSsott9wS29eqOUgAAJA0Ro0apX6/5+XlJXosCdNBE2T0Ll68KCLdu3cPd0NaWlowGEzUMdZq+Xvy5MksZAMAkBzKy8tVYxYz67i12Ib069cv3FtduyY+JVOLDQBA0mBWSJJgDlIJBAKJHkLLTFuiBQBAssrOzla/383ca6XTJ8iUlBRpWstuUW1trYiEnG19zbCKbU6UZJoWf/WmxV+9qbCKLUmwim21WkUkQqGMCpeRe5LHG6vYAAAkDWaFJAnmIFUTn5qamoaGBjUfqXfx4sVLly6JyODBgxMwOFaxAQBIOqxiSxIkyO9///vqxcGDB2+++eaQd9XBNqJrDHmNqdlH/rECAEDSYGlRkmAVe/To0WqP46efftr83QMHDohI165dx4wZc61HJiIi06ZNmzZt2saNGxPydAAA0O6qqqrU7/dEDySROv0cZK9evW677bYdO3asXbv2gQceyMjI0N46d+7cO++8IyJ33313WlpaQoZHR3EAAJIMHcUlCeYgRWTu3Lkicu7cuVmzZn3zzTfqYmVl5cMPP3z+/Plu3brNmTMnoQMEAABIKp1+DlJEhgwZMn/+/GXLlh04cMDpdI4cObKhoWHv3r319fUismzZMqOHWQMAACCCZJiDFJHCwsKXXnopKyvr0qVLu3btKi8vr6+vz8nJ+eUvfzlx4sQEDiwvLy8vL499kAAAJI2NGzeq3++JHkgidbl8+XKix9CeKioqzpw5IyLZ2dkJ/6vNy8ujxywAAMnKzL/ok2EVW2/YsGHDhg1L9CgAAACSWZKsYgMAAOCaSbY5yI6GjuIAACQZOooLCTLeVLvRoqKiSZMmJXosAACgHVRVVT3zzDOJHkWCJVslTYdi5g22AAAkPTP/omcfJAAAAIwhQQIAAMAYEiQAAACMIUECAADAGGqx40vVak2ePHnUqFGJHgsAAGgH5eXlGzZsSPQoEowEGV+33nqr0A8SAIAkkp2drX6/b9y4MdFjSRi6+cSRmYv8AQBIemb+Rc8+SAAAABhDggQAAIAxJEgAAAAYQ4IEAACAMSRIAAAAGEOCBAAAgDH0g4wvOooDAJBk6CguJMh4o6M4AABJho7iQkfxuDJzo1EAAJKemX/Rsw8SAAAAxpAgAQAAYAwJEgAAAMaQIAEAAGAMCRIAAADGkCABAABgDAkSAAAAxpAgAQAAYAwJEgAAAMaQIAEAAGAMCRIAAADGkCABAABgTNdEDyDJlZeXi0h2dnZ2dnaixwIAANpBVVVVVVVVokeRYCTI+Fq5cqWIFBUVkSABAEgOVVVV6ve7mXW5fPlyoseQtPLy8o4cOZLoUQAAgLgw8y969kHGV0FBQUFBwcaNGxM9EAAA0D7Ky8vV7/dEDySRmIOMo7y8vG3btokIS9gAACQNbRNkQUGBaecg2QcZX9r/yAiRAAAkDSppSJDxRSUNAABJhkoaYRU7rsy8wRYAgKRn5l/0zEHGF/0gAQBIMvSDFBJkvLGKDQBAkmEVW1jFjiszT24DAJD0zPyLnn6QAAAAMIYEGV90FAcAIMnQUVxYxY4rOooDAJB86CguVNLEG9kRAIAkwy93YRUbAAAARjEHGV/Tpk0TkaKiolGjRiV6LAAAoB2Ul5fTzYcEGV9FRUXCdDcAAEkkOztb/X5X80TmRIKML6YeAQBIMhw1J+yDBAAAgFEkSAAAABjDKnZ8UUkDAECSoZJGSJDxRiUNAABJhkoaIUHGG1OPAAAkGSpphH2QAAAAMIoECQAAAGNIkAAAADCGfZDxtXHjRhEZNWoUGyYAAEgOVVVV5eXliR5FgpEg42v37t3CllsAAJJIVVWV+v1uZl0uX76c6DEkrby8vCNHjiR6FAAAIC7M/IuefZAAAAAwhgQJAAAAY0iQAAAAMIYECQAAAGNIkAAAADCGBAkAAABj6AcZX3QUBwAgydBRXEiQ8UZHcQAAkgwdxYWO4tHYt2/foUOHKisrhw8fPmLEiKysrCi/0MyNRgEASHpm/kXPHGQkgUDgySef3LVrl/rjW2+9lZqaWlRUNHv27MQODAAAIIGopIlExcdRo0atWbNm9+7dy5cvz8jI+Nd//dd33nkn0UMDAABIGBJkWPv379+1a1f//v3/3//7f7feemtGRsakSZN+9rOficirr76a6NEBAAAkDAkyrK+//lpERowYYbVatYtjxozp2rXr2bNn6+rqEjc0AACARCJBhqWC4+nTp/UXA4HApUuXUlNTU1NTEzQuAACABCNBhjVu3Lj+/fvv3bv3/fffV1fq6+uXLFkiIhMnTkxJ4UcHAABMim4+kVRWVj755JMVFRU33HDD9ddff+jQodOnT0+cOHHJkiXp6emtfrmZi/wBAOhEit3VIuLMtTnslui/ysy/6OnmE0kwGOzdu7eIHDt27KuvvqqtrbVarX379k30uAAAQLuZWXrY5fF7fcEZ+Zmrpw4REa8vKCKG0qTZkCDDqqioeOCBB4LB4Ny5c//2b/82NTW1srLyn//5n998883du3evW7cuLS0t0WMEAHQyXl+wcbprUIYz15bo4SSzYne11xds9ees/Y2IiMvjd3n8Je7TLo/fYbMU5mfOyM8Mudnl8TvsFv7ukipBBgKByZMnjxgxYsWKFRFu27Rp08cff6xKrR0OR0FBwd133938tuXLlweDwZ/85CePPvqounL99devWrXq/vvvP3DgwLvvvjt9+vR4fBcAgCS2eOsJlVfKPBmOqVZmuZToF5HVnSHBrsXbFm894fUFyzwZMkEiBD4tPoqIw2ZxHQ+o+UivL+iwW/UP8vqCM0u/8PqDDpvFmx9sdQzJLakS5Lx586qqqgYPHhzuBp/PN2vWrM8++0y7UlFR8eGHH5aWlq5atapXr176m/fu3SsiP/rRj0I+5KGHHjpw4EB5eTkJEgBglNdX0/jCH/T6azpggvT6gg67pe3LuFFOAYrIoi0nSvZU6xeRww1s8dYTLo9fRMo8gbG5GSXuahFpPlOoblDfgssTKPQFJTeqMbs8gcIwubDYXV3irnZ5AtL4I7KSIJPEvHnzXC5XhBsaGhoeeeSRiooKEZk+ffptt93W0NDw8ccfb9iwwe12P/7442+99Zb+5vr6ehG57rrrQj5HXaEfJAAgBg67VTwBEXHYLA6btdX7Y+D1Bb3+GpXbit3VKgWqOBUh9CzacqLM43fYrV5fjcNuDbeMGyUtFLY4BahG6LA1TsGWefxNac/v8vjVzS6P32Gzaiv+Kj6q20TEJX5X01epD1w0IUf/iAG2xuzrsFsi5+CT/qD2euH4HLVC7bXViEhhfv/Gx3n8+qfrP9+0kiFBBgKBp556aseOHZFvKykpUfFx5cqV48ePVxfvuOOOIUOGLF26tLy8/L333rv33nvV9ZSUlH79+p09e/bgwYM333yz/nOOHz8uIhkZGe3/nQAAkt3qqUNU+HAOylBTfRHyjT4LRsnl8S/ecsLrDzpzbV5fjdcf1HKPelCLibDYXa0Cn0q30jTTFu7+Vp1sem7zKUBthA6bZeGEHGeurXmqVqUt2hjKPBna6+a8/qB3T/VJf1A/f7loQs5Jf7DYXe2wNe5ZVPsdT/qDY3MzyjwBESnM7++wWcfmZmhhtMzjL9lT3Wp0nhFrsE4mnT5Bbt68eenSpWfPnhWRHj16/PnPfw5355o1a0RkzJgxWnxUpk+fvnXrVrfbXVJSoiVIEZk8efJrr722fPnyNWvWdO/eXV2srKx84403ROT++++PZnh5eXkhV0xb9g8AEUS/4qnRCiDKPH4Js5SZcC6P33U8ICIOu0Ubnpot8/qCM0sPqwm/ATZL8+9dnwXV3Fg0Tyxxn1YrrcW+6pC3vL5gmScQ8lNSIyzTzee1kUq92mK9w24pcVfr5whdxwPaWrBsOeHNDw6wWWbkZxa7q12ewOKtJwbYLK6rx6PipvZHh92yeuoQ1/HA4q0npClZusQ/s/RwYX5/LS+qMXj9wZylO525Nm2/o75uRuTK/KjDbtEGNvbqvwtnrs2Za1v79eciYv326OYDx8peOJr23bft8hPrpDp3gpw5c+bOnTtFxGq1Lly4cPPmzeEWsvfv33/q1CkRueeee5q/O2XKFLfbffTo0a+++mrgwIHq4pw5c3bu3HngwIH//b//93333Xf99ddXVFSsW7fuwoUL06ZNu+WWW6IZ4bZt20QkOzs7pu8PAEwh8opnOFpJisZoM7/40ep5RdcXJmSltdhd3Th+T0BaKqzRZ0Gvr6ZdInLI2uu4VfvUI7QRhtzvsBtbZ1eZWPtMaUxyQa+/cW/lSX9Q/VgUlyegzZKqG4rd1c7c0FU+Z66tML+/t/Rw4502i4ic9AdDxlzsrvb6atSP0eXxe/1Bafr5N8/Tzd+KnKEXjs8Zm5shIiXu3D8c+p7DPuW5CTlLHp1i5MeTVDp3glQLygUFBc8++2xWVtbmzZvD3Xno0CH1YsSIEc3fHT58uHpRUVGhJcju3buXlJS8+OKL77777osvvqgu9u7de/78+YWFhVGOcMOGDSIyefJkQiQAhBNhxTMc1VTlqiv+VqbQmjbS1YzNtYXsmWtOzcw17dILqEmy6ONpift0SLpV4Ul/JeSPLk/A5fHPsF/JiPq0p5KWhF9TVpO4DrtFbd1T32aZx6+FOWduxthcm/7Li5vqQhQVy0JSlDaVqH2JKmFpcRhq2k//mXozSw9feZZua6Z+L2PTu1Y1eJVf1Q9fjbDxS/zBxVtOhDxIe2tm6Rfb59wS278ltEh60h9ctOWE9peufrYz7JmL1HPTex8LSrH79He9vxd5H0IS69wJcty4cVOmTNHyXwRqB2RqampWVlbzdx0Oh3rhdrsnTpyoXU9PT/+nf/qn+fPn79u3789//nNWVlaEQu8IqqqqSJAAEE70RQ+iK/jQrqgvKRzZSsLT5vzUfFi4KKbWT0uuTlciot9mt2jLCbm6oaOadFTfy6IJOSHBSw1y7NVTa4X5/fV5q/n3PiM/U83YaUmr+Rq09q2pOg+H3bJwfM7qqUNUwi7Zc2UHZMgUpvqSq7/xQPMfoJogVNdnlh5WP0CV3VsOkWFyfEgwbZ5WHXaLw2ZRq9VNCTU05TvsVoc/2DipGW5PpJpWdFfPyM/UEqf+Kc2vOGyWq5J001SoiJR5/KunDi12V6udEirXaneWHffL8OkzS79QuzlbHE8S69wJUp1SHY2amhoRCXcUYUpKisViCQaD3333XYvvjhw5MrYRFhUVxfaFANDZadN4ra69qhtUiUPzol19A2eXx68v+HDYLYUjM52DMqRpN5v2u7/5lKE25xchfGjNYprfo4VCbeVXv+4cMuk4NtemL2GRpvyn1tm1EFyYn7lwQo5a7144PjSFqN1+xe5q/exdc6rLTEjK9PprtNph9dObkZ+plZIU5vfXviTkJ9D889XMaLG7Wpv01QJcyO7VxhR4deFOix+rZkNnln5x1Xp3Uzp02K0ttuxePXVIztKd4VKg9gNXP4QyT6D5bGgLy/RXL+uH3ODyBHKW7tT/Uf9uXXpvdXHs8QAJMmldvHhRRLSCmObS0tKCwWAw2D77iDUFBQUiUlRUNGnSpPb9ZACIWYTuzVF2AQwpQWjxBrXO2GL9b0gudNgtLS4r6yOdM9emptb0NziuXlz2+oLjXt2nrUIW5vcvcZ9Wa6Be/5XCDq04V5pWJ0W3F/Oqz9e1RRyr1WdoSdQf1Nad9ZOOarbSYbeE9H9RIaxwZOZVVc+Sob5W5Uv9z1YNTM1NNmWjGv3SquiO49P/5LUOPho1e6rtHFU12s1/4C3+FTQVKQf0Tynz+GeWNs6PlnkyXLkB9Teomim6dKXcLSrz+NWPVB/7mv+gmu60at9ai5/ZfEoyZAtBBOHW3A05Gd0PM8mYJUEq/fr1C/dW165x+VGoHpMsYQPoOLSo5MzNWD11qD5q6It/W2zsvGjLiZP+oJY/Ckdm6pOffkOY1xfUYkTI2qs+XC4cnxNhhlJ1B9QqbVXoVG+pF2OvDsHFunk1lULUH1V/FjWewpGZKoFp2yJVKXTIkq4zN0Ndn5GfqS3aqi/R7tEnUX0YamzWk2srsYVGUvUJ+jFrU2WqXEYr/tD+dlzHr0Q3lyfg8gRK9lQ7c22NydhX0/wRJe7q7XNucebaXOJX45xZenhsboa+mbl6N5r66zKPf9EWCdl16vIEmhJwYzMdLepFk03VN9Ji7Y7+B9X4h/YIeXE1tlnpjxmYK0EGAtf6f4VkRwDx0+pEYIu0vi36KTRFK/51yZV5LK3t85WWgVd9VKZqtqyWEbW+M/qZswHNFgrDhcsQ+qSlet+o1zPyM8fmZkR/NrF+jkoV8EqzUmj9Q/Xdc7QYqu0ClKa5SdV6RrWPWTQhxzkoQyXjkj2NK8WF+ZkqVOknz9Tnu8Sv1k9DCpOvjNkfdHn8TrGV7GmhKU+xr+lvp6mTYvN7VEmNSxXTeAIh/bdVx+xouFpaDg55VuP/NRj1osmvnULk/xknK7MkyJSUFGlay25RbW2tiKSmprbvc1U/yOXLl7OKDaBV0fREVDlANbdT2SJkIlCj7QgM+cCrujeHX61Wca0pRFoWTshpsXzB669RO+q0xiiqlESFMFXFrIanvju13te8CYvKoCKiL5RWTfjUVJkzN0PLMV5bTYv9EZ2DMso8jbeFPEL7o8vjV3UwZVdPql35EN38q9fXQs2v6KKPth9A/d/F0tiesNhXrXWlabEhjmr3HW5ZVinRbXBsLmRCVM/lCYRsMZRmca1dVm9hZmZJkFarVURaLJRRVLjs0aNH+z6X/uFAElO//sPNhGndVaKcnIimJ6JWP7tYrmywUxOBzeOUtuktpNHgwvE5A2yWkLIVVfVyZZXz6gYrXl9QtpxYOCGnzJOhqmUbpyo9gbHHA+FWLfXndizackKLO/psp1KUPoOqT1s0IUf99FZPHdK02S4gVxfMiq6nj3qQM9fmytV1q27izM3w6spowgUvRT9j6vW3vl9QC4LN/wpcuvNddPcHW+xN2Oxjw5YbR4OAeC2Z84RDsyRI1cSnpqamoaFBzUfqXbx48dKlSyISW7MeACak38zXfBZQq59t3kc6nGh6IoZUM4Tw6vodqh1yjdeb1kO1ygznoAx1UErI9xJheF5/0HU8sHrq0MbNiE33h6SxcIlZP+F3VYVys8Z+6rso8/jVmrgKuyGrwKpcQ92pVtuj/CFHSUv/Xl+weUeYEC5PQOt0DXMK96+45GaWBPn9739fvWh+zrWIqINtRNcYsr2sXLlS6CgOXBOq17HRzs8x02/mK9lTXebx63vClWnrrb5gmcffvLNdc9o0hjM3I9z4W5zq8Dbb2KdyrX6HnFoPlabSE9XsUAte2veit3rqEH0psfpGFk3IudJUuSVqeT1k3dwVZr1Yws+0hTuXTz1ChVSvv0brvFPm8bs8YasZDE3IRZ6hbBHxEWaLj2KeBDl69OjU1NT6+vpPP/20eYI8cOCAiHTt2nXMmDHxeDodxYF48+paQOs7P+vpmvD1b3vztqt7rAS9vqDDfVr72JCoN7P0cPNoW9yU6lSrZzWF1mJPRMXl8YdrGqLmzELm+RaOz1FTd/qUFjLbp+1KbL5rUEROLBitLx/RyoRb3EHY1JnZH7IQrzW7FhH9Xkb9a/2HtJrGvL6acav26Q+sU9+Xa9X+yF8IoB2ZJUH26tXrtttu27Fjx9q1ax944IGMjCv/VD137tw777wjInfffXdaWlr7PpeO4kDbtbjDTKO2D+pPlXB5/CqxhZxBrG/C1/YEqVWKtNh5TouDA2yWMo9f3aOPtt6rTz1pbDQdZh3Wq2uL2OK7LXacDmlGGE7jarvN4sy16ReLS9zVzZs4ziw9vHB82PlUh92q7Y+ULScWywmH3XpVCXAUBw+2OmB2+KGjGWu+duJingQpInPnzt2xY8e5c+dmzZr1yiuv9O3bV0QqKyufeOKJ8+fPd+vWbc6cOYkeI2Be2myZfiOdOiku5CBj/Ukn2gklV22ta+p1Eq6oWZU+tD1EqkoRLUEOsFlUGtPau0jTGSrac2N7kL4tYpSat4DR6M930U7VU+2dnbk2tXCsnqVN9elHIlvDBkF9mA5XRBJ6A9D50VE8yQ0ZMmT+/PnLli07cOCA0+kcOXJkQ0PD3r176+vrRWTZsmUDBgxo94eyDxKIhn6hU18VoZ0Upx1krK9fUY1vwn2mipWLjjeuXKulYdUXRs2QyQQRXbPDcAOLXE+t+sIo2v45r6/GOacxnjps+uObrzrKuXknP/0JyGr+Uv0cIhfQaFXJzX8CLd7v9QUltzHOunT7NUP2/7Xcuyd8HTF7AWFaMf/jsFMzUYIUkcLCwr59+65YseLUqVO7du1SF3NychYsWHD77bfH77nsg0Q0YusO3QFFnt5rcTOiPiFFLj3R16+c9AedubaQc3gLR2ZqSahM66LsCYjI6qlDZpYeVgFIhUjVmEZfAaOn5VpVeqJiaEiUDDf3oK28qwm/pom9GnU0iDrdRF8rPbP0C4fdqs0Iat9Omcc/NtcWoRJFwkS3yHku+jPfALSqxZafSS+pEuTrr7/e6j133XXXXXfdVVFRcebMGRHJzs5WTb/jhH2QiIa2y81hs3jzg533bAP9mXgtNnzWFp1DNiOG1J1o/++4ML+/OudNbRNsar6YoeYg1VctnJCjZUGH3aov8mh+OvDY3Iwrp+Q1JVF9BYw0TQTOyM/Ucm3jbJwn4PL4yzyBsbkZugKO0GynlUWLiHNQhsNm1e7RjgZRH6J9ifb5IR+lrrPaC6ADSqoEGb1hw4YNGzYs0aMAGmm73Ly+oMNu7YAJUlUNq0m4xuXjXJvXXxMydec6fuWE35BCFuXq3YpX1n1m5Gdqk3mqZlmaFogL8zMddkuJ+/TM0sMOm6UwlqYilQAAIABJREFUP1NFRpcnUObxF7stM/IzHVOtXn9NUzfEq/pIO+xWtXKt9j6qyT91srOWzLT86vUFZ5Z+oTb5qZAXMlfnbTprJMLPSh2souZBS/a0sL4czYcA6ERYxQaQGLE1EjPU/jCa4/LCuVI17Amog9pcnoA65CPcXKM0fVOqFEZE1NKtmthziV9ECvMztQ7Y6kvG5tq05jLaESbqXDiv/0pLmu1zbimxnxZPwOUJqP2RKs7q46O6ePVkYUC2nHDlBtQjCptiuj6yF+uKo13ij7x2HE5Iu5wYPgFApxO5ZURSIkHGF5U0iIYz11Y4MlPbHRjNl7g8fn1gan4gir7RoLafr8yTEcMqecjBblfatYgU+6q9vprtc25Rb83Iz9RXY2jH9IkqLsm1aYfUiYjDZh336r5wxbll+pVfHbXA3fxf/Iu3XDX7qE0Ehny+9mkqCqv22i6Pv2xrQLXdufJdE/4AIDwS5LVAJQ1atWhCTjTHlihNPW4aI05IMUdIo0H9fj79pF3kRzRu48u1qZtVtUqL3Z69/mBxU+NA/cpsSHpTB+t53UERUVOhi7aE7VZ40h8M1y9GFaN4m6Yqnbk21/HAzGZnyrmuPkO5RfpACQAxa7XRaVIiQcYXlTSImdZdJaT+N+QIY4fdomoytPViufr/nXl9QX2ditcXdB0PRE6Q2txh4wKxr3EO0plrWzg7p9hdrT+nWAXWMk8gZPY0JNI5c21a8+2T/kxn04J1c+o78vpqwh52p2tA47XVsKEQAK49EiSQSOG2J6qSjqZi4cb1X/WWVq0iIs7cDK0TjdY60dnU+FBEHHar11+zaEJOmcevNY4+6Q8u2nIiwp7IMl061Df/U2vHasW82F2tnYOiUp3q+93iBzpzMwrz++vu96tcG+4Iu7KoZweZRASAhCBBAvGlFVmfbDzGt0bbyacd+KY/RPjKVzVN0Xn9Qa+/pvkebYfdUpifqX2Vvrngwgk5hfn9S9ynVZW3M9e2eupQtelQO7m4ZE9jrUnzbZHNO13rR6JKsLX2Ovobwp2D4vUH9QvNWj5uceN5hJ7VAIAOggQJtBuVzPS7DPVHrVyhhbMr5zgHxh4POJsaR6twpjXKdtgsruMB7egU7cBl9ThtD+LYXJu21qwGoBWX6HvH6M8gKfZVq96EA2wWdQKKanMTfg9i4/nLLU5eRpgObD7RqPViDPclANCJmK0QW0iQ8VZVVSUilNEkk6aSlCtRT13XwqIzt3FCUW0QjBySrnTJHpShdh+KSOHIzEUTcrz5Qe2QEtX7cPXUoVqILHZXq3Jsh91S5gmIiNoN6bBZoqzm1r4dbcIv3Jpy82+fOUIA0KObD9rZtGnTRKSoqGjSpEmJHgvaSpWwNL0OiMiM/MzVU4eoK/p6Z9lyosR+OuSEOiUkpRWOzFQXHTZrmadxylA1yvb6go3HlqjpOn/Q5fHPsGdKU5FNyFbFxvOjfUHZckK17Am3GB0OM4IAEAOHzWK2+CgkyHjbtm1boocAA/QtbJq/W+I+HZIIvb6aRVtOqA2O+u7TzVvJzMjPLMzvr/6R6joe0M81Nn3UVW0LVQPtkAHo5zsjpD2vP7h464kSd/X2ObdoKXZGfqZWPQ0AQBuRIIFGM0sPawciazOLkXn9Qe+eVtappXHescZ1PKDKn525NuegDNHtJlSfUJifqd+kGPIh2u5GadYAMnRUTV/b5akr/4Ch5Q0AxAn9IAHzUucma3scm+9o0RKYKpTROizqj2DRbtCfracKsb2+oNcfLNlTrY4B1H++2v7osFnG5trUgYHNh6daJDYVbgeiOW2P6UYAuGbYBwl0Ai6P33U84LBbIp/Op9aXB9gsISf+tUj/X77DdtX/F1CdurUl4MKRmQ67RZ0Z2GLmU1+ubVLUrms1KFr+c+baCvP7q97dXl8wci2z1kwRAICEI0Gik/H6gupEFjW9t2hCjtcXVJlsRn7moi0nRMQ5KMPrC2qnqpR5/Op46MifvHBCjsN9WkQK8/urQKkKVkLWf0uuXrYuzM/U2jqqK03tHsPvU2x6yyX+aGYTAQAdWci8g0m0kiAPH47XtMeQIVHtMwNCeP2N3Qq9vmCZxy+Ss3jrCZXDtFm6Mk+Gw27VZgHVCrKIRA6R+o2GSrG7uvn2wZCznlXXHu2KdiJf9J1xAACdGvsgQ508efKee+6Jx1Ovv/76jz76KB6fjKTnsFmvtNq2W9WZKyFRTP3HrM9wajZRS5BaAfXY3Ax9A/DQZzXb1OLMzSjMz9Q66ThsFpVf9QNooYU4ACCpmW0TpLCKjU7HYbcsnJAz9nhjhxoR0QJlCNXcW98Wx+XxO2xW7bxp0TUGXzg+J+S//0VbTpSFWWJ25tpUC8bmXXvIjgBgQiaspOly+fLlCG/X19fH6cGpqalx+uSOIy8vT71Yvnw5HcU1qpdhi3UwTY2ya8bm2tQGx2j+gyx2V6tDWQrz+7uOB8o8fi016hOkNtfYYl+b1VOHzMjPVB+l6qxVkXU0i9EAADNz5mZoZ4aZRytzkGbIeXF15MiRRA+hY9GO/lP/pYWESG3fodcf1Ob/Fk7ICbfKrCVR9Tkuj/+kP6jfj6Kvbvb6gi5puaW2w25ZvPWE6pITuiBOfAQARMQ+SCDuVF2LelHiri7zBMbmZmg5UmuUrd0mIqo+2usL6o+KUbOVLo/fYbMU5meq+cUS9+nIfbO1yUgVPfW7JIWzngEAMaEWG4g7h92iRTe1idDl8atcqHouNv+SYndjA8Wy3IC2W9Hl8WvHQDfWzUT3H7D2dCYXAQDtgjnIWFy8eLG6uvrChQt1dXW33HKLuvjNN9/07du3zWNDJxau6bf6o2rEo5aY1XRjmScQMn2okqLDZnF5Ao2JU/xjPRkz7C3snpSoEyHBEQCAtos9QR47dmzWrFlVVVXalffee+/GG2+sqakZM2ZMVlbW2rVrs7Ky2mOQ6DS0fYQRNjuqP84sDaoq5qYF6NAVZDWnuHrqUK2nd1OdTfCkPxhlw0UAABAPMSbIX/ziF//2b//W4lvnz58XkVOnTo0bN+7ll1++8847Yx8dOhWXx794ywmt3bc0bXZsXnOtrUGLiMNmcdgtY3NtakpSq55Wf5xZ+oX+C1WIvAbfCwAAiCAlhq955ZVXtPjYr1+/m266qWfPntq7Fy5c6NWrl3r95JNP+ny+to8SnYLreECtOLdYzqxPjRHqnR12q77y2uUJRDgtGgAAJIThOUifz7dy5Ur1+pNPPvmLv/gLERk5cqR2w6BBg9xu98svv7xq1SoReeihh37729+202jRcbk8/pI9LdQyuzyBca/uc9gsam6yzBNYPXVIyMGAIS2+zVnUBgBAJ2I4QS5btky92L9/f3p6erjbnnzyyVOnTv3qV7/yeDx1dXVpaWmxjxGdQYn7tJYLZ+RnDrBZtOVm/aykS/zF7uoZ+Zkn/cErxdT6QMnWRgBAp2LOiQ/Dq9iffvqpiPyv//W/IsRH5dlnn1UvvvnmmxhGhjjx+oJa4+44GWCzhDsPUHF5/F5fTbh3CZEAgE6Ebj5RUYUyRUVFrd553XXXde3a9dKlS8GgGX+yHZPX17hkrAqZF03IieET5Ooj5FUYVScBqsLqk/6gtiodUjGt1VO38RsBAAAJZDhBNjQ0iEhKSlSTl5cuXTI8IsSTy+PXaqXLPH6RHO26iDhs1sjHei7ackJNLhY2HSQ4s/SwSpCqVbjDZlk9dcjM0sPalzQPi8RHAEAyMecqtuEE2bNnT7/f//rrr7/44ouR79QWry0WM/5kOyYV8prmEa3qYrG7usRd7fUHHTaLw271+mocduvY3Iyyxo7fNWNzbYsm5CzaciKkk47XF9QWo7VcuGgL3XYAACbi9Qcjz78kJcMJcuDAgXv37v3www9bTZA//vGP1Qv6incczlybNz/osFsH2CwOu0WdHFOyp/rKsS5q9fnqE2LUqvdJ3T4P1WSneU9v+jUCAExIO0TDPAwnyJ///OdOp1NE7rjjjq1bt4Zbzl6xYoXb7RaR0aNHt22EndszzzwjIpMnTx41alSix9JoRn7mjPzMmaWHDUW9spaaMrIeDQAAq9hRyczMLCgo2LZtW2Vl5ZAhQ+65557Zs2erty5evPjNN9988sknK1as8PsbS3G15pHmdOutt4pIdnZ2ogdyhZomdLVUK639+0lr36jVzWjHFQIAAD1zrmJ3uXz5cgxfNmnSpC+++KLV29asWaMilDnl5eW99dZbIpKdnd1xQqRW+xJCLUmr/wYWjs+ZkZ9Z7G5c3dZ6NwIAgBAOu2X77FvMFiJjOdVQRDZu3Pjoo49GuKFPnz6ffPKJmeOjsnLlypUrV1ZVVSV6II28vqB+9tGZm6F/S5r6ey/eemJm6eEZ+ZnOQRllutMIAQBACHOuYsc4B6nU19cfPHjwpz/96R//+MeLFy+mpKT06NFj1KhRjz32GNUzIpKXl3fkyJFEjyLUuFX7VLNGh91SODIz3G5I9W6Zx8+x1AAARODMzdg+55ZEj+Jaa1OCRGR5eXmTJk2SRFTSqCJr1d+72F190h8cm5uhOjhqCRIAALSdOVexDVfSwJCEVNJ4fcHFW06objszfYebLtaoQOmwW4UECQBAOzHnKjYJMr7UHOS1oQ6MUb0e9ZXUitcf9PqCkiuF+f1FRHUCb7wIAABixbnYUXnhhRc+//zz6O9PSUkpKSkx+pSkcc36Qbo8/sbG4E17HLW3GousbRZnrk1dUWdY06AHAADExnCC3L17d0VFRfT3p6amGn1EMklUP0gtGs7Izxybm+H1BZ2DMlSUVAvc13g8AAAgmbCKHV/XbBXbmWtrcULR5fGPzc1wDsrw+oJem+olTnwEAKDdOGwWs5XRSAwJ8qWXXgr31uXLl+vq6nbv3v3mm2+qDogbNmwYNmxYmwbYyZWXl8s16Sg+s/Rw81OqlTJPYPFWv4gslhMsWwMA0L5UUYHZQmS8uvls3LhRbQHcvXt3RkZGq/cnpby8PLX9saioKK77IL2+4MzSL1qcXFT/gyY4AgAQJ87cjNVTh5otQcZrFXvSpEkul2vz5s0//OEPt27dGqendHzqVMN4c9gt4Xr0kB0BAIgrc56LHeOphtGYP3++iJw8efJPf/pT/J5iKhHioOrOAwAArj0TztfEsZLGbrerF2fPnr3uuuvi96COTO0HbfsmSJfHv3jLCREZm2tbNCEn5N1idzV9wgEASAg6irezmprGWbGGhob4PaWDmzZtmogUFRW1sSi7xH1abXP0+oOqsLrMExCRsbkZIrJ4KyUyAAAkBh3F29maNWvUi/T