{"name":"Matrix Algebras Identity Tables","version":"2026-11-10","license":"https://creativecommons.org/licenses/by/4.0/","url":"https://www.dm.ufscar.br/profs/waldeck/pi/","creator":"Waldeck Schützer","note":"status is one of exact, probable, lower bound, upper bound, unchecked. Only exact values are certified equalities. A partition that is not listed is not claimed, it is not a zero.","columns":["order","degree","type","partition","specht_dim","multiplicity","status","lower_bound","upper_bound"],"rows":[[6,15,"e","(15)",1,0,"exact",0,0],[6,15,"e","(14,1)",14,0,"exact",0,0],[6,15,"e","(13,2)",90,0,"exact",0,0],[6,15,"e","(13,1,1)",91,0,"exact",0,0],[6,15,"e","(12,3)",350,0,"exact",0,0],[6,15,"e","(12,2,1)",715,0,"exact",0,0],[6,15,"e","(12,1,1,1)",364,0,"exact",0,0],[6,15,"e","(11,4)",910,0,"exact",0,0],[6,15,"e","(11,3,1)",2835,0,"exact",0,0],[6,15,"e","(11,2,2)",1925,0,"exact",0,0],[6,15,"e","(11,2,1,1)",2925,0,"exact",0,0],[6,15,"e","(11,1,1,1,1)",1001,0,"exact",0,0],[6,15,"e","(10,5)",1638,0,"exact",0,0],[6,15,"e","(10,4,1)",7007,0,"exact",0,0],[6,15,"e","(10,3,2)",9100,0,"exact",0,0],[6,15,"e","(10,3,1,1)",11088,0,"exact",0,0],[6,15,"e","(10,2,2,1)",9450,0,"exact",0,0],[6,15,"e","(10,2,1,1,1)",7722,0,"exact",0,0],[6,15,"e","(10,1,1,1,1,1)",2002,0,"exact",0,0],[6,15,"e","(9,6)",2002,0,"exact",0,0],[6,15,"e","(9,5,1)",11375,0,"exact",0,0],[6,15,"e","(9,4,2)",22113,756,"upper 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32,0,"exact",0,0],[6,13,"f","(4,4,1,1,1,1,1)",4004,0,"exact",0,0],[6,13,"f","(4,4,2,1,1,1)",12012,0,"exact",0,0],[6,13,"f","(4,4,2,2,1)",12870,0,"exact",0,0],[6,13,"f","(4,4,3,1,1)",11583,0,"exact",0,0],[6,13,"f","(4,4,3,2)",8580,0,"exact",0,0],[6,13,"f","(4,4,4,1)",3432,0,"exact",0,0],[6,13,"f","(5,1,1,1,1,1,1,1,1)",495,0,"exact",0,0],[6,13,"f","(5,2,1,1,1,1,1,1)",3003,0,"exact",0,0],[6,13,"f","(5,2,2,1,1,1,1)",7800,0,"exact",0,0],[6,13,"f","(5,2,2,2,1,1)",10296,0,"exact",0,0],[6,13,"f","(5,2,2,2,2)",5005,0,"exact",0,0],[6,13,"f","(5,3,1,1,1,1,1)",7371,0,"exact",0,0],[6,13,"f","(5,3,2,1,1,1)",20592,0,"exact",0,0],[6,13,"f","(5,3,2,2,1)",21450,0,"exact",0,0],[6,13,"f","(5,3,3,1,1)",16016,0,"exact",0,0],[6,13,"f","(5,3,3,2)",11583,0,"exact",0,0],[6,13,"f","(5,4,1,1,1,1)",9009,0,"exact",0,0],[6,13,"f","(5,4,2,1,1)",21450,0,"exact",0,0],[6,13,"f","(5,4,2,2)",12870,0,"exact",0,0],[6,13,"f","(5,4,3,1)",15015,0,"exact",0,0],[6,13,"f","(5,4,4)",2574,0,"exact",0,0],[6,13,"f","(5,5,1,1,1)",5005,0,"exact",0,0],[6,13,"f","(5,5,2,1)",8580,0,"exact",0,0],[6,13,"f","(5,5,3)",3432,0,"exact",0,0],[6,13,"f","(6,1,1,1,1,1,1,1)",792,0,"exact",0,0],[6,13,"f","(6,2,1,1,1,1,1)",4290,0,"exact",0,0],[6,13,"f","(6,2,2,1,1,1)",9360,0,"exact",0,0],[6,13,"f","(6,2,2,2,1)",9009,0,"exact",0,0],[6,13,"f","(6,3,1,1,1,1)",9360,0,"exact",0,0],[6,13,"f","(6,3,2,1,1)",20592,0,"exact",0,0],[6,13,"f","(6,3,2,2)",12012,0,"exact",0,0],[6,13,"f","(6,3,3,1)",11440,0,"exact",0,0],[6,13,"f","(6,4,1,1,1)",10296,0,"exact",0,0],[6,13,"f","(6,4,2,1)",17160,0,"exact",0,0],[6,13,"f","(6,4,3)",6435,0,"exact",0,0],[6,13,"f","(6,5,1,1)",5720,0,"exact",0,0],[6,13,"f","(6,5,2)",5148,0,"exact",0,0],[6,13,"f","(6,6,1)",1287,0,"exact",0,0],[6,13,"f","(7,1,1,1,1,1,1)",924,0,"exact",0,0],[6,13,"f","(7,2,1,1,1,1)",4290,0,"exact",0,0],[6,13,"f","(7,2,2,1,1)",7371,0,"exact",0,0],[6,13,"f","(7,2,2,2)",4004,0,"exact",0,0],[6,13,"f","(7,3,1,1,1)",7800,0,"exact",0,0],[6,13,"f","(7,3,2,1)",12012,0,"exact",0,0],[6,13,"f","(7,3,3)",3575,0,"exact",0,0],[6,13,"f","(7,4,1,1)",6864,0,"exact",0,0],[6,13,"f","(7,4,2)",6006,0,"exact",0,0],[6,13,"f","(7,5,1)",2860,0,"exact",0,0],[6,13,"f","(7,6)",429,0,"exact",0,0],[6,13,"f","(8,1,1,1,1,1)",792,0,"exact",0,0],[6,13,"f","(8,2,1,1,1)",3003,0,"exact",0,0],[6,13,"f","(8,2,2,1)",3640,0,"exact",0,0],[6,13,"f","(8,3,1,1)",4212,0,"exact",0,0],[6,13,"f","(8,3,2)",3432,0,"exact",0,0],[6,13,"f","(8,4,1)",2574,0,"exact",0,0],[6,13,"f","(8,5)",572,0,"exact",0,0],[6,13,"f","(9,1,1,1,1)",495,0,"exact",0,0],[6,13,"f","(9,2,1,1)",1430,0,"exact",0,0],[6,13,"f","(9,2,2)",936,0,"exact",0,0],[6,13,"f","(9,3,1)",1365,0,"exact",0,0],[6,13,"f","(9,4)",429,0,"exact",0,0],[6,13,"f","(10,1,1,1)",220,0,"exact",0,0],[6,13,"f","(10,2,1)",429,0,"exact",0,0],[6,13,"f","(10,3)",208,0,"exact",0,0],[6,13,"f","(11,1,1)",66,0,"exact",0,0],[6,13,"f","(11,2)",65,0,"exact",0,0],[6,13,"f","(12,1)",12,0,"exact",0,0],[6,13,"f","(13)",1,0,"exact",0,0],[6,14,"f","(1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,14,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1)",13,5,"exact",5,5],[6,14,"f","(2,2,1,1,1,1,1,1,1,1,1,1)",77,8,"exact",8,8],[6,14,"f","(2,2,2,1,1,1,1,1,1,1,1)",273,4,"exact",4,4],[6,14,"f","(2,2,2,2,1,1,1,1,1,1)",637,0,"exact",0,0],[6,14,"f","(2,2,2,2,2,1,1,1,1)",1001,0,"exact",0,0],[6,14,"f","(2,2,2,2,2,2,1,1)",1001,0,"exact",0,0],[6,14,"f","(2,2,2,2,2,2,2)",429,0,"exact",0,0],[6,14,"f","(3,1,1,1,1,1,1,1,1,1,1,1)",78,9,"exact",9,9],[6,14,"f","(3,2,1,1,1,1,1,1,1,1,1)",560,8,"exact",8,8],[6,14,"f","(3,2,2,1,1,1,1,1,1,1)",2002,2,"exact",2,2],[6,14,"f","(3,2,2,2,1,1,1,1,1)",4368,0,"exact",0,0],[6,14,"f","(3,2,2,2,2,1,1,1)",6006,0,"exact",0,0],[6,14,"f","(3,2,2,2,2,2,1)",4576,0,"exact",0,0],[6,14,"f","(3,3,1,1,1,1,1,1,1,1)",1365,0,"exact",0,0],[6,14,"f","(3,3,2,1,1,1,1,1,1)",5733,0,"exact",0,0],[6,14,"f","(3,3,2,2,1,1,1,1)",12012,0,"exact",0,0],[6,14,"f","(3,3,2,2,2,1,1)",14014,0,"exact",0,0],[6,14,"f","(3,3,2,2,2,2)",6435,0,"exact",0,0],[6,14,"f","(3,3,3,1,1,1,1,1)",7007,0,"exact",0,0],[6,14,"f","(3,3,3,2,1,1,1)",16016,0,"exact",0,0],[6,14,"f","(3,3,3,2,2,1)",15015,0,"exact",0,0],[6,14,"f","(3,3,3,3,1,1)",9009,0,"exact",0,0],[6,14,"f","(3,3,3,3,2)",6006,0,"exact",0,0],[6,14,"f","(4,1,1,1,1,1,1,1,1,1,1)",286,4,"exact",4,4],[6,14,"f","(4,2,1,1,1,1,1,1,1,1)",2079,2,"exact",2,2],[6,14,"f","(4,2,2,1,1,1,1,1,1)",7007,0,"exact",0,0],[6,14,"f","(4,2,2,2,1,1,1,1)",13650,0,"exact",0,0],[6,14,"f","(4,2,2,2,2,1,1)",15444,0,"exact",0,0],[6,14,"f","(4,2,2,2,2,2)",7007,0,"exact",0,0],[6,14,"f","(4,3,1,1,1,1,1,1,1)",6006,0,"exact",0,0],[6,14,"f","(4,3,2,1,1,1,1,1)",23296,6376,"upper bound",0,6376],[6,14,"f","(4,3,2,2,1,1,1)",42042,10494,"upper bound",0,10494],[6,14,"f","(4,3,2,2,2,1)",36608,8640,"upper bound",0,8640],[6,14,"f","(4,3,3,1,1,1,1)",27027,6375,"upper bound",0,6375],[6,14,"f","(4,3,3,2,1,1)",50050,10890,"upper bound",0,10890],[6,14,"f","(4,3,3,2,2)",27027,5640,"upper bound",0,5640],[6,14,"f","(4,3,3,3,1)",21021,4171,"upper bound",0,4171],[6,14,"f","(4,4,1,1,1,1,1,1)",7644,0,"exact",0,0],[6,14,"f","(4,4,2,1,1,1,1)",28028,6085,"upper bound",0,6085],[6,14,"f","(4,4,2,2,1,1)",42042,8415,"upper bound",0,8415],[6,14,"f","(4,4,2,2,2)",21450,4120,"upper bound",0,4120],[6,14,"f","(4,4,3,1,1,1)",35035,6605,"upper bound",0,6605],[6,14,"f","(4,4,3,2,1)",48048,8480,"upper bound",0,8480],[6,14,"f","(4,4,3,3)",12012,0,"exact",0,0],[6,14,"f","(4,4,4,1,1)",15015,0,"exact",0,0],[6,14,"f","(4,4,4,2)",12012,0,"exact",0,0],[6,14,"f","(5,1,1,1,1,1,1,1,1,1)",715,0,"exact",0,0],[6,14,"f","(5,2,1,1,1,1,1,1,1)",4928,0,"exact",0,0],[6,14,"f","(5,2,2,1,1,1,1,1)",15015,0,"exact",0,0],[6,14,"f","(5,2,2,2,1,1,1)",24960,5100,"upper bound",0,5100],[6,14,"f","(5,2,2,2,2,1)",21021,4041,"upper bound",0,4041],[6,14,"f","(5,3,1,1,1,1,1,1)",14014,0,"exact",0,0],[6,14,"f","(5,3,2,1,1,1,1)",47775,8880,"upper bound",0,8880],[6,14,"f","(5,3,2,2,1,1)",69498,11871,"upper bound",0,11871],[6,14,"f","(5,3,2,2,2)",35035,5730,"upper bound",0,5730],[6,14,"f","(5,3,3,1,1,1)",48048,7710,"upper bound",0,7710],[6,14,"f","(5,3,3,2,1)",64064,9624,"upper bound",0,9624],[6,14,"f","(5,3,3,3)",15015,0,"exact",0,0],[6,14,"f","(5,4,1,1,1,1,1)",20384,3414,"upper bound",0,3414],[6,14,"f","(5,4,2,1,1,1)",63063,9411,"upper bound",0,9411],[6,14,"f","(5,4,2,2,1)",68640,9570,"upper bound",0,9570],[6,14,"f","(5,4,3,1,1)",64064,8364,"upper bound",0,8364],[6,14,"f","(5,4,3,2)",48048,5994,"upper bound",0,5994],[6,14,"f","(5,4,4,1)",21021,2346,"upper bound",0,2346],[6,14,"f","(5,5,1,1,1,1)",14014,0,"exact",0,0],[6,14,"f","(5,5,2,1,1)",35035,4065,"upper bound",0,4065],[6,14,"f","(5,5,2,2)",21450,2370,"upper bound",0,2370],[6,14,"f","(5,5,3,1)",27027,2781,"upper bound",0,2781],[6,14,"f","(5,5,4)",6006,0,"exact",0,0],[6,14,"f","(6,1,1,1,1,1,1,1,1)",1287,0,"exact",0,0],[6,14,"f","(6,2,1,1,1,1,1,1)",8085,0,"exact",0,0],[6,14,"f","(6,2,2,1,1,1,1)",21450,2710,"upper bound",0,2710],[6,14,"f","(6,2,2,2,1,1)",28665,3330,"upper bound",0,3330],[6,14,"f","(6,2,2,2,2)",14014,0,"exact",0,0],[6,14,"f","(6,3,1,1,1,1,1)",21021,2544,"upper bound",0,2544],[6,14,"f","(6,3,2,1,1,1)",59904,6456,"upper bound",0,6456],[6,14,"f","(6,3,2,2,1)",63063,6360,"upper bound",0,6360],[6,14,"f","(6,3,3,1,1)",48048,4564,"upper bound",0,4564],[6,14,"f","(6,3,3,2)",35035,3180,"upper bound",0,3180],[6,14,"f","(6,4,1,1,1,1)",28665,2880,"upper bound",0,2880],[6,14,"f","(6,4,2,1,1)",69498,6300,"upper bound",0,6300],[6,14,"f","(6,4,2,2)",42042,3636,"upper bound",0,3636],[6,14,"f","(6,4,3,1)",50050,4040,"upper bound",0,4040],[6,14,"f","(6,4,4)",9009,0,"exact",0,0],[6,14,"f","(6,5,1,1,1)",21021,1720,"upper bound",0,1720],[6,14,"f","(6,5,2,1)",36608,2744,"upper bound",0,2744],[6,14,"f","(6,5,3)",15015,0,"exact",0,0],[6,14,"f","(6,6,1,1)",7007,0,"exact",0,0],[6,14,"f","(6,6,2)",6435,0,"exact",0,0],[6,14,"f","(7,1,1,1,1,1,1,1)",1716,0,"exact",0,0],[6,14,"f","(7,2,1,1,1,1,1)",9504,0,"exact",0,0],[6,14,"f","(7,2,2,1,1,1)",21021,1124,"upper bound",0,1124],[6,14,"f","(7,2,2,2,1)",20384,1034,"upper bound",0,1034],[6,14,"f","(7,3,1,1,1,1)",21450,1140,"upper bound",0,1140],[6,14,"f","(7,3,2,1,1)",47775,2360,"upper bound",0,2360],[6,14,"f","(7,3,2,2)",28028,1326,"upper bound",0,1326],[6,14,"f","(7,3,3,1)",27027,1236,"upper bound",0,1236],[6,14,"f","(7,4,1,1,1)",24960,1220,"upper bound",0,1220],[6,14,"f","(7,4,2,1)",42042,1910,"upper bound",0,1910],[6,14,"f","(7,4,3)",16016,0,"exact",0,0],[6,14,"f","(7,5,1,1)",15444,0,"exact",0,0],[6,14,"f","(7,5,2)",14014,0,"exact",0,0],[6,14,"f","(7,6,1)",4576,0,"exact",0,0],[6,14,"f","(7,7)",429,0,"exact",0,0],[6,14,"f","(8,1,1,1,1,1,1)",1716,0,"exact",0,0],[6,14,"f","(8,2,1,1,1,1)",8085,0,"exact",0,0],[6,14,"f","(8,2,2,1,1)",14014,0,"exact",0,0],[6,14,"f","(8,2,2,2)",7644,0,"exact",0,0],[6,14,"f","(8,3,1,1,1)",15015,0,"exact",0,0],[6,14,"f","(8,3,2,1)",23296,336,"upper bound",0,336],[6,14,"f","(8,3,3)",7007,0,"exact",0,0],[6,14,"f","(8,4,1,1)",13650,0,"exact",0,0],[6,14,"f","(8,4,2)",12012,0,"exact",0,0],[6,14,"f","(8,5,1)",6006,0,"exact",0,0],[6,14,"f","(8,6)",1001,0,"exact",0,0],[6,14,"f","(9,1,1,1,1,1)",1287,0,"exact",0,0],[6,14,"f","(9,2,1,1,1)",4928,0,"exact",0,0],[6,14,"f","(9,2,2,1)",6006,0,"exact",0,0],[6,14,"f","(9,3,1,1)",7007,0,"exact",0,0],[6,14,"f","(9,3,2)",5733,0,"exact",0,0],[6,14,"f","(9,4,1)",4368,0,"exact",0,0],[6,14,"f","(9,5)",1001,0,"exact",0,0],[6,14,"f","(10,1,1,1,1)",715,0,"exact",0,0],[6,14,"f","(10,2,1,1)",2079,0,"exact",0,0],[6,14,"f","(10,2,2)",1365,0,"exact",0,0],[6,14,"f","(10,3,1)",2002,0,"exact",0,0],[6,14,"f","(10,4)",637,0,"exact",0,0],[6,14,"f","(11,1,1,1)",286,0,"exact",0,0],[6,14,"f","(11,2,1)",560,0,"exact",0,0],[6,14,"f","(11,3)",273,0,"exact",0,0],[6,14,"f","(12,1,1)",78,0,"exact",0,0],[6,14,"f","(12,2)",77,0,"exact",0,0],[6,14,"f","(13,1)",13,0,"exact",0,0],[6,14,"f","(14)",1,0,"exact",0,0],[6,15,"f","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,15,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1,1)",14,7,"exact",7,7],[6,15,"f","(2,2,1,1,1,1,1,1,1,1,1,1,1)",90,18,"exact",18,18],[6,15,"f","(2,2,2,1,1,1,1,1,1,1,1,1)",350,22,"exact",22,22],[6,15,"f","(2,2,2,2,1,1,1,1,1,1,1)",910,11,"exact",11,11],[6,15,"f","(2,2,2,2,2,1,1,1,1,1)",1638,1,"exact",1,1],[6,15,"f","(2,2,2,2,2,2,1,1,1)",2002,0,"exact",0,0],[6,15,"f","(2,2,2,2,2,2,2,1)",1430,0,"exact",0,0],[6,15,"f","(3,1,1,1,1,1,1,1,1,1,1,1,1)",91,19,"exact",19,19],[6,15,"f","(3,2,1,1,1,1,1,1,1,1,1,1)",715,46,"exact",46,46],[6,15,"f","(3,2,2,1,1,1,1,1,1,1,1)",2835,36,"exact",36,36],[6,15,"f","(3,2,2,2,1,1,1,1,1,1)",7007,10,"exact",10,10],[6,15,"f","(3,2,2,2,2,1,1,1,1)",11375,0,"exact",0,0],[6,15,"f","(3,2,2,2,2,2,1,1)",11583,0,"exact",0,0],[6,15,"f","(3,2,2,2,2,2,2)",5005,0,"exact",0,0],[6,15,"f","(3,3,1,1,1,1,1,1,1,1,1)",1925,23,"exact",23,23],[6,15,"f","(3,3,2,1,1,1,1,1,1,1)",9100,11,"exact",11,11],[6,15,"f","(3,3,2,2,1,1,1,1,1)",22113,1,"lower bound",1,9306],[6,15,"f","(3,3,2,2,2,1,1,1)",32032,13334,"upper bound",0,13334],[6,15,"f","(3,3,2,2,2,2,1)",25025,10350,"upper bound",0,10350],[6,15,"f","(3,3,3,1,1,1,1,1,1)",12740,1,"exact",1,1],[6,15,"f","(3,3,3,2,1,1,1,1)",35035,14434,"upper bound",0,14434],[6,15,"f","(3,3,3,2,2,1,1)",45045,18390,"upper bound",0,18390],[6,15,"f","(3,3,3,2,2,2)",21450,8718,"upper bound",0,8718],[6,15,"f","(3,3,3,3,1,1,1)",25025,10152,"upper bound",0,10152],[6,15,"f","(3,3,3,3,2,1)",30030,12096,"upper bound",0,12096],[6,15,"f","(3,3,3,3,3)",6006,0,"exact",0,0],[6,15,"f","(4,1,1,1,1,1,1,1,1,1,1,1)",364,25,"exact",25,25],[6,15,"f","(4,2,1,1,1,1,1,1,1,1,1)",2925,37,"exact",37,37],[6,15,"f","(4,2,2,1,1,1,1,1,1,1)",11088,18,"exact",18,18],[6,15,"f","(4,2,2,2,1,1,1,1,1)",25025,3,"lower bound",3,10400],[6,15,"f","(4,2,2,2,2,1,1,1)",35100,14430,"upper bound",0,14430],[6,15,"f","(4,2,2,2,2,2,1)",27027,11040,"upper bound",0,11040],[6,15,"f","(4,3,1,1,1,1,1,1,1,1)",9450,11,"exact",11,11],[6,15,"f","(4,3,2,1,1,1,1,1,1)",42042,2,"lower bound",2,23643],[6,15,"f","(4,3,2,2,1,1,1,1)",91000,53735,"upper bound",0,53735],[6,15,"f","(4,3,2,2,2,1,1)",108108,62537,"upper bound",0,62537],[6,15,"f","(4,3,2,2,2,2)",50050,28645,"upper bound",0,28645],[6,15,"f","(4,3,3,1,1,1,1,1)",57330,35809,"upper bound",0,35809],[6,15,"f","(4,3,3,2,1,1,1)",135135,81467,"upper bound",0,81467],[6,15,"f","(4,3,3,2,2,1)",128700,75962,"upper bound",0,75962],[6,15,"f","(4,3,3,3,1,1)",80080,46000,"upper bound",0,46000],[6,15,"f","(4,3,3,3,2)",54054,30102,"upper bound",0,30102],[6,15,"f","(4,4,1,1,1,1,1,1,1)",13650,1,"exact",1,1],[6,15,"f","(4,4,2,1,1,1,1,1)",58968,35948,"upper bound",0,35948],[6,15,"f","(4,4,2,2,1,1,1)",112112,65828,"upper bound",0,65828],[6,15,"f","(4,4,2,2,2,1)",100100,56240,"upper bound",0,56240],[6,15,"f","(4,4,3,1,1,1,1)",90090,50700,"upper bound",0,50700],[6,15,"f","(4,4,3,2,1,1)",175175,92465,"upper bound",0,92465],[6,15,"f","(4,4,3,2,2)",96525,49335,"upper bound",0,49335],[6,15,"f","(4,4,3,3,1)",81081,39783,"upper bound",0,39783],[6,15,"f","(4,4,4,1,1,1)",50050,24570,"upper bound",0,24570],[6,15,"f","(4,4,4,2,1)",75075,34945,"upper bound",0,34945],[6,15,"f","(4,4,4,3)",24024,9042,"upper bound",0,9042],[6,15,"f","(5,1,1,1,1,1,1,1,1,1,1)",1001,12,"exact",12,12],[6,15,"f","(5,2,1,1,1,1,1,1,1,1)",7722,10,"exact",10,10],[6,15,"f","(5,2,2,1,1,1,1,1,1)",26950,3,"lower