### This work done by Omar A. AbuGhneim from Jordan University (Email: o_abughneim@yahoo.com). # There are 267 groups of order 64. Among them, there are 259 groups that # admit (64,28,12) difference sets. The other 8 groups do not have any # (64,28,12) difference sets. We wrote programs using the software GAP # to construct all (64,28,12) difference sets in the 259 groups of order # 64 that admit (64,28,12) difference sets. # We refer to the groups as they appear in the SmallGroups library of # the software package GAP. For instance, when we work in groups of # order 64 and write [64,14] we mean group number 14 of order 64 in the # GAP library. # The 8 groups that do not admit (64,28,12) difference sets are # [64, 1], [64, 38], [64, 47], [64, 50], [64, 52], [64, 53], [64, 54], # and [64, 186]. Indeed, these groups are the ones that have either # the cyclic group of order 32 as a factor group or have the dihedral # group of order 32 as a factor group. # Also, we find all (64,28,12) difference sets that are reversible # i.e. all (64,28,12) difference sets D with D=D^(-1). There are 184 # groups of order 64 that have reversible (64,28,12) difference sets. # These groups are [64,i] where i in {2, 3, 4, 5, 8, 9, 10, 11, 12, 13, # 15, 16, 18, 20, 22, 23, 24, 25, 28, 30, 31, 32, 33, 34, 35, 36, 37, 40, # 41, 42, 43, 45, 46, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, # 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 87, # 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 104, 105, 106, # 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 126, # 127, 128, 129, 130, 131, 133, 134, 135, 138, 140, 141, 142, 144, 145, 146, # 147, 149, 150, 151, 152, 153, 155, 156, 157, 159, 160, 161, 162, 163, 164, # 166, 167, 169, 170, 172, 173, 174, 177, 178, 179, 182, 184, 187, 190, 192, # 193, 194, 195, 196, 197, 199, 200, 202, 203, 204, 205, 206, 207, 208, 209, # 210, 211, 213, 214, 215, 216, 219, 221, 222, 226, 227, 231, 232, 234, 236, # 240, 241, 242, 245, 247, 249, 250, 251, 254, 260, 261, 263, 267 }. # We used the software GAP to find all (64,28,12) difference sets and # reversible (64,28,12) difference sets. # In this file we list all inequivalent (64,28,12) difference sets # in group [64,107]. Also, we determine the nonisomorphic # symmetric (64,28,12) designs that rise from these DSs. # Note that there is no reversible (64,28,12) difference sets in # group [64,107]. # To determine the nonisomorphic symmetric (64,28,12) designs, we used # the DESIGN package for GAP, Version 1.6, 2011, by L.H. Soicher, # http://designtheory.org/software/gap design/. # Note: The GAP command 'e:=Elements(SmallGroup(64,107));' can be # used to create a list e of the elements of the group [64,107]. # In our list of (64,28,12) DSs in group [64,107], we have [1, # 2, 3, 4, 5, 6, 8, 9, 12, 13, 18, 20, 21, 25, 30, # 33, 35, 36, 37, 38, 42, 45, 49, 50, 51, 52, 54, 60]. # This list denotes the elements [ e[1], e[2], e[3], # e[4], e[5], e[6], e[8], e[9], e[12], e[13], e[18], e[20], e[21], e[25], e[30], e[33], # e[35], e[36], e[37], e[38], e[42], e[45], e[49], e[50], e[51], e[52], e[54], e[60]] # where e is the list of the elements of the group [64,107] as they # appear when one uses the GAP command 'e:=Elements(SmallGroup(96,10))(64,107));' ########################### ########################### ########################### ### List of all (64,28,12) difference sets and the nonisomorphic symmetric (64,28,12) designs ### that rise from these DSs in group [64, 107] ### The number of inequivalent (64,28,12) DSs in group [64,107] is 314 ### The list of all inequivalent (64,28,12) DSs in group [64,107] is DS107:=[ [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 18, 20, 21, 25, 30, 33, 35, 36, 37, 38, 42, 45, 49, 50, 51, 52, 54, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 14, 16, 18, 20, 25, 26, 30, 33, 37, 40, 48, 49, 50, 51, 52, 55, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 14, 16, 18, 20, 21, 25, 30, 37, 42, 45, 49, 50, 51, 52, 53, 54, 55, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 12, 13, 14, 16, 18, 20, 21, 25, 30, 33, 37, 42, 45, 49, 50, 51, 52, 55, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 18, 24, 26, 29, 32, 33, 37, 38, 39, 40, 42, 47, 49, 53, 55, 56, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 