{"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":[[5,16,"c","(2,2,2,2,2,2,2,2)",1430,1,"lower 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,13,"f","(5,4,2,1,1)",21450,0,"exact",0,0],[5,13,"f","(5,4,2,2)",12870,0,"exact",0,0],[5,13,"f","(5,4,3,1)",15015,0,"exact",0,0],[5,13,"f","(5,4,4)",2574,0,"exact",0,0],[5,13,"f","(5,5,1,1,1)",5005,0,"exact",0,0],[5,13,"f","(5,5,2,1)",8580,0,"exact",0,0],[5,13,"f","(5,5,3)",3432,0,"exact",0,0],[5,13,"f","(6,1,1,1,1,1,1,1)",792,1,"exact",1,1],[5,13,"f","(6,2,1,1,1,1,1)",4290,0,"exact",0,0],[5,13,"f","(6,2,2,1,1,1)",9360,0,"exact",0,0],[5,13,"f","(6,2,2,2,1)",9009,0,"exact",0,0],[5,13,"f","(6,3,1,1,1,1)",9360,0,"exact",0,0],[5,13,"f","(6,3,2,1,1)",20592,0,"exact",0,0],[5,13,"f","(6,3,2,2)",12012,0,"exact",0,0],[5,13,"f","(6,3,3,1)",11440,0,"exact",0,0],[5,13,"f","(6,4,1,1,1)",10296,0,"exact",0,0],[5,13,"f","(6,4,2,1)",17160,0,"exact",0,0],[5,13,"f","(6,4,3)",6435,0,"exact",0,0],[5,13,"f","(6,5,1,1)",5720,0,"exact",0,0],[5,13,"f","(6,5,2)",5148,0,"exact",0,0],[5,13,"f","(6,6,1)",1287,0,"exact",0,0],[5,13,"f","(7,1,1,1,1,1,1)",924,0,"exact",0,0],[5,13,"f","(7,2,1,1,1,1)",4290,0,"exact",0,0],[5,13,"f","(7,2,2,1,1)",7371,0,"exact",0,0],[5,13,"f","(7,2,2,2)",4004,0,"exact",0,0],[5,13,"f","(7,3,1,1,1)",7800,0,"exact",0,0],[5,13,"f","(7,3,2,1)",12012,0,"exact",0,0],[5,13,"f","(7,3,3)",3575,0,"exact",0,0],[5,13,"f","(7,4,1,1)",6864,0,"exact",0,0],[5,13,"f","(7,4,2)",6006,0,"exact",0,0],[5,13,"f","(7,5,1)",2860,0,"exact",0,0],[5,13,"f","(7,6)",429,0,"exact",0,0],[5,13,"f","(8,1,1,1,1,1)",792,0,"exact",0,0],[5,13,"f","(8,2,1,1,1)",3003,0,"exact",0,0],[5,13,"f","(8,2,2,1)",3640,0,"exact",0,0],[5,13,"f","(8,3,1,1)",4212,0,"exact",0,0],[5,13,"f","(8,3,2)",3432,0,"exact",0,0],[5,13,"f","(8,4,1)",2574,0,"exact",0,0],[5,13,"f","(8,5)",572,0,"exact",0,0],[5,13,"f","(9,1,1,1,1)",495,0,"exact",0,0],[5,13,"f","(9,2,1,1)",1430,0,"exact",0,0],[5,13,"f","(9,2,2)",936,0,"exact",0,0],[5,13,"f","(9,3,1)",1365,0,"exact",0,0],[5,13,"f","(9,4)",429,0,"exact",0,0],[5,13,"f","(10,1,1,1)",220,0,"exact",0,0],[5,13,"f","(10,2,1)",429,0,"exact",0,0],[5,13,"f","(10,3)",208,0,"exact",0,0],[5,13,"f","(11,1,1)",66,0,"exact",0,0],[5,13,"f","(11,2)",65,0,"exact",0,0],[5,13,"f","(12,1)",12,0,"exact",0,0],[5,13,"f","(13)",1,0,"exact",0,0],[5,14,"f","(1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[5,14,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1)",13,9,"exact",9,9],[5,14,"f","(2,2,1,1,1,1,1,1,1,1,1,1)",77,31,"exact",31,31],[5,14,"f","(2,2,2,1,1,1,1,1,1,1,1)",273,57,"exact",57,57],[5,14,"f","(2,2,2,2,1,1,1,1,1,1)",637,58,"exact",58,58],[5,14,"f","(2,2,2,2,2,1,1,1,1)",1001,28,"exact",28,28],[5,14,"f","(2,2,2,2,2,2,1,1)",1001,5,"exact",5,5],[5,14,"f","(2,2,2,2,2,2,2)",429,0,"exact",0,0],[5,14,"f","(3,1,1,1,1,1,1,1,1,1,1,1)",78,32,"exact",32,32],[5,14,"f","(3,2,1,1,1,1,1,1,1,1,1)",560,118,"exact",118,118],[5,14,"f","(3,2,2,1,1,1,1,1,1,1)",2002,178,"exact",178,178],[5,14,"f","(3,2,2,2,1,1,1,1,1)",4368,125,"exact",125,125],[5,14,"f","(3,2,2,2,2,1,1,1)",6006,36,"exact",36,36],[5,14,"f","(3,2,2,2,2,2,1)",4576,2,"lower bound",2,12],[5,14,"f","(3,3,1,1,1,1,1,1,1,1)",1365,122,"exact",122,122],[5,14,"f","(3,3,2,1,1,1,1,1,1)",5733,156,"lower bound",156,186],[5,14,"f","(3,3,2,2,1,1,1,1)",12012,73,"exact",73,73],[5,14,"f","(3,3,2,2,2,1,1)",14014,9,"exact",9,9],[5,14,"f","(3,3,2,2,2,2)",6435,0,"exact",0,0],[5,14,"f","(3,3,3,1,1,1,1,1)",7007,36,"exact",36,36],[5,14,"f","(3,3,3,2,1,1,1)",16016,12,"exact",12,12],[5,14,"f","(3,3,3,2,2,1)",15015,0,"exact",0,0],[5,14,"f","(3,3,3,3,1,1)",9009,1,"lower bound",1,2],[5,14,"f","(3,3,3,3,2)",6006,0,"exact",0,0],[5,14,"f","(4,1,1,1,1,1,1,1,1,1,1)",286,62,"exact",62,62],[5,14,"f","(4,2,1,1,1,1,1,1,1,1)",2079,186,"exact",186,186],[5,14,"f","(4,2,2,1,1,1,1,1,1)",7007,198,"lower bound",198,311],[5,14,"f","(4,2,2,2,1,1,1,1)",13650,91,"exact",91,91],[5,14,"f","(4,2,2,2,2,1,1)",15444,17,"exact",17,17],[5,14,"f","(4,2,2,2,2,2)",7007,0,"exact",0,0],[5,14,"f","(4,3,1,1,1,1,1,1,1)",6006,160,"lower bound",160,239],[5,14,"f","(4,3,2,1,1,1,1,1)",23296,134,"lower bound",134,9478],[5,14,"f","(4,3,2,2,1,1,1)",42042,36,"lower bound",36,16820],[5,14,"f","(4,3,2,2,2,1)",36608,2,"lower bound",2,14528],[5,14,"f","(4,3,3,1,1,1,1)",27027,19,"lower bound",19,10725],[5,14,"f","(4,3,3,2,1,1)",50050,3,"lower bound",3,19640],[5,14,"f","(4,3,3,2,2)",27027,10548,"upper bound",0,10548],[5,14,"f","(4,3,3,3,1)",21021,8148,"upper bound",0,8148],[5,14,"f","(4,4,1,1,1,1,1,1)",7644,41,"exact",41,41],[5,14,"f","(4,4,2,1,1,1,1)",28028,19,"lower bound",19,11000],[5,14,"f","(4,4,2,2,1,1)",42042,3,"lower bound",3,16317],[5,14,"f","(4,4,2,2,2)",21450,8280,"upper bound",0,8280],[5,14,"f","(4,4,3,1,1,1)",35035,13486,"upper bound",0,13486],[5,14,"f","(4,4,3,2,1)",48048,18336,"upper bound",0,18336],[5,14,"f","(4,4,3,3)",12012,0,"exact",0,0],[5,14,"f","(4,4,4,1,1)",15015,0,"exact",0,0],[5,14,"f","(4,4,4,2)",12012,0,"exact",0,0],[5,14,"f","(5,1,1,1,1,1,1,1,1,1)",715,67,"exact",67,67],[5,14,"f","(5,2,1,1,1,1,1,1,1)",4928,133,"lower bound",133,225],[5,14,"f","(5,2,2,1,1,1,1,1)",15015,95,"exact",95,95],[5,14,"f","(5,2,2,2,1,1,1)",24960,30,"lower bound",30,9746],[5,14,"f","(5,2,2,2,2,1)",21021,4,"lower bound",4,8141],[5,14,"f","(5,3,1,1,1,1,1,1)",14014,70,"lower bound",70,73],[5,14,"f","(5,3,2,1,1,1,1)",47775,36,"lower bound",36,18416],[5,14,"f","(5,3,2,2,1,1)",69498,4,"lower bound",4,26496],[5,14,"f","(5,3,2,2,2)",35035,13286,"upper bound",0,13286],[5,14,"f","(5,3,3,1,1,1)",48048,3,"lower bound",3,18170],[5,14,"f","(5,3,3,2,1)",64064,24020,"upper bound",0,24020],[5,14,"f","(5,3,3,3)",15015,0,"exact",0,0],[5,14,"f","(5,4,1,1,1,1,1)",20384,12,"lower bound",12,7744],[5,14,"f","(5,4,2,1,1,1)",63063,3,"lower bound",3,23596],[5,14,"f","(5,4,2,2,1)",68640,25454,"upper bound",0,25454],[5,14,"f","(5,4,3,1,1)",64064,23552,"upper bound",0,23552],[5,14,"f","(5,4,3,2)",48048,17550,"upper bound",0,17550],[5,14,"f","(5,4,4,1)",21021,7566,"upper bound",0,7566],[5,14,"f","(5,5,1,1,1,1)",14014,1,"exact",1,1],[5,14,"f","(5,5,2,1,1)",35035,12631,"upper bound",0,12631],[5,14,"f","(5,5,2,2)",21450,7680,"upper bound",0,7680],[5,14,"f","(5,5,3,1)",27027,9585,"upper bound",0,9585],[5,14,"f","(5,5,4)",6006,0,"exact",0,0],[5,14,"f","(6,1,1,1,1,1,1,1,1)",1287,32,"exact",32,32],[5,14,"f","(6,2,1,1,1,1,1,1)",8085,39,"lower bound",39,49],[5,14,"f","(6,2,2,1,1,1,1)",21450,17,"lower bound",17,7968],[5,14,"f","(6,2,2,2,1,1)",28665,4,"lower bound",4,10535],[5,14,"f","(6,2,2,2,2)",14014,0,"exact",0,0],[5,14,"f","(6,3,1,1,1,1,1)",21021,9,"lower bound",9,7743],[5,14,"f","(6,3,2,1,1,1)",59904,2,"lower bound",2,21736],[5,14,"f","(6,3,2,2,1)",63063,22674,"upper bound",0,22674],[5,14,"f","(6,3,3,1,1)",48048,17124,"upper bound",0,17124],[5,14,"f","(6,3,3,2)",35035,12400,"upper bound",0,12400],[5,14,"f","(6,4,1,1,1,1)",28665,10234,"upper bound",0,10234],[5,14,"f","(6,4,2,1,1)",69498,24462,"upper bound",0,24462],[5,14,"f","(6,4,2,2)",42042,14692,"upper bound",0,14692],[5,14,"f","(6,4,3,1)",50050,17320,"upper bound",0,17320],[5,14,"f","(6,4,4)",9009,0,"exact",0,0],[5,14,"f","(6,5,1,1,1)",21021,7194,"upper bound",0,7194],[5,14,"f","(6,5,2,1)",36608,12368,"upper bound",0,12368],[5,14,"f","(6,5,3)",15015,0,"exact",0,0],[5,14,"f","(6,6,1,1)",7007,0,"exact",0,0],[5,14,"f","(6,6,2)",6435,0,"exact",0,0],[5,14,"f","(7,1,1,1,1,1,1,1)",1716,4,"exact",4,4],[5,14,"f","(7,2,1,1,1,1,1)",9504,2,"lower bound",2,4],[5,14,"f","(7,2,2,1,1,1)",21021,7224,"upper bound",0,7224],[5,14,"f","(7,2,2,2,1)",20384,6930,"upper bound",0,6930],[5,14,"f","(7,3,1,1,1,1)",21450,7280,"upper bound",0,7280],[5,14,"f","(7,3,2,1,1)",47775,15960,"upper bound",0,15960],[5,14,"f","(7,3,2,2)",28028,9286,"upper bound",0,9286],[5,14,"f","(7,3,3,1)",27027,8856,"upper bound",0,8856],[5,14,"f","(7,4,1,1,1)",24960,8148,"upper bound",0,8148],[5,14,"f","(7,4,2,1)",42042,13530,"upper bound",0,13530],[5,14,"f","(7,4,3)",16016,0,"exact",0,0],[5,14,"f","(7,5,1,1)",15444,0,"exact",0,0],[5,14,"f","(7,5,2)",14014,0,"exact",0,0],[5,14,"f","(7,6,1)",4576,0,"exact",0,0],[5,14,"f","(7,7)",429,0,"exact",0,0],[5,14,"f","(8,1,1,1,1,1,1)",1716,0,"exact",0,0],[5,14,"f","(8,2,1,1,1,1)",8085,0,"exact",0,0],[5,14,"f","(8,2,2,1,1)",14014,0,"exact",0,0],[5,14,"f","(8,2,2,2)",7644,0,"exact",0,0],[5,14,"f","(8,3,1,1,1)",15015,0,"exact",0,0],[5,14,"f","(8,3,2,1)",23296,6608,"upper bound",0,6608],[5,14,"f","(8,3,3)",7007,0,"exact",0,0],[5,14,"f","(8,4,1,1)",13650,0,"exact",0,0],[5,14,"f","(8,4,2)",12012,0,"exact",0,0],[5,14,"f","(8,5,1)",6006,0,"exact",0,0],[5,14,"f","(8,6)",1001,0,"exact",0,0],[5,14,"f","(9,1,1,1,1,1)",1287,0,"exact",0,0],[5,14,"f","(9,2,1,1,1)",4928,0,"exact",0,0],[5,14,"f","(9,2,2,1)",6006,0,"exact",0,0],[5,14,"f","(9,3,1,1)",7007,0,"exact",0,0],[5,14,"f","(9,3,2)",5733,0,"exact",0,0],[5,14,"f","(9,4,1)",4368,0,"exact",0,0],[5,14,"f","(9,5)",1001,0,"exact",0,0],[5,14,"f","(10,1,1,1,1)",715,0,"exact",0,0],[5,14,"f","(10,2,1,1)",2079,0,"exact",0,0],[5,14,"f","(10,2,2)",1365,0,"exact",0,0],[5,14,"f","(10,3,1)",2002,0,"exact",0,0],[5,14,"f","(10,4)",637,0,"exact",0,0],[5,14,"f","(11,1,1,1)",286,0,"exact",0,0],[5,14,"f","(11,2,1)",560,0,"exact",0,0],[5,14,"f","(11,3)",273,0,"exact",0,0],[5,14,"f","(12,1,1)",78,0,"exact",0,0],[5,14,"f","(12,2)",77,0,"exact",0,0],[5,14,"f","(13,1)",13,0,"exact",0,0],[5,14,"f","(14)",1,0,"exact",0,0],[5,15,"f","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[5,15,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1,1)",14,11,"exact",11,11],[5,15,"f","(2,2,1,1,1,1,1,1,1,1,1,1,1)",90,47,"exact",47,47],[5,15,"f","(2,2,2,1,1,1,1,1,1,1,1,1)",350,113,"exact",113,113],[5,15,"f","(2,2,2,2,1,1,1,1,1,1,1)",910,165,"exact",165,165],[5,15,"f","(2,2,2,2,2,1,1,1,1,1)",1638,145,"exact",145,145],[5,15,"f","(2,2,2,2,2,2,1,1,1)",2002,69,"exact",69,69],[5,15,"f","(2,2,2,2,2,2,2,1)",1430,15,"exact",15,15],[5,15,"f","(3,1,1,1,1,1,1,1,1,1,1,1,1)",91,48,"exact",48,48],[5,15,"f","(3,2,1,1,1,1,1,1,1,1,1,1)",715,232,"exact",232,232],[5,15,"f","(3,2,2,1,1,1,1,1,1,1,1)",2835,507,"exact",507,507],[5,15,"f","(3,2,2,2,1,1,1,1,1,1)",7007,598,"exact",598,598],[5,15,"f","(3,2,2,2,2,1,1,1,1)",11375,380,"exact",380,380],[5,15,"f","(3,2,2,2,2,2,1,1)",11583,116,"exact",116,116],[5,15,"f","(3,2,2,2,2,2,2)",5005,12,"exact",12,12],[5,15,"f","(3,3,1,1,1,1,1,1,1,1,1)",1925,344,"exact",344,344],[5,15,"f","(3,3,2,1,1,1,1,1,1,1)",9100,759,"exact",759,759],[5,15,"f","(3,3,2,2,1,1,1,1,1)",22113,705,"lower bound",705,9611],[5,15,"f","(3,3,2,2,2,1,1,1)",32032,307,"lower bound",307,13431],[5,15,"f","(3,3,2,2,2,2,1)",25025,50,"lower bound",50,10370],[5,15,"f","(3,3,3,1,1,1,1,1,1)",12740,388,"exact",388,388],[5,15,"f","(3,3,3,2,1,1,1,1)",35035,310,"lower bound",310,14534],[5,15,"f","(3,3,3,2,2,1,1)",45045,85,"lower bound",85,18409],[5,15,"f","(3,3,3,2,2,2)",21450,4,"lower bound",4,8718],[5,15,"f","(3,3,3,3,1,1,1)",25025,47,"lower bound",47,10165],[5,15,"f","(3,3,3,3,2,1)",30030,8,"lower bound",8,12098],[5,15,"f","(3,3,3,3,3)",6006,0,"exact",0,0],[5,15,"f","(4,1,1,1,1,1,1,1,1,1,1,1)",364,120,"exact",120,120],[5,15,"f","(4,2,1,1,1,1,1,1,1,1,1)",2925,525,"exact",525,525],[5,15,"f","(4,2,2,1,1,1,1,1,1,1)",11088,928,"exact",928,928],[5,15,"f","(4,2,2,2,1,1,1,1,1)",25025,814,"lower bound",814,10838],[5,15,"f","(4,2,2,2,2,1,1,1)",35100,358,"lower bound",358,14547],[5,15,"f","(4,2,2,2,2,2,1)",27027,70,"lower bound",70,11066],[5,15,"f","(4,3,1,1,1,1,1,1,1,1)",9450,781,"exact",781,781],[5,15,"f","(4,3,2,1,1,1,1,1,1)",42042,1284,"lower bound",1284,27355],[5,15,"f","(4,3,2,2,1,1,1,1)",91000,334,"lower bound",334,63275],[5,15,"f","(4,3,2,2,2,1,1)",108108,64,"lower bound",64,74771],[5,15,"f","(4,3,2,2,2,2)",50050,20,"lower bound",20,34533],[5,15,"f","(4,3,3,1,1,1,1,1)",57330,482,"lower bound",482,43267],[5,15,"f","(4,3,3,2,1,1,1)",135135,70,"lower bound",70,100898],[5,15,"f","(4,3,3,2,2,1)",128700,5,"lower bound",5,95508],[5,15,"f","(4,3,3,3,1,1)",80080,4,"lower bound",4,59198],[5,15,"f","(4,3,3,3,2)",54054,2,"lower bound",2,39792],[5,15,"f","(4,4,1,1,1,1,1,1,1)",13650,404,"exact",404,404],[5,15,"f","(4,4,2,1,1,1,1,1)",58968,490,"lower bound",490,43981],[5,15,"f","(4,4,2,2,1,1,1)",112112,58,"lower bound",58,88261],[5,15,"f","(4,4,2,2,2,1)",100100,5,"lower bound",5,78250],[5,15,"f","(4,4,3,1,1,1,1)",90090,38,"lower bound",38,70416],[5,15,"f","(4,4,3,2,1,1)",175175,6,"lower bound",6,135567],[5,15,"f","(4,4,3,2,2)",96525,74334,"upper bound",0,74334],[5,15,"f","(4,4,3,3,1)",81081,57516,"upper bound",0,57516],[5,15,"f","(4,4,4,1,1,1)",50050,6,"lower bound",6,32633],[5,15,"f","(4,4,4,2,1)",75075,46836,"upper bound",0,46836],[5,15,"f","(4,4,4,3)",24024,9042,"upper bound",0,9042],[5,15,"f","(5,1,1,1,1,1,1,1,1,1,1)",1001,184,"exact",184,184],[5,15,"f","(5,2,1,1,1,1,1,1,1,1)",7722,644,"exact",644,644],[5,15,"f","(5,2,2,1,1,1,1,1,1)",26950,841,"lower bound",841,11397],[5,15,"f","(5,2,2,2,1,1,1,1)",53625,528,"lower bound",528,31180],[5,15,"f","(5,2,2,2,2,1,1)",61425,166,"lower bound",166,42058],[5,15,"f","(5,2,2,2,2,2)",28028,24,"lower bound",24,19117],[5,15,"f","(5,3,1,1,1,1,1,1,1)",24948,736,"lower bound",736,10434],[5,15,"f","(5,3,2,1,1,1,1,1)",100100,335,"lower bound",335,67294],[5,15,"f","(5,3,2,2,1,1,1)",184275,106,"lower bound",106,142929],[5,15,"f","(5,3,2,2,2,1)",162162,10,"lower bound",10,124902],[5,15,"f","(5,3,3,1,1,1,1)",122850,58,"lower bound",58,94614],[5,15,"f","(5,3,3,2,1,1)",231660,10,"lower bound",10,176670],[5,15,"f","(5,3,3,2,2)",126126,95720,"upper bound",0,95720],[5,15,"f","(5,3,3,3,1)",100100,69928,"upper bound",0,69928],[5,15,"f","(5,4,1,1,1,1,1,1)",42042,320,"lower bound",320,24127],[5,15,"f","(5,4,2,1,1,1,1)",159250,70,"lower bound",70,121512],[5,15,"f","(5,4,2,2,1,1)",243243,10,"lower bound",10,183771],[5,15,"f","(5,4,2,2,2)",125125,94070,"upper bound",0,94070],[5,15,"f","(5,4,3,1,1,1)",210210,6,"lower bound",6,157680],[5,15,"f","(5,4,3,2,1)",292864,217968,"upper bound",0,217968],[5,15,"f","(5,4,3,3)",75075,45270,"upper bound",0,45270],[5,15,"f","(5,4,4,1,1)",100100,67978,"upper bound",0,67978],[5,15,"f","(5,4,4,2)",81081,54816,"upper bound",0,54816],[5,15,"f","(5,5,1,1,1,1,1)",34398,47,"lower bound",47,20624],[5,15,"f","(5,5,2,1,1,1)",112112,4,"lower bound",4,77668],[5,15,"f","(5,5,2,2,1)",125125,91665,"upper bound",0,91665],[5,15,"f","(5,5,3,1,1)",126126,91716,"upper bound",0,91716],[5,15,"f","(5,5,3,2)",96525,69795,"upper bound",0,69795],[5,15,"f","(5,5,4,1)",54054,36522,"upper bound",0,36522],[5,15,"f","(5,5,5)",6006,0,"exact",0,0],[5,15,"f","(6,1,1,1,1,1,1,1,1,1)",2002,170,"exact",170,170],[5,15,"f","(6,2,1,1,1,1,1,1,1)",14300,418,"exact",418,418],[5,15,"f","(6,2,2,1,1,1,1,1)",44550,384,"lower bound",384,25048],[5,15,"f","(6,2,2,2,1,1,1)",75075,51,"lower bound",51,56486],[5,15,"f","(6,2,2,2,2,1)",63700,42,"lower bound",42,42476],[5,15,"f","(6,3,1,1,1,1,1,1)",43120,313,"lower bound",313,24136],[5,15,"f","(6,3,2,1,1,1,1)",150150,64,"lower bound",64,111736],[5,15,"f","(6,3,2,2,1,1)",221130,10,"lower bound",10,162954],[5,15,"f","(6,3,2,2,2)",112112,77092,"upper bound",0,77092],[5,15,"f","(6,3,3,1,1,1)",156000,5,"lower bound",5,114150],[5,15,"f","(6,3,3,2,1)",210210,152616,"upper bound",0,152616],[5,15,"f","(6,3,3,3)",50050,30440,"upper bound",0,30440],[5,15,"f","(6,4,1,1,1,1,1)",70070,21,"lower bound",21,51480],[5,15,"f","(6,4,2,1,1,1)",221130,5,"lower bound",5,160299],[5,15,"f","(6,4,2,2,1)",243243,174924,"upper bound",0,174924],[5,15,"f","(6,4,3,1,1)",231660,165366,"upper bound",0,165366],[5,15,"f","(6,4,3,2)",175175,124332,"upper bound",0,124332],[5,15,"f","(6,4,4,1)",80080,53090,"upper bound",0,53090],[5,15,"f","(6,5,1,1,1,1)",63700,8,"lower bound",8,40151],[5,15,"f","(6,5,2,1,1)",162162,113886,"upper bound",0,113886],[5,15,"f","(6,5,2,2)",100100,69885,"upper bound",0,69885],[5,15,"f","(6,5,3,1)",128700,84153,"upper bound",0,84153],[5,15,"f","(6,5,4)",30030,10329,"upper bound",0,10329],[5,15,"f","(6,6,1,1,1)",28028,16854,"upper bound",0,16854],[5,15,"f","(6,6,2,1)",50050,29473,"upper bound",0,29473],[5,15,"f","(6,6,3)",21450,7260,"upper bound",0,7260],[5,15,"f","(7,1,1,1,1,1,1,1,1)",3003,80,"exact",80,80],[5,15,"f","(7,2,1,1,1,1,1,1)",19305,126,"exact",126,126],[5,15,"f","(7,2,2,1,1,1,1)",51975,76,"lower bound",76,33724],[5,15,"f","(7,2,2,2,1,1)",70070,4,"lower bound",4,49441],[5,15,"f","(7,2,2,2,2)",34398,5,"lower bound",5,19026],[5,15,"f","(7,3,1,1,1,1,1)",51975,49,"lower bound",49,33427],[5,15,"f","(7,3,2,1,1,1)",150150,2,"lower bound",2,104715],[5,15,"f","(7,3,2,2,1)",159250,110150,"upper bound",0,110150],[5,15,"f","(7,3,3,1,1)",122850,84330,"upper bound",0,84330],[5,15,"f","(7,3,3,2)",90090,61474,"upper bound",0,61474],[5,15,"f","(7,4,1,1,1,1)",75075,51630,"upper bound",0,51630],[5,15,"f","(7,4,2,1,1)",184275,125190,"upper bound",0,125190],[5,15,"f","(7,4,2,2)",112112,75700,"upper bound",0,75700],[5,15,"f","(7,4,3,1)",135135,85444,"upper bound",0,85444],[5,15,"f","(7,4,4)",25025,8360,"upper bound",0,8360],[5,15,"f","(7,5,1,1,1)",61425,36042,"upper bound",0,36042],[5,15,"f","(7,5,2,1)",108108,62033,"upper bound",0,62033],[5,15,"f","(7,5,3)",45045,14916,"upper bound",0,14916],[5,15,"f","(7,6,1,1)",27027,8844,"upper bound",0,8844],[5,15,"f","(7,6,2)",25025,8140,"upper bound",0,8140],[5,15,"f","(7,7,1)",5005,0,"exact",0,0],[5,15,"f","(8,1,1,1,1,1,1,1)",3432,13,"exact",13,13],[5,15,"f","(8,2,1,1,1,1,1)",19305,11,"exact",11,11],[5,15,"f","(8,2,2,1,1,1)",43120,3,"lower bound",3,21448],[5,15,"f","(8,2,2,2,1)",42042,20706,"upper bound",0,20706],[5,15,"f","(8,3,1,1,1,1)",44550,1,"lower bound",1,21887],[5,15,"f","(8,3,2,1,1)",100100,55078,"upper bound",0,55078],[5,15,"f","(8,3,2,2)",58968,32592,"upper bound",0,32592],[5,15,"f","(8,3,3,1)",57330,30660,"upper bound",0,30660],[5,15,"f","(8,4,1,1,1)",53625,25398,"upper bound",0,25398],[5,15,"f","(8,4,2,1)",91000,47040,"upper bound",0,47040],[5,15,"f","(8,4,3)",35035,11088,"upper bound",0,11088],[5,15,"f","(8,5,1,1)",35100,11055,"upper bound",0,11055],[5,15,"f","(8,5,2)",32032,10032,"upper bound",0,10032],[5,15,"f","(8,6,1)",11583,0,"exact",0,0],[5,15,"f","(8,7)",1430,0,"exact",0,0],[5,15,"f","(9,1,1,1,1,1,1)",3003,0,"exact",0,0],[5,15,"f","(9,2,1,1,1,1)",14300,0,"exact",0,0],[5,15,"f","(9,2,2,1,1)",24948,7488,"upper bound",0,7488],[5,15,"f","(9,2,2,2)",13650,0,"exact",0,0],[5,15,"f","(9,3,1,1,1)",26950,8050,"upper bound",0,8050],[5,15,"f","(9,3,2,1)",42042,14448,"upper bound",0,14448],[5,15,"f","(9,3,3)",12740,0,"exact",0,0],[5,15,"f","(9,4,1,1)",25025,7370,"upper bound",0,7370],[5,15,"f","(9,4,2)",22113,6480,"upper bound",0,6480],[5,15,"f","(9,5,1)",11375,0,"exact",0,0],[5,15,"f","(9,6)",2002,0,"exact",0,0],[5,15,"f","(10,1,1,1,1,1)",2002,0,"exact",0,0],[5,15,"f","(10,2,1,1,1)",7722,0,"exact",0,0],[5,15,"f","(10,2,2,1)",9450,0,"exact",0,0],[5,15,"f","(10,3,1,1)",11088,0,"exact",0,0],[5,15,"f","(10,3,2)",9100,0,"exact",0,0],[5,15,"f","(10,4,1)",7007,0,"exact",0,0],[5,15,"f","(10,5)",1638,0,"exact",0,0],[5,15,"f","(11,1,1,1,1)",1001,0,"exact",0,0],[5,15,"f","(11,2,1,1)",2925,0,"exact",0,0],[5,15,"f","(11,2,2)",1925,0,"exact",0,0],[5,15,"f","(11,3,1)",2835,0,"exact",0,0],[5,15,"f","(11,4)",910,0,"exact",0,0],[5,15,"f","(12,1,1,1)",364,0,"exact",0,0],[5,15,"f","(12,2,1)",715,0,"exact",0,0],[5,15,"f","(12,3)",350,0,"exact",0,0],[5,15,"f","(13,1,1)",91,0,"exact",0,0],[5,15,"f","(13,2)",90,0,"exact",0,0],[5,15,"f","(14,1)",14,0,"exact",0,0],[5,15,"f","(15)",1,0,"exact",0,0],[5,16,"f","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[5,16,"f","(10,1,1,1,1,1,1)",5005,76,"upper bound",0,76],[5,16,"f","(10,2,1,1,1,1)",24024,10500,"upper