bound",3,10840],[6,15,"f","(5,2,2,2,1,1,1,1)",53625,26380,"upper bound",0,26380],[6,15,"f","(5,2,2,2,2,1,1)",61425,33301,"upper bound",0,33301],[6,15,"f","(5,2,2,2,2,2)",28028,15017,"upper bound",0,15017],[6,15,"f","(5,3,1,1,1,1,1,1,1)",24948,1,"lower bound",1,9954],[6,15,"f","(5,3,2,1,1,1,1,1)",100100,54531,"upper bound",0,54531],[6,15,"f","(5,3,2,2,1,1,1)",184275,98835,"upper bound",0,98835],[6,15,"f","(5,3,2,2,2,1)",162162,82974,"upper bound",0,82974],[6,15,"f","(5,3,3,1,1,1,1)",122850,62940,"upper bound",0,62940],[6,15,"f","(5,3,3,2,1,1)",231660,110970,"upper bound",0,110970],[6,15,"f","(5,3,3,2,2)",126126,58392,"upper bound",0,58392],[6,15,"f","(5,3,3,3,1)",100100,44450,"upper bound",0,44450],[6,15,"f","(5,4,1,1,1,1,1,1)",42042,19696,"upper bound",0,19696],[6,15,"f","(5,4,2,1,1,1,1)",159250,76510,"upper bound",0,76510],[6,15,"f","(5,4,2,2,1,1)",243243,109251,"upper bound",0,109251],[6,15,"f","(5,4,2,2,2)",125125,54325,"upper bound",0,54325],[6,15,"f","(5,4,3,1,1,1)",210210,90070,"upper bound",0,90070],[6,15,"f","(5,4,3,2,1)",292864,118848,"upper bound",0,118848],[6,15,"f","(5,4,3,3)",75075,28675,"upper bound",0,28675],[6,15,"f","(5,4,4,1,1)",100100,37550,"upper bound",0,37550],[6,15,"f","(5,4,4,2)",81081,29277,"upper bound",0,29277],[6,15,"f","(5,5,1,1,1,1,1)",34398,14511,"upper bound",0,14511],[6,15,"f","(5,5,2,1,1,1)",112112,43204,"upper bound",0,43204],[6,15,"f","(5,5,2,2,1)",125125,45650,"upper bound",0,45650],[6,15,"f","(5,5,3,1,1)",126126,43812,"upper bound",0,43812],[6,15,"f","(5,5,3,2)",96525,32250,"upper bound",0,32250],[6,15,"f","(5,5,4,1)",54054,16638,"upper bound",0,16638],[6,15,"f","(5,5,5)",6006,0,"exact",0,0],[6,15,"f","(6,1,1,1,1,1,1,1,1,1)",2002,1,"exact",1,1],[6,15,"f","(6,2,1,1,1,1,1,1,1)",14300,0,"exact",0,0],[6,15,"f","(6,2,2,1,1,1,1,1)",44550,19660,"upper bound",0,19660],[6,15,"f","(6,2,2,2,1,1,1)",75075,32360,"upper bound",0,32360],[6,15,"f","(6,2,2,2,2,1)",63700,26080,"upper bound",0,26080],[6,15,"f","(6,3,1,1,1,1,1,1)",43120,18826,"upper bound",0,18826],[6,15,"f","(6,3,2,1,1,1,1)",150150,59920,"upper bound",0,59920],[6,15,"f","(6,3,2,2,1,1)",221130,82170,"upper bound",0,82170],[6,15,"f","(6,3,2,2,2)",112112,40184,"upper bound",0,40184],[6,15,"f","(6,3,3,1,1,1)",156000,55160,"upper bound",0,55160],[6,15,"f","(6,3,3,2,1)",210210,70300,"upper bound",0,70300],[6,15,"f","(6,3,3,3)",50050,15750,"upper bound",0,15750],[6,15,"f","(6,4,1,1,1,1,1)",70070,25690,"upper bound",0,25690],[6,15,"f","(6,4,2,1,1,1)",221130,73710,"upper bound",0,73710],[6,15,"f","(6,4,2,2,1)",243243,76626,"upper bound",0,76626],[6,15,"f","(6,4,3,1,1)",231660,69360,"upper bound",0,69360],[6,15,"f","(6,4,3,2)",175175,50450,"upper bound",0,50450],[6,15,"f","(6,4,4,1)",80080,21220,"upper bound",0,21220],[6,15,"f","(6,5,1,1,1,1)",63700,18830,"upper bound",0,18830],[6,15,"f","(6,5,2,1,1)",162162,44184,"upper bound",0,44184],[6,15,"f","(6,5,2,2)",100100,26200,"upper bound",0,26200],[6,15,"f","(6,5,3,1)",128700,31950,"upper bound",0,31950],[6,15,"f","(6,5,4)",30030,6680,"upper bound",0,6680],[6,15,"f","(6,6,1,1,1)",28028,6496,"upper bound",0,6496],[6,15,"f","(6,6,2,1)",50050,10850,"upper bound",0,10850],[6,15,"f","(6,6,3)",21450,4300,"upper bound",0,4300],[6,15,"f","(7,1,1,1,1,1,1,1,1)",3003,0,"exact",0,0],[6,15,"f","(7,2,1,1,1,1,1,1)",19305,0,"exact",0,0],[6,15,"f","(7,2,2,1,1,1,1)",51975,13965,"upper bound",0,13965],[6,15,"f","(7,2,2,2,1,1)",70070,17535,"upper bound",0,17535],[6,15,"f","(7,2,2,2,2)",34398,8316,"upper bound",0,8316],[6,15,"f","(7,3,1,1,1,1,1)",51975,13440,"upper bound",0,13440],[6,15,"f","(7,3,2,1,1,1)",150150,35280,"upper bound",0,35280],[6,15,"f","(7,3,2,2,1)",159250,35385,"upper bound",0,35385],[6,15,"f","(7,3,3,1,1)",122850,26040,"upper bound",0,26040],[6,15,"f","(7,3,3,2)",90090,18375,"upper bound",0,18375],[6,15,"f","(7,4,1,1,1,1)",75075,16590,"upper bound",0,16590],[6,15,"f","(7,4,2,1,1)",184275,37485,"upper bound",0,37485],[6,15,"f","(7,4,2,2)",112112,21924,"upper bound",0,21924],[6,15,"f","(7,4,3,1)",135135,25095,"upper bound",0,25095],[6,15,"f","(7,4,4)",25025,4200,"upper bound",0,4200],[6,15,"f","(7,5,1,1,1)",61425,11445,"upper bound",0,11445],[6,15,"f","(7,5,2,1)",108108,18816,"upper bound",0,18816],[6,15,"f","(7,5,3)",45045,7245,"upper bound",0,7245],[6,15,"f","(7,6,1,1)",27027,4179,"upper bound",0,4179],[6,15,"f","(7,6,2)",25025,3675,"upper bound",0,3675],[6,15,"f","(7,7,1)",5005,0,"exact",0,0],[6,15,"f","(8,1,1,1,1,1,1,1)",3432,0,"exact",0,0],[6,15,"f","(8,2,1,1,1,1,1)",19305,0,"exact",0,0],[6,15,"f","(8,2,2,1,1,1)",43120,5040,"upper bound",0,5040],[6,15,"f","(8,2,2,2,1)",42042,4704,"upper bound",0,4704],[6,15,"f","(8,3,1,1,1,1)",44550,5160,"upper bound",0,5160],[6,15,"f","(8,3,2,1,1)",100100,10920,"upper bound",0,10920],[6,15,"f","(8,3,2,2)",58968,6216,"upper bound",0,6216],[6,15,"f","(8,3,3,1)",57330,5880,"upper bound",0,5880],[6,15,"f","(8,4,1,1,1)",53625,5760,"upper bound",0,5760],[6,15,"f","(8,4,2,1)",91000,9240,"upper bound",0,9240],[6,15,"f","(8,4,3)",35035,3360,"upper bound",0,3360],[6,15,"f","(8,5,1,1)",35100,3480,"upper bound",0,3480],[6,15,"f","(8,5,2)",32032,3024,"upper bound",0,3024],[6,15,"f","(8,6,1)",11583,0,"exact",0,0],[6,15,"f","(8,7)",1430,0,"exact",0,0],[6,15,"f","(9,1,1,1,1,1,1)",3003,0,"exact",0,0],[6,15,"f","(9,2,1,1,1,1)",14300,0,"exact",0,0],[6,15,"f","(9,2,2,1,1)",24948,756,"upper bound",0,756],[6,15,"f","(9,2,2,2)",13650,0,"exact",0,0],[6,15,"f","(9,3,1,1,1)",26950,840,"upper bound",0,840],[6,15,"f","(9,3,2,1)",42042,1344,"upper bound",0,1344],[6,15,"f","(9,3,3)",12740,0,"exact",0,0],[6,15,"f","(9,4,1,1)",25025,840,"upper bound",0,840],[6,15,"f","(9,4,2)",22113,756,"upper bound",0,756],[6,15,"f","(9,5,1)",11375,0,"exact",0,0],[6,15,"f","(9,6)",2002,0,"exact",0,0],[6,15,"f","(10,1,1,1,1,1)",2002,0,"exact",0,0],[6,15,"f","(10,2,1,1,1)",7722,0,"exact",0,0],[6,15,"f","(10,2,2,1)",9450,0,"exact",0,0],[6,15,"f","(10,3,1,1)",11088,0,"exact",0,0],[6,15,"f","(10,3,2)",9100,0,"exact",0,0],[6,15,"f","(10,4,1)",7007,0,"exact",0,0],[6,15,"f","(10,5)",1638,0,"exact",0,0],[6,15,"f","(11,1,1,1,1)",1001,0,"exact",0,0],[6,15,"f","(11,2,1,1)",2925,0,"exact",0,0],[6,15,"f","(11,2,2)",1925,0,"exact",0,0],[6,15,"f","(11,3,1)",2835,0,"exact",0,0],[6,15,"f","(11,4)",910,0,"exact",0,0],[6,15,"f","(12,1,1,1)",364,0,"exact",0,0],[6,15,"f","(12,2,1)",715,0,"exact",0,0],[6,15,"f","(12,3)",350,0,"exact",0,0],[6,15,"f","(13,1,1)",91,0,"exact",0,0],[6,15,"f","(13,2)",90,0,"exact",0,0],[6,15,"f","(14,1)",14,0,"exact",0,0],[6,15,"f","(15)",1,0,"exact",0,0],[6,16,"f","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,16,"f","(10,1,1,1,1,1,1)",5005,0,"exact",0,0],[6,16,"f","(10,2,1,1,1,1)",24024,1050,"upper bound",0,1050],[6,16,"f","(10,2,2,1,1)",42120,1890,"upper bound",0,1890],[6,16,"f","(10,2,2,2)",23100,1050,"upper bound",0,1050],[6,16,"f","(10,3,1,1,1)",45760,2100,"upper bound",0,2100],[6,16,"f","(10,3,2,1)",71680,3360,"upper bound",0,3360],[6,16,"f","(10,3,3)",21840,1050,"upper bound",0,1050],[6,16,"f","(10,4,1,1)",43120,2100,"upper bound",0,2100],[6,16,"f","(10,4,2)",38220,1890,"upper bound",0,1890],[6,16,"f","(10,5,1)",20020,1050,"upper bound",0,1050],[6,16,"f","(10,6)",3640,0,"exact",0,0],[6,16,"f","(11,1,1,1,1,1)",3003,0,"exact",0,0],[6,16,"f","(11,2,1,1,1)",11648,0,"exact",0,0],[6,16,"f","(11,2,2,1)",14300,0,"exact",0,0],[6,16,"f","(11,3,1,1)",16848,0,"exact",0,0],[6,16,"f","(11,3,2)",13860,0,"exact",0,0],[6,16,"f","(11,4,1)",10752,0,"exact",0,0],[6,16,"f","(11,5)",2548,0,"exact",0,0],[6,16,"f","(12,1,1,1,1)",1365,0,"exact",0,0],[6,16,"f","(12,2,1,1)",4004,0,"exact",0,0],[6,16,"f","(12,2,2)",2640,0,"exact",0,0],[6,16,"f","(12,3,1)",3900,0,"exact",0,0],[6,16,"f","(12,4)",1260,0,"exact",0,0],[6,16,"f","(13,1,1,1)",455,0,"exact",0,0],[6,16,"f","(13,2,1)",896,0,"exact",0,0],[6,16,"f","(13,3)",440,0,"exact",0,0],[6,16,"f","(14,1,1)",105,0,"exact",0,0],[6,16,"f","(14,2)",104,0,"exact",0,0],[6,16,"f","(15,1)",15,0,"exact",0,0],[6,16,"f","(16)",1,0,"exact",0,0],[6,16,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",15,8,"lower bound",8,9],[6,16,"f","(2,2,1,1,1,1,1,1,1,1,1,1,1,1)",104,25,"lower bound",25,31],[6,16,"f","(2,2,2,1,1,1,1,1,1,1,1,1,1)",440,40,"lower bound",40,57],[6,16,"f","(2,2,2,2,1,1,1,1,1,1,1,1)",1260,33,"lower bound",33,58],[6,16,"f","(2,2,2,2,2,1,1,1,1,1,1)",2548,12,"lower bound",12,2542],[6,16,"f","(2,2,2,2,2,2,1,1,1,1)",3640,1,"lower bound",1,3615],[6,16,"f","(2,2,2,2,2,2,2,1,1)",3432,3393,"upper bound",0,3393],[6,16,"f","(2,2,2,2,2,2,2,2)",1430,0,"exact",0,0],[6,16,"f","(3,1,1,1,1,1,1,1,1,1,1,1,1,1)",105,26,"lower bound",26,32],[6,16,"f","(3,2,1,1,1,1,1,1,1,1,1,1,1)",896,83,"lower bound",83,118],[6,16,"f","(3,2,2,1,1,1,1,1,1,1,1,1)",3900,104,"lower bound",104,3900],[6,16,"f","(3,2,2,2,1,1,1,1,1,1,1)",10752,57,"lower bound",57,10668],[6,16,"f","(3,2,2,2,2,1,1,1,1,1)",20020,11,"lower bound",11,19625],[6,16,"f","(3,2,2,2,2,2,1,1,1)",24960,24180,"upper bound",0,24180],[6,16,"f","(3,2,2,2,2,2,2,1)",18018,17307,"upper bound",0,17307],[6,16,"f","(3,3,1,1,1,1,1,1,1,1,1,1)",2640,69,"lower bound",69,122],[6,16,"f","(3,3,2,1,1,1,1,1,1,1,1)",13860,70,"lower bound",70,13650],[6,16,"f","(3,3,2,2,1,1,1,1,1,1)",38220,22,"lower bound",22,36855],[6,16,"f","(3,3,2,2,2,1,1,1,1)",65520,1,"lower bound",1,61860],[6,16,"f","(3,3,2,2,2,2,1,1)",68640,63750,"upper bound",0,63750],[6,16,"f","(3,3,2,2,2,2,2)",30030,27645,"upper bound",0,27645],[6,16,"f","(3,3,3,1,1,1,1,1,1,1)",21840,12,"lower bound",12,20825],[6,16,"f","(3,3,3,2,1,1,1,1,1)",69888,2,"lower bound",2,64692],[6,16,"f","(3,3,3,2,2,1,1,1)",112112,101198,"upper bound",0,101198],[6,16,"f","(3,3,3,2,2,2,1)",91520,81260,"upper bound",0,81260],[6,16,"f","(3,3,3,3,1,1,1,1)",60060,53370,"upper bound",0,53370],[6,16,"f","(3,3,3,3,2,1,1)",100100,86750,"upper bound",0,86750],[6,16,"f","(3,3,3,3,2,2)",51480,44025,"upper bound",0,44025],[6,16,"f","(3,3,3,3,3,1)",36036,30303,"upper bound",0,30303],[6,16,"f","(4,1,1,1,1,1,1,1,1,1,1,1,1)",455,44,"lower bound",44,62],[6,16,"f","(4,2,1,1,1,1,1,1,1,1,1,1)",4004,108,"lower bound",108,1147],[6,16,"f","(4,2,2,1,1,1,1,1,1,1,1)",16848,91,"lower bound",91,16512],[6,16,"f","(4,2,2,2,1,1,1,1,1,1)",43120,31,"lower bound",31,41160],[6,16,"f","(4,2,2,2,2,1,1,1,1)",71500,3,"lower bound",3,66535],[6,16,"f","(4,2,2,2,2,2,1,1)",73710,67275,"upper bound",0,67275],[6,16,"f","(4,2,2,2,2,2,2)",32032,28938,"upper bound",0,28938],[6,16,"f","(4,3,1,1,1,1,1,1,1,1,1)",14300,71,"lower bound",71,13880],[6,16,"f","(4,3,2,1,1,1,1,1,1,1)",71680,42,"lower bound",42,66920],[6,16,"f","(4,3,2,2,1,1,1,1,1)",180180,6,"lower bound",6,162015],[6,16,"f","(4,3,2,2,2,1,1,1)",266240,232240,"upper bound",0,232240],[6,16,"f","(4,3,2,2,2,2,1)",210210,179815,"upper bound",0,179815],[6,16,"f","(4,3,3,1,1,1,1,1,1)",112112,3,"lower bound",3,98903],[6,16,"f","(4,3,3,2,1,1,1,1)",318500,269550,"upper bound",0,269550],[6,16,"f","(4,3,3,2,2,1,1)",416988,342522,"upper bound",0,342522],[6,16,"f","(4,3,3,2,2,2)",200200,161895,"upper bound",0,161895],[6,16,"f","(4,3,3,3,1,1,1)",240240,193130,"upper bound",0,193130],[6,16,"f","(4,3,3,3,2,1)",292864,229472,"upper bound",0,229472],[6,16,"f","(4,3,3,3,3)",60060,45695,"upper bound",0,45695],[6,16,"f","(4,4,1,1,1,1,1,1,1,1)",23100,12,"lower bound",12,20930],[6,16,"f","(4,4,2,1,1,1,1,1,1)",114660,3,"lower bound",3,98490],[6,16,"f","(4,4,2,2,1,1,1,1)",262080,215250,"upper bound",0,215250],[6,16,"f","(4,4,2,2,2,1,1)",320320,254830,"upper bound",0,254830],[6,16,"f","(4,4,2,2,2,2)",150150,117495,"upper bound",0,117495],[6,16,"f","(4,4,3,1,1,1,1,1)",206388,165522,"upper bound",0,165522],[6,16,"f","(4,4,3,2,1,1,1)",512512,393208,"upper bound",0,393208],[6,16,"f","(4,4,3,2,2,1)",500500,373525,"upper bound",0,373525],[6,16,"f","(4,4,3,3,1,1)",336336,244848,"upper bound",0,244848],[6,16,"f","(4,4,3,3,2)",231660,165255,"upper bound",0,165255],[6,16,"f","(4,4,4,1,1,1,1)",140140,103020,"upper bound",0,103020],[6,16,"f","(4,4,4,2,1,1)",300300,211755,"upper bound",0,211755],[6,16,"f","(4,4,4,2,2)",171600,118480,"upper bound",0,118480],[6,16,"f","(4,4,4,3,1)",180180,121065,"upper bound",0,121065],[6,16,"f","(4,4,4,4)",24024,15257,"upper bound",0,15257],[6,16,"f","(5,1,1,1,1,1,1,1,1,1,1,1)",1365,37,"lower bound",37,67],[6,16,"f","(5,2,1,1,1,1,1,1,1,1,1)",11648,59,"lower bound",59,11144],[6,16,"f","(5,2,2,1,1,1,1,1,1,1)",45760,31,"lower bound",31,41560],[6,16,"f","(5,2,2,2,1,1,1,1,1)",105600,6,"lower bound",6,91440],[6,16,"f","(5,2,2,2,2,1,1,1)",150150,125290,"upper bound",0,125290],[6,16,"f","(5,2,2,2,2,2,1)",116480,94940,"upper bound",0,94940],[6,16,"f","(5,3,1,1,1,1,1,1,1,1)",42120,22,"lower bound",22,37290],[6,16,"f","(5,3,2,1,1,1,1,1,1)",194040,6,"lower bound",6,161490],[6,16,"f","(5,3,2,2,1,1,1,1)",429000,339345,"upper bound",0,339345],[6,16,"f","(5,3,2,2,2,1,1)",515970,393885,"upper bound",0,393885],[6,16,"f","(5,3,2,2,2,2)",240240,180075,"upper bound",0,180075],[6,16,"f","(5,3,3,1,1,1,1,1)",280280,215845,"upper bound",0,215845],[6,16,"f","(5,3,3,2,1,1,1)",673920,494160,"upper bound",0,494160],[6,16,"f","(5,3,3,2,2,1)",648648,461496,"upper bound",0,461496],[6,16,"f","(5,3,3,3,1,1)",411840,285210,"upper bound",0,285210],[6,16,"f","(5,3,3,3,2)",280280,189890,"upper bound",0,189890],[6,16,"f","(5,4,1,1,1,1,1,1,1)",80640,2,"lower bound",2,63840],[6,16,"f","(5,4,2,1,1,1,1,1)",360360,266910,"upper bound",0,266910],[6,16,"f","(5,4,2,2,1,1,1)",698880,492240,"upper bound",0,492240],[6,16,"f","(5,4,2,2,2,1)",630630,430590,"upper bound",0,430590],[6,16,"f","(5,4,3,1,1,1,1)",582400,398300,"upper bound",0,398300],[6,16,"f","(5,4,3,2,1,1)",1153152,753804,"upper bound",0,753804],[6,16,"f","(5,4,3,2,2)",640640,409300,"upper bound",0,409300],[6,16,"f","(5,4,3,3,1)",549120,340860,"upper bound",0,340860],[6,16,"f","(5,4,4,1,1,1)",360360,223995,"upper bound",0,223995],[6,16,"f","(5,4,4,2,1)",549120,328620,"upper bound",0,328620],[6,16,"f","(5,4,4,3)",180180,103290,"upper bound",0,103290],[6,16,"f","(5,5,1,1,1,1,1,1)",76440,52150,"upper bound",0,52150],[6,16,"f","(5,5,2,1,1,1,1)",305760,195020,"upper bound",0,195020],[6,16,"f","(5,5,2,2,1,1)",480480,292530,"upper bound",0,292530],[6,16,"f","(5,5,2,2,2)",250250,148800,"upper bound",0,148800],[6,16,"f","(5,5,3,1,1,1)",448448,264446,"upper bound",0,264446],[6,16,"f","(5,5,3,2,1)",640640,363560,"upper bound",0,363560],[6,16,"f","(5,5,3,3)",171600,93250,"upper bound",0,93250],[6,16,"f","(5,5,4,1,1)",280280,150755,"upper bound",0,150755],[6,16,"f","(5,5,4,2)",231660,121140,"upper bound",0,121140],[6,16,"f","(5,5,5,1)",60060,28975,"upper bound",0,28975],[6,16,"f","(6,1,1,1,1,1,1,1,1,1,1)",3003,13,"lower