09Pg9pYPbtm1bu39mifu01gzc5fGLKSfPAQDoONgH2T4aGhrWrVu3cuVK9cesrKx4PMVUxuZmaFXV+i2PXh/HEgIAkEisYkfl4YcfjnAmTX19fV1dnbZ+LSL3339/jEODzoz8zBJ3ddO8I/sdAQBAIhlOkH6/3+/3R3nzDTfcsGTJEqOPSCZt6Sju9QWL3dUi4hyU4cy1USsDAEAHxD7IqHTr1q1bt24RbkhJSenWrZvNZvvHf/zHcePGtWFsyUAt5RcVFcWQIBdvPaESZJknwznH1v6DAwAAiInhBFlaWhqPcSSr2DqKuzz+maWHtQ2OXn9w0ZYT7TouAADQbkx4qmEca7ERsxL3aX19jNcXXLyVBAkAQEfkzLWZLT5KXM+kAQAASHpeX40J+6KQIDuiwvz+M/IzEz0KAADQOippovLCCy98/vnnbXzqc889N3jw4DZ+SLJSTcIHmLK5FAAA6BQMJ8jdu3dH6AeJENqphqNGjYrm/pmlhzlmBgAAdHBU0sRXUVGRiETZysfl8WvHFQIAgM7ChJU0hhPkhg0bRGTkyJEXLlwQkQcffPCRRx7JyMjo3r17Q0NDTU3N2bNn//7v//7YsWMiMmXKlFmzZjX/kAEDBrR55J1DlFOPAACg86KbT1SGDRt26dKlm266ad26dSkpV2pxUlNT09LSevXq9cEHH2zfvv2xxx57//33CwoK7rjjjvYbcDJz5toKR2aWefxeP6ddAwCAjstwLfYrr7xy6dIlq9W6fv16fXwMMW7cuLlz54qI+r+I0qIJOQ67NdGjAAAABphtAlJimIN85513RGThwoWt3jljxox/+Zd/qampOXPmzF/8xV/EMrrkpZ/uLnZXe33BMo9fRBx2qzrJEAAAdAoOU7ZPMZwg//jHP4rIrbfe2uqdaWlp3bp1q62tvXDhAglSow6Y8fpqHHbrwvE5xe7qq86b8QQSNzQAABAL9kFG8QVdu166dOmPf/xjVlZW5Du/++672tpaEUlLS4txdMmo2F3dOMvoCXh9NYkeDgAAaBNzdhQ3vA/SbreLyJw5c1q982c/+5l60b9/f6NPMQmXJ+Bi0hEAgM7MnKvYhhPkjBkzROTUqVNLliyJcNu6deveffddEbnhhhu6d+8e6/A6vWnTpk2bNq28vFy74hyU4czNSOCQAAAA2qjL5cuXjX7N8OHDg8GgiPTu3buoqKigoED1g6yrq7tw4cIXX3zx3HPPVVVVqZv37t173XXXtfOory2fz7dz586DBw9mZWXdeOONI0eOjPIL8/Ly3nrrLRHJzs4OaSo+s/QwFTMAACQBh92yffYtZtsHGUuCPHXq1Lhx46K5c+3atdHnrY5p9erV//Iv/3Lp0iXtyv/4H//jpZdeUqv5keXl5R05cqTFt4rd1TNLD7fbKAEAQII47JYTC0YnehTXmuFVbBHJysr67LPPhg4dGuGe7Ozs3bt3d/b4WFJSsnz58v/23/7bsmXLdu/evWbNmptuumnXrl1PP/10zJ/p8vjHrdp3Vf01AABApxLLHKQmEAj89re/ffvtty9cuFBXV5eSkpKenu50Oh999NEkaN/zzTffFBQUpKSkvP/++4MGDVIXz58/P378eL/f/+tf/zovLy/yJ7Q4B8n6NQAAycScq9iGu/l88MEHixYtmjp16pw5czIyMh544IEHHnggHiNLuA0bNtTW1j722GNafBSRXr16zZ49+/PPP1c7QQEAAEzIcIL8+c9/fuHChX//939/8MEH09PT4zGmDmLXrl0ictddd4VcLywsbMvHFub39/pqOPkaAAB0XoYT5Llz50SkW7dumZmZcRhPB7Jnz57U1NS8vLxAILB+/fojR46kpqbm5+dPmjQpNTU15o915tocU60uj59KGgAA0EkZTpDdu3evra1Vh80ksfr6+tra2p49e+7cufP//t//e+HCBXX9V7/6VXFx8erVq/v27RvzhzvsFq+bCUgAAJIBHcWjMnv2bPXinXfeae/BdCAXL14Ukbq6uieeeGLIkCFr1qzZv3//L3/5y2HDhh07duyRRx5paGhoy+eXefztNFIAAJBIXr/pDsWWGBLkww8//JOf/EREFi9e/OSTT1ZXV7cxS3VkwWDQ4XAUFxffeuut6enpt99++9tvv3399dd/+eWXmzdvjuEDvb6gy+NftOUEhxkCAJAczDkHaXgV+7nnnvv888+vv/76ysrKzZs3qyDVo0ePlJSWw2iXLl3cbndbhxmdQCAwefLkESNGrFixIsJtmzZt+vjjj7/++msRcTgcBQUFd999d8g9Xbp0US8eeeQR/a7H9PT0++6778UXXywrK2teZBPZoi0nSvZUiwg1NAAAJA1VHWu2aUjDCfLzzz+vqKgIufjnP/853P1tKToxat68eVVVVYMHDw53g8/nmzVr1meffaZdqaio+PDDD0tLS1etWtWrVy/tutVqTU1Nra+v79OnT8iH5OTkSMRvOZyT1F8DAJB0mIOMSnp6utVqjf7+cHOT7W7evHkulyvCDQ0NDY888oiKv9OnT7/tttsaGho+/vjjDRs2uN3uxx9/XJ1hrcnNzT169GhNTU3I56gTDrt162Z0hF5f6EcBAIDOzpz7IA0nyLfffjse42iLQCDw1FNP7dixI/JtJSUlKj6uXLly/Pjx6uIdd9wxZMiQpUuXlpeXv/fee/fee692/+jRo48ePbpr166xY8fqP2fnzp0icuONNxod59hcG9sfAQBIMg6bxYSr2NdogjB+Nm/ePHHiRBUfe/ToEeHONWvWiMiYMWO0+KhMnz49Pz9fREpKSvTXf/SjH6Wmpr799tsHDx7ULh48eHDTpk0Wi2XixInRDK+8vLy8vLyqqkpEZuRnOnMzov3GAAAAOirDc5AdysyZM9WMoNVqXbhw4ebNm8MtZO/fv//UqVMics899zR/d8qUKW63++jRo1999dXAgQPVRYfDMX/+/J/+9KcPPfTQ1KlThw8ffuzYsZKSktra2qVLlzbfH9miadOmaa+/6/29M8OnS3pvg98lAADouFjFjsWpU6f27t379ttvNzQ0pKam3nXXXaNHjx4wYEBaWlq7jC+y48ePi0hBQcGzzz6blZUVocPOoUOH1IsRI0Y0f3f48OHqRUVFhZYgReShhx7q06fPCy+8oOYvRaR///7PP/9889rtcI4cOaK99vqC417dRzENAADJhEoaY377298+99xz2mEtyv79+9ULp9P5+uuvt2loURg3btyUKVO0/BeB2gGZmpqalZXV/F2Hw6FeuN3ukOXpO++888477/zqq68qKyv79OkzbNgwQyPMy8sTkeXLl9tucpa4TxMfAQBIMg67gQrjpBFjgpw7d+5vfvObCDe4XK68vLxPP/3UbrfH9ohoLFmyJMo7VUl1enp6i++mpKRYLJZgMPjdd9+1eMPAgQP1c5PR0+YgZ5YeLnZXx/AJAACgIzNnr5VYEuTSpUu1+JiVlfXAAw+MGzeue/fudXV1p06dWrFixZdffqneHTt2rLZ8nFjqlMLu3buHuyEtLS0YDAaD7TxHuHHjRhHpN+gmF8cYAgCAZGE4Qfp8Pm1T4H/8x3+ErCAPHDhwzJgxDQ0NhYWF5eXltbW1L7300o9//OP2GWyb9evXL9xbXbvGpaho9+7dIjI5O1uV+sfjEQAAANeY4W4+y5YtUy9+97vfhduAmJKS8tZbb6kdh8XFxW0YXjsLBK51O8bly5cvX778iy7X0wkSAICk5PWbcYbIcIJUk2rf+973Wt0XuHbtWhEJBoPnzp2LbXDtSB2No9ayW1RbWytxOINx48aNGzduXPtJ6DmQAAAgOZhzmdHw0q2axtNmIiPQqp7/9Kc/Rdk9MX7USYzhCmWkKVxG7kkeAxW403rcLNK3fT8ZAAB0EPSDjFaUp12npqbW19erg6QTS8XZmpqahoaG5oO/ePGiGuTgwYPb97nLly8XkUVbTvxu64n2/WQAAIBEMbyKrWbpojkdOxAI1NfXS/geOtfS97//ffVCf0ShRh1sI7rGkO3rpCl3SAAAYAbm7AdpOEFmZmaKyIYNG1q9c+nSpepF376JX8AdPXq02uP46aefNn/3wIEDItK1a9cxY8a073MLCgoKCgr2uX7Xvh8LAAA6CHP2gzScIP/1X/9Vvbjvvvsi3LZu3bpf//rXIjJ48OBrc8JhZL169brttttEZO3atSEV2efOnXvnnXdE5O677273ob711ltvvfWW/SZn+34sAABAAhlOkAMGDBg6dKiIfPbZZzfeeOOaNWt8Pp/27nfffXfy5Mk777zzueeeU1c6TjefuXPnisi5c+dmzZr1zTffqIuVlZUPP/zw+fPnu3XrNmfOnHZ/aHZ29u9PpZizzh8AACSrWCppNm7cqI57rq2tXbp0qVqt7tatm2qIo7d8+fKEV2FrhgwZMn/+/GXLlh04cMDpdI4cObKhoWHv3r1qs+ayZcsGDBgQj+d6fUETFvkDAIAkZngOUjly5MgPfvAD/ZWQ+Gi1WteuXTtp0qTYhxYHhYWFL730UlZW1qVLl3bt2lVeXl5fX5+Tk/PLX/5y4sSJ8XhiQUHBS2+8E49PBgAASJQuly9fjvmLz5w5s3Llyp07d54/f/7SpUspKSlWqzUrK2vZsmXt3hanfVVUVJw5c0ZEsrOz1XxqPOTl5W359OC4V/cxBwkAQLJy5masnjrUbC0h25QgEVleXt7oxb8qdlcneiAAACBenLkZ2+fckuhRXGuGV7FPNWn1Tp/Pt2fPnvvvvz+mgSWD73p/z+XxJ3oUAAAA7cxwJc0TTzxRUVHxgx/8YN26dZHvrKysfPDBB0Xk/PnzvXr1inGAnVlazbcDTHlWJgAASG4xVtJE49ixY+pF8xptk0j77lt6iQMAgOTT+hzkoUOHDF1XPvroo9dee029tljMtbdU74uXZvx/Lx5J9CgAAEC8mLPrc+sJ8rHHHjt37lzIxQMHDtx7773RPKBXr17XXXddLENLCv/+uUnnXwEAMAmHzYwzZa2vYq9fv74tD1izZk1bvrxTq0vvXUYlDQAASDqtz0FmZWV98MEH2h/nzZunKmmef/75CF+VmppqtVozMzPbYYydVp21t8sTaP0+AACATiWqWuwW24N38J7hHUFNb35EAAAkOfZBRmXx4sXxGEdSqrP2TvQQAABAfDlsFq8vaLYzaQwnyBtvvDEe40hKaTXfJnoIAAAg7swWHyWu/SDBHCQAAEnP6w+a8PQQEiQAAEDs6OYDAAAAY7x+022CFBJk/Hh9wZre30v0KAAAQHwxB4n2ZMJ/jgAAYEIOuzXRQ0gAEmS8uDiNBgAAJCkSJAAAQOy8vppEDyEBSJDx4sy11aXTzQcAgCRnzjNpSJDxwio2AABmQCUN2pPreCDRQwAAAHFnzkoaw6caao4fP/7aa6+dPHmyvr4+wm2pqanr16+P+SmdF7XYAAAgWcWSILdt2zZ79uwob05NTY3hEUmABAkAgBlQSROVM2fORB8fzazEfTrRQwAAAIgLw3OQjz32mHrRp0+f4uLi6667rmvX2JfCk5g5/0UCAIDZmLMW23D4q6ysFJEePXr84Q9/iMN4kofDbhUPxTQAACQ5Z64t0UMbKp9AAAAgAElEQVRIAMOr2DU1NSJy++23x2EwSYVuPgAAmIE5Vx0NJ8j09HQR+au/+qs4DCapmPNfJAAAwAwMJ8jBgweLyGuvvRaHwSQVc/6LBAAAszFnP0jDCfIXv/iFiBw7dqy6ujoO40keY5mDBADABLy+Gq/PdMU0hhNknz59Fi5cKCJOp7OsrCwOQ0oSJ01ZmQUAgAmZsAl0LI14HnjgAavV+swzz/zd3/1damqqzWaL0NAnJSVl+/btbRhhp+T1BVnFBgAAySqWBPnKK6+sXLlSva6vrz937lyEm017Jo05u0MBAGA27IOMyv79+7X4iHC8fiYgAQBA0jI8B/n000+rF06nc9GiRXa7vXv37u09KgAAgM7BnPvWDCdItWadnZ39+uuvx2E8ycOEZVkAAJgQq9hRqaurE5EHH3wwDoNJHl5f0IRlWQAAmJA55yANJ8iePXuKCCvXrWIOEgAAJCvDCXLUqFEi8uabb8ZhMAAAAJ2PCaeNDCfIF154QUSqqqo++uijOIwHAACgM3HYrSbcumY4QVqt1ldffVVEHn/88X/6p386c+ZMQ0NDHAbWuTk50hAAAHMw56mGhmux58+fX1FR0bt372+//Xb9+vXr168XEYvF0qVLlxbvT0lJ2bdvX1uH2dm4PP5EDwEAACBeDCfIL7/88ssvvwy5GAyGjd6mPZMGAACYgTlPoTOcIHv27KnKsaMUbm4yuZlwPwQAAOZUODLThL/3DSfIkpKSeIwjyZhwPwQAAOZ00pRzkIYraRANh91iwn+OAABgQgNsZvyNT4KMF6YhAQAwgzJTls+SIOOFOUgAAMzAnOdiG94H+cILL3z++efR35+SkmLCrZNeX5A5SAAAkKwMJ8jdu3dXVFREf785u/kQHwEAQBJjFTsuWMIGAMAkvL6aRA8hAQzPQb700kvh3rp8+XJdXd3u3bvffPPNqqoqEdmwYcOwYcPaNMDOiTlIAACQxLpcvnw5Hp+7cePGZ555RkR2796dkZERj0d0ZDNLDxe7qxM9CgAAEHcOu+XEgtGJHsW1Fq9V7EmTJt15550i8sMf/jBOjwAAAEg4Z64t0UNIgDjug5w/f76InDx58k9/+lP8ngIAAJBALvpBti+73a5enD17Nn5P6ZjM2Z4eAAATctgsJqx/iGOCrKlpLE1qaGiI31M6JnMekQkAAEwijglyzZo16kV6enr8ngIAAJBAXn/QhF38DHfziUZDQ8P69etXrlyp/piVlRWPpwAAACAhDCfIhx9+OMKZNPX19XV1ddr6tYjcf//9MQ4NAACgwzNnLbbhBOn3+/3+aGuObrjhhiVLlhh9BAAAQGfh9dV4faZbyDacILt169atW7cIN6SkpHTr1s1ms/3jP/7juHHj2jC2ToxabAAAzMNs8VFiSJClpaXxGEeSoRYbAAAksTjWYpsZc5AAAJiE15TTRiTIuCgzZXt6AABMyJwdxWPv5nP8+PHXXnvt5MmT9fX1EW5LTU1dv359zE/ppBx2q3gCiR4FAAC4FtgHGZVt27bNnj07yptTU1NjeERn5/XVtH4TAADo/Lz+oAlrsQ2vYp85cyb6+GhaDrs10UMAAADXgjPXZrb4KDHMQT722GPqRZ8+fYqLi6+77rquXeNysA0AAEDH5zJl8YPh8FdZWSkiPXr0+MMf/hCH8QAAAHQmDlM2YDG8iq1OLLz99tvjMBgAAIBORu2DTPQorjXDCTI9PV1E/uqv/ioOg+noTp48+d5773m93kQPBAAAdBTMQUZl8ODBIvLaa6/FYTAdWl1d3RNPPLFgwYI9e/a0ejO12AAAmITXb7pCbIkhQf7iF78QkWPHjlVXV8dhPB3Xiy++ePTo0USPAgAAdCzMQUalT58+CxcuFBGn01lWVhaHIXVEu3fvfvPNN6k6BwAAzZlwH2QskeiBBx6wWq3PPPPM3/3d36WmptpstgjRKiUlZfv27W0YYeKdP39+7ty52dnZP/jBDz788MNovsScR2QCAACTiCVBvvLKKytXrlSv6+vrz507F+HmJDiT5tlnnz179mxpaen7778f5Zc4c23FPnOt8gMAYFrsg2zd/v37tfhoBps2bdq8efOjjz568803R/9VVNIAAGAS5jyIzvAc5NNPP61eOJ3ORYsW2e327t27t/eoOopTp04tXrz4hhtu+PGPf5zosQAAAHQUhhOkWrPOzs5+/fXX4zCejuUnP/lJXV3dz3/+c6Nr8Q67VTyBOI0KAAB0HOZceDS8il1XVyciDz74YBwG07GsWrVq//79c+fOHTRokNGvNecRmQAAmBCr2FHp2bOn3+/vmCvXgUBg8uTJI0aMWLFiRYTbNm3a9PHHH3/99dci4nA4CgoK7r777pB7KioqXnnllfz8/MLCwhhG4rBZTFjYDwCACZlzDtJwghw1atSWLVvefPPNhx56KB4Daot58+ZVVVWpU3Na5PP5Zs2a9dlnn2lXKioqPvzww9LS0lWrVvXq1Uu7/vrrr9fX11+8eHHWrFnaRdVRvKSk5Pe///3IkSMfffTR+HwfAAAAHZrhBPnCCy9s2bKlqqrqo48+uuOOO+IxptjMmzfP5XJFuKGhoeGRRx6pqKgQkenTp992220NDQ0ff/zxhg0b3G73448//tZbb+lvFhF91tQcPXr06NGjPXr0aOdvAAAAoJMwnCCtVuurr746e/bsxx9//L777isqKurbt29KiuH9lO0oEAg89dRTO3bsiHxbSUmJio8rV64cP368unjHHXcMGTJk6dKl5eXl77333r333quuv/zyyypE6i1cuPD9999ftGjRvffeG/lbpqM4AAAmYc5f+oYT5Pz58ysqKnr37v3tt9+uX79+/fr1ImKxWLp06dLi/SkpKfv27WvrMMPbvHnz0qVLz549KyI9evT485//HO7ONWvWiMiYMWO0+KhMnz5969atbre7pKRES5CpqanN669VakxLS0tLS4s8KvZBAgBgEpyLHZUvv/zyyy+//Pbbb/UXg8FgTRjBYByD1MyZM5988smzZ89ardbly5fn5+eHu3P//v2nTp0SkXvuuaf5u1OmTBGRo0ePfvXVV+0yMHP+cwQAAJhELLXYPXv2jP7+cHOT7eL48eMiUlBQ8Oyzz2ZlZW3evDncnYcOHVIvRowY0fzd4cOHqxcVFRUDBw6Mw0gBAEByGptrS/QQEsBwgiwpKYnHOGIzbty4KVOmaPkvArUDMjU1NSsrq/m7DodDvXC73RMnTgz3Ic8///zzzz8f41gBAEAyMuGh2BLDKnaHsmTJkmjio4jU1NSISHp6eovvpqSkWCwWEfnuu+/acXgAACDplZnyFLrOnSCjd/HiRRGJ0AhdFce0y65Nry9ozk21AADAJMySIJV+/fqFe6trV8ML+uE47BYqaQAAMAlznkljrgQZCJhxnhkAAKB9tTLxlp+frxZ2N23apIqUp06dqqpSopSSknLw4MG2DLFdqFaOai27RbW1tSLSvAdkDOgECQCAqXh9QbPV07SSIOvq6lS00tTW1oZciaxdMlnbWa1WiVgoo8IlZxUCAACjzBYfpdUEabPZVJGy/orNZqDvUWIPPNSoJj41NTUNDQ3Nh3Tx4sVLly6JyODBgxMwOAAA0GnRD7IF27dvD7nyxhtvxG0wcfT9739fvTh48ODNN98c8u7OnTvVC60xJAAAAMLpEBOE18Do0aPVevqnn37a/N0DBw6ISNeuXceMGdMuj6ObDwAASGJmSZC9evW67bbbRGTt2rUhFdnnzp175513ROTuu+9WXSHbjm4+AACYRJnHb8Ii2tibIFZWVpaWlu7Zs6euri7CbampqevXr4/5Ke1o7ty5O3bsOHfu3KxZs1555ZW+ffuKSGVl5RNPPHH+/Plu3brNmTOnXR7ksFscNosJ/8cEAIA5UUkTlcrKyvvuu8/v90dzcwepxRaRIUOGzJ8/f9myZQcOHHA6nSNHjmxoaNi7d299fb2ILFu2bMCAAe3yIK8vyBwkAAAm4fUH6ebTuoaGhjvuuCMeQ7kGCgsL+/btu2LFilOnTu3atUtdzMnJWbBgwe23395eTzHb/4YAADAzh81iwl/9hhPkyy+/rL3++7//+7vuustisXSQlj2vv/56q/fcddddd911V0VFxZkzZ0QkOzs7Ly+vfYehzsVmFRsAACQrwwlyw4YN6sX+/fvT09PbezzXyLBhw4YNG5boUQAAgE7PYbcmeggJYHjuUBUyDx06tPPGRwAAgPbi9dWYcOHRcIJUC9YLFiyIw2CSB5U0AACYhMNuNeE+SMMJ8rrrrhORDz74IA6DAQAAQCdgOEHeddddIvL73/8+DoMBAABAJ2A4Qf7DP/yDiJw7d+69996Lw3gAAAA6E/ZBRiUtLW3NmjUismDBgkWLFp07dy4OowIAAOgczLkP0nA3n/nz51dUVPTr1+/s2bPvvvvuu+++KyIWi6VLly4t3p+SkrJv3762DhMAAKBD8vpqEj2EBDCcIL/88ssvv/wy5GIwGHbytuOcaggAANDuzNkP0nCC7NmzZ8+ePaO/P9zcJAAAADopwwmypKQkHuMAAABAZ9EhzrMGAABAJ0KCBAAAiB3dfAAAAGAM3XxakJ+fr+qsN23aNHDgQBGZOnVqRUVF9A9ISUk5ePBgW4YIAACADqWVBFlXV1dbW6u/UltbG3IlMrr5AAAAJJlWEqTNZrNYLCFXbDZb9A9ISWGhHAAAJK0BNtMtYUurCXL79u0hV9544424DQYAAACdABOEAAAAsTvpN10htpAgAQAA2oJuPgAAADBmbK6Nbj6hqqur2/6MzMzMtn8IAABAB2TOVexWEuRf//Vf19TUtOUBqampX3zxRVs+oTNy2CwmnNAGAAAmwSp2XHhN+c8RAABMyOtr01xbJ9XKHKRednZ2enq60Qd06dLF6JcAAAB0Fg67NdFDSIBWEqS+H3hVVdX111+/YMGC//k//ycnzUTGKjYAACZRmN8/0UNIgFZWsfft2/e73/3uhhtuUH+srKx87LHHhg4deueddx46dCj+w+usWMUGAMAkStynEz2EBGh9H+TAgQM3bdp05MiRDRs25OTkqIsnTpy499578/LyJk2a5PV64ztGAAAAdCQGKmmGDRu2efPmL7744o033sjOzlYXv/jiiwkTJtx4440PP/zwqVOn4jNIAACADsqclTSGa7FTU1PHjBmzbdu2AwcO/PznP8/KyhKR2traHTt2jBs37gc/+MHTTz995syZOAwVAAAAHUKXy5cvt/Ej/vSnP/36179+9dVXz549q13s1avX5MmTH3300T59+rTx8zsdry847tV9VNIAAGAGztyM7XNuSfQorrV2SJCaQCDw7rvvvv322+fOndMu9uvX7z//8z/b6xGdAgkSAADzMGeCbM+O4hkZGbNnz/7DH/7wySef/J//8/+3d+/xTdX3/8Df9EZClUcTxNF2fJsSoFZgXNsBgg0do7vAVwSdqECp4HB4QScTJmMUBijD6Q9BvKDSigoqQ5lj35aJpoKIDUiRVQQJTcW2gJBk1TYptuX3x0c+fDgnSZP2JKdJXs+HDx/h5Fze53Muefecz+V/2cTz588ruAkAAACATiXHqFM7BBUE0KN4m1wu1+7du5988smamhoFVwsAAAAAnYoCGaTL5frggw+eeOIJSeKo0WhMJtPChQs7vgkAAACAzqk6KjuBbn8G6S1xTEhIGDNmzJIlS1gzbQAAAACIMAFnkN4Sx7i4uOzs7OXLl/fu3Vu58AAAAAA6tTSdRu0QVOBvBuktcYyNjf3JT37y+OOPGwwG5aMDAAAA6NxMfZPUDkEFbWSQ3hJHIurfv//atWv79OkTtNgAAAAAOjWDXmNCW2y5UaNGuVxXjNVjNBrXrl3br1+/YEYFAAAAEAZsdneRpW5WVrLagYRaAPUgn3jiiUGDBnXp0oWIqqur/V8wLS0t4LgAAAAAwkF0jiESQAa5YMGCdmwgNjb2888/b8eCAAAAANA5KTkmDQAAAABEgzaeQQ4cOLCxsbEjG4iNje3I4gAAAACdWZnVYbMnG/TR1adPGxnkq6++Gpo4AAAAAMJUtKWPhLfYAACRIQp/wDoVlH/YUeqQGfSapXnpiqwqvCgwLjbIGXSa6GyZBQCKY79zbd5ScM9RkcmYRDgE4UaR46U9f7zqb/d0fD3hCM8gg8IWlYOsA0Aw2OxupCadnM3hNludakcBKmjW9igsrYrOKxQZJAAAQIdEZwIBRPR9tx7LdlUVWerUDkQFbbzFPnr0aJA2nJmZGaQ1AwAAAIRMdVS+ePSVQVZXV0+ePDkYW+3du/d7770XjDUDAAAAhFKaLhrbUeEtdlAYovJkAgAAiEJlVofaIajA1zPItLS0Y8eOhSyUSIKWNAAAAFEix6hTOwQVoDefaMc6oRBbEZqMSTZHG20/Dforuivi/zQZkwx6rTinze4SVz4rK1kyhU0kIrPVwdc5KyuZV0xm34qrMug1pkuXq2Sij+rMkk2LKyEivuDSCelEVO1wp+k08qotbDa+bJpOs2xXlbctihuSzLl0Qnq1wy1GazImsdj4Bx/EeXjhs4JiYcuDl5cMX1D+QbKPbIU8fhY8e2vDtsKPnSQYjsfDwxBPPHG7kgW9Be+xKHysgRNPM3F3JLOxvZMcXI8lLJaDN3xm8QyclZUsrqTM6pBcKR4Dll9iPlYiEgtK3BFxnkBbA/D1kOySkayc/ZPvC9sL+TVOni5z8dqUrF/ylWT93mLzFh4J7yKLD9R5u6fxRdgHtnLJ/B5L0luxi3KMSfxwS64ySXGJJ4a3q8lkTMox6vhpLLnb83sd+6fvmNmcHo8FP2Rsc9UOd44xqWDrUb4G+U1J3Bc2XX7cJQUl+eEQf3T4gvkjksXTYFZWsvzWJP/xMl2Z/Ik3eR4nX7n8TP7U/H8Pzb7D920nUiGDDBvshLbZXW2mdwGuVktEJPy0bJqWOW7Dp743IflWSDu0m6Zd0UaqsLRKzHVyjEk2u0ucwWRMys/qRUQ2u4tf4Wk6Db/O03Sawrx0IirYepTFadBplk5IZ53kiRPFpYQd1NjsboNek5/Vq9hymu+puJLC0io+s6lvksnLX5P8nsiXLbLUybcowWYW784GvUbeky0vJX/6BBHnEbcuKXxhfoc8c+L/lH+gK8uHiPiesuALhe5zbXa3besPx048goWyLnbNVofwO3H5xBO3K1+wyFInD55hv4gido55u5uLofL5vR1xs9VRfOCKlDo/q5e3c8NP/HJgp724toKtbrrySmF7UbD1aJFd+BnLSvbxWyWuRLY7l1fucUf46e0n+S74Jha+Qa/NMSaxwyo5ZJLL3OZwiUdfPMMlZ/XSCeni+r1dCxLswpQUqc3uLrucebS9Ksn8fNfEeXyfmW0qLK0Sb2Umo46fGOysKLM6+dXEb0o5Rp2pbxI/jdlzssuJmnDme7xF0JXXoxgDX9Zmdxds/fzSPmrZzGarQ34D97gv4nkuv72LJcy3wqdcivzyLX1WVjI7YS7N4xLnZxuVHpcrNyfe5MXZTEYd3wt2H2PrOfJ/r/Y6vrMwbzFFJdSDDCf5Wb0Meq2y3UbY7JevNyJK02lsdreCb+Gv/CPSQ+7LEmKb/XJvaja7m/9BL66B3w5sDrfN4ZJPLPN0B+SZjfmE84obirASYRNes3Ob3S0PoMzqbLufZ4fb5nDJy0Hxtnv8pubpq4D/6hDLR1yDh1uwXiN78Ox578RTy2Z3Sf6WYOQL+joosk74fO+pzeGSnNttHfErjpr5hNfDbbY6iix1bRby5TPNIV255NdOKO3L0/NH+Eof6cqfTO/zeN5lf5a9Yv4A/5QVC99md/FrR4xHfpWJ31Z7P3bVbOYrzq62YyssrVq2q2rZripJ9ixZVaC75vlG17FOPasdl08J8wknEeUYk0zGJPZkwaDXSM4fcSnxn97udd7CE8tcHoPHfSfZofGxL8Kh93B7vxye7MqVk58wNodbTAQ9n/ZX/JpccfqJv4xiei3exybdebfvqCIbnkGGk2LLafntrM1nYL6xa4yvoczq6EhmY7O7pPdiIWCDnj3/lz4jKbM6bXaX+FaCrngw9sM6xTtIseW0ze4u87sLX7ZpcQ0GnabYcrrYcloM0mRMstndfBekr1EufRaX9Yf5hDPHmCQ+hiyzOjy+GusIm8NdZKmTvGDlL0/bsUJxH8U1lFkdRRaN78JnR03+HuqKHy3ZmcafK/t+03d5fp2HwVqqHVccwcK89CJLHYs2P6uXZLwog17DUhmxxHKMSeyclGyuzOpgB87DfjncNrubvcFki3sMWPxNkpxpktLwWMhs1+SFc/lA+1Noeo3Hk7wdfzeWWZ0e91QSIS8QXvg2h1s8/8usjsJSkochuePZ7K7C0ir+KIg9Dr+Ui0hPLXYt5BiTWJzi62DJa1MiMpODFQh7jyHZqTafzkq27q1Rhfzw+fNGW3IJs1sZDyl/RHJhXnphadXlu5PwiyD5O42dqHw28fB5u0WIt3QxBoNew/bF1DdJPKys2CUbLdh6lB8IybZ4mUiOe7HltHgxeisiCXa/uvzCWqeR1/bxuJT5hJNVnZL8RoiLiHVaxBI+PXimeFpGlS4XL15UO4ZIY7O701fuUzuKzsLPAdk6iSBFy+rQEJGPamrA+FMNNCDhdQYqJah73cG/Wju4afFBbMHWz6P8gpLUdKSQHx2DXiMmasHbSlB3qoPrZ6dlFCaRyCCVZ7O7xz3bRj1CAABoH15rDbdZ6CRMxqQP5g1TO4pQw1tsAAAIJ0gcoRNijXXUjiKk0JIGAAAAAAKDDBIAAACg/Qx6bbQ9gCRkkEGCUQ0BAAAggiGDDAqMaggA4cWg18h7aA9xACpuPcp5HOYgeNtq80xrXzAK7kWg60mLysdGyCABIBqF5ifToPcwwEbnlD8i+YN5wz6YN1SVaGdlJXdwvB//hTJb8ofqwZiMSZumZYam/A16zaZpmR/MG8bGVPQWTzuCYXuhyAvAWVnJPtbzw4aEo9bZzqiQQVtsNclH5JQQ+8Fvc+aOE8cs9tHftdgztnzQapKNW82eyLYZ/A+jDioUraQfWjE833tHXnoV9tj3b5sdX/u/XT/70PaTP4M1K77RNoV4c/Ktk1Am+Vm9AuqUnq8koF3gQ7p5G4WZdxHq/+khGRK6zTuDPzHzOE1G3dIJ6W0Wi7zXehLOdjEkP0ssx5gU0G9wm31xs13wOJvk0Ivz5Gf1Mp9weuuwPUjSdJpZWcmSQdgDIvY9TrK7nz+Lm4w6g87r8N8+dj+gAeL5tohIfl1wfJxbj78pbaw5jwyW0yQ7arzbf9aBJb/WPB7cHGNSflYvj+th4ZmMOl7g27dvz58QpeNixxYWFqodQ6RxupqLD9Q5Xc1tzjkk5aqK2u8Meq3N7mIf2JAVTlez09VcUfud2GnFkJSr2HT2FVtqcMrVh2u/TdLG2+yuJG08EbEPNrvL6WpmHypqv2Pr5NPZGviG+JTLMXf5YdAIPr+4FHUhNie747MYDHptkjaOJYtDUq5K0san6TQ7Kr9xupuJyKDTsGUlAfOwiehw7Xcsfr45cTanq5kty6azq/qHgLsQEfHdZ8serv1O3Ecbn/nS/GIxihu6aWDPJG1csaWO7y+bjW1aDMzpai476eRlu2laZkXNd4drv+Xbraj9zulu5ttdmpdu6pvEdjPHmCS5u3Xp0iU/q9eQ1KsO134nCUly7MTDl6SNZ4M98JJhs1U73GyFD97Ym/2TbYgdFL7sf93NZquDFwI7/Spqv2PHUbJdfqT4Wcq2zgbJoB8Gw718Dovlzw5Z8YE6yVkn3x2PZ7J49CXn/5DUq8qsDr7s4JSr/+tulpz2Syekz8pKLj5wWjx/ii11/3W3sK94EbE1JGnjeCnx+dl5m6SNYyvxeFmJ/7HpBr3WbHWWWR0sMFZKuktFzcZJ4qcxv+L4vrCNsrOdH53/Xnm1JmnjeGmwTYgHhZ8bvAwlpxb7r0uXLms/PFVmde74z7kyq4MdWVaw8tvF4JSrC/PSJw/sOXlgT1Nf3eSBPYekXF1mdfKoWEhs6ywkfm0maeMlpyWb/l93y+Ha7/KzejldzeK1Jh4C8aB06dKFLSvGxu+iXagLKxC+C+JFyg49P9PEzZVZndUOt3jdiQmEeH+W3w1uGthTTKbFO5J4q+FXPbsJ2OyuspNOfnz5OvmFyQqcndV8Oj8Z+Gr5EZk8sGeSNl5+B+MLym/sSdp4U1/dO//5hl9KfDZ2J+GXxuHabwenXP3/Jvdjh4+dzCyAw7XfsnuyeB6KUbHzpPjA6Yd2fLnjP98UW+p4UYv3dpvdRdSl2FIn3rTZb4p4WxDvFawky6yOZbuq/utq4ReXU/gRHJJ6NctHk7RxQ1Kv5nvEd5lPefDG3tTlh/GQnK5mU18dO415nNWOph3/Occvpa/OOm4Y1JfNFm3Qo7jyorZHcVa1JTqHiGB/Ips9DczNmIxJS/PSl5VW+Sgf9les+Ii3g2ZlJS+dkB7UcTtMxqRAx0cOPfa+zOMzHpZBRtjQJsE+KOzVvPjQpWDrUf/P21lZyZumZY7b8KnHMg/e6CPs4VPnP13bQXJE2HjfAa0hoHNmVlay+IDQxzo3TbtefLQc0HmilqUT0sVn/P6QXxFRAvUgQTFmq7PzNyEKUm0Vm/2KoWDlcry8JLpyJS7fK2mfoB6Uzn/EyeebtWqH2+ZwhcVe+C/Y2bDN3tEkzMfiwUvvbHZ3RKaP5Glo+KBv0Y9NRNhl5UPHr4gwhXqQnZqPP8clmRCr3iH+n668rUimiMOCiQt6nN/jDOI87EP+iORqh9tMDjEqcXGPAfiIwWOo7DN74CeZ6DFg/q1Bp8nPSi6zOovsdWLZehxBWPzWx16I4S3NSy+2nDaTQ5yNfzsrK9mg1+QYdbYf3tx5OF45Rh0R8R85b1rQFJsAACAASURBVIdYvmnJPPyf7G2myagrstfJi1Gc2ePKPZ57knJj432z19PeTj+PR5A8nR5sgF35uSHOLFkPe6p0ObxL/xTnYeVQZk2SrNyg07C6Uyajjp+3ksdUki22WUSS8pGH5PsalJeSjwXlRcQ+mIw6XmdAfpK3uSMezyvJdFPfK9rS5hiT2PUo3yP5suxwsGtBUoCSh1vyPRUD9uf2KNn60gnp7PWox9VK1uzt0Mu3Lr9bks/Tgx8msXKej3uX70IgIoPuimqC7HB4XKHN7mZDz0tW7uP2JW7F5nAbdBpWT5HP7K3ETEadZCs8MMl0PrI2X7DIUicp4TZvyN6OC/lxiYmRmPom2exuFgDJribJVuIbzxNR6o9TJVdElMBb7Lbt27fvyy+/rK6uvv766wcMGJCZmel7ftuVb7HZTzirMt/mX8CzspL5w/NZWcmsiluZ1Sk+UWcrZJXBTUadzeEi2dXOtjIrK1nSFsfHrY0tW3ygji+7dEI6/1XwsSxL5gyXajqzLfLPkvn5zD7ukuYTzjKrw6DXshYtfA08a2Tbstnd4voNeo1BpxV/xiTY7Uy+FI+k2FIntgPIMSaxHxte2vJIJCsnL++gxTspW1CyBrZysQDlP8Ae904sCslqDULd88sThZWwk0f+G+Att5D8KoubELN5yUoKth4l4XTy+KsgFhSbh2Rpk8eTmRUsK3M+RdxfMUheSrww5UXkbQ3i/HxOMRJvadmsrGS2XcmlKrko2Fd05W+heGWJZ4W4IAlXGV+PuAv8iIt7ITkT5HthkNXKEDctzwxIuPD5vkjwXZOUOa/aYdBrPvjdsMuRX7lFEi4Nkp2N4r3LoNewegtimZOnO4CkTMR0U4xWUpJibOLM7BTlUcmzWMntju2UePbyldOV54nHS1WMRH5EJDVqfFzjJLt9iaefuHU2hc8suVOJ5SyehxJiYJI185VIfibExSUFy5M8ScYs2XHJBz6/+JvCjq9k7+hS5SJxfh5A+Sfl33frsX7d+o/fes5bShrZkEH6cuLEiQceeMBqtYoTb7zxxr/97W/du3f3tpRNVg+S1YEjIvMJJ6ueYtBr+F9dEuKJnj8i2dQ3yXzCyW+ORDQrK5n9CShi7QfTdJoO/iXEqg8b9Fr5Jjwyn3AagtmRQbDXL+K/ZCZjEntaeemukZSflRydN4gOEpODcOnUBkKsYOtRMfNr90kiXr/sfgsQAjNmzNy8+ZWQ9UXVqSCD9MrpdP7qV786f/78pEmTfvOb36Snpx8+fHjt2rXHjx/Pzs7evHmztwXlGSSAUrw9P4bogXNAFaoXu+oBdFoKlkw7VhXfeD71x6n5I5ILo+/vFrSk8aq4uPj8+fN5eXlPPPFEdnZ2z549x48f/8Ybb6SkpJSXl+/du1ftACEa4ScEcA6oQvViVz2ATkvBkmnHqr7v1sNmd5d5r0AVwZBBelVWVkZEU6dOFSd269bthhtuIKL9+/erExYAAACA2tAW26uHHnro22+/HTx4cAfX4+2p+KX67JcqBTvc7LO8HahkNv5Ptgj/P8lav0qW8rg5Evr+MFzqL83j5uRxypvBeisEMVT5qjyu2ceq5JvzuAgP3sde+IjWx0TJMQp0HC3JQeTTJRGSpwMtCcb3jviIX1yh79PDY+TyGSQrEf/psfxJdsL4WLm3HSFPBSWfKLRG8lpo3orU/xLmxPrNbY7/63G7gZaAx0IOKH6Pp4THeDweevFW4GN3/LxdkKxY5PvY7oBZR9n8n+KQUW0Wkbcd9Lgh/w+ofDcl/xcD+KExh88N+blp/0/1dpyQJDvu3m4p7SgZkv26sWFm2JH1cYqK/5fcw71dR95uVnzKJ+Xlt/0iJ0fVMeXVggzSq7Fjx8ontra27tu3j4iGDRvmY1mDTmgrp9Pkj7hixCpW0dtjxVub3V2w9XO+bECdlBZsPcr6qSEiSZ0Ms9Vh0Gk9VlEvFPq4Nhl1m6a10dIciKjIUseaGBMKrXMrstTxSy9kR6pg61HWwDM6q0aFkcLSKpZJ+LgnQ0QyWx2s+SkbopB8/kr6lrH29k1F9wQhxjCADDIw69evr6mpSU9PN5lMfi6SY9QV5l3u417spp/3leBxwUBPZd7VlsmYJGmR7ePOaLjUXY5Br0lTYkz6aGAy6ljPHbxrNOicVGn9vWlapu9LGzqJ6ksPosxWZ77dTUYVYmh34gIdwXqBlUxRK5jwhQwyAG+//fYzzzyTkJCwevXqmBhfVUjFlzXFB+pY74bsn2arc9muqvysXqyPHhIejbBbSc6l89ig1wY0ShLrs1rsWdBmdy/bVWWzu1gW620pm93NegLC8xI/GfQaliXg1t/JmYy6pRPSy6zONJ0mlGOO4dcoLPC/mU3GJFUuZPa42qDT5GclR+GYeBDukEH669VXX/3LX/4SGxu7du3aNitHim+xbWy8I6FqFHsYabO7fvjzlxxmq6PYcprfSgrzhsl7UvWHyagT/4wustT9sC2H26D3/AtqtjrYEFjR0KV++0rVG2QJYWEWfpvBC/Y3c7XDzYYmCvHWzVYHe2sk9lwNEEYiKoN0Op1TpkwZPnz4mjVrfMy2Y8eO3bt3f/3110RkMBhyc3MnTpzoe80rVqzYvHmzVqtdu3ZtTk5Om5FIRs2SkwwYYD7hlNxKFEl0+Oio3noosNndy66sB9nxjXqj+nu9wtIq1uEC/twHAKaTvHjhL6kAwkhEZZALFy6sqanp16+ftxnsdvvcuXM/++wzPqWysnLnzp1bt27dsGGDx2FmGhsb58+f/+GHH/bo0eP5558fNGhQRyLk7bI9jr90aR7FbiU5xiSPg+xxNofLdjnLdCn7iE5UWFrFXtmr1bbAbHUIg54FVj0AAEBxJqMuf0Qyq+OE6tQQjiIng1y4cKHZbPYxQ2tr65w5cyorK4lo5syZo0aNam1t3b179/bt2y0Wy7333isfZqa+vv7uu++uqKjo16/fxo0bk5M7mnZI8kWD7oexDYsP1JmMOpvORUT+dwoQUD28MqtTnjax2sRmchBRjqexbhXBeltl+158oM7UV4EXRuKgtIEv63ncXgCAUCrMSyfqFA9BAdohEjJIp9P58MMPtzlITHFxMUsf161bN2HCBDZx/PjxmZmZK1euLC8v37Zt2y233MLnb21tveeeeyoqKrKysrw9oeyIS82xncTyISPxNtr+8LMKdptjNG2alsmeUwbvsZy4UwadxqDr6ENW9kQzoOrnPFdmS3UwAAAAgCgX9hlkSUnJypUrz549S0SJiYkNDQ3e5nzllVeIaMyYMTx9ZGbOnLlr1y6LxVJcXCxmkBs2bDh48GC/fv1eeOGFbt26BRSV2JJGzmRM4g/8WG9krCcd/9NHP6tgs3bWbb4lCcErXZ605Xe4iid/Hx1o9XO0ngYAAEXU1NSoHYL6wjuDLCgoYP17a7XapUuXlpSUeHuRfejQodraWiKaPHmy/NupU6daLJbjx4+fPHmyT58+RPT999+/+OKLRFRVVTVmzBj5IlOmTPnTn/7kLbA2W9LwuoAd70mH1ZtkHfcQkWRVneQtiYLtYTvyCLPdb8958eYYk1CHEgAgOmVkZKgdQicS3hnkiRMniCg3N3fJkiUpKSklJSXe5jxy5Aj7MHz4cPm3vHeeyspKlkHu37/f5XIRUXNzc3Nzs3wRt9tXjuj7GaSofYkjr4JNl+pNLttVxV5GG/QaRSoadloGvYbve8jeR/PiNVsdvLtNAACIKseOHZNMieacMrwzyHHjxk2dOtWfoatZDcjY2NiUlBT5twaDgX2wWCyTJk0iorFjx8pPFP/5eAZp0GuWKtEYuTAv3Wb38Eb4h9e7agyuEDLe9r0j/O9sKOKLFwD8x3rzJbygiDLl5eXr1q1TOwqVhXcGuXz5cj/nZA8UvVVnjImJ0Wg0bre7sbFRseBk2PDt+VnJSj3BElMoNqQhERl0Xp+QRVItQGX3go+e7G3oZF688rGwOif+q8ZHfQWAYCi2nOaDROAFRfRITU29//77iWjGjBlqx6Ka8M4g/dfU1EREXbt29TZDfHy82+32/W7aTyxTFN9is9tKjjFJvL8UWepsdrdSb5z5kIYmT53ysGp8vO02iy2yX3YHpNhSx8cHKrLUyR8k+C7eTkj8VaM8DJ8DUUTZW2ubeO9gbVZ/hwiTmpqqdggqi5YMkrn22mu9fRUXp1hR2Oxu8VYS33jelDWQ1Va02d1F9jpiKYvDbbO7y6xJZqNTwaTEbHWQVTqx2FLHuw3iI9AovunIYLO7fXTD7rF4Oxub3c2emBKRzeFeVlpVrD8dUGN/gDAVvFtrm9iDA3aHh4hXXn7g7e1vExH9eJTZ6ojOv9KjK4N0Op1tz6S077v14ONTy5mtTrNVhajU3XSnxdtcRwz5sOwA0SD09zfcUaPM1TRkJvtUsPXo0gnpUVgLNkbtAEIkJiaGLr3L9ujChQtEFBsbG7qYAAAAIMzZ7O6yqPzjIVoySK1WS0Q+Gsqw5DIxMTF0MQEAAED4S9NFYx2haHmLzTrxcblcra2t7HmkqKmpiXX62K9fv6CGYTImsQ7A/cFffKvbvs9md/FXM2hpCACdnHjLCuiWC9AO27dvf2j2HVH4CpuiJ4McOHAg+3D48OGhQ4dKvmUD25DQMaSCWNNs9vmDecP8XEqsOumti5nQKLpUM92g10RnVQ8ACCMFW4/yir85Rl27h/sC8Me+pa8U5i1WOwp1REsGOXr06NjY2JaWlo8//lieQVZUVBBRXFycxwEMO8hmdy+dkB5oLzAmo85kTDJbnQa9hrXjVgsbXJsNvYj0EQA6OdZ7q83uNhmTTH3VvHlCBEOP4hQ9GWT37t1HjRq1d+/e11577Y477khKunxbOXfu3Ouvv05EEydOjI+P7/i2JJliP01DvOu8QR9Y7mXQazZNu76TjKHXkT/iC0uryqwOg14bdl1b2+xum8MVXjEDAO+9tTPcPCFSoUdxip4MkogWLFiwd+/ec+fOzZ07d/369T179iSiU6dO3XffffX19QkJCfPmzVNkQ5IRsVNTU++8cWA71mPQa2YFmHd2NkWWuuIDdbw3mTC6mxdZ6ljHcupWIQCAdjAZdRh6FIIqNTUVPYpHUQaZmZn56KOPrlq1qqKiwmQyjRgxorW19eDBgy0tLUS0atWqtLQ0pbYljkmTEz5pE3Bll7p28zZKDQAAQDSLogySiPLz83v27LlmzZra2tr9+/ezienp6YsXLx47dmyQNvr6h/+Jd52/YZAxjJ7AKcVk1JUZnWZyGHQq1+bsCAzlAuGCNb8Ll7E3AcJXeXn59u3b1Y5CZV0uXryodgwqqKysPHPmDBGlpqZmZGQou3Kb3V2w9XPJ4AQmY9LSvPQoTCKJyGx1GHTa8PpJM1sdy0qrCG05IXwUllaxSiOzspJR9QIgqGpqasrLy4lo0aJFx44dUzscdURpBhlUHjNIIlo6IR25SHhhlfHVjgLAL+M2fMpuOwa9ZtO0zOj8exUgxDIyMqI2g4yWMWlCyWPOYdBrkIuEHRwyCCO862yDTmPQoRttAAiu6KoHGRo2u9vmcEsmmow6tMYACCqz1RHND97ys3qxDznGJPzxAwDBhgwyKMS22Ex0DpoJEBo2u3vZriqz1WHQaaK2wrHJqIvOHQcIPfQoTsggg0TyDBKvsAGCio8CarO7c044kUgBQFChR3FCBhkCBr0mf0QyGxuwyFJX7XCH3egsAJ0c/kIDgFBCj+KEDDJIxLfYpkvdwSzbVXXpMYnLMC3MercB6MxYPWOb3WXQa1HhGAAgBJBBBoX4Fpv3pG2zu/i3NocLGSSAUlj/Neh9CQAgZNCbj/IMeo1BaDfDX1jnXBoowqDTFFtOj9vwKXskGWyFpVXjNnxaWFoladwDEGGQPgIAhAyeQSpPkqi99uF/ZmUlp6amFualG/Qam91d7XD/8Drb4TboNUGtE1lkqWPDVLCuhtGlOQAAQAfV1NTU1NSoHYXKkEEGhfgW+82SD3+eMoZVuWU1tMZt+PTynHY3GYMZid2NR48AAAAKqqmpQW8+yCCDbu0fCrKvfMqYn5Vsc7hZbldmdQb1MaSpb1KZNcnmcBt0GlPfpCBtBQAAIHpkZ2dv3ryZiDIyMtSORTXIIJXH6kHyJ3/yp4yzspINes2y0iqz1VlkqQtq02yTUWeYpmVjdaCWGAAAACgCLWmUJxnV0ONLZPGhI2uaHbx4DHoNy1mDtwkAAACIKsggg+KKtthe3h3zptkYiwwAAADCC95iB51Bp/U4nTfNRgfIAAAAEF6QQSrPoNcY9FqyOtlnH52HI3cEAACAcIS32EHBh58BAAAAiDx4Bqk8semMze7udv7LGg2GYAcAAIgQ6FGckEEGCW+LrT1//MmXvphy882NtTHE+tZBm2gAAIBwhh7FiajLxYsX1Y4hAhVsPcrGLZyVlbxpWqbkn2pHBwAAAArIyMg4duyY2lGoA/UglWezu81WB/tstjrMVgevFmm2OjDGIAAAAIQ7ZJDKY2PS/PBZpzEZdQa9lv8Tb7EBAAAg3KEepPKuaEnjcNvs7vysXmk6DXnvXRwAAAAgjCCDDC72MBKjzgAAAEAkQQapPAXfUxeWVpVZHQa9dumE9JC9/jZbHcWW0za7Kz8rWdk+z4ssdWVWJxHlGJPQm7qEKscaAACgfZBBKk98i222OossdYV56e1YT5GlrvhAnc3uJqszTadp30raodhymrUctzncBr1GqaenNru72FJntjqJyGZ3oWMjkVrHGgAAoH3QkiYoeH+QRFTtaGfja5vdzZPRdq+kXdvFgDqhJh5rAACAzg/PIJVn0GvyRyQv21XF/pmma+eTtllZyWVWh83hNug0+Vm9lAuwDflZySwDVrb6pkGvyTHq2Jpz8ADySqa+SWXWJHas0dwKAAA6P2SQQVGtxDNIg16zadr1NofLoNOGMt+alZXMNqd465/CvHSWHqFdkYTJqDNM04b+WAMAALQPxqRRns3uHvfsp/ylpEGv2TQtEzkTAABAhMGYNKAksUdxYr2I67QqxgMAAACgLGSQQbH0UltakzFpaR46Zwkpm91dZKnjA0sCAACA4pBBBkWx5TTLGg16LR5AhpLN7i7Y+nnB1qMFW4+yPokAAABAccgglWezu81WB6sHabY6FixfU15ernZQ0cJsdVzqctLNei8HAABQVnl5+YwZM2bMmKF2IGpCBhkUvB5kfOP57Ozs1NRUdeOJHga9htcZaHc/SgAAAD6kpqbef//9999/v9qBqAm9+SjPoNcszUs3WE5v3769u7ZR26sX0UC1g4oWJqNu6YT0MqszTafBwIkAABAMNTU1n3zyidpRqAwZZFAYdNocY1LJ+S9NOQOIqKamhj+GZC+4FRwtsBNiFRDVGrdwltLDeQMAAIjwapHQH2SQ8GYcs7KSN03L5NOLLHXLdlXZ7G7WRjsik8jC0io2xLPJmLRp2vVohw4AAJEK/UGCklhLGvbZbHWMuvWet99+m/2zzOq81MLGaT4Rme08qh3uy/uILnUAACDilJeX5+bm5ubmqh2ImvAWOygMOg3LouIbzz/x5z/cMMjIpvO2HWKDjwgTDfsIAADRLDU1dfPmzUQUzUkkMkjliS1pHv3DXTcMulwnrzAvnYiqHe4cY1Kk1tVj+8X2MSJf0wMAQJRDPUhCPcigysjIYCfZ/ffff/PNN6sdDgAAACigvLx80aJFRFRTUxO19SCRQQZRn6Gj9/zzLRL+WGGtsFUNCgAAADqkpqaGfcjNzY3aDBJvsYOiYOtRm911evDMjf+5UHhpjOzC0qoyq4OI8tHdDAAAQNjCW2xCBhkMNrvbZneZrU7q0b/4QF2388fvzBn4pbsb6+OGiAx6LTJIAACAMFVTU4PxipFBBlfN1zXl33xh6qujHv34RJvdpWJIAAAA0BEYk4aQQQaDQa/JMeqI6KMj1hsGGbfNu5VNNxl1ZnIYdJp8PIAEAAAIW9nZ2dnZ2UTE+3uOQmhJEyw2u3vsxFtP7XtXnGi2Ogw6LRrTAAAARIBoHpMGzyCDxaDXdDt/nP11kp2dzWrdon9EAACAcId6kIQMMthYPYnU1FS02wIAAIgMqAdJeIsdVNH8cBsAACDiRfMPfYzaAUQF1omPt38CAAAAhBe8xQ6KIktdsaXu1KiHiix1ZVanze4y6LVLJ6TbHK5iy2mb3ZVj1BXmpbPZCH2MAwAAQFhBBqk8m91dbKljPYoXbD36w1SrM02nqXa4iyx1RGRzuImozOowW53se2SQAAAAYQEtaQgZZChVO6Qvr23CFAyZDQAAEBbQkoaQQQYD61Hc5nDXfF1zZ85A+qEbSE1+Vi824KHN4TYZdeyhY/GBOiLKMeqQPgIAAIQF9ChOaIsdPGar465bfn3y0D66siNxm91tc7h4x5DoYxwAACBMRXNbbGSQQRTNJxYAAEDEi+YfevTmExQ2u7uwtOp8/1+j4x4AAACIPMggg2LZrqplu6rO95+4bFeV2rEAAAAAKAwZpPJsdrfZ6mCf3ygp6zN0dDTXtAUAAIgwb7/9dkZGRkZGhtqBqAn1IIOiYOtR1u/jrKzkTdMy1Q4HAAAAlId6kKCwpRPSl05I73H8n0snpKsdCwAAAIDC8AwyiKL5TxMAAICIF80/9HgGCQAAAACBQQYJAAAAAIFBBgkAAAAAgUEGGRToURwAAAAiGDLIoECP4gAAABDBkEEqDz2KAwAARDD0KE7ozccflZWVBw8e/OqrrwYPHnzDDTfo9fo2F0GP4gAAABEvmnvzQQbpS0tLy8KFC999910+RavVrlixYuLEib4XNFsd5hPO9evXHSheZdBrghwmAAAAqCCaM0i8xfblL3/5y7vvvvuTn/xk06ZN77333uLFiy9evPjwww9/+umnvhc0GXWFeek9ju9E+ggAAACRBxmkVydPntyyZcs111zz0ksvjR49unfv3jNnzlyzZg0R/fWvf1U7OgAAAADVIIP0aseOHUT0m9/8pnv37nzihAkT0tPTDx06dPLkSfVCAwAAAFATMkivPvvsMyL6yU9+Ipk+ePBgIjp06JAKMQEAAAB0AsggvTp8+DARXXfddZLp/fv3J2SQAAAAEMWQQXrldruJ6Nprr5VMv+aaa/i3AAAAAFEIGaRXLS0tRBQbGyuZzqa0traqEBOEiSjvZjaa4dBHLRx6iDbIIAOGHjQBAAAgysWpHYCSnE7nlClThg8fzvrc8WbHjh27d+/++uuvichgMOTm5nrsITwuLq65ubmlpUXyGLK5uZmI4uPjFY0dAAAAIGxEVAa5cOHCmpqafv36eZvBbrfPnTuXNbJmKisrd+7cuXXr1g0bNoi99hCRXq8/e/ZsdXV1nz59xOlfffUV+1bp8AEAAADCQ+S8xV64cKHZbPYxQ2tr65w5c1j6OHPmzGefffaZZ56ZMmUKEVkslnvvvVcyP+u1R97vI5vCvgUAAACIQpGQQTqdztmzZ7/zzju+ZysuLq6srCSidevWLV68ODc3d/z48Y899tjixYuJqLy8fNu2beL8w4cPJ6L9+/eLE1tbWz/55BP+LQAAAEAU6hLu7UJKSkpWrlx59uxZIkpMTGxoaDCZTM8//7x8znHjxtXW1o4ZM+all16SfDV9+nSLxdK/f/93332XT7Tb7Tk5OUT05ptvZmZmsolPPfXUc889l5ub++yzz7YZG5rmAQAARLZjx46pHYI6wrseZEFBwb59+4hIq9UuXbq0pKTE24vsQ4cO1dbWEtHkyZPl306dOtVisRw/fvzkyZO81qNer//DH/6wcuXKGTNmzJo1y2Aw7Nq1q7S0tHv37kuWLPEnvPvuu499+OlPf5qdnR34/gEAAECnU1NTs337drWjUFl4Z5AnTpwgotzc3CVLlqSkpJSUlHib88iRI+yDx7fPvFJjZWWl2G5m5syZ8fHxa9euXbduHZty/fXXr1mzJiUlxZ/w7r//fv/2AwAAAMJGamoqfuLDO4McN27c1KlT/WnUwmpAxsbGekz+DAYD+2CxWCZNmiR+dfvtt992220VFRXffvutwWBIS0tTIG4AAACAcBbeGeTy5cv9nNPlchFRt27dPH4bExOj0WjcbndjY6PHb4cNG9buIAEAAAAiTCS0xfZHU1MTEXXt2tXbDKyHcIx2DQAAANCmaMkgmWuvvdbbV3Fx4f04FgAAACBkoiuDdDqdaocAAAAAEPaiJYOMiYmhS++yPbpw4QIRSYbABgAAAAC5aMkgtVotEXlsKMOw5DIxMTF0MQEAAACEp2jJIFknPi6Xq7W1Vf5tU1NTc3MzEfXr1y/UkQEAAACEm2jJIAcOHMg+HD58WP4tG9iGhI4hAQAAAMCbaMkgR48ezeo4fvzxx/JvKyoqiCguLm7MmDGhjgwAAAAg3ERLBtm9e/dRo0YR0WuvvSZpkX3u3LnXX3+diCZOnMh6hQQAAAAAH6IlgySiBQsWENG5c+fmzp37zTffsImnTp2aPXt2fX19QkLCvHnzVA0QAAAAIDxEUTfamZmZjz766KpVqyoqKkwm04gRI1pbWw8ePNjS0kJEq1atwpjXAAAAAP6IogySiPLz83v27LlmzZra2tr9+/ezienp6YsXLx47dqy6sQEAAACEiy4XL15UOwYVVFZWnjlzhohSU1MzMjLUDgcAAAAgnERpBgkAAAAA7RZFLWkAAAAAQBHRVQ8yNHbs2LF79+6vv/6aiAwGQ25u7sSJE9UOCjqq44f11KlTn3zyibdvu3TpMnXq1I5GCWpzOp1TpkwZPnz4mjVr1I4FFNPuw4qrPlI5nc6333770KFDX3/99cWLF1NTU/v373/LLbewAfCiBN5iK8lut8+dO/ezzz6TTM/KytqwYUP37t1ViQo6SKnD+vTTTz/zzDPevk1ISDhy5Ej7o4TOYe7cuWaz2WQyPf/8bSEHRwAAFu5JREFU82rHAopp92HFVR+R3n333SVLlrhcLsn0uLi4hQsXzpw5U5WoQg/PIBXT2to6Z86cyspKIpo5c+aoUaNaW1t37969fft2i8Vy7733bt68We0YIWAKHtYTJ04QUWxsLBseSQK92UeAhQsXms1mtaMAhXXksOKqjzzvvfce615ap9NNnz59wIABRPTFF19s3rz5/PnzK1eujI+Pv/3229UOMxSQQSqmuLiY5Rnr1q2bMGECmzh+/PjMzMyVK1eWl5dv27btlltuUTVGCJiCh5WNyT5lypQVK1YEL2BQhdPpfPjhh/fu3at2IKCkjh9WXPURpqWlZdmyZUSUkpLy5ptv9uzZk00fN27cbbfdNm3atOrq6tWrV+fl5en1elUjDQW0pFHMK6+8QkRjxozheQYzc+bMrKwsIiouLlYnMugApQ5rU1PT6dOniWjkyJFBCBPUVFJSMmnSJJZnJCYmqh0OKKPjhxVXfeQpKys7e/YsEf3+97/n6SOj1+sXLVpERC6Xa8+ePerEF1rIIJVx6NCh2tpaIpo8ebL8W1ZX+vjx4ydPngx1ZNABCh5W3oO90WhUNEZQWUFBwfz588+ePavVah9//HH2dwWEO0UOK676yPPxxx+zD7/4xS/k395www3sw8GDB0MXk3qQQSqD14YePny4/NvBgwezD+x9KIQLBQ9rdXU1EcXFxaEH+wjDKrrl5ub+61//uvnmm9UOB5ShyGHFVR95pk+f/sILL6xdu9ZjHdaGhgb2oWvXrqGNSx2oB6kMlkPExsZ6bMlvMBjYB4vFMmnSpFAGBh2h4GFlTbkHDx7sdrvfeeedAwcONDQ0JCYmZmZmTp06NRpqzESqcePGTZ06lf85AZFBkcOKqz7ypKWlpaWlefu2tLSUffD40CHyIINUBmvV361bN4/fxsTEaDQat