bound",0,10500],[5,16,"f","(10,2,2,1,1)",42120,17640,"upper bound",0,17640],[5,16,"f","(10,2,2,2)",23100,9450,"upper bound",0,9450],[5,16,"f","(10,3,1,1,1)",45760,18900,"upper bound",0,18900],[5,16,"f","(10,3,2,1)",71680,28560,"upper bound",0,28560],[5,16,"f","(10,3,3)",21840,8400,"upper bound",0,8400],[5,16,"f","(10,4,1,1)",43120,16800,"upper bound",0,16800],[5,16,"f","(10,4,2)",38220,14490,"upper bound",0,14490],[5,16,"f","(10,5,1)",20020,7350,"upper bound",0,7350],[5,16,"f","(10,6)",3640,0,"exact",0,0],[5,16,"f","(11,1,1,1,1,1)",3003,0,"exact",0,0],[5,16,"f","(11,2,1,1,1)",11648,0,"exact",0,0],[5,16,"f","(11,2,2,1)",14300,0,"exact",0,0],[5,16,"f","(11,3,1,1)",16848,0,"exact",0,0],[5,16,"f","(11,3,2)",13860,0,"exact",0,0],[5,16,"f","(11,4,1)",10752,0,"exact",0,0],[5,16,"f","(11,5)",2548,0,"exact",0,0],[5,16,"f","(12,1,1,1,1)",1365,0,"exact",0,0],[5,16,"f","(12,2,1,1)",4004,0,"exact",0,0],[5,16,"f","(12,2,2)",2640,0,"exact",0,0],[5,16,"f","(12,3,1)",3900,0,"exact",0,0],[5,16,"f","(12,4)",1260,0,"exact",0,0],[5,16,"f","(13,1,1,1)",455,0,"exact",0,0],[5,16,"f","(13,2,1)",896,0,"exact",0,0],[5,16,"f","(13,3)",440,0,"exact",0,0],[5,16,"f","(14,1,1)",105,0,"exact",0,0],[5,16,"f","(14,2)",104,0,"exact",0,0],[5,16,"f","(15,1)",15,0,"exact",0,0],[5,16,"f","(16)",1,0,"exact",0,0],[5,16,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",15,12,"lower bound",12,13],[5,16,"f","(2,2,1,1,1,1,1,1,1,1,1,1,1,1)",104,58,"lower bound",58,66],[5,16,"f","(2,2,2,1,1,1,1,1,1,1,1,1,1)",440,160,"lower bound",160,194],[5,16,"f","(2,2,2,2,1,1,1,1,1,1,1,1)",1260,278,"lower bound",278,363],[5,16,"f","(2,2,2,2,2,1,1,1,1,1,1)",2548,310,"lower bound",310,2548],[5,16,"f","(2,2,2,2,2,2,1,1,1,1)",3640,214,"lower bound",214,3640],[5,16,"f","(2,2,2,2,2,2,2,1,1)",3432,84,"lower bound",84,3432],[5,16,"f","(2,2,2,2,2,2,2,2)",1430,15,"lower bound",15,34],[5,16,"f","(3,1,1,1,1,1,1,1,1,1,1,1,1,1)",105,59,"lower bound",59,67],[5,16,"f","(3,2,1,1,1,1,1,1,1,1,1,1,1)",896,327,"lower bound",327,396],[5,16,"f","(3,2,2,1,1,1,1,1,1,1,1,1)",3900,852,"lower bound",852,3900],[5,16,"f","(3,2,2,2,1,1,1,1,1,1,1)",10752,1270,"lower bound",1270,10752],[5,16,"f","(3,2,2,2,2,1,1,1,1,1)",20020,1123,"lower bound",1123,20020],[5,16,"f","(3,2,2,2,2,2,1,1,1)",24960,565,"lower bound",565,24960],[5,16,"f","(3,2,2,2,2,2,2,1)",18018,143,"lower bound",143,18018],[5,16,"f","(3,3,1,1,1,1,1,1,1,1,1,1)",2640,576,"lower bound",576,751],[5,16,"f","(3,3,2,1,1,1,1,1,1,1,1)",13860,1610,"lower bound",1610,13860],[5,16,"f","(3,3,2,2,1,1,1,1,1,1)",38220,2062,"lower bound",2062,38220],[5,16,"f","(3,3,2,2,2,1,1,1,1)",65520,1392,"lower bound",1392,65510],[5,16,"f","(3,3,2,2,2,2,1,1)",68640,473,"lower bound",473,68610],[5,16,"f","(3,3,2,2,2,2,2)",30030,62,"lower bound",62,30010],[5,16,"f","(3,3,3,1,1,1,1,1,1,1)",21840,1147,"lower bound",1147,21840],[5,16,"f","(3,3,3,2,1,1,1,1,1)",69888,1403,"lower bound",1403,69848],[5,16,"f","(3,3,3,2,2,1,1,1)",112112,702,"lower bound",702,111952],[5,16,"f","(3,3,3,2,2,2,1)",91520,139,"lower bound",139,91320],[5,16,"f","(3,3,3,3,1,1,1,1)",60060,357,"lower bound",357,59925],[5,16,"f","(3,3,3,3,2,1,1)",100100,140,"lower bound",140,99725],[5,16,"f","(3,3,3,3,2,2)",51480,12,"lower bound",12,51240],[5,16,"f","(3,3,3,3,3,1)",36036,8,"lower bound",8,35815],[5,16,"f","(4,1,1,1,1,1,1,1,1,1,1,1,1)",455,168,"lower bound",168,203],[5,16,"f","(4,2,1,1,1,1,1,1,1,1,1,1)",4004,877,"lower bound",877,1147],[5,16,"f","(4,2,2,1,1,1,1,1,1,1,1)",16848,1960,"lower bound",1960,16848],[5,16,"f","(4,2,2,2,1,1,1,1,1,1)",43120,2340,"lower bound",2340,43120],[5,16,"f","(4,2,2,2,2,1,1,1,1)",71500,1552,"lower bound",1552,71485],[5,16,"f","(4,2,2,2,2,2,1,1)",73710,544,"lower bound",544,73665],[5,16,"f","(4,2,2,2,2,2,2)",32032,82,"lower bound",82,32002],[5,16,"f","(4,3,1,1,1,1,1,1,1,1,1)",14300,1650,"lower bound",1650,14300],[5,16,"f","(4,3,2,1,1,1,1,1,1,1)",71680,3752,"lower bound",3752,71680],[5,16,"f","(4,3,2,2,1,1,1,1,1)",180180,3137,"lower bound",3137,180005],[5,16,"f","(4,3,2,2,2,1,1,1)",266240,1063,"lower bound",1063,265600],[5,16,"f","(4,3,2,2,2,2,1)",210210,204,"lower bound",204,209455],[5,16,"f","(4,3,3,1,1,1,1,1,1)",112112,2154,"lower bound",2154,111902],[5,16,"f","(4,3,3,2,1,1,1,1)",318500,1196,"lower bound",1196,317050],[5,16,"f","(4,3,3,2,2,1,1)",416988,224,"lower bound",224,414018],[5,16,"f","(4,3,3,2,2,2)",200200,29,"lower bound",29,198470],[5,16,"f","(4,3,3,3,1,1,1)",240240,121,"lower bound",121,237990],[5,16,"f","(4,3,3,3,2,1)",292864,19,"lower bound",19,289240],[5,16,"f","(4,3,3,3,3)",60060,2,"lower bound",2,59075],[5,16,"f","(4,4,1,1,1,1,1,1,1,1)",23100,1185,"lower bound",1185,23100],[5,16,"f","(4,4,2,1,1,1,1,1,1)",114660,2178,"lower bound",2178,114345],[5,16,"f","(4,4,2,2,1,1,1,1)",262080,882,"lower bound",882,260400],[5,16,"f","(4,4,2,2,2,1,1)",320320,127,"lower bound",127,317200],[5,16,"f","(4,4,2,2,2,2)",150150,25,"lower bound",25,148395],[5,16,"f","(4,4,3,1,1,1,1,1)",206388,1010,"lower bound",1010,204498],[5,16,"f","(4,4,3,2,1,1,1)",512512,172,"lower bound",172,505052],[5,16,"f","(4,4,3,2,2,1)",500500,16,"lower bound",16,491250],[5,16,"f","(4,4,3,3,1,1)",336336,10,"lower bound",10,328800],[5,16,"f","(4,4,3,3,2)",231660,2,"lower bound",2,225675],[5,16,"f","(4,4,4,1,1,1,1)",140140,44,"lower bound",44,137170],[5,16,"f","(4,4,4,2,1,1)",300300,12,"lower bound",12,291880],[5,16,"f","(4,4,4,2,2)",171600,166130,"upper bound",0,166130],[5,16,"f","(4,4,4,3,1)",180180,173505,"upper bound",0,173505],[5,16,"f","(4,4,4,4)",24024,22850,"upper bound",0,22850],[5,16,"f","(5,1,1,1,1,1,1,1,1,1,1,1)",1365,304,"lower bound",304,395],[5,16,"f","(5,2,1,1,1,1,1,1,1,1,1)",11648,1353,"lower bound",1353,11648],[5,16,"f","(5,2,2,1,1,1,1,1,1,1)",45760,2413,"lower bound",2413,45760],[5,16,"f","(5,2,2,2,1,1,1,1,1)",105600,2183,"lower bound",2183,105440],[5,16,"f","(5,2,2,2,2,1,1,1)",150150,1052,"lower bound",1052,149590],[5,16,"f","(5,2,2,2,2,2,1)",116480,260,"lower bound",260,115840],[5,16,"f","(5,3,1,1,1,1,1,1,1,1)",42120,2161,"lower bound",2161,42120],[5,16,"f","(5,3,2,1,1,1,1,1,1)",194040,3196,"lower bound",3196,193340],[5,16,"f","(5,3,2,2,1,1,1,1)",429000,1303,"lower bound",1303,425445],[5,16,"f","(5,3,2,2,2,1,1)",515970,346,"lower bound",346,509535],[5,16,"f","(5,3,2,2,2,2)",240240,54,"lower bound",54,236660],[5,16,"f","(5,3,3,1,1,1,1,1)",280280,875,"lower bound",875,276990],[5,16,"f","(5,3,3,2,1,1,1)",673920,244,"lower bound",244,661500],[5,16,"f","(5,3,3,2,2,1)",648648,25,"lower bound",25,633582],[5,16,"f","(5,3,3,3,1,1)",411840,14,"lower bound",14,400310],[5,16,"f","(5,3,3,3,2)",280280,2,"lower bound",2,271290],[5,16,"f","(5,4,1,1,1,1,1,1,1)",80640,1460,"lower bound",1460,80080],[5,16,"f","(5,4,2,1,1,1,1,1)",360360,1215,"lower bound",1215,354585],[5,16,"f","(5,4,2,2,1,1,1)",698880,244,"lower bound",244,681940],[5,16,"f","(5,4,2,2,2,1)",630630,25,"lower bound",25,611795],[5,16,"f","(5,4,3,1,1,1,1)",582400,172,"lower bound",172,564900],[5,16,"f","(5,4,3,2,1,1)",1153152,32,"lower bound",32,1108208],[5,16,"f","(5,4,3,2,2)",640640,612580,"upper bound",0,612580],[5,16,"f","(5,4,3,3,1)",549120,521460,"upper bound",0,521460],[5,16,"f","(5,4,4,1,1,1)",360360,12,"lower bound",12,342170],[5,16,"f","(5,4,4,2,1)",549120,516580,"upper bound",0,516580],[5,16,"f","(5,4,4,3)",180180,167565,"upper bound",0,167565],[5,16,"f","(5,5,1,1,1,1,1,1)",76440,367,"lower bound",367,74270],[5,16,"f","(5,5,2,1,1,1,1)",305760,121,"lower bound",121,292670],[5,16,"f","(5,5,2,2,1,1)",480480,14,"lower bound",14,454720],[5,16,"f","(5,5,2,2,2)",250250,235400,"upper bound",0,235400],[5,16,"f","(5,5,3,1,1,1)",448448,10,"lower bound",10,420742],[5,16,"f","(5,5,3,2,1)",640640,594780,"upper bound",0,594780],[5,16,"f","(5,5,3,3)",171600,157300,"upper bound",0,157300],[5,16,"f","(5,5,4,1,1)",280280,256100,"upper bound",0,256100],[5,16,"f","(5,5,4,2)",231660,209850,"upper bound",0,209850],[5,16,"f","(5,5,5,1)",60060,53010,"upper bound",0,53010],[5,16,"f","(6,1,1,1,1,1,1,1,1,1,1)",3003,354,"lower bound",354,517],[5,16,"f","(6,2,1,1,1,1,1,1,1,1)",24024,1232,"lower bound",1232,24024],[5,16,"f","(6,2,2,1,1,1,1,1,1)",85800,1643,"lower bound",1643,85260],[5,16,"f","(6,2,2,2,1,1,1,1)",173250,963,"lower bound",963,170835],[5,16,"f","(6,2,2,2,2,1,1)",200200,259,"lower bound",259,196105],[5,16,"f","(6,2,2,2,2,2)",91728,66,"lower bound",66,89508],[5,16,"f","(6,3,1,1,1,1,1,1,1)",82368,1467,"lower bound",1467,81528],[5,16,"f","(6,3,2,1,1,1,1,1)",337920,1096,"lower bound",1096,330240],[5,16,"f","(6,3,2,2,1,1,1)",630630,231,"lower bound",231,609350],[5,16,"f","(6,3,2,2,2,1)",559104,62,"lower bound",62,536120],[5,16,"f","(6,3,3,1,1,1,1)",429000,127,"lower bound",127,411270],[5,16,"f","(6,3,3,2,1,1)",819000,25,"lower bound",25,775700],[5,16,"f","(6,3,3,2,2)",448448,422018,"upper bound",0,422018],[5,16,"f","(6,3,3,3,1)",360360,336120,"upper bound",0,336120],[5,16,"f","(6,4,1,1,1,1,1,1)",155232,654,"lower bound",654,149772],[5,16,"f","(6,4,2,1,1,1,1)",600600,160,"lower bound",160,569205],[5,16,"f","(6,4,2,2,1,1)",928746,25,"lower bound",25,868455],[5,16,"f","(6,4,2,2,2)",480480,446100,"upper bound",0,446100],[5,16,"f","(6,4,3,1,1,1)",819000,16,"lower bound",16,758100],[5,16,"f","(6,4,3,2,1)",1153152,1054392,"upper bound",0,1054392],[5,16,"f","(6,4,3,3)",300300,270555,"upper bound",0,270555],[5,16,"f","(6,4,4,1,1)",411840,369690,"upper bound",0,369690],[5,16,"f","(6,4,4,2)",336336,298910,"upper bound",0,298910],[5,16,"f","(6,5,1,1,1,1,1)",168168,76,"lower bound",76,155078],[5,16,"f","(6,5,2,1,1,1)",559104,17,"lower bound",17,504840],[5,16,"f","(6,5,2,2,1)",630630,561750,"upper bound",0,561750],[5,16,"f","(6,5,3,1,1)",648648,570738,"upper bound",0,570738],[5,16,"f","(6,5,3,2)",500500,435800,"upper bound",0,435800],[5,16,"f","(6,5,4,1)",292864,249640,"upper bound",0,249640],[5,16,"f","(6,5,5)",36036,29550,"upper bound",0,29550],[5,16,"f","(6,6,1,1,1,1)",91728,8,"lower bound",8,78932],[5,16,"f","(6,6,2,1,1)",240240,202230,"upper bound",0,202230],[5,16,"f","(6,6,2,2)",150150,124950,"upper bound",0,124950],[5,16,"f","(6,6,3,1)",200200,164220,"upper bound",0,164220],[5,16,"f","(6,6,4)",51480,40960,"upper bound",0,40960],[5,16,"f","(7,1,1,1,1,1,1,1,1,1)",5005,250,"lower bound",250,2258],[5,16,"f","(7,2,1,1,1,1,1,1,1)",36608,624,"lower bound",624,35888],[5,16,"f","(7,2,2,1,1,1,1,1)",115830,586,"lower bound",586,111105],[5,16,"f","(7,2,2,2,1,1,1)",197120,131,"lower bound",131,185640],[5,16,"f","(7,2,2,2,2,1)",168168,51,"lower bound",51,156527],[5,16,"f","(7,3,1,1,1,1,1,1)",114400,488,"lower bound",488,108220],[5,16,"f","(7,3,2,1,1,1,1)",404250,191,"lower bound",191,372855],[5,16,"f","(7,3,2,2,1,1)",600600,16,"lower bound",16,543795],[5,16,"f","(7,3,2,2,2)",305760,5,"lower bound",5,274190],[5,16,"f","(7,3,3,1,1,1)",429000,7,"lower bound",7,383130],[5,16,"f","(7,3,3,2,1)",582400,511700,"upper bound",0,511700],[5,16,"f","(7,3,3,3)",140140,120785,"upper bound",0,120785],[5,16,"f","(7,4,1,1,1,1,1)",197120,70,"lower bound",70,176960],[5,16,"f","(7,4,2,1,1,1)",630630,7,"lower bound",7,551460],[5,16,"f","(7,4,2,2,1)",698880,601020,"upper bound",0,601020],[5,16,"f","(7,4,3,1,1)",673920,570900,"upper bound",0,570900],[5,16,"f","(7,4,3,2)",512512,428708,"upper bound",0,428708],[5,16,"f","(7,4,4,1)",240240,195860,"upper bound",0,195860],[5,16,"f","(7,5,1,1,1,1)",200200,8,"lower bound",8,167510],[5,16,"f","(7,5,2,1,1)",515970,421050,"upper bound",0,421050],[5,16,"f","(7,5,2,2)",320320,258020,"upper bound",0,258020],[5,16,"f","(7,5,3,1)",416988,330462,"upper bound",0,330462],[5,16,"f","(7,5,4)",100100,76650,"upper bound",0,76650],[5,16,"f","(7,6,1,1,1)",116480,89040,"upper bound",0,89040],[5,16,"f","(7,6,2,1)",210210,157220,"upper bound",0,157220],[5,16,"f","(7,6,3)",91520,66760,"upper bound",0,66760],[5,16,"f","(7,7,1,1)",32032,21868,"upper bound",0,21868],[5,16,"f","(7,7,2)",30030,20160,"upper bound",0,20160],[5,16,"f","(8,1,1,1,1,1,1,1,1)",6435,93,"lower bound",93,488],[5,16,"f","(8,2,1,1,1,1,1,1)",42042,150,"lower bound",150,37737],[5,16,"f","(8,2,2,1,1,1,1)",114400,90,"lower bound",90,98580],[5,16,"f","(8,2,2,2,1,1)",155232,7,"lower bound",7,130088],[5,16,"f","(8,2,2,2,2)",76440,5,"lower bound",5,63140],[5,16,"f","(8,3,1,1,1,1,1)",115830,61,"lower bound",61,97335],[5,16,"f","(8,3,2,1,1,1)",337920,6,"lower bound",6,273680],[5,16,"f","(8,3,2,2,1)",360360,285320,"upper bound",0,285320],[5,16,"f","(8,3,3,1,1)",280280,217420,"upper bound",0,217420],[5,16,"f","(8,3,3,2)",206388,157542,"upper bound",0,157542],[5,16,"f","(8,4,1,1,1,1)",173250,1,"lower bound",1,134785],[5,16,"f","(8,4,2,1,1)",429000,323280,"upper bound",0,323280],[5,16,"f","(8,4,2,2)",262080,194320,"upper bound",0,194320],[5,16,"f","(8,4,3,1)",318500,231350,"upper bound",0,231350],[5,16,"f","(8,4,4)",60060,41790,"upper bound",0,41790],[5,16,"f","(8,5,1,1,1)",150150,106855,"upper bound",0,106855],[5,16,"f","(8,5,2,1)",266240,184640,"upper bound",0,184640],[5,16,"f","(8,5,3)",112112,75488,"upper bound",0,75488],[5,16,"f","(8,6,1,1)",73710,47355,"upper bound",0,47355],[5,16,"f","(8,6,2)",68640,43280,"upper bound",0,43280],[5,16,"f","(8,7,1)",18018,0,"exact",0,0],[5,16,"f","(8,8)",1430,0,"exact",0,0],[5,16,"f","(9,1,1,1,1,1,1,1)",6435,13,"lower bound",13,114],[5,16,"f","(9,2,1,1,1,1,1)",36608,11,"lower bound",11,26088],[5,16,"f","(9,2,2,1,1,1)",82368,3,"lower bound",3,55692],[5,16,"f","(9,2,2,2,1)",80640,52920,"upper bound",0,52920],[5,16,"f","(9,3,1,1,1,1)",85800,1,"lower bound",1,56400],[5,16,"f","(9,3,2,1,1)",194040,122220,"upper bound",0,122220],[5,16,"f","(9,3,2,2)",114660,70770,"upper bound",0,70770],[5,16,"f","(9,3,3,1)",112112,67368,"upper bound",0,67368],[5,16,"f","(9,4,1,1,1)",105600,63720,"upper bound",0,63720],[5,16,"f","(9,4,2,1)",180180,105210,"upper bound",0,105210],[5,16,"f","(9,4,3)",69888,39312,"upper bound",0,39312],[5,16,"f","(9,5,1,1)",71500,39390,"upper bound",0,39390],[5,16,"f","(9,5,2)",65520,35280,"upper bound",0,35280],[5,16,"f","(9,6,1)",24960,12480,"upper bound",0,12480],[5,16,"f","(9,7)",3432,0,"exact",0,0],[5,17,"f","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[5,17,"f","(10,1,1,1,1,1,1,1)",11440,13,"lower bound",13,203],[5,17,"f","(10,2,1,1,1,1,1)",65637,11,"lower bound",11,49698],[5,17,"f","(10,2,2,1,1,1)",148512,3,"lower bound",3,107592],[5,17,"f","(10,2,2,2,1)",145860,103050,"upper bound",0,103050],[5,17,"f","(10,3,1,1,1,1)",155584,1,"lower bound",1,110040],[5,17,"f","(10,3,2,1,1)",353600,241320,"upper bound",0,241320],[5,17,"f","(10,3,2,2)",209440,140520,"upper bound",0,140520],[5,17,"f","(10,3,3,1)",205632,134928,"upper bound",0,134928],[5,17,"f","(10,4,1,1,1)",194480,127980,"upper bound",0,127980],[5,17,"f","(10,4,2,1)",333200,213360,"upper bound",0,213360],[5,17,"f","(10,4,3)",129948,80682,"upper bound",0,80682],[5,17,"f","(10,5,1,1)",134640,82080,"upper bound",0,82080],[5,17,"f","(10,5,2)",123760,74040,"upper bound",0,74040],[5,17,"f","(10,6,1)",48620,27330,"upper bound",0,27330],[5,17,"f","(10,7)",7072,0,"exact",0,0],[5,17,"f","(11,1,1,1,1,1,1)",8008,345,"upper bound",0,345],[5,17,"f","(11,2,1,1,1,1)",38675,18810,"upper bound",0,18810],[5,17,"f","(11,2,2,1,1)",68068,31878,"upper bound",0,31878],[5,17,"f","(11,2,2,2)",37400,17160,"upper bound",0,17160],[5,17,"f","(11,3,1,1,1)",74256,34320,"upper bound",0,34320],[5,17,"f","(11,3,2,1)",116688,52272,"upper bound",0,52272],[5,17,"f","(11,3,3)",35700,15510,"upper bound",0,15510],[5,17,"f","(11,4,1,1)",70720,31020,"upper bound",0,31020],[5,17,"f","(11,4,2)",62832,26928,"upper bound",0,26928],[5,17,"f","(11,5,1)",33320,13860,"upper bound",0,13860],[5,17,"f","(11,6)",6188,0,"exact",0,0],[5,17,"f","(12,1,1,1,1,1)",4368,0,"exact",0,0],[5,17,"f","(12,2,1,1,1)",17017,0,"exact",0,0],[5,17,"f","(12,2,2,1)",20944,3960,"upper bound",0,3960],[5,17,"f","(12,3,1,1)",24752,4752,"upper bound",0,4752],[5,17,"f","(12,3,2)",20400,3960,"upper bound",0,3960],[5,17,"f","(12,4,1)",15912,0,"exact",0,0],[5,17,"f","(12,5)",3808,0,"exact",0,0],[5,17,"f","(13,1,1,1,1)",1820,0,"exact",0,0],[5,17,"f","(13,2,1,1)",5355,0,"exact",0,0],[5,17,"f","(13,2,2)",3536,0,"exact",0,0],[5,17,"f","(13,3,1)",5236,0,"exact",0,0],[5,17,"f","(13,4)",1700,0,"exact",0,0],[5,17,"f","(14,1,1,1)",560,0,"exact",0,0],[5,17,"f","(14,2,1)",1105,0,"exact",0,0],[5,17,"f","(14,3)",544,0,"exact",0,0],[5,17,"f","(15,1,1)",120,0,"exact",0,0],[5,17,"f","(15,2)",119,0,"exact",0,0],[5,17,"f","(16,1)",16,0,"exact",0,0],[5,17,"f","(17)",1,0,"exact",0,0],[5,17,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",16,13,"lower bound",13,15],[5,17,"f","(2,2,1,1,1,1,1,1,1,1,1,1,1,1,1)",119,70,"lower bound",70,88],[5,17,"f","(2,2,2,1,1,1,1,1,1,1,1,1,1,1)",544,218,"lower bound",218,304],[5,17,"f","(2,2,2,2,1,1,1,1,1,1,1,1,1)",1700,438,"lower bound",438,1700],[5,17,"f","(2,2,2,2,2,1,1,1,1,1,1,1)",3808,588,"lower bound",588,3808],[5,17,"f","(2,2,2,2,2,2,1,1,1,1,1)",6188,524,"lower bound",524,6188],[5,17,"f","(2,2,2,2,2,2,2,1,1,1)",7072,298,"lower bound",298,7072],[5,17,"f","(2,2,2,2,2,2,2,2,1)",4862,99,"lower bound",99,4862],[5,17,"f","(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",120,71,"lower bound",71,89],[5,17,"f","(3,2,1,1,1,1,1,1,1,1,1,1,1,1)",1105,444,"lower bound",444,1105],[5,17,"f","(3,2,2,1,1,1,1,1,1,1,1,1,1)",5236,1339,"lower bound",1339,5236],[5,17,"f","(3,2,2,2,1,1,1,1,1,1,1,1)",15912,2400,"lower bound",2400,15912],[5,17,"f","(3,2,2,2,2,1,1,1,1,1,1)",33320,2703,"lower bound",2703,33320],[5,17,"f","(3,2,2,2,2,2,1,1,1,1)",48620,1902,"lower bound",1902,48620],[5,17,"f","(3,2,2,2,2,2,2,1,1)",46410,792,"lower bound",792,46410],[5,17,"f","(3,2,2,2,2,2,2,2)",19448,158,"lower bound",158,19448],[5,17,"f","(3,3,1,1,1,1,1,1,1,1,1,1,1)",3536,903,"lower bound",903,3536],[5,17,"f","(3,3,2,1,1,1,1,1,1,1,1,1)",20400,3038,"lower bound",3038,20400],[5,17,"f","(3,3,2,2,1,1,1,1,1,1,1)",62832,4942,"lower bound",4942,62832],[5,17,"f","(3,3,2,2,2,1,1,1,1,1)",123760,4577,"lower bound",4577,123760],[5,17,"f","(3,3,2,2,2,2,1,1,1)",159120,2430,"lower bound",2430,159120],[5,17,"f","(3,3,2,2,2,2,2,1)",116688,678,"lower bound",678,116688],[5,17,"f","(3,3,3,1,1,1,1,1,1,1,1)",35700,2757,"lower bound",2757,35700],[5,17,"f","(3,3,3,2,1,1,1,1,1,1)",129948,4612,"lower bound",4612,129948],[5,17,"f","(3,3,3,2,2,1,1,1,1)",247520,3497,"lower bound",3497,247510],[5,17,"f","(3,3,3,2,2,2,1,1)",272272,1314,"lower bound",1314,272242],[5,17,"f","(3,3,3,2,2,2,2)",121550,201,"lower bound",201,121530],[5,17,"f","(3,3,3,3,1,1,1,1,1)",129948,1760,"lower bound",1760,129933],[5,17,"f","(3,3,3,3,2,1,1,1)",272272,1199,"lower bound",1199,272192],[5,17,"f","(3,3,3,3,2,2,1)",243100,291,"lower bound",291,242985],[5,17,"f","(3,3,3,3,3,1,1)",136136,148,"lower bound",148,136040],[5,17,"f","(3,3,3,3,3,2)",87516,20,"lower bound",20,87435],[5,17,"f","(4,1,1,1,1,1,1,1,1,1,1,1,1,1)",560,227,"lower bound",227,315],[5,17,"f","(4,2,1,1,1,1,1,1,1,1,1,1,1)",5355,1372,"lower bound",1372,5355],[5,17,"f","(4,2,2,1,1,1,1,1,1,1,1,1)",24752,3689,"lower bound",3689,24752],[5,17,"f","(4,2,2,2,1,1,1,1,1,1,1)",70720,5570,"lower bound",5570,70720],[5,17,"f","(4,2,2,2,2,1,1,1,1,1)",134640,5015,"lower bound",5015,134640],[5,17,"f","(4,2,2,2,2,2,1,1,1)",170170,2661,"lower bound",2661,170170],[5,17,"f","(4,2,2,2,2,2,2,1)",123760,769,"lower bound",769,123760],[5,17,"f","(4,3,1,1,1,1,1,1,1,1,1,1)",20944,3103,"lower bound",3103,20944],[5,17,"f","(4,3,2,1,1,1,1,1,1,1,1)",116688,8972,"lower bound",8972,116688],[5,17,"f","(4,3,2,2,1,1,1,1,1,1)",333200,11291,"lower bound",11291,333200],[5,17,"f","(4,3,2,2,2,1,1,1,1)",583440,7144,"lower bound",7144,583400],[5,17,"f","(4,3,2,2,2,2,1,1)",618800,2284,"lower