bound",13,32],[6,16,"f","(6,2,1,1,1,1,1,1,1,1)",24024,11,"lower bound",11,19950],[6,16,"f","(6,2,2,1,1,1,1,1,1)",85800,3,"lower bound",3,65730],[6,16,"f","(6,2,2,2,1,1,1,1)",173250,124635,"upper bound",0,124635],[6,16,"f","(6,2,2,2,2,1,1)",200200,137985,"upper bound",0,137985],[6,16,"f","(6,2,2,2,2,2)",91728,61881,"upper bound",0,61881],[6,16,"f","(6,3,1,1,1,1,1,1,1)",82368,1,"lower bound",1,60696],[6,16,"f","(6,3,2,1,1,1,1,1)",337920,230280,"upper bound",0,230280],[6,16,"f","(6,3,2,2,1,1,1)",630630,405720,"upper bound",0,405720],[6,16,"f","(6,3,2,2,2,1)",559104,347328,"upper bound",0,347328],[6,16,"f","(6,3,3,1,1,1,1)",429000,266895,"upper bound",0,266895],[6,16,"f","(6,3,3,2,1,1)",819000,484650,"upper bound",0,484650],[6,16,"f","(6,3,3,2,2)",448448,258726,"upper bound",0,258726],[6,16,"f","(6,3,3,3,1)",360360,201540,"upper bound",0,201540],[6,16,"f","(6,4,1,1,1,1,1,1)",155232,99204,"upper bound",0,99204],[6,16,"f","(6,4,2,1,1,1,1)",600600,356580,"upper bound",0,356580],[6,16,"f","(6,4,2,2,1,1)",928746,524412,"upper bound",0,524412],[6,16,"f","(6,4,2,2,2)",480480,264510,"upper bound",0,264510],[6,16,"f","(6,4,3,1,1,1)",819000,446775,"upper bound",0,446775],[6,16,"f","(6,4,3,2,1)",1153152,603984,"upper bound",0,603984],[6,16,"f","(6,4,3,3)",300300,150300,"upper bound",0,150300],[6,16,"f","(6,4,4,1,1)",411840,203730,"upper bound",0,203730],[6,16,"f","(6,4,4,2)",336336,161622,"upper bound",0,161622],[6,16,"f","(6,5,1,1,1,1,1)",168168,90846,"upper bound",0,90846],[6,16,"f","(6,5,2,1,1,1)",559104,282408,"upper bound",0,282408],[6,16,"f","(6,5,2,2,1)",630630,305760,"upper bound",0,305760],[6,16,"f","(6,5,3,1,1)",648648,303471,"upper bound",0,303471],[6,16,"f","(6,5,3,2)",500500,227400,"upper bound",0,227400],[6,16,"f","(6,5,4,1)",292864,125448,"upper bound",0,125448],[6,16,"f","(6,5,5)",36036,13917,"upper bound",0,13917],[6,16,"f","(6,6,1,1,1,1)",91728,40656,"upper bound",0,40656],[6,16,"f","(6,6,2,1,1)",240240,100380,"upper bound",0,100380],[6,16,"f","(6,6,2,2)",150150,60900,"upper bound",0,60900],[6,16,"f","(6,6,3,1)",200200,78225,"upper bound",0,78225],[6,16,"f","(6,6,4)",51480,18615,"upper bound",0,18615],[6,16,"f","(7,1,1,1,1,1,1,1,1,1)",5005,1,"lower bound",1,277],[6,16,"f","(7,2,1,1,1,1,1,1,1)",36608,22784,"upper bound",0,22784],[6,16,"f","(7,2,2,1,1,1,1,1)",115830,65535,"upper bound",0,65535],[6,16,"f","(7,2,2,2,1,1,1)",197120,104300,"upper bound",0,104300],[6,16,"f","(7,2,2,2,2,1)",168168,85456,"upper bound",0,85456],[6,16,"f","(7,3,1,1,1,1,1,1)",114400,62020,"upper bound",0,62020],[6,16,"f","(7,3,2,1,1,1,1)",404250,201355,"upper bound",0,201355],[6,16,"f","(7,3,2,2,1,1)",600600,282870,"upper bound",0,282870],[6,16,"f","(7,3,2,2,2)",305760,140000,"upper bound",0,140000],[6,16,"f","(7,3,3,1,1,1)",429000,194480,"upper bound",0,194480],[6,16,"f","(7,3,3,2,1)",582400,252700,"upper bound",0,252700],[6,16,"f","(7,3,3,3)",140140,57960,"upper bound",0,57960],[6,16,"f","(7,4,1,1,1,1,1)",197120,91840,"upper bound",0,91840],[6,16,"f","(7,4,2,1,1,1)",630630,272895,"upper bound",0,272895],[6,16,"f","(7,4,2,2,1)",698880,289380,"upper bound",0,289380],[6,16,"f","(7,4,3,1,1)",673920,268500,"upper bound",0,268500],[6,16,"f","(7,4,3,2)",512512,198044,"upper bound",0,198044],[6,16,"f","(7,4,4,1)",240240,87220,"upper bound",0,87220],[6,16,"f","(7,5,1,1,1,1)",200200,78890,"upper bound",0,78890],[6,16,"f","(7,5,2,1,1)",515970,190995,"upper bound",0,190995],[6,16,"f","(7,5,2,2)",320320,114940,"upper bound",0,114940],[6,16,"f","(7,5,3,1)",416988,143856,"upper bound",0,143856],[6,16,"f","(7,5,4)",100100,31850,"upper bound",0,31850],[6,16,"f","(7,6,1,1,1)",116480,38080,"upper bound",0,38080],[6,16,"f","(7,6,2,1)",210210,65345,"upper bound",0,65345],[6,16,"f","(7,6,3)",91520,26860,"upper bound",0,26860],[6,16,"f","(7,7,1,1)",32032,8484,"upper bound",0,8484],[6,16,"f","(7,7,2)",30030,7665,"upper bound",0,7665],[6,16,"f","(8,1,1,1,1,1,1,1,1)",6435,0,"exact",0,0],[6,16,"f","(8,2,1,1,1,1,1,1)",42042,15981,"upper bound",0,15981],[6,16,"f","(8,2,2,1,1,1,1)",114400,39780,"upper bound",0,39780],[6,16,"f","(8,2,2,2,1,1)",155232,50904,"upper bound",0,50904],[6,16,"f","(8,2,2,2,2)",76440,24360,"upper bound",0,24360],[6,16,"f","(8,3,1,1,1,1,1)",115830,38955,"upper bound",0,38955],[6,16,"f","(8,3,2,1,1,1)",337920,105120,"upper bound",0,105120],[6,16,"f","(8,3,2,2,1)",360360,107100,"upper bound",0,107100],[6,16,"f","(8,3,3,1,1)",280280,80220,"upper bound",0,80220],[6,16,"f","(8,3,3,2)",206388,57246,"upper bound",0,57246],[6,16,"f","(8,4,1,1,1,1)",173250,51135,"upper bound",0,51135],[6,16,"f","(8,4,2,1,1)",429000,118530,"upper bound",0,118530],[6,16,"f","(8,4,2,2)",262080,70140,"upper bound",0,70140],[6,16,"f","(8,4,3,1)",318500,81900,"upper bound",0,81900],[6,16,"f","(8,4,4)",60060,14280,"upper bound",0,14280],[6,16,"f","(8,5,1,1,1)",150150,38535,"upper bound",0,38535],[6,16,"f","(8,5,2,1)",266240,64800,"upper bound",0,64800],[6,16,"f","(8,5,3)",112112,25704,"upper bound",0,25704],[6,16,"f","(8,6,1,1)",73710,16275,"upper bound",0,16275],[6,16,"f","(8,6,2)",68640,14580,"upper bound",0,14580],[6,16,"f","(8,7,1)",18018,0,"exact",0,0],[6,16,"f","(8,8)",1430,0,"exact",0,0],[6,16,"f","(9,1,1,1,1,1,1,1)",6435,0,"exact",0,0],[6,16,"f","(9,2,1,1,1,1,1)",36608,6264,"upper bound",0,6264],[6,16,"f","(9,2,2,1,1,1)",82368,13356,"upper bound",0,13356],[6,16,"f","(9,2,2,2,1)",80640,12600,"upper bound",0,12600],[6,16,"f","(9,3,1,1,1,1)",85800,13770,"upper bound",0,13770],[6,16,"f","(9,3,2,1,1)",194040,29610,"upper bound",0,29610],[6,16,"f","(9,3,2,2)",114660,17010,"upper bound",0,17010],[6,16,"f","(9,3,3,1)",112112,16254,"upper bound",0,16254],[6,16,"f","(9,4,1,1,1)",105600,15840,"upper bound",0,15840],[6,16,"f","(9,4,2,1)",180180,25830,"upper bound",0,25830],[6,16,"f","(9,4,3)",69888,9576,"upper bound",0,9576],[6,16,"f","(9,5,1,1)",71500,9990,"upper bound",0,9990],[6,16,"f","(9,5,2)",65520,8820,"upper bound",0,8820],[6,16,"f","(9,6,1)",24960,3240,"upper bound",0,3240],[6,16,"f","(9,7)",3432,0,"exact",0,0],[6,17,"f","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,17,"f","(10,1,1,1,1,1,1,1)",11440,0,"exact",0,0],[6,17,"f","(10,2,1,1,1,1,1)",65637,14328,"upper bound",0,14328],[6,17,"f","(10,2,2,1,1,1)",148512,30912,"upper bound",0,30912],[6,17,"f","(10,2,2,2,1)",145860,29400,"upper bound",0,29400],[6,17,"f","(10,3,1,1,1,1)",155584,32040,"upper bound",0,32040],[6,17,"f","(10,3,2,1,1)",353600,69720,"upper bound",0,69720],[6,17,"f","(10,3,2,2)",209440,40320,"upper bound",0,40320],[6,17,"f","(10,3,3,1)",205632,38808,"upper bound",0,38808],[6,17,"f","(10,4,1,1,1)",194480,37680,"upper bound",0,37680],[6,17,"f","(10,4,2,1)",333200,62160,"upper bound",0,62160],[6,17,"f","(10,4,3)",129948,23352,"upper bound",0,23352],[6,17,"f","(10,5,1,1)",134640,24480,"upper bound",0,24480],[6,17,"f","(10,5,2)",123760,21840,"upper bound",0,21840],[6,17,"f","(10,6,1)",48620,8280,"upper bound",0,8280],[6,17,"f","(10,7)",7072,0,"exact",0,0],[6,17,"f","(11,1,1,1,1,1,1)",8008,0,"exact",0,0],[6,17,"f","(11,2,1,1,1,1)",38675,2310,"upper bound",0,2310],[6,17,"f","(11,2,2,1,1)",68068,4158,"upper bound",0,4158],[6,17,"f","(11,2,2,2)",37400,2310,"upper bound",0,2310],[6,17,"f","(11,3,1,1,1)",74256,4620,"upper bound",0,4620],[6,17,"f","(11,3,2,1)",116688,7392,"upper bound",0,7392],[6,17,"f","(11,3,3)",35700,2310,"upper bound",0,2310],[6,17,"f","(11,4,1,1)",70720,4620,"upper bound",0,4620],[6,17,"f","(11,4,2)",62832,4158,"upper bound",0,4158],[6,17,"f","(11,5,1)",33320,2310,"upper bound",0,2310],[6,17,"f","(11,6)",6188,0,"exact",0,0],[6,17,"f","(12,1,1,1,1,1)",4368,0,"exact",0,0],[6,17,"f","(12,2,1,1,1)",17017,0,"exact",0,0],[6,17,"f","(12,2,2,1)",20944,0,"exact",0,0],[6,17,"f","(12,3,1,1)",24752,0,"exact",0,0],[6,17,"f","(12,3,2)",20400,0,"exact",0,0],[6,17,"f","(12,4,1)",15912,0,"exact",0,0],[6,17,"f","(12,5)",3808,0,"exact",0,0],[6,17,"f","(13,1,1,1,1)",1820,0,"exact",0,0],[6,17,"f","(13,2,1,1)",5355,0,"exact",0,0],[6,17,"f","(13,2,2)",3536,0,"exact",0,0],[6,17,"f","(13,3,1)",5236,0,"exact",0,0],[6,17,"f","(13,4)",1700,0,"exact",0,0],[6,17,"f","(14,1,1,1)",560,0,"exact",0,0],[6,17,"f","(14,2,1)",1105,0,"exact",0,0],[6,17,"f","(14,3)",544,0,"exact",0,0],[6,17,"f","(15,1,1)",120,0,"exact",0,0],[6,17,"f","(15,2)",119,0,"exact",0,0],[6,17,"f","(16,1)",16,0,"exact",0,0],[6,17,"f","(17)",1,0,"exact",0,0],[6,17,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",16,9,"lower bound",9,11],[6,17,"f","(2,2,1,1,1,1,1,1,1,1,1,1,1,1,1)",119,33,"lower bound",33,47],[6,17,"f","(2,2,2,1,1,1,1,1,1,1,1,1,1,1)",544,65,"lower bound",65,113],[6,17,"f","(2,2,2,2,1,1,1,1,1,1,1,1,1)",1700,73,"lower bound",73,1700],[6,17,"f","(2,2,2,2,2,1,1,1,1,1,1,1)",3808,45,"lower bound",45,3808],[6,17,"f","(2,2,2,2,2,2,1,1,1,1,1)",6188,13,"lower bound",13,6187],[6,17,"f","(2,2,2,2,2,2,2,1,1,1)",7072,1,"lower bound",1,7068],[6,17,"f","(2,2,2,2,2,2,2,2,1)",4862,4857,"upper bound",0,4857],[6,17,"f","(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",120,34,"lower bound",34,48],[6,17,"f","(3,2,1,1,1,1,1,1,1,1,1,1,1,1)",1105,134,"lower bound",134,1105],[6,17,"f","(3,2,2,1,1,1,1,1,1,1,1,1,1)",5236,227,"lower bound",227,5236],[6,17,"f","(3,2,2,2,1,1,1,1,1,1,1,1)",15912,194,"lower bound",194,15912],[6,17,"f","(3,2,2,2,2,1,1,1,1,1,1)",33320,80,"lower bound",80,33285],[6,17,"f","(3,2,2,2,2,2,1,1,1,1)",48620,12,"lower bound",12,48470],[6,17,"f","(3,2,2,2,2,2,2,1,1)",46410,46170,"upper bound",0,46170],[6,17,"f","(3,2,2,2,2,2,2,2)",19448,19323,"upper bound",0,19323],[6,17,"f","(3,3,1,1,1,1,1,1,1,1,1,1,1)",3536,152,"lower bound",152,3536],[6,17,"f","(3,3,2,1,1,1,1,1,1,1,1,1)",20400,243,"lower bound",243,20400],[6,17,"f","(3,3,2,2,1,1,1,1,1,1,1)",62832,149,"lower bound",149,62643],[6,17,"f","(3,3,2,2,2,1,1,1,1,1)",123760,34,"lower bound",34,122780],[6,17,"f","(3,3,2,2,2,2,1,1,1)",159120,1,"lower bound",1,157050],[6,17,"f","(3,3,2,2,2,2,2,1)",116688,114732,"upper bound",0,114732],[6,17,"f","(3,3,3,1,1,1,1,1,1,1,1)",35700,82,"lower bound",82,35525],[6,17,"f","(3,3,3,2,1,1,1,1,1,1)",129948,36,"lower bound",36,128282],[6,17,"f","(3,3,3,2,2,1,1,1,1)",247520,3,"lower bound",3,242210],[6,17,"f","(3,3,3,2,2,2,1,1)",272272,264508,"upper bound",0,264508],[6,17,"f","(3,3,3,2,2,2,2)",121550,117605,"upper bound",0,117605],[6,17,"f","(3,3,3,3,1,1,1,1,1)",129948,2,"lower bound",2,126498],[6,17,"f","(3,3,3,3,2,1,1,1)",272272,262132,"upper bound",0,262132],[6,17,"f","(3,3,3,3,2,2,1)",243100,232285,"upper bound",0,232285],[6,17,"f","(3,3,3,3,3,1,1)",136136,129155,"upper bound",0,129155],[6,17,"f","(3,3,3,3,3,2)",87516,82518,"upper bound",0,82518],[6,17,"f","(4,1,1,1,1,1,1,1,1,1,1,1,1,1)",560,70,"lower bound",70,120],[6,17,"f","(4,2,1,1,1,1,1,1,1,1,1,1,1)",5355,235,"lower bound",235,5355],[6,17,"f","(4,2,2,1,1,1,1,1,1,1,1,1)",24752,303,"lower bound",303,24752],[6,17,"f","(4,2,2,2,1,1,1,1,1,1,1)",70720,179,"lower bound",179,70440],[6,17,"f","(4,2,2,2,2,1,1,1,1,1)",134640,45,"lower bound",45,133260],[6,17,"f","(4,2,2,2,2,2,1,1,1)",170170,3,"lower bound",3,167350],[6,17,"f","(4,2,2,2,2,2,2,1)",123760,121140,"upper bound",0,121140],[6,17,"f","(4,3,1,1,1,1,1,1,1,1,1,1)",20944,248,"lower bound",248,20944],[6,17,"f","(4,3,2,1,1,1,1,1,1,1,1)",116688,274,"lower bound",274,115792],[6,17,"f","(4,3,2,2,1,1,1,1,1,1)",333200,101,"lower bound",101,326900],[6,17,"f","(4,3,2,2,2,1,1,1,1)",583440,10,"lower bound",10,565700],[6,17,"f","(4,3,2,2,2,2,1,1)",618800,594380,"upper bound",0,594380],[6,17,"f","(4,3,2,2,2,2,2)",272272,260188,"upper bound",0,260188],[6,17,"f","(4,3,3,1,1,1,1,1,1,1)",205632,57,"lower bound",57,200508],[6,17,"f","(4,3,3,2,1,1,1,1,1)",680680,11,"lower bound",11,652610],[6,17,"f","(4,3,3,2,2,1,1,1)",1113840,1052340,"upper bound",0,1052340],[6,17,"f","(4,3,3,2,2,2,1)",918918,859722,"upper bound",0,859722],[6,17,"f","(4,3,3,3,1,1,1,1)",618800,579260,"upper bound",0,579260],[6,17,"f","(4,3,3,3,2,1,1)",1050192,968388,"upper bound",0,968388],[6,17,"f","(4,3,3,3,2,2)",544544,498092,"upper bound",0,498092],[6,17,"f","(4,3,3,3,3,1)",388960,352120,"upper bound",0,352120],[6,17,"f","(4,4,1,1,1,1,1,1,1,1,1)",37400,83,"lower bound",83,36910],[6,17,"f","(4,4,2,1,1,1,1,1,1,1)",209440,57,"lower bound",57,202720],[6,17,"f","(4,4,2,2,1,1,1,1,1)",556920,9,"lower bound",9,528465],[6,17,"f","(4,4,2,2,2,1,1,1)",848640,791960,"upper bound",0,791960],[6,17,"f","(4,4,2,2,2,2,1)",680680,628280,"upper bound",0,628280],[6,17,"f","(4,4,3,1,1,1,1,1,1)",433160,6,"lower bound",6,406805],[6,17,"f","(4,4,3,2,1,1,1,1)",1299480,1192450,"upper bound",0,1192450],[6,17,"f","(4,4,3,2,2,1,1)",1750320,1578735,"upper bound",0,1578735],[6,17,"f","(4,4,3,2,2,2)",850850,760465,"upper bound",0,760465],[6,17,"f","(4,4,3,3,1,1,1)",1089088,970182,"upper bound",0,970182],[6,17,"f","(4,4,3,3,2,1)",1361360,1194300,"upper bound",0,1194300],[6,17,"f","(4,4,3,3,3)",291720,251390,"upper bound",0,251390],[6,17,"f","(4,4,4,1,1,1,1,1)",346528,311472,"upper bound",0,311472],[6,17,"f","(4,4,4,2,1,1,1)",952952,835153,"upper bound",0,835153],[6,17,"f","(4,4,4,2,2,1)",972400,838460,"upper bound",0,838460],[6,17,"f","(4,4,4,3,1,1)",816816,694068,"upper bound",0,694068],[6,17,"f","(4,4,4,3,2)",583440,489700,"upper bound",0,489700],[6,17,"f","(4,4,4,4,1)",204204,167102,"upper bound",0,167102],[6,17,"f","(5,1,1,1,1,1,1,1,1,1,1,1,1)",1820,81,"lower bound",81,184],[6,17,"f","(5,2,1,1,1,1,1,1,1,1,1,1)",17017,204,"lower bound",204,17017],[6,17,"f","(5,2,2,1,1,1,1,1,1,1,1)",74256,181,"lower bound",181,73416],[6,17,"f","(5,2,2,2,1,1,1,1,1,1)",194480,68,"lower bound",68,189280],[6,17,"f","(5,2,2,2,2,1,1,1,1)",327250,9,"lower bound",9,313565],[6,17,"f","(5,2,2,2,2,2,1,1)",340340,322185,"upper bound",0,322185],[6,17,"f","(5,2,2,2,2,2,2)",148512,139682,"upper bound",0,139682],[6,17,"f","(5,3,1,1,1,1,1,1,1,1,1)",68068,152,"lower bound",152,66934],[6,17,"f","(5,3,2,1,1,1,1,1,1,1)",353600,101,"lower bound",101,339600],[6,17,"f","(5,3,2,2,1,1,1,1,1)",908820,18,"lower bound",18,852570],[6,17,"f","(5,3,2,2,2,1,1,1)",1361360,1252580,"upper bound",0,1252580],[6,17,"f","(5,3,2,2,2,2,1)",1082900,983865,"upper bound",0,983865],[6,17,"f","(5,3,3,1,1,1,1,1,1)",586432,9,"lower bound",9,543522],[6,17,"f","(5,3,3,2,1,1,1,1)",1701700,1535590,"upper bound",0,1535590],[6,17,"f","(5,3,3,2,2,1,1)",2255526,1995975,"upper bound",0,1995975],[6,17,"f","(5,3,3,2,2,2)",1089088,953886,"upper bound",0,953886],[6,17,"f","(5,3,3,3,1,1,1)",1326000,1157000,"upper bound",0,1157000],[6,17,"f","(5,3,3,3,2,1)",1633632,1401292,"upper bound",0,1401292],[6,17,"f","(5,3,3,3,3)",340340,286225,"upper bound",0,286225],[6,17,"f","(5,4,1,1,1,1,1,1,1,1)",145860,36,"lower bound",36,137600],[6,17,"f","(5,4,2,1,1,1,1,1,1)",749700,11,"lower