//the five known 2-(56,11,2) designs and dimension of each ternary code //b1 // print Dim(ec); //20 bloxb1:= [ { 3, 10, 17, 20, 23, 30, 36, 40, 47, 53, 55 }, { 5, 11, 14, 17, 18, 20, 26, 33, 34, 44, 50 }, { 2, 7, 11, 13, 17, 19, 24, 32, 41, 45, 55 }, { 11, 13, 15, 18, 38, 39, 42, 43, 46, 47, 53 }, { 1, 7, 14, 15, 22, 25, 30, 33, 39, 40, 45 }, { 1, 4, 5, 9, 11, 16, 19, 37, 40, 47, 49 }, { 12, 16, 18, 19, 22, 26, 30, 31, 38, 52, 55 }, { 5, 8, 29, 30, 34, 37, 38, 41, 45, 51, 53 }, { 5, 6, 9, 15, 18, 23, 32, 36, 45, 52, 54 }, { 15, 24, 26, 28, 34, 37, 40, 46, 48, 54, 55 }, { 6, 16, 24, 31, 32, 33, 40, 42, 44, 51, 53 }, { 5, 7, 16, 20, 21, 30, 32, 43, 46, 48, 56 }, { 1, 3, 6, 11, 20, 28, 31, 35, 38, 45, 48 }, { 2, 15, 16, 17, 23, 27, 33, 35, 37, 38, 56 }, { 3, 4, 8, 12, 16, 17, 39, 44, 45, 46, 54 }, { 3, 4, 15, 26, 30, 32, 35, 41, 42, 49, 50 }, { 2, 3, 7, 9, 14, 31, 37, 46, 50, 52, 53 }, { 5, 7, 10, 12, 15, 27, 28, 31, 41, 44, 47 }, { 1, 3, 12, 18, 21, 24, 33, 36, 37, 41, 43 }, { 1, 2, 5, 12, 23, 39, 42, 48, 50, 51, 55 }, { 8, 9, 19, 20, 22, 23, 28, 33, 41, 42, 46 }, { 9, 10, 12, 13, 26, 33, 45, 48, 49, 53, 56 }, { 10, 18, 19, 21, 27, 35, 40, 45, 46, 50, 51 }, { 9, 12, 17, 25, 28, 29, 32, 38, 40, 43, 50 }, { 1, 9, 13, 17, 21, 27, 30, 31, 34, 42, 54 }, { 8, 10, 11, 21, 23, 25, 26, 31, 32, 37, 39 }, { 4, 22, 23, 24, 31, 34, 43, 45, 47, 50, 56 }, { 6, 9, 10, 14, 16, 34, 35, 39, 41, 43, 55 }, { 1, 7, 19, 23, 26, 29, 35, 43, 44, 53, 54 }, { 2, 14, 16, 21, 26, 28, 29, 36, 42, 45, 47 }, { 6, 7, 8, 21, 33, 38, 47, 49, 50, 54, 55 }, { 8, 14, 15, 17, 19, 31, 36, 43, 48, 49, 51 }, { 1, 4, 8, 14, 18, 27, 28, 32, 53, 55, 56 }, { 2, 8, 9, 18, 24, 25, 30, 35, 44, 47, 48 }, { 2, 18, 20, 29, 31, 39, 40, 41, 49, 54, 56 }, { 1, 2, 10, 22, 32, 34, 36, 38, 44, 46, 49 }, { 11, 16, 22, 25, 27, 36, 41, 48, 50, 53, 54 }, { 6, 11, 12, 14, 23, 24, 27, 29, 30, 46, 49 }, { 2, 4, 10, 11, 28, 30, 33, 43, 51, 52, 54 }, { 4, 5, 13, 25, 29, 31, 33, 35, 36, 46, 55 }, { 3, 19, 27, 29, 32, 33, 34, 39, 47, 48, 52 }, { 3, 7, 13, 16, 18, 23, 25, 28, 34, 49, 51 }, { 4, 6, 7, 10, 17, 18, 22, 29, 37, 42, 48 }, { 5, 17, 21, 22, 24, 28, 35, 39, 49, 52, 53 }, { 6, 13, 19, 28, 30, 36, 37, 39, 44, 50, 56 }, { 12, 13, 14, 20, 22, 