bound",2284,618680],[5,17,"f","(4,3,2,2,2,2,2)",272272,348,"lower bound",348,272192],[5,17,"f","(4,3,3,1,1,1,1,1,1,1)",205632,7053,"lower bound",7053,205632],[5,17,"f","(4,3,3,2,1,1,1,1,1)",680680,7890,"lower bound",7890,680505],[5,17,"f","(4,3,3,2,2,1,1,1)",1113840,3185,"lower bound",3185,1113120],[5,17,"f","(4,3,3,2,2,2,1)",918918,596,"lower bound",596,918003],[5,17,"f","(4,3,3,3,1,1,1,1)",618800,1674,"lower bound",1674,618160],[5,17,"f","(4,3,3,3,2,1,1)",1050192,504,"lower bound",504,1048368],[5,17,"f","(4,3,3,3,2,2)",544544,60,"lower bound",60,543360],[5,17,"f","(4,3,3,3,3,1)",388960,29,"lower bound",29,387840],[5,17,"f","(4,4,1,1,1,1,1,1,1,1,1)",37400,2835,"lower bound",2835,37400],[5,17,"f","(4,4,2,1,1,1,1,1,1,1)",209440,7115,"lower bound",7115,209440],[5,17,"f","(4,4,2,2,1,1,1,1,1)",556920,6197,"lower bound",6197,556710],[5,17,"f","(4,4,2,2,2,1,1,1)",848640,2072,"lower bound",2072,847840],[5,17,"f","(4,4,2,2,2,2,1)",680680,356,"lower bound",356,679710],[5,17,"f","(4,4,3,1,1,1,1,1,1)",433160,5342,"lower bound",5342,432845],[5,17,"f","(4,4,3,2,1,1,1,1)",1299480,3260,"lower bound",3260,1297100],[5,17,"f","(4,4,3,2,2,1,1)",1750320,539,"lower bound",539,1745220],[5,17,"f","(4,4,3,2,2,2)",850850,70,"lower bound",70,847815],[5,17,"f","(4,4,3,3,1,1,1)",1089088,303,"lower bound",303,1084842],[5,17,"f","(4,4,3,3,2,1)",1361360,47,"lower bound",47,1354260],[5,17,"f","(4,4,3,3,3)",291720,4,"lower bound",4,289670],[5,17,"f","(4,4,4,1,1,1,1,1)",346528,1054,"lower bound",1054,345408],[5,17,"f","(4,4,4,2,1,1,1)",952952,228,"lower bound",228,947862],[5,17,"f","(4,4,4,2,2,1)",972400,28,"lower bound",28,965660],[5,17,"f","(4,4,4,3,1,1)",816816,22,"lower bound",22,809820],[5,17,"f","(4,4,4,3,2)",583440,2,"lower bound",2,577580],[5,17,"f","(4,4,4,4,1)",204204,201475,"upper bound",0,201475],[5,17,"f","(5,1,1,1,1,1,1,1,1,1,1,1,1)",1820,472,"lower bound",472,738],[5,17,"f","(5,2,1,1,1,1,1,1,1,1,1,1)",17017,2534,"lower bound",2534,17017],[5,17,"f","(5,2,2,1,1,1,1,1,1,1,1)",74256,5726,"lower bound",5726,74256],[5,17,"f","(5,2,2,2,1,1,1,1,1,1)",194480,6936,"lower bound",6936,194480],[5,17,"f","(5,2,2,2,2,1,1,1,1)",327250,4787,"lower bound",4787,327215],[5,17,"f","(5,2,2,2,2,2,1,1)",340340,1856,"lower bound",1856,340235],[5,17,"f","(5,2,2,2,2,2,2)",148512,342,"lower bound",342,148442],[5,17,"f","(5,3,1,1,1,1,1,1,1,1,1)",68068,5164,"lower bound",5164,68068],[5,17,"f","(5,3,2,1,1,1,1,1,1,1)",353600,11522,"lower bound",11522,353600],[5,17,"f","(5,3,2,2,1,1,1,1,1)",908820,9819,"lower bound",9819,908370],[5,17,"f","(5,3,2,2,2,1,1,1)",1361360,3764,"lower bound",3764,1359680],[5,17,"f","(5,3,2,2,2,2,1)",1082900,864,"lower bound",864,1080890],[5,17,"f","(5,3,3,1,1,1,1,1,1)",586432,6225,"lower bound",6225,585872],[5,17,"f","(5,3,3,2,1,1,1,1)",1701700,3618,"lower bound",3618,1697665],[5,17,"f","(5,3,3,2,2,1,1)",2255526,839,"lower bound",839,2247075],[5,17,"f","(5,3,3,2,2,2)",1089088,108,"lower bound",108,1084112],[5,17,"f","(5,3,3,3,1,1,1)",1326000,379,"lower bound",379,1319400],[5,17,"f","(5,3,3,3,2,1)",1633632,60,"lower bound",60,1622812],[5,17,"f","(5,3,3,3,3)",340340,4,"lower bound",4,337325],[5,17,"f","(5,4,1,1,1,1,1,1,1,1)",145860,4806,"lower bound",4806,145860],[5,17,"f","(5,4,2,1,1,1,1,1,1)",749700,8049,"lower bound",8049,748650],[5,17,"f","(5,4,2,2,1,1,1,1)",1750320,3644,"lower bound",3644,1744470],[5,17,"f","(5,4,2,2,2,1,1)",2165800,742,"lower bound",742,2154670],[5,17,"f","(5,4,2,2,2,2)",1021020,104,"lower bound",104,1014690],[5,17,"f","(5,4,3,1,1,1,1,1)",1429428,3272,"lower bound",3272,1422533],[5,17,"f","(5,4,3,2,1,1,1)",3620864,864,"lower bound",864,3592640],[5,17,"f","(5,4,3,2,2,1)",3573570,98,"lower bound",98,3537895],[5,17,"f","(5,4,3,3,1,1)",2450448,56,"lower bound",56,2420538],[5,17,"f","(5,4,3,3,2)",1701700,4,"lower bound",4,1677605],[5,17,"f","(5,4,4,1,1,1,1)",1082900,228,"lower bound",228,1070440],[5,17,"f","(5,4,4,2,1,1)",2362932,56,"lower bound",56,2326518],[5,17,"f","(5,4,4,2,2)",1361360,1337370,"upper bound",0,1337370],[5,17,"f","(5,4,4,3,1)",1458600,1428510,"upper bound",0,1428510],[5,17,"f","(5,4,4,4)",204204,198575,"upper bound",0,198575],[5,17,"f","(5,5,1,1,1,1,1,1,1)",157080,1827,"lower bound",1827,156590],[5,17,"f","(5,5,2,1,1,1,1,1)",742560,1703,"lower bound",1703,736960],[5,17,"f","(5,5,2,2,1,1,1)",1485120,379,"lower bound",379,1467770],[5,17,"f","(5,5,2,2,2,1)",1361360,39,"lower bound",39,1341500],[5,17,"f","(5,5,3,1,1,1,1)",1336608,303,"lower bound",303,1316952],[5,17,"f","(5,5,3,2,1,1)",2722720,56,"lower bound",56,2669890],[5,17,"f","(5,5,3,2,2)",1531530,1497840,"upper bound",0,1497840],[5,17,"f","(5,5,3,3,1)",1361360,1326580,"upper bound",0,1326580],[5,17,"f","(5,5,4,1,1,1)",1089088,22,"lower bound",22,1061172],[5,17,"f","(5,5,4,2,1)",1701700,1649870,"upper bound",0,1649870],[5,17,"f","(5,5,4,3)",583440,562180,"upper bound",0,562180],[5,17,"f","(5,5,5,1,1)",340340,326190,"upper bound",0,326190],[5,17,"f","(5,5,5,2)",291720,278340,"upper bound",0,278340],[5,17,"f","(6,1,1,1,1,1,1,1,1,1,1,1)",4368,658,"lower bound",658,1225],[5,17,"f","(6,2,1,1,1,1,1,1,1,1,1)",38675,2939,"lower bound",2939,38675],[5,17,"f","(6,2,2,1,1,1,1,1,1,1)",155584,5288,"lower bound",5288,155584],[5,17,"f","(6,2,2,2,1,1,1,1,1)",364650,4789,"lower bound",4789,364335],[5,17,"f","(6,2,2,2,2,1,1,1)",523600,2274,"lower bound",2274,522480],[5,17,"f","(6,2,2,2,2,2,1)",408408,585,"lower bound",585,407113],[5,17,"f","(6,3,1,1,1,1,1,1,1,1)",148512,4860,"lower bound",4860,148512],[5,17,"f","(6,3,2,1,1,1,1,1,1)",700128,7402,"lower bound",7402,698688],[5,17,"f","(6,3,2,2,1,1,1,1)",1570800,3593,"lower bound",3593,1563240],[5,17,"f","(6,3,2,2,2,1,1)",1905904,898,"lower bound",898,1891960],[5,17,"f","(6,3,2,2,2,2)",891072,182,"lower bound",182,883248],[5,17,"f","(6,3,3,1,1,1,1,1)",1047200,2098,"lower bound",2098,1040000],[5,17,"f","(6,3,3,2,1,1,1)",2552550,627,"lower bound",627,2524620],[5,17,"f","(6,3,3,2,2,1)",2475200,112,"lower bound",112,2440820],[5,17,"f","(6,3,3,3,1,1)",1591200,39,"lower bound",39,1564380],[5,17,"f","(6,3,3,3,2)",1089088,2,"lower bound",2,1067948],[5,17,"f","(6,4,1,1,1,1,1,1,1)",318240,3581,"lower bound",3581,316980],[5,17,"f","(6,4,2,1,1,1,1,1)",1454112,3125,"lower bound",3125,1440432],[5,17,"f","(6,4,2,2,1,1,1)",2858856,660,"lower bound",660,2817570],[5,17,"f","(6,4,2,2,2,1)",2598960,112,"lower bound",112,2552340],[5,17,"f","(6,4,3,1,1,1,1)",2431000,475,"lower bound",475,2387075],[5,17,"f","(6,4,3,2,1,1)",4873050,98,"lower bound",98,4757655],[5,17,"f","(6,4,3,2,2)",2722720,2649890,"upper bound",0,2649890],[5,17,"f","(6,4,3,3,1)",2362932,2289807,"upper bound",0,2289807],[5,17,"f","(6,4,4,1,1,1)",1591200,28,"lower bound",28,1541820],[5,17,"f","(6,4,4,2,1)",2450448,2360532,"upper bound",0,2360532],[5,17,"f","(6,4,4,3)",816816,781140,"upper bound",0,781140],[5,17,"f","(6,5,1,1,1,1,1,1)",399840,1097,"lower bound",1097,393120],[5,17,"f","(6,5,2,1,1,1,1)",1633632,374,"lower bound",374,1591328],[5,17,"f","(6,5,2,2,1,1)",2598960,56,"lower bound",56,2513700],[5,17,"f","(6,5,2,2,2)",1361360,1311660,"upper bound",0,1311660],[5,17,"f","(6,5,3,1,1,1)",2475200,43,"lower bound",43,2380820],[5,17,"f","(6,5,3,2,1)",3573570,3414460,"upper bound",0,3414460],[5,17,"f","(6,5,3,3)",972400,921580,"upper bound",0,921580],[5,17,"f","(6,5,4,1,1)",1633632,1544948,"upper bound",0,1544948],[5,17,"f","(6,5,4,2)",1361360,1280340,"upper bound",0,1280340],[5,17,"f","(6,5,5,1)",388960,359680,"upper bound",0,359680],[5,17,"f","(6,6,1,1,1,1,1)",259896,84,"lower bound",84,248570],[5,17,"f","(6,6,2,1,1,1)",891072,25,"lower bound",25,841632],[5,17,"f","(6,6,2,2,1)",1021020,956550,"upper bound",0,956550],[5,17,"f","(6,6,3,1,1)",1089088,1012708,"upper bound",0,1012708],[5,17,"f","(6,6,3,2)",850850,786170,"upper bound",0,786170],[5,17,"f","(6,6,4,1)",544544,496600,"upper bound",0,496600],[5,17,"f","(6,6,5)",87516,77910,"upper bound",0,77910],[5,17,"f","(7,1,1,1,1,1,1,1,1,1,1)",8008,604,"lower bound",604,5997],[5,17,"f","(7,2,1,1,1,1,1,1,1,1)",65637,2106,"lower bound",2106,65637],[5,17,"f","(7,2,2,1,1,1,1,1,1)",238238,2853,"lower bound",2853,237293],[5,17,"f","(7,2,2,2,1,1,1,1)",486200,1680,"lower bound",1680,481860],[5,17,"f","(7,2,2,2,2,1,1)",565488,441,"lower bound",441,558012],[5,17,"f","(7,2,2,2,2,2)",259896,117,"lower bound",117,255815],[5,17,"f","(7,3,1,1,1,1,1,1,1)",233376,2579,"lower bound",2579,231876],[5,17,"f","(7,3,2,1,1,1,1,1)",972400,2361,"lower bound",2361,958120],[5,17,"f","(7,3,2,2,1,1,1)",1832600,569,"lower bound",569,1792140],[5,17,"f","(7,3,2,2,2,1)",1633632,134,"lower bound",134,1589392],[5,17,"f","(7,3,3,1,1,1,1)",1262250,325,"lower bound",325,1227855],[5,17,"f","(7,3,3,2,1,1)",2431000,48,"lower bound",48,2345525],[5,17,"f","(7,3,3,2,2)",1336608,5,"lower bound",5,1283988],[5,17,"f","(7,3,3,3,1)",1082900,1034005,"upper bound",0,1034005],[5,17,"f","(7,4,1,1,1,1,1,1)",466752,1212,"lower bound",1212,456072],[5,17,"f","(7,4,2,1,1,1,1)",1832600,428,"lower bound",428,1769180],[5,17,"f","(7,4,2,2,1,1)",2858856,48,"lower bound",48,2734830],[5,17,"f","(7,4,2,2,2)",1485120,5,"lower bound",5,1413790],[5,17,"f","(7,4,3,1,1,1)",2552550,30,"lower bound",30,2424830],[5,17,"f","(7,4,3,2,1)",3620864,3410880,"upper bound",0,3410880],[5,17,"f","(7,4,3,3)",952952,888608,"upper bound",0,888608],[5,17,"f","(7,4,4,1,1)",1326000,1233250,"upper bound",0,1233250],[5,17,"f","(7,4,4,2)",1089088,1005958,"upper bound",0,1005958],[5,17,"f","(7,5,1,1,1,1,1)",565488,154,"lower bound",154,536028],[5,17,"f","(7,5,2,1,1,1)",1905904,32,"lower bound",32,1780520],[5,17,"f","(7,5,2,2,1)",2165800,2004380,"upper bound",0,2004380],[5,17,"f","(7,5,3,1,1)",2255526,2069550,"upper bound",0,2069550],[5,17,"f","(7,5,3,2)",1750320,1594350,"upper bound",0,1594350],[5,17,"f","(7,5,4,1)",1050192,942432,"upper bound",0,942432],[5,17,"f","(7,5,5)",136136,118880,"upper bound",0,118880],[5,17,"f","(7,6,1,1,1,1)",408408,16,"lower bound",16,369242],[5,17,"f","(7,6,2,1,1)",1082900,964040,"upper bound",0,964040],[5,17,"f","(7,6,2,2)",680680,601090,"upper bound",0,601090],[5,17,"f","(7,6,3,1)",918918,803262,"upper bound",0,803262],[5,17,"f","(7,6,4)",243100,207970,"upper bound",0,207970],[5,17,"f","(7,7,1,1,1)",148512,125468,"upper bound",0,125468],[5,17,"f","(7,7,2,1)",272272,226688,"upper bound",0,226688],[5,17,"f","(7,7,3)",121550,99520,"upper bound",0,99520],[5,17,"f","(8,1,1,1,1,1,1,1,1,1)",11440,343,"lower bound",343,4760],[5,17,"f","(8,2,1,1,1,1,1,1,1)",85085,867,"lower bound",867,83930],[5,17,"f","(8,2,2,1,1,1,1,1)",272272,826,"lower bound",826,264432],[5,17,"f","(8,2,2,2,1,1,1)",466752,228,"lower bound",228,447348],[5,17,"f","(8,2,2,2,2,1)",399840,63,"lower bound",63,379960],[5,17,"f","(8,3,1,1,1,1,1,1)",272272,699,"lower bound",699,261832],[5,17,"f","(8,3,2,1,1,1,1)",972400,348,"lower bound",348,918000],[5,17,"f","(8,3,2,2,1,1)",1454112,29,"lower bound",29,1354248],[5,17,"f","(8,3,2,2,2)",742560,10,"lower bound",10,686680],[5,17,"f","(8,3,3,1,1,1)",1047200,13,"lower bound",13,965440],[5,17,"f","(8,3,3,2,1)",1429428,1302042,"upper bound",0,1302042],[5,17,"f","(8,3,3,3)",346528,311192,"upper bound",0,311192],[5,17,"f","(8,4,1,1,1,1,1)",486200,132,"lower bound",132,450080],[5,17,"f","(8,4,2,1,1,1)",1570800,14,"lower bound",14,1426080],[5,17,"f","(8,4,2,2,1)",1750320,1569480,"upper bound",0,1569480],[5,17,"f","(8,4,3,1,1)",1701700,1508850,"upper bound",0,1508850],[5,17,"f","(8,4,3,2)",1299480,1141420,"upper bound",0,1141420],[5,17,"f","(8,4,4,1)",618800,533200,"upper bound",0,533200],[5,17,"f","(8,5,1,1,1,1)",523600,9,"lower bound",9,460200],[5,17,"f","(8,5,2,1,1)",1361360,1174320,"upper bound",0,1174320],[5,17,"f","(8,5,2,2)",848640,724960,"upper bound",0,724960],[5,17,"f","(8,5,3,1)",1113840,939960,"upper bound",0,939960],[5,17,"f","(8,5,4)",272272,223928,"upper bound",0,223928],[5,17,"f","(8,6,1,1,1)",340340,279730,"upper bound",0,279730],[5,17,"f","(8,6,2,1)",618800,500320,"upper bound",0,500320],[5,17,"f","(8,6,3)",272272,216048,"upper bound",0,216048],[5,17,"f","(8,7,1,1)",123760,93520,"upper bound",0,93520],[5,17,"f","(8,7,2)",116688,87072,"upper bound",0,87072],[5,17,"f","(8,8,1)",19448,0,"exact",0,0],[5,17,"f","(9,1,1,1,1,1,1,1,1)",12870,106,"lower bound",106,821],[5,17,"f","(9,2,1,1,1,1,1,1)",85085,174,"lower bound",174,78375],[5,17,"f","(9,2,2,1,1,1,1)",233376,104,"lower bound",104,208200],[5,17,"f","(9,2,2,2,1,1)",318240,10,"lower bound",10,277740],[5,17,"f","(9,2,2,2,2)",157080,5,"lower bound",5,135540],[5,17,"f","(9,3,1,1,1,1,1)",238238,73,"lower bound",73,208383],[5,17,"f","(9,3,2,1,1,1)",700128,10,"lower bound",10,594792],[5,17,"f","(9,3,2,2,1)",749700,625590,"upper bound",0,625590],[5,17,"f","(9,3,3,1,1)",586432,481488,"upper bound",0,481488],[5,17,"f","(9,3,3,2)",433160,351120,"upper bound",0,351120],[5,17,"f","(9,4,1,1,1,1)",364650,2,"lower bound",2,300105],[5,17,"f","(9,4,2,1,1)",908820,729270,"upper bound",0,729270],[5,17,"f","(9,4,2,2)",556920,441180,"upper bound",0,441180],[5,17,"f","(9,4,3,1)",680680,530520,"upper bound",0,530520],[5,17,"f","(9,4,4)",129948,97902,"upper bound",0,97902],[5,17,"f","(9,5,1,1,1)",327250,250965,"upper bound",0,250965],[5,17,"f","(9,5,2,1)",583440,438360,"upper bound",0,438360],[5,17,"f","(9,5,3)",247520,181680,"upper bound",0,181680],[5,17,"f","(9,6,1,1)",170170,120345,"upper bound",0,120345],[5,17,"f","(9,6,2)",159120,110880,"upper bound",0,110880],[5,17,"f","(9,7,1)",46410,29925,"upper bound",0,29925],[5,17,"f","(9,8)",4862,0,"exact",0,0],[5,18,"f","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[5,18,"f","(10,1,1,1,1,1,1,1,1)",24310,119,"lower bound",119,23595],[5,18,"f","(10,2,1,1,1,1,1,1)",162162,198,"lower bound",198,152163],[5,18,"f","(10,2,2,1,1,1,1)",447525,118,"lower bound",118,409365],[5,18,"f","(10,2,2,2,1,1)",612612,13,"lower bound",13,550617],[5,18,"f","(10,2,2,2,2)",302940,5,"lower bound",5,269820],[5,18,"f","(10,3,1,1,1,1,1)",459459,85,"lower bound",85,413721],[5,18,"f","(10,3,2,1,1,1)",1357824,14,"lower bound",14,1194384],[5,18,"f","(10,3,2,2,1)",1458600,1264680,"upper bound",0,1264680],[5,18,"f","(10,3,3,1,1)",1145664,980496,"upper bound",0,980496],[5,18,"f","(10,3,3,2)",848232,718488,"upper bound",0,718488],[5,18,"f","(10,4,1,1,1,1)",714714,3,"lower bound",3,612885],[5,18,"f","(10,4,2,1,1)",1790100,1504080,"upper bound",0,1504080],[5,18,"f","(10,4,2,2)",1099560,914340,"upper bound",0,914340],[5,18,"f","(10,4,3,1)",1349460,1107540,"upper bound",0,1107540],[5,18,"f","(10,4,4)",259896,207564,"upper bound",0,207564],[5,18,"f","(10,5,1,1,1)",656370,531765,"upper bound",0,531765],[5,18,"f","(10,5,2,1)",1175040,936360,"upper bound",0,936360],[5,18,"f","(10,5,3)",501228,391977,"upper bound",0,391977],[5,18,"f","(10,6,1,1)",353430,268245,"upper bound",0,268245],[5,18,"f","(10,6,2)",331500,248625,"upper bound",0,248625],[5,18,"f","(10,7,1)",102102,71943,"upper bound",0,71943],[5,18,"f","(10,8)",11934,0,"exact",0,0],[5,18,"f","(11,1,1,1,1,1,1,1)",19448,13,"lower bound",13,358],[5,18,"f","(11,2,1,1,1,1,1)",112320,11,"lower bound",11,89100],[5,18,"f","(11,2,2,1,1,1)",255255,3,"lower bound",3,195030],[5,18,"f","(11,2,2,2,1)",251328,187968,"upper bound",0,187968],[5,18,"f","(11,3,1,1,1,1)",268515,1,"lower bound",1,200970],[5,18,"f","(11,3,2,1,1)",612612,444840,"upper bound",0,444840],[5,18,"f","(11,3,2,2)",363528,260172,"upper bound",0,260172],[5,18,"f","(11,3,3,1)",358020,251460,"upper bound",0,251460],[5,18,"f","(11,4,1,1,1)",339456,238920,"upper bound",0,238920],[5,18,"f","(11,4,2,1)",583440,401280,"upper bound",0,401280],[5,18,"f","(11,4,3)",228480,153120,"upper bound",0,153120],[5,18,"f","(11,5,1,1)",238680,157410,"upper bound",0,157410],[5,18,"f","(11,5,2)",219912,142758,"upper bound",0,142758],[5,18,"f","(11,6,1)",88128,54252,"upper bound",0,54252],[5,18,"f","(11,7)",13260,0,"exact",0,0],[5,18,"f","(12,1,1,1,1,1,1)",12376,2776,"upper bound",0,2776],[5,18,"f","(12,2,1,1,1,1)",60060,31845,"upper bound",0,31845],[5,18,"f","(12,2,2,1,1)",106029,54351,"upper bound",0,54351],[5,18,"f","(12,2,2,2)",58344,29370,"upper bound",0,29370],[5,18,"f","(12,3,1,1,1)",116025,58740,"upper bound",0,58740],[5,18,"f","(12,3,2,1)",182784,90024,"upper bound",0,90024],[5,18,"f","(12,3,3)",56100,26895,"upper bound",0,26895],[5,18,"f","(12,4,1,1)",111384,53790,"upper bound",0,53790],[5,18,"f","(12,4,2)",99144,46926,"upper bound",0,46926],[5,18,"f","(12,5,1)",53040,24420,"upper bound",0,24420],[5,18,"f","(12,6)",9996,0,"exact",0,0],[5,18,"f","(13,1,1,1,1,1)",6188,0,"exact",0,0],[5,18,"f","(13,2,1,1,1)",24192,5148,"upper bound",0,5148],[5,18,"f","(13,2,2,1)",29835,6435,"upper bound",0,6435],[5,18,"f","(13,3,1,1)",35343,7722,"upper bound",0,7722],[5,18,"f","(13,3,2)",29172,6435,"upper bound",0,6435],[5,18,"f","(13,4,1)",22848,5148,"upper bound",0,5148],[5,18,"f","(13,5)",5508,0,"exact",0,0],[5,18,"f","(14,1,1,1,1)",2380,0,"exact",0,0],[5,18,"f","(14,2,1,1)",7020,0,"exact",0,0],[5,18,"f","(14,2,2)",4641,0,"exact",0,0],[5,18,"f","(14,3,1)",6885,0,"exact",0,0],[5,18,"f","(14,4)",2244,0,"exact",0,0],[5,18,"f","(15,1,1,1)",680,0,"exact",0,0],[5,18,"f","(15,2,1)",1344,0,"exact",0,0],[5,18,"f","(15,3)",663,0,"exact",0,0],[5,18,"f","(16,1,1)",136,0,"exact",0,0],[5,18,"f","(16,2)",135,0,"exact",0,0],[5,18,"f","(17,1)",17,0,"exact",0,0],[5,18,"f","(18)",1,0,"exact",0,0],[5,18,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",17,14,"lower bound",14,17],[5,18,"f","(2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",135,83,"lower bound",83,112],[5,18,"f","(2,2,2,1,1,1,1,1,1,1,1,1,1,1,1)",663,288,"lower bound",288,663],[5,18,"f","(2,2,2,2,1,1,1,1,1,1,1,1,1,1)",2244,656,"lower bound",656,2244],[5,18,"f","(2,2,2,2,2,1,1,1,1,1,1,1,1)",5508,1026,"lower bound",1026,5508],[5,18,"f","(2,2,2,2,2,2,1,1,1,1,1,1)",9996,1112,"lower bound",1112,9996],[5,18,"f","(2,2,2,2,2,2,2,1,1,1,1)",13260,822,"lower bound",822,13260],[5,18,"f","(2,2,2,2,2,2,2,2,1,1)",11934,397,"lower bound",397,11934],[5,18,"f","(2,2,2,2,2,2,2,2,2)",4862,99,"lower bound",99,4862],[5,18,"f","(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",136,84,"lower bound",84,113],[5,18,"f","(3,2,1,1,1,1,1,1,1,1,1,1,1,1,1)",1344,585,"lower bound",585,1344],[5,18,"f","(3,2,2,1,1,1,1,1,1,1,1,1,1,1)",6885,2001,"lower bound",2001,6885],[5,18,"f","(3,2,2,2,1,1,1,1,1,1,1,1,1)",22848,4177,"lower bound",4177,22848],[5,18,"f","(3,2,2,2,2,1,1,1,1,1,1,1)",53040,5691,"lower bound",5691,53040],[5,18,"f","(3,2,2,2,2,2,1,1,1,1,1)",88128,5129,"lower bound",5129,88128],[5,18,"f","(3,2,2,2,2,2,2,1,1,1)",102102,2992,"lower bound",2992,102102],[5,18,"f","(3,2,2,2,2,2,2,2,1)",70720,1049,"lower bound",1049,70720],[5,18,"f","(3,3,1,1,1,1,1,1,1,1,1,1,1,1)",4641,1347,"lower bound",1347,4641],[5,18,"f","(3,3,2,1,1,1,1,1,1,1,1,1,1)",29172,5280,"lower bound",5280,29172],[5,18,"f","(3,3,2,2,1,1,1,1,1,1,1,1)",99144,10380,"lower bound",10380,99144],[5,18,"f","(3,3,2,2,2,1,1,1,1,1,1)",219912,12222,"lower bound",12222,219912],[5,18,"f","(3,3,2,2,2,2,1,1,1,1)",331500,8909,"lower bound",8909,331500],[5,18,"f","(3,3,2,2,2,2,2,1,1)",322218,3900,"lower bound",3900,322218],[5,18,"f","(3,3,2,2,2,2,2,2)",136136,836,"lower bound",836,136136],[5,18,"f","(3,3,3,1,1,1,1,1,1,1,1,1)",56100,5795,"lower bound",5795,56100],[5,18,"f","(3,3,3,2,1,1,1,1,1,1,1)",228480,12311,"lower bound",12311,228480],[5,18,"f","(3,3,3,2,2,1,1,1,1,1)",501228,12686,"lower bound",12686,501228],[5,18,"f","(3,3,3,2,2,2,1,1,1)",678912,7241,"lower bound",7241,678912],[5,18,"f","(3,3,3,2,2,2,2,1)",510510,2193,"lower bound",2193,510510],[5,18,"f","(3,3,3,3,1,1,1,1,1,1)",259896,6372,"lower bound",6372,259896],[5,18,"f","(3,3,3,3,2,1,1,1,1)",649740,6456,"lower