18, 24, 26, 29, 32, 36, 38, 39, 40, 42, 47, 49, 54, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 18, 20, 24, 26, 29, 32, 38, 40, 47, 49, 53, 54, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 18, 20, 29, 32, 33, 37, 40, 46, 47, 48, 49, 55, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 18, 20, 24, 29, 32, 33, 37, 40, 48, 49, 55, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 18, 21, 25, 30, 31, 32, 33, 34, 35, 37, 38, 39, 45, 51, 52, 54, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 17, 18, 21, 25, 30, 31, 32, 34, 35, 37, 38, 40, 45, 51, 52, 53, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 16, 18, 25, 30, 31, 32, 33, 34, 37, 39, 40, 42, 45, 51, 52, 54, 55, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 16, 18, 20, 30, 31, 32, 33, 34, 37, 40, 44, 45, 48, 51, 52, 54, 55, 57 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 16, 18, 20, 25, 26, 32, 33, 34, 37, 40, 48, 49, 50, 51, 52, 54, 55, 57 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 16, 18, 20, 23, 26, 30, 31, 32, 34, 40, 45, 51, 52, 53, 54, 55, 56, 57 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 16, 18, 20, 23, 25, 26, 32, 37, 40, 45, 48, 49, 50, 51, 52, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 16, 18, 20, 21, 25, 32, 33, 34, 37, 42, 45, 49, 50, 51, 52, 54, 55, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 16, 17, 18, 21, 25, 30, 31, 32, 34, 40, 45, 51, 52, 53, 54, 55, 56, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 15, 18, 26, 30, 31, 32, 33, 35, 37, 39, 40, 42, 44, 51, 52, 54, 55, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 15, 18, 23, 26, 30, 31, 32, 35, 37, 39, 40, 42, 45, 51, 52, 53, 55, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 15, 17, 18, 21, 30, 31, 32, 35, 37, 40, 44, 45, 48, 51, 52, 53, 55, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 15, 17, 18, 21, 26, 30, 31, 32, 35, 40, 44, 51, 52, 53, 54, 55, 56, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 15, 16, 18, 21, 25, 32, 33, 37, 38, 39, 45, 49, 50, 51, 52, 54, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 15, 16, 18, 21, 23, 26, 32, 36, 38, 39, 45, 49, 50, 51, 52, 54, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 15, 16, 18, 20, 26, 32, 33, 37, 38, 40, 44, 49, 50, 51, 52, 54, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 16, 18, 24, 26, 30, 32, 34, 35, 36, 39, 40, 42, 47, 50, 51, 55, 56, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 16, 18, 21, 30, 31, 32, 33, 35, 37, 39, 44, 45, 48, 51, 52, 53, 56, 57 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 16, 18, 20, 24, 26, 28, 29, 32, 33, 36, 40, 47, 51, 52, 55, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 15, 16, 18, 24, 26, 30, 32, 35, 38, 39, 40, 42, 47, 50, 51, 53, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 15, 16, 18, 20, 24, 26, 32, 35, 38, 40, 47, 49, 50, 51, 52, 53, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 15, 16, 18, 20, 24, 26, 29, 32, 33, 38, 40, 47, 49, 52, 55, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 18, 20, 24, 26, 29, 32, 34, 35, 38, 40, 47, 49, 52, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 18, 20, 24, 26, 28, 29, 32, 35, 38, 40, 47, 51, 52, 53, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 18, 20, 21, 25, 29, 32, 33, 35, 38, 42, 45, 49, 52, 54, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 17, 18, 28, 29, 31, 32, 35, 36, 38, 40, 42, 46, 48, 51, 54, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 26, 30, 31, 32, 35, 36, 39, 40, 42, 44, 51, 52, 54, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 25, 30, 31, 32, 35, 37, 39, 40, 42, 45, 51, 52, 53, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 23, 26, 29, 30, 31, 32, 36, 39, 42, 52, 54, 55, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 21, 30, 31, 32, 35, 36, 39, 44, 45, 48, 51, 52, 54, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 21, 25, 32, 35, 36, 37, 39, 45, 49, 50, 51, 52, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 21, 25, 30, 31, 32, 35, 39, 45, 51, 52, 53, 54, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 21, 25, 26, 32, 35, 36, 39, 48, 49, 50, 51, 52, 54, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 20, 30, 31, 32, 35, 37, 40, 44, 45, 48, 51, 52, 53, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 