bound",11,683550],[6,17,"f","(5,4,2,2,1,1,1,1)",1750320,1549995,"upper bound",0,1549995],[6,17,"f","(5,4,2,2,2,1,1)",2165800,1877995,"upper bound",0,1877995],[6,17,"f","(5,4,2,2,2,2)",1021020,875670,"upper bound",0,875670],[6,17,"f","(5,4,3,1,1,1,1,1)",1429428,1246203,"upper bound",0,1246203],[6,17,"f","(5,4,3,2,1,1,1)",3620864,3065280,"upper bound",0,3065280],[6,17,"f","(5,4,3,2,2,1)",3573570,2969615,"upper bound",0,2969615],[6,17,"f","(5,4,3,3,1,1)",2450448,2002758,"upper bound",0,2002758],[6,17,"f","(5,4,3,3,2)",1701700,1371705,"upper bound",0,1371705],[6,17,"f","(5,4,4,1,1,1,1)",1082900,891065,"upper bound",0,891065],[6,17,"f","(5,4,4,2,1,1)",2362932,1890504,"upper bound",0,1890504],[6,17,"f","(5,4,4,2,2)",1361360,1073600,"upper bound",0,1073600],[6,17,"f","(5,4,4,3,1)",1458600,1129335,"upper bound",0,1129335],[6,17,"f","(5,4,4,4)",204204,152135,"upper bound",0,152135],[6,17,"f","(5,5,1,1,1,1,1,1,1)",157080,2,"lower bound",2,137830],[6,17,"f","(5,5,2,1,1,1,1,1)",742560,624960,"upper bound",0,624960],[6,17,"f","(5,5,2,2,1,1,1)",1485120,1210370,"upper bound",0,1210370],[6,17,"f","(5,5,2,2,2,1)",1361360,1087380,"upper bound",0,1087380],[6,17,"f","(5,5,3,1,1,1,1)",1336608,1068942,"upper bound",0,1068942],[6,17,"f","(5,5,3,2,1,1)",2722720,2114140,"upper bound",0,2114140],[6,17,"f","(5,5,3,2,2)",1531530,1171320,"upper bound",0,1171320],[6,17,"f","(5,5,3,3,1)",1361360,1021530,"upper bound",0,1021530],[6,17,"f","(5,5,4,1,1,1)",1089088,818356,"upper bound",0,818356],[6,17,"f","(5,5,4,2,1)",1701700,1246645,"upper bound",0,1246645],[6,17,"f","(5,5,4,3)",583440,415180,"upper bound",0,415180],[6,17,"f","(5,5,5,1,1)",340340,237000,"upper bound",0,237000],[6,17,"f","(5,5,5,2)",291720,199225,"upper bound",0,199225],[6,17,"f","(6,1,1,1,1,1,1,1,1,1,1,1)",4368,50,"lower bound",50,1225],[6,17,"f","(6,2,1,1,1,1,1,1,1,1,1)",38675,83,"lower bound",83,37625],[6,17,"f","(6,2,2,1,1,1,1,1,1,1)",155584,45,"lower bound",45,146224],[6,17,"f","(6,2,2,2,1,1,1,1,1)",364650,9,"lower bound",9,331785],[6,17,"f","(6,2,2,2,2,1,1,1)",523600,464380,"upper bound",0,464380],[6,17,"f","(6,2,2,2,2,2,1)",408408,356348,"upper bound",0,356348],[6,17,"f","(6,3,1,1,1,1,1,1,1,1)",148512,34,"lower bound",34,137256],[6,17,"f","(6,3,2,1,1,1,1,1,1)",700128,10,"lower bound",10,620088],[6,17,"f","(6,3,2,2,1,1,1,1)",1570800,1342740,"upper bound",0,1342740],[6,17,"f","(6,3,2,2,2,1,1)",1905904,1588860,"upper bound",0,1588860],[6,17,"f","(6,3,2,2,2,2)",891072,733284,"upper bound",0,733284],[6,17,"f","(6,3,3,1,1,1,1,1)",1047200,878500,"upper bound",0,878500],[6,17,"f","(6,3,3,2,1,1,1)",2552550,2068395,"upper bound",0,2068395],[6,17,"f","(6,3,3,2,2,1)",2475200,1963020,"upper bound",0,1963020],[6,17,"f","(6,3,3,3,1,1)",1591200,1237980,"upper bound",0,1237980],[6,17,"f","(6,3,3,3,2)",1089088,834068,"upper bound",0,834068],[6,17,"f","(6,4,1,1,1,1,1,1,1)",318240,3,"lower bound",3,272460],[6,17,"f","(6,4,2,1,1,1,1,1)",1454112,1187712,"upper bound",0,1187712],[6,17,"f","(6,4,2,2,1,1,1)",2858856,2252880,"upper bound",0,2252880],[6,17,"f","(6,4,2,2,2,1)",2598960,2002980,"upper bound",0,2002980],[6,17,"f","(6,4,3,1,1,1,1)",2431000,1875950,"upper bound",0,1875950],[6,17,"f","(6,4,3,2,1,1)",4873050,3640455,"upper bound",0,3640455],[6,17,"f","(6,4,3,2,2)",2722720,2000680,"upper bound",0,2000680],[6,17,"f","(6,4,3,3,1)",2362932,1700712,"upper bound",0,1700712],[6,17,"f","(6,4,4,1,1,1)",1591200,1146720,"upper bound",0,1146720],[6,17,"f","(6,4,4,2,1)",2450448,1718196,"upper bound",0,1718196],[6,17,"f","(6,4,4,3)",816816,555180,"upper bound",0,555180],[6,17,"f","(6,5,1,1,1,1,1,1)",399840,308560,"upper bound",0,308560],[6,17,"f","(6,5,2,1,1,1,1)",1633632,1201088,"upper bound",0,1201088],[6,17,"f","(6,5,2,2,1,1)",2598960,1847580,"upper bound",0,1847580],[6,17,"f","(6,5,2,2,2)",1361360,951300,"upper bound",0,951300],[6,17,"f","(6,5,3,1,1,1)",2475200,1719620,"upper bound",0,1719620],[6,17,"f","(6,5,3,2,1)",3573570,2414405,"upper bound",0,2414405],[6,17,"f","(6,5,3,3)",972400,636580,"upper bound",0,636580],[6,17,"f","(6,5,4,1,1)",1633632,1061984,"upper bound",0,1061984],[6,17,"f","(6,5,4,2)",1361360,866940,"upper bound",0,866940],[6,17,"f","(6,5,5,1)",388960,233800,"upper bound",0,233800],[6,17,"f","(6,6,1,1,1,1,1)",259896,175350,"upper bound",0,175350],[6,17,"f","(6,6,2,1,1,1)",891072,573552,"upper bound",0,573552],[6,17,"f","(6,6,2,2,1)",1021020,638400,"upper bound",0,638400],[6,17,"f","(6,6,3,1,1)",1089088,664188,"upper bound",0,664188],[6,17,"f","(6,6,3,2)",850850,508095,"upper bound",0,508095],[6,17,"f","(6,6,4,1)",544544,312060,"upper bound",0,312060],[6,17,"f","(6,6,5)",87516,46650,"upper bound",0,46650],[6,17,"f","(7,1,1,1,1,1,1,1,1,1,1)",8008,14,"lower bound",14,290],[6,17,"f","(7,2,1,1,1,1,1,1,1,1)",65637,12,"lower bound",12,57609],[6,17,"f","(7,2,2,1,1,1,1,1,1)",238238,3,"lower bound",3,196973],[6,17,"f","(7,2,2,2,1,1,1,1)",486200,383510,"upper bound",0,383510],[6,17,"f","(7,2,2,2,2,1,1)",565488,431907,"upper bound",0,431907],[6,17,"f","(7,2,2,2,2,2)",259896,195307,"upper bound",0,195307],[6,17,"f","(7,3,1,1,1,1,1,1,1)",233376,1,"lower bound",1,187500],[6,17,"f","(7,3,2,1,1,1,1,1)",972400,736640,"upper bound",0,736640],[6,17,"f","(7,3,2,2,1,1,1)",1832600,1329195,"upper bound",0,1329195],[6,17,"f","(7,3,2,2,2,1)",1633632,1153824,"upper bound",0,1153824],[6,17,"f","(7,3,3,1,1,1,1)",1262250,892680,"upper bound",0,892680],[6,17,"f","(7,3,3,2,1,1)",2431000,1655100,"upper bound",0,1655100],[6,17,"f","(7,3,3,2,2)",1336608,892626,"upper bound",0,892626],[6,17,"f","(7,3,3,3,1)",1082900,706300,"upper bound",0,706300],[6,17,"f","(7,4,1,1,1,1,1,1)",466752,337064,"upper bound",0,337064],[6,17,"f","(7,4,2,1,1,1,1)",1832600,1251530,"upper bound",0,1251530],[6,17,"f","(7,4,2,2,1,1)",2858856,1879227,"upper bound",0,1879227],[6,17,"f","(7,4,2,2,2)",1485120,957530,"upper bound",0,957530],[6,17,"f","(7,4,3,1,1,1)",2552550,1634780,"upper bound",0,1634780],[6,17,"f","(7,4,3,2,1)",3620864,2248128,"upper bound",0,2248128],[6,17,"f","(7,4,3,3)",952952,571508,"upper bound",0,571508],[6,17,"f","(7,4,4,1,1)",1326000,788650,"upper bound",0,788650],[6,17,"f","(7,4,4,2)",1089088,633486,"upper bound",0,633486],[6,17,"f","(7,5,1,1,1,1,1)",565488,359856,"upper bound",0,359856],[6,17,"f","(7,5,2,1,1,1)",1905904,1152368,"upper bound",0,1152368],[6,17,"f","(7,5,2,2,1)",2165800,1269205,"upper bound",0,1269205],[6,17,"f","(7,5,3,1,1)",2255526,1286712,"upper bound",0,1286712],[6,17,"f","(7,5,3,2)",1750320,976380,"upper bound",0,976380],[6,17,"f","(7,5,4,1)",1050192,560544,"upper bound",0,560544],[6,17,"f","(7,5,5)",136136,67277,"upper bound",0,67277],[6,17,"f","(7,6,1,1,1,1)",408408,223986,"upper bound",0,223986],[6,17,"f","(7,6,2,1,1)",1082900,567840,"upper bound",0,567840],[6,17,"f","(7,6,2,2)",680680,348915,"upper bound",0,348915],[6,17,"f","(7,6,3,1)",918918,458052,"upper bound",0,458052],[6,17,"f","(7,6,4)",243100,114375,"upper bound",0,114375],[6,17,"f","(7,7,1,1,1)",148512,68404,"upper bound",0,68404],[6,17,"f","(7,7,2,1)",272272,120848,"upper bound",0,120848],[6,17,"f","(7,7,3)",121550,51745,"upper bound",0,51745],[6,17,"f","(8,1,1,1,1,1,1,1,1,1)",11440,1,"lower bound",1,1072],[6,17,"f","(8,2,1,1,1,1,1,1,1)",85085,59150,"upper bound",0,59150],[6,17,"f","(8,2,2,1,1,1,1,1)",272272,175392,"upper bound",0,175392],[6,17,"f","(8,2,2,2,1,1,1)",466752,284948,"upper bound",0,284948],[6,17,"f","(8,2,2,2,2,1)",399840,236320,"upper bound",0,236320],[6,17,"f","(8,3,1,1,1,1,1,1)",272272,169456,"upper bound",0,169456],[6,17,"f","(8,3,2,1,1,1,1)",972400,565600,"upper bound",0,565600],[6,17,"f","(8,3,2,2,1,1)",1454112,808704,"upper bound",0,808704],[6,17,"f","(8,3,2,2,2)",742560,403760,"upper bound",0,403760],[6,17,"f","(8,3,3,1,1,1)",1047200,565040,"upper bound",0,565040],[6,17,"f","(8,3,3,2,1)",1429428,744646,"upper bound",0,744646],[6,17,"f","(8,3,3,3)",346528,173712,"upper bound",0,173712],[6,17,"f","(8,4,1,1,1,1,1)",486200,268030,"upper bound",0,268030],[6,17,"f","(8,4,2,1,1,1)",1570800,816480,"upper bound",0,816480],[6,17,"f","(8,4,2,2,1)",1750320,878310,"upper bound",0,878310],[6,17,"f","(8,4,3,1,1)",1701700,828450,"upper bound",0,828450],[6,17,"f","(8,4,3,2)",1299480,617330,"upper bound",0,617330],[6,17,"f","(8,4,4,1)",618800,280000,"upper bound",0,280000],[6,17,"f","(8,5,1,1,1,1)",523600,252560,"upper bound",0,252560],[6,17,"f","(8,5,2,1,1)",1361360,624960,"upper bound",0,624960],[6,17,"f","(8,5,2,2)",848640,380080,"upper bound",0,380080],[6,17,"f","(8,5,3,1)",1113840,483840,"upper bound",0,483840],[6,17,"f","(8,5,4)",272272,111104,"upper bound",0,111104],[6,17,"f","(8,6,1,1,1)",340340,141610,"upper bound",0,141610],[6,17,"f","(8,6,2,1)",618800,247520,"upper bound",0,247520],[6,17,"f","(8,6,3)",272272,104188,"upper bound",0,104188],[6,17,"f","(8,7,1,1)",123760,43680,"upper bound",0,43680],[6,17,"f","(8,7,2)",116688,40032,"upper bound",0,40032],[6,17,"f","(8,8,1)",19448,0,"exact",0,0],[6,17,"f","(9,1,1,1,1,1,1,1,1)",12870,0,"exact",0,0],[6,17,"f","(9,2,1,1,1,1,1,1)",85085,38535,"upper bound",0,38535],[6,17,"f","(9,2,2,1,1,1,1)",233376,98040,"upper bound",0,98040],[6,17,"f","(9,2,2,2,1,1)",318240,127260,"upper bound",0,127260],[6,17,"f","(9,2,2,2,2)",157080,61320,"upper bound",0,61320],[6,17,"f","(9,3,1,1,1,1,1)",238238,97209,"upper bound",0,97209],[6,17,"f","(9,3,2,1,1,1)",700128,267696,"upper bound",0,267696],[6,17,"f","(9,3,2,2,1)",749700,275940,"upper bound",0,275940],[6,17,"f","(9,3,3,1,1)",586432,209244,"upper bound",0,209244],[6,17,"f","(9,3,3,2)",433160,150570,"upper bound",0,150570],[6,17,"f","(9,4,1,1,1,1)",364650,133245,"upper bound",0,133245],[6,17,"f","(9,4,2,1,1)",908820,314550,"upper bound",0,314550],[6,17,"f","(9,4,2,2)",556920,187740,"upper bound",0,187740],[6,17,"f","(9,4,3,1)",680680,222180,"upper bound",0,222180],[6,17,"f","(9,4,4)",129948,39816,"upper bound",0,39816],[6,17,"f","(9,5,1,1,1)",327250,106365,"upper bound",0,106365],[6,17,"f","(9,5,2,1)",583440,181680,"upper bound",0,181680],[6,17,"f","(9,5,3)",247520,73500,"upper bound",0,73500],[6,17,"f","(9,6,1,1)",170170,48825,"upper bound",0,48825],[6,17,"f","(9,6,2)",159120,44280,"upper bound",0,44280],[6,17,"f","(9,7,1)",46410,11655,"upper bound",0,11655],[6,17,"f","(9,8)",4862,0,"exact",0,0],[6,18,"f","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,18,"f","(10,1,1,1,1,1,1,1,1)",24310,13695,"upper bound",0,13695],[6,18,"f","(10,2,1,1,1,1,1,1)",162162,83853,"upper bound",0,83853],[6,18,"f","(10,2,2,1,1,1,1)",447525,216990,"upper bound",0,216990],[6,18,"f","(10,2,2,2,1,1)",612612,284802,"upper bound",0,284802],[6,18,"f","(10,2,2,2,2)",302940,137970,"upper bound",0,137970],[6,18,"f","(10,3,1,1,1,1,1)",459459,217161,"upper bound",0,217161],[6,18,"f","(10,3,2,1,1,1)",1357824,607344,"upper bound",0,607344],[6,18,"f","(10,3,2,2,1)",1458600,631680,"upper bound",0,631680],[6,18,"f","(10,3,3,1,1)",1145664,483336,"upper bound",0,483336],[6,18,"f","(10,3,3,2)",848232,350028,"upper bound",0,350028],[6,18,"f","(10,4,1,1,1,1)",714714,307335,"upper bound",0,307335],[6,18,"f","(10,4,2,1,1)",1790100,735480,"upper bound",0,735480],[6,18,"f","(10,4,2,2)",1099560,441840,"upper bound",0,441840],[6,18,"f","(10,4,3,1)",1349460,527940,"upper bound",0,527940],[6,18,"f","(10,4,4)",259896,96474,"upper bound",0,96474],[6,18,"f","(10,5,1,1,1)",656370,255465,"upper bound",0,255465],[6,18,"f","(10,5,2,1)",1175040,441360,"upper bound",0,441360],[6,18,"f","(10,5,3)",501228,181062,"upper bound",0,181062],[6,18,"f","(10,6,1,1)",353430,123795,"upper bound",0,123795],[6,18,"f","(10,6,2)",331500,113250,"upper bound",0,113250],[6,18,"f","(10,7,1)",102102,31983,"upper bound",0,31983],[6,18,"f","(10,8)",11934,0,"exact",0,0],[6,18,"f","(11,1,1,1,1,1,1,1)",19448,0,"exact",0,0],[6,18,"f","(11,2,1,1,1,1,1)",112320,29700,"upper bound",0,29700],[6,18,"f","(11,2,2,1,1,1)",255255,64680,"upper bound",0,64680],[6,18,"f","(11,2,2,2,1)",251328,61908,"upper bound",0,61908],[6,18,"f","(11,3,1,1,1,1)",268515,67320,"upper bound",0,67320],[6,18,"f","(11,3,2,1,1)",612612,147840,"upper bound",0,147840],[6,18,"f","(11,3,2,2)",363528,85932,"upper bound",0,85932],[6,18,"f","(11,3,3,1)",358020,83160,"upper bound",0,83160],[6,18,"f","(11,4,1,1,1)",339456,80520,"upper bound",0,80520],[6,18,"f","(11,4,2,1)",583440,133980,"upper bound",0,133980],[6,18,"f","(11,4,3)",228480,50820,"upper bound",0,50820],[6,18,"f","(11,5,1,1)",238680,53460,"upper bound",0,53460],[6,18,"f","(11,5,2)",219912,48048,"upper bound",0,48048],[6,18,"f","(11,6,1)",88128,18612,"upper bound",0,18612],[6,18,"f","(11,7)",13260,0,"exact",0,0],[6,18,"f","(12,1,1,1,1,1,1)",12376,0,"exact",0,0],[6,18,"f","(12,2,1,1,1,1)",60060,4620,"upper bound",0,4620],[6,18,"f","(12,2,2,1,1)",106029,8316,"upper bound",0,8316],[6,18,"f","(12,2,2,2)",58344,4620,"upper bound",0,4620],[6,18,"f","(12,3,1,1,1)",116025,9240,"upper bound",0,9240],[6,18,"f","(12,3,2,1)",182784,14784,"upper bound",0,14784],[6,18,"f","(12,3,3)",56100,4620,"upper bound",0,4620],[6,18,"f","(12,4,1,1)",111384,9240,"upper bound",0,9240],[6,18,"f","(12,4,2)",99144,8316,"upper bound",0,8316],[6,18,"f","(12,5,1)",53040,4620,"upper bound",0,4620],[6,18,"f","(12,6)",9996,0,"exact",0,0],[6,18,"f","(13,1,1,1,1,1)",6188,0,"exact",0,0],[6,18,"f","(13,2,1,1,1)",24192,0,"exact",0,0],[6,18,"f","(13,2,2,1)",29835,0,"exact",0,0],[6,18,"f","(13,3,1,1)",35343,0,"exact",0,0],[6,18,"f","(13,3,2)",29172,0,"exact",0,0],[6,18,"f","(13,4,1)",22848,0,"exact",0,0],[6,18,"f","(13,5)",5508,0,"exact",0,0],[6,18,"f","(14,1,1,1,1)",2380,0,"exact",0,0],[6,18,"f","(14,2,1,1)",7020,0,"exact",0,0],[6,18,"f","(14,2,2)",4641,0,"exact",0,0],[6,18,"f","(14,3,1)",6885,0,"exact",0,0],[6,18,"f","(14,4)",2244,0,"exact",0,0],[6,18,"f","(15,1,1,1)",680,0,"exact",0,0],[6,18,"f","(15,2,1)",1344,0,"exact",0,0],[6,18,"f","(15,3)",663,0,"exact",0,0],[6,18,"f","(16,1,1)",136,0,"exact",0,0],[6,18,"f","(16,2)",135,0,"exact",0,0],[6,18,"f","(17,1)",17,0,"exact",0,0],[6,18,"f","(18)",1,0,"exact",0,0],[6,18,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",17,10,"lower bound",10,13],[6,18,"f","(2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",135,42,"lower bound",42,66],[6,18,"f","(2,2,2,1,1,1,1,1,1,1,1,1,1,1,1)",663,98,"lower bound",98,663],[6,18,"f","(2,2,2,2,1,1,1,1,1,1,1,1,1,1)",2244,138,"lower bound",138,2244],[6,18,"f","(2,2,2,2,2,1,1,1,1,1,1,1,1)",5508,118,"lower bound",118,5508],[6,18,"f","(2,2,2,2,2,2,1,1,1,1,1,1)",9996,58,"lower bound",58,9996],[6,18,"f","(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",136,43,"lower bound",43,67],[6,18,"f","(3,2,1,1,1,1,1,1,1,1,1,1,1,1,1)",1344,201,"lower bound",201,1344],[6,18,"f","(3,2,2,1,1,1,1,1,1,1,1,1,1,1)",6885,426,"lower bound",426,6885],[6,18,"f","(3,2,2,2,1,1,1,1,1,1,1,1,1)",22848,494,"lower