32, 35, 37, 47, 51, 54 }, { 1, 8, 10, 13, 15, 16, 20, 24, 29, 50, 52 }, { 2, 4, 6, 12, 15, 19, 20, 21, 25, 34, 53 }, { 3, 9, 11, 15, 21, 22, 29, 44, 51, 55, 56 }, { 1, 6, 17, 25, 26, 41, 46, 47, 51, 52, 56 }, { 4, 13, 14, 21, 23, 38, 40, 41, 44, 48, 52 }, { 3, 5, 10, 14, 19, 24, 25, 38, 42, 54, 56 }, { 20, 25, 27, 37, 42, 43, 44, 45, 49, 52, 55 }, { 7, 8, 11, 12, 34, 35, 36, 40, 42, 52, 56 }, { 4, 7, 9, 20, 24, 26, 27, 36, 38, 39, 51 }, { 2, 3, 5, 6, 8, 13, 22, 26, 27, 40, 43 } ]; //> restore "b2.w"; //b2 //> print Dim(dc); 22 bloxb2:= [ { 1, 12, 19, 23, 30, 37, 45, 47, 48, 49, 51 }, { 1, 4, 5, 6, 14, 20, 22, 31, 36, 45, 53 }, { 1, 2, 3, 5, 11, 17, 26, 35, 40, 49, 50 }, { 1, 17, 21, 29, 30, 31, 38, 41, 44, 54, 56 }, { 3, 8, 13, 23, 24, 29, 34, 45, 50, 53, 56 }, { 7, 17, 21, 22, 24, 27, 39, 40, 45, 51, 52 }, { 1, 15, 18, 23, 25, 28, 40, 41, 46, 52, 53 }, { 7, 12, 13, 25, 26, 32, 35, 36, 38, 41, 45 }, { 1, 3, 6, 7, 9, 15, 24, 33, 38, 47, 55 }, { 3, 10, 11, 14, 16, 18, 37, 38, 45, 52, 54 }, { 1, 13, 14, 26, 27, 29, 33, 37, 39, 42, 46 }, { 4, 8, 15, 26, 33, 40, 43, 44, 45, 48, 54 }, { 1, 2, 4, 7, 10, 16, 25, 34, 39, 48, 56 }, { 1, 8, 10, 18, 19, 20, 24, 27, 32, 35, 44 }, { 1, 11, 13, 22, 28, 32, 34, 43, 51, 54, 55 }, { 2, 15, 18, 30, 31, 32, 39, 42, 45, 50, 55 }, { 6, 10, 17, 28, 35, 42, 43, 45, 46, 47, 56 }, { 5, 9, 16, 27, 34, 41, 44, 45, 46, 49, 55 }, { 2, 9, 11, 19, 20, 21, 25, 28, 29, 33, 45 }, { 1, 8, 9, 12, 16, 21, 36, 42, 43, 50, 52 }, { 5, 10, 11, 23, 24, 30, 33, 36, 39, 41, 43 }, { 2, 3, 4, 6, 12, 18, 27, 29, 41, 43, 51 }, { 7, 14, 16, 19, 23, 29, 31, 35, 40, 43, 55 }, { 4, 15, 16, 17, 24, 28, 29, 32, 36, 37, 49 }, { 4, 18, 21, 22, 23, 33, 34, 35, 38, 42, 49 }, { 3, 14, 21, 25, 32, 39, 43, 44, 47, 49, 53 }, { 3, 4, 5, 7, 13, 19, 28, 30, 42, 44, 52 }, { 5, 12, 14, 18, 21, 24, 26, 28, 48, 55, 56 }, { 6, 9, 13, 18, 19, 36, 39, 40, 49, 54, 56 }, { 2, 33, 35, 36, 37, 44, 51, 52, 53, 55, 56 }, { 3, 8, 9, 22, 28, 31, 35, 37, 39, 41, 48 }, { 5, 12, 15, 20, 29, 34, 35, 39, 47, 52, 54 }, { 2, 8, 14, 27, 28, 30, 34, 36, 38, 40, 47 }, { 5, 8, 13, 16, 17, 18, 25, 31, 33, 47, 51 }, { 5, 9, 10, 29, 32, 38, 40, 42, 48, 51, 53 }, { 4, 9, 14, 24, 25, 30, 35, 46, 50, 51, 54 }, { 4, 9, 11, 23, 