bound",6456,649735],[5,18,"f","(3,3,3,3,2,2,1,1)",787644,2804,"lower bound",2804,787629],[5,18,"f","(3,3,3,3,2,2,2)",364650,492,"lower bound",492,364640],[5,18,"f","(3,3,3,3,3,1,1,1)",408408,1347,"lower bound",1347,408392],[5,18,"f","(3,3,3,3,3,2,1)",466752,459,"lower bound",459,466720],[5,18,"f","(3,3,3,3,3,3)",87516,20,"lower bound",20,87505],[5,18,"f","(4,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",680,298,"lower bound",298,458],[5,18,"f","(4,2,1,1,1,1,1,1,1,1,1,1,1,1)",7020,2043,"lower bound",2043,7020],[5,18,"f","(4,2,2,1,1,1,1,1,1,1,1,1,1)",35343,6400,"lower bound",6400,35343],[5,18,"f","(4,2,2,2,1,1,1,1,1,1,1,1)",111384,11659,"lower bound",11659,111384],[5,18,"f","(4,2,2,2,2,1,1,1,1,1,1)",238680,13288,"lower bound",13288,238680],[5,18,"f","(4,2,2,2,2,2,1,1,1,1)",353430,9578,"lower bound",9578,353430],[5,18,"f","(4,2,2,2,2,2,2,1,1)",340340,4222,"lower bound",4222,340340],[5,18,"f","(4,2,2,2,2,2,2,2)",143208,927,"lower bound",927,143208],[5,18,"f","(4,3,1,1,1,1,1,1,1,1,1,1,1)",29835,5378,"lower bound",5378,29835],[5,18,"f","(4,3,2,1,1,1,1,1,1,1,1,1)",182784,18802,"lower bound",18802,182784],[5,18,"f","(4,3,2,2,1,1,1,1,1,1,1)",583440,30775,"lower bound",30775,583440],[5,18,"f","(4,3,2,2,2,1,1,1,1,1)",1175040,28027,"lower bound",28027,1175040],[5,18,"f","(4,3,2,2,2,2,1,1,1)",1531530,14519,"lower bound",14519,1531530],[5,18,"f","(4,3,2,2,2,2,2,1)",1131520,4079,"lower bound",4079,1131520],[5,18,"f","(4,3,3,1,1,1,1,1,1,1,1)",358020,18782,"lower bound",18782,358020],[5,18,"f","(4,3,3,2,1,1,1,1,1,1)",1349460,30846,"lower bound",30846,1349460],[5,18,"f","(4,3,3,2,2,1,1,1,1)",2625480,21716,"lower bound",21716,2625435],[5,18,"f","(4,3,3,2,2,2,1,1)",2923830,7379,"lower bound",7379,2923695],[5,18,"f","(4,3,3,2,2,2,2)",1312740,1145,"lower bound",1145,1312650],[5,18,"f","(4,3,3,3,1,1,1,1,1)",1429428,11324,"lower bound",11324,1429358],[5,18,"f","(4,3,3,3,2,1,1,1)",3055104,6562,"lower bound",6562,3054720],[5,18,"f","(4,3,3,3,2,2,1)",2756754,1451,"lower bound",1451,2756196],[5,18,"f","(4,3,3,3,3,1,1)",1575288,681,"lower bound",681,1574808],[5,18,"f","(4,3,3,3,3,2)",1021020,109,"lower bound",109,1020610],[5,18,"f","(4,4,1,1,1,1,1,1,1,1,1,1)",58344,5938,"lower bound",5938,58344],[5,18,"f","(4,4,2,1,1,1,1,1,1,1,1)",363528,18922,"lower bound",18922,363528],[5,18,"f","(4,4,2,2,1,1,1,1,1,1)",1099560,24603,"lower bound",24603,1099560],[5,18,"f","(4,4,2,2,2,1,1,1,1)",1989000,15413,"lower bound",15413,1988950],[5,18,"f","(4,4,2,2,2,2,1,1)",2148120,4712,"lower bound",4712,2147970],[5,18,"f","(4,4,2,2,2,2,2)",952952,704,"lower bound",704,952852],[5,18,"f","(4,4,3,1,1,1,1,1,1,1)",848232,19510,"lower bound",19510,848232],[5,18,"f","(4,4,3,2,1,1,1,1,1)",2970240,22689,"lower bound",22689,2969960],[5,18,"f","(4,4,3,2,2,1,1,1)",5012280,9056,"lower bound",9056,5011080],[5,18,"f","(4,4,3,2,2,2,1)",4200768,1561,"lower bound",1561,4199208],[5,18,"f","(4,4,3,3,1,1,1,1)",3007368,5237,"lower bound",5237,3006192],[5,18,"f","(4,4,3,3,2,1,1)",5250960,1393,"lower bound",1393,5247480],[5,18,"f","(4,4,3,3,2,2)",2756754,177,"lower bound",177,2754450],[5,18,"f","(4,4,3,3,3,1)",2042040,80,"lower bound",80,2039760],[5,18,"f","(4,4,4,1,1,1,1,1,1)",779688,6396,"lower bound",6396,779513],[5,18,"f","(4,4,4,2,1,1,1,1)",2598960,4542,"lower bound",4542,2597420],[5,18,"f","(4,4,4,2,2,1,1)",3675672,795,"lower bound",795,3672132],[5,18,"f","(4,4,4,2,2,2)",1823250,98,"lower bound",98,1821075],[5,18,"f","(4,4,4,3,1,1,1)",2858856,553,"lower bound",553,2855084],[5,18,"f","(4,4,4,3,2,1)",3734016,99,"lower bound",99,3727320],[5,18,"f","(4,4,4,3,3)",875160,6,"lower bound",6,873000],[5,18,"f","(4,4,4,4,1,1)",1021020,22,"lower bound",22,1018315],[5,18,"f","(4,4,4,4,2)",787644,2,"lower bound",2,785145],[5,18,"f","(5,1,1,1,1,1,1,1,1,1,1,1,1,1)",2380,699,"lower bound",699,2380],[5,18,"f","(5,2,1,1,1,1,1,1,1,1,1,1,1)",24192,4378,"lower bound",4378,24192],[5,18,"f","(5,2,2,1,1,1,1,1,1,1,1,1)",116025,11949,"lower bound",11949,116025],[5,18,"f","(5,2,2,2,1,1,1,1,1,1,1)",339456,18232,"lower bound",18232,339456],[5,18,"f","(5,2,2,2,2,1,1,1,1,1)",656370,16738,"lower bound",16738,656370],[5,18,"f","(5,2,2,2,2,2,1,1,1)",837760,9304,"lower bound",9304,837760],[5,18,"f","(5,2,2,2,2,2,2,1)",612612,2967,"lower bound",2967,612612],[5,18,"f","(5,3,1,1,1,1,1,1,1,1,1,1)",106029,10801,"lower bound",10801,106029],[5,18,"f","(5,3,2,1,1,1,1,1,1,1,1)",612612,31384,"lower bound",31384,612612],[5,18,"f","(5,3,2,2,1,1,1,1,1,1)",1790100,39568,"lower bound",39568,1790100],[5,18,"f","(5,3,2,2,2,1,1,1,1)",3180870,25514,"lower bound",25514,3180765],[5,18,"f","(5,3,2,2,2,2,1,1)",3403400,8768,"lower bound",8768,3403085],[5,18,"f","(5,3,2,2,2,2,2)",1503684,1554,"lower bound",1554,1503474],[5,18,"f","(5,3,3,1,1,1,1,1,1,1)",1145664,24800,"lower bound",24800,1145664],[5,18,"f","(5,3,3,2,1,1,1,1,1)",3877632,27552,"lower bound",27552,3877152],[5,18,"f","(5,3,3,2,2,1,1,1)",6432426,11406,"lower bound",11406,6430410],[5,18,"f","(5,3,3,2,2,2,1)",5346432,2407,"lower bound",2407,5343840],[5,18,"f","(5,3,3,3,1,1,1,1)",3646500,5671,"lower bound",5671,3644650],[5,18,"f","(5,3,3,3,2,1,1)",6265350,1782,"lower bound",1782,6259980],[5,18,"f","(5,3,3,3,2,2)",3267264,228,"lower bound",228,3263744],[5,18,"f","(5,3,3,3,3,1)",2362932,93,"lower bound",93,2359542],[5,18,"f","(5,4,1,1,1,1,1,1,1,1,1)",251328,12805,"lower bound",12805,251328],[5,18,"f","(5,4,2,1,1,1,1,1,1,1)",1458600,31492,"lower bound",31492,1458600],[5,18,"f","(5,4,2,2,1,1,1,1,1)",3965760,27709,"lower bound",27709,3965040],[5,18,"f","(5,4,2,2,2,1,1,1)",6126120,10222,"lower bound",10222,6123320],[5,18,"f","(5,4,2,2,2,2,1)",4950400,2066,"lower bound",2066,4946960],[5,18,"f","(5,4,3,1,1,1,1,1,1)",3198720,22888,"lower bound",22888,3197600],[5,18,"f","(5,4,3,2,1,1,1,1)",9801792,14658,"lower bound",14658,9792968],[5,18,"f","(5,4,3,2,2,1,1)",13366080,3082,"lower bound",3082,13346760],[5,18,"f","(5,4,3,2,2,2)",6534528,380,"lower bound",380,6522912],[5,18,"f","(5,4,3,3,1,1,1)",8486400,1602,"lower bound",1602,8469820],[5,18,"f","(5,4,3,3,2,1)",10720710,265,"lower bound",265,10692510],[5,18,"f","(5,4,3,3,3)",2333760,12,"lower bound",12,2325420],[5,18,"f","(5,4,4,1,1,1,1,1)",2858856,4554,"lower bound",4554,2854271],[5,18,"f","(5,4,4,2,1,1,1)",8019648,1376,"lower bound",1376,7998060],[5,18,"f","(5,4,4,2,2,1)",8270262,182,"lower bound",182,8241153],[5,18,"f","(5,4,4,3,1,1)",7088796,134,"lower bound",134,7057701],[5,18,"f","(5,4,4,3,2)",5105100,6,"lower bound",6,5078715],[5,18,"f","(5,4,4,4,1)",1867008,1854020,"upper bound",0,1854020],[5,18,"f","(5,5,1,1,1,1,1,1,1,1)",302940,6633,"lower bound",6633,302940],[5,18,"f","(5,5,2,1,1,1,1,1,1)",1649340,11579,"lower bound",11579,1648360],[5,18,"f","(5,5,2,2,1,1,1,1)",3978000,5726,"lower bound",5726,3972200],[5,18,"f","(5,5,2,2,2,1,1)",5012280,1160,"lower bound",1160,5000880],[5,18,"f","(5,5,2,2,2,2)",2382380,143,"lower bound",143,2375800],[5,18,"f","(5,5,3,1,1,1,1,1)",3508596,5278,"lower bound",5278,3501120],[5,18,"f","(5,5,3,2,1,1,1)",9165312,1602,"lower bound",1602,9133092],[5,18,"f","(5,5,3,2,2,1)",9189180,193,"lower bound",193,9147360],[5,18,"f","(5,5,3,3,1,1)",6534528,112,"lower bound",112,6497768],[5,18,"f","(5,5,3,3,2)",4594590,4,"lower bound",4,4564380],[5,18,"f","(5,5,4,1,1,1,1)",3508596,553,"lower bound",553,3490074],[5,18,"f","(5,5,4,2,1,1)",7876440,134,"lower bound",134,7819875],[5,18,"f","(5,5,4,2,2)",4594590,4556580,"upper bound",0,4556580],[5,18,"f","(5,5,4,3,1)",5105100,5055190,"upper bound",0,5055190],[5,18,"f","(5,5,4,4)",787644,777180,"upper bound",0,777180],[5,18,"f","(5,5,5,1,1,1)",1429428,22,"lower bound",22,1413727],[5,18,"f","(5,5,5,2,1)",2333760,2302820,"upper bound",0,2302820],[5,18,"f","(5,5,5,3)",875160,861050,"upper bound",0,861050],[5,18,"f","(6,1,1,1,1,1,1,1,1,1,1,1,1)",6188,1130,"lower bound",1130,6188],[5,18,"f","(6,2,1,1,1,1,1,1,1,1,1,1)",60060,6131,"lower bound",6131,60060],[5,18,"f","(6,2,2,1,1,1,1,1,1,1,1)",268515,13953,"lower bound",13953,268515],[5,18,"f","(6,2,2,2,1,1,1,1,1,1)",714714,17013,"lower bound",17013,714714],[5,18,"f","(6,2,2,2,2,1,1,1,1)",1215500,11850,"lower bound",11850,1215430],[5,18,"f","(6,2,2,2,2,2,1,1)",1272348,4715,"lower bound",4715,1272138],[5,18,"f","(6,2,2,2,2,2,2)",556920,927,"lower bound",927,556780],[5,18,"f","(6,3,1,1,1,1,1,1,1,1,1)",255255,12963,"lower bound",12963,255255],[5,18,"f","(6,3,2,1,1,1,1,1,1,1)",1357824,29072,"lower bound",29072,1357824],[5,18,"f","(6,3,2,2,1,1,1,1,1)",3544398,25603,"lower bound",25603,3543453],[5,18,"f","(6,3,2,2,2,1,1,1)",5361664,10529,"lower bound",10529,5358080],[5,18,"f","(6,3,2,2,2,2,1)",4288284,2529,"lower bound",2529,4283951],[5,18,"f","(6,3,3,1,1,1,1,1,1)",2333760,15725,"lower bound",15725,2332560],[5,18,"f","(6,3,3,2,1,1,1,1)",6872250,9936,"lower bound",9936,6863325],[5,18,"f","(6,3,3,2,2,1,1)",9189180,2476,"lower bound",2476,9170175],[5,18,"f","(6,3,3,2,2,2)",4455360,402,"lower bound",402,4444080],[5,18,"f","(6,3,3,3,1,1,1)",5469750,1045,"lower bound",1045,5454600],[5,18,"f","(6,3,3,3,2,1)",6789120,213,"lower bound",213,6763960],[5,18,"f","(6,3,3,3,3)",1429428,6,"lower bound",6,1422293],[5,18,"f","(6,4,1,1,1,1,1,1,1,1)",612612,13247,"lower bound",13247,612612],[5,18,"f","(6,4,2,1,1,1,1,1,1)",3222180,22157,"lower bound",22157,3219750],[5,18,"f","(6,4,2,2,1,1,1,1)",7634088,11022,"lower bound",11022,7620102],[5,18,"f","(6,4,2,2,2,1,1)",9529520,2412,"lower bound",2412,9502430],[5,18,"f","(6,4,2,2,2,2)",4511052,398,"lower bound",398,4495518],[5,18,"f","(6,4,3,1,1,1,1,1)",6361740,8970,"lower bound",8970,6344790],[5,18,"f","(6,4,3,2,1,1,1)",16336320,2724,"lower bound",2724,16265060],[5,18,"f","(6,4,3,2,2,1)",16243500,420,"lower bound",420,16152150],[5,18,"f","(6,4,3,3,1,1)",11277630,193,"lower bound",193,11199555],[5,18,"f","(6,4,3,3,2)",7876440,6,"lower bound",6,7812900],[5,18,"f","(6,4,4,1,1,1,1)",5105100,731,"lower bound",731,5071885],[5,18,"f","(6,4,4,2,1,1)",11277630,182,"lower bound",182,11178405],[5,18,"f","(6,4,4,2,2)",6534528,6468492,"upper bound",0,6468492],[5,18,"f","(6,4,4,3,1)",7088796,7004439,"upper bound",0,7004439],[5,18,"f","(6,4,4,4)",1021020,1004615,"upper bound",0,1004615],[5,18,"f","(6,5,1,1,1,1,1,1,1)",875160,6505,"lower bound",6505,873690],[5,18,"f","(6,5,2,1,1,1,1,1)",4230144,6299,"lower bound",6299,4212480],[5,18,"f","(6,5,2,2,1,1,1)",8576568,1469,"lower bound",1469,8520288],[5,18,"f","(6,5,2,2,2,1)",7920640,207,"lower bound",207,7855240],[5,18,"f","(6,5,3,1,1,1,1)",7876440,1195,"lower bound",1195,7810800],[5,18,"f","(6,5,3,2,1,1)",16243500,253,"lower bound",253,16063075],[5,18,"f","(6,5,3,2,2)",9189180,9072900,"upper bound",0,9072900],[5,18,"f","(6,5,3,3,1)",8270262,8147982,"upper bound",0,8147982],[5,18,"f","(6,5,4,1,1,1)",6789120,93,"lower bound",93,6688360],[5,18,"f","(6,5,4,2,1)",10720710,10530310,"upper bound",0,10530310],[5,18,"f","(6,5,4,3)",3734016,3654080,"upper bound",0,3654080],[5,18,"f","(6,5,5,1,1)",2362932,2304858,"upper bound",0,2304858],[5,18,"f","(6,5,5,2)",2042040,1986430,"upper bound",0,1986430],[5,18,"f","(6,6,1,1,1,1,1,1)",659736,1181,"lower bound",1181,654150],[5,18,"f","(6,6,2,1,1,1,1)",2784600,483,"lower bound",483,2747280],[5,18,"f","(6,6,2,2,1,1)",4511052,81,"lower bound",81,4433337],[5,18,"f","(6,6,2,2,2)",2382380,2336390,"upper bound",0,2336390],[5,18,"f","(6,6,3,1,1,1)",4455360,68,"lower bound",68,4365160],[5,18,"f","(6,6,3,2,1)",6534528,6378508,"upper bound",0,6378508],[5,18,"f","(6,6,3,3)",1823250,1771600,"upper bound",0,1771600],[5,18,"f","(6,6,4,1,1)",3267264,3170716,"upper bound",0,3170716],[5,18,"f","(6,6,4,2)",2756754,2666910,"upper bound",0,2666910],[5,18,"f","(6,6,5,1)",1021020,978140,"upper bound",0,978140],[5,18,"f","(6,6,6)",87516,82405,"upper bound",0,82405],[5,18,"f","(7,1,1,1,1,1,1,1,1,1,1,1)",12376,1262,"lower bound",1262,12376],[5,18,"f","(7,2,1,1,1,1,1,1,1,1,1)",112320,5649,"lower bound",5649,112320],[5,18,"f","(7,2,2,1,1,1,1,1,1,1)",459459,10247,"lower bound",10247,459459],[5,18,"f","(7,2,2,2,1,1,1,1,1)",1089088,9322,"lower bound",9322,1088528],[5,18,"f","(7,2,2,2,2,1,1,1)",1575288,4395,"lower bound",4395,1573272],[5,18,"f","(7,2,2,2,2,2,1)",1233792,1143,"lower bound",1143,1231440],[5,18,"f","(7,3,1,1,1,1,1,1,1,1)",447525,9545,"lower bound",9545,447525],[5,18,"f","(7,3,2,1,1,1,1,1,1)",2144142,15195,"lower bound",15195,2141517],[5,18,"f","(7,3,2,2,1,1,1,1)",4862000,8203,"lower bound",8203,4847860],[5,18,"f","(7,3,2,2,2,1,1)",5937624,2042,"lower bound",2042,5911164],[5,18,"f","(7,3,2,2,2,2)",2784600,433,"lower bound",433,2769655],[5,18,"f","(7,3,3,1,1,1,1,1)",3281850,4784,"lower bound",4784,3268125],[5,18,"f","(7,3,3,2,1,1,1)",8078400,1569,"lower bound",1569,8024040],[5,18,"f","(7,3,3,2,2,1)",7876440,299,"lower bound",299,7808775],[5,18,"f","(7,3,3,3,1,1)",5105100,87,"lower bound",87,5051585],[5,18,"f","(7,3,3,3,2)",3508596,7,"lower bound",7,3466071],[5,18,"f","(7,4,1,1,1,1,1,1,1)",1018368,7372,"lower bound",7372,1015968],[5,18,"f","(7,4,2,1,1,1,1,1)",4725864,7126,"lower bound",7126,4698774],[5,18,"f","(7,4,2,2,1,1,1)",9382912,1705,"lower bound",1705,9299360],[5,18,"f","(7,4,2,2,2,1)",8576568,299,"lower bound",299,8481102],[5,18,"f","(7,4,3,1,1,1,1)",8078400,1258,"lower bound",1258,7987740],[5,18,"f","(7,4,3,2,1,1)",16336320,224,"lower bound",224,16094040],[5,18,"f","(7,4,3,2,2)",9165312,10,"lower bound",10,9011148],[5,18,"f","(7,4,3,3,1)",8019648,7862820,"upper bound",0,7862820],[5,18,"f","(7,4,4,1,1,1)",5469750,58,"lower bound",58,5362450],[5,18,"f","(7,4,4,2,1)",8486400,8288420,"upper bound",0,8288420],[5,18,"f","(7,4,4,3)",2858856,2778986,"upper bound",0,2778986],[5,18,"f","(7,5,1,1,1,1,1,1)",1432080,2463,"lower bound",2463,1417320],[5,18,"f","(7,5,2,1,1,1,1)",5937624,988,"lower bound",988,5841696],[5,18,"f","(7,5,2,2,1,1)",9529520,136,"lower bound",136,9332680],[5,18,"f","(7,5,2,2,2)",5012280,5,"lower bound",5,4896570],[5,18,"f","(7,5,3,1,1,1)",9189180,105,"lower bound",105,8967045],[5,18,"f","(7,5,3,2,1)",13366080,12986460,"upper bound",0,12986460],[5,18,"f","(7,5,3,3)",3675672,3552318,"upper bound",0,3552318],[5,18,"f","(7,5,4,1,1)",6265350,6046380,"upper bound",0,6046380],[5,18,"f","(7,5,4,2)",5250960,5049030,"upper bound",0,5049030],[5,18,"f","(7,5,5,1)",1575288,1497792,"upper bound",0,1497792],[5,18,"f","(7,6,1,1,1,1,1)",1233792,254,"lower bound",254,1199880],[5,18,"f","(7,6,2,1,1,1)",4288284,73,"lower bound",73,4136279],[5,18,"f","(7,6,2,2,1)",4950400,4749360,"upper bound",0,4749360],[5,18,"f","(7,6,3,1,1)",5346432,5103780,"upper bound",0,5103780],[5,18,"f","(7,6,3,2)",4200768,3993252,"upper bound",0,3993252],[5,18,"f","(7,6,4,1)",2756754,2597634,"upper bound",0,2597634],[5,18,"f","(7,6,5)",466752,432720,"upper bound",0,432720],[5,18,"f","(7,7,1,1,1,1)",556920,16,"lower bound",16,524910],[5,18,"f","(7,7,2,1,1)",1503684,1403556,"upper bound",0,1403556],[5,18,"f","(7,7,2,2)",952952,884968,"upper bound",0,884968],[5,18,"f","(7,7,3,1)",1312740,1211220,"upper bound",0,1211220],[5,18,"f","(7,7,4)",364650,331840,"upper bound",0,331840],[5,18,"f","(8,1,1,1,1,1,1,1,1,1,1)",19448,947,"lower bound",947,19448],[5,18,"f","(8,2,1,1,1,1,1,1,1,1)",162162,3316,"lower bound",3316,162162],[5,18,"f","(8,2,2,1,1,1,1,1,1)",595595,4546,"lower bound",4546,594055],[5,18,"f","(8,2,2,2,1,1,1,1)",1225224,2734,"lower bound",2734,1218000],[5,18,"f","(8,2,2,2,2,1,1)",1432080,732,"lower bound",732,1419480],[5,18,"f","(8,2,2,2,2,2)",659736,180,"lower bound",180,652820],[5,18,"f","(8,3,1,1,1,1,1,1,1)",590733,4145,"lower bound",4145,588258],[5,18,"f","(8,3,2,1,1,1,1,1)",2489344,4234,"lower bound",4234,2465024],[5,18,"f","(8,3,2,2,1,1,1)",4725864,1174,"lower bound",1174,4655736],[5,18,"f","(8,3,2,2,2,1)",4230144,236,"lower bound",236,4152720],[5,18,"f","(8,3,3,1,1,1,1)",3281850,686,"lower bound",686,3221370],[5,18,"f","(8,3,3,2,1,1)",6361740,90,"lower bound",90,6209385],[5,18,"f","(8,3,3,2,2)",3508596,15,"lower bound",15,3414180],[5,18,"f","(8,3,3,3,1)",2858856,2770264,"upper bound",0,2770264],[5,18,"f","(8,4,1,1,1,1,1,1)",1225224,2043,"lower bound",2043,1206474],[5,18,"f","(8,4,2,1,1,1,1)",4862000,922,"lower bound",922,4747840],[5,18,"f","(8,4,2,2,1,1)",7634088,91,"lower bound",91,7407648],[5,18,"f","(8,4,2,2,2)",3978000,15,"lower bound",15,3846900],[5,18,"f","(8,4,3,1,1,1)",6872250,57,"lower bound",57,6635825],[5,18,"f","(8,4,3,2,1)",9801792,9408952,"upper bound",0,9408952],[5,18,"f","(8,4,3,3)",2598960,2477020,"upper bound",0,2477020],[5,18,"f","(8,4,4,1,1)",3646500,3468900,"upper bound",0,3468900],[5,18,"f","(8,4,4,2)",3007368,2847048,"upper bound",0,2847048],[5,18,"f","(8,5,1,1,1,1,1)",1575288,295,"lower bound",295,1519128],[5,18,"f","(8,5,2,1,1,1)",5361664,55,"lower bound",55,5117760],[5,18,"f","(8,5,2,2,1)",6126120,5808680,"upper bound",0,5808680],[5,18,"f","(8,5,3,1,1)",6432426,6061860,"upper bound",0,6061860],[5,18,"f","(8,5,3,2)",5012280,4699170,"upper bound",0,4699170],[5,18,"f","(8,5,4,1)",3055104,2833800,"upper bound",0,2833800],[5,18,"f","(8,5,5)",408408,371478,"upper bound",0,371478],[5,18,"f","(8,6,1,1,1,1)",1272348,25,"lower bound",25,1187037],[5,18,"f","(8,6,2,1,1)",3403400,3140260,"upper bound",0,3140260],[5,18,"f","(8,6,2,2)",2148120,1970580,"upper bound",0,1970580],[5,18,"f","(8,6,3,1)",2923830,2662590,"upper bound",0,2662590],[5,18,"f","(8,6,4)",787644,706191,"upper bound",0,706191],[5,18,"f","(8,7,1,1,1)",612612,544758,"upper bound",0,544758],[5,18,"f","(8,7,2,1)",1131520,995600,"upper bound",0,995600],[5,18,"f","(8,7,3)",510510,443765,"upper bound",0,443765],[5,18,"f","(8,8,1,1)",143208,119232,"upper bound",0,119232],[5,18,"f","(8,8,2)",136136,112364,"upper bound",0,112364],[5,18,"f","(9,1,1,1,1,1,1,1,1,1)",24310,449,"lower bound",449,24310],[5,18,"f","(9,2,1,1,1,1,1,1,1)",183040,1147,"lower bound",1147,181280],[5,18,"f","(9,2,2,1,1,1,1,1)",590733,1104,"lower bound",1104,578457],[5,18,"f","(9,2,2,2,1,1,1)",1018368,342,"lower bound",342,987528],[5,18,"f","(9,2,2,2,2,1)",875160,78,"lower bound",78,843300],[5,18,"f","(9,3,1,1,1,1,1,1)",595595,946,"lower bound",946,579040],[5,18,"f","(9,3,2,1,1,1,1)",2144142,535,"lower bound",535,2056110],[5,18,"f","(9,3,2,2,1,1)",3222180,49,"lower bound",49,3058695],[5,18,"f","(9,3,2,2,2)",1649340,15,"lower bound",15,1557360],[5,18,"f","(9,3,3,1,1,1)",2333760,23,"lower bound",23,2198520],[5,18,"f","(9,3,3,2,1)",3198720,2986200,"upper bound",0,2986200],[5,18,"f","(9,3,3,3)",779688,720132,"upper bound",0,720132],[5,18,"f","(9,4,1,1,1,1,1)",1089088,207,"lower bound",207,1029308],[5,18,"f","(9,4,2,1,1,1)",3544398,26,"lower bound",26,3301047],[5,18,"f","(9,4,2,2,1)",3965760,3659040,"upper bound",0,3659040],[5,18,"f","(9,4,3,1,1)",3877632,3547368,"upper bound",0,3547368],[5,18,"f","(9,4,3,2)",2970240,2697960,"upper bound",0,2697960],[5,18,"f","(9,4,4,1)",1429428,1279572,"upper bound",0,1279572],[5,18,"f","(9,5,1,1,1,1)",1215500,11,"lower bound",11,1104895],[5,18,"f","(9,5,2,1,1)",3180870,2850480,"upper bound",0,2850480],[5,18,"f","(9,5,2,2)",1989000,1769250,"upper bound",0,1769250],[5,18,"f","(9,5,3,1)",2625480,2313720,"upper bound",0,2313720],[5,18,"f","(9,5,4)",649740,561435,"upper bound",0,561435],[5,18,"f","(9,6,1,1,1)",837760,723860,"upper bound",0,723860],[5,18,"f","(9,6,2,1)",1531530,1306770,"upper bound",0,1306770],[5,18,"f","(9,6,3)",678912,571008,"upper bound",0,571008],[5,18,"f","(9,7,1,1)",340340,275890,"upper bound",0,275890],[5,18,"f","(9,7,2)",322218,258687,"upper bound",0,258687],[5,18,"f","(9,8,1)",70720,53000,"upper bound",0,53000],[5,18,"f","(9,9)",4862,0,"exact",0,0],[5,19,"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],[5,19,"f","(10,9)",16796,1392,"upper