9vd2NgY2rigQxQ8rF9++SURnTt3Licnp76+nk/fuXPnM888s3TpUjy+ClPLly9XOwRQniKHFVd9VGlsbHzhhReI6Oqrrx43bpza4YQCMkhlNDU1kc8H1/Hx8W632+12hzAo6CilDmtrayv7Lamuro6Li/v1r3/dp0+fb7/99vPPPy8vL3e5XIsWLWpoaJg+fbqy8QOAWnDVR5tHHnmE1Zt/8MEH8RYbAnbttdd6+youDkUdrjp+WI8cOdLS0kJE/fr1e/bZZ3v37s2/2rNnz/z58xsaGh577LGxY8f6eD8CAGEEV31U+dOf/vTvf/+biH72s59Fz18FaEmjJKfTqXYIoLyOH9bevXs/99xzf/3rX4uKisQfEiIaO3bso48+SkTNzc2vv/56BzcEAJ0Ervoo0dLS8vvf//6tt94iopEjRz711FNqRxQ6yCCVERMTQ5deenp04cIFIvI4LAF0WkodVr1eP27cuJtuuumaa66RfztlyhSNRkNE+/bt61C4ANBp4KqPBvX19XfdddfOnTuJaMyYMS+88EKUvL9mkEEqQ6vVEpGPFhUsC0Fvw+ElNIc1JiYmOzubiL766quOrAcAwgWu+ghw6tSp3/zmN6zXz8mTJ2/cuDGq0kdCPUilsN5eXC5Xa2sre3Alampqam5uJqJ+/fqpEBy0V8gOK1t5ly5dOrgeAAgXuOrD2oEDB+677z6Hw0FEDz744O9+9zu1I1IBMkhlDBw4kH04fPjw0KFDJd/y9xS8B0EIC0od1rKysg8++ODChQurVq3yOMOpU6eICBXqASIGrvoItm/fvnnz5rlcLo1G89hjj/3qV79SOyJ14C22MkaPHs0qw/Ehj0QVFRVEFBcXN2bMmFBHBh2g1GH95z//uWXLlr///e9sjAqJU6dOWa1WImJvtQAgAuCqj1THjh277777XC5X9+7dN23aFLXpIyGDVEr37t1HjRpFRK+99pqk6e65c+dYa7uJEyd6HAcJOi2lDusvf/lL9mHjxo3ybx977DEiio2Nvf322xUJGwBUh6s+IjU1Nd17770NDQ0JCQkvvvjisGHD1I5ITcggFbNgwQIiOnfu3Ny5c7/55hs28dSpU7Nnz66vr09ISJg3b56qAUJ7BHpYd+3aNWzYsGHDhq1evZpPzM3Nvf7664norbfeeuKJJ1pbW9l0p9M5f/783bt3E1FBQUGfPn1Cs1MAoCBc9dHjpZdeYtUPRowY8eWXX27z4sCBA2pHGgqoB6mYzMzMRx99dNWqVRUVFSaTacSIEa2trQcPHmSdyq5atQr1XcJRoIe1ubm5oaGBZH0APffcc7fffntNTc3GjRtfffXVUaNGNTY2HjhwgLXFycvL+8Mf/hDC3QIAxeCqjx5btmxhH/bt2+ejJ6Zbb711xIgRoQpKNcgglZSfn9+zZ881a9bU1tayFv5ElJ6evnjx4rFjx6obG7SbIof1Rz/60fbt29evX79lyxaXy/X++++z6SkpKb/97W/xJgsg8uCqjzAul+vs2bNqR9GJdLl48aLaMUSgysrKM2fOEFFqampGRoba4YAyFDmsLS0tBw4c+Pbbb2NiYv7nf/6nb9++isYIAJ0OrnqISMggAQAAACAwaEkDAAAAAIFBBgkAAAAAgUEGCQAAAACBQQYJAAAAAIFBBgkAAAAAgUEGCQAAAACBQQYJAAAAAIFBBgkAAAAAgUEGCQAAAACBQQYJAAAAAIFBBgkAAAAAgUEGCQAAAACBQQYJAAAAAIFBBgkAAAAAgYlTOwAAAACAzmjv3r0tLS3evtXr9YMGDQplPJ1Kl4sXL6odAwAAAECnM2zYsIaGBm/fmkym559/PpTxdCp4BgkAAADgQV5eXlNTk3x6SUlJS0vL9ddfH/qQOg88gwSAtq1evfqNN97w9m1CQkJKSsqPf/zjQYMG/frXv05JSQl0/bm5uU6nMzExcc+ePR2LFPwyduzYhoYGFDhAO2zYsGHt2rUjR44sLi5WOxY14RkkALStqanJx6uchoYGh8NRWVlZWlr61FNP3XPPPQ888EBA629sbPSxflBcQ0MDChygHT799NO1a9f26NHjb3/7m9qxqAwZJAAEIDU1tV+/fpKJbrf7888/r6+vJ6KWlpZnnnnmwoULCxYsUCNAAIBgaWlpWbRoEREtXLjwmmuuUTsclSGDBIAAmEymP//5zx6/OnPmzMqVK0tLS4lo48aNkyZNysjI8HO1q1ev/v7772NjYxULFABAaS+//HJ1dfXQoUNvuukmtWNRH/qDBABl/OhHP3r66acHDBjA/rl582b/l83JyRk/fvy4ceOCExoAQEc1Nja+8MILRPTHP/5R7Vg6BWSQAKCkOXPmsA8HDhxQNxIAAAVt3ry5vr4+Ozt78ODBasfSKeAtNgAoidcNOnv2LJ+4YsUKt9s9dOjQqVOnvvLKK6+88so333wzaNCgW2+9lb0MeuyxxxoaGjQazZ/+9Ce+FJvIlqqrq3vppZfMZvOZM2fi4+NHjhw5ffr00aNHszlPnDjx8ssvf/TRR3a7vXv37qNHj77rrrsyMzO9BXnkyJEtW7ZUVFTU1tYSUXp6+ujRo++8885AW5GLEX7zzTdFRUV79+612WxdunS57rrrfvazn91+++1XXXWVuEhhYWFzc3NiYqLHxxhHjx597bXXiGjkyJETJ04MQVEQ0cmTJ19++eU9e/bY7Xa9Xp+VlXXHHXcMGzbMxyIBFWCbRx8gLGzdupWIfvvb36odSGeB3nwAoG3Lly9nmc2dd97prR4ks2/fvoKCAiK6+uqr+WNI1ivv5MmTr7vuuscff5zPnJqa+v777xPRyJEjHQ5HYmLip59+yr9lEydPnpyXl/f73//e5XJJtvXII4/Mnj3773//+5IlSyTjRsTGxj799NPjx4+XLOJyuf785z//4x//kEceFxf3yCOP5Ofnt1UYl/EIJ02a9OCDD3777beSGa699tpNmzb17duXTxk0aNCFCxd0Ot3+/fvlK3zvvffuvfdekpWz4kXBjkhiYuKKFSsWLlx44cIFyQr/93//d8WKFV27dpVMb0cBtnn0ARTkdDqnTJkyfPjwNWvW+Jhtx44du3fv/vrrr4nIYDDk5uaKf7PJsTtbr169ysrKFI44bOEZJAAo6dixY+yD/EWPzWZ79913iSg2NrZLly7Nzc1Tpkxpc4VffPHFP//5z+bm5uHDh48ePTo2NnbPnj0HDx4kItabxl//+tfY2Nhf/OIXw4YNO3v2bGlp6alTp1paWv74xz+OHTtWzIFaWlruvvtui8VCRDqd7uabb2a1Ng8cOPDOO++4XK5Vq1Y1Njb+7ne/C2iXjx8/fu+997rd7uuuu27kyJEGg+HgwYOlpaUXLlw4e/bsAw888K9//SugFYagKJimpqaHHnqIiLKzs2+66aarrrrq0KFDb7zxhsvl+sc//nHx4sUnnnhCnL8jBdi+ow8QqIULF9bU1Mi7jODsdvvcuXM/++wzPqWysnLnzp1bt27dsGFD9+7dPS5VUlJCRJMmTVI84DB2EQCgLcuWLevfv3///v2XLVvmY7azZ8+OGjWKzfnyyy/z6UOHDu1/SXFxcUtLy8WLFy0Wy1dffcVm+OlPf9q/f/+hQ4eKa2MT+/fvn5mZuXPnTvGrBx54gK9w1KhRx48f51+53e7Jkyezr/7v//5PXGrdunVs+m233Xb+/HnxK5vNZjKZ2LefffaZn8XCI+zfv/9bb70lfmW1Wvm3H330EZ8+cODA/v37//SnP/W4wn//+98ey1nxohCPSFFRkaQoxowZw7768MMPxa/aV4BtHn0ApTzyyCPsTPvtb3/rcYaWlpabb76ZzbNixYrdu3f/+9//XrRoEZsyffp0b2u+8cYb+/fvb7FYghZ7+EFLGgDoqJaWlqNHj27cuPGmm246f/48EfXq1euOO+6Qzzlz5syZM2fGxMQQ0YgRI3r37u3P+u+8885f/epX4hTxVemf//xn8XlD165d77rrLvb58OHDfHpjYyMbwbZ79+7PPfecXq8XV5iWlrZhwwb2+cknn/QnKtGsWbNuueUWcUqfPn14kBUVFYGu0BtFikJ06623St47p6Wl8a6SWctTpuMF2L6jD+APp9M5e/bsd955x/dsxcXFlZWVRLRu3brFixfn5uaOHz/+scceW7x4MRGVl5dv27ZNvtSZM2dOnz6dkJDgu35wtMFbbAAIwGuvvcYqRPqg0Wieeuop+TtTIpJkP36aPHmyZAp/RZ6QkDBhwgTJtzqdjn0QKybu3r2b1fa77bbbkpKS5FvJzMwcMmRIRUXFJ598Ul9f7+1llkeS9JG57rrr2IfTp0/7vyrfFCkK0dy5c+UTs7Ozr7vuui+++KK8vNzpdLLi6ngBtu/oA7SppKRk5cqVrPVeYmKij/GWXnnlFSIaM2aM5GKZOXPmrl27LBZLcXGx/HJmf4ANGTKE/f0DDMoCAJQ0ZMiQN9980+Nf6rGxse3oBSM2NlbelJj3Pd6vXz/5Pd3jXf7DDz9kH3w8RWAP8FpaWg4dOhRQhB4rXfEcurW11f+1+d6QIkXB9e7d29uDQH6keHOoDhZg+44+QJsKCgrmz59/9uxZrVb7+OOPZ2VleZvz0KFDrPcA+V9iRDR16lQiOn78+MmTJyVfVVVVEVGgfTVEPDyDBIAApKWlDRw4UDIxJiZGo9FkZWUNGjSoT58+3pbVaDTt+As+ISHBx1I9e/b0cz3fffcd+7BgwYKEhASP87jdbvaBjdDoJ41G4//MHaFUUXD8Kanc4MGD33jjDRIeXnawANt39CHi1dbW9ujRw+MrC9HJkye93VtOnDhBRLm5uUuWLElJSWFNXjw6cuQI+zB8+HD5t/wvnMrKSsm2qquriahXr16+g4w2yCABIABjxozx3ZuPD97SDt+USjt4ctPQ0ODjJRfT1NSkyEaVpXgG5uOIxMX98OvA+wbqYAG27+hDxNuwYcPJkydffPHFbt26eZunrKxs3rx577zzjseH/ePGjZs6dao/T7hZDcjY2FiPTxMNBgP7YLFYJG2uV61atWrVqjbXH22QQQJAVODp18qVK+Pj433PPGTIkOBHpD5Jz5Ei/uadvyVHAUIwLFmyZM6cOXPmzPGWRO7Zs2fevHlr16711kHP8uXL/dwW60jVW6rK3qW43e7GxkY/VxjlkEECQFTQarXsQ0ZGxqBBg9QNxpvm5uZQbo6/mJaz2Wzsw9VXX80+hEUBQtjp2rXriy++6C2J3LNnzz333LN27Vr56ADtwB6N+3hjHh8f73a7+eN28A21UgAgKvAmI7wulNzRo0fLy8u///774IXBnuR5e/hXU1MTvE3L+Ri7nPdAxB/8dJIChMjDksjY2Ng5c+aIz/+UTR+5a6+91ttXvPIG+AMZJABEhZ///Ofsw5YtWzzO0NraOn/+/BkzZgwcONBb74kdx57kNTQ0eEwid+/eHaTteuR2u/ft2yefXltbywaeMRqNaWlpbGInKUCISPIkMkjpIxE5nU5lVxi1kEECQFQYNmwYa3p8/PhxyWB9zLp161iLy+uvvz54/c6wrnBaWlrk3Wq+/fbbbIjCUCosLJS0m2ajILIEd/r06Xx6JylAiFRiEllSUsLqPiqbPrI3AD7aybEeT3ndX/ANGSQARItVq1axt1QbN26cP3/+l19+yabX1dUtX76cDakSGxvb7sbm/sjNzWUfVq9e/fzzz585c6a1tfXw4cN//OMfFy1a1KNHj+Bt2qPq6uo77riDv86urKycMWPG/v37iWjIkCGSgYU6QwFCBGNJZENDw/z581esWKH400f2BsBHQxmWXCYmJiq73UiFV/4AEC0GDBiwfv36hx9+uKGhoaSkpKSkJC4uLi4ujlecj4uLW7169dChQ4MXw5QpU7Zt23bo0KHm5uYnn3xSHAAwMTHx6aefvvPOO4O3dQmTyeR0OisqKu688864uLiYmBj2DIaIBgwY8Oyzz0rm7wwFCJHto48+OnHixIABA954442f//znPrr4aQfWiY/L5WptbZX3jdXU1MSasnlr9A0SeAYJAFFk3LhxO3bsmDRpEnuW1tzczLKf2NjYG2+8cfv27RMnTgxqADExMZs2bZozZ46kH/Ls7Oxt27aNGDEiqFuXiI+P37Rp02233RYbG9vc3MzSR61We/fdd2/ZskUy8jWjegFCBHv//ffvu+++tWvXbtmyJTExsaCgQNmOdfhoCB7r6fI6wbxjSPCty8WLF9WOAQAg1FpaWj755BPWnU3Xrl2zsrKUfdrhTwAff/zxd999l5CQMGDAgB/96Eeh3LpEfX39wYMHm5qarrrqqlGjRvlTD0z1AoQI8957782fP5/XfWxqarrvvvvq6+s3btwY0CD1c+fONZvNJpPp+eefl3xVX18/cuTIlpaW+fPnz5s3T/LtU0899dxzz8XFxVVUVLTZ4ykQMkgAAABQlyR9ZNqXRPrIIIlo9uzZe/fuveaaa3bu3JmUlMSnnzt37pe//GV9ff3kyZNXr17dwd2JEniLDQAAAKp57733HnjgAXnL665du65fv7579+533313QEPV+7BgwQIiOnfu3Ny5c7/55hs28dSpU7Nnz66vr09ISJA/mwRvkEECAACAOt5///358+evX7/eY8trMYlUpE5kZmbmo48+SkQVFRUmkyk/P3/GjBl5eXlffPEFEa1atYp3gAptQgYJAAAA6jh16tT69et5L1dyLInMzMw8e/asIlvMz89/6qmnUlJSmpub9+/fX15e3tLSkp6e/uKLL06aNEmRTUQJ1IMEAACAqFNZWXnmzBkiSk1NzcjIUDuc8IMMEgAAAAACg7fYAAAAABAYZJAAAAAAEBhkkAAAAAAQGGSQAAAAABAYZJAAAAAAEJj/D/sDDZwK/hHZAAAAAElFTkSuQmCC\" alt=\"Absolute value of minimum torque vs. prime on semilog scales\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [tf,Tmin,m,n] = isSeesawPrime(x)\r\n%  tf    = logical variable, true if input is a seesaw prime\r\n%  Tmin  = \r\n  tf = false; Tmin = NaN; m = NaN; n = NaN;\r\nend","test_suite":"%%\r\nx = 2;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = -3;\r\nm_correct = 0;\r\nn_correct = 1;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 11;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = 2;\r\nm_correct = 1;\r\nn_correct = 1;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 23;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = 4;\r\nm_correct = 2;\r\nn_correct = 1;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 53;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = -8;\r\nm_correct = 8;\r\nn_correct = 5;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 167;\r\n[tf,~,m,n] = isSeesawPrime(x);\r\nm_correct = 6;\r\nn_correct = 5;\r\nassert(tf)\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 859;\r\n[tf,~,m,n] = isSeesawPrime(x);\r\nTmin_correct = 192;\r\nm_correct = 98;\r\nn_correct = 58;\r\nassert(~tf)\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 493127;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = 256372;\r\nm_correct = 33006;\r\nn_correct = 18519;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 1989499;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = -2039752;\r\nm_correct = 147476;\r\nn_correct = 70022;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 4869863;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = 2596198;\r\nm_correct = 499;\r\nn_correct = 485;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 6844843;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = -125290;\r\nm_correct = 449054;\r\nn_correct = 221335;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 17750989;\r\n[tf,~,m,n] = isSeesawPrime(x);\r\nTmin_correct = -125290;\r\nm_correct = 459948;\r\nn_correct = 349225;\r\nassert(tf)\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 49999991;\r\n[tf,~,m,n] = isSeesawPrime(x);\r\nTmin_correct = -36000;\r\nm_correct = 3;\r\nn_correct = 5;\r\nassert(~tf)\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = randi(50000)*randi(50000);\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nassert(~tf \u0026\u0026 isnan(Tmin) \u0026\u0026 isnan(m) \u0026\u0026 isnan(n))\r\n\r\n%%\r\np = primes(76207); N = length(p);  \r\n[tf,Tmin,m,n] = deal(false(1,N),NaN(1,N),NaN(1,N),NaN(1,N));\r\nfor k = 1:length(p)\r\n    [tf(k),Tmin(k),m(k),n(k)] = isSeesawPrime(p(k));\r\nend\r\nsumtf_correct = 1;\r\nsumTmin_correct = 2789337;\r\nNmlt40_correct = 3709;\r\nNnlt20_correct = 3093;\r\nNmgt2000_correct = 534;\r\nNngt1000_correct = 808;\r\nNngtm_correct = 1427;\r\nassert(isequal(sum(tf),sumtf_correct))\r\nassert(isequal(sum(Tmin),sumTmin_correct))\r\nassert(isequal(length(find(m\u003c40)),Nmlt40_correct))\r\nassert(isequal(length(find(n\u003c20)),Nnlt20_correct))\r\nassert(isequal(length(find(m\u003e2000)),Nmgt2000_correct))\r\nassert(isequal(length(find(n\u003e1000)),Nngt1000_correct))\r\nassert(isequal(length(find(n\u003em)),Nngtm_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":8,"created_by":46909,"edited_by":46909,"edited_at":"2025-08-14T12:04:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2025-08-14T12:01:21.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-08-04T00:02:18.000Z","updated_at":"2025-09-27T07:37:24.000Z","published_at":"2025-08-04T01:15:55.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60958\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 60958\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e introduced seesaw numbers. A number \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=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a seesaw number if the next \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e smaller numbers can be placed on a seesaw to the left of \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=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at the fulcrum and the \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e larger numbers can be placed to the right to make the net torque about the fulcrum zero. Recall that the torque is equal to the product of the number and its distance from the fulcrum. Let’s take torque leading to counterclockwise rotation as positive and torque leading to clockwise rotation as negative.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem deals with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eseesaw primes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which are like seesaw numbers except that they use primes instead of integers. The number 11 is not a seesaw prime because no values of \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be found to make the net torque zero. The minimum value of torque of 2 units occurs with one prime (7) to the left and one prime (13) to the right—i.e., \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=\\\"m = n = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em = n = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number 167 is a seesaw prime because with six primes on the left (137, 139, 149, 151, 157, 163) and five on the right (173, 179, 181, 191, 193) the torque on the left is 15,322 units, the torque on the right is -15,322 units, and the net torque is zero. \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\u003eSeesaw primes seem to be rare: 167 and 17,750,989 are the only ones smaller than 20,000,000. Although the envelope of the minimum torques increases, the dense cluster of points around zero on a plot with linear axes suggests suggests that other seesaw primes should be possible. A plot of the absolute value of the minimum torque \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=\\\"Tmin\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{min}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e on semilog axes is less encouraging: for primes between 1 and 20 million, only thirteen have an absolute value of minimum torque less than 72 units.\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\u003eWrite a function to determine whether the input number is a seesaw prime. Also return the minimum torque, and \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the number of primes on the left and right when the minimum torque occurs. At least one of \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e must be greater than zero. If the input is not prime, set \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the minimum torque to \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\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Minimum torque vs. prime on linear scales\\\"/\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Absolute value of minimum torque vs. prime on semilog scales\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\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\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image2.png\",\"relationshipId\":\"rId2\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":60952,"title":"List even numbers whose Goldbach partition does not use the largest prime","description":"The strong Goldbach conjecture says that every even number greater than 2 can be expressed as a sum of two prime numbers—that is, they all have Goldbach partitions. Several Cody problems involve some form or variation of the Goldbach conjecture. Problems 60 and 56190 ask us to provide Goldbach partitions, and Problem 64 asks us to count Goldbach partitions for an even number. Problem 60739 restricts the Goldbach partitions to twin primes. Problem 44403 involves writing integers greater than 5 as the sum of three primes, and Problem 60949 involves writing integers greater than 2 as a sum of no more than two primes and the number 1. \r\nOne approach to finding Goldbach partitions of a target number is to start with the largest prime smaller than that number and determine whether the difference is prime. For example, 10 = 7 + 3, 14 = 11 + 3, and 16 = 13 + 3. However, that approach fails for numbers such as 18, 20, and 23 because in those cases, the difference between the numbers and the largest primes smaller than the numbers is 1, which is not prime.  \r\nWrite a function that takes an integer and lists even numbers smaller than or equal to that integer whose Goldbach partitions do not use the largest prime. In other words, for each number in the list, the difference between that number and the largest prime smaller than the number must not be prime (i.e., either 1 or composite).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 291px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 145.5px; transform-origin: 408px 145.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 63px; text-align: left; transform-origin: 385px 63px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe strong Goldbach conjecture says that every even number greater than 2 can be expressed as a sum of two prime numbers—that is, they all have \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eGoldbach partitions\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Several Cody problems involve some form or variation of the Goldbach conjecture. Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e60\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56190\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e56190\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ask us to provide Goldbach partitions, and Problem \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/64\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e64\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asks us to count Goldbach partitions for an even number. Problem \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60739\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e60739\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e restricts the Goldbach partitions to twin primes. Problem \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44403\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e44403\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves writing integers greater than 5 as the sum of three primes, and Problem \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60949\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e60949\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves writing integers greater than 2 as a sum of no more than two primes and the number 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 42px; text-align: left; transform-origin: 385px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOne approach to finding Goldbach partitions of a target number is to start with the largest prime smaller than that number and determine whether the difference is prime. For example, 10 = 7 + 3, 14 = 11 + 3, and 16 = 13 + 3. However, that approach fails for numbers such as 18, 20, and 23 because in those cases, the difference between the numbers and the largest primes smaller than the numbers is 1, which is not prime. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes an integer and lists even numbers smaller than or equal to that integer whose Goldbach partitions do not use the largest prime. In other words, for each number in the list, the difference between that number and the largest prime smaller than the number must not be prime (i.e., either 1 or composite).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = goldbaching(x)\r\n  y = 1:x;\r\nend","test_suite":"%%\r\nx = 30;\r\ny = goldbaching(x);\r\ny_correct = [4 6 8 12 14 18 20 24 30];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = 100;\r\ny = goldbaching(x);\r\ny_correct = [4 6 8 12 14 18 20 24 30 32 38 42 44 48 54 60 62 68 72 74 80 84 90 98];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = 150;\r\ny = goldbaching(x);\r\ny_correct = [4 6 8 12 14 18 20 24 30 32 38 42 44 48 54 60 62 68 72 74 80 84 90 98 102 104 108 110 114 122 128 132 138 140 148 150];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nx = 800;\r\ny = goldbaching(x);\r\nlen_correct = 163;\r\nsum_correct = 61606;\r\nassert(isequal(length(y),len_correct))\r\nassert(isequal(sum(y),sum_correct))\r\n\r\n%%\r\nx = 4000;\r\ny = goldbaching(x);\r\nlen_correct = 774;\r\nsum_correct = 1523050;\r\nassert(isequal(length(y),len_correct))\r\nassert(isequal(sum(y),sum_correct))\r\n\r\n%%\r\nx = 25000;\r\ny = goldbaching(x);\r\nlen_correct = 4679;\r\nystr_correct = [21292 21298 21304 21308 21310 21314 21318 21320 21324 21332 21338 21342 21348 21356 21362 21368 21372 21374 21378 21380 21384 21392 21398 21402 21408 21416 21420 21428 21434 21442 21448];\r\nassert(isequal(length(y),len_correct))\r\nassert(isequal(y(3992:4022),ystr_correct))\r\n\r\n%%\r\nx = 53606;\r\ny = goldbaching(x);\r\nlen_correct = 10000;\r\nsum_correct = 267146550;\r\nsumsqrt_correct = 1539275.930840296;\r\nystr_correct = [48222 48230 48236 48240 48248 48256 48260 48268 48272 48280 48282 48290 48296 48300 48308 48312 48314 48322 48328 48334 48338 48342 48350 48354 48362 48368];\r\nassert(isequal(length(y),len_correct))\r\nassert(isequal(sum(y),sum_correct))\r\nassert(abs(sum(sqrt(y))-sumsqrt_correct)\u003c1e-7)\r\nassert(isequal(y(9000:9025),ystr_correct))\r\n\r\n%%\r\nx = 500000;\r\ny = goldbaching(x);\r\nL = [];\r\nfor p = [13 29 67 127 191]\r\n    L(end+1) = length(y(mod(y,p)==0));\r\nend\r\nlen_correct = 93640;\r\nsum_correct = 23440930328;\r\nystr_correct = [53606 80628 107348 134078 160826 187508 214172 240826 267582 294146 320760 347374 373862 400628 427150 453766 480518];\r\nL_correct = [7541 3219 1375 757 489];\r\nassert(isequal(length(y),len_correct))\r\nassert(isequal(sum(y),sum_correct))\r\nassert(isequal(y(10000:5000:90000),ystr_correct))\r\nassert(isequal(L,L_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-02T00:54:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-02T00:53:37.000Z","updated_at":"2025-10-02T12:04:26.000Z","published_at":"2025-07-02T00:54:19.000Z","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\u003eThe strong Goldbach conjecture says that every even number greater than 2 can be expressed as a sum of two prime numbers—that is, they all have \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGoldbach partitions\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Several Cody problems involve some form or variation of the Goldbach conjecture. Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e60\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56190\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e56190\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ask us to provide Goldbach partitions, and Problem \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/64\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e64\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks us to count Goldbach partitions for an even number. Problem \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60739\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e60739\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e restricts the Goldbach partitions to twin primes. Problem \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44403\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e44403\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves writing integers greater than 5 as the sum of three primes, and Problem \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60949\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e60949\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves writing integers greater than 2 as a sum of no more than two primes and the number 1. \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\u003eOne approach to finding Goldbach partitions of a target number is to start with the largest prime smaller than that number and determine whether the difference is prime. For example, 10 = 7 + 3, 14 = 11 + 3, and 16 = 13 + 3. However, that approach fails for numbers such as 18, 20, and 23 because in those cases, the difference between the numbers and the largest primes smaller than the numbers is 1, which is not prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes an integer and lists even numbers smaller than or equal to that integer whose Goldbach partitions do not use the largest prime. In other words, for each number in the list, the difference between that number and the largest prime smaller than the number must not be prime (i.e., either 1 or composite).\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":57810,"title":"List the two-bit primes","description":"Each year at Christmas, my father-in-law and his partner send me the Puzzle Mania section from the New York Times. This year’s edition had a puzzle by Mike Shenk called “Two Bits”, which asked solvers to find words whose first two letters could be shifted as a unit elsewhere in the word to form a new word. For example, the clue “??BID” had the answer RABID, with the accompanying word BRAID. The clue “??PREME” had the answer SUPREME, with the accompanying word PRESUME.\r\nIn a similar way, one can define two-bit primes: prime numbers whose first two digits can be shifted, as a unit, elsewhere in the number to form a new prime number. The first in the sequence is 113, with accompanying prime 311, followed by 131, with accompanying prime 113. Some two-bit primes can have multiple accompanying primes. For example, the two-bit prime 99611 has two accompanying primes: 69911 and 61991. Leading zeros are allowed: 1103 is a two-bit prime because 311 is also prime. \r\nRemember that the two-bit prime and its accompanying prime must differ. For example, the first two digits of 99991 can be moved one or two places to the right, but the resulting number (99991) is the same. Because 99199 is not prime, 99991 is not a two-bit prime. \r\nWrite a function to list the th two-bit and all its accompanying primes. ","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: 321px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 160.5px; transform-origin: 407px 160.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; 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: 313.108px 8px; transform-origin: 313.108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach year at Christmas, my father-in-law and his partner send me the Puzzle Mania section from the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.8417px 8px; transform-origin: 52.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eNew York Times.\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: 17.1083px 8px; transform-origin: 17.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e This year’s edition had a puzzle by Mike Shenk called “Two Bits”, which asked solvers to find words whose first two letters could be shifted as a unit elsewhere in the word to form a new word. For example, the clue “??BID” had the answer RABID, with the accompanying word BRAID. The clue “??PREME” had the answer SUPREME, with the accompanying word PRESUME.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; 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 52.5px; text-align: left; transform-origin: 384px 52.5px; 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: 381.058px 8px; transform-origin: 381.058px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a similar way, one can define two-bit primes: prime numbers whose first two digits can be shifted, as a unit, elsewhere in the number to form a new prime number. The first in the sequence is 113, with accompanying prime 311, followed by 131, with accompanying prime 113. Some two-bit primes can have multiple accompanying primes. For example, the two-bit prime 99611 has two accompanying primes: 69911 and 61991. Leading zeros are allowed: 1103 is a two-bit prime because 311 is also prime. \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: 379.875px 8px; transform-origin: 379.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemember that the two-bit prime and its accompanying prime must differ. For example, the first two digits of 99991 can be moved one or two places to the right, but the resulting number (99991) is the same. Because 99199 is not prime, 99991 is not a two-bit prime. \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: 80.375px 8px; transform-origin: 80.375px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 133.808px 8px; transform-origin: 133.808px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth two-bit and all its accompanying primes. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y,a] = twobitPrime(n)\r\n  y = isprime(n); a = primes(n);\r\nend","test_suite":"%%\r\nn = 1;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 113;\r\na_correct = 311;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 5;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 199;\r\na_correct = 919;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 31;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 977;\r\na_correct = 797;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 311;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 5119;\r\na_correct = 1951;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 500;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 7963;\r\na_correct = [6379 6793];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),sort(a_correct)))\r\n\r\n%%\r\nn = 873;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 13591;\r\na_correct = 59113;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 873;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 13591;\r\na_correct = 59113;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 1876;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 29009;\r\na_correct = [929 2909];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nn = 5277;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 86069;\r\na_correct = [6869 8669];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nn = 8153;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 134921;\r\na_correct = 492113;\r\nassert(isequal(y,y_correct))\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 10003;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 168617;\r\na_correct = [861167 861617];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nn = 25000;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 433261;\r\na_correct = [324361 326143 343261];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nn = 39000;\r\n[y,a] = twobitPrime(n);\r\ny_correct = 697877;\r\na_correct = [787697 787769];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\n[y,a] = twobitPrime(twobitPrime(54));\r\ny_correct = 19853;\r\na_correct = [81953 85193];\r\nassert(isequal(y,y_correct))\r\nassert(isequal(sort(a),a_correct))\r\n\r\n%%\r\nfiletext = fileread('twobitPrime.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-03-19T00:22:09.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-19T00:21:05.000Z","updated_at":"2025-01-02T08:51:14.000Z","published_at":"2023-03-19T00:22:09.000Z","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\u003eEach year at Christmas, my father-in-law and his partner send me the Puzzle Mania section from the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNew York Times.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e This year’s edition had a puzzle by Mike Shenk called “Two Bits”, which asked solvers to find words whose first two letters could be shifted as a unit elsewhere in the word to form a new word. For example, the clue “??BID” had the answer RABID, with the accompanying word BRAID. The clue “??PREME” had the answer SUPREME, with the accompanying word PRESUME.\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\u003eIn a similar way, one can define two-bit primes: prime numbers whose first two digits can be shifted, as a unit, elsewhere in the number to form a new prime number. The first in the sequence is 113, with accompanying prime 311, followed by 131, with accompanying prime 113. Some two-bit primes can have multiple accompanying primes. For example, the two-bit prime 99611 has two accompanying primes: 69911 and 61991. Leading zeros are allowed: 1103 is a two-bit prime because 311 is also prime. \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\u003eRemember that the two-bit prime and its accompanying prime must differ. For example, the first two digits of 99991 can be moved one or two places to the right, but the resulting number (99991) is the same. Because 99199 is not prime, 99991 is not a two-bit prime. \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\u003eWrite a function to list the \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth two-bit and all its accompanying primes. \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":60958,"title":"Determine whether a number is a seesaw number","description":"Cody Problem 60957 dealt with balanced primes. In that case, balance was measured in terms of the average of primes around a given prime. \r\nThis problem involves a different sense of balance. Consider the input number  to be at the fulcrum of a massless seesaw (or teeter-totter). Then place the next  smaller numbers to the left and the next  larger numbers to the right. Each number creates a torque about the fulcrum equal to the product of the number and its distance from the fulcrum. In the example below with 14 at the fulcrum, the number 10 creates a torque of 140 units about the fulcrum. The number  is a seesaw number if  and  can be found to balance the seesaw; that is, the torque on the left balances the torque on the right.\r\nFor example, 14 is a seesaw number—as shown below—because the numbers 4 through 13 create a total torque of 385 units on the left and the numbers 15 through 20 create an opposing torque of 385 units on the right. \r\nWrite a function to determine whether the input number is a seesaw number. \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 523.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 261.9px; transform-origin: 408px 261.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60957-list-balanced-primes\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 60957\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e dealt with balanced primes. In that case, balance was measured in terms of the average of primes around a given prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 52.5px; text-align: left; transform-origin: 385px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem involves a different sense of balance. Consider the input number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to be at the fulcrum of a massless seesaw (or teeter-totter). Then place the next \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e smaller numbers to the left and the next \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e larger numbers to the right. Each number creates a torque about the fulcrum equal to the product of the number and its distance from the fulcrum. In the example below with 14 at the fulcrum, the number 10 creates a torque of 140 units about the fulcrum. The number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a seesaw number if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be found to balance the seesaw; that is, the torque on the left balances the torque on the right.\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: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, 14 is a seesaw number—as shown below—because the numbers 4 through 13 create a total torque of 385 units on the left and the numbers 15 through 20 create an opposing torque of 385 units on the right. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether the input number is a seesaw number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 247.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 123.9px; text-align: left; transform-origin: 385px 123.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"872\" height=\"242\" style=\"vertical-align: baseline;width: 872px;height: 242px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isSeesawNumber(x)\r\n  y = false;\r\nend","test_suite":"%% \r\nassert(isSeesawNumber(5))\r\n\r\n%% \r\nassert(~isSeesawNumber(8))\r\n\r\n%% \r\nassert(isSeesawNumber(14))\r\n\r\n%% \r\nassert(isSeesawNumber(50))\r\n\r\n%% \r\nassert(~isSeesawNumber(60))\r\n\r\n%% \r\nassert(~isSeesawNumber(84))\r\n\r\n%% \r\nassert(~isSeesawNumber(238))\r\n\r\n%% \r\nassert(isSeesawNumber(680))\r\n\r\n%% \r\nassert(isSeesawNumber(1001))\r\n\r\n%% \r\nassert(isSeesawNumber(1378))\r\n\r\n%% \r\nassert(isSeesawNumber(5182))\r\n\r\n%% \r\nassert(~isSeesawNumber(7276))\r\n\r\n%% \r\nassert(~isSeesawNumber(11648))\r\n\r\n%% \r\nassert(~isSeesawNumber(15102))\r\n\r\n%% \r\nassert(~isSeesawNumber(32586))\r\n\r\n%% \r\nassert(isSeesawNumber(40000))\r\n\r\n%%\r\nassert(isSeesawNumber(2*randi(2^15)+1))\r\n\r\n%%\r\na = NaN(1,10000); \r\nk = 0; x = 2; \r\nwhile any(isnan(a))\r\n    if isSeesawNumber(x)\r\n        k = k+1; \r\n        a(k) = x; \r\n    end\r\n    x = x+2;\r\nend\r\nd = diff(a); \r\nu = unique(d);\r\nh = hist(d,u);\r\nsuma_correct = 153539516;\r\nhist_correct = [6588 2370 673 250 83 23 8 4];\r\nassert(isequal(sum(a),suma_correct))\r\nassert(isequal(h,hist_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-16T02:59:05.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-16T02:58:01.000Z","updated_at":"2026-04-03T12:34:57.000Z","published_at":"2025-07-16T02:58:11.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60957-list-balanced-primes\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 60957\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e dealt with balanced primes. In that case, balance was measured in terms of the average of primes around a given prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem involves a different sense of balance. Consider the input number \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=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to be at the fulcrum of a massless seesaw (or teeter-totter). Then place the next \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e smaller numbers to the left and the next \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e larger numbers to the right. Each number creates a torque about the fulcrum equal to the product of the number and its distance from the fulcrum. In the example below with 14 at the fulcrum, the number 10 creates a torque of 140 units about the fulcrum. The number \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=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a seesaw number if \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be found to balance the seesaw; that is, the torque on the left balances the torque on the right.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, 14 is a seesaw number—as shown below—because the numbers 4 through 13 create a total torque of 385 units on the left and the numbers 15 through 20 create an opposing torque of 385 units on the right. \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\u003eWrite a function to determine whether the input number is a seesaw number. \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=\\\"242\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"872\\\"/\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\u003e\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":53990,"title":"Classify product/digit-sum sequences","description":"Cody Problem 53120 involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\r\nWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved Cody Problem 53120, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \r\nWrite a function to classify the product/digit-sum sequences given the first two terms  and . To encourage solvers to find the pattern, loops are banned, and to allow for large inputs,  and  are specified as strings. ","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: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 93px; transform-origin: 407.5px 93px; 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: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\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: 309.642px 7.66667px; transform-origin: 309.642px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 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: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 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: 383.883px 7.66667px; transform-origin: 383.883px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\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: 103.075px 7.66667px; transform-origin: 103.075px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \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: 384.5px 21px; text-align: left; transform-origin: 384.5px 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: 262.017px 7.66667px; transform-origin: 262.017px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\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 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\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: 93.35px 7.66667px; transform-origin: 93.35px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\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 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\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: 77.4px 7.66667px; transform-origin: 77.4px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are specified as strings. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = PDSseq(a,b)\r\n  c = [1 9 26 62 163];\r\n  y = c(a+b);\r\nend","test_suite":"%%\r\na = '1';\r\nb = '2';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7';\r\nb = '31';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '17';\r\nb = '28';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '51';\r\nb = '77';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '82';\r\nb = '262';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7021';\r\nb = '8878';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264';\r\nb = '412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8675308';\r\nb = '2941300';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '9142534264';\r\nb = '8424812653';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164';\r\nb = '8424812753';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '1352408463575';\r\nb = '9898989898985';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264534264534264534264';\r\nb = '412578412578412578412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '86753088675308867530886753088675308';\r\nb = '28413002941300294130029413002941300';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '914253426491425342649142534264914253463';\r\nb = '842481265384248126538424812653842481265324';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164842481275380314231648424812753';\r\nb = '84248127538031423164842481275380314231648424812756';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '43524084635758031423164842481275380314231648424812753';\r\nb = '98989898989858031423164842481275380614231648424812753';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = num2str(randi(835042)*57);\r\nb = char(randi(9,20,1)+48);\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = repelem('1',1,23);\r\na(randi(23)) = '4';\r\nb = num2str(10^randi(14));\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\nfiletext = fileread('PDSseq.