bound",494,22848],[6,18,"f","(3,2,2,2,2,1,1,1,1,1,1,1)",53040,319,"lower bound",319,53040],[6,18,"f","(3,2,2,2,2,2,1,1,1,1,1)",88128,105,"lower bound",105,88122],[6,18,"f","(3,2,2,2,2,2,2,1,1,1)",102102,13,"lower bound",13,102078],[6,18,"f","(3,2,2,2,2,2,2,2,1)",70720,70690,"upper bound",0,70690],[6,18,"f","(3,3,1,1,1,1,1,1,1,1,1,1,1,1)",4641,286,"lower bound",286,4641],[6,18,"f","(3,3,2,1,1,1,1,1,1,1,1,1,1)",29172,622,"lower bound",622,29172],[6,18,"f","(3,3,2,2,1,1,1,1,1,1,1,1)",99144,586,"lower bound",586,99144],[6,18,"f","(3,3,2,2,2,1,1,1,1,1,1)",219912,263,"lower bound",263,219828],[6,18,"f","(3,3,2,2,2,2,1,1,1,1)",331500,47,"lower bound",47,331125],[6,18,"f","(3,3,2,2,2,2,2,1,1)",322218,1,"lower bound",1,321597],[6,18,"f","(3,3,2,2,2,2,2,2)",136136,135806,"upper bound",0,135806],[6,18,"f","(3,3,3,1,1,1,1,1,1,1,1,1)",56100,325,"lower bound",325,56100],[6,18,"f","(3,3,3,2,1,1,1,1,1,1,1)",228480,267,"lower bound",267,228270],[6,18,"f","(3,3,3,2,2,1,1,1,1,1)",501228,73,"lower bound",73,499947],[6,18,"f","(3,3,3,2,2,2,1,1,1)",678912,4,"lower bound",4,675928],[6,18,"f","(3,3,3,2,2,2,2,1)",510510,507545,"upper bound",0,507545],[6,18,"f","(3,3,3,3,1,1,1,1,1,1)",259896,38,"lower bound",38,258951],[6,18,"f","(3,3,3,3,2,1,1,1,1)",649740,5,"lower bound",5,645440],[6,18,"f","(3,3,3,3,2,2,1,1)",787644,780354,"upper bound",0,780354],[6,18,"f","(3,3,3,3,2,2,2)",364650,360715,"upper bound",0,360715],[6,18,"f","(3,3,3,3,3,1,1,1)",408408,403762,"upper bound",0,403762],[6,18,"f","(3,3,3,3,3,2,1)",466752,460130,"upper bound",0,460130],[6,18,"f","(3,3,3,3,3,3)",87516,85963,"upper bound",0,85963],[6,18,"f","(4,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",680,104,"lower bound",104,203],[6,18,"f","(4,2,1,1,1,1,1,1,1,1,1,1,1,1)",7020,439,"lower bound",439,7020],[6,18,"f","(4,2,2,1,1,1,1,1,1,1,1,1,1)",35343,765,"lower bound",765,35343],[6,18,"f","(4,2,2,2,1,1,1,1,1,1,1,1)",111384,676,"lower bound",676,111384],[6,18,"f","(4,2,2,2,2,1,1,1,1,1,1)",238680,304,"lower bound",304,238560],[6,18,"f","(4,2,2,2,2,2,1,1,1,1)",353430,60,"lower bound",60,352905],[6,18,"f","(4,2,2,2,2,2,2,1,1)",340340,3,"lower bound",3,339485],[6,18,"f","(4,2,2,2,2,2,2,2)",143208,142758,"upper bound",0,142758],[6,18,"f","(4,3,1,1,1,1,1,1,1,1,1,1,1)",29835,635,"lower bound",635,29835],[6,18,"f","(4,3,2,1,1,1,1,1,1,1,1,1)",182784,1068,"lower bound",1068,182784],[6,18,"f","(4,3,2,2,1,1,1,1,1,1,1)",583440,703,"lower bound",703,582600],[6,18,"f","(4,3,2,2,2,1,1,1,1,1)",1175040,190,"lower bound",190,1170480],[6,18,"f","(4,3,2,2,2,2,1,1,1)",1531530,14,"lower bound",14,1521590],[6,18,"f","(4,3,2,2,2,2,2,1)",1131520,1121960,"upper bound",0,1121960],[6,18,"f","(4,3,3,1,1,1,1,1,1,1,1)",358020,413,"lower bound",413,357180],[6,18,"f","(4,3,3,2,1,1,1,1,1,1)",1349460,205,"lower bound",205,1340850],[6,18,"f","(4,3,3,2,2,1,1,1,1)",2625480,24,"lower bound",24,2596785],[6,18,"f","(4,3,3,2,2,2,1,1)",2923830,2880705,"upper bound",0,2880705],[6,18,"f","(4,3,3,2,2,2,2)",1312740,1290540,"upper bound",0,1290540],[6,18,"f","(4,3,3,3,1,1,1,1,1)",1429428,13,"lower bound",13,1409863],[6,18,"f","(4,3,3,3,2,1,1,1)",3055104,2995320,"upper bound",0,2995320],[6,18,"f","(4,3,3,3,2,2,1)",2756754,2691561,"upper bound",0,2691561],[6,18,"f","(4,3,3,3,3,1,1)",1575288,1531938,"upper bound",0,1531938],[6,18,"f","(4,3,3,3,3,2)",1021020,989475,"upper bound",0,989475],[6,18,"f","(4,4,1,1,1,1,1,1,1,1,1,1)",58344,331,"lower bound",331,58344],[6,18,"f","(4,4,2,1,1,1,1,1,1,1,1)",363528,414,"lower bound",414,362352],[6,18,"f","(4,4,2,2,1,1,1,1,1,1)",1099560,167,"lower bound",167,1090320],[6,18,"f","(4,4,2,2,2,1,1,1,1)",1989000,19,"lower bound",19,1961200],[6,18,"f","(4,4,2,2,2,2,1,1)",2148120,2108310,"upper bound",0,2108310],[6,18,"f","(4,4,2,2,2,2,2)",952952,932878,"upper bound",0,932878],[6,18,"f","(4,4,3,1,1,1,1,1,1,1)",848232,120,"lower bound",120,838698],[6,18,"f","(4,4,3,2,1,1,1,1,1)",2970240,26,"lower bound",26,2912630],[6,18,"f","(4,4,3,2,2,1,1,1)",5012280,4878510,"upper bound",0,4878510],[6,18,"f","(4,4,3,2,2,2,1)",4200768,4067862,"upper bound",0,4067862],[6,18,"f","(4,4,3,3,1,1,1,1)",3007368,2913162,"upper bound",0,2913162],[6,18,"f","(4,4,3,3,2,1,1)",5250960,5046000,"upper bound",0,5046000],[6,18,"f","(4,4,3,3,2,2)",2756754,2637672,"upper bound",0,2637672],[6,18,"f","(4,4,3,3,3,1)",2042040,1942830,"upper bound",0,1942830],[6,18,"f","(4,4,4,1,1,1,1,1,1)",779688,6,"lower bound",6,759052],[6,18,"f","(4,4,4,2,1,1,1,1)",2598960,2501520,"upper bound",0,2501520],[6,18,"f","(4,4,4,2,2,1,1)",3675672,3506838,"upper bound",0,3506838],[6,18,"f","(4,4,4,2,2,2)",1823250,1731250,"upper bound",0,1731250],[6,18,"f","(4,4,4,3,1,1,1)",2858856,2710074,"upper bound",0,2710074],[6,18,"f","(4,4,4,3,2,1)",3734016,3510848,"upper bound",0,3510848],[6,18,"f","(4,4,4,3,3)",875160,814870,"upper bound",0,814870],[6,18,"f","(4,4,4,4,1,1)",1021020,948610,"upper bound",0,948610],[6,18,"f","(4,4,4,4,2)",787644,726912,"upper bound",0,726912],[6,18,"f","(5,1,1,1,1,1,1,1,1,1,1,1,1,1)",2380,151,"lower bound",151,2380],[6,18,"f","(5,2,1,1,1,1,1,1,1,1,1,1,1)",24192,520,"lower bound",520,24192],[6,18,"f","(5,2,2,1,1,1,1,1,1,1,1,1)",116025,688,"lower bound",688,116025],[6,18,"f","(5,2,2,2,1,1,1,1,1,1,1)",339456,428,"lower bound",428,338736],[6,18,"f","(5,2,2,2,2,1,1,1,1,1)",656370,122,"lower bound",122,652695],[6,18,"f","(5,2,2,2,2,2,1,1,1)",837760,12,"lower bound",12,830060],[6,18,"f","(5,2,2,2,2,2,2,1)",612612,605357,"upper bound",0,605357],[6,18,"f","(5,3,1,1,1,1,1,1,1,1,1,1)",106029,604,"lower bound",604,106029],[6,18,"f","(5,3,2,1,1,1,1,1,1,1,1)",612612,708,"lower bound",708,610092],[6,18,"f","(5,3,2,2,1,1,1,1,1,1)",1790100,288,"lower bound",288,1771350],[6,18,"f","(5,3,2,2,2,1,1,1,1)",3180870,37,"lower bound",37,3126165],[6,18,"f","(5,3,2,2,2,2,1,1)",3403400,3326435,"upper bound",0,3326435],[6,18,"f","(5,3,2,2,2,2,2)",1503684,1465194,"upper bound",0,1465194],[6,18,"f","(5,3,3,1,1,1,1,1,1,1)",1145664,167,"lower bound",167,1129704],[6,18,"f","(5,3,3,2,1,1,1,1,1)",3877632,38,"lower bound",38,3785892],[6,18,"f","(5,3,3,2,2,1,1,1)",6432426,6225240,"upper bound",0,6225240],[6,18,"f","(5,3,3,2,2,2,1)",5346432,5143560,"upper bound",0,5143560],[6,18,"f","(5,3,3,3,1,1,1,1)",3646500,3509375,"upper bound",0,3509375],[6,18,"f","(5,3,3,3,2,1,1)",6265350,5974305,"upper bound",0,5974305],[6,18,"f","(5,3,3,3,2,2)",3267264,3099984,"upper bound",0,3099984],[6,18,"f","(5,3,3,3,3,1)",2362932,2227557,"upper bound",0,2227557],[6,18,"f","(5,4,1,1,1,1,1,1,1,1,1)",251328,271,"lower bound",271,249564],[6,18,"f","(5,4,2,1,1,1,1,1,1,1)",1458600,205,"lower bound",205,1432350],[6,18,"f","(5,4,2,2,1,1,1,1,1)",3965760,38,"lower bound",38,3848940],[6,18,"f","(5,4,2,2,2,1,1,1)",6126120,5886020,"upper bound",0,5886020],[6,18,"f","(5,4,2,2,2,2,1)",4950400,4724510,"upper bound",0,4724510],[6,18,"f","(5,4,3,1,1,1,1,1,1)",3198720,26,"lower bound",26,3085320],[6,18,"f","(5,4,3,2,1,1,1,1)",9801792,9321298,"upper bound",0,9321298],[6,18,"f","(5,4,3,2,2,1,1)",13366080,12575640,"upper bound",0,12575640],[6,18,"f","(5,4,3,2,2,2)",6534528,6113036,"upper bound",0,6113036],[6,18,"f","(5,4,3,3,1,1,1)",8486400,7922820,"upper bound",0,7922820],[6,18,"f","(5,4,3,3,2,1)",10720710,9912310,"upper bound",0,9912310],[6,18,"f","(5,4,3,3,3)",2333760,2133320,"upper bound",0,2133320],[6,18,"f","(5,4,4,1,1,1,1,1)",2858856,2684276,"upper bound",0,2684276],[6,18,"f","(5,4,4,2,1,1,1)",8019648,7411110,"upper bound",0,7411110],[6,18,"f","(5,4,4,2,2,1)",8270262,7564044,"upper bound",0,7564044],[6,18,"f","(5,4,4,3,1,1)",7088796,6423336,"upper bound",0,6423336],[6,18,"f","(5,4,4,3,2)",5105100,4589190,"upper bound",0,4589190],[6,18,"f","(5,4,4,4,1)",1867008,1651220,"upper bound",0,1651220],[6,18,"f","(5,5,1,1,1,1,1,1,1,1)",302940,38,"lower bound",38,294120],[6,18,"f","(5,5,2,1,1,1,1,1,1)",1649340,13,"lower bound",13,1571010],[6,18,"f","(5,5,2,2,1,1,1,1)",3978000,3725700,"upper bound",0,3725700],[6,18,"f","(5,5,2,2,2,1,1)",5012280,4636380,"upper bound",0,4636380],[6,18,"f","(5,5,2,2,2,2)",2382380,2189285,"upper bound",0,2189285],[6,18,"f","(5,5,3,1,1,1,1,1)",3508596,3256050,"upper bound",0,3256050],[6,18,"f","(5,5,3,2,1,1,1)",9165312,8357532,"upper bound",0,8357532],[6,18,"f","(5,5,3,2,2,1)",9189180,8285235,"upper bound",0,8285235],[6,18,"f","(5,5,3,3,1,1)",6534528,5832428,"upper bound",0,5832428],[6,18,"f","(5,5,3,3,2)",4594590,4065855,"upper bound",0,4065855],[6,18,"f","(5,5,4,1,1,1,1)",3508596,3145044,"upper bound",0,3145044],[6,18,"f","(5,5,4,2,1,1)",7876440,6939225,"upper bound",0,6939225],[6,18,"f","(5,5,4,2,2)",4594590,4011510,"upper bound",0,4011510],[6,18,"f","(5,5,4,3,1)",5105100,4406515,"upper bound",0,4406515],[6,18,"f","(5,5,4,4)",787644,663525,"upper bound",0,663525],[6,18,"f","(5,5,5,1,1,1)",1429428,1224391,"upper bound",0,1224391],[6,18,"f","(5,5,5,2,1)",2333760,1967690,"upper bound",0,1967690],[6,18,"f","(5,5,5,3)",875160,724500,"upper bound",0,724500],[6,18,"f","(6,1,1,1,1,1,1,1,1,1,1,1,1)",6188,131,"lower bound",131,6188],[6,18,"f","(6,2,1,1,1,1,1,1,1,1,1,1)",60060,337,"lower bound",337,60060],[6,18,"f","(6,2,2,1,1,1,1,1,1,1,1)",268515,309,"lower bound",309,266715],[6,18,"f","(6,2,2,2,1,1,1,1,1,1)",714714,122,"lower bound",122,703059],[6,18,"f","(6,2,2,2,2,1,1,1,1)",1215500,18,"lower bound",18,1183930],[6,18,"f","(6,2,2,2,2,2,1,1)",1272348,1229718,"upper bound",0,1229718],[6,18,"f","(6,2,2,2,2,2,2)",556920,536005,"upper bound",0,536005],[6,18,"f","(6,3,1,1,1,1,1,1,1,1,1)",255255,269,"lower bound",269,252735],[6,18,"f","(6,3,2,1,1,1,1,1,1,1)",1357824,190,"lower bound",190,1324704],[6,18,"f","(6,3,2,2,1,1,1,1,1)",3544398,37,"lower bound",37,3406113],[6,18,"f","(6,3,2,2,2,1,1,1)",5361664,5087600,"upper bound",0,5087600],[6,18,"f","(6,3,2,2,2,2,1)",4288284,4035311,"upper bound",0,4035311],[6,18,"f","(6,3,3,1,1,1,1,1,1)",2333760,19,"lower bound",19,2225160],[6,18,"f","(6,3,3,2,1,1,1,1)",6872250,6438075,"upper bound",0,6438075],[6,18,"f","(6,3,3,2,2,1,1)",9189180,8497125,"upper bound",0,8497125],[6,18,"f","(6,3,3,2,2,2)",4455360,4091440,"upper bound",0,4091440],[6,18,"f","(6,3,3,3,1,1,1)",5469750,5010400,"upper bound",0,5010400],[6,18,"f","(6,3,3,3,2,1)",6789120,6147560,"upper bound",0,6147560],[6,18,"f","(6,3,3,3,3)",1429428,1277053,"upper bound",0,1277053],[6,18,"f","(6,4,1,1,1,1,1,1,1,1)",612612,73,"lower bound",73,591066],[6,18,"f","(6,4,2,1,1,1,1,1,1)",3222180,24,"lower bound",24,3040380],[6,18,"f","(6,4,2,2,1,1,1,1)",7634088,7065072,"upper bound",0,7065072],[6,18,"f","(6,4,2,2,2,1,1)",9529520,8695400,"upper bound",0,8695400],[6,18,"f","(6,4,2,2,2,2)",4511052,4085739,"upper bound",0,4085739],[6,18,"f","(6,4,3,1,1,1,1,1)",6361740,5826240,"upper bound",0,5826240],[6,18,"f","(6,4,3,2,1,1,1)",16336320,14666960,"upper bound",0,14666960],[6,18,"f","(6,4,3,2,2,1)",16243500,14400225,"upper bound",0,14400225],[6,18,"f","(6,4,3,3,1,1)",11277630,9885330,"upper bound",0,9885330],[6,18,"f","(6,4,3,3,2)",7876440,6838575,"upper bound",0,6838575],[6,18,"f","(6,4,4,1,1,1,1)",5105100,4495960,"upper bound",0,4495960],[6,18,"f","(6,4,4,2,1,1)",11277630,9742635,"upper bound",0,9742635],[6,18,"f","(6,4,4,2,2)",6534528,5589156,"upper bound",0,5589156],[6,18,"f","(6,4,4,3,1)",7088796,5987079,"upper bound",0,5987079],[6,18,"f","(6,4,4,4)",1021020,839665,"upper bound",0,839665],[6,18,"f","(6,5,1,1,1,1,1,1,1)",875160,5,"lower bound",5,805650],[6,18,"f","(6,5,2,1,1,1,1,1)",4230144,3786000,"upper bound",0,3786000],[6,18,"f","(6,5,2,2,1,1,1)",8576568,7509348,"upper bound",0,7509348],[6,18,"f","(6,5,2,2,2,1)",7920640,6839560,"upper bound",0,6839560],[6,18,"f","(6,5,3,1,1,1,1)",7876440,6807450,"upper bound",0,6807450],[6,18,"f","(6,5,3,2,1,1)",16243500,13755700,"upper bound",0,13755700],[6,18,"f","(6,5,3,2,2)",9189180,7700280,"upper bound",0,7700280],[6,18,"f","(6,5,3,3,1)",8270262,6839322,"upper bound",0,6839322],[6,18,"f","(6,5,4,1,1,1)",6789120,5620280,"upper bound",0,5620280],[6,18,"f","(6,5,4,2,1)",10720710,8719410,"upper bound",0,8719410],[6,18,"f","(6,5,4,3)",3734016,2975960,"upper bound",0,2975960],[6,18,"f","(6,5,5,1,1)",2362932,1855209,"upper bound",0,1855209],[6,18,"f","(6,5,5,2)",2042040,1581520,"upper bound",0,1581520],[6,18,"f","(6,6,1,1,1,1,1,1)",659736,564690,"upper bound",0,564690],[6,18,"f","(6,6,2,1,1,1,1)",2784600,2308530,"upper bound",0,2308530],[6,18,"f","(6,6,2,2,1,1)",4511052,3656772,"upper bound",0,3656772],[6,18,"f","(6,6,2,2,2)",2382380,1909040,"upper bound",0,1909040],[6,18,"f","(6,6,3,1,1,1)",4455360,3556560,"upper bound",0,3556560],[6,18,"f","(6,6,3,2,1)",6534528,5118848,"upper bound",0,5118848],[6,18,"f","(6,6,3,3)",1823250,1397950,"upper bound",0,1397950],[6,18,"f","(6,6,4,1,1)",3267264,2493736,"upper bound",0,2493736],[6,18,"f","(6,6,4,2)",2756754,2074590,"upper bound",0,2074590],[6,18,"f","(6,6,5,1)",1021020,738815,"upper bound",0,738815],[6,18,"f","(6,6,6)",87516,59425,"upper bound",0,59425],[6,18,"f","(7,1,1,1,1,1,1,1,1,1,1,1)",12376,64,"lower bound",64,12376],[6,18,"f","(7,2,1,1,1,1,1,1,1,1,1)",112320,109,"lower bound",109,110340],[6,18,"f","(7,2,2,1,1,1,1,1,1,1)",459459,60,"lower bound",60,440874],[6,18,"f","(7,2,2,2,1,1,1,1,1)",1089088,12,"lower bound",12,1021748],[6,18,"f","(7,2,2,2,2,1,1,1)",1575288,1451472,"upper bound",0,1451472],[6,18,"f","(7,2,2,2,2,2,1)",1233792,1123710,"upper bound",0,1123710],[6,18,"f","(7,3,1,1,1,1,1,1,1,1)",447525,47,"lower bound",47,424575],[6,18,"f","(7,3,2,1,1,1,1,1,1)",2144142,14,"lower bound",14,1974147],[6,18,"f","(7,3,2,2,1,1,1,1)",4862000,4364860,"upper bound",0,4364860],[6,18,"f","(7,3,2,2,2,1,1)",5937624,5235384,"upper bound",0,5235384],[6,18,"f","(7,3,2,2,2,2)",2784600,2432430,"upper bound",0,2432430],[6,18,"f","(7,3,3,1,1,1,1,1)",3281850,2906925,"upper bound",0,2906925],[6,18,"f","(7,3,3,2,1,1,1)",8078400,6978990,"upper bound",0,6978990],[6,18,"f","(7,3,3,2,2,1)",7876440,6699090,"upper bound",0,6699090],[6,18,"f","(7,3,3,3,1,1)",5105100,4282110,"upper bound",0,4282110],[6,18,"f","(7,3,3,3,2)",3508596,2909256,"upper bound",0,2909256],[6,18,"f","(7,4,1,1,1,1,1,1,1)",1018368,4,"lower bound",4,915744],[6,18,"f","(7,4,2,1,1,1,1,1)",4725864,4108044,"upper bound",0,4108044],[6,18,"f","(7,4,2,2,1,1,1)",9382912,7946960,"upper bound",0,7946960],[6,18,"f","(7,4,2,2,2,1)",8576568,7147056,"upper bound",0,7147056],[6,18,"f","(7,4,3,1,1,1,1)",8078400,6738540,"upper bound",0,6738540],[6,18,"f","(7,4,3,2,1,1)",16336320,13307910,"upper bound",0,13307910],[6,18,"f","(7,4,3,2,2)",9165312,7376244,"upper bound",0,7376244],[6,18,"f","(7,4,3,3,1)",8019648,6357120,"upper bound",0,6357120],[6,18,"f","(7,4,4,1,1,1)",5469750,4340325,"upper bound",0,4340325],[6,18,"f","(7,4,4,2,1)",8486400,6599820,"upper