bound",0,1392],[5,19,"f","(13,1,1,1,1,1,1)",18564,11011,"upper bound",0,11011],[5,19,"f","(13,6)",15504,5904,"upper bound",0,5904],[5,19,"f","(14,1,1,1,1,1)",8568,2002,"upper bound",0,2002],[5,19,"f","(14,5)",7752,2002,"upper bound",0,2002],[5,19,"f","(15,1,1,1,1)",3060,0,"exact",0,0],[5,19,"f","(15,2,1,1)",9044,0,"exact",0,0],[5,19,"f","(15,2,2)",5985,0,"exact",0,0],[5,19,"f","(15,3,1)",8892,0,"exact",0,0],[5,19,"f","(15,4)",2907,0,"exact",0,0],[5,19,"f","(16,1,1,1)",816,0,"exact",0,0],[5,19,"f","(16,2,1)",1615,0,"exact",0,0],[5,19,"f","(16,3)",798,0,"exact",0,0],[5,19,"f","(17,1,1)",153,0,"exact",0,0],[5,19,"f","(17,2)",152,0,"exact",0,0],[5,19,"f","(18,1)",18,0,"exact",0,0],[5,19,"f","(19)",1,0,"exact",0,0],[5,19,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",18,15,"lower bound",15,18],[5,19,"f","(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",153,98,"lower bound",98,138],[5,20,"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],[5,20,"f","(10,10)",16796,13596,"upper bound",0,13596],[5,20,"f","(15,1,1,1,1,1)",11628,3003,"upper bound",0,3003],[5,20,"f","(15,5)",10659,3003,"upper bound",0,3003],[5,20,"f","(16,1,1,1,1)",3876,0,"exact",0,0],[5,20,"f","(16,2,1,1)",11475,0,"exact",0,0],[5,20,"f","(16,2,2)",7600,0,"exact",0,0],[5,20,"f","(16,3,1)",11305,0,"exact",0,0],[5,20,"f","(16,4)",3705,0,"exact",0,0],[5,20,"f","(17,1,1,1)",969,0,"exact",0,0],[5,20,"f","(17,2,1)",1920,0,"exact",0,0],[5,20,"f","(17,3)",950,0,"exact",0,0],[5,20,"f","(18,1,1)",171,0,"exact",0,0],[5,20,"f","(18,2)",170,0,"exact",0,0],[5,20,"f","(19,1)",19,0,"exact",0,0],[5,20,"f","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",19,16,"lower bound",16,19],[5,20,"f","(20)",1,0,"exact",0,0],[5,21,"f","(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],[5,21,"f","(16,1,1,1,1,1)",15504,4368,"upper bound",0,4368],[5,21,"f","(16,5)",14364,4368,"upper bound",0,4368],[5,21,"f","(17,1,1,1,1)",4845,0,"exact",0,0],[5,21,"f","(17,2,1,1)",14364,0,"exact",0,0],[5,21,"f","(17,2,2)",9520,0,"exact",0,0],[5,21,"f","(17,3,1)",14175,0,"exact",0,0],[5,21,"f","(17,4)",4655,0,"exact",0,0],[5,21,"f","(18,1,1,1)",1140,0,"exact",0,0],[5,21,"f","(18,2,1)",2261,0,"exact",0,0],[5,21,"f","(18,3)",1120,0,"exact",0,0],[5,21,"f","(19,1,1)",190,0,"exact",0,0],[5,21,"f","(19,2)",189,0,"exact",0,0],[5,21,"f","(20,1)",20,0,"exact",0,0],[5,21,"f","(21)",1,0,"exact",0,0],[5,22,"f","(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],[5,22,"f","(17,5)",19019,6188,"upper 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",0,0],[5,13,"p","(8,2,2,1)",3640,0,"exact",0,0],[5,13,"p","(8,3,1,1)",4212,0,"exact",0,0],[5,13,"p","(8,3,2)",3432,0,"exact",0,0],[5,13,"p","(8,4,1)",2574,0,"exact",0,0],[5,13,"p","(8,5)",572,0,"exact",0,0],[5,13,"p","(9,1,1,1,1)",495,0,"exact",0,0],[5,13,"p","(9,2,1,1)",1430,0,"exact",0,0],[5,13,"p","(9,2,2)",936,0,"exact",0,0],[5,13,"p","(9,3,1)",1365,0,"exact",0,0],[5,13,"p","(9,4)",429,0,"exact",0,0],[5,13,"p","(10,1,1,1)",220,0,"exact",0,0],[5,13,"p","(10,2,1)",429,0,"exact",0,0],[5,13,"p","(10,3)",208,0,"exact",0,0],[5,13,"p","(11,1,1)",66,0,"exact",0,0],[5,13,"p","(11,2)",65,0,"exact",0,0],[5,13,"p","(12,1)",12,0,"exact",0,0],[5,13,"p","(13)",1,0,"exact",0,0],[5,14,"p","(1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[5,14,"p","(2,1,1,1,1,1,1,1,1,1,1,1,1)",13,4,"exact",4,4],[5,14,"p","(2,2,1,1,1,1,1,1,1,1,1,1)",77,16,"exact",16,16],[5,14,"p","(2,2,2,1,1,1,1,1,1,1,1)",273,30,"exact",30,30],[5,14,"p","(2,2,2,2,1,1,1,1,1,1)",637,34,"exact",34,34],[5,14,"p","(2,2,2,2,2,1,1,1,1)",1001,19,"exact",19,19],[5,14,"p","(2,2,2,2,2,2,1,1)",1001,4,"exact",4,4],[5,14,"p","(2,2,2,2,2,2,2)",429,0,"exact",0,0],[5,14,"p","(3,1,1,1,1,1,1,1,1,1,1,1)",78,16,"exact",16,16],[5,14,"p","(3,2,1,1,1,1,1,1,1,1,1)",560,60,"exact",60,60],[5,14,"p","(3,2,2,1,1,1,1,1,1,1)",2002,100,"exact",100,100],[5,14,"p","(3,2,2,2,1,1,1,1,1)",4368,80,"exact",80,80],[5,14,"p","(3,2,2,2,2,1,1,1)",6006,27,"exact",27,27],[5,14,"p","(3,3,1,1,1,1,1,1,1,1)",1365,68,"exact",68,68],[5,14,"p","(3,3,2,1,1,1,1,1,1)",5733,99,"lower 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bound",50,53],[5,14,"p","(5,3,3,1,1,1)",48048,3,"lower bound",3,18170],[5,14,"p","(5,3,3,2,1)",64064,24020,"upper bound",0,24020],[5,14,"p","(5,3,3,3)",15015,0,"exact",0,0],[5,14,"p","(5,4,2,1,1,1)",63063,3,"lower bound",3,23596],[5,14,"p","(5,4,2,2,1)",68640,25454,"upper bound",0,25454],[5,14,"p","(5,4,3,1,1)",64064,23552,"upper bound",0,23552],[5,14,"p","(5,4,3,2)",48048,17550,"upper bound",0,17550],[5,14,"p","(5,4,4,1)",21021,7566,"upper bound",0,7566],[5,14,"p","(5,5,1,1,1,1)",14014,1,"exact",1,1],[5,14,"p","(5,5,2,1,1)",35035,12631,"upper bound",0,12631],[5,14,"p","(5,5,2,2)",21450,7680,"upper bound",0,7680],[5,14,"p","(5,5,3,1)",27027,9585,"upper bound",0,9585],[5,14,"p","(5,5,4)",6006,0,"exact",0,0],[5,14,"p","(6,1,1,1,1,1,1,1,1)",1287,19,"exact",19,19],[5,14,"p","(6,3,2,1,1,1)",59904,2,"lower bound",2,21736],[5,14,"p","(6,3,2,2,1)",63063,22674,"upper bound",0,22674],[5,14,"p","(6,3,3,1,1)",48048,17124,"upper bound",0,17124],[5,14,"p","(6,3,3,2)",35035,12400,"upper bound",0,12400],[5,14,"p","(6,4,1,1,1,1)",28665,10234,"upper bound",0,10234],[5,14,"p","(6,4,2,1,1)",69498,24462,"upper bound",0,24462],[5,14,"p","(6,4,2,2)",42042,14692,"upper bound",0,14692],[5,14,"p","(6,4,3,1)",50050,17320,"upper bound",0,17320],[5,14,"p","(6,4,4)",9009,0,"exact",0,0],[5,14,"p","(6,5,1,1,1)",21021,7194,"upper bound",0,7194],[5,14,"p","(6,5,2,1)",36608,12368,"upper bound",0,12368],[5,14,"p","(6,5,3)",15015,0,"exact",0,0],[5,14,"p","(6,6,1,1)",7007,0,"exact",0,0],[5,14,"p","(6,6,2)",6435,0,"exact",0,0],[5,14,"p","(7,2,2,1,1,1)",21021,7224,"upper bound",0,7224],[5,14,"p","(7,2,2,2,1)",20384,6930,"upper bound",0,6930],[5,14,"p","(7,3,1,1,1,1)",21450,7280,"upper bound",0,7280],[5,14,"p","(7,3,2,1,1)",47775,15960,"upper bound",0,15960],[5,14,"p","(7,3,2,2)",28028,9286,"upper bound",0,9286],[5,14,"p","(7,3,3,1)",27027,8856,"upper bound",0,8856],[5,14,"p","(7,4,1,1,1)",24960,8148,"upper bound",0,8148],[5,14,"p","(7,4,2,1)",42042,13530,"upper bound",0,13530],[5,14,"p","(7,4,3)",16016,0,"exact",0,0],[5,14,"p","(7,5,1,1)",15444,0,"exact",0,0],[5,14,"p","(7,5,2)",14014,0,"exact",0,0],[5,14,"p","(7,6,1)",4576,0,"exact",0,0],[5,14,"p","(7,7)",429,0,"exact",0,0],[5,14,"p","(8,1,1,1,1,1,1)",1716,0,"exact",0,0],[5,14,"p","(8,2,1,1,1,1)",8085,0,"exact",0,0],[5,14,"p","(8,2,2,1,1)",14014,0,"exact",0,0],[5,14,"p","(8,2,2,2)",7644,0,"exact",0,0],[5,14,"p","(8,3,1,1,1)",15015,0,"exact",0,0],[5,14,"p","(8,3,2,1)",23296,6608,"upper bound",0,6608],[5,14,"p","(8,3,3)",7007,0,"exact",0,0],[5,14,"p","(8,4,1,1)",13650,0,"exact",0,0],[5,14,"p","(8,4,2)",12012,0,"exact",0,0],[5,14,"p","(8,5,1)",6006,0,"exact",0,0],[5,14,"p","(8,6)",1001,0,"exact",0,0],[5,14,"p","(9,1,1,1,1,1)",1287,0,"exact",0,0],[5,14,"p","(9,2,1,1,1)",4928,0,"exact",0,0],[5,14,"p","(9,2,2,1)",6006,0,"exact",0,0],[5,14,"p","(9,3,1,1)",7007,0,"exact",0,0],[5,14,"p","(9,3,2)",5733,0,"exact",0,0],[5,14,"p","(9,4,1)",4368,0,"exact",0,0],[5,14,"p","(9,5)",1001,0,"exact",0,0],[5,14,"p","(10,1,1,1,1)",715,0,"exact",0,0],[5,14,"p","(10,2,1,1)",2079,0,"exact",0,0],[5,14,"p","(10,2,2)",1365,0,"exact",0,0],[5,14,"p","(10,3,1)",2002,0,"exact",0,0],[5,14,"p","(10,4)",637,0,"exact",0,0],[5,14,"p","(11,1,1,1)",286,0,"exact",0,0],[5,14,"p","(11,2,1)",560,0,"exact",0,0],[5,14,"p","(11,3)",273,0,"exact",0,0],[5,14,"p","(12,1,1)",78,0,"exact",0,0],[5,14,"p","(12,2)",77,0,"exact",0,0],[5,14,"p","(13,1)",13,0,"exact",0,0],[5,14,"p","(14)",1,0,"exact",0,0],[5,14,"p","(3,2,2,2,2,2,1)",4576,2,"lower bound",2,12],[5,14,"p","(3,3,2,2,2,1,1)",14014,8,"exact",8,8],[5,14,"p","(3,3,2,2,2,2)",6435,0,"exact",0,0],[5,14,"p","(3,3,3,2,1,1,1)",16016,10,"exact",10,10],[5,14,"p","(3,3,3,2,2,1)",15015,0,"exact",0,0],[5,14,"p","(3,3,3,3,1,1)",9009,1,"lower bound",1,2],[5,14,"p","(3,3,3,3,2)",6006,0,"exact",0,0],[5,14,"p","(4,2,2,2,2,1,1)",15444,14,"exact",14,14],[5,14,"p","(4,2,2,2,2,2)",7007,0,"exact",0,0],[5,14,"p","(4,3,2,2,1,1,1)",42042,30,"lower bound",30,16814],[5,14,"p","(4,3,2,2,2,1)",36608,2,"lower bound",2,14528],[5,14,"p","(4,3,3,1,1,1,1)",27027,16,"lower bound",16,10722],[5,14,"p","(4,3,3,2,1,1)",50050,3,"lower bound",3,19640],[5,14,"p","(4,3,3,2,2)",27027,10548,"upper bound",0,10548],[5,14,"p","(4,3,3,3,1)",21021,8148,"upper bound",0,8148],[5,14,"p","(4,4,1,1,1,1,1,1)",7644,29,"exact",29,29],[5,14,"p","(4,4,2,1,1,1,1)",28028,16,"lower bound",16,10997],[5,14,"p","(4,4,2,2,1,1)",42042,3,"lower bound",3,16317],[5,14,"p","(4,4,2,2,2)",21450,8280,"upper bound",0,8280],[5,14,"p","(5,2,2,2,1,1,1)",24960,24,"lower bound",24,9740],[5,14,"p","(5,2,2,2,2,1)",21021,4,"lower bound",4,8141],[5,14,"p","(5,3,2,1,1,1,1)",47775,30,"lower bound",30,18410],[5,14,"p","(5,3,2,2,1,1)",69498,4,"lower bound",4,26496],[5,14,"p","(5,3,2,2,2)",35035,13286,"upper bound",0,13286],[5,14,"p","(5,4,1,1,1,1,1)",20384,10,"lower bound",10,7742],[5,14,"p","(6,2,1,1,1,1,1,1)",8085,28,"lower bound",28,38],[5,14,"p","(6,2,2,1,1,1,1)",21450,14,"lower bound",14,7965],[5,14,"p","(6,2,2,2,1,1)",28665,4,"lower bound",4,10535],[5,14,"p","(6,2,2,2,2)",14014,0,"exact",0,0],[5,14,"p","(6,3,1,1,1,1,1)",21021,8,"lower bound",8,7742],[5,14,"p","(7,1,1,1,1,1,1,1)",1716,3,"exact",3,3],[5,14,"p","(7,2,1,1,1,1,1)",9504,2,"lower bound",2,4],[5,15,"p","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,0,"exact",0,0],[5,15,"p","(2,1,1,1,1,1,1,1,1,1,1,1,1,1)",14,6,"exact",6,6],[5,15,"p","(10,1,1,1,1,1)",2002,0,"exact",0,0],[5,15,"p","(10,2,1,1,1)",7722,0,"exact",0,0],[5,15,"p","(10,2,2,1)",9450,0,"exact",0,0],[5,15,"p","(10,3,1,1)",11088,0,"exact",0,0],[5,15,"p","(10,3,2)",9100,0,"exact",0,0],[5,15,"p","(10,4,1)",7007,0,"exact",0,0],[5,15,"p","(10,5)",1638,0,"exact",0,0],[5,15,"p","(11,1,1,1,1)",1001,0,"exact",0,0],[5,15,"p","(11,2,1,1)",2925,0,"exact",0,0],[5,15,"p","(11,2,2)",1925,0,"exact",0,0],[5,15,"p","(11,3,1)",2835,0,"exact",0,0],[5,15,"p","(11,4)",910,0,"exact",0,0],[5,15,"p","(12,1,1,1)",364,0,"exact",0,0],[5,15,"p","(12,2,1)",715,0,"exact",0,0],[5,15,"p","(12,3)",350,0,"exact",0,0],[5,15,"p","(13,1,1)",91,0,"exact",0,0],[5,15,"p","(13,2)",90,0,"exact",0,0],[5,15,"p","(14,1)",14,0,"exact",0,0],[5,15,"p","(15)",1,0,"exact",0,0],[5,15,"p","(2,2,1,1,1,1,1,1,1,1,1,1,1)",90,23,"exact",23,23],[5,15,"p","(2,2,2,1,1,1,1,1,1,1,1,1)",350,58,"exact",58,58],[5,15,"p","(2,2,2,2,1,1,1,1,1,1,1)",910,88,"exact",88,88],[5,15,"p","(2,2,2,2,2,1,1,1,1,1)",1638,84,"exact",84,84],[5,15,"p","(2,2,2,2,2,2,1,1,1)",2002,45,"exact",45,45],[5,15,"p","(2,2,2,2,2,2,2,1)",1430,11,"exact",11,11],[5,15,"p","(3,1,1,1,1,1,1,1,1,1,1,1,1)",91,23,"exact",23,23],[5,15,"p","(3,2,1,1,1,1,1,1,1,1,1,1)",715,116,"exact",116,116],[5,15,"p","(3,2,2,1,1,1,1,1,1,1,1)",2835,264,"exact",264,264],[5,15,"p","(3,2,2,2,1,1,1,1,1,1)",7007,336,"lower bound",336,3032],[5,15,"p","(3,2,2,2,2,1,1,1,1)",11375,237,"lower bound",237,4860],[5,15,"p","(3,2,2,2,2,2,1,1)",11583,72,"lower bound",72,4908],[5,15,"p","(3,2,2,2,2,2,2)",5005,10,"upper bound",0,10],[5,15,"p","(3,3,1,1,1,1,1,1,1,1,1)",1925,176,"exact",176,176],[5,15,"p","(3,3,2,1,1,1,1,1,1,1)",9100,390,"lower bound",390,3890],[5,15,"p","(3,3,2,2,1,1,1,1,1)",22113,400,"lower bound",400,9306],[5,15,"p","(3,3,2,2,2,1,1,1)",32032,210,"lower bound",210,13334],[5,15,"p","(3,3,2,2,2,2,1)",25025,30,"lower bound",30,10350],[5,15,"p","(3,3,3,1,1,1,1,1,1)",12740,208,"lower bound",208,238],[5,15,"p","(3,3,3,2,1,1,1,1)",35035,210,"lower bound",210,14434],[5,15,"p","(3,3,3,2,2,1,1)",45045,66,"lower bound",66,18390],[5,15,"p","(3,3,3,2,2,2)",21450,4,"lower bound",4,8718],[5,15,"p","(3,3,3,3,1,1,1)",25025,34,"lower bound",34,10152],[5,15,"p","(3,3,3,3,2,1)",30030,6,"lower bound",6,12096],[5,15,"p","(3,3,3,3,3)",6006,0,"exact",0,0],[5,15,"p","(4,1,1,1,1,1,1,1,1,1,1,1)",364,58,"exact",58,58],[5,15,"p","(4,2,1,1,1,1,1,1,1,1,1)",2925,264,"exact",264,264],[5,15,"p","(4,2,2,1,1,1,1,1,1,1)",11088,391,"lower bound",391,4680],[5,15,"p","(4,2,2,2,1,1,1,1,1)",25025,376,"lower bound",376,10400],[5,15,"p","(4,2,2,2,2,1,1,1)",35100,241,"lower bound",241,14430],[5,15,"p","(4,2,2,2,2,2,1)",27027,44,"lower bound",44,11040],[5,15,"p","(4,3,1,1,1,1,1,1,1,1)",9450,341,"lower bound",341,3955],[5,15,"p","(4,3,2,1,1,1,1,1,1)",42042,17267,"upper bound",0,17267],[5,15,"p","(4,3,2,2,1,1,1,1)",91000,36865,"upper bound",0,36865],[5,15,"p","(4,3,2,2,2,1,1)",108108,43403,"upper bound",0,43403],[5,15,"p","(4,3,2,2,2,2)",50050,20005,"upper bound",0,20005],[5,15,"p","(4,3,3,1,1,1,1,1)",57330,23058,"upper bound",0,23058],[5,15,"p","(4,3,3,2,1,1,1)",135135,53708,"upper bound",0,53708],[5,15,"p","(4,3,3,2,2,1)",128700,50792,"upper bound",0,50792],[5,15,"p","(4,3,3,3,1,1)",80080,31408,"upper bound",0,31408],[5,15,"p","(4,3,3,3,2)",54054,21096,"upper bound",0,21096],[5,15,"p","(4,4,1,1,1,1,1,1,1)",13650,159,"lower bound",159,382],[5,15,"p","(4,4,2,1,1,1,1,1)",58968,23487,"upper bound",0,23487],[5,15,"p","(4,4,2,2,1,1,1)",112112,44128,"upper bound",0,44128],[5,15,"p","(4,4,2,2,2,1)",100100,39125,"upper bound",0,39125],[5,15,"p","(4,4,3,1,1,1,1)",90090,35208,"upper bound",0,35208],[5,15,"p","(4,4,3,2,1,1)",175175,67788,"upper bound",0,67788],[5,15,"p","(4,4,3,2,2)",96525,37170,"upper bound",0,37170],[5,15,"p","(4,4,3,3,1)",81081,31032,"upper bound",0,31032],[5,15,"p","(4,4,4,1,1,1)",50050,19147,"upper bound",0,19147],[5,15,"p","(4,4,4,2,1)",75075,28500,"upper bound",0,28500],[5,15,"p","(4,4,4,3)",24024,9042,"upper bound",0,9042],[5,15,"p","(5,1,1,1,1,1,1,1,1,1,1)",1001,88,"exact",88,88],[5,15,"p","(5,2,1,1,1,1,1,1,1,1)",7722,244,"lower bound",244,3164],[5,15,"p","(5,2,2,1,1,1,1,1,1)",26950,284,"lower bound",284,10840],[5,15,"p","(5,2,2,2,1,1,1,1)",53625,21280,"upper bound",0,21280],[5,15,"p","(5,2,2,2,2,1,1)",61425,24160,"upper bound",0,24160],[5,15,"p","(5,2,2,2,2,2)",28028,10976,"upper bound",0,10976],[5,15,"p","(5,3,1,1,1,1,1,1,1)",24948,256,"lower bound",256,9954],[5,15,"p","(5,3,2,1,1,1,1,1)",100100,39275,"upper bound",0,39275],[5,15,"p","(5,3,2,2,1,1,1)",184275,71460,"upper bound",0,71460],[5,15,"p","(5,3,2,2,2,1)",162162,62451,"upper bound",0,62451],[5,15,"p","(5,3,3,1,1,1,1)",122850,47308,"upper bound",0,47308],[5,15,"p","(5,3,3,2,1,1)",231660,88344,"upper bound",0,88344],[5,15,"p","(5,3,3,2,2)",126126,47866,"upper bound",0,47866],[5,15,"p","(5,3,3,3,1)",100100,37760,"upper bound",0,37760],[5,15,"p","(5,4,1,1,1,1,1,1)",42042,16282,"upper bound",0,16282],[5,15,"p","(5,4,2,1,1,1,1)",159250,60760,"upper bound",0,60760],[5,15,"p","(5,4,2,2,1,1)",243243,91908,"upper bound",0,91908],[5,15,"p","(5,4,2,2,2)",125125,47050,"upper bound",0,47050],[5,15,"p","(5,4,3,1,1,1)",210210,78876,"upper bound",0,78876],[5,15,"p","(5,4,3,2,1)",292864,109056,"upper bound",0,109056],[5,15,"p","(5,4,3,3)",75075,27720,"upper bound",0,27720],[5,15,"p","(5,4,4,1,1)",100100,36860,"upper bound",0,36860],[5,15,"p","(5,4,4,2)",81081,29700,"upper bound",0,29700],[5,15,"p","(5,5,1,1,1,1,1)",34398,12880,"upper bound",0,12880],[5,15,"p","(5,5,2,1,1,1)",112112,41440,"upper bound",0,41440],[5,15,"p","(5,5,2,2,1)",125125,45900,"upper bound",0,45900],[5,15,"p","(5,5,3,1,1)",126126,45948,"upper bound",0,45948],[5,15,"p","(5,5,3,2)",96525,34980,"upper bound",0,34980],[5,15,"p","(5,5,4,1)",54054,19371,"upper bound",0,19371],[5,15,"p","(5,5,5)",6006,0,"exact",0,0],[5,15,"p","(6,1,1,1,1,1,1,1,1,1)",2002,84,"exact",84,84],[5,15,"p","(6,2,1,1,1,1,1,1,1)",14300,135,"lower bound",135,858],[5,15,"p","(6,2,2,1,1,1,1,1)",44550,16950,"upper bound",0,16950],[5,15,"p","(6,2,2,2,1,1,1)",75075,28240,"upper bound",0,28240],[5,15,"p","(6,2,2,2,2,1)",63700,23800,"upper bound",0,23800],[5,15,"p","(6,3,1,1,1,1,1,1)",43120,16282,"upper bound",0,16282],[5,15,"p","(6,3,2,1,1,1,1)",150150,55877,"upper bound",0,55877],[5,15,"p","(6,3,2,2,1,1)",221130,81513,"upper bound",0,81513],[5,15,"p","(6,3,2,2,2)",112112,41132,"upper bound",0,41132],[5,15,"p","(6,3,3,1,1,1)",156000,57120,"upper bound",0,57120],[5,15,"p","(6,3,3,2,1)",210210,76398,"upper bound",0,76398],[5,15,"p","(6,3,3,3)",50050,18040,"upper bound",0,18040],[5,15,"p","(6,4,1,1,1,1,1)",70070,25760,"upper bound",0,25760],[5,15,"p","(6,4,2,1,1,1)",221130,80271,"upper bound",0,80271],[5,15,"p","(6,4,2,2,1)",243243,87642,"upper bound",0,87642],[5,15,"p","(6,4,3,1,1)",231660,82908,"upper bound",0,82908],[5,15,"p","(6,4,3,2)",175175,62370,"upper bound",0,62370],[5,15,"p","(6,4,4,1)",80080,28204,"upper bound",0,28204],[5,15,"p","(6,5,1,1,1,1)",63700,22722,"upper bound",0,22722],[5,15,"p","(6,5,2,1,1)",162162,57231,"upper bound",0,57231],[5,15,"p","(6,5,2,2)",100100,35145,"upper bound",0,35145],[5,15,"p","(6,5,3,1)",128700,44880,"upper bound",0,44880],[5,15,"p","(6,5,4)",30030,10329,"upper bound",0,10329],[5,15,"p","(6,6,1,1,1)",28028,9660,"upper bound",0,9660],[5,15,"p","(6,6,2,1)",50050,17105,"upper bound",0,17105],[5,15,"p","(6,6,3)",21450,7260,"upper bound",0,7260],[5,15,"p","(7,1,1,1,1,1,1,1,1)",3003,45,"lower bound",45,51],[5,15,"p","(7,2,1,1,1,1,1,1)",19305,70,"lower bound",70,97],[5,15,"p","(7,2,2,1,1,1,1)",51975,18528,"upper bound",0,18528],[5,15,"p","(7,2,2,2,1,1)",70070,24752,"upper bound",0,24752],[5,15,"p","(7,2,2,2,2)",34398,12096,"upper bound",0,12096],[5,15,"p","(7,3,1,1,1,1,1)",51975,18400,"upper bound",0,18400],[5,15,"p","(7,3,2,1,1,1)",150150,52515,"upper bound",0,52515],[5,15,"p","(7,3,2,2,1)",159250,55300,"upper bound",0,55300],[5,15,"p","(7,3,3,1,1)",122850,42390,"upper bound",0,42390],[5,15,"p","(7,3,3,2)",90090,30932,"upper bound",0,30932],[5,15,"p","(7,4,1,1,1,1)",75075,25968,"upper bound",0,25968],[5,15,"p","(7,4,2,1,1)",184275,63090,"upper bound",0,63090],[5,15,"p","(7,4,2,2)",112112,38192,"upper bound",0,38192],[5,15,"p","(7,4,3,1)",135135,45738,"upper bound",0,45738],[5,15,"p","(7,4,4)",25025,8360,"upper bound",0,8360],[5,15,"p","(7,5,1,1,1)",61425,20700,"upper bound",0,20700],[5,15,"p","(7,5,2,1)",108108,36135,"upper bound",0,36135],[5,15,"p","(7,5,3)",45045,14916,"upper bound",0,14916],[5,15,"p","(7,6,1,1)",27027,8844,"upper bound",0,8844],[5,15,"p","(7,6,2)",25025,8140,"upper bound",0,8140],[5,15,"p","(7,7,1)",5005,0,"exact",0,0],[5,15,"p","(8,1,1,1,1,1,1,1)",3432,9,"lower bound",9,38],[5,15,"p","(8,2,1,1,1,1,1)",19305,7,"lower bound",7,22],[5,15,"p","(8,2,2,1,1,1)",43120,14224,"upper bound",0,14224],[5,15,"p","(8,2,2,2,1)",42042,13776,"upper bound",0,13776],[5,15,"p","(8,3,1,1,1,1)",44550,14607,"upper bound",0,14607],[5,15,"p","(8,3,2,1,1)",100100,32510,"upper 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bound",0,63063],[5,14,"s","(5,4,1,1,1,1,1)",20384,2,"lower bound",2,20384],[5,14,"s","(5,3,3,3)",15015,0,"lower bound",0,15015],[5,14,"s","(5,3,3,2,1)",64064,0,"lower bound",0,64064],[5,14,"s","(5,3,3,1,1,1)",48048,0,"lower bound",0,48048],[5,14,"s","(5,3,2,2,2)",35035,0,"lower bound",0,35035],[5,14,"s","(5,3,2,2,1,1)",69498,0,"lower bound",0,69498],[5,14,"s","(5,3,2,1,1,1,1)",47775,6,"lower bound",6,47775],[5,14,"s","(5,3,1,1,1,1,1,1)",14014,22,"lower bound",22,14014],[5,14,"s","(5,2,2,2,2,1)",21021,0,"lower bound",0,21021],[5,14,"s","(5,2,2,2,1,1,1)",24960,6,"lower bound",6,24960],[5,14,"s","(5,2,2,1,1,1,1,1)",15015,31,"lower bound",31,15015],[5,14,"s","(5,2,1,1,1,1,1,1,1)",4928,59,"lower bound",59,4928],[5,14,"s","(5,1,1,1,1,1,1,1,1,1)",715,37,"lower bound",37,715],[5,14,"s","(4,4,4,2)",12012,0,"lower bound",0,12012],[5,14,"s","(4,4,4,1,1)",15015,0,"lower bound",0,15015],[5,14,"s","(4,4,3,3)",12012,0,"lower bound",0,12012],[5,14,"s","(4,4,3,2,1)",48048,0,"lower 