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'system') || contains(filetext,'regexp') || contains(filetext,'java') || contains(filetext,'for') || contains(filetext,'while') || contains(filetext,'numpy'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2022-02-05T01:46:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-02-04T04:01:11.000Z","updated_at":"2026-01-15T18:05:52.000Z","published_at":"2022-02-04T04:04:20.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 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\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \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\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \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\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \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=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \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\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \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=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are specified as strings. \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":58977,"title":"Find the smallest number leading to a maximal product of two numbers that concatenate to another number","description":"Cody Problem 58971 involves the maximal product of numbers that concatenate to a number . For example, if , then the products are , , and , and the maximal product is 492. For , the maximal product is zero.\r\nThis problem seeks the smallest number leading to a given maximal product. If the product is 492, the smallest number is 682. Some products have no solution. For example, 13 is a product of both 113 and 131, but the maximal products are 33 and 31, respectively. \r\nWrite a function that takes a maximal product and returns the smallest number leading to that product. If the product has no corresponding number, return the empty set.  ","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: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 93px; transform-origin: 407px 93px; 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\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58971\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58971\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: 224.042px 8px; transform-origin: 224.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves the maximal product of numbers that concatenate to a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 52.1083px 8px; transform-origin: 52.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59\" height=\"18\" alt=\"n = 1234\" style=\"width: 59px; 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: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then the products are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKoAAAAkCAYAAAAZzKEqAAAF20lEQVR4Xu2bTci2QxTH33dPPnYsKCyIhZKPiIVEKUnykaS3yMdCkiiShd4okoWFj2KhCCWJFIkiIimJWLBgwQqJPf9fzb/Oe71zXdfMfd/Pe93zPDN1eu77vmbOdeY//zlz5sw8+/f10hFoAIH9DdjYTewI7OtE7SRoAoFO1CaGqRvZido50AQCnahNDFM3shO1c6AJBGqIeqd69IjkaslXC/YOOw5Izk82/Ku/n0seLrCLttdILpQcJfld8qnkLsmfK/TpdbW5XnJewbtXUL+jTS6X9vsCFrzsS8nTEvo1VWh7q+RiyQmSmjHI6WVcnpU8JHk8V6GEqCYoBlGWGpTj9e73JCZorj83ToBsUv2oOn9LzpRAVgpAny35eWaA4uMb9OW1hTGpMPeQqs/r2+0TjV/QsztGnptUTPJfJSdJzA2aTI1BTuWp+vGbNBYrEfVcNb4tab4pDOpSRAVc7ICsLya7ztHfuwdA5eyj7SWSeyQfBLQe1OfH0vc39BfylZQILvWXwqTE1mEdTzBweEnyl+QUyQFJdAI50tAWj/uMJHo+POybiSMQ+MQKw35Q3dNT/ZWIymDYwzyhz/cnZUsMCpPmo2TDcxkQ3tdvgEUZEo5+vCu5SJJb3t0Wr3p0IcCASzHAS2BSaOph1f7RL69Kch4zTtwc4ej3LZJc6BfbluJhB7IWUWMPlyaqY6YxjwcZf0oGDwEGwK8l0ZPm+lbqCcDiZsm9ktaWfpZtVpWxSQsuv0m8lJ+mz3ZWOAJWsGwMqd95zqRnwl86QuaIu73wtakdz1byqNtE1KmZbDu9hNR4Rto6XpuKy/yOCC6/MTCUUg8SMV3iMxP+Y0luVbI9MX6t6ZdDCvYAZ8x0jv3GLxLCLoj/X6rfPFFLBvULVSLGKgEq6sODUNjBTm2mAPc7ieMze5CWiFqCo1fP2g0mk+BKCfuauayBJ/gVyaA9RVR71BLP6AED0JMlbMjmUm6Ae4zkgtR4txLVHrVmwjszRDg0R1JCMfCOjmHPEBVv94ekND4ipn0leWDakMN7YMLdeCAiuOsSNbYv8XRjdUaXyxWVesKTW54KEVAP7izdTnWxkZ3KSbMpflsyJPSeIapze3PeFHI8mgg6HMcxDwKpORSgXRy43UhUb0rnvCn1iC857BiWqZCBSfCJZJhx2EqiQqrj0kxccdIf1sxx5ll6UnrC5NOVCHaO6ID7rWSYcViXqJvq+yb1OM5kJz6WJRm+Dy95XfKkPkDJEd2pqFzGYeuIGtNcAOFgeh2wnS5a9Wg3njANMwbovkqSA3e3EdUZDfLlc0t+brymDkGseyxttXVEjYn50rzlFInXBde6fbzKd6dk5sDdTUR1umjsIKDUkTgEo75jZ+uemgBbR1QH03RkGPOVguF61rWuHvTlzu2d7qq1qyb3WKt7J+pDpM8kudix9n3e1EaixlW0Rt8hm8SSSykoX/pkKhcXsXvcBEnRHU9VSFcR5+40Ubdh179JknqM7B0J6wjv9ixRSzwpA1C6qYoetSZuXnfpX5qopSStwdIelbCuZmO7dUt/jevP1TW4L+vh2Jkz7YiFn0ozuuSdNacq1rcuUUvs2sk69PlYydSGluQ8GZqpHHO00THqkxVtaL+riGqS0jEuVowVLgNzR9Lnzb5ozdlyLhm9KrgtEzVOTK755cplCS/f02Ul4/iYu7y5S+q+4fa9nvv0rnSibYyoMV6rvRhbauxUPZPU18HmdMZAPGYafAr1YVJAvpD00/B+5Zx+nrdK1JjhmOtnDIXiNT7acQo1vBf8jn6jXk3Yha61iEpeDJfPQMYb3DaSW9lTy+8cCDXP4+XauXbDkxFm+sFELLclIc3t9LcS4LXAtkrUuZv9Q2yjU8JZcNTMxRMn9n3Ln40txK35D4n4rrWIOkeI/rwjcMQQKE1PHTGD+os6AjkEOlE7L5pAoBO1iWHqRnaidg40gUAnahPD1I3sRO0caAKBTtQmhqkb2YnaOdAEAv8DBDeQNHiRr2IAAAAASUVORK5CYII=\" width=\"85\" height=\"18\" alt=\"1x234 = 234\" style=\"width: 85px; 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: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKoAAAAkCAYAAAAZzKEqAAAGRklEQVR4Xu1bTchuUxT+7pyEEQMGDNwYKPnpioEBpW6SQpIU+RlIEiFJ0lVkZOCnTJRCSUqKZEDkJyURAwYMGFFizvPc9lOr/e69zjrn7HM+x7dPrd77ve/e6+z9rGevvfba6x7a609HYAMIHNrAGPsQOwJ7naidBJtAoBN1E2bqg+xE7RzYBAKdqJswUx9kJ2rnwCYQGEPUuzCjxyDXQL4MzI7tb4VcnNr+jc9PIY8G+wdeMboJx3Qt5AjkBMhvkI8hd0P+GK1tb+919LkectE+zmnCsKtdiM/zkEcgTzmKT8FvD0EuT21OSp+P45OYeM+V+PF+0499Ka4dIkQVQU9LyoeMwkm8CxFBS4O+MTChlgagLpHqB/z7T8i5EJKVDxfR+ZCfRrz0BrR9LYjJCLX71vQsvPnrhIlH1AvR5kPIXxDrtERy4nu4Mgva4GrIMYhdCNLJbkU7eERl59vTC28yRh0i6otoy/Yk68up/wX4vAcisvPrIT0tLcYxcfXfC3nfKH44gcav3oCQfJHHGnXtuUTGN6XN9+h0TupYIyqd0M+JCyVn8x5+o8ckxldlg3gafz/g4KyFXyS6R1QaQx5GLxkyilYGB/RCAS1NZCwxpgCvPpzHO5BLIaXtXWOiVz0x+CIalY8Mu+aiCw5xVDMt5CGialdiyHR64Q20/xfpexLVOoVf8Tcdleet/0l9zzbcO/5VZOtnuyhRFZ/UPBNJ82MaTG2yoxAONKbX/CoDzXbT3KLjYfubIfdB/g9bPz3gm5DrIFy0fEpksrbzdh+GBAypPodcYoAWCZ/Bdw9W7KY2Owu/NVHpaW6BeIctbTFjPFiAj5Ob0JvcAXkJcueAFmtUNpVht+pRtZUrZhRRSkS1YZLnFT8DLjqfnIp/axeTR63ZXd646DBaEzXCFk3EC7ojelq1IYB8LoN4hyka9VvIcxAeBEjarRNV41c86RHVEtBbmHb3tXGs/b5ke4VgxUWwH0SVR414sFZkrOlhqHImhAe9oZQbgWQaRdvZ1olKD8l52wXqEVUekVhGiWq3eS70TyCKg+k5mTWgc2BKjOOQE9ix19pE5WB/h9D9XxEgx1JEZbz1KoRbFMdCoGpxE8egFJ016lyi2v5z5jmU8yzp5jb7NoRxts17ekTVb2OImp/+c7JSl3LZnEd1R1ubqMq17Zc3JTmeSATNDVgLRUhqJqPZz2YytkxU7mofQfKYPEJULmzuQrULEptfLqWpSnl2ktUNvdYmquLB85yJet6FRD8Z4t2aRL0TiXYbhDdLekoLiEb9BpJnMuYSNTrO1u2Uiiql66JE9dJ4FpcSUZUu5LwUBmiO1YugNYmqtE70CjY3kA3GSwBMNaj1APmJlO88CikZdYtEVdaiFnZFiEqcozFqbifl2b+DDt5QkbSvZIQtknUtogqg2kVAhGT2siCa84zoZRslsq0Rhoy6NaIqFeXZwCOqvbmKEtUepnSbR4zza1KLfzG0WIOoCtzzGC9KIrWTHv49V1f+7tK9vU3HjBnrfzWnanekMfPRYc06iihRWeyjuF5krF0WWLLafsfHujRRW5F0DLBT2so72tW8NFHXPvXPJapN+O8QyYBur6RtiKEbK6+OgBkhPjuh3ZJEjZCU29GU8ropZPT6yKOOiX3nbv1rEzWCmbf12ytUL2ujfGueRfF0a2xyDqsRVfkyBsreCZ2r79m0giJALtVG5WesFhuqp9QY5hJ1qbnM0TtEpjFFKfmhKHLRI6Lu1AMs4VFFUgLGsrraw+LZMyC12sU5gNu+KuBmeVqpQFq5Xa9YojSWg0jUoTI/Ebm0Mwnn2l2/vQzaqUmNEtXGa17Rc+nmwSPclFuVsQS2hwDdQn2QlLBiiOmn6tWd87KDSFTCUStyFhFZNcXUUymks8XrNuWnSwAWsxezEkP1qLxWpCFtwTMHy5Mbq8Hzbd2mMIYINaWqfkhn6XcC+ySExNLD+OkXyFtpLlPi5INKVGLIeJUVV7xNIo6sgeD/muC1LC8UPDyJG3fTIxDmU/Vwx6teo0Y96hSC9D4dgWYIdKI2g7IrWhKBTtQl0e26myHQidoMyq5oSQQ6UZdEt+tuhkAnajMou6IlEehEXRLdrrsZAp2ozaDsipZEoBN1SXS77mYI/AsQar80KmbQ3AAAAABJRU5ErkJggg==\" width=\"85\" height=\"18\" alt=\"12x34 = 408\" style=\"width: 85px; 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: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"85\" height=\"18\" alt=\"123x4 = 492\" style=\"width: 85px; 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: 117.458px 8px; transform-origin: 117.458px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the maximal product is 492. For \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"18\" alt=\"n \u003c 10\" style=\"width: 44px; 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: 15.55px 8px; transform-origin: 15.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the maximal product is zero.\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: 376.908px 8px; transform-origin: 376.908px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem seeks the smallest number leading to a given maximal product. If the product is 492, the smallest number is 682. Some products have no solution. For example, 13 is a product of both 113 and 131, but the maximal products are 33 and 31, respectively. \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: 382.983px 8px; transform-origin: 382.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a maximal product and returns the smallest number leading to that product. If the product has no corresponding number, return the empty set. \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\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = minWithMaxProd(n)\r\n  y = min(max(prod(n)));\r\nend","test_suite":"%%\r\nassert(isequal(minWithMaxProd(0),0))\r\n\r\n%%\r\nn = randi(9,1,randi(9));\r\ny = arrayfun(@minWithMaxProd,n);\r\nassert(all(isequal(y,n+10)));\r\n\r\n%%\r\nassert(isequal(minWithMaxProd(689),1353))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(943),1943))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(1615),1795))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(3196),3494))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(3252),4813))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(4077),4539))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(4710),5942))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(5986),7382))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(6386),10362))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(6545),7785))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(6960),8087))\r\n \r\n%%\r\nassert(isequal(minWithMaxProd(8200),10082))\r\n\r\n%%\r\nassert(isequal(minWithMaxProd(1e6),1250008))\r\n\r\n%%\r\nassert(isequal(minWithMaxProd(1e7-1),11111119))\r\n\r\n%%\r\nassert(isequal(minWithMaxProd(2122556450),3032223507))\r\n\r\n%%\r\nassert(isequal(minWithMaxProd(7777777777),10000177777))\r\n\r\n%%\r\nassert(isequal(minWithMaxProd(7199254740980),7254680599236))\r\n\r\n%%\r\np = primes(100000); \r\nlen = length(p);\r\na = zeros(1,len);\r\nfor k = 1:len\r\n    m = minWithMaxProd(p(k));\r\n    if ~isempty(m)\r\n        a(k) = m;\r\n    end\r\nend\r\nassert(isequal(length(find(a==0)),9257))\r\nassert(isequal(sum(a),40526242))\r\n\r\n%%\r\na = zeros(1,10000);\r\nfor k = 1:10000\r\n    m = minWithMaxProd(k);\r\n    if ~isempty(m)\r\n        a(k) = m;\r\n    end\r\nend\r\nassert(isequal(sum(a),39095445))\r\nassert(isequal(sum(diff(a)),12497))\r\nassert(isequal(a*(-1).^(1:10000)',6961479))\r\n\r\n%%\r\nfiletext = fileread('minWithMaxProd.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-17T16:21:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-16T05:27:31.000Z","updated_at":"2023-09-17T16:21:27.000Z","published_at":"2023-09-16T05:27:31.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58971\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58971\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves the maximal product of numbers that concatenate to a number \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, if \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=\\\"n = 1234\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 1234\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then the products are \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=\\\"1x234 = 234\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\\\\cdot234 = 234\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \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=\\\"12x34 = 408\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e12\\\\cdot34 = 408\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \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=\\\"123x4 = 492\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e123\\\\cdot4 = 492\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the maximal product is 492. For \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=\\\"n \u0026lt; 10\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026lt; 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the maximal product is zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem seeks the smallest number leading to a given maximal product. If the product is 492, the smallest number is 682. Some products have no solution. For example, 13 is a product of both 113 and 131, but the maximal products are 33 and 31, respectively. \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\u003eWrite a function that takes a maximal product and returns the smallest number leading to that product. If the product has no corresponding number, return the empty set. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\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":60991,"title":"Search for seesaw primes","description":"Cody Problem 60958 introduced seesaw numbers. A number  is a seesaw number if the next  smaller numbers can be placed on a seesaw to the left of  at the fulcrum and the  larger numbers can be placed to the right to make the net torque about the fulcrum zero. Recall that the torque is equal to the product of the number and its distance from the fulcrum. Let’s take torque leading to counterclockwise rotation as positive and torque leading to clockwise rotation as negative.\r\nThis problem deals with seesaw primes, which are like seesaw numbers except that they use primes instead of integers. The number 11 is not a seesaw prime because no values of  and  can be found to make the net torque zero. The minimum value of torque of 2 units occurs with one prime (7) to the left and one prime (13) to the right—i.e., . \r\nThe number 167 is a seesaw prime because with six primes on the left (137, 139, 149, 151, 157, 163) and five on the right (173, 179, 181, 191, 193) the torque on the left is 15,322 units, the torque on the right is -15,322 units, and the net torque is zero. \r\nSeesaw primes seem to be rare: 167 and 17,750,989 are the only ones smaller than 20,000,000. Although the envelope of the minimum torques increases, the dense cluster of points around zero on a plot with linear axes suggests suggests that other seesaw primes should be possible. A plot of the absolute value of the minimum torque  on semilog axes is less encouraging: for primes between 1 and 20 million, only thirteen have an absolute value of minimum torque less than 72 units.