bound",0,6599820],[6,18,"f","(7,4,4,3)",2858856,2172996,"upper bound",0,2172996],[6,18,"f","(7,5,1,1,1,1,1,1)",1432080,1195740,"upper bound",0,1195740],[6,18,"f","(7,5,2,1,1,1,1)",5937624,4784976,"upper bound",0,4784976],[6,18,"f","(7,5,2,2,1,1)",9529520,7491820,"upper bound",0,7491820],[6,18,"f","(7,5,2,2,2)",5012280,3890880,"upper bound",0,3890880],[6,18,"f","(7,5,3,1,1,1)",9189180,7103250,"upper bound",0,7103250],[6,18,"f","(7,5,3,2,1)",13366080,10121370,"upper bound",0,10121370],[6,18,"f","(7,5,3,3)",3675672,2719248,"upper bound",0,2719248],[6,18,"f","(7,5,4,1,1)",6265350,4611705,"upper bound",0,4611705],[6,18,"f","(7,5,4,2)",5250960,3806520,"upper bound",0,3806520],[6,18,"f","(7,5,5,1)",1575288,1094496,"upper bound",0,1094496],[6,18,"f","(7,6,1,1,1,1,1)",1233792,934920,"upper bound",0,934920],[6,18,"f","(7,6,2,1,1,1)",4288284,3138114,"upper bound",0,3138114],[6,18,"f","(7,6,2,2,1)",4950400,3545360,"upper bound",0,3545360],[6,18,"f","(7,6,3,1,1)",5346432,3759000,"upper bound",0,3759000],[6,18,"f","(7,6,3,2)",4200768,2907582,"upper bound",0,2907582],[6,18,"f","(7,6,4,1)",2756754,1850919,"upper bound",0,1850919],[6,18,"f","(7,6,5)",466752,297090,"upper bound",0,297090],[6,18,"f","(7,7,1,1,1,1)",556920,373170,"upper bound",0,373170],[6,18,"f","(7,7,2,1,1)",1503684,975576,"upper bound",0,975576],[6,18,"f","(7,7,2,2)",952952,608188,"upper bound",0,608188],[6,18,"f","(7,7,3,1)",1312740,821220,"upper bound",0,821220],[6,18,"f","(7,7,4)",364650,218865,"upper bound",0,218865],[6,18,"f","(8,1,1,1,1,1,1,1,1,1,1)",19448,15,"lower bound",15,18656],[6,18,"f","(8,2,1,1,1,1,1,1,1,1)",162162,13,"lower bound",13,147609],[6,18,"f","(8,2,2,1,1,1,1,1,1)",595595,3,"lower bound",3,518245],[6,18,"f","(8,2,2,2,1,1,1,1)",1225224,1028580,"upper bound",0,1028580],[6,18,"f","(8,2,2,2,2,1,1)",1432080,1172940,"upper bound",0,1172940],[6,18,"f","(8,2,2,2,2,2)",659736,533652,"upper bound",0,533652],[6,18,"f","(8,3,1,1,1,1,1,1,1)",590733,1,"lower bound",1,503046],[6,18,"f","(8,3,2,1,1,1,1,1)",2489344,2026544,"upper bound",0,2026544],[6,18,"f","(8,3,2,2,1,1,1)",4725864,3720696,"upper bound",0,3720696],[6,18,"f","(8,3,2,2,2,1)",4230144,3262848,"upper bound",0,3262848],[6,18,"f","(8,3,3,1,1,1,1)",3281850,2534145,"upper bound",0,2534145],[6,18,"f","(8,3,3,2,1,1)",6361740,4770150,"upper bound",0,4770150],[6,18,"f","(8,3,3,2,2)",3508596,2591862,"upper bound",0,2591862],[6,18,"f","(8,3,3,3,1)",2858856,2073624,"upper bound",0,2073624],[6,18,"f","(8,4,1,1,1,1,1,1)",1225224,961800,"upper bound",0,961800],[6,18,"f","(8,4,2,1,1,1,1)",4862000,3655540,"upper bound",0,3655540],[6,18,"f","(8,4,2,2,1,1)",7634088,5572476,"upper bound",0,5572476],[6,18,"f","(8,4,2,2,2)",3978000,2860500,"upper bound",0,2860500],[6,18,"f","(8,4,3,1,1,1)",6872250,4916625,"upper bound",0,4916625],[6,18,"f","(8,4,3,2,1)",9801792,6845664,"upper bound",0,6845664],[6,18,"f","(8,4,3,3)",2598960,1766940,"upper bound",0,1766940],[6,18,"f","(8,4,4,1,1)",3646500,2463750,"upper bound",0,2463750],[6,18,"f","(8,4,4,2)",3007368,1997016,"upper bound",0,1997016],[6,18,"f","(8,5,1,1,1,1,1)",1575288,1122156,"upper bound",0,1122156],[6,18,"f","(8,5,2,1,1,1)",5361664,3670688,"upper bound",0,3670688],[6,18,"f","(8,5,2,2,1)",6126120,4093320,"upper bound",0,4093320],[6,18,"f","(8,5,3,1,1)",6432426,4209597,"upper bound",0,4209597],[6,18,"f","(8,5,3,2)",5012280,3223500,"upper bound",0,3223500],[6,18,"f","(8,5,4,1)",3055104,1899168,"upper bound",0,1899168],[6,18,"f","(8,5,5)",408408,239316,"upper bound",0,239316],[6,18,"f","(8,6,1,1,1,1)",1272348,808416,"upper bound",0,808416],[6,18,"f","(8,6,2,1,1)",3403400,2088310,"upper bound",0,2088310],[6,18,"f","(8,6,2,2)",2148120,1294980,"upper bound",0,1294980],[6,18,"f","(8,6,3,1)",2923830,1725045,"upper bound",0,1725045],[6,18,"f","(8,6,4)",787644,444516,"upper bound",0,444516],[6,18,"f","(8,7,1,1,1)",612612,340494,"upper bound",0,340494],[6,18,"f","(8,7,2,1)",1131520,611120,"upper bound",0,611120],[6,18,"f","(8,7,3)",510510,267015,"upper bound",0,267015],[6,18,"f","(8,8,1,1)",143208,68076,"upper bound",0,68076],[6,18,"f","(8,8,2)",136136,63364,"upper bound",0,63364],[6,18,"f","(9,1,1,1,1,1,1,1,1,1)",24310,1,"lower bound",1,19855],[6,18,"f","(9,2,1,1,1,1,1,1,1)",183040,137720,"upper bound",0,137720],[6,18,"f","(9,2,2,1,1,1,1,1)",590733,417807,"upper bound",0,417807],[6,18,"f","(9,2,2,2,1,1,1)",1018368,689448,"upper bound",0,689448],[6,18,"f","(9,2,2,2,2,1)",875160,577080,"upper bound",0,577080],[6,18,"f","(9,3,1,1,1,1,1,1)",595595,409570,"upper bound",0,409570],[6,18,"f","(9,3,2,1,1,1,1)",2144142,1395555,"upper bound",0,1395555],[6,18,"f","(9,3,2,2,1,1)",3222180,2022030,"upper bound",0,2022030],[6,18,"f","(9,3,2,2,2)",1649340,1016190,"upper bound",0,1016190],[6,18,"f","(9,3,3,1,1,1)",2333760,1429080,"upper bound",0,1429080],[6,18,"f","(9,3,3,2,1)",3198720,1903440,"upper bound",0,1903440],[6,18,"f","(9,3,3,3)",779688,449652,"upper bound",0,449652],[6,18,"f","(9,4,1,1,1,1,1)",1089088,678524,"upper bound",0,678524],[6,18,"f","(9,4,2,1,1,1)",3544398,2105271,"upper bound",0,2105271],[6,18,"f","(9,4,2,2,1)",3965760,2289060,"upper bound",0,2289060],[6,18,"f","(9,4,3,1,1)",3877632,2184264,"upper bound",0,2184264],[6,18,"f","(9,4,3,2)",2970240,1640100,"upper bound",0,1640100],[6,18,"f","(9,4,4,1)",1429428,759066,"upper bound",0,759066],[6,18,"f","(9,5,1,1,1,1)",1215500,679420,"upper bound",0,679420],[6,18,"f","(9,5,2,1,1)",3180870,1708245,"upper bound",0,1708245],[6,18,"f","(9,5,2,2)",1989000,1047000,"upper bound",0,1047000],[6,18,"f","(9,5,3,1)",2625480,1348650,"upper bound",0,1348650],[6,18,"f","(9,5,4)",649740,317520,"upper bound",0,317520],[6,18,"f","(9,6,1,1,1)",837760,415520,"upper bound",0,415520],[6,18,"f","(9,6,2,1)",1531530,735945,"upper bound",0,735945],[6,18,"f","(9,6,3)",678912,314928,"upper bound",0,314928],[6,18,"f","(9,7,1,1)",340340,147910,"upper bound",0,147910],[6,18,"f","(9,7,2)",322218,136917,"upper bound",0,136917],[6,18,"f","(9,8,1)",70720,26540,"upper bound",0,26540],[6,18,"f","(9,9)",4862,0,"exact",0,0],[6,18,"f","(2,2,2,2,2,2,2,1,1,1,1)",13260,14,"lower bound",14,13260],[6,18,"f","(2,2,2,2,2,2,2,2,1,1)",11934,1,"lower bound",1,11934],[6,19,"f","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,19,"f","(10,9)",16796,0,"exact",0,0],[6,19,"f","(13,1,1,1,1,1,1)",18564,1716,"upper bound",0,1716],[6,19,"f","(13,6)",15504,0,"exact",0,0],[6,19,"f","(14,1,1,1,1,1)",8568,0,"exact",0,0],[6,19,"f","(14,5)",7752,0,"exact",0,0],[6,19,"f","(15,1,1,1,1)",3060,0,"exact",0,0],[6,19,"f","(15,2,1,1)",9044,0,"exact",0,0],[6,19,"f","(15,2,2)",5985,0,"exact",0,0],[6,19,"f","(15,3,1)",8892,0,"exact",0,0],[6,19,"f","(15,4)",2907,0,"exact",0,0],[6,19,"f","(16,1,1,1)",816,0,"exact",0,0],[6,19,"f","(16,2,1)",1615,0,"exact",0,0],[6,19,"f","(16,3)",798,0,"exact",0,0],[6,19,"f","(17,1,1)",153,0,"exact",0,0],[6,19,"f","(17,2)",152,0,"exact",0,0],[6,19,"f","(18,1)",18,0,"exact",0,0],[6,19,"f","(19)",1,0,"exact",0,0],[6,19,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",18,11,"lower bound",11,15],[6,19,"f","(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",153,53,"lower bound",53,89],[6,20,"f","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,20,"f","(10,10)",16796,8398,"upper bound",0,8398],[6,20,"f","(15,1,1,1,1,1)",11628,0,"exact",0,0],[6,20,"f","(15,5)",10659,0,"exact",0,0],[6,20,"f","(16,1,1,1,1)",3876,0,"exact",0,0],[6,20,"f","(16,2,1,1)",11475,0,"exact",0,0],[6,20,"f","(16,2,2)",7600,0,"exact",0,0],[6,20,"f","(16,3,1)",11305,0,"exact",0,0],[6,20,"f","(16,4)",3705,0,"exact",0,0],[6,20,"f","(17,1,1,1)",969,0,"exact",0,0],[6,20,"f","(17,2,1)",1920,0,"exact",0,0],[6,20,"f","(17,3)",950,0,"exact",0,0],[6,20,"f","(18,1,1)",171,0,"exact",0,0],[6,20,"f","(18,2)",170,0,"exact",0,0],[6,20,"f","(19,1)",19,0,"exact",0,0],[6,20,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",19,12,"lower 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bound",0,6300],[6,14,"p","(6,4,2,2)",42042,0,"lower bound",0,3636],[6,14,"p","(6,4,3,1)",50050,0,"lower bound",0,4040],[6,14,"p","(6,4,4)",9009,0,"exact",0,0],[6,14,"p","(6,5,1,1,1)",21021,0,"lower bound",0,1720],[6,14,"p","(6,5,2,1)",36608,0,"lower bound",0,2744],[6,14,"p","(6,5,3)",15015,0,"exact",0,0],[6,14,"p","(6,6,1,1)",7007,0,"exact",0,0],[6,14,"p","(6,6,2)",6435,0,"exact",0,0],[6,14,"p","(7,1,1,1,1,1,1,1)",1716,0,"exact",0,0],[6,14,"p","(7,2,1,1,1,1,1)",9504,0,"exact",0,0],[6,14,"p","(7,2,2,1,1,1)",21021,0,"lower bound",0,1124],[6,14,"p","(7,2,2,2,1)",20384,0,"lower bound",0,1034],[6,14,"p","(7,3,1,1,1,1)",21450,0,"lower bound",0,1140],[6,14,"p","(7,3,2,1,1)",47775,0,"lower bound",0,2360],[6,14,"p","(7,3,2,2)",28028,0,"lower bound",0,1326],[6,14,"p","(7,3,3,1)",27027,0,"lower bound",0,1236],[6,14,"p","(7,4,1,1,1)",24960,0,"lower bound",0,1220],[6,14,"p","(7,4,2,1)",42042,0,"lower 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bound",0,336],[6,14,"p","(8,3,3)",7007,0,"exact",0,0],[6,14,"p","(8,4,1,1)",13650,0,"exact",0,0],[6,14,"p","(8,4,2)",12012,0,"exact",0,0],[6,14,"p","(8,5,1)",6006,0,"exact",0,0],[6,14,"p","(8,6)",1001,0,"exact",0,0],[6,14,"p","(9,1,1,1,1,1)",1287,0,"exact",0,0],[6,14,"p","(9,2,1,1,1)",4928,0,"exact",0,0],[6,14,"p","(9,2,2,1)",6006,0,"exact",0,0],[6,14,"p","(9,3,1,1)",7007,0,"exact",0,0],[6,14,"p","(9,3,2)",5733,0,"exact",0,0],[6,14,"p","(9,4,1)",4368,0,"exact",0,0],[6,14,"p","(9,5)",1001,0,"exact",0,0],[6,14,"p","(10,1,1,1,1)",715,0,"exact",0,0],[6,14,"p","(10,2,1,1)",2079,0,"exact",0,0],[6,14,"p","(10,2,2)",1365,0,"exact",0,0],[6,14,"p","(10,3,1)",2002,0,"exact",0,0],[6,14,"p","(10,4)",637,0,"exact",0,0],[6,14,"p","(11,1,1,1)",286,0,"exact",0,0],[6,14,"p","(11,2,1)",560,0,"exact",0,0],[6,14,"p","(11,3)",273,0,"exact",0,0],[6,14,"p","(12,1,1)",78,0,"exact",0,0],[6,14,"p","(12,2)",77,0,"exact",0,0],[6,14,"p","(13,1)",13,0,"exact",0,0],[6,14,"p","(14)",1,0,"exact",0,0],[6,15,"p","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,0,"exact",0,0],[6,15,"p","(5,4,4,2)",81081,29277,"upper bound",0,29277],[6,15,"p","(5,5,2,2,1)",125125,45650,"upper bound",0,45650],[6,15,"p","(5,5,3,1,1)",126126,43812,"upper bound",0,43812],[6,15,"p","(5,5,3,2)",96525,32250,"upper bound",0,32250],[6,15,"p","(5,5,4,1)",54054,16638,"upper bound",0,16638],[6,15,"p","(5,5,5)",6006,0,"exact",0,0],[6,15,"p","(6,3,2,2,2)",112112,40184,"upper bound",0,40184],[6,15,"p","(6,3,3,1,1,1)",156000,55160,"upper bound",0,55160],[6,15,"p","(6,3,3,2,1)",210210,70300,"upper bound",0,70300],[6,15,"p","(6,3,3,3)",50050,15750,"upper bound",0,15750],[6,15,"p","(6,4,1,1,1,1,1)",70070,25690,"upper bound",0,25690],[6,15,"p","(6,4,2,1,1,1)",221130,73710,"upper bound",0,73710],[6,15,"p","(6,4,2,2,1)",243243,76626,"upper bound",0,76626],[6,15,"p","(6,4,3,1,1)",231660,69360,"upper bound",0,69360],[6,15,"p","(6,4,3,2)",175175,50450,"upper bound",0,50450],[6,15,"p","(6,4,4,1)",80080,21220,"upper bound",0,21220],[6,15,"p","(6,5,1,1,1,1)",63700,18830,"upper bound",0,18830],[6,15,"p","(6,5,2,1,1)",162162,44184,"upper bound",0,44184],[6,15,"p","(6,5,2,2)",100100,26200,"upper bound",0,26200],[6,15,"p","(6,5,3,1)",128700,31950,"upper bound",0,31950],[6,15,"p","(6,5,4)",30030,6680,"upper bound",0,6680],[6,15,"p","(6,6,1,1,1)",28028,6496,"upper bound",0,6496],[6,15,"p","(6,6,2,1)",50050,10850,"upper bound",0,10850],[6,15,"p","(6,6,3)",21450,4300,"upper bound",0,4300],[6,15,"p","(7,1,1,1,1,1,1,1,1)",3003,0,"exact",0,0],[6,15,"p","(7,2,1,1,1,1,1,1)",19305,0,"exact",0,0],[6,15,"p","(7,2,2,1,1,1,1)",51975,13965,"upper bound",0,13965],[6,15,"p","(7,2,2,2,1,1)",70070,17535,"upper bound",0,17535],[6,15,"p","(7,2,2,2,2)",34398,8316,"upper bound",0,8316],[6,15,"p","(7,3,1,1,1,1,1)",51975,13440,"upper bound",0,13440],[6,15,"p","(7,3,2,1,1,1)",150150,35280,"upper bound",0,35280],[6,15,"p","(7,3,2,2,1)",159250,35385,"upper bound",0,35385],[6,15,"p","(7,3,3,1,1)",122850,26040,"upper bound",0,26040],[6,15,"p","(7,3,3,2)",90090,18375,"upper bound",0,18375],[6,15,"p","(7,4,1,1,1,1)",75075,16590,"upper bound",0,16590],[6,15,"p","(7,4,2,1,1)",184275,37485,"upper bound",0,37485],[6,15,"p","(7,4,2,2)",112112,21924,"upper bound",0,21924],[6,15,"p","(7,4,3,1)",135135,25095,"upper bound",0,25095],[6,15,"p","(7,4,4)",25025,4200,"upper bound",0,4200],[6,15,"p","(7,5,1,1,1)",61425,11445,"upper bound",0,11445],[6,15,"p","(7,5,2,1)",108108,18816,"upper bound",0,18816],[6,15,"p","(7,5,3)",45045,7245,"upper bound",0,7245],[6,15,"p","(7,6,1,1)",27027,4179,"upper bound",0,4179],[6,15,"p","(7,6,2)",25025,3675,"upper bound",0,3675],[6,15,"p","(7,7,1)",5005,0,"exact",0,0],[6,15,"p","(8,1,1,1,1,1,1,1)",3432,0,"exact",0,0],[6,15,"p","(8,2,1,1,1,1,1)",19305,0,"exact",0,0],[6,15,"p","(8,2,2,1,1,1)",43120,5040,"upper bound",0,5040],[6,15,"p","(8,2,2,2,1)",42042,4704,"upper bound",0,4704],[6,15,"p","(8,3,1,1,1,1)",44550,5160,"upper bound",0,5160],[6,15,"p","(8,3,2,1,1)",100100,10920,"upper bound",0,10920],[6,15,"p","(8,3,2,2)",58968,6216,"upper bound",0,6216],[6,15,"p","(8,3,3,1)",57330,5880,"upper bound",0,5880],[6,15,"p","(8,4,1,1,1)",53625,5760,"upper bound",0,5760],[6,15,"p","(8,4,2,1)",91000,9240,"upper bound",0,9240],[6,15,"p","(8,4,3)",35035,3360,"upper bound",0,3360],[6,15,"p","(8,5,1,1)",35100,3480,"upper bound",0,3480],[6,15,"p","(8,5,2)",32032,3024,"upper bound",0,3024],[6,15,"p","(8,6,1)",11583,0,"exact",0,0],[6,15,"p","(8,7)",1430,0,"exact",0,0],[6,15,"p","(9,1,1,1,1,1,1)",3003,0,"exact",0,0],[6,15,"p","(9,2,1,1,1,1)",14300,0,"exact",0,0],[6,15,"p","(9,2,2,1,1)",24948,756,"upper bound",0,756],[6,15,"p","(9,2,2,2)",13650,0,"exact",0,0],[6,15,"p","(9,3,1,1,1)",26950,840,"upper bound",0,840],[6,15,"p","(9,3,2,1)",42042,1344,"upper bound",0,1344],[6,15,"p","(9,3,3)",12740,0,"exact",0,0],[6,15,"p","(9,4,1,1)",25025,840,"upper bound",0,840],[6,15,"p","(9,4,2)",22113,756,"upper bound",0,756],[6,15,"p","(9,5,1)",11375,0,"exact",0,0],[6,15,"p","(9,6)",2002,0,"exact",0,0],[6,15,"p","(10,1,1,1,1,1)",2002,0,"exact",0,0],[6,15,"p","(10,2,1,1,1)",7722,0,"exact",0,0],[6,15,"p","(10,2,2,1)",9450,0,"exact",0,0],[6,15,"p","(10,3,1,1)",11088,0,"exact",0,0],[6,15,"p","(10,3,2)",9100,0,"exact",0,0],[6,15,"p","(10,4,1)",7007,0,"exact",0,0],[6,15,"p","(10,5)",1638,0,"exact",0,0],[6,15,"p","(11,1,1,1,1)",1001,0,"exact",0,0],[6,15,"p","(11,2,1,1)",2925,0,"exact",0,0],[6,15,"p","(11,2,2)",1925,0,"exact",0,0],[6,15,"p","(11,3,1)",2835,0,"exact",0,0],[6,15,"p","(11,4)",910,0,"exact",0,0],[6,15,"p","(12,1,1,1)",364,0,"exact",0,0],[6,15,"p","(12,2,1)",715,0,"exact",0,0],[6,15,"p","(12,3)",350,0,"exact",0,0],[6,15,"p","(13,1,1)",91,0,"exact",0,0],[6,15,"p","(13,2)",90,0,"exact",0,0],[6,15,"p","(14,1)",14,0,"exact",0,0],[6,15,"p","(15)",1,0,"exact",0,0],[6,15,"p","(2,1,1,1,1,1,1,1,1,1,1,1,1,1)",14,4,"exact",4,4],[6,15,"p","(2,2,1,1,1,1,1,1,1,1,1,1,1)",90,9,"exact",9,9],[6,15,"p","(2,2,2,1,1,1,1,1,1,1,1,1)",350,13,"exact",13,13],[6,15,"p","(2,2,2,2,1,1,1,1,1,1,1)",910,8,"exact",8,8],[6,15,"p","(2,2,2,2,2,1,1,1,1,1)",1638,1,"exact",1,1],[6,15,"p","(2,2,2,2,2,2,1,1,1)",2002,0,"exact",0,0],[6,15,"p","(2,2,2,2,2,2,2,1)",1430,0,"exact",0,0],[6,15,"p","(3,1,1,1,1,1,1,1,1,1,1,1,1)",91,9,"exact",9,9],[6,15,"p","(3,2,1,1,1,1,1,1,1,1,1,1)",715,26,"exact",26,26],[6,15,"p","(3,2,2,1,1,1,1,1,1,1,1)",2835,24,"exact",24,24],[6,15,"p","(3,2,2,2,1,1,1,1,1,1)",7007,8,"exact",8,8],[6,15,"p","(3,2,2,2,2,1,1,1,1)",11375,4860,"upper