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bound",91,7007],[5,14,"s","(4,2,1,1,1,1,1,1,1,1)",2079,108,"lower bound",108,2079],[5,14,"s","(4,1,1,1,1,1,1,1,1,1,1)",286,44,"lower bound",44,286],[5,14,"s","(3,3,3,3,2)",6006,0,"lower bound",0,6006],[5,14,"s","(3,3,3,3,1,1)",9009,0,"lower bound",0,9009],[5,14,"s","(3,3,3,2,2,1)",15015,0,"lower bound",0,15015],[5,14,"s","(3,3,3,2,1,1,1)",16016,2,"lower bound",2,16016],[5,14,"s","(3,3,3,1,1,1,1,1)",7007,12,"lower bound",12,7007],[5,14,"s","(3,3,2,2,2,2)",6435,0,"lower bound",0,6435],[5,14,"s","(3,3,2,2,2,1,1)",14014,1,"lower bound",1,14014],[5,14,"s","(3,3,2,2,1,1,1,1)",12012,22,"lower bound",22,12012],[5,14,"s","(3,3,2,1,1,1,1,1,1)",5733,70,"lower bound",70,5733],[5,14,"s","(3,3,1,1,1,1,1,1,1,1)",1365,69,"lower bound",69,1365],[5,14,"s","(3,2,2,2,2,2,1)",4576,0,"lower bound",0,4576],[5,14,"s","(3,2,2,2,2,1,1,1)",6006,11,"lower bound",11,6006],[5,14,"s","(3,2,2,2,1,1,1,1,1)",4368,57,"lower bound",57,4368],[5,14,"s","(3,2,2,1,1,1,1,1,1,1)",2002,104,"lower bound",104,2002],[5,14,"s","(3,2,1,1,1,1,1,1,1,1,1)",560,83,"lower bound",83,560],[5,14,"s","(3,1,1,1,1,1,1,1,1,1,1,1)",78,26,"lower bound",26,78],[5,14,"s","(2,2,2,2,2,2,2)",429,0,"lower bound",0,429],[5,14,"s","(2,2,2,2,2,2,1,1)",1001,1,"lower bound",1,1001],[5,14,"s","(2,2,2,2,2,1,1,1,1)",1001,12,"lower bound",12,1001],[5,14,"s","(2,2,2,2,1,1,1,1,1,1)",637,33,"lower bound",33,637],[5,14,"s","(2,2,2,1,1,1,1,1,1,1,1)",273,40,"lower bound",40,273],[5,14,"s","(2,2,1,1,1,1,1,1,1,1,1,1)",77,25,"lower bound",25,77],[5,14,"s","(2,1,1,1,1,1,1,1,1,1,1,1,1)",13,8,"lower 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bound",0,3],[5,14,"t","(4,2,2,2,2,1,1)",15444,17,"exact",17,17],[5,14,"t","(7,5,1,1)",15444,0,"exact",0,0],[5,14,"t","(3,3,3,2,1,1,1)",16016,12,"exact",12,12],[5,14,"t","(7,4,3)",16016,0,"exact",0,0],[5,14,"t","(4,3,2,1,1,1,1,1)",23296,134,"lower bound",134,23296],[5,14,"t","(4,3,2,2,1,1,1)",42042,36,"lower bound",36,42042],[5,14,"t","(4,3,3,1,1,1,1)",27027,19,"lower bound",19,27027],[5,14,"t","(4,4,2,1,1,1,1)",28028,19,"lower bound",19,28028],[5,14,"t","(5,2,2,2,1,1,1)",24960,30,"lower bound",30,24960],[5,14,"t","(5,3,2,1,1,1,1)",47775,36,"lower bound",36,47775],[5,14,"t","(5,4,1,1,1,1,1)",20384,12,"lower bound",12,20384],[5,14,"t","(6,2,2,1,1,1,1)",21450,17,"lower bound",17,21450],[5,14,"t","(6,3,1,1,1,1,1)",21021,9,"lower bound",9,21021],[5,14,"t","(4,3,3,2,1,1)",50050,3,"lower bound",3,50050],[5,14,"t","(4,3,2,2,2,1)",36608,2,"lower bound",2,36608],[5,14,"t","(5,3,3,1,1,1)",48048,3,"lower bound",3,48048],[5,14,"t","(5,4,2,1,1,1)",63063,3,"lower bound",3,63063],[5,14,"t","(6,3,2,1,1,1)",59904,2,"lower bound",2,59904],[5,14,"t","(5,3,2,2,1,1)",69498,4,"lower bound",4,69498],[5,14,"t","(4,4,2,2,1,1)",42042,3,"lower bound",3,42042],[5,14,"t","(5,2,2,2,2,1)",21021,4,"lower bound",4,21021],[5,14,"t","(6,2,2,2,1,1)",28665,4,"lower bound",4,28665],[5,15,"t","(15)",1,0,"exact",0,0],[5,15,"t","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[5,15,"t","(2,1,1,1,1,1,1,1,1,1,1,1,1,1)",14,11,"exact",11,11],[5,15,"t","(14,1)",14,0,"exact",0,0],[5,15,"t","(2,2,1,1,1,1,1,1,1,1,1,1,1)",90,47,"exact",47,47],[5,15,"t","(13,2)",90,0,"exact",0,0],[5,15,"t","(3,1,1,1,1,1,1,1,1,1,1,1,1)",91,48,"exact",48,48],[5,15,"t","(13,1,1)",91,0,"exact",0,0],[5,15,"t","(2,2,2,1,1,1,1,1,1,1,1,1)",350,113,"exact",113,113],[5,15,"t","(12,3)",350,0,"exact",0,0],[5,15,"t","(4,1,1,1,1,1,1,1,1,1,1,1)",364,120,"exact",120,120],[5,15,"t","(12,1,1,1)",364,0,"exact",0,0],[5,15,"t","(3,2,1,1,1,1,1,1,1,1,1,1)",715,232,"exact",232,232],[5,15,"t","(12,2,1)",715,0,"exact",0,0],[5,15,"t","(2,2,2,2,1,1,1,1,1,1,1)",910,165,"exact",165,165],[5,15,"t","(11,4)",910,1,"upper bound",0,1],[5,15,"t","(5,1,1,1,1,1,1,1,1,1,1)",1001,184,"exact",184,184],[5,15,"t","(11,1,1,1,1)",1001,1,"upper bound",0,1],[5,15,"t","(2,2,2,2,2,2,2,1)",1430,15,"lower bound",15,19],[5,15,"t","(8,7)",1430,0,"exact",0,0],[5,15,"t","(2,2,2,2,2,1,1,1,1,1)",1638,145,"exact",145,145],[5,15,"t","(10,5)",1638,0,"exact",0,0],[5,15,"t","(3,3,1,1,1,1,1,1,1,1,1)",1925,344,"exact",344,344],[5,15,"t","(11,2,2)",1925,2,"upper bound",0,2],[5,15,"t","(2,2,2,2,2,2,1,1,1)",2002,69,"lower bound",69,70],[5,15,"t","(6,1,1,1,1,1,1,1,1,1)",2002,170,"lower bound",170,172],[5,15,"t","(9,6)",2002,0,"exact",0,0],[5,15,"t","(10,1,1,1,1,1)",2002,13,"upper bound",0,13],[5,15,"t","(3,2,2,1,1,1,1,1,1,1,1)",2835,507,"exact",507,507],[5,15,"t","(11,3,1)",2835,3,"upper bound",0,3],[5,15,"t","(4,2,1,1,1,1,1,1,1,1,1)",2925,525,"exact",525,525],[5,15,"t","(11,2,1,1)",2925,3,"upper bound",0,3],[5,15,"t","(7,1,1,1,1,1,1,1,1)",3003,80,"lower bound",80,86],[5,15,"t","(9,1,1,1,1,1,1)",3003,16,"upper bound",0,16],[5,15,"t","(8,1,1,1,1,1,1,1)",3432,13,"lower bound",13,42],[5,15,"t","(3,2,2,2,2,2,2)",5005,12,"lower bound",12,15],[5,15,"t","(7,7,1)",5005,0,"exact",0,0],[5,15,"t","(3,3,3,3,3)",6006,0,"exact",0,0],[5,15,"t","(5,5,5)",6006,0,"exact",0,0],[5,15,"t","(3,2,2,2,1,1,1,1,1,1)",7007,598,"lower bound",598,5513],[5,15,"t","(10,4,1)",7007,0,"exact",0,0],[5,15,"t","(5,2,1,1,1,1,1,1,1,1)",7722,644,"lower bound",644,6600],[5,15,"t","(10,2,1,1,1)",7722,1017,"upper bound",0,1017],[5,15,"t","(3,3,2,1,1,1,1,1,1,1)",9100,759,"lower bound",759,7444],[5,15,"t","(10,3,2)",9100,0,"exact",0,0],[5,15,"t","(4,3,1,1,1,1,1,1,1,1)",9450,781,"lower bound",781,8418],[5,15,"t","(10,2,2,1)",9450,77,"upper bound",0,77],[5,15,"t","(4,2,2,1,1,1,1,1,1,1)",11088,928,"lower bound",928,6519],[5,15,"t","(10,3,1,1)",11088,22,"upper bound",0,22],[5,15,"t","(9,5,1)",11375,0,"exact",0,0],[5,15,"t","(8,6,1)",11583,0,"exact",0,0],[5,15,"t","(3,3,3,1,1,1,1,1,1)",12740,388,"exact",388,388],[5,15,"t","(9,3,3)",12740,0,"exact",0,0],[5,15,"t","(4,4,1,1,1,1,1,1,1)",13650,404,"lower bound",404,651],[5,15,"t","(9,2,2,2)",13650,13,"upper bound",0,13],[5,15,"t","(6,2,1,1,1,1,1,1,1)",14300,418,"lower bound",418,1129],[5,15,"t","(9,2,1,1,1,1)",14300,4700,"upper bound",0,4700],[5,15,"t","(7,2,1,1,1,1,1,1)",19305,126,"lower bound",126,141],[5,15,"t","(8,2,1,1,1,1,1)",19305,11,"lower bound",11,40],[5,15,"t","(3,2,2,2,2,1,1,1,1)",11375,380,"lower bound",380,11375],[5,15,"t","(3,2,2,2,2,2,1,1)",11583,116,"lower bound",116,11583],[5,15,"t","(3,3,2,2,1,1,1,1,1)",22113,705,"lower bound",705,22113],[5,15,"t","(3,3,2,2,2,1,1,1)",32032,307,"lower bound",307,32032],[5,15,"t","(3,3,2,2,2,2,1)",25025,50,"lower bound",50,25025],[5,15,"t","(3,3,3,2,1,1,1,1)",35035,310,"lower bound",310,35035],[5,15,"t","(3,3,3,2,2,1,1)",45045,85,"lower bound",85,45045],[5,15,"t","(3,3,3,3,1,1,1)",25025,47,"lower bound",47,25025],[5,15,"t","(4,2,2,2,1,1,1,1,1)",25025,814,"lower bound",814,25025],[5,15,"t","(4,2,2,2,2,1,1,1)",35100,358,"lower bound",358,35100],[5,15,"t","(4,2,2,2,2,2,1)",27027,70,"lower bound",70,27027],[5,15,"t","(4,3,2,1,1,1,1,1,1)",42042,1284,"lower bound",1284,42042],[5,15,"t","(4,3,2,2,1,1,1,1)",91000,334,"lower bound",334,91000],[5,15,"t","(4,3,2,2,2,1,1)",108108,64,"lower bound",64,108108],[5,15,"t","(4,3,3,1,1,1,1,1)",57330,482,"lower bound",482,57330],[5,15,"t","(4,3,3,2,1,1,1)",135135,70,"lower bound",70,135135],[5,15,"t","(4,4,2,1,1,1,1,1)",58968,490,"lower bound",490,58968],[5,15,"t","(4,4,2,2,1,1,1)",112112,58,"lower bound",58,112112],[5,15,"t","(4,4,3,1,1,1,1)",90090,38,"lower bound",38,90090],[5,15,"t","(5,2,2,1,1,1,1,1,1)",26950,841,"lower bound",841,26950],[5,15,"t","(5,2,2,2,1,1,1,1)",53625,528,"lower bound",528,53625],[5,15,"t","(5,2,2,2,2,1,1)",61425,166,"lower bound",166,61425],[5,15,"t","(5,3,1,1,1,1,1,1,1)",24948,736,"lower bound",736,24948],[5,15,"t","(5,3,2,1,1,1,1,1)",100100,335,"lower bound",335,100100],[5,15,"t","(5,3,2,2,1,1,1)",184275,106,"lower bound",106,184275],[5,15,"t","(5,3,3,1,1,1,1)",122850,58,"lower bound",58,122850],[5,15,"t","(5,4,1,1,1,1,1,1)",42042,320,"lower bound",320,42042],[5,15,"t","(5,4,2,1,1,1,1)",159250,70,"lower bound",70,159250],[5,15,"t","(5,5,1,1,1,1,1)",34398,47,"lower bound",47,34398],[5,15,"t","(6,2,2,1,1,1,1,1)",44550,384,"lower bound",384,44550],[5,15,"t","(6,2,2,2,1,1,1)",75075,51,"lower bound",51,75075],[5,15,"t","(6,3,1,1,1,1,1,1)",43120,313,"lower bound",313,43120],[5,15,"t","(6,3,2,1,1,1,1)",150150,64,"lower bound",64,150150],[5,15,"t","(6,4,1,1,1,1,1)",70070,21,"lower bound",21,70070],[5,15,"t","(7,2,2,1,1,1,1)",51975,76,"lower bound",76,51975],[5,15,"t","(7,3,1,1,1,1,1)",51975,49,"lower bound",49,51975],[5,15,"t","(5,2,2,2,2,2)",28028,24,"lower bound",24,28028],[5,15,"t","(7,3,2,1,1,1)",150150,2,"lower bound",2,150150],[5,15,"t","(4,3,3,3,1,1)",80080,4,"lower bound",4,80080],[5,15,"t","(5,4,3,1,1,1)",210210,6,"lower bound",6,210210],[5,15,"t","(5,5,2,1,1,1)",112112,4,"lower bound",4,112112],[5,15,"t","(4,3,3,2,2,1)",128700,5,"lower bound",5,128700],[5,15,"t","(4,3,2,2,2,2)",50050,20,"lower bound",20,50050],[5,15,"t","(5,4,2,2,1,1)",243243,10,"lower bound",10,243243],[5,15,"t","(6,3,3,1,1,1)",156000,5,"lower bound",5,156000],[5,15,"t","(5,3,3,2,1,1)",231660,10,"lower bound",10,231660],[5,15,"t","(7,2,2,2,1,1)",70070,4,"lower bound",4,70070],[5,15,"t","(4,4,3,2,1,1)",175175,6,"lower bound",6,175175],[5,15,"t","(6,4,2,1,1,1)",221130,5,"lower bound",5,221130],[5,15,"t","(5,3,2,2,2,1)",162162,10,"lower bound",10,162162],[5,15,"t","(3,3,3,3,2,1)",30030,8,"lower bound",8,30030],[5,15,"t","(4,4,2,2,2,1)",100100,5,"lower bound",5,100100],[5,15,"t","(6,3,2,2,1,1)",221130,10,"lower bound",10,221130],[5,15,"t","(6,5,1,1,1,1)",63700,8,"lower bound",8,63700],[5,15,"t","(6,2,2,2,2,1)",63700,42,"lower bound",42,63700],[5,15,"t","(4,3,3,3,2)",54054,2,"lower bound",2,54054],[5,15,"t","(4,4,4,1,1,1)",50050,6,"lower bound",6,50050],[5,15,"t","(8,2,2,1,1,1)",43120,3,"lower bound",3,43120],[5,15,"t","(7,2,2,2,2)",34398,5,"lower bound",5,34398],[5,15,"t","(3,3,3,2,2,2)",21450,4,"lower bound",4,21450],[5,15,"t","(8,3,1,1,1,1)",44550,1,"lower bound",1,44550],[5,16,"t","(16)",1,0,"exact",0,0],[5,16,"t","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",15,12,"lower bound",12,13],[5,16,"t","(15,1)",15,0,"exact",0,0],[5,16,"t","(2,2,1,1,1,1,1,1,1,1,1,1,1,1)",104,58,"lower bound",58,66],[5,16,"t","(14,2)",104,0,"exact",0,0],[5,16,"t","(3,1,1,1,1,1,1,1,1,1,1,1,1,1)",105,59,"lower bound",59,67],[5,16,"t","(14,1,1)",105,0,"exact",0,0],[5,16,"t","(2,2,2,1,1,1,1,1,1,1,1,1,1)",440,160,"lower bound",160,194],[5,16,"t","(13,3)",440,0,"exact",0,0],[5,16,"t","(4,1,1,1,1,1,1,1,1,1,1,1,1)",455,168,"lower bound",168,203],[5,16,"t","(13,1,1,1)",455,0,"exact",0,0],[5,16,"t","(3,2,1,1,1,1,1,1,1,1,1,1,1)",896,327,"lower bound",327,396],[5,16,"t","(13,2,1)",896,0,"exact",0,0],[5,16,"t","(2,2,2,2,1,1,1,1,1,1,1,1)",1260,278,"lower bound",278,363],[5,16,"t","(12,4)",1260,5,"upper bound",0,5],[5,16,"t","(5,1,1,1,1,1,1,1,1,1,1,1)",1365,304,"lower bound",304,396],[5,16,"t","(12,1,1,1,1)",1365,5,"upper bound",0,5],[5,16,"t","(2,2,2,2,2,2,2,2)",1430,15,"lower bound",15,48],[5,16,"t","(8,8)",1430,0,"exact",0,0],[5,16,"t","(11,5)",2548,7,"upper bound",0,7],[5,16,"t","(3,3,1,1,1,1,1,1,1,1,1,1)",2640,576,"lower bound",576,751],[5,16,"t","(12,2,2)",2640,10,"upper bound",0,10],[5,16,"t","(6,1,1,1,1,1,1,1,1,1,1)",3003,354,"lower bound",354,517],[5,16,"t","(11,1,1,1,1,1)",3003,41,"upper bound",0,41],[5,16,"t","(9,7)",3432,55,"upper bound",0,55],[5,16,"t","(10,6)",3640,69,"upper bound",0,69],[5,16,"t","(12,3,1)",3900,700,"upper bound",0,700],[5,16,"t","(4,2,1,1,1,1,1,1,1,1,1,1)",4004,877,"lower bound",877,1147],[5,16,"t","(12,2,1,1)",4004,804,"upper bound",0,804],[5,16,"t","(7,1,1,1,1,1,1,1,1,1)",5005,250,"lower bound",250,2298],[5,16,"t","(10,1,1,1,1,1,1)",5005,461,"upper bound",0,461],[5,16,"t","(8,1,1,1,1,1,1,1,1)",6435,93,"lower bound",93,488],[5,16,"t","(9,1,1,1,1,1,1,1)",6435,13,"lower bound",13,114],[5,16,"t","(11,4,1)",10752,1152,"upper bound",0,1152],[5,16,"t","(11,2,1,1,1)",11648,1017,"upper bound",0,1017],[5,16,"t","(11,3,2)",13860,3043,"upper bound",0,3043],[5,16,"t","(11,2,2,1)",14300,4700,"upper bound",0,4700],[5,16,"t","(11,3,1,1)",16848,848,"upper bound",0,848],[5,16,"t","(8,7,1)",18018,0,"exact",0,0],[5,16,"t","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[5,16,"t","(2,2,2,2,2,1,1,1,1,1,1)",2548,310,"lower bound",310,2548],[5,16,"t","(2,2,2,2,2,2,1,1,1,1)",3640,214,"lower bound",214,3640],[5,16,"t","(2,2,2,2,2,2,2,1,1)",3432,84,"lower bound",84,3432],[5,16,"t","(3,2,2,1,1,1,1,1,1,1,1,1)",3900,852,"lower bound",852,3900],[5,16,"t","(3,2,2,2,1,1,1,1,1,1,1)",10752,1270,"lower bound",1270,10752],[5,16,"t","(3,2,2,2,2,1,1,1,1,1)",20020,1123,"lower bound",1123,20020],[5,16,"t","(3,2,2,2,2,2,1,1,1)",24960,565,"lower bound",565,24960],[5,16,"t","(3,2,2,2,2,2,2,1)",18018,143,"lower bound",143,18018],[5,16,"t","(3,3,2,1,1,1,1,1,1,1,1)",13860,1610,"lower bound",1610,13860],[5,16,"t","(3,3,2,2,1,1,1,1,1,1)",38220,2062,"lower bound",2062,38220],[5,16,"t","(3,3,2,2,2,1,1,1,1)",65520,1392,"lower bound",1392,65520],[5,16,"t","(3,3,2,2,2,2,1,1)",68640,473,"lower bound",473,68640],[5,16,"t","(3,3,2,2,2,2,2)",30030,62,"lower bound",62,30030],[5,16,"t","(3,3,3,1,1,1,1,1,1,1)",21840,1147,"lower bound",1147,21840],[5,16,"t","(3,3,3,2,1,1,1,1,1)",69888,1403,"lower bound",1403,69888],[5,16,"t","(3,3,3,2,2,1,1,1)",112112,702,"lower bound",702,112112],[5,16,"t","(3,3,3,2,2,2,1)",91520,139,"lower bound",139,91520],[5,16,"t","(3,3,3,3,1,1,1,1)",60060,357,"lower bound",357,60060],[5,16,"t","(3,3,3,3,2,1,1)",100100,140,"lower bound",140,100100],[5,16,"t","(4,2,2,1,1,1,1,1,1,1,1)",16848,1960,"lower bound",1960,16848],[5,16,"t","(4,2,2,2,1,1,1,1,1,1)",43120,2340,"lower bound",2340,43120],[5,16,"t","(4,2,2,2,2,1,1,1,1)",71500,1552,"lower bound",1552,71500],[5,16,"t","(4,2,2,2,2,2,1,1)",73710,544,"lower bound",544,73710],[5,16,"t","(4,2,2,2,2,2,2)",32032,82,"lower bound",82,32032],[5,16,"t","(4,3,1,1,1,1,1,1,1,1,1)",14300,1650,"lower bound",1650,14300],[5,16,"t","(4,3,2,1,1,1,1,1,1,1)",71680,3752,"lower bound",3752,71680],[5,16,"t","(4,3,2,2,1,1,1,1,1)",180180,3137,"lower bound",3137,180180],[5,16,"t","(4,3,2,2,2,1,1,1)",266240,1063,"lower bound",1063,266240],[5,16,"t","(4,3,2,2,2,2,1)",210210,204,"lower bound",204,210210],[5,16,"t","(4,3,3,1,1,1,1,1,1)",112112,2154,"lower bound",2154,112112],[5,16,"t","(4,3,3,2,1,1,1,1)",318500,1196,"lower bound",1196,318500],[5,16,"t","(4,3,3,2,2,1,1)",416988,224,"lower bound",224,416988],[5,16,"t","(4,3,3,3,1,1,1)",240240,121,"lower bound",121,240240],[5,16,"t","(4,4,1,1,1,1,1,1,1,1)",23100,1185,"lower bound",1185,23100],[5,16,"t","(4,4,2,1,1,1,1,1,1)",114660,2178,"lower bound",2178,114660],[5,16,"t","(4,4,2,2,1,1,1,1)",262080,882,"lower bound",882,262080],[5,16,"t","(4,4,2,2,2,1,1)",320320,127,"lower bound",127,320320],[5,16,"t","(4,4,3,1,1,1,1,1)",206388,1010,"lower bound",1010,206388],[5,16,"t","(4,4,3,2,1,1,1)",512512,172,"lower bound",172,512512],[5,16,"t","(4,4,4,1,1,1,1)",140140,44,"lower bound",44,140140],[5,16,"t","(5,2,1,1,1,1,1,1,1,1,1)",11648,1353,"lower bound",1353,11648],[5,16,"t","(5,2,2,1,1,1,1,1,1,1)",45760,2413,"lower bound",2413,45760],[5,16,"t","(5,2,2,2,1,1,1,1,1)",105600,2183,"lower bound",2183,105600],[5,16,"t","(5,2,2,2,2,1,1,1)",150150,1052,"lower bound",1052,150150],[5,16,"t","(5,2,2,2,2,2,1)",116480,260,"lower bound",260,116480],[5,16,"t","(5,3,1,1,1,1,1,1,1,1)",42120,2161,"lower bound",2161,42120],[5,16,"t","(5,3,2,1,1,1,1,1,1)",194040,3196,"lower bound",3196,194040],[5,16,"t","(5,3,2,2,1,1,1,1)",429000,1303,"lower bound",1303,429000],[5,16,"t","(5,3,2,2,2,1,1)",515970,346,"lower bound",346,515970],[5,16,"t","(5,3,3,1,1,1,1,1)",280280,875,"lower bound",875,280280],[5,16,"t","(5,3,3,2,1,1,1)",673920,244,"lower bound",244,673920],[5,16,"t","(5,4,1,1,1,1,1,1,1)",80640,1460,"lower bound",1460,80640],[5,16,"t","(5,4,2,1,1,1,1,1)",360360,1215,"lower bound",1215,360360],[5,16,"t","(5,4,2,2,1,1,1)",698880,244,"lower bound",244,698880],[5,16,"t","(5,4,3,1,1,1,1)",582400,172,"lower bound",172,582400],[5,16,"t","(5,5,1,1,1,1,1,1)",76440,367,"lower bound",367,76440],[5,16,"t","(5,5,2,1,1,1,1)",305760,121,"lower bound",121,305760],[5,16,"t","(6,2,1,1,1,1,1,1,1,1)",24024,1232,"lower bound",1232,24024],[5,16,"t","(6,2,2,1,1,1,1,1,1)",85800,1643,"lower bound",1643,85800],[5,16,"t","(6,2,2,2,1,1,1,1)",173250,963,"lower bound",963,173250],[5,16,"t","(6,2,2,2,2,1,1)",200200,259,"lower bound",259,200200],[5,16,"t","(6,3,1,1,1,1,1,1,1)",82368,1467,"lower bound",1467,82368],[5,16,"t","(6,3,2,1,1,1,1,1)",337920,1096,"lower bound",1096,337920],[5,16,"t","(6,3,2,2,1,1,1)",630630,231,"lower bound",231,630630],[5,16,"t","(6,3,3,1,1,1,1)",429000,127,"lower bound",127,429000],[5,16,"t","(6,4,1,1,1,1,1,1)",155232,654,"lower bound",654,155232],[5,16,"t","(6,4,2,1,1,1,1)",600600,160,"lower bound",160,600600],[5,16,"t","(6,5,1,1,1,1,1)",168168,76,"lower bound",76,168168],[5,16,"t","(7,2,1,1,1,1,1,1,1)",36608,624,"lower bound",624,36608],[5,16,"t","(7,2,2,1,1,1,1,1)",115830,586,"lower bound",586,115830],[5,16,"t","(7,2,2,2,1,1,1)",197120,131,"lower bound",131,197120],[5,16,"t","(7,3,1,1,1,1,1,1)",114400,488,"lower bound",488,114400],[5,16,"t","(7,3,2,1,1,1,1)",404250,191,"lower bound",191,404250],[5,16,"t","(7,4,1,1,1,1,1)",197120,70,"lower bound",70,197120],[5,16,"t","(8,2,1,1,1,1,1,1)",42042,150,"lower bound",150,42042],[5,16,"t","(8,2,2,1,1,1,1)",114400,90,"lower bound",90,114400],[5,16,"t","(8,3,1,1,1,1,1)",115830,61,"lower bound",61,115830],[5,16,"t","(5,3,3,2,2,1)",648648,25,"lower bound",25,648648],[5,16,"t","(7,2,2,2,2,1)",168168,51,"lower bound",51,168168],[5,16,"t","(7,3,2,2,1,1)",600600,16,"lower bound",16,600600],[5,16,"t","(6,2,2,2,2,2)",91728,66,"lower bound",66,91728],[5,16,"t","(5,5,2,2,1,1)",480480,14,"lower bound",14,480480],[5,16,"t","(4,3,3,3,2,1)",292864,19,"lower bound",19,292864],[5,16,"t","(7,4,2,1,1,1)",630630,7,"lower bound",7,630630],[5,16,"t","(6,3,2,2,2,1)",559104,62,"lower bound",62,559104],[5,16,"t","(4,4,3,2,2,1)",500500,16,"lower bound",16,500500],[5,16,"t","(6,6,1,1,1,1)",91728,8,"lower bound",8,91728],[5,16,"t","(4,3,3,2,2,2)",200200,29,"lower bound",29,200200],[5,16,"t","(6,3,3,2,1,1)",819000,25,"lower bound",25,819000],[5,16,"t","(8,2,2,2,1,1)",155232,7,"lower bound",7,155232],[5,16,"t","(6,5,2,1,1,1)",559104,17,"lower bound",17,559104],[5,16,"t","(9,2,1,1,1,1,1)",36608,11,"lower bound",11,36608],[5,16,"t","(5,4,2,2,2,1)",630630,25,"lower bound",25,630630],[5,16,"t","(5,3,2,2,2,2)",240240,54,"lower bound",54,240240],[5,16,"t","(5,3,3,3,1,1)",411840,14,"lower bound",14,411840],[5,16,"t","(3,3,3,3,3,1)",36036,8,"lower bound",8,36036],[5,16,"t","(4,4,3,3,1,1)",336336,10,"lower bound",10,336336],[5,16,"t","(4,4,4,2,1,1)",300300,12,"lower bound",12,300300],[5,16,"t","(6,4,2,2,1,1)",928746,25,"lower bound",25,928746],[5,16,"t","(5,5,3,1,1,1)",448448,10,"lower bound",10,448448],[5,16,"t","(5,4,3,2,1,1)",1153152,32,"lower bound",32,1153152],[5,16,"t","(7,5,1,1,1,1)",200200,8,"lower bound",8,200200],[5,16,"t","(8,3,2,1,1,1)",337920,6,"lower bound",6,337920],[5,16,"t","(6,4,3,1,1,1)",819000,16,"lower bound",16,819000],[5,16,"t","(3,3,3,3,2,2)",51480,12,"lower bound",12,51480],[5,16,"t","(5,4,4,1,1,1)",360360,12,"lower bound",12,360360],[5,16,"t","(4,4,2,2,2,2)",150150,25,"lower bound",25,150150],[5,16,"t","(7,3,3,1,1,1)",429000,7,"lower bound",7,429000],[5,16,"t","(5,3,3,3,2)",280280,2,"lower bound",2,280280],[5,16,"t","(8,2,2,2,2)",76440,5,"lower bound",5,76440],[5,16,"t","(8,4,1,1,1,1)",173250,1,"lower bound",1,173250],[5,16,"t","(4,4,3,3,2)",231660,2,"lower bound",2,231660],[5,16,"t","(9,3,1,1,1,1)",85800,1,"lower bound",1,85800],[5,16,"t","(9,2,2,1,1,1)",82368,3,"lower bound",3,82368],[5,16,"t","(7,3,2,2,2)",305760,5,"lower