26, 27, 31, 32, 47, 52, 56 }, { 3, 10, 15, 19, 21, 26, 31, 34, 36, 46, 51 }, { 3, 17, 20, 23, 25, 27, 36, 42, 48, 54, 55 }, { 2, 5, 6, 7, 8, 21, 23, 32, 37, 46, 54 }, { 7, 10, 12, 27, 28, 31, 33, 49, 50, 53, 54 }, { 7, 11, 18, 22, 29, 36, 44, 46, 47, 48, 50 }, { 6, 16, 20, 23, 26, 28, 38, 39, 44, 50, 51 }, { 6, 11, 13, 15, 16, 21, 27, 30, 35, 48, 53 }, { 2, 16, 19, 22, 24, 26, 41, 42, 47, 53, 54 }, { 2, 13, 20, 24, 31, 38, 43, 46, 48, 49, 52 }, { 3, 12, 16, 20, 22, 30, 32, 33, 40, 46, 56 }, { 7, 9, 17, 18, 20, 26, 30, 34, 37, 43, 53 }, { 2, 9, 10, 12, 13, 14, 15, 17, 22, 23, 44 }, { 7, 8, 11, 14, 15, 20, 41, 42, 49, 51, 56 }, { 6, 14, 17, 19, 32, 33, 34, 41, 48, 50, 52 }, { 5, 15, 19, 22, 25, 27, 37, 38, 43, 50, 56 }, { 4, 8, 11, 12, 17, 19, 38, 39, 46, 53, 55 }, { 4, 10, 13, 20, 21, 37, 40, 41, 47, 50, 55 }, { 6, 8, 10, 22, 25, 26, 29, 30, 49, 52, 55 }, { 6, 11, 12, 24, 25, 31, 34, 37, 40, 42, 44 } ]; //> restore "b3.w"; //b3 > print Dim(dc); 26 bloxb3:= [ { 1, 12, 19, 23, 30, 37, 45, 47, 48, 49, 51 }, { 1, 4, 5, 6, 14, 20, 22, 31, 36, 45, 53 }, { 3, 9, 10, 13, 25, 27, 30, 31, 40, 43, 45 }, { 1, 2, 3, 5, 11, 17, 26, 35, 40, 49, 50 }, { 1, 17, 21, 29, 30, 31, 38, 41, 44, 54, 56 }, { 2, 14, 15, 21, 24, 34, 35, 37, 41, 43, 45 }, { 1, 15, 18, 23, 25, 28, 40, 41, 46, 52, 53 }, { 1, 3, 6, 7, 9, 15, 24, 33, 38, 47, 55 }, { 1, 13, 14, 26, 27, 29, 33, 37, 39, 42, 46 }, { 7, 10, 11, 21, 23, 26, 42, 44, 45, 53, 55 }, { 1, 2, 4, 7, 10, 16, 25, 34, 39, 48, 56 }, { 4, 27, 28, 29, 35, 38, 45, 48, 50, 52, 55 }, { 1, 8, 10, 18, 19, 20, 24, 27, 32, 35, 44 }, { 1, 11, 13, 22, 28, 32, 34, 43, 51, 54, 55 }, { 2, 8, 9, 18, 22, 26, 38, 45, 46, 51, 56 }, { 6, 8, 11, 16, 29, 32, 39, 40, 41, 45, 47 }, { 5, 24, 25, 32, 33, 42, 45, 49, 52, 54, 56 }, { 7, 13, 15, 16, 17, 19, 20, 45, 46, 50, 54 }, { 1, 8, 9, 12, 16, 21, 36, 42, 43, 50, 52 }, { 3, 12, 17, 18, 28, 33, 34, 36, 39, 44, 45 }, { 9, 11, 14, 17, 20, 23, 27, 34, 47, 52, 56 }, { 4, 10, 11, 12, 20, 33, 38, 41, 43, 46, 49 }, { 10, 14, 15, 17, 32, 36, 38, 40, 42, 48, 51 }, { 2, 11, 13, 19, 24, 30, 36, 38, 39, 52, 53 }, { 5, 7, 8, 12, 27, 34, 37, 38, 40, 53, 54 }, { 5, 14, 16, 19, 25, 26, 28, 38, 43, 44, 47 }, { 5, 10, 13, 18, 36, 37, 41, 47, 50, 55, 56 }, { 9, 10, 16, 17, 22, 24, 28, 29, 37, 49, 53 }, { 7, 11, 12, 14, 18, 24, 25, 29, 31, 50, 51 }, { 3, 5, 6, 10, 19, 21, 29, 34, 46, 51, 52 }, { 4, 8, 13, 17, 21, 25, 33, 35, 47, 51, 53 }, { 2, 6, 12, 17, 19, 22, 25, 27, 41, 42, 55 }, { 7, 19, 22, 23, 29, 33, 35, 36, 40, 43, 56 }, { 6, 9, 11, 25, 35, 36, 37, 44, 46, 48, 54 }, { 5, 7, 9, 20, 28, 30, 35, 39, 41, 42, 51 }, { 3, 7, 8, 13, 14, 22, 41, 44, 48, 49, 52 }, { 10, 12, 15, 22, 26, 31, 35, 39, 47, 52, 54 }, { 8, 15, 20, 25, 26, 29, 30, 34, 36, 49, 55 }, { 2, 16, 20, 31, 33, 37, 40, 44, 51, 52, 55 }, { 9, 19, 26, 31, 32, 33, 34, 41, 48, 50, 53 }, { 6, 15, 27, 39, 43, 44, 49, 50, 51, 53, 56 }, { 2, 4, 5, 9, 12, 13, 15, 23, 29, 32, 44 }, { 3, 12, 14, 16, 30, 32, 35, 46, 53, 55, 56 }, { 2, 3, 18, 20, 29, 42, 43, 47, 48, 53, 54 }, { 3, 4, 8, 11, 15, 19, 28, 31, 37, 42, 56 }, { 5, 8, 17, 23, 24, 31, 39, 43, 46, 48, 55 }, { 2, 6, 8, 10, 14, 23, 28, 30, 33, 50, 54 }, { 4, 9, 14, 18, 19, 21, 39, 40, 49, 54, 55 }, { 4, 22, 24, 30, 34, 40, 42, 44, 46, 47, 50 }, { 6, 12, 13, 20, 21, 24, 26, 28, 40, 48, 56 }, { 4, 6, 7, 17, 18, 26, 30, 32, 37, 43, 52 }, { 5, 11, 15, 16, 18, 21, 22, 27, 30, 33, 48 }, { 2, 7, 21, 27, 28, 31, 32, 36, 46, 47, 49 }, { 3, 20, 21, 22, 23, 25, 32, 37, 38, 39, 50 }, { 3, 4, 16, 23, 24, 26, 27, 36, 41, 51, 54 }, { 6, 13, 16, 18, 23, 31, 34, 35, 38, 42, 49 } ]; //> restore "b4.w"; //b4 //> print Dim(descode(56,blox,3)); 24 bloxb4:= [ { 1, 3, 5, 7, 18, 20, 22, 24, 53, 54, 56 }, { 2, 4, 6, 8, 17, 19, 21, 23, 53, 54, 55 }, { 9, 11, 13, 15, 26, 28, 30, 32, 54, 55, 56 }, { 10, 12, 14, 16, 25, 27, 29, 31, 53, 55, 56 }, { 2, 6, 12, 16, 20, 24, 26, 30, 49, 50, 51 }, { 3, 7, 9, 13, 17, 21, 27, 31, 50, 51, 52 }, { 1, 5, 11, 15, 19, 23, 25, 29, 49, 50, 52 }, { 4, 8, 10, 14, 18, 22, 28, 32, 49, 51, 52 }, { 3, 8, 11, 16, 18, 19, 26, 27, 41, 43, 45 }, { 3, 6, 10, 15, 19, 20, 31, 32, 33, 35, 37 }, { 3, 6, 11, 14, 21, 22, 29, 30, 44, 46, 48 }, { 3, 8, 12, 15, 17, 24, 28, 29, 34, 38, 40 }, { 4, 7, 12, 15, 22, 23, 30, 31, 41, 45, 47 }, { 1, 6, 10, 13, 22, 23, 26, 27, 36, 38, 40 }, { 1, 4, 13, 16, 17, 18, 29, 30, 33, 35, 39 }, { 2, 7, 10, 15, 17, 18, 25, 26, 42, 44, 48 }, { 2, 5, 9, 14, 18, 19, 30, 31, 34, 36, 40 }, { 1, 6, 9, 14, 17, 