bound",0,4860],[6,15,"p","(3,2,2,2,2,2,1,1)",11583,4908,"upper bound",0,4908],[6,15,"p","(3,2,2,2,2,2,2)",5005,0,"exact",0,0],[6,15,"p","(3,3,1,1,1,1,1,1,1,1,1)",1925,16,"exact",16,16],[6,15,"p","(3,3,2,1,1,1,1,1,1,1)",9100,9,"exact",9,9],[6,15,"p","(3,3,2,2,1,1,1,1,1)",22113,1,"lower bound",1,9306],[6,15,"p","(3,3,2,2,2,1,1,1)",32032,13334,"upper bound",0,13334],[6,15,"p","(3,3,2,2,2,2,1)",25025,10350,"upper bound",0,10350],[6,15,"p","(3,3,3,1,1,1,1,1,1)",12740,1,"lower bound",1,9],[6,15,"p","(3,3,3,2,1,1,1,1)",35035,14434,"upper bound",0,14434],[6,15,"p","(3,3,3,2,2,1,1)",45045,18390,"upper bound",0,18390],[6,15,"p","(3,3,3,2,2,2)",21450,8718,"upper bound",0,8718],[6,15,"p","(3,3,3,3,1,1,1)",25025,10152,"upper bound",0,10152],[6,15,"p","(3,3,3,3,2,1)",30030,12096,"upper bound",0,12096],[6,15,"p","(3,3,3,3,3)",6006,0,"exact",0,0],[6,15,"p","(4,1,1,1,1,1,1,1,1,1,1,1)",364,13,"exact",13,13],[6,15,"p","(4,2,1,1,1,1,1,1,1,1,1)",2925,24,"exact",24,24],[6,15,"p","(4,2,2,1,1,1,1,1,1,1)",11088,14,"exact",14,14],[6,15,"p","(4,2,2,2,1,1,1,1,1)",25025,3,"lower bound",3,10400],[6,15,"p","(4,2,2,2,2,1,1,1)",35100,14430,"upper bound",0,14430],[6,15,"p","(4,2,2,2,2,2,1)",27027,11040,"upper bound",0,11040],[6,15,"p","(4,3,1,1,1,1,1,1,1,1)",9450,9,"exact",9,9],[6,15,"p","(4,3,2,1,1,1,1,1,1)",42042,17267,"upper bound",0,17267],[6,15,"p","(4,3,2,2,1,1,1,1)",91000,36865,"upper bound",0,36865],[6,15,"p","(4,3,2,2,2,1,1)",108108,43403,"upper bound",0,43403],[6,15,"p","(4,3,2,2,2,2)",50050,20005,"upper bound",0,20005],[6,15,"p","(4,3,3,1,1,1,1,1)",57330,23058,"upper bound",0,23058],[6,15,"p","(4,3,3,2,1,1,1)",135135,53708,"upper bound",0,53708],[6,15,"p","(4,3,3,2,2,1)",128700,50792,"upper bound",0,50792],[6,15,"p","(4,3,3,3,1,1)",80080,31408,"upper bound",0,31408],[6,15,"p","(4,3,3,3,2)",54054,21096,"upper bound",0,21096],[6,15,"p","(4,4,1,1,1,1,1,1,1)",13650,1,"lower bound",1,3],[6,15,"p","(4,4,2,1,1,1,1,1)",58968,23487,"upper bound",0,23487],[6,15,"p","(4,4,2,2,1,1,1)",112112,44128,"upper bound",0,44128],[6,15,"p","(4,4,2,2,2,1)",100100,39125,"upper bound",0,39125],[6,15,"p","(4,4,3,1,1,1,1)",90090,35208,"upper bound",0,35208],[6,15,"p","(4,4,3,2,1,1)",175175,67788,"upper bound",0,67788],[6,15,"p","(4,4,3,2,2)",96525,37170,"upper bound",0,37170],[6,15,"p","(4,4,3,3,1)",81081,31032,"upper bound",0,31032],[6,15,"p","(4,4,4,1,1,1)",50050,19147,"upper bound",0,19147],[6,15,"p","(4,4,4,2,1)",75075,28500,"upper bound",0,28500],[6,15,"p","(4,4,4,3)",24024,9042,"upper bound",0,9042],[6,15,"p","(5,1,1,1,1,1,1,1,1,1,1)",1001,8,"exact",8,8],[6,15,"p","(5,2,1,1,1,1,1,1,1,1)",7722,8,"lower bound",8,15],[6,15,"p","(5,2,2,1,1,1,1,1,1)",26950,3,"lower bound",3,10840],[6,15,"p","(5,2,2,2,1,1,1,1)",53625,21280,"upper bound",0,21280],[6,15,"p","(5,2,2,2,2,1,1)",61425,24160,"upper bound",0,24160],[6,15,"p","(5,2,2,2,2,2)",28028,10976,"upper bound",0,10976],[6,15,"p","(5,3,1,1,1,1,1,1,1)",24948,1,"lower bound",1,9954],[6,15,"p","(5,3,2,1,1,1,1,1)",100100,39275,"upper bound",0,39275],[6,15,"p","(5,3,2,2,1,1,1)",184275,71460,"upper bound",0,71460],[6,15,"p","(5,3,2,2,2,1)",162162,62451,"upper bound",0,62451],[6,15,"p","(5,3,3,1,1,1,1)",122850,47308,"upper bound",0,47308],[6,15,"p","(5,3,3,2,1,1)",231660,88344,"upper bound",0,88344],[6,15,"p","(5,3,3,2,2)",126126,47866,"upper bound",0,47866],[6,15,"p","(5,3,3,3,1)",100100,37760,"upper bound",0,37760],[6,15,"p","(5,4,1,1,1,1,1,1)",42042,16282,"upper bound",0,16282],[6,15,"p","(5,4,2,1,1,1,1)",159250,60760,"upper bound",0,60760],[6,15,"p","(5,4,2,2,1,1)",243243,91908,"upper bound",0,91908],[6,15,"p","(5,4,2,2,2)",125125,47050,"upper bound",0,47050],[6,15,"p","(5,4,3,1,1,1)",210210,78876,"upper bound",0,78876],[6,15,"p","(5,4,3,2,1)",292864,109056,"upper bound",0,109056],[6,15,"p","(5,4,3,3)",75075,27720,"upper bound",0,27720],[6,15,"p","(5,4,4,1,1)",100100,36860,"upper bound",0,36860],[6,15,"p","(5,5,1,1,1,1,1)",34398,12880,"upper bound",0,12880],[6,15,"p","(5,5,2,1,1,1)",112112,41440,"upper bound",0,41440],[6,15,"p","(6,1,1,1,1,1,1,1,1,1)",2002,1,"exact",1,1],[6,15,"p","(6,2,1,1,1,1,1,1,1)",14300,0,"exact",0,0],[6,15,"p","(6,2,2,1,1,1,1,1)",44550,16950,"upper bound",0,16950],[6,15,"p","(6,2,2,2,1,1,1)",75075,28240,"upper bound",0,28240],[6,15,"p","(6,2,2,2,2,1)",63700,23800,"upper bound",0,23800],[6,15,"p","(6,3,1,1,1,1,1,1)",43120,16282,"upper bound",0,16282],[6,15,"p","(6,3,2,1,1,1,1)",150150,55877,"upper bound",0,55877],[6,15,"p","(6,3,2,2,1,1)",221130,81513,"upper bound",0,81513],[6,12,"s","(12)",1,0,"lower bound",0,1],[6,12,"s","(11,1)",11,0,"lower bound",0,11],[6,12,"s","(10,2)",54,0,"lower bound",0,54],[6,12,"s","(10,1,1)",55,0,"lower bound",0,55],[6,12,"s","(9,3)",154,0,"lower bound",0,154],[6,12,"s","(9,2,1)",320,0,"lower bound",0,320],[6,12,"s","(9,1,1,1)",165,0,"lower bound",0,165],[6,12,"s","(8,4)",275,0,"lower bound",0,275],[6,12,"s","(8,3,1)",891,0,"lower bound",0,891],[6,12,"s","(8,2,2)",616,0,"lower bound",0,616],[6,12,"s","(8,2,1,1)",945,0,"lower bound",0,945],[6,12,"s","(8,1,1,1,1)",330,0,"lower bound",0,330],[6,12,"s","(7,5)",297,0,"lower bound",0,297],[6,12,"s","(7,4,1)",1408,0,"lower bound",0,1408],[6,12,"s","(7,3,2)",1925,0,"lower bound",0,1925],[6,12,"s","(7,3,1,1)",2376,0,"lower bound",0,2376],[6,12,"s","(7,2,2,1)",2079,0,"lower bound",0,2079],[6,12,"s","(7,2,1,1,1)",1728,0,"lower bound",0,1728],[6,12,"s","(7,1,1,1,1,1)",462,0,"lower bound",0,462],[6,12,"s","(6,6)",132,0,"lower bound",0,132],[6,12,"s","(6,5,1)",1155,0,"lower bound",0,1155],[6,12,"s","(6,4,2)",2673,0,"lower bound",0,2673],[6,12,"s","(6,4,1,1)",3080,0,"lower bound",0,3080],[6,12,"s","(6,3,3)",1650,0,"lower bound",0,1650],[6,12,"s","(6,3,2,1)",5632,0,"lower bound",0,5632],[6,12,"s","(6,3,1,1,1)",3696,0,"lower 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bound",3,26950],[6,15,"t","(3,3,2,2,1,1,1,1,1)",22113,1,"lower bound",1,22113],[6,15,"t","(5,3,1,1,1,1,1,1,1)",24948,1,"lower bound",1,24948],[6,15,"t","(4,3,2,1,1,1,1,1,1)",42042,2,"lower bound",2,42042],[6,16,"t","(16)",1,0,"exact",0,0],[6,16,"t","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",15,8,"lower bound",8,9],[6,16,"t","(15,1)",15,0,"exact",0,0],[6,16,"t","(2,2,1,1,1,1,1,1,1,1,1,1,1,1)",104,25,"lower bound",25,31],[6,16,"t","(14,2)",104,0,"exact",0,0],[6,16,"t","(3,1,1,1,1,1,1,1,1,1,1,1,1,1)",105,26,"lower bound",26,32],[6,16,"t","(14,1,1)",105,0,"exact",0,0],[6,16,"t","(2,2,2,1,1,1,1,1,1,1,1,1,1)",440,40,"lower bound",40,57],[6,16,"t","(13,3)",440,0,"exact",0,0],[6,16,"t","(4,1,1,1,1,1,1,1,1,1,1,1,1)",455,44,"lower bound",44,62],[6,16,"t","(13,1,1,1)",455,0,"exact",0,0],[6,16,"t","(3,2,1,1,1,1,1,1,1,1,1,1,1)",896,83,"lower bound",83,118],[6,16,"t","(13,2,1)",896,0,"exact",0,0],[6,16,"t","(2,2,2,2,1,1,1,1,1,1,1,1)",1260,33,"lower bound",33,58],[6,16,"t","(12,4)",1260,0,"exact",0,0],[6,16,"t","(5,1,1,1,1,1,1,1,1,1,1,1)",1365,37,"lower bound",37,67],[6,16,"t","(12,1,1,1,1)",1365,0,"exact",0,0],[6,16,"t","(2,2,2,2,2,2,2,2)",1430,0,"exact",0,0],[6,16,"t","(8,8)",1430,0,"exact",0,0],[6,16,"t","(11,5)",2548,0,"exact",0,0],[6,16,"t","(3,3,1,1,1,1,1,1,1,1,1,1)",2640,69,"lower bound",69,122],[6,16,"t","(12,2,2)",2640,0,"exact",0,0],[6,16,"t","(6,1,1,1,1,1,1,1,1,1,1)",3003,13,"lower bound",13,32],[6,16,"t","(11,1,1,1,1,1)",3003,0,"exact",0,0],[6,16,"t","(9,7)",3432,0,"exact",0,0],[6,16,"t","(10,6)",3640,0,"exact",0,0],[6,16,"t","(12,3,1)",3900,0,"exact",0,0],[6,16,"t","(12,2,1,1)",4004,0,"exact",0,0],[6,16,"t","(7,1,1,1,1,1,1,1,1,1)",5005,1,"lower bound",1,277],[6,16,"t","(10,1,1,1,1,1,1)",5005,0,"exact",0,0],[6,16,"t","(8,1,1,1,1,1,1,1,1)",6435,0,"exact",0,0],[6,16,"t","(9,1,1,1,1,1,1,1)",6435,0,"exact",0,0],[6,16,"t","(11,4,1)",10752,0,"exact",0,0],[6,16,"t","(11,2,1,1,1)",11648,0,"exact",0,0],[6,16,"t","(11,3,2)",13860,0,"exact",0,0],[6,16,"t","(11,2,2,1)",14300,0,"exact",0,0],[6,16,"t","(11,3,1,1)",16848,0,"exact",0,0],[6,16,"t","(8,7,1)",18018,0,"exact",0,0],[6,16,"t","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,16,"t","(3,2,2,1,1,1,1,1,1,1,1,1)",3900,104,"lower bound",104,3900],[6,16,"t","(4,2,1,1,1,1,1,1,1,1,1,1)",4004,108,"lower bound",108,1147],[6,16,"t","(4,3,1,1,1,1,1,1,1,1,1)",14300,71,"lower bound",71,14300],[6,16,"t","(3,2,2,2,1,1,1,1,1,1,1)",10752,57,"lower bound",57,10752],[6,16,"t","(2,2,2,2,2,1,1,1,1,1,1)",2548,12,"lower bound",12,2548],[6,16,"t","(3,3,2,1,1,1,1,1,1,1,1)",13860,70,"lower bound",70,13860],[6,16,"t","(4,2,2,1,1,1,1,1,1,1,1)",16848,91,"lower bound",91,16848],[6,16,"t","(5,2,1,1,1,1,1,1,1,1,1)",11648,59,"lower bound",59,11648],[6,16,"t","(3,2,2,2,2,1,1,1,1,1)",20020,11,"lower bound",11,20020],[6,16,"t","(3,3,3,1,1,1,1,1,1,1)",21840,12,"lower bound",12,21840],[6,16,"t","(5,3,1,1,1,1,1,1,1,1)",42120,22,"lower bound",22,42120],[6,16,"t","(6,2,1,1,1,1,1,1,1,1)",24024,11,"lower bound",11,24024],[6,16,"t","(4,3,2,1,1,1,1,1,1,1)",71680,42,"lower bound",42,71680],[6,16,"t","(5,2,2,1,1,1,1,1,1,1)",45760,31,"lower bound",31,45760],[6,16,"t","(3,3,2,2,1,1,1,1,1,1)",38220,22,"lower bound",22,38220],[6,16,"t","(4,2,2,2,1,1,1,1,1,1)",43120,31,"lower bound",31,43120],[6,16,"t","(4,4,1,1,1,1,1,1,1,1)",23100,12,"lower bound",12,23100],[6,16,"t","(5,3,2,1,1,1,1,1,1)",194040,6,"lower bound",6,194040],[6,16,"t","(4,2,2,2,2,1,1,1,1)",71500,3,"lower bound",3,71500],[6,16,"t","(2,2,2,2,2,2,1,1,1,1)",3640,1,"lower bound",1,3640],[6,16,"t","(3,3,3,2,1,1,1,1,1)",69888,2,"lower bound",2,69888],[6,16,"t","(5,2,2,2,1,1,1,1,1)",105600,6,"lower bound",6,105600],[6,16,"t","(5,4,1,1,1,1,1,1,1)",80640,2,"lower bound",2,80640],[6,16,"t","(6,3,1,1,1,1,1,1,1)",82368,1,"lower bound",1,82368],[6,16,"t","(3,3,2,2,2,1,1,1,1)",65520,1,"lower bound",1,65520],[6,16,"t","(4,3,3,1,1,1,1,1,1)",112112,3,"lower bound",3,112112],[6,16,"t","(4,3,2,2,1,1,1,1,1)",180180,6,"lower bound",6,180180],[6,16,"t","(6,2,2,1,1,1,1,1,1)",85800,3,"lower bound",3,85800],[6,16,"t","(4,4,2,1,1,1,1,1,1)",114660,3,"lower bound",3,114660],[6,17,"t","(17)",1,0,"exact",0,0],[6,17,"t","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",16,9,"lower bound",9,11],[6,17,"t","(16,1)",16,0,"exact",0,0],[6,17,"t","(2,2,1,1,1,1,1,1,1,1,1,1,1,1,1)",119,33,"lower bound",33,47],[6,17,"t","(15,2)",119,0,"exact",0,0],[6,17,"t","(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",120,34,"lower bound",34,48],[6,17,"t","(15,1,1)",120,0,"exact",0,0],[6,17,"t","(2,2,2,1,1,1,1,1,1,1,1,1,1,1)",544,65,"lower bound",65,113],[6,17,"t","(14,3)",544,0,"exact",0,0],[6,17,"t","(4,1,1,1,1,1,1,1,1,1,1,1,1,1)",560,70,"lower bound",70,120],[6,17,"t","(14,1,1,1)",560,0,"exact",0,0],[6,17,"t","(14,2,1)",1105,0,"exact",0,0],[6,17,"t","(13,4)",1700,0,"exact",0,0],[6,17,"t","(5,1,1,1,1,1,1,1,1,1,1,1,1)",1820,81,"lower bound",81,184],[6,17,"t","(13,1,1,1,1)",1820,0,"exact",0,0],[6,17,"t","(13,2,2)",3536,0,"exact",0,0],[6,17,"t","(12,5)",3808,0,"exact",0,0],[6,17,"t","(12,1,1,1,1,1)",4368,0,"exact",0,0],[6,17,"t","(9,8)",4862,0,"exact",0,0],[6,17,"t","(13,3,1)",5236,0,"exact",0,0],[6,17,"t","(13,2,1,1)",5355,0,"exact",0,0],[6,17,"t","(11,6)",6188,0,"exact",0,0],[6,17,"t","(10,7)",7072,0,"exact",0,0],[6,17,"t","(7,1,1,1,1,1,1,1,1,1,1)",8008,14,"lower bound",14,290],[6,17,"t","(11,1,1,1,1,1,1)",8008,0,"exact",0,0],[6,17,"t","(8,1,1,1,1,1,1,1,1,1)",11440,1,"lower bound",1,4902],[6,17,"t","(10,1,1,1,1,1,1,1)",11440,0,"exact",0,0],[6,17,"t","(9,1,1,1,1,1,1,1,1)",12870,0,"exact",0,0],[6,17,"t","(12,4,1)",15912,0,"exact",0,0],[6,17,"t","(12,2,1,1,1)",17017,0,"exact",0,0],[6,17,"t","(8,8,1)",19448,0,"exact",0,0],[6,17,"t","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,17,"t","(2,2,2,2,1,1,1,1,1,1,1,1,1)",1700,73,"lower bound",73,1700],[6,17,"t","(2,2,2,2,2,1,1,1,1,1,1,1)",3808,45,"lower bound",45,3808],[6,17,"t","(3,2,1,1,1,1,1,1,1,1,1,1,1,1)",1105,134,"lower bound",134,1105],[6,17,"t","(3,2,2,1,1,1,1,1,1,1,1,1,1)",5236,227,"lower bound",227,5236],[6,17,"t","(3,2,2,2,1,1,1,1,1,1,1,1)",15912,194,"lower bound",194,15912],[6,17,"t","(3,3,1,1,1,1,1,1,1,1,1,1,1)",3536,152,"lower bound",152,3536],[6,17,"t","(3,3,2,1,1,1,1,1,1,1,1,1)",20400,243,"lower bound",243,20400],[6,17,"t","(4,2,1,1,1,1,1,1,1,1,1,1,1)",5355,235,"lower bound",235,5355],[6,17,"t","(4,2,2,1,1,1,1,1,1,1,1,1)",24752,303,"lower bound",303,24752],[6,17,"t","(4,3,1,1,1,1,1,1,1,1,1,1)",20944,248,"lower bound",248,20944],[6,17,"t","(5,2,1,1,1,1,1,1,1,1,1,1)",17017,204,"lower bound",204,17017],[6,17,"t","(6,1,1,1,1,1,1,1,1,1,1,1)",4368,50,"lower bound",50,1225],[6,17,"t","(4,3,2,1,1,1,1,1,1,1,1)",116688,274,"lower bound",274,116688],[6,17,"t","(4,4,1,1,1,1,1,1,1,1,1)",37400,83,"lower bound",83,37400],[6,17,"t","(5,3,1,1,1,1,1,1,1,1,1)",68068,152,"lower bound",152,68068],[6,17,"t","(4,2,2,2,1,1,1,1,1,1,1)",70720,179,"lower bound",179,70720],[6,17,"t","(2,2,2,2,2,2,1,1,1,1,1)",6188,13,"lower bound",13,6188],[6,17,"t","(6,2,1,1,1,1,1,1,1,1,1)",38675,83,"lower bound",83,38675],[6,17,"t","(3,3,2,2,1,1,1,1,1,1,1)",62832,149,"lower bound",149,62832],[6,17,"t","(5,2,2,1,1,1,1,1,1,1,1)",74256,181,"lower bound",181,74256],[6,17,"t","(3,2,2,2,2,1,1,1,1,1,1)",33320,80,"lower bound",80,33320],[6,17,"t","(3,3,3,1,1,1,1,1,1,1,1)",35700,82,"lower bound",82,35700],[6,17,"t","(3,3,3,2,1,1,1,1,1,1)",129948,36,"lower bound",36,129948],[6,17,"t","(7,2,1,1,1,1,1,1,1,1)",65637,12,"lower bound",12,65637],[6,17,"t","(4,4,2,1,1,1,1,1,1,1)",209440,57,"lower bound",57,209440],[6,17,"t","(5,2,2,2,1,1,1,1,1,1)",194480,68,"lower bound",68,194480],[6,17,"t","(3,3,2,2,2,1,1,1,1,1)",123760,34,"lower bound",34,123760],[6,17,"t","(6,3,1,1,1,1,1,1,1,1)",148512,34,"lower bound",34,148512],[6,17,"t","(5,4,1,1,1,1,1,1,1,1)",145860,36,"lower bound",36,145860],[6,17,"t","(5,3,2,1,1,1,1,1,1,1)",353600,101,"lower bound",101,353600],[6,17,"t","(6,2,2,1,1,1,1,1,1,1)",155584,45,"lower bound",45,155584],[6,17,"t","(4,2,2,2,2,1,1,1,1,1)",134640,45,"lower bound",45,134640],[6,17,"t","(4,3,2,2,1,1,1,1,1,1)",333200,101,"lower bound",101,333200],[6,17,"t","(4,3,3,1,1,1,1,1,1,1)",205632,57,"lower bound",57,205632],[6,17,"t","(3,2,2,2,2,2,1,1,1,1)",48620,12,"lower