\r\nWrite a function to determine whether the input number is a seesaw prime. Also return the minimum torque, and  and , the number of primes on the left and right when the minimum torque occurs. At least one of  and  must be greater than zero. If the input is not prime, set , , and the minimum torque to NaN.\r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1101.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 550.55px; transform-origin: 408px 550.55px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 42px; text-align: left; transform-origin: 385px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/60958\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 60958\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e introduced seesaw numbers. A number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a seesaw number if the next \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e smaller numbers can be placed on a seesaw to the left of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at the fulcrum and the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e larger numbers can be placed to the right to make the net torque about the fulcrum zero. Recall that the torque is equal to the product of the number and its distance from the fulcrum. Let’s take torque leading to counterclockwise rotation as positive and torque leading to clockwise rotation as negative.\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: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem deals with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eseesaw primes\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which are like seesaw numbers except that they use primes instead of integers. The number 11 is not a seesaw prime because no values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e can be found to make the net torque zero. The minimum value of torque of 2 units occurs with one prime (7) to the left and one prime (13) to the right—i.e., \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"66\" height=\"18\" alt=\"m = n = 1\" style=\"width: 66px; 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 167 is a seesaw prime because with six primes on the left (137, 139, 149, 151, 157, 163) and five on the right (173, 179, 181, 191, 193) the torque on the left is 15,322 units, the torque on the right is -15,322 units, and the net torque is zero. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 106.5px; 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: 385px 53.25px; text-align: left; transform-origin: 385px 53.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSeesaw primes seem to be rare: 167 and 17,750,989 are the only ones smaller than 20,000,000. Although the envelope of the minimum torques increases, the dense cluster of points around zero on a plot with linear axes suggests suggests that other seesaw primes should be possible. A plot of the absolute value of the minimum torque \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"26.5\" height=\"20\" alt=\"Tmin\" style=\"width: 26.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e on semilog axes is less encouraging: for primes between 1 and 20 million, only thirteen have an absolute value of minimum torque less than 72 units.\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: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether the input number is a seesaw prime. Also return the minimum torque, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the number of primes on the left and right when the minimum torque occurs. At least one of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e must be greater than zero. If the input is not prime, set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the minimum torque to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eNaN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 166.9px; text-align: left; transform-origin: 385px 166.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" src=\"data:image/png;base64,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\" alt=\"Minimum torque vs. prime on linear scales\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 333.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 166.9px; text-align: left; transform-origin: 385px 166.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"438\" height=\"328\" style=\"vertical-align: baseline;width: 438px;height: 328px\" src=\"data:image/png;base64,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\" alt=\"Absolute value of minimum torque vs. prime on semilog scales\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [tf,Tmin,m,n] = isSeesawPrime(x)\r\n%  tf    = logical variable, true if input is a seesaw prime\r\n%  Tmin  = \r\n  tf = false; Tmin = NaN; m = NaN; n = NaN;\r\nend","test_suite":"%%\r\nx = 2;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = -3;\r\nm_correct = 0;\r\nn_correct = 1;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 11;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = 2;\r\nm_correct = 1;\r\nn_correct = 1;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 23;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = 4;\r\nm_correct = 2;\r\nn_correct = 1;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 53;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = -8;\r\nm_correct = 8;\r\nn_correct = 5;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 167;\r\n[tf,~,m,n] = isSeesawPrime(x);\r\nm_correct = 6;\r\nn_correct = 5;\r\nassert(tf)\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 859;\r\n[tf,~,m,n] = isSeesawPrime(x);\r\nTmin_correct = 192;\r\nm_correct = 98;\r\nn_correct = 58;\r\nassert(~tf)\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 493127;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = 256372;\r\nm_correct = 33006;\r\nn_correct = 18519;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 1989499;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = -2039752;\r\nm_correct = 147476;\r\nn_correct = 70022;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 4869863;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = 2596198;\r\nm_correct = 499;\r\nn_correct = 485;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 6844843;\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nTmin_correct = -125290;\r\nm_correct = 449054;\r\nn_correct = 221335;\r\nassert(~tf)\r\nassert(isequal(Tmin,Tmin_correct))\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 17750989;\r\n[tf,~,m,n] = isSeesawPrime(x);\r\nTmin_correct = -125290;\r\nm_correct = 459948;\r\nn_correct = 349225;\r\nassert(tf)\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = 49999991;\r\n[tf,~,m,n] = isSeesawPrime(x);\r\nTmin_correct = -36000;\r\nm_correct = 3;\r\nn_correct = 5;\r\nassert(~tf)\r\nassert(isequal(m,m_correct))\r\nassert(isequal(n,n_correct))\r\n\r\n%%\r\nx = randi(50000)*randi(50000);\r\n[tf,Tmin,m,n] = isSeesawPrime(x);\r\nassert(~tf \u0026\u0026 isnan(Tmin) \u0026\u0026 isnan(m) \u0026\u0026 isnan(n))\r\n\r\n%%\r\np = primes(76207); N = length(p);  \r\n[tf,Tmin,m,n] = deal(false(1,N),NaN(1,N),NaN(1,N),NaN(1,N));\r\nfor k = 1:length(p)\r\n    [tf(k),Tmin(k),m(k),n(k)] = isSeesawPrime(p(k));\r\nend\r\nsumtf_correct = 1;\r\nsumTmin_correct = 2789337;\r\nNmlt40_correct = 3709;\r\nNnlt20_correct = 3093;\r\nNmgt2000_correct = 534;\r\nNngt1000_correct = 808;\r\nNngtm_correct = 1427;\r\nassert(isequal(sum(tf),sumtf_correct))\r\nassert(isequal(sum(Tmin),sumTmin_correct))\r\nassert(isequal(length(find(m\u003c40)),Nmlt40_correct))\r\nassert(isequal(length(find(n\u003c20)),Nnlt20_correct))\r\nassert(isequal(length(find(m\u003e2000)),Nmgt2000_correct))\r\nassert(isequal(length(find(n\u003e1000)),Nngt1000_correct))\r\nassert(isequal(length(find(n\u003em)),Nngtm_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":8,"created_by":46909,"edited_by":46909,"edited_at":"2025-08-14T12:04:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2025-08-14T12:01:21.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-08-04T00:02:18.000Z","updated_at":"2025-09-27T07:37:24.000Z","published_at":"2025-08-04T01:15:55.000Z","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:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/60958\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 60958\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e introduced seesaw numbers. A number \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=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a seesaw number if the next \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e smaller numbers can be placed on a seesaw to the left of \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=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at the fulcrum and the \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e larger numbers can be placed to the right to make the net torque about the fulcrum zero. Recall that the torque is equal to the product of the number and its distance from the fulcrum. Let’s take torque leading to counterclockwise rotation as positive and torque leading to clockwise rotation as negative.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem deals with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eseesaw primes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which are like seesaw numbers except that they use primes instead of integers. The number 11 is not a seesaw prime because no values of \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be found to make the net torque zero. The minimum value of torque of 2 units occurs with one prime (7) to the left and one prime (13) to the right—i.e., \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=\\\"m = n = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em = n = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number 167 is a seesaw prime because with six primes on the left (137, 139, 149, 151, 157, 163) and five on the right (173, 179, 181, 191, 193) the torque on the left is 15,322 units, the torque on the right is -15,322 units, and the net torque is zero. \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\u003eSeesaw primes seem to be rare: 167 and 17,750,989 are the only ones smaller than 20,000,000. Although the envelope of the minimum torques increases, the dense cluster of points around zero on a plot with linear axes suggests suggests that other seesaw primes should be possible. A plot of the absolute value of the minimum torque \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=\\\"Tmin\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{min}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e on semilog axes is less encouraging: for primes between 1 and 20 million, only thirteen have an absolute value of minimum torque less than 72 units.\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\u003eWrite a function to determine whether the input number is a seesaw prime. Also return the minimum torque, and \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the number of primes on the left and right when the minimum torque occurs. At least one of \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e must be greater than zero. If the input is not prime, set \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=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \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=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the minimum torque to \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\u003eNaN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Minimum torque vs. prime on linear scales\\\"/\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"328\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"438\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Absolute value of minimum torque vs. prime on semilog scales\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\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\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image2.png\",\"relationshipId\":\"rId2\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"noeis\"","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:\"noeis\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"noeis\"","","\"","noeis","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f535830a978\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f535830a8d8\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f5358309398\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f535830abf8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f535830ab58\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f535830aab8\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f535830aa18\u003e":"tag:\"noeis\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f535830aa18\u003e":"tag:\"noeis\""},"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":"search","password":"J3bGPZzQ7asjJcCk","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:\"noeis\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"noeis\"","","\"","noeis","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f535830a978\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f535830a8d8\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f5358309398\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f535830abf8\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f535830ab58\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f535830aab8\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f535830aa18\u003e":"tag:\"noeis\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f535830aa18\u003e":"tag:\"noeis\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":60952,"difficulty_rating":"easy-medium"},{"id":57810,"difficulty_rating":"medium"},{"id":60958,"difficulty_rating":"medium"},{"id":53990,"difficulty_rating":"medium-hard"},{"id":58977,"difficulty_rating":"medium-hard"},{"id":60991,"difficulty_rating":"hard"}]}}