bound",5,305760],[5,16,"t","(4,3,3,3,3)",60060,2,"lower bound",2,60060],[5,17,"t","(17)",1,0,"exact",0,0],[5,17,"t","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",16,13,"lower bound",13,15],[5,17,"t","(16,1)",16,0,"exact",0,0],[5,17,"t","(2,2,1,1,1,1,1,1,1,1,1,1,1,1,1)",119,70,"lower bound",70,88],[5,17,"t","(15,2)",119,0,"exact",0,0],[5,17,"t","(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",120,71,"lower bound",71,89],[5,17,"t","(15,1,1)",120,0,"exact",0,0],[5,17,"t","(2,2,2,1,1,1,1,1,1,1,1,1,1,1)",544,218,"lower bound",218,304],[5,17,"t","(14,3)",544,0,"exact",0,0],[5,17,"t","(4,1,1,1,1,1,1,1,1,1,1,1,1,1)",560,227,"lower bound",227,315],[5,17,"t","(14,1,1,1)",560,0,"exact",0,0],[5,17,"t","(14,2,1)",1105,0,"exact",0,0],[5,17,"t","(13,4)",1700,15,"upper bound",0,15],[5,17,"t","(5,1,1,1,1,1,1,1,1,1,1,1,1)",1820,472,"lower bound",472,742],[5,17,"t","(13,1,1,1,1)",1820,15,"upper bound",0,15],[5,17,"t","(13,2,2)",3536,336,"upper bound",0,336],[5,17,"t","(12,5)",3808,396,"upper bound",0,396],[5,17,"t","(6,1,1,1,1,1,1,1,1,1,1,1)",4368,658,"lower bound",658,1225],[5,17,"t","(12,1,1,1,1,1)",4368,1168,"upper bound",0,1168],[5,17,"t","(9,8)",4862,90,"upper bound",0,90],[5,17,"t","(13,3,1)",5236,2036,"upper bound",0,2036],[5,17,"t","(13,2,1,1)",5355,2155,"upper bound",0,2155],[5,17,"t","(11,6)",6188,396,"upper bound",0,396],[5,17,"t","(10,7)",7072,1392,"upper bound",0,1392],[5,17,"t","(7,1,1,1,1,1,1,1,1,1,1)",8008,604,"lower bound",604,5997],[5,17,"t","(11,1,1,1,1,1,1)",8008,1762,"upper bound",0,1762],[5,17,"t","(8,1,1,1,1,1,1,1,1,1)",11440,343,"lower bound",343,4902],[5,17,"t","(10,1,1,1,1,1,1,1)",11440,13,"lower bound",13,474],[5,17,"t","(9,1,1,1,1,1,1,1,1)",12870,106,"lower bound",106,1461],[5,17,"t","(12,4,1)",15912,6312,"upper bound",0,6312],[5,17,"t","(12,2,1,1,1)",17017,1017,"upper bound",0,1017],[5,17,"t","(8,8,1)",19448,19,"upper bound",0,19],[5,17,"t","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[5,17,"t","(2,2,2,2,1,1,1,1,1,1,1,1,1)",1700,438,"lower bound",438,1700],[5,17,"t","(2,2,2,2,2,1,1,1,1,1,1,1)",3808,588,"lower bound",588,3808],[5,17,"t","(2,2,2,2,2,2,1,1,1,1,1)",6188,524,"lower bound",524,6188],[5,17,"t","(2,2,2,2,2,2,2,1,1,1)",7072,298,"lower bound",298,7072],[5,17,"t","(2,2,2,2,2,2,2,2,1)",4862,99,"lower bound",99,4862],[5,17,"t","(3,2,1,1,1,1,1,1,1,1,1,1,1,1)",1105,444,"lower bound",444,1105],[5,17,"t","(3,2,2,1,1,1,1,1,1,1,1,1,1)",5236,1339,"lower bound",1339,5236],[5,17,"t","(3,2,2,2,1,1,1,1,1,1,1,1)",15912,2400,"lower bound",2400,15912],[5,17,"t","(3,2,2,2,2,1,1,1,1,1,1)",33320,2703,"lower bound",2703,33320],[5,17,"t","(3,2,2,2,2,2,1,1,1,1)",48620,1902,"lower bound",1902,48620],[5,17,"t","(3,2,2,2,2,2,2,1,1)",46410,792,"lower bound",792,46410],[5,17,"t","(3,2,2,2,2,2,2,2)",19448,158,"lower bound",158,19448],[5,17,"t","(3,3,1,1,1,1,1,1,1,1,1,1,1)",3536,903,"lower bound",903,3536],[5,17,"t","(3,3,2,1,1,1,1,1,1,1,1,1)",20400,3038,"lower bound",3038,20400],[5,17,"t","(3,3,2,2,1,1,1,1,1,1,1)",62832,4942,"lower bound",4942,62832],[5,17,"t","(3,3,2,2,2,1,1,1,1,1)",123760,4577,"lower bound",4577,123760],[5,17,"t","(3,3,2,2,2,2,1,1,1)",159120,2430,"lower bound",2430,159120],[5,17,"t","(3,3,2,2,2,2,2,1)",116688,678,"lower bound",678,116688],[5,17,"t","(3,3,3,1,1,1,1,1,1,1,1)",35700,2757,"lower bound",2757,35700],[5,17,"t","(3,3,3,2,1,1,1,1,1,1)",129948,4612,"lower bound",4612,129948],[5,17,"t","(3,3,3,2,2,1,1,1,1)",247520,3497,"lower bound",3497,247520],[5,17,"t","(3,3,3,2,2,2,1,1)",272272,1314,"lower bound",1314,272272],[5,17,"t","(3,3,3,2,2,2,2)",121550,201,"lower bound",201,121550],[5,17,"t","(3,3,3,3,1,1,1,1,1)",129948,1760,"lower bound",1760,129948],[5,17,"t","(3,3,3,3,2,1,1,1)",272272,1199,"lower bound",1199,272272],[5,17,"t","(3,3,3,3,2,2,1)",243100,291,"lower bound",291,243100],[5,17,"t","(3,3,3,3,3,1,1)",136136,148,"lower bound",148,136136],[5,17,"t","(4,2,1,1,1,1,1,1,1,1,1,1,1)",5355,1372,"lower bound",1372,5355],[5,17,"t","(4,2,2,1,1,1,1,1,1,1,1,1)",24752,3689,"lower bound",3689,24752],[5,17,"t","(4,2,2,2,1,1,1,1,1,1,1)",70720,5570,"lower bound",5570,70720],[5,17,"t","(4,2,2,2,2,1,1,1,1,1)",134640,5015,"lower bound",5015,134640],[5,17,"t","(4,2,2,2,2,2,1,1,1)",170170,2661,"lower bound",2661,170170],[5,17,"t","(4,2,2,2,2,2,2,1)",123760,769,"lower bound",769,123760],[5,17,"t","(4,3,1,1,1,1,1,1,1,1,1,1)",20944,3103,"lower bound",3103,20944],[5,17,"t","(4,3,2,1,1,1,1,1,1,1,1)",116688,8972,"lower bound",8972,116688],[5,17,"t","(4,3,2,2,1,1,1,1,1,1)",333200,11291,"lower bound",11291,333200],[5,17,"t","(4,3,2,2,2,1,1,1,1)",583440,7144,"lower bound",7144,583440],[5,17,"t","(4,3,2,2,2,2,1,1)",618800,2284,"lower bound",2284,618800],[5,17,"t","(4,3,2,2,2,2,2)",272272,348,"lower bound",348,272272],[5,17,"t","(4,3,3,1,1,1,1,1,1,1)",205632,7053,"lower bound",7053,205632],[5,17,"t","(4,3,3,2,1,1,1,1,1)",680680,7890,"lower bound",7890,680680],[5,17,"t","(4,3,3,2,2,1,1,1)",1113840,3185,"lower bound",3185,1113840],[5,17,"t","(4,3,3,2,2,2,1)",918918,596,"lower bound",596,918918],[5,17,"t","(4,3,3,3,1,1,1,1)",618800,1674,"lower bound",1674,618800],[5,17,"t","(4,3,3,3,2,1,1)",1050192,504,"lower bound",504,1050192],[5,17,"t","(4,4,1,1,1,1,1,1,1,1,1)",37400,2835,"lower bound",2835,37400],[5,17,"t","(4,4,2,1,1,1,1,1,1,1)",209440,7115,"lower bound",7115,209440],[5,17,"t","(4,4,2,2,1,1,1,1,1)",556920,6197,"lower bound",6197,556920],[5,17,"t","(4,4,2,2,2,1,1,1)",848640,2072,"lower bound",2072,848640],[5,17,"t","(4,4,2,2,2,2,1)",680680,356,"lower bound",356,680680],[5,17,"t","(4,4,3,1,1,1,1,1,1)",433160,5342,"lower bound",5342,433160],[5,17,"t","(4,4,3,2,1,1,1,1)",1299480,3260,"lower bound",3260,1299480],[5,17,"t","(4,4,3,2,2,1,1)",1750320,539,"lower bound",539,1750320],[5,17,"t","(4,4,3,3,1,1,1)",1089088,303,"lower bound",303,1089088],[5,17,"t","(4,4,4,1,1,1,1,1)",346528,1054,"lower bound",1054,346528],[5,17,"t","(4,4,4,2,1,1,1)",952952,228,"lower bound",228,952952],[5,17,"t","(5,2,1,1,1,1,1,1,1,1,1,1)",17017,2534,"lower bound",2534,17017],[5,17,"t","(5,2,2,1,1,1,1,1,1,1,1)",74256,5726,"lower bound",5726,74256],[5,17,"t","(5,2,2,2,1,1,1,1,1,1)",194480,6936,"lower bound",6936,194480],[5,17,"t","(5,2,2,2,2,1,1,1,1)",327250,4787,"lower bound",4787,327250],[5,17,"t","(5,2,2,2,2,2,1,1)",340340,1856,"lower bound",1856,340340],[5,17,"t","(5,2,2,2,2,2,2)",148512,342,"lower bound",342,148512],[5,17,"t","(5,3,1,1,1,1,1,1,1,1,1)",68068,5164,"lower bound",5164,68068],[5,17,"t","(5,3,2,1,1,1,1,1,1,1)",353600,11522,"lower bound",11522,353600],[5,17,"t","(5,3,2,2,1,1,1,1,1)",908820,9819,"lower bound",9819,908820],[5,17,"t","(5,3,2,2,2,1,1,1)",1361360,3764,"lower bound",3764,1361360],[5,17,"t","(5,3,2,2,2,2,1)",1082900,864,"lower bound",864,1082900],[5,17,"t","(5,3,3,1,1,1,1,1,1)",586432,6225,"lower bound",6225,586432],[5,17,"t","(5,3,3,2,1,1,1,1)",1701700,3618,"lower bound",3618,1701700],[5,17,"t","(5,3,3,2,2,1,1)",2255526,839,"lower bound",839,2255526],[5,17,"t","(5,3,3,3,1,1,1)",1326000,379,"lower bound",379,1326000],[5,17,"t","(5,4,1,1,1,1,1,1,1,1)",145860,4806,"lower bound",4806,145860],[5,17,"t","(5,4,2,1,1,1,1,1,1)",749700,8049,"lower bound",8049,749700],[5,17,"t","(5,4,2,2,1,1,1,1)",1750320,3644,"lower bound",3644,1750320],[5,17,"t","(5,4,2,2,2,1,1)",2165800,742,"lower bound",742,2165800],[5,17,"t","(5,4,3,1,1,1,1,1)",1429428,3272,"lower bound",3272,1429428],[5,17,"t","(5,4,3,2,1,1,1)",3620864,864,"lower bound",864,3620864],[5,17,"t","(5,4,4,1,1,1,1)",1082900,228,"lower bound",228,1082900],[5,17,"t","(5,5,1,1,1,1,1,1,1)",157080,1827,"lower bound",1827,157080],[5,17,"t","(5,5,2,1,1,1,1,1)",742560,1703,"lower bound",1703,742560],[5,17,"t","(5,5,2,2,1,1,1)",1485120,379,"lower bound",379,1485120],[5,17,"t","(5,5,3,1,1,1,1)",1336608,303,"lower bound",303,1336608],[5,17,"t","(6,2,1,1,1,1,1,1,1,1,1)",38675,2939,"lower bound",2939,38675],[5,17,"t","(6,2,2,1,1,1,1,1,1,1)",155584,5288,"lower bound",5288,155584],[5,17,"t","(6,2,2,2,1,1,1,1,1)",364650,4789,"lower bound",4789,364650],[5,17,"t","(6,2,2,2,2,1,1,1)",523600,2274,"lower bound",2274,523600],[5,17,"t","(6,2,2,2,2,2,1)",408408,585,"lower bound",585,408408],[5,17,"t","(6,3,1,1,1,1,1,1,1,1)",148512,4860,"lower bound",4860,148512],[5,17,"t","(6,3,2,1,1,1,1,1,1)",700128,7402,"lower bound",7402,700128],[5,17,"t","(6,3,2,2,1,1,1,1)",1570800,3593,"lower bound",3593,1570800],[5,17,"t","(6,3,2,2,2,1,1)",1905904,898,"lower bound",898,1905904],[5,17,"t","(6,3,3,1,1,1,1,1)",1047200,2098,"lower bound",2098,1047200],[5,17,"t","(6,3,3,2,1,1,1)",2552550,627,"lower bound",627,2552550],[5,17,"t","(6,4,1,1,1,1,1,1,1)",318240,3581,"lower bound",3581,318240],[5,17,"t","(6,4,2,1,1,1,1,1)",1454112,3125,"lower bound",3125,1454112],[5,17,"t","(6,4,2,2,1,1,1)",2858856,660,"lower bound",660,2858856],[5,17,"t","(6,4,3,1,1,1,1)",2431000,475,"lower bound",475,2431000],[5,17,"t","(6,5,1,1,1,1,1,1)",399840,1097,"lower bound",1097,399840],[5,17,"t","(6,5,2,1,1,1,1)",1633632,374,"lower bound",374,1633632],[5,17,"t","(6,6,1,1,1,1,1)",259896,84,"lower bound",84,259896],[5,17,"t","(7,2,1,1,1,1,1,1,1,1)",65637,2106,"lower bound",2106,65637],[5,17,"t","(7,2,2,1,1,1,1,1,1)",238238,2853,"lower bound",2853,238238],[5,17,"t","(7,2,2,2,1,1,1,1)",486200,1680,"lower bound",1680,486200],[5,17,"t","(7,2,2,2,2,1,1)",565488,441,"lower bound",441,565488],[5,17,"t","(7,3,1,1,1,1,1,1,1)",233376,2579,"lower bound",2579,233376],[5,17,"t","(7,3,2,1,1,1,1,1)",972400,2361,"lower bound",2361,972400],[5,17,"t","(7,3,2,2,1,1,1)",1832600,569,"lower bound",569,1832600],[5,17,"t","(7,3,3,1,1,1,1)",1262250,325,"lower bound",325,1262250],[5,17,"t","(7,4,1,1,1,1,1,1)",466752,1212,"lower bound",1212,466752],[5,17,"t","(7,4,2,1,1,1,1)",1832600,428,"lower bound",428,1832600],[5,17,"t","(7,5,1,1,1,1,1)",565488,154,"lower bound",154,565488],[5,17,"t","(8,2,1,1,1,1,1,1,1)",85085,867,"lower bound",867,85085],[5,17,"t","(8,2,2,1,1,1,1,1)",272272,826,"lower bound",826,272272],[5,17,"t","(8,2,2,2,1,1,1)",466752,228,"lower bound",228,466752],[5,17,"t","(8,3,1,1,1,1,1,1)",272272,699,"lower bound",699,272272],[5,17,"t","(8,3,2,1,1,1,1)",972400,348,"lower bound",348,972400],[5,17,"t","(8,4,1,1,1,1,1)",486200,132,"lower bound",132,486200],[5,17,"t","(9,2,1,1,1,1,1,1)",85085,174,"lower bound",174,85085],[5,17,"t","(9,2,2,1,1,1,1)",233376,104,"lower bound",104,233376],[5,17,"t","(9,3,1,1,1,1,1)",238238,73,"lower bound",73,238238],[5,17,"t","(7,3,3,2,1,1)",2431000,48,"lower bound",48,2431000],[5,17,"t","(7,6,1,1,1,1)",408408,16,"lower bound",16,408408],[5,17,"t","(8,3,2,2,1,1)",1454112,29,"lower bound",29,1454112],[5,17,"t","(5,5,4,1,1,1)",1089088,22,"lower bound",22,1089088],[5,17,"t","(6,5,3,1,1,1)",2475200,43,"lower bound",43,2475200],[5,17,"t","(5,3,3,3,2,1)",1633632,60,"lower bound",60,1633632],[5,17,"t","(8,4,2,1,1,1)",1570800,14,"lower bound",14,1570800],[5,17,"t","(4,3,3,3,2,2)",544544,60,"lower bound",60,544544],[5,17,"t","(6,3,3,3,1,1)",1591200,39,"lower bound",39,1591200],[5,17,"t","(6,5,2,2,1,1)",2598960,56,"lower bound",56,2598960],[5,17,"t","(4,4,3,3,2,1)",1361360,47,"lower bound",47,1361360],[5,17,"t","(6,3,2,2,2,2)",891072,182,"lower bound",182,891072],[5,17,"t","(7,3,2,2,2,1)",1633632,134,"lower bound",134,1633632],[5,17,"t","(5,3,3,2,2,2)",1089088,108,"lower bound",108,1089088],[5,17,"t","(7,2,2,2,2,2)",259896,117,"lower bound",117,259896],[5,17,"t","(4,4,4,3,1,1)",816816,22,"lower bound",22,816816],[5,17,"t","(5,5,3,2,1,1)",2722720,56,"lower bound",56,2722720],[5,17,"t","(3,3,3,3,3,2)",87516,20,"lower bound",20,87516],[5,17,"t","(6,4,2,2,2,1)",2598960,112,"lower bound",112,2598960],[5,17,"t","(8,3,3,1,1,1)",1047200,13,"lower bound",13,1047200],[5,17,"t","(6,6,2,1,1,1)",891072,25,"lower bound",25,891072],[5,17,"t","(6,3,3,2,2,1)",2475200,112,"lower bound",112,2475200],[5,17,"t","(7,4,2,2,1,1)",2858856,48,"lower bound",48,2858856],[5,17,"t","(8,2,2,2,2,1)",399840,63,"lower bound",63,399840],[5,17,"t","(4,4,3,2,2,2)",850850,70,"lower bound",70,850850],[5,17,"t","(7,5,2,1,1,1)",1905904,32,"lower bound",32,1905904],[5,17,"t","(5,4,2,2,2,2)",1021020,104,"lower bound",104,1021020],[5,17,"t","(4,4,4,2,2,1)",972400,28,"lower bound",28,972400],[5,17,"t","(5,4,3,3,1,1)",2450448,56,"lower bound",56,2450448],[5,17,"t","(5,4,3,2,2,1)",3573570,98,"lower bound",98,3573570],[5,17,"t","(5,5,2,2,2,1)",1361360,39,"lower bound",39,1361360],[5,17,"t","(4,3,3,3,3,1)",388960,29,"lower bound",29,388960],[5,17,"t","(9,2,2,2,1,1)",318240,10,"lower bound",10,318240],[5,17,"t","(9,3,2,1,1,1)",700128,10,"lower bound",10,700128],[5,17,"t","(6,4,4,1,1,1)",1591200,28,"lower bound",28,1591200],[5,17,"t","(5,4,4,2,1,1)",2362932,56,"lower bound",56,2362932],[5,17,"t","(6,4,3,2,1,1)",4873050,98,"lower bound",98,4873050],[5,17,"t","(7,4,3,1,1,1)",2552550,30,"lower bound",30,2552550],[5,17,"t","(10,2,1,1,1,1,1)",65637,11,"lower bound",11,65637],[5,17,"t","(8,5,1,1,1,1)",523600,9,"lower bound",9,523600],[5,17,"t","(9,4,1,1,1,1)",364650,2,"lower bound",2,364650],[5,17,"t","(9,2,2,2,2)",157080,5,"lower bound",5,157080],[5,17,"t","(5,3,3,3,3)",340340,4,"lower bound",4,340340],[5,17,"t","(4,4,4,3,2)",583440,2,"lower bound",2,583440],[5,17,"t","(7,4,2,2,2)",1485120,5,"lower bound",5,1485120],[5,17,"t","(8,3,2,2,2)",742560,10,"lower bound",10,742560],[5,17,"t","(5,4,3,3,2)",1701700,4,"lower bound",4,1701700],[5,17,"t","(10,3,1,1,1,1)",155584,1,"lower bound",1,155584],[5,17,"t","(4,4,3,3,3)",291720,4,"lower bound",4,291720],[5,17,"t","(6,3,3,3,2)",1089088,2,"lower bound",2,1089088],[5,17,"t","(10,2,2,1,1,1)",148512,3,"lower bound",3,148512],[5,17,"t","(7,3,3,2,2)",1336608,5,"lower bound",5,1336608],[5,18,"t","(18)",1,0,"exact",0,0],[5,18,"t","(17,1)",17,0,"exact",0,0],[5,18,"t","(2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",135,83,"lower bound",83,112],[5,18,"t","(16,2)",135,0,"exact",0,0],[5,18,"t","(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",136,84,"lower bound",84,113],[5,18,"t","(16,1,1)",136,0,"exact",0,0],[5,18,"t","(15,3)",663,0,"exact",0,0],[5,18,"t","(4,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",680,298,"lower bound",298,458],[5,18,"t","(15,1,1,1)",680,0,"exact",0,0],[5,18,"t","(15,2,1)",1344,0,"exact",0,0],[5,18,"t","(14,4)",2244,35,"upper bound",0,35],[5,18,"t","(14,1,1,1,1)",2380,35,"upper bound",0,35],[5,18,"t","(14,2,2)",4641,1441,"upper bound",0,1441],[5,18,"t","(9,9)",4862,470,"upper bound",0,470],[5,18,"t","(13,5)",5508,2308,"upper bound",0,2308],[5,18,"t","(13,1,1,1,1,1)",6188,2988,"upper bound",0,2988],[5,18,"t","(14,3,1)",6885,3127,"upper bound",0,3127],[5,18,"t","(14,2,1,1)",7020,3331,"upper bound",0,3331],[5,18,"t","(12,6)",9996,396,"upper bound",0,396],[5,18,"t","(10,8)",11934,1392,"upper bound",0,1392],[5,18,"t","(12,1,1,1,1,1,1)",12376,2776,"upper bound",0,2776],[5,18,"t","(11,7)",13260,3660,"upper bound",0,3660],[5,18,"t","(11,1,1,1,1,1,1,1)",19448,13,"lower bound",13,1775],[5,18,"t","(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",1,1,"exact",1,1],[5,18,"t","(10,1,1,1,1,1,1,1,1)",24310,119,"lower bound",119,24310],[5,18,"t","(10,2,1,1,1,1,1,1)",162162,198,"lower bound",198,162162],[5,18,"t","(10,2,2,1,1,1,1)",447525,118,"lower bound",118,447525],[5,18,"t","(10,3,1,1,1,1,1)",459459,85,"lower bound",85,459459],[5,18,"t","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",17,14,"lower bound",14,17],[5,18,"t","(2,2,2,1,1,1,1,1,1,1,1,1,1,1,1)",663,288,"lower bound",288,663],[5,18,"t","(2,2,2,2,1,1,1,1,1,1,1,1,1,1)",2244,656,"lower bound",656,2244],[5,18,"t","(2,2,2,2,2,1,1,1,1,1,1,1,1)",5508,1026,"lower bound",1026,5508],[5,18,"t","(2,2,2,2,2,2,1,1,1,1,1,1)",9996,1112,"lower bound",1112,9996],[5,18,"t","(2,2,2,2,2,2,2,1,1,1,1)",13260,822,"lower bound",822,13260],[5,18,"t","(2,2,2,2,2,2,2,2,1,1)",11934,397,"lower bound",397,11934],[5,18,"t","(2,2,2,2,2,2,2,2,2)",4862,99,"lower bound",99,4862],[5,18,"t","(3,2,1,1,1,1,1,1,1,1,1,1,1,1,1)",1344,585,"lower bound",585,1344],[5,18,"t","(3,2,2,1,1,1,1,1,1,1,1,1,1,1)",6885,2001,"lower bound",2001,6885],[5,18,"t","(3,2,2,2,1,1,1,1,1,1,1,1,1)",22848,4177,"lower bound",4177,22848],[5,18,"t","(3,2,2,2,2,1,1,1,1,1,1,1)",53040,5691,"lower bound",5691,53040],[5,18,"t","(3,2,2,2,2,2,1,1,1,1,1)",88128,5129,"lower bound",5129,88128],[5,18,"t","(3,2,2,2,2,2,2,1,1,1)",102102,2992,"lower bound",2992,102102],[5,18,"t","(3,2,2,2,2,2,2,2,1)",70720,1049,"lower bound",1049,70720],[5,18,"t","(3,3,1,1,1,1,1,1,1,1,1,1,1,1)",4641,1347,"lower bound",1347,4641],[5,18,"t","(3,3,2,1,1,1,1,1,1,1,1,1,1)",29172,5280,"lower bound",5280,29172],[5,18,"t","(3,3,2,2,1,1,1,1,1,1,1,1)",99144,10380,"lower bound",10380,99144],[5,18,"t","(3,3,2,2,2,1,1,1,1,1,1)",219912,12222,"lower bound",12222,219912],[5,18,"t","(3,3,2,2,2,2,1,1,1,1)",331500,8909,"lower bound",8909,331500],[5,18,"t","(3,3,2,2,2,2,2,1,1)",322218,3900,"lower bound",3900,322218],[5,18,"t","(3,3,2,2,2,2,2,2)",136136,836,"lower bound",836,136136],[5,18,"t","(3,3,3,1,1,1,1,1,1,1,1,1)",56100,5795,"lower bound",5795,56100],[5,18,"t","(3,3,3,2,1,1,1,1,1,1,1)",228480,12311,"lower bound",12311,228480],[5,18,"t","(3,3,3,2,2,1,1,1,1,1)",501228,12686,"lower bound",12686,501228],[5,18,"t","(3,3,3,2,2,2,1,1,1)",678912,7241,"lower bound",7241,678912],[5,18,"t","(3,3,3,2,2,2,2,1)",510510,2193,"lower bound",2193,510510],[5,18,"t","(3,3,3,3,1,1,1,1,1,1)",259896,6372,"lower bound",6372,259896],[5,18,"t","(3,3,3,3,2,1,1,1,1)",649740,6456,"lower bound",6456,649740],[5,18,"t","(3,3,3,3,2,2,1,1)",787644,2804,"lower bound",2804,787644],[5,18,"t","(3,3,3,3,2,2,2)",364650,492,"lower bound",492,364650],[5,18,"t","(3,3,3,3,3,1,1,1)",408408,1347,"lower bound",1347,408408],[5,18,"t","(3,3,3,3,3,2,1)",466752,459,"lower bound",459,466752],[5,18,"t","(4,2,1,1,1,1,1,1,1,1,1,1,1,1)",7020,2043,"lower bound",2043,7020],[5,18,"t","(4,2,2,1,1,1,1,1,1,1,1,1,1)",35343,6400,"lower bound",6400,35343],[5,18,"t","(4,2,2,2,1,1,1,1,1,1,1,1)",111384,11659,"lower bound",11659,111384],[5,18,"t","(4,2,2,2,2,1,1,1,1,1,1)",238680,13288,"lower bound",13288,238680],[5,18,"t","(4,2,2,2,2,2,1,1,1,1)",353430,9578,"lower bound",9578,353430],[5,18,"t","(4,2,2,2,2,2,2,1,1)",340340,4222,"lower bound",4222,340340],[5,18,"t","(4,2,2,2,2,2,2,2)",143208,927,"lower bound",927,143208],[5,18,"t","(4,3,1,1,1,1,1,1,1,1,1,1,1)",29835,5378,"lower bound",5378,29835],[5,18,"t","(4,3,2,1,1,1,1,1,1,1,1,1)",182784,18802,"lower bound",18802,182784],[5,18,"t","(4,3,2,2,1,1,1,1,1,1,1)",583440,30775,"lower bound",30775,583440],[5,18,"t","(4,3,2,2,2,1,1,1,1,1)",1175040,28027,"lower bound",28027,1175040],[5,18,"t","(4,3,2,2,2,2,1,1,1)",1531530,14519,"lower bound",14519,1531530],[5,18,"t","(4,3,2,2,2,2,2,1)",1131520,4079,"lower bound",4079,1131520],[5,18,"t","(4,3,3,1,1,1,1,1,1,1,1)",358020,18782,"lower bound",18782,358020],[5,18,"t","(4,3,3,2,1,1,1,1,1,1)",1349460,30846,"lower bound",30846,1349460],[5,18,"t","(4,3,3,2,2,1,1,1,1)",2625480,21716,"lower bound",21716,2625480],[5,18,"t","(4,3,3,2,2,2,1,1)",2923830,7379,"lower bound",7379,2923830],[5,18,"t","(4,3,3,2,2,2,2)",1312740,1145,"lower bound",1145,1312740],[5,18,"t","(4,3,3,3,1,1,1,1,1)",1429428,11324,"lower bound",11324,1429428],[5,18,"t","(4,3,3,3,2,1,1,1)",3055104,6562,"lower bound",6562,3055104],[5,18,"t","(4,3,3,3,2,2,1)",2756754,1451,"lower bound",1451,2756754],[5,18,"t","(4,3,3,3,3,1,1)",1575288,681,"lower bound",681,1575288],[5,18,"t","(4,4,1,1,1,1,1,1,1,1,1,1)",58344,5938,"lower bound",5938,58344],[5,18,"t","(4,4,2,1,1,1,1,1,1,1,1)",363528,18922,"lower bound",18922,363528],[5,18,"t","(4,4,2,2,1,1,1,1,1,1)",1099560,24603,"lower bound",24603,1099560],[5,18,"t","(4,4,2,2,2,1,1,1,1)",1989000,15413,"lower