bound",12,48620],[6,17,"t","(4,3,2,2,2,1,1,1,1)",583440,10,"lower bound",10,583440],[6,17,"t","(3,3,3,2,2,1,1,1,1)",247520,3,"lower bound",3,247520],[6,17,"t","(4,4,2,2,1,1,1,1,1)",556920,9,"lower bound",9,556920],[6,17,"t","(4,2,2,2,2,2,1,1,1)",170170,3,"lower bound",3,170170],[6,17,"t","(5,4,2,1,1,1,1,1,1)",749700,11,"lower bound",11,749700],[6,17,"t","(5,2,2,2,2,1,1,1,1)",327250,9,"lower bound",9,327250],[6,17,"t","(7,3,1,1,1,1,1,1,1)",233376,1,"lower bound",1,233376],[6,17,"t","(7,2,2,1,1,1,1,1,1)",238238,3,"lower bound",3,238238],[6,17,"t","(5,5,1,1,1,1,1,1,1)",157080,2,"lower bound",2,157080],[6,17,"t","(6,4,1,1,1,1,1,1,1)",318240,3,"lower bound",3,318240],[6,17,"t","(5,3,2,2,1,1,1,1,1)",908820,18,"lower bound",18,908820],[6,17,"t","(4,3,3,2,1,1,1,1,1)",680680,11,"lower bound",11,680680],[6,17,"t","(3,3,3,3,1,1,1,1,1)",129948,2,"lower bound",2,129948],[6,17,"t","(5,3,3,1,1,1,1,1,1)",586432,9,"lower bound",9,586432],[6,17,"t","(6,3,2,1,1,1,1,1,1)",700128,10,"lower bound",10,700128],[6,17,"t","(6,2,2,2,1,1,1,1,1)",364650,9,"lower bound",9,364650],[6,17,"t","(3,3,2,2,2,2,1,1,1)",159120,1,"lower bound",1,159120],[6,17,"t","(4,4,3,1,1,1,1,1,1)",433160,6,"lower bound",6,433160],[6,17,"t","(2,2,2,2,2,2,2,1,1,1)",7072,1,"lower bound",1,7072],[6,18,"t","(18)",1,0,"exact",0,0],[6,18,"t","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",17,10,"lower bound",10,13],[6,18,"t","(17,1)",17,0,"exact",0,0],[6,18,"t","(2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",135,42,"lower bound",42,66],[6,18,"t","(16,2)",135,0,"exact",0,0],[6,18,"t","(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",136,43,"lower bound",43,67],[6,18,"t","(16,1,1)",136,0,"exact",0,0],[6,18,"t","(15,3)",663,0,"exact",0,0],[6,18,"t","(4,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",680,104,"lower bound",104,203],[6,18,"t","(15,1,1,1)",680,0,"exact",0,0],[6,18,"t","(15,2,1)",1344,0,"exact",0,0],[6,18,"t","(14,4)",2244,0,"exact",0,0],[6,18,"t","(14,1,1,1,1)",2380,0,"exact",0,0],[6,18,"t","(14,2,2)",4641,0,"exact",0,0],[6,18,"t","(9,9)",4862,0,"exact",0,0],[6,18,"t","(13,5)",5508,0,"exact",0,0],[6,18,"t","(13,1,1,1,1,1)",6188,0,"exact",0,0],[6,18,"t","(14,3,1)",6885,0,"exact",0,0],[6,18,"t","(14,2,1,1)",7020,0,"exact",0,0],[6,18,"t","(12,6)",9996,0,"exact",0,0],[6,18,"t","(10,8)",11934,0,"exact",0,0],[6,18,"t","(12,1,1,1,1,1,1)",12376,103,"upper bound",0,103],[6,18,"t","(11,7)",13260,0,"exact",0,0],[6,18,"t","(11,1,1,1,1,1,1,1)",19448,0,"exact",0,0],[6,18,"t","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,18,"t","(2,2,2,1,1,1,1,1,1,1,1,1,1,1,1)",663,98,"lower bound",98,663],[6,18,"t","(2,2,2,2,1,1,1,1,1,1,1,1,1,1)",2244,138,"lower bound",138,2244],[6,18,"t","(2,2,2,2,2,1,1,1,1,1,1,1,1)",5508,118,"lower bound",118,5508],[6,18,"t","(2,2,2,2,2,2,1,1,1,1,1,1)",9996,58,"lower bound",58,9996],[6,18,"t","(3,2,1,1,1,1,1,1,1,1,1,1,1,1,1)",1344,201,"lower bound",201,1344],[6,18,"t","(3,2,2,1,1,1,1,1,1,1,1,1,1,1)",6885,426,"lower bound",426,6885],[6,18,"t","(3,2,2,2,1,1,1,1,1,1,1,1,1)",22848,494,"lower bound",494,22848],[6,18,"t","(3,2,2,2,2,1,1,1,1,1,1,1)",53040,319,"lower bound",319,53040],[6,18,"t","(3,3,1,1,1,1,1,1,1,1,1,1,1,1)",4641,286,"lower bound",286,4641],[6,18,"t","(3,3,2,1,1,1,1,1,1,1,1,1,1)",29172,622,"lower bound",622,29172],[6,18,"t","(3,3,2,2,1,1,1,1,1,1,1,1)",99144,586,"lower bound",586,99144],[6,18,"t","(3,3,3,1,1,1,1,1,1,1,1,1)",56100,325,"lower bound",325,56100],[6,18,"t","(4,2,1,1,1,1,1,1,1,1,1,1,1,1)",7020,439,"lower bound",439,7020],[6,18,"t","(4,2,2,1,1,1,1,1,1,1,1,1,1)",35343,765,"lower bound",765,35343],[6,18,"t","(4,2,2,2,1,1,1,1,1,1,1,1)",111384,676,"lower bound",676,111384],[6,18,"t","(4,3,1,1,1,1,1,1,1,1,1,1,1)",29835,635,"lower bound",635,29835],[6,18,"t","(4,3,2,1,1,1,1,1,1,1,1,1)",182784,1068,"lower bound",1068,182784],[6,18,"t","(4,4,1,1,1,1,1,1,1,1,1,1)",58344,331,"lower bound",331,58344],[6,18,"t","(5,1,1,1,1,1,1,1,1,1,1,1,1,1)",2380,151,"lower bound",151,2380],[6,18,"t","(5,2,1,1,1,1,1,1,1,1,1,1,1)",24192,520,"lower bound",520,24192],[6,18,"t","(5,2,2,1,1,1,1,1,1,1,1,1)",116025,688,"lower bound",688,116025],[6,18,"t","(5,3,1,1,1,1,1,1,1,1,1,1)",106029,604,"lower bound",604,106029],[6,18,"t","(6,1,1,1,1,1,1,1,1,1,1,1,1)",6188,131,"lower bound",131,6188],[6,18,"t","(6,2,1,1,1,1,1,1,1,1,1,1)",60060,337,"lower bound",337,60060],[6,18,"t","(7,1,1,1,1,1,1,1,1,1,1,1)",12376,64,"lower bound",64,12376],[6,18,"t","(8,1,1,1,1,1,1,1,1,1,1)",19448,15,"lower bound",15,19448],[6,18,"t","(4,3,2,2,1,1,1,1,1,1,1)",583440,703,"lower bound",703,583440],[6,18,"t","(5,3,2,1,1,1,1,1,1,1,1)",612612,708,"lower bound",708,612612],[6,18,"t","(5,2,2,2,1,1,1,1,1,1,1)",339456,428,"lower bound",428,339456],[6,18,"t","(3,2,2,2,2,2,1,1,1,1,1)",88128,105,"lower bound",105,88128],[6,18,"t","(7,2,1,1,1,1,1,1,1,1,1)",112320,109,"lower bound",109,112320],[6,18,"t","(3,3,2,2,2,1,1,1,1,1,1)",219912,263,"lower bound",263,219912],[6,18,"t","(2,2,2,2,2,2,2,1,1,1,1)",13260,14,"lower bound",14,13260],[6,18,"t","(6,2,2,1,1,1,1,1,1,1,1)",268515,309,"lower bound",309,268515],[6,18,"t","(5,4,1,1,1,1,1,1,1,1,1)",251328,271,"lower bound",271,251328],[6,18,"t","(3,3,3,2,1,1,1,1,1,1,1)",228480,267,"lower bound",267,228480],[6,18,"t","(4,4,2,1,1,1,1,1,1,1,1)",363528,414,"lower bound",414,363528],[6,18,"t","(6,3,1,1,1,1,1,1,1,1,1)",255255,269,"lower bound",269,255255],[6,18,"t","(4,2,2,2,2,1,1,1,1,1,1)",238680,304,"lower bound",304,238680],[6,18,"t","(4,3,3,1,1,1,1,1,1,1,1)",358020,413,"lower bound",413,358020],[6,18,"t","(7,2,2,1,1,1,1,1,1,1)",459459,60,"lower bound",60,459459],[6,18,"t","(4,4,3,1,1,1,1,1,1,1)",848232,120,"lower bound",120,848232],[6,18,"t","(3,2,2,2,2,2,2,1,1,1)",102102,13,"lower bound",13,102102],[6,18,"t","(6,4,1,1,1,1,1,1,1,1)",612612,73,"lower bound",73,612612],[6,18,"t","(4,3,2,2,2,1,1,1,1,1)",1175040,190,"lower bound",190,1175040],[6,18,"t","(3,3,3,3,1,1,1,1,1,1)",259896,38,"lower bound",38,259896],[6,18,"t","(5,2,2,2,2,1,1,1,1,1)",656370,122,"lower bound",122,656370],[6,18,"t","(5,3,2,2,1,1,1,1,1,1)",1790100,288,"lower bound",288,1790100],[6,18,"t","(6,2,2,2,1,1,1,1,1,1)",714714,122,"lower bound",122,714714],[6,18,"t","(3,3,3,2,2,1,1,1,1,1)",501228,73,"lower bound",73,501228],[6,18,"t","(4,4,2,2,1,1,1,1,1,1)",1099560,167,"lower bound",167,1099560],[6,18,"t","(6,3,2,1,1,1,1,1,1,1)",1357824,190,"lower bound",190,1357824],[6,18,"t","(7,3,1,1,1,1,1,1,1,1)",447525,47,"lower bound",47,447525],[6,18,"t","(5,3,3,1,1,1,1,1,1,1)",1145664,167,"lower bound",167,1145664],[6,18,"t","(5,4,2,1,1,1,1,1,1,1)",1458600,205,"lower bound",205,1458600],[6,18,"t","(4,2,2,2,2,2,1,1,1,1)",353430,60,"lower bound",60,353430],[6,18,"t","(5,5,1,1,1,1,1,1,1,1)",302940,38,"lower bound",38,302940],[6,18,"t","(4,3,3,2,1,1,1,1,1,1)",1349460,205,"lower bound",205,1349460],[6,18,"t","(3,3,2,2,2,2,1,1,1,1)",331500,47,"lower bound",47,331500],[6,18,"t","(8,2,1,1,1,1,1,1,1,1)",162162,13,"lower bound",13,162162],[6,18,"t","(4,3,3,2,2,1,1,1,1)",2625480,24,"lower bound",24,2625480],[6,18,"t","(4,2,2,2,2,2,2,1,1)",340340,3,"lower bound",3,340340],[6,18,"t","(2,2,2,2,2,2,2,2,1,1)",11934,1,"lower bound",1,11934],[6,18,"t","(5,4,3,1,1,1,1,1,1)",3198720,26,"lower bound",26,3198720],[6,18,"t","(6,3,3,1,1,1,1,1,1)",2333760,19,"lower bound",19,2333760],[6,18,"t","(5,5,2,1,1,1,1,1,1)",1649340,13,"lower bound",13,1649340],[6,18,"t","(6,3,2,2,1,1,1,1,1)",3544398,37,"lower bound",37,3544398],[6,18,"t","(7,3,2,1,1,1,1,1,1)",2144142,14,"lower bound",14,2144142],[6,18,"t","(4,4,3,2,1,1,1,1,1)",2970240,26,"lower bound",26,2970240],[6,18,"t","(4,4,4,1,1,1,1,1,1)",779688,6,"lower bound",6,779688],[6,18,"t","(5,3,2,2,2,1,1,1,1)",3180870,37,"lower bound",37,3180870],[6,18,"t","(6,2,2,2,2,1,1,1,1)",1215500,18,"lower bound",18,1215500],[6,18,"t","(9,1,1,1,1,1,1,1,1,1)",24310,1,"lower bound",1,24310],[6,18,"t","(4,3,3,3,1,1,1,1,1)",1429428,13,"lower bound",13,1429428],[6,18,"t","(7,4,1,1,1,1,1,1,1)",1018368,4,"lower bound",4,1018368],[6,18,"t","(4,3,2,2,2,2,1,1,1)",1531530,14,"lower bound",14,1531530],[6,18,"t","(5,3,3,2,1,1,1,1,1)",3877632,38,"lower bound",38,3877632],[6,18,"t","(6,5,1,1,1,1,1,1,1)",875160,5,"lower bound",5,875160],[6,18,"t","(6,4,2,1,1,1,1,1,1)",3222180,24,"lower bound",24,3222180],[6,18,"t","(8,2,2,1,1,1,1,1,1)",595595,3,"lower bound",3,595595],[6,18,"t","(3,3,2,2,2,2,2,1,1)",322218,1,"lower bound",1,322218],[6,18,"t","(7,2,2,2,1,1,1,1,1)",1089088,12,"lower bound",12,1089088],[6,18,"t","(4,4,2,2,2,1,1,1,1)",1989000,19,"lower bound",19,1989000],[6,18,"t","(3,3,3,2,2,2,1,1,1)",678912,4,"lower bound",4,678912],[6,18,"t","(5,4,2,2,1,1,1,1,1)",3965760,38,"lower bound",38,3965760],[6,18,"t","(8,3,1,1,1,1,1,1,1)",590733,1,"lower bound",1,590733],[6,18,"t","(5,2,2,2,2,2,1,1,1)",837760,12,"lower bound",12,837760],[6,18,"t","(3,3,3,3,2,1,1,1,1)",649740,5,"lower bound",5,649740],[6,19,"t","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",18,11,"lower bound",11,15],[6,19,"t","(18,1)",18,0,"exact",0,0],[6,19,"t","(17,2)",152,0,"exact",0,0],[6,19,"t","(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",153,53,"lower bound",53,89],[6,19,"t","(17,1,1)",153,0,"exact",0,0],[6,19,"t","(16,3)",798,0,"exact",0,0],[6,19,"t","(16,1,1,1)",816,0,"exact",0,0],[6,19,"t","(16,2,1)",1615,0,"exact",0,0],[6,19,"t","(15,4)",2907,0,"exact",0,0],[6,19,"t","(15,1,1,1,1)",3060,0,"exact",0,0],[6,19,"t","(15,2,2)",5985,0,"exact",0,0],[6,19,"t","(14,5)",7752,0,"exact",0,0],[6,19,"t","(14,1,1,1,1,1)",8568,0,"exact",0,0],[6,19,"t","(15,3,1)",8892,0,"exact",0,0],[6,19,"t","(15,2,1,1)",9044,0,"exact",0,0],[6,19,"t","(13,6)",15504,0,"exact",0,0],[6,19,"t","(10,9)",16796,0,"exact",0,0],[6,19,"t","(13,1,1,1,1,1,1)",18564,4740,"upper bound",0,4740],[6,19,"t","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,19,"t","(19)",1,0,"exact",0,0],[6,20,"t","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",19,12,"lower bound",12,17],[6,20,"t","(19,1)",19,0,"exact",0,0],[6,20,"t","(18,2)",170,0,"exact",0,0],[6,20,"t","(18,1,1)",171,0,"exact",0,0],[6,20,"t","(17,3)",950,0,"exact",0,0],[6,20,"t","(17,1,1,1)",969,0,"exact",0,0],[6,20,"t","(17,2,1)",1920,0,"exact",0,0],[6,20,"t","(16,4)",3705,0,"exact",0,0],[6,20,"t","(16,1,1,1,1)",3876,0,"exact",0,0],[6,20,"t","(16,2,2)",7600,2992,"upper bound",0,2992],[6,20,"t","(15,5)",10659,6051,"upper bound",0,6051],[6,20,"t","(16,3,1)",11305,6697,"upper bound",0,6697],[6,20,"t","(16,2,1,1)",11475,6867,"upper bound",0,6867],[6,20,"t","(15,1,1,1,1,1)",11628,7020,"upper bound",0,7020],[6,20,"t","(10,10)",16796,12188,"upper bound",0,12188],[6,20,"t","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,20,"t","(20)",1,0,"exact",0,0],[6,21,"t","(20,1)",20,0,"exact",0,0],[6,21,"t","(19,2)",189,0,"exact",0,0],[6,21,"t","(19,1,1)",190,0,"exact",0,0],[6,21,"t","(18,3)",1120,0,"exact",0,0],[6,21,"t","(18,1,1,1)",1140,0,"exact",0,0],[6,21,"t","(18,2,1)",2261,0,"exact",0,0],[6,21,"t","(17,4)",4655,47,"upper bound",0,47],[6,21,"t","(17,1,1,1,1)",4845,237,"upper bound",0,237],[6,21,"t","(17,2,2)",9520,4912,"upper bound",0,4912],[6,21,"t","(17,3,1)",14175,9567,"upper bound",0,9567],[6,21,"t","(16,5)",14364,9756,"upper bound",0,9756],[6,21,"t","(17,2,1,1)",14364,9756,"upper bound",0,9756],[6,21,"t","(16,1,1,1,1,1)",15504,10896,"upper bound",0,10896],[6,21,"t","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,21,"t","(21)",1,0,"exact",0,0],[6,22,"t","(21,1)",21,0,"exact",0,0],[6,22,"t","(20,2)",209,0,"exact",0,0],[6,22,"t","(20,1,1)",210,0,"exact",0,0],[6,22,"t","(19,3)",1309,0,"exact",0,0],[6,22,"t","(19,1,1,1)",1330,0,"exact",0,0],[6,22,"t","(19,2,1)",2640,0,"exact",0,0],[6,22,"t","(18,4)",5775,1167,"upper bound",0,1167],[6,22,"t","(18,1,1,1,1)",5985,1377,"upper bound",0,1377],[6,22,"t","(18,2,2)",11781,7173,"upper bound",0,7173],[6,22,"t","(18,3,1)",17556,12948,"upper bound",0,12948],[6,22,"t","(18,2,1,1)",17765,13157,"upper bound",0,13157],[6,22,"t","(17,5)",19019,14411,"upper bound",0,14411],[6,22,"t","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,22,"t","(22)",1,0,"exact",0,0],[6,23,"t","(22,1)",22,0,"exact",0,0],[6,23,"t","(21,2)",230,0,"exact",0,0],[6,23,"t","(21,1,1)",231,0,"exact",0,0],[6,23,"t","(20,3)",1518,0,"exact",0,0],[6,23,"t","(20,1,1,1)",1540,0,"exact",0,0],[6,23,"t","(20,2,1)",3059,0,"exact",0,0],[6,23,"t","(19,4)",7084,2476,"upper bound",0,2476],[6,23,"t","(19,1,1,1,1)",7315,2707,"upper bound",0,2707],[6,23,"t","(19,2,2)",14421,9813,"upper bound",0,9813],[6,23,"t","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[6,23,"t","(23)",1,0,"exact",0,0],[6,24,"t","(23,1)",23,0,"exact",0,0],[6,24,"t","(22,2)",252,0,"exact",0,0],[6,24,"t","(22,1,1)",253,0,"exact",0,0],[6,24,"t","(21,3)",1748,0,"exact",0,0],[6,24,"t","(21,1,1,1)",1771,0,"exact",0,0],[6,24,"t","(21,2,1)",3520,0,"exact",0,0],[6,24,"t","(20,4)",8602,3994,"upper bound",0,3994],[6,24,"t","(20,1,1,1,1)",8855,4247,"upper bound",0,4247],[6,24,"t","(20,2,2)",17480,12872,"upper bound",0,12872],[6,24,"t","(24)",1,0,"exact",0,0],[6,25,"t","(24,1)",24,0,"exact",0,0],[6,25,"t","(23,2)",275,0,"exact",0,0],[6,25,"t","(23,1,1)",276,0,"exact",0,0],[6,25,"t","(22,3)",2000,0,"exact",0,0],[6,25,"t","(22,1,1,1)",2024,0,"exact",0,0],[6,25,"t","(22,2,1)",4025,0,"exact",0,0],[6,25,"t","(21,4)",10350,5742,"upper bound",0,5742],[6,25,"t","(21,1,1,1,1)",10626,6018,"upper bound",0,6018],[6,25,"t","(25)",1,0,"exact",0,0],[6,26,"t","(25,1)",25,0,"exact",0,0],[6,26,"t","(24,2)",299,0,"exact",0,0],[6,26,"t","(24,1,1)",300,0,"exact",0,0],[6,26,"t","(23,3)",2275,0,"exact",0,0],[6,26,"t","(23,1,1,1)",2300,0,"exact",0,0],[6,26,"t","(23,2,1)",4576,195,"upper bound",0,195],[6,26,"t","(22,4)",12350,7742,"upper bound",0,7742],[6,26,"t","(22,1,1,1,1)",12650,8042,"upper 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bound",0,12942],[6,28,"t","(28)",1,0,"exact",0,0],[6,29,"t","(28,1)",28,0,"exact",0,0],[6,29,"t","(27,2)",377,0,"exact",0,0],[6,29,"t","(27,1,1)",378,0,"exact",0,0],[6,29,"t","(26,3)",3248,0,"exact",0,0],[6,29,"t","(26,1,1,1)",3276,0,"exact",0,0],[6,29,"t","(26,2,1)",6525,1984,"upper bound",0,1984],[6,29,"t","(29)",1,0,"exact",0,0],[6,30,"t","(29,1)",29,0,"exact",0,0],[6,30,"t","(28,2)",405,0,"exact",0,0],[6,30,"t","(28,1,1)",406,0,"exact",0,0],[6,30,"t","(27,3)",3625,0,"exact",0,0],[6,30,"t","(27,1,1,1)",3654,0,"exact",0,0],[6,30,"t","(27,2,1)",7280,2685,"upper bound",0,2685],[6,30,"t","(30)",1,0,"exact",0,0],[6,31,"t","(30,1)",30,0,"exact",0,0],[6,31,"t","(29,2)",434,0,"exact",0,0],[6,31,"t","(29,1,1)",435,0,"exact",0,0],[6,31,"t","(28,3)",4030,0,"exact",0,0],[6,31,"t","(28,1,1,1)",4060,0,"exact",0,0],[6,31,"t","(28,2,1)",8091,3483,"upper bound",0,3483]]}