20, 26, 32, 35, 36, 37, 40, 44, 49, 50, 51, 52, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 20, 26, 32, 34, 35, 37, 40, 46, 49, 50, 51, 52, 55, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 20, 26, 30, 31, 32, 35, 40, 44, 51, 52, 53, 54, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 20, 26, 28, 29, 32, 37, 40, 46, 51, 52, 53, 54, 55, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 20, 26, 28, 29, 32, 33, 37, 40, 46, 51, 52, 55, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 20, 25, 26, 32, 35, 37, 40, 48, 49, 50, 51, 52, 53, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 20, 25, 26, 29, 32, 33, 37, 40, 48, 49, 52, 55, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 20, 21, 26, 32, 35, 36, 42, 44, 49, 50, 51, 52, 54, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 20, 21, 25, 32, 35, 37, 42, 45, 49, 50, 51, 52, 53, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 20, 21, 25, 29, 32, 37, 42, 45, 49, 52, 53, 54, 55, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 18, 20, 21, 25, 29, 32, 33, 37, 42, 45, 49, 52, 55, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 17, 18, 21, 29, 30, 31, 32, 36, 44, 48, 52, 54, 55, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 16, 17, 18, 21, 28, 29, 31, 32, 36, 46, 48, 51, 54, 55, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 25, 29, 30, 31, 34, 39, 40, 42, 45, 46, 47, 52, 55, 58, 59, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 24, 25, 29, 30, 31, 34, 39, 40, 42, 43, 45, 52, 55, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 24, 25, 27, 29, 34, 39, 40, 42, 45, 46, 47, 52, 55, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 24, 25, 26, 29, 30, 34, 39, 40, 42, 43, 48, 50, 55, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 24, 25, 26, 27, 29, 34, 39, 40, 42, 46, 48, 52, 55, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 23, 29, 30, 31, 34, 39, 40, 42, 43, 47, 48, 52, 55, 58, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 23, 24, 29, 30, 34, 39, 40, 42, 46, 47, 48, 50, 55, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 23, 24, 29, 30, 31, 34, 39, 40, 42, 46, 48, 52, 55, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 29, 30, 31, 34, 40, 43, 44, 45, 48, 52, 55, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 25, 26, 29, 34, 40, 43, 48, 49, 50, 52, 55, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 23, 24, 29, 34, 40, 46, 47, 48, 49, 50, 52, 55, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 23, 24, 29, 30, 31, 34, 40, 48, 52, 55, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 23, 24, 28, 29, 31, 36, 40, 48, 51, 56, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 21, 25, 29, 34, 36, 37, 42, 45, 49, 50, 52, 53, 54, 55, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 21, 24, 29, 30, 34, 42, 43, 44, 45, 48, 50, 55, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 21, 24, 27, 29, 34, 42, 44, 45, 46, 48, 52, 55, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 21, 24, 25, 29, 34, 42, 43, 45, 49, 50, 52, 55, 60, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 21, 24, 25, 27, 29, 34, 42, 45, 52, 55, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 21, 23, 24, 29, 34, 42, 46, 48, 49, 50, 52, 55, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 21, 23, 24, 29, 30, 34, 42, 48, 50, 55, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 25, 28, 29, 31, 36, 42, 43, 45, 46, 47, 51, 56, 57, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 24, 29, 30, 34, 42, 44, 45, 46, 47, 48, 50, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 24, 29, 30, 31, 34, 42, 44, 45, 46, 48, 52, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 24, 25, 29, 34, 42, 45, 46, 47, 49, 50, 52, 55, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 24, 25, 29, 30, 31, 34, 42, 45, 52, 55, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 24, 25, 28, 29, 31, 36, 42, 45, 51, 56, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 24, 25, 26, 29, 34, 42, 46, 48, 49, 50, 52, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 24, 25, 26, 29, 30, 34, 42, 48, 50, 55, 57, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 21, 24, 29, 30, 31, 35, 39, 43, 44, 45, 48, 52, 55, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 