24, 25, 32, 41, 43, 47 }, { 5, 8, 13, 16, 23, 24, 31, 32, 42, 46, 48 }, { 4, 7, 11, 16, 20, 21, 25, 32, 34, 36, 38 }, { 5, 8, 9, 12, 21, 22, 25, 26, 35, 37, 39 }, { 2, 5, 10, 13, 20, 21, 28, 29, 43, 45, 47 }, { 1, 4, 9, 12, 19, 20, 27, 28, 42, 44, 46 }, { 2, 7, 11, 14, 23, 24, 27, 28, 33, 37, 39 }, { 7, 19, 26, 29, 32, 39, 40, 46, 47, 51, 53 }, { 1, 7, 8, 10, 30, 34, 37, 43, 46, 50, 55 }, { 3, 4, 5, 14, 26, 33, 38, 42, 47, 50, 55 }, { 14, 17, 20, 23, 26, 34, 35, 45, 46, 52, 56 }, { 3, 23, 25, 28, 30, 35, 36, 42, 43, 51, 53 }, { 2, 22, 27, 29, 32, 34, 35, 41, 42, 50, 54 }, { 5, 10, 11, 12, 17, 33, 36, 41, 46, 51, 54 }, { 12, 18, 21, 23, 32, 33, 40, 43, 44, 50, 56 }, { 15, 18, 21, 24, 27, 35, 36, 46, 47, 49, 55 }, { 2, 3, 4, 13, 25, 37, 40, 41, 46, 49, 56 }, { 4, 9, 10, 11, 24, 35, 40, 45, 48, 50, 53 }, { 5, 17, 27, 30, 32, 37, 38, 44, 45, 49, 53 }, { 6, 11, 12, 13, 18, 34, 37, 42, 47, 52, 53 }, { 9, 18, 20, 23, 29, 37, 38, 41, 48, 51, 55 }, { 5, 6, 7, 16, 28, 35, 40, 41, 44, 52, 55 }, { 8, 13, 14, 15, 20, 36, 39, 41, 44, 50, 53 }, { 13, 19, 22, 24, 25, 33, 34, 44, 45, 51, 55 }, { 3, 9, 10, 16, 23, 34, 39, 44, 47, 49, 54 }, { 1, 2, 3, 12, 32, 36, 39, 45, 48, 52, 55 }, { 16, 17, 19, 22, 28, 36, 37, 47, 48, 50, 56 }, { 4, 24, 26, 29, 31, 36, 37, 43, 44, 52, 54 }, { 1, 2, 8, 11, 31, 35, 38, 44, 47, 51, 56 }, { 8, 20, 25, 27, 30, 33, 40, 47, 48, 52, 54 }, { 2, 9, 15, 16, 22, 33, 38, 43, 46, 52, 53 }, { 6, 18, 25, 28, 31, 38, 39, 45, 46, 50, 54 }, { 4, 5, 6, 15, 27, 34, 39, 43, 48, 51, 56 }, { 1, 14, 15, 16, 21, 37, 40, 42, 45, 51, 54 }, { 1, 21, 26, 28, 31, 33, 34, 41, 48, 49, 53 }, { 7, 12, 13, 14, 19, 35, 38, 43, 48, 49, 54 }, { 6, 7, 8, 9, 29, 33, 36, 42, 45, 49, 56 }, { 11, 17, 20, 22, 31, 39, 40, 42, 43, 49, 55 }, { 10, 19, 21, 24, 30, 38, 39, 41, 42, 52, 56 } ]; //b5 //> print Dim(descode(56,blox,3)); 26 bloxb5:= [ { 1, 2, 3, 4, 5, 6, 7, 8, 9, 55, 56 }, { 10, 11, 12, 13, 14, 15, 16, 17, 18, 55, 56 }, { 2, 11, 20, 21, 30, 31, 34, 37, 41, 43, 55 }, { 3, 12, 19, 21, 28, 32, 35, 38, 42, 44, 55 }, { 1, 10, 19, 20, 29, 33, 36, 39, 40, 45, 55 }, { 4, 15, 22, 23, 28, 31, 36, 47, 49, 53, 55 }, { 5, 13, 23, 24, 29, 32, 34, 48, 50, 54, 55 }, { 6, 14, 22, 24, 30, 33, 35, 46, 51, 52, 55 }, { 