bound",15413,1989000],[5,18,"t","(4,4,2,2,2,2,1,1)",2148120,4712,"lower bound",4712,2148120],[5,18,"t","(4,4,2,2,2,2,2)",952952,704,"lower bound",704,952952],[5,18,"t","(4,4,3,1,1,1,1,1,1,1)",848232,19510,"lower bound",19510,848232],[5,18,"t","(4,4,3,2,1,1,1,1,1)",2970240,22689,"lower bound",22689,2970240],[5,18,"t","(4,4,3,2,2,1,1,1)",5012280,9056,"lower bound",9056,5012280],[5,18,"t","(4,4,3,2,2,2,1)",4200768,1561,"lower bound",1561,4200768],[5,18,"t","(4,4,3,3,1,1,1,1)",3007368,5237,"lower bound",5237,3007368],[5,18,"t","(4,4,3,3,2,1,1)",5250960,1393,"lower bound",1393,5250960],[5,18,"t","(4,4,4,1,1,1,1,1,1)",779688,6396,"lower bound",6396,779688],[5,18,"t","(4,4,4,2,1,1,1,1)",2598960,4542,"lower bound",4542,2598960],[5,18,"t","(4,4,4,2,2,1,1)",3675672,795,"lower bound",795,3675672],[5,18,"t","(4,4,4,3,1,1,1)",2858856,553,"lower bound",553,2858856],[5,18,"t","(5,1,1,1,1,1,1,1,1,1,1,1,1,1)",2380,699,"lower bound",699,2380],[5,18,"t","(5,2,1,1,1,1,1,1,1,1,1,1,1)",24192,4378,"lower bound",4378,24192],[5,18,"t","(5,2,2,1,1,1,1,1,1,1,1,1)",116025,11949,"lower bound",11949,116025],[5,18,"t","(5,2,2,2,1,1,1,1,1,1,1)",339456,18232,"lower bound",18232,339456],[5,18,"t","(5,2,2,2,2,1,1,1,1,1)",656370,16738,"lower bound",16738,656370],[5,18,"t","(5,2,2,2,2,2,1,1,1)",837760,9304,"lower bound",9304,837760],[5,18,"t","(5,2,2,2,2,2,2,1)",612612,2967,"lower bound",2967,612612],[5,18,"t","(5,3,1,1,1,1,1,1,1,1,1,1)",106029,10801,"lower bound",10801,106029],[5,18,"t","(5,3,2,1,1,1,1,1,1,1,1)",612612,31384,"lower bound",31384,612612],[5,18,"t","(5,3,2,2,1,1,1,1,1,1)",1790100,39568,"lower bound",39568,1790100],[5,18,"t","(5,3,2,2,2,1,1,1,1)",3180870,25514,"lower bound",25514,3180870],[5,18,"t","(5,3,2,2,2,2,1,1)",3403400,8768,"lower bound",8768,3403400],[5,18,"t","(5,3,2,2,2,2,2)",1503684,1554,"lower bound",1554,1503684],[5,18,"t","(5,3,3,1,1,1,1,1,1,1)",1145664,24800,"lower bound",24800,1145664],[5,18,"t","(5,3,3,2,1,1,1,1,1)",3877632,27552,"lower bound",27552,3877632],[5,18,"t","(5,3,3,2,2,1,1,1)",6432426,11406,"lower bound",11406,6432426],[5,18,"t","(5,3,3,2,2,2,1)",5346432,2407,"lower bound",2407,5346432],[5,18,"t","(5,3,3,3,1,1,1,1)",3646500,5671,"lower bound",5671,3646500],[5,18,"t","(5,3,3,3,2,1,1)",6265350,1782,"lower bound",1782,6265350],[5,18,"t","(5,4,1,1,1,1,1,1,1,1,1)",251328,12805,"lower bound",12805,251328],[5,18,"t","(5,4,2,1,1,1,1,1,1,1)",1458600,31492,"lower bound",31492,1458600],[5,18,"t","(5,4,2,2,1,1,1,1,1)",3965760,27709,"lower bound",27709,3965760],[5,18,"t","(5,4,2,2,2,1,1,1)",6126120,10222,"lower bound",10222,6126120],[5,18,"t","(5,4,2,2,2,2,1)",4950400,2066,"lower bound",2066,4950400],[5,18,"t","(5,4,3,1,1,1,1,1,1)",3198720,22888,"lower bound",22888,3198720],[5,18,"t","(5,4,3,2,1,1,1,1)",9801792,14658,"lower bound",14658,9801792],[5,18,"t","(5,4,3,2,2,1,1)",13366080,3082,"lower bound",3082,13366080],[5,18,"t","(5,4,3,3,1,1,1)",8486400,1602,"lower bound",1602,8486400],[5,18,"t","(5,4,4,1,1,1,1,1)",2858856,4554,"lower bound",4554,2858856],[5,18,"t","(5,4,4,2,1,1,1)",8019648,1376,"lower bound",1376,8019648],[5,18,"t","(5,5,1,1,1,1,1,1,1,1)",302940,6633,"lower bound",6633,302940],[5,18,"t","(5,5,2,1,1,1,1,1,1)",1649340,11579,"lower bound",11579,1649340],[5,18,"t","(5,5,2,2,1,1,1,1)",3978000,5726,"lower bound",5726,3978000],[5,18,"t","(5,5,2,2,2,1,1)",5012280,1160,"lower bound",1160,5012280],[5,18,"t","(5,5,3,1,1,1,1,1)",3508596,5278,"lower bound",5278,3508596],[5,18,"t","(5,5,3,2,1,1,1)",9165312,1602,"lower bound",1602,9165312],[5,18,"t","(5,5,4,1,1,1,1)",3508596,553,"lower bound",553,3508596],[5,18,"t","(6,1,1,1,1,1,1,1,1,1,1,1,1)",6188,1130,"lower bound",1130,6188],[5,18,"t","(6,2,1,1,1,1,1,1,1,1,1,1)",60060,6131,"lower bound",6131,60060],[5,18,"t","(6,2,2,1,1,1,1,1,1,1,1)",268515,13953,"lower bound",13953,268515],[5,18,"t","(6,2,2,2,1,1,1,1,1,1)",714714,17013,"lower bound",17013,714714],[5,18,"t","(6,2,2,2,2,1,1,1,1)",1215500,11850,"lower bound",11850,1215500],[5,18,"t","(6,2,2,2,2,2,1,1)",1272348,4715,"lower bound",4715,1272348],[5,18,"t","(6,2,2,2,2,2,2)",556920,927,"lower bound",927,556920],[5,18,"t","(6,3,1,1,1,1,1,1,1,1,1)",255255,12963,"lower bound",12963,255255],[5,18,"t","(6,3,2,1,1,1,1,1,1,1)",1357824,29072,"lower bound",29072,1357824],[5,18,"t","(6,3,2,2,1,1,1,1,1)",3544398,25603,"lower bound",25603,3544398],[5,18,"t","(6,3,2,2,2,1,1,1)",5361664,10529,"lower bound",10529,5361664],[5,18,"t","(6,3,2,2,2,2,1)",4288284,2529,"lower bound",2529,4288284],[5,18,"t","(6,3,3,1,1,1,1,1,1)",2333760,15725,"lower bound",15725,2333760],[5,18,"t","(6,3,3,2,1,1,1,1)",6872250,9936,"lower bound",9936,6872250],[5,18,"t","(6,3,3,2,2,1,1)",9189180,2476,"lower bound",2476,9189180],[5,18,"t","(6,3,3,3,1,1,1)",5469750,1045,"lower bound",1045,5469750],[5,18,"t","(6,4,1,1,1,1,1,1,1,1)",612612,13247,"lower bound",13247,612612],[5,18,"t","(6,4,2,1,1,1,1,1,1)",3222180,22157,"lower bound",22157,3222180],[5,18,"t","(6,4,2,2,1,1,1,1)",7634088,11022,"lower bound",11022,7634088],[5,18,"t","(6,4,2,2,2,1,1)",9529520,2412,"lower bound",2412,9529520],[5,18,"t","(6,4,3,1,1,1,1,1)",6361740,8970,"lower bound",8970,6361740],[5,18,"t","(6,4,3,2,1,1,1)",16336320,2724,"lower bound",2724,16336320],[5,18,"t","(6,4,4,1,1,1,1)",5105100,731,"lower bound",731,5105100],[5,18,"t","(6,5,1,1,1,1,1,1,1)",875160,6505,"lower bound",6505,875160],[5,18,"t","(6,5,2,1,1,1,1,1)",4230144,6299,"lower bound",6299,4230144],[5,18,"t","(6,5,2,2,1,1,1)",8576568,1469,"lower bound",1469,8576568],[5,18,"t","(6,5,3,1,1,1,1)",7876440,1195,"lower bound",1195,7876440],[5,18,"t","(6,6,1,1,1,1,1,1)",659736,1181,"lower bound",1181,659736],[5,18,"t","(6,6,2,1,1,1,1)",2784600,483,"lower bound",483,2784600],[5,18,"t","(7,1,1,1,1,1,1,1,1,1,1,1)",12376,1262,"lower bound",1262,12376],[5,18,"t","(7,2,1,1,1,1,1,1,1,1,1)",112320,5649,"lower bound",5649,112320],[5,18,"t","(7,2,2,1,1,1,1,1,1,1)",459459,10247,"lower bound",10247,459459],[5,18,"t","(7,2,2,2,1,1,1,1,1)",1089088,9322,"lower bound",9322,1089088],[5,18,"t","(7,2,2,2,2,1,1,1)",1575288,4395,"lower bound",4395,1575288],[5,18,"t","(7,2,2,2,2,2,1)",1233792,1143,"lower bound",1143,1233792],[5,18,"t","(7,3,1,1,1,1,1,1,1,1)",447525,9545,"lower bound",9545,447525],[5,18,"t","(7,3,2,1,1,1,1,1,1)",2144142,15195,"lower bound",15195,2144142],[5,18,"t","(7,3,2,2,1,1,1,1)",4862000,8203,"lower bound",8203,4862000],[5,18,"t","(7,3,2,2,2,1,1)",5937624,2042,"lower bound",2042,5937624],[5,18,"t","(7,3,3,1,1,1,1,1)",3281850,4784,"lower bound",4784,3281850],[5,18,"t","(7,3,3,2,1,1,1)",8078400,1569,"lower bound",1569,8078400],[5,18,"t","(7,4,1,1,1,1,1,1,1)",1018368,7372,"lower bound",7372,1018368],[5,18,"t","(7,4,2,1,1,1,1,1)",4725864,7126,"lower bound",7126,4725864],[5,18,"t","(7,4,2,2,1,1,1)",9382912,1705,"lower bound",1705,9382912],[5,18,"t","(7,4,3,1,1,1,1)",8078400,1258,"lower bound",1258,8078400],[5,18,"t","(7,5,1,1,1,1,1,1)",1432080,2463,"lower bound",2463,1432080],[5,18,"t","(7,5,2,1,1,1,1)",5937624,988,"lower bound",988,5937624],[5,18,"t","(7,6,1,1,1,1,1)",1233792,254,"lower bound",254,1233792],[5,18,"t","(8,1,1,1,1,1,1,1,1,1,1)",19448,947,"lower bound",947,19448],[5,18,"t","(8,2,1,1,1,1,1,1,1,1)",162162,3316,"lower bound",3316,162162],[5,18,"t","(8,2,2,1,1,1,1,1,1)",595595,4546,"lower bound",4546,595595],[5,18,"t","(8,2,2,2,1,1,1,1)",1225224,2734,"lower bound",2734,1225224],[5,18,"t","(8,2,2,2,2,1,1)",1432080,732,"lower bound",732,1432080],[5,18,"t","(8,3,1,1,1,1,1,1,1)",590733,4145,"lower bound",4145,590733],[5,18,"t","(8,3,2,1,1,1,1,1)",2489344,4234,"lower bound",4234,2489344],[5,18,"t","(8,3,2,2,1,1,1)",4725864,1174,"lower bound",1174,4725864],[5,18,"t","(8,3,3,1,1,1,1)",3281850,686,"lower bound",686,3281850],[5,18,"t","(8,4,1,1,1,1,1,1)",1225224,2043,"lower bound",2043,1225224],[5,18,"t","(8,4,2,1,1,1,1)",4862000,922,"lower bound",922,4862000],[5,18,"t","(8,5,1,1,1,1,1)",1575288,295,"lower bound",295,1575288],[5,18,"t","(9,1,1,1,1,1,1,1,1,1)",24310,449,"lower bound",449,24310],[5,18,"t","(9,2,1,1,1,1,1,1,1)",183040,1147,"lower bound",1147,183040],[5,18,"t","(9,2,2,1,1,1,1,1)",590733,1104,"lower bound",1104,590733],[5,18,"t","(9,2,2,2,1,1,1)",1018368,342,"lower bound",342,1018368],[5,18,"t","(9,3,1,1,1,1,1,1)",595595,946,"lower bound",946,595595],[5,18,"t","(9,3,2,1,1,1,1)",2144142,535,"lower bound",535,2144142],[5,18,"t","(9,4,1,1,1,1,1)",1089088,207,"lower bound",207,1089088],[5,18,"t","(9,5,1,1,1,1)",1215500,11,"lower bound",11,1215500],[5,18,"t","(4,3,3,3,3,2)",1021020,109,"lower bound",109,1021020],[5,18,"t","(7,4,4,1,1,1)",5469750,58,"lower bound",58,5469750],[5,18,"t","(7,6,2,1,1,1)",4288284,73,"lower bound",73,4288284],[5,18,"t","(7,3,2,2,2,2)",2784600,433,"lower bound",433,2784600],[5,18,"t","(5,5,4,2,1,1)",7876440,134,"lower bound",134,7876440],[5,18,"t","(8,4,2,2,1,1)",7634088,91,"lower bound",91,7634088],[5,18,"t","(5,3,3,3,3,1)",2362932,93,"lower bound",93,2362932],[5,18,"t","(8,4,3,1,1,1)",6872250,57,"lower bound",57,6872250],[5,18,"t","(4,4,4,4,1,1)",1021020,22,"lower bound",22,1021020],[5,18,"t","(5,5,3,3,1,1)",6534528,112,"lower bound",112,6534528],[5,18,"t","(6,3,3,3,2,1)",6789120,213,"lower bound",213,6789120],[5,18,"t","(6,5,2,2,2,1)",7920640,207,"lower bound",207,7920640],[5,18,"t","(8,6,1,1,1,1)",1272348,25,"lower bound",25,1272348],[5,18,"t","(7,7,1,1,1,1)",556920,16,"lower bound",16,556920],[5,18,"t","(7,4,2,2,2,1)",8576568,299,"lower bound",299,8576568],[5,18,"t","(6,6,2,2,1,1)",4511052,81,"lower bound",81,4511052],[5,18,"t","(6,4,3,3,1,1)",11277630,193,"lower bound",193,11277630],[5,18,"t","(9,3,3,1,1,1)",2333760,23,"lower bound",23,2333760],[5,18,"t","(6,3,3,2,2,2)",4455360,402,"lower bound",402,4455360],[5,18,"t","(6,5,4,1,1,1)",6789120,93,"lower bound",93,6789120],[5,18,"t","(4,4,3,3,2,2)",2756754,177,"lower bound",177,2756754],[5,18,"t","(6,6,3,1,1,1)",4455360,68,"lower bound",68,4455360],[5,18,"t","(5,4,4,2,2,1)",8270262,182,"lower bound",182,8270262],[5,18,"t","(6,4,3,2,2,1)",16243500,420,"lower bound",420,16243500],[5,18,"t","(4,4,4,3,2,1)",3734016,99,"lower bound",99,3734016],[5,18,"t","(8,3,3,2,1,1)",6361740,90,"lower bound",90,6361740],[5,18,"t","(4,4,3,3,3,1)",2042040,80,"lower bound",80,2042040],[5,18,"t","(7,3,3,2,2,1)",7876440,299,"lower bound",299,7876440],[5,18,"t","(4,4,4,2,2,2)",1823250,98,"lower bound",98,1823250],[5,18,"t","(9,2,2,2,2,1)",875160,78,"lower bound",78,875160],[5,18,"t","(3,3,3,3,3,3)",87516,20,"lower bound",20,87516],[5,18,"t","(6,4,2,2,2,2)",4511052,398,"lower bound",398,4511052],[5,18,"t","(8,5,2,1,1,1)",5361664,55,"lower bound",55,5361664],[5,18,"t","(10,2,2,2,1,1)",612612,13,"lower bound",13,612612],[5,18,"t","(9,4,2,1,1,1)",3544398,26,"lower bound",26,3544398],[5,18,"t","(5,5,2,2,2,2)",2382380,143,"lower bound",143,2382380],[5,18,"t","(6,4,4,2,1,1)",11277630,182,"lower bound",182,11277630],[5,18,"t","(5,5,5,1,1,1)",1429428,22,"lower bound",22,1429428],[5,18,"t","(8,2,2,2,2,2)",659736,180,"lower bound",180,659736],[5,18,"t","(7,4,3,2,1,1)",16336320,224,"lower bound",224,16336320],[5,18,"t","(7,5,3,1,1,1)",9189180,105,"lower bound",105,9189180],[5,18,"t","(11,2,1,1,1,1,1)",112320,11,"lower bound",11,112320],[5,18,"t","(6,5,3,2,1,1)",16243500,253,"lower bound",253,16243500],[5,18,"t","(5,4,3,3,2,1)",10720710,265,"lower bound",265,10720710],[5,18,"t","(7,3,3,3,1,1)",5105100,87,"lower bound",87,5105100],[5,18,"t","(7,5,2,2,1,1)",9529520,136,"lower bound",136,9529520],[5,18,"t","(8,3,2,2,2,1)",4230144,236,"lower bound",236,4230144],[5,18,"t","(9,3,2,2,1,1)",3222180,49,"lower bound",49,3222180],[5,18,"t","(5,4,4,3,1,1)",7088796,134,"lower bound",134,7088796],[5,18,"t","(5,5,3,2,2,1)",9189180,193,"lower bound",193,9189180],[5,18,"t","(5,3,3,3,2,2)",3267264,228,"lower bound",228,3267264],[5,18,"t","(10,3,2,1,1,1)",1357824,14,"lower bound",14,1357824],[5,18,"t","(5,4,3,2,2,2)",6534528,380,"lower bound",380,6534528],[5,18,"t","(9,3,2,2,2)",1649340,15,"lower bound",15,1649340],[5,18,"t","(5,5,3,3,2)",4594590,4,"lower bound",4,4594590],[5,18,"t","(7,3,3,3,2)",3508596,7,"lower bound",7,3508596],[5,18,"t","(6,4,3,3,2)",7876440,6,"lower bound",6,7876440],[5,18,"t","(7,5,2,2,2)",5012280,5,"lower bound",5,5012280],[5,18,"t","(11,2,2,1,1,1)",255255,3,"lower bound",3,255255],[5,18,"t","(4,4,4,3,3)",875160,6,"lower bound",6,875160],[5,18,"t","(11,3,1,1,1,1)",268515,1,"lower bound",1,268515],[5,18,"t","(7,4,3,2,2)",9165312,10,"lower bound",10,9165312],[5,18,"t","(8,4,2,2,2)",3978000,15,"lower bound",15,3978000],[5,18,"t","(5,4,4,3,2)",5105100,6,"lower bound",6,5105100],[5,18,"t","(8,3,3,2,2)",3508596,15,"lower bound",15,3508596],[5,18,"t","(4,4,4,4,2)",787644,2,"lower bound",2,787644],[5,18,"t","(5,4,3,3,3)",2333760,12,"lower bound",12,2333760],[5,18,"t","(10,2,2,2,2)",302940,5,"lower bound",5,302940],[5,18,"t","(6,3,3,3,3)",1429428,6,"lower bound",6,1429428],[5,18,"t","(10,4,1,1,1,1)",714714,3,"lower bound",3,714714],[5,19,"t","(18,1)",18,0,"exact",0,0],[5,19,"t","(17,2)",152,0,"exact",0,0],[5,19,"t","(3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",153,98,"lower bound",98,138],[5,19,"t","(17,1,1)",153,0,"exact",0,0],[5,19,"t","(16,3)",798,0,"exact",0,0],[5,19,"t","(16,1,1,1)",816,0,"exact",0,0],[5,19,"t","(16,2,1)",1615,0,"exact",0,0],[5,19,"t","(15,4)",2907,70,"upper bound",0,70],[5,19,"t","(15,1,1,1,1)",3060,70,"upper bound",0,70],[5,19,"t","(15,2,2)",5985,2785,"upper bound",0,2785],[5,19,"t","(14,5)",7752,4552,"upper bound",0,4552],[5,19,"t","(14,1,1,1,1,1)",8568,5368,"upper bound",0,5368],[5,19,"t","(15,3,1)",8892,4429,"upper bound",0,4429],[5,19,"t","(15,2,1,1)",9044,4667,"upper bound",0,4667],[5,19,"t","(13,6)",15504,5904,"upper bound",0,5904],[5,19,"t","(10,9)",16796,1392,"upper bound",0,1392],[5,19,"t","(13,1,1,1,1,1,1)",18564,15364,"upper bound",0,15364],[5,19,"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],[5,19,"t","(19)",1,0,"exact",0,0],[5,19,"t","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",18,15,"lower bound",15,18],[5,20,"t","(19,1)",19,0,"exact",0,0],[5,20,"t","(18,2)",170,0,"exact",0,0],[5,20,"t","(18,1,1)",171,0,"exact",0,0],[5,20,"t","(17,3)",950,0,"exact",0,0],[5,20,"t","(17,1,1,1)",969,0,"exact",0,0],[5,20,"t","(17,2,1)",1920,0,"exact",0,0],[5,20,"t","(16,4)",3705,505,"upper bound",0,505],[5,20,"t","(16,1,1,1,1)",3876,676,"upper bound",0,676],[5,20,"t","(16,2,2)",7600,4400,"upper bound",0,4400],[5,20,"t","(15,5)",10659,7459,"upper bound",0,7459],[5,20,"t","(16,3,1)",11305,8105,"upper bound",0,8105],[5,20,"t","(16,2,1,1)",11475,8275,"upper bound",0,8275],[5,20,"t","(15,1,1,1,1,1)",11628,8428,"upper bound",0,8428],[5,20,"t","(10,10)",16796,13596,"upper bound",0,13596],[5,20,"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],[5,20,"t","(2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)",19,16,"lower bound",16,19],[5,20,"t","(20)",1,0,"exact",0,0],[5,21,"t","(20,1)",20,0,"exact",0,0],[5,21,"t","(19,2)",189,0,"exact",0,0],[5,21,"t","(19,1,1)",190,0,"exact",0,0],[5,21,"t","(18,3)",1120,0,"exact",0,0],[5,21,"t","(18,1,1,1)",1140,0,"exact",0,0],[5,21,"t","(18,2,1)",2261,0,"exact",0,0],[5,21,"t","(17,4)",4655,1455,"upper bound",0,1455],[5,21,"t","(17,1,1,1,1)",4845,1645,"upper bound",0,1645],[5,21,"t","(17,2,2)",9520,6320,"upper bound",0,6320],[5,21,"t","(17,3,1)",14175,10975,"upper bound",0,10975],[5,21,"t","(16,5)",14364,11164,"upper bound",0,11164],[5,21,"t","(17,2,1,1)",14364,11164,"upper bound",0,11164],[5,21,"t","(16,1,1,1,1,1)",15504,12304,"upper bound",0,12304],[5,21,"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],[5,21,"t","(21)",1,0,"exact",0,0],[5,22,"t","(21,1)",21,0,"exact",0,0],[5,22,"t","(20,2)",209,0,"exact",0,0],[5,22,"t","(20,1,1)",210,0,"exact",0,0],[5,22,"t","(19,3)",1309,0,"exact",0,0],[5,22,"t","(19,1,1,1)",1330,0,"exact",0,0],[5,22,"t","(19,2,1)",2640,0,"exact",0,0],[5,22,"t","(18,4)",5775,2575,"upper bound",0,2575],[5,22,"t","(18,1,1,1,1)",5985,2785,"upper bound",0,2785],[5,22,"t","(18,2,2)",11781,8581,"upper bound",0,8581],[5,22,"t","(18,3,1)",17556,14356,"upper bound",0,14356],[5,22,"t","(18,2,1,1)",17765,14565,"upper bound",0,14565],[5,22,"t","(17,5)",19019,15819,"upper bound",0,15819],[5,22,"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],[5,22,"t","(22)",1,0,"exact",0,0],[5,23,"t","(22,1)",22,0,"exact",0,0],[5,23,"t","(21,2)",230,0,"exact",0,0],[5,23,"t","(21,1,1)",231,0,"exact",0,0],[5,23,"t","(20,3)",1518,0,"exact",0,0],[5,23,"t","(20,1,1,1)",1540,0,"exact",0,0],[5,23,"t","(20,2,1)",3059,0,"exact",0,0],[5,23,"t","(19,4)",7084,3884,"upper bound",0,3884],[5,23,"t","(19,1,1,1,1)",7315,4115,"upper bound",0,4115],[5,23,"t","(19,2,2)",14421,11221,"upper bound",0,11221],[5,23,"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],[5,23,"t","(23)",1,0,"exact",0,0],[5,24,"t","(23,1)",23,0,"exact",0,0],[5,24,"t","(22,2)",252,0,"exact",0,0],[5,24,"t","(22,1,1)",253,0,"exact",0,0],[5,24,"t","(21,3)",1748,0,"exact",0,0],[5,24,"t","(21,1,1,1)",1771,0,"exact",0,0],[5,24,"t","(21,2,1)",3520,0,"exact",0,0],[5,24,"t","(20,4)",8602,5402,"upper bound",0,5402],[5,24,"t","(20,1,1,1,1)",8855,5655,"upper bound",0,5655],[5,24,"t","(20,2,2)",17480,14280,"upper bound",0,14280],[5,24,"t","(24)",1,0,"exact",0,0],[5,25,"t","(24,1)",24,0,"exact",0,0],[5,25,"t","(23,2)",275,0,"exact",0,0],[5,25,"t","(23,1,1)",276,0,"exact",0,0],[5,25,"t","(22,3)",2000,0,"exact",0,0],[5,25,"t","(22,1,1,1)",2024,0,"exact",0,0],[5,25,"t","(22,2,1)",4025,0,"exact",0,0],[5,25,"t","(21,4)",10350,7150,"upper bound",0,7150],[5,25,"t","(21,1,1,1,1)",10626,7426,"upper bound",0,7426],[5,25,"t","(25)",1,0,"exact",0,0],[5,26,"t","(25,1)",25,0,"exact",0,0],[5,26,"t","(24,2)",299,0,"exact",0,0],[5,26,"t","(24,1,1)",300,0,"exact",0,0],[5,26,"t","(23,3)",2275,0,"exact",0,0],[5,26,"t","(23,1,1,1)",2300,0,"exact",0,0],[5,26,"t","(23,2,1)",4576,1465,"upper bound",0,1465],[5,26,"t","(22,4)",12350,9150,"upper bound",0,9150],[5,26,"t","(22,1,1,1,1)",12650,9450,"upper bound",0,9450],[5,26,"t","(26)",1,0,"exact",0,0],[5,27,"t","(26,1)",26,0,"exact",0,0],[5,27,"t","(25,2)",324,0,"exact",0,0],[5,27,"t","(25,1,1)",325,0,"exact",0,0],[5,27,"t","(24,3)",2574,0,"exact",0,0],[5,27,"t","(24,1,1,1)",2600,0,"exact",0,0],[5,27,"t","(24,2,1)",5175,2016,"upper bound",0,2016],[5,27,"t","(23,4)",14625,11425,"upper bound",0,11425],[5,27,"t","(23,1,1,1,1)",14950,11750,"upper bound",0,11750],[5,27,"t","(27)",1,0,"exact",0,0],[5,28,"t","(27,1)",27,0,"exact",0,0],[5,28,"t","(26,2)",350,0,"exact",0,0],[5,28,"t","(26,1,1)",351,0,"exact",0,0],[5,28,"t","(25,3)",2898,0,"exact",0,0],[5,28,"t","(25,1,1,1)",2925,0,"exact",0,0],[5,28,"t","(25,2,1)",5824,2624,"upper bound",0,2624],[5,28,"t","(24,4)",17199,13999,"upper bound",0,13999],[5,28,"t","(24,1,1,1,1)",17550,14350,"upper bound",0,14350],[5,28,"t","(28)",1,0,"exact",0,0],[5,29,"t","(28,1)",28,0,"exact",0,0],[5,29,"t","(27,2)",377,0,"exact",0,0],[5,29,"t","(27,1,1)",378,0,"exact",0,0],[5,29,"t","(26,3)",3248,0,"exact",0,0],[5,29,"t","(26,1,1,1)",3276,0,"exact",0,0],[5,29,"t","(26,2,1)",6525,3325,"upper bound",0,3325],[5,29,"t","(29)",1,0,"exact",0,0],[5,30,"t","(29,1)",29,0,"exact",0,0],[5,30,"t","(28,2)",405,0,"exact",0,0],[5,30,"t","(28,1,1)",406,0,"exact",0,0],[5,30,"t","(27,3)",3625,0,"exact",0,0],[5,30,"t","(27,1,1,1)",3654,0,"exact",0,0],[5,30,"t","(27,2,1)",7280,4080,"upper bound",0,4080],[5,30,"t","(30)",1,0,"exact",0,0],[5,31,"t","(30,1)",30,0,"exact",0,0],[5,31,"t","(29,2)",434,0,"exact",0,0],[5,31,"t","(29,1,1)",435,0,"exact",0,0],[5,31,"t","(28,3)",4030,0,"exact",0,0],[5,31,"t","(28,1,1,1)",4060,0,"exact",0,0],[5,31,"t","(28,2,1)",8091,4891,"upper bound",0,4891]]}