9, 16, 26, 27, 37, 40, 44, 48, 51, 53, 55 }, { 7, 17, 25, 27, 38, 41, 45, 46, 49, 54, 55 }, { 8, 18, 25, 26, 39, 42, 43, 47, 50, 52, 55 }, { 3, 16, 29, 31, 36, 37, 38, 46, 50, 52, 56 }, { 1, 17, 30, 32, 34, 38, 39, 47, 51, 53, 56 }, { 2, 18, 28, 33, 35, 37, 39, 48, 49, 54, 56 }, { 4, 12, 20, 22, 25, 29, 41, 42, 48, 51, 56 }, { 5, 10, 21, 23, 26, 30, 40, 42, 46, 49, 56 }, { 6, 11, 19, 24, 27, 28, 40, 41, 47, 50, 56 }, { 8, 14, 19, 22, 26, 31, 34, 44, 45, 54, 56 }, { 9, 15, 20, 23, 27, 32, 35, 43, 45, 52, 56 }, { 7, 13, 21, 24, 25, 33, 36, 43, 44, 53, 56 }, { 2, 3, 13, 17, 21, 22, 40, 45, 47, 48, 52 }, { 1, 3, 14, 18, 19, 23, 41, 43, 46, 48, 53 }, { 1, 2, 15, 16, 20, 24, 42, 44, 46, 47, 54 }, { 5, 6, 13, 16, 31, 35, 39, 41, 42, 45, 53 }, { 4, 6, 14, 17, 32, 36, 37, 40, 42, 43, 54 }, { 4, 5, 15, 18, 33, 34, 38, 40, 41, 44, 52 }, { 8, 9, 14, 16, 21, 29, 32, 33, 41, 47, 49 }, { 7, 9, 15, 17, 19, 30, 31, 33, 42, 48, 50 }, { 7, 8, 13, 18, 20, 28, 31, 32, 40, 46, 51 }, { 2, 4, 11, 12, 26, 32, 33, 45, 46, 50, 53 }, { 3, 5, 10, 12, 27, 31, 33, 43, 47, 51, 54 }, { 1, 6, 10, 11, 25, 31, 32, 44, 48, 49, 52 }, { 1, 5, 14, 15, 21, 25, 28, 37, 45, 50, 51 }, { 2, 6, 13, 15, 19, 26, 29, 38, 43, 49, 51 }, { 3, 4, 13, 14, 20, 27, 30, 39, 44, 49, 50 }, { 1, 4, 17, 18, 21, 24, 26, 27, 29, 31, 35 }, { 2, 5, 16, 18, 19, 22, 25, 27, 30, 32, 36 }, { 3, 6, 16, 17, 20, 23, 25, 26, 28, 33, 34 }, { 2, 9, 12, 14, 23, 24, 25, 31, 38, 39, 40 }, { 3, 7, 10, 15, 22, 24, 26, 32, 37, 39, 41 }, { 1, 8, 11, 13, 22, 23, 27, 33, 37, 38, 42 }, { 2, 7, 10, 14, 27, 28, 29, 34, 42, 52, 53 }, { 3, 8, 11, 15, 25, 29, 30, 35, 40, 53, 54 }, { 1, 9, 12, 13, 26, 28, 30, 36, 41, 52, 54 }, { 2, 8, 10, 17, 23, 35, 36, 41, 44, 50, 51 }, { 3, 9, 11, 18, 24, 34, 36, 42, 45, 49, 51 }, { 1, 7, 12, 16, 22, 34, 35, 40, 43, 49, 50 }, { 5, 7, 11, 14, 20, 26, 35, 36, 38, 47, 48 }, { 6, 8, 12, 15, 21, 27, 34, 36, 39, 46, 48 }, { 4, 9, 10, 13, 19, 25, 34, 35, 37, 46, 47 }, { 6, 7, 12, 18, 23, 29, 30, 37, 44, 45, 47 }, { 4, 8, 10, 16, 24, 28, 30, 38, 43, 45, 48 }, { 5, 9, 11, 17, 22, 28, 29, 39, 43, 44, 46 }, { 6, 9, 10, 18, 20, 21, 22, 38, 50, 53, 54 }, { 4, 7, 11, 16, 19, 21, 23, 39, 51, 52, 54 }, { 5, 8, 12, 17, 19, 20, 24, 37, 49, 52, 53 } ];