21, 24, 27, 29, 35, 39, 44, 45, 46, 47, 48, 52, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 21, 24, 25, 26, 29, 35, 39, 43, 48, 49, 50, 52, 55, 57, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 21, 24, 25, 26, 27, 29, 35, 39, 48, 52, 55, 57, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 21, 23, 24, 29, 35, 39, 46, 47, 48, 49, 50, 52, 55, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 21, 23, 24, 29, 30, 31, 35, 39, 48, 52, 55, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 21, 24, 29, 31, 35, 42, 43, 44, 45, 48, 49, 55, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 21, 24, 26, 27, 29, 35, 42, 44, 52, 55, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 21, 23, 29, 35, 42, 43, 46, 48, 49, 50, 52, 55, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 21, 23, 24, 29, 35, 42, 47, 48, 49, 50, 52, 55, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 21, 23, 24, 29, 31, 35, 42, 48, 49, 55, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 17, 18, 24, 29, 31, 35, 42, 44, 45, 46, 47, 48, 49, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 17, 18, 24, 29, 30, 31, 35, 42, 44, 45, 47, 48, 52, 55, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 17, 18, 24, 26, 29, 35, 42, 44, 46, 47, 49, 50, 52, 55, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 17, 18, 24, 26, 29, 30, 31, 35, 42, 44, 52, 55, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 17, 18, 24, 25, 26, 29, 35, 42, 47, 48, 49, 50, 52, 55, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 17, 18, 24, 25, 26, 29, 31, 35, 42, 48, 49, 55, 57, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 21, 29, 30, 36, 37, 38, 39, 44, 45, 48, 50, 53, 54, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 29, 31, 38, 40, 43, 44, 45, 48, 49, 57, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24, 29, 38, 40, 47, 48, 49, 50, 52, 57, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24, 29, 31, 38, 40, 48, 49, 57, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 24, 29, 31, 38, 42, 44, 45, 46, 48, 49, 57, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 24, 29, 30, 38, 42, 44, 45, 47, 48, 50, 57, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 24, 26, 29, 38, 42, 44, 46, 49, 50, 52, 57, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 24, 26, 29, 30, 38, 42, 44, 50, 57, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 24, 25, 29, 38, 42, 45, 47, 49, 50, 52, 57, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 24, 25, 29, 31, 38, 42, 45, 49, 57, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 21, 25, 29, 30, 31, 33, 34, 35, 38, 39, 45, 52, 56, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 21, 25, 27, 29, 34, 35, 36, 37, 38, 39, 45, 52, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 21, 25, 26, 29, 30, 33, 34, 35, 38, 39, 48, 50, 56, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 26, 29, 30, 31, 33, 34, 35, 38, 40, 44, 52, 56, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 25, 26, 29, 31, 33, 34, 35, 38, 40, 48, 49, 56, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 23, 26, 28, 29, 31, 38, 40, 46, 51, 56, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 23, 25, 26, 31, 38, 40, 45, 48, 49, 50, 51, 56, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 23, 25, 26, 29, 31, 38, 40, 43, 48, 49, 56, 57, 60, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 23, 25, 26, 27, 31, 38, 40, 45, 48, 51, 56, 57, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 23, 24, 29, 31, 38, 40, 44, 45, 48, 49, 56, 57, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 23, 24, 28, 29, 31, 38, 40, 45, 48, 51, 56, 57, 58, 61, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 21, 26, 29, 30, 33, 34, 35, 38, 42, 44, 50, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 21, 25, 29, 31, 33, 34, 35, 38, 42, 45, 49, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 18, 20, 21, 25, 27, 29, 34, 35, 37, 38, 42, 45, 52, 53, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 17, 18, 26, 29, 30, 34, 35, 36, 37, 38, 42, 44, 50, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 17, 18, 25, 29, 30, 31, 34, 35, 37, 38, 42, 45, 52, 53, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 17, 18, 25, 26, 29, 30, 34, 35, 37, 38, 42, 48, 50, 53, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 18, 25, 29, 30, 31, 33, 34, 39, 40, 42, 45, 52, 55, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 18, 25, 27, 29, 34, 36, 37, 39, 40, 42, 45, 52, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 18, 25, 26, 29, 30, 33, 34, 39, 40, 42, 48, 50, 55, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 18, 20, 29, 30, 31, 33, 34, 40, 44, 45, 48, 52, 55, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 18, 20, 25, 26, 29, 33, 34, 40, 48, 49, 50, 52, 55, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 29, 30, 33, 34, 42, 44, 45, 48, 50, 55, 56, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 25, 29, 33, 34, 42, 45, 49, 50, 52, 55, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 25, 27, 29, 34, 42, 45, 52, 53, 54, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 17, 18, 29, 30, 34, 36, 37, 42, 44, 45, 48, 50, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 17, 18, 25, 29, 34, 36, 37, 42, 45, 49, 50, 52, 55, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 17, 18, 25, 29, 30, 31, 34, 42, 45, 52, 53, 54, 55, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 17, 18, 25, 26, 30, 40, 42, 44, 48, 50, 51, 56, 58, 59, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 17, 18, 25, 26, 29, 30, 34, 42, 48, 50, 53, 54, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 18, 21, 29, 30, 31, 33, 35, 39, 44, 45, 48, 52, 55, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 18, 21, 27, 29, 35, 36, 37, 39, 44, 45, 48, 52, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 18, 21, 25, 26, 29, 33, 35, 39, 48, 49, 50, 52, 55, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 18, 21, 25, 26, 27, 29, 35, 39, 48, 52, 53, 54, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 18, 21, 23, 29, 35, 36, 37, 39, 48, 49, 50, 52, 55, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 18, 21, 23, 29, 30, 31, 35, 39, 48, 52, 53, 54, 55, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 17, 18, 29, 30, 31, 35, 37, 42, 44, 45, 48, 52, 53, 55, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 17, 18, 26, 29, 35, 36, 37, 42, 44, 49, 50, 52, 55, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 17, 18, 26, 29, 30, 31, 35, 42, 44, 52, 53, 54, 55, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 17, 18, 25, 26, 29, 35, 37, 42, 48, 49, 50, 52, 53, 55, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 26, 29, 30, 33, 38, 39, 40, 42, 44, 50, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 26, 27, 29, 36, 38, 39, 40, 42, 44, 52, 54, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 25, 29, 31, 33, 38, 39, 40, 42, 45, 49, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 25, 27, 29, 37, 38, 39, 40, 42, 45, 52, 53, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 23, 29, 31, 36, 38, 39, 40, 42, 48, 49, 54, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21, 29, 30, 33, 38, 39, 44, 45, 48, 50, 56, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21, 27, 29, 36, 38, 39, 44, 45, 48, 52, 54, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21, 25, 29, 33, 38, 39, 45, 49, 50, 52, 56, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21, 25, 27, 29, 38, 39, 45, 52, 53, 54, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21, 23, 29, 36, 38, 39, 48, 49, 50, 52, 54, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 29, 31, 33, 38, 40, 44, 45, 48, 49, 56, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 27, 29, 37, 38, 40, 44, 45, 48, 52, 53, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 26, 29, 33, 38, 40, 44, 49, 50, 52, 56, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 23, 29, 37, 38, 40, 48, 49, 50, 52, 53, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 29, 30, 37, 38, 42, 44, 45, 48, 50, 53, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 26, 29, 36, 38, 42, 44, 49, 50, 52, 54, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 26, 29, 30, 38, 42, 44, 50, 53, 54, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 25, 29, 37, 38, 42, 45, 49, 50, 52, 53, 57, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 26, 29, 30, 31, 33, 37, 38, 39, 40, 42, 44, 52, 53, 55, 56, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 24, 26, 29, 30, 38, 39, 40, 42, 44, 46, 47, 50, 55, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 24, 26, 29, 30, 31, 38, 39, 40, 42, 44, 46, 52, 55, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 24, 25, 29, 31, 38, 39, 40, 42, 45, 46, 47, 49, 55, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 24, 25, 29, 30, 31, 38, 39, 40, 42, 45, 47, 52, 55, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 24, 25, 26, 29, 31, 38, 39, 40, 42, 46, 48, 49, 55, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 24, 25, 26, 29, 30, 38, 39, 40, 42, 47, 48, 50, 55, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 29, 30, 34, 35, 36, 37, 38, 39, 46, 47, 48, 50, 55, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 29, 30, 33, 38, 39, 44, 45, 48, 50, 53, 54, 55, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 24, 29, 30, 38, 39, 44, 45, 46, 47, 48, 50, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 24, 29, 30, 34, 35, 36, 37, 38, 39, 48, 50, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 24, 29, 30, 31, 38, 39, 44, 45, 46, 48, 52, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 24, 25, 29, 38, 39, 45, 46, 47, 49, 50, 52, 55, 57, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 24, 25, 29, 30, 31, 38, 39, 45, 52, 55, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 24, 25, 26, 29, 38, 39, 46, 48, 49, 50, 52, 55, 57, 59, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 21, 24, 25, 26, 29, 30, 38, 39, 48, 50, 55, 57, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 24, 29, 31, 38, 40, 44, 45, 46, 47, 48, 49, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 24, 26, 29, 30, 31, 38, 40, 44, 52, 55, 57, 58, 59, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 24, 25, 26, 29, 38, 40, 47, 48, 49, 50, 52, 55, 57, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 24, 25, 26, 29, 31, 38, 40, 48, 49, 55, 57, 58, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 21, 25, 31, 35, 36, 37, 38, 42, 45, 49, 50, 51, 53, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 21, 25, 29, 33, 36, 38, 42, 45, 49, 50, 52, 54, 55, 56, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 21, 25, 27, 33, 35, 36, 38, 42, 45, 50, 51, 52, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 21, 24, 29, 31, 38, 42, 44, 45, 46, 48, 49, 55, 59, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 21, 24, 29, 30, 38, 42, 44, 45, 47, 48, 50, 55, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 21, 24, 26, 29, 38, 42, 44, 46, 49, 50, 52, 55, 59, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 21, 24, 26, 29, 30, 38, 42, 44, 50, 55, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 21, 24, 25, 29, 38, 42, 45, 47, 49, 50, 52, 55, 58, 60, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 18, 20, 21, 24, 25, 29, 31, 38, 42, 45, 49, 55, 58, 59, 60, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 16, 18, 24, 25, 26, 30, 39, 42, 43, 48, 50, 51, 55, 57, 59, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 16, 18, 20, 21, 25, 31, 36, 42, 45, 49, 50, 51, 53, 54, 55, 56, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 16, 18, 20, 21, 25, 27, 36, 37, 42, 45, 50, 51, 52, 53, 55, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 16, 18, 20, 21, 25, 27, 31, 36, 42, 45, 51, 53, 54, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 16, 18, 20, 21, 25, 27, 31, 33, 36, 42, 45, 51, 55, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 16, 17, 18, 30, 31, 40, 42, 43, 44, 47, 48, 51, 52, 55, 58, 60, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 16, 17, 18, 24, 25, 26, 30, 40, 42, 48, 50, 51, 55, 58, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 16, 17, 18, 21, 25, 26, 30, 43, 46, 48, 50, 51, 55, 57, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 24, 30, 33, 38, 39, 42, 47, 48, 50, 51, 54, 55, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 24, 26, 30, 35, 38, 39, 42, 50, 51, 53, 54, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 24, 26, 30, 33, 38, 39, 42, 50, 51, 54, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 21, 29, 30, 38, 39, 46, 47, 48, 50, 53, 54, 55, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 21, 29, 30, 33, 38, 39, 46, 47, 48, 50, 55, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 21, 24, 29, 30, 38, 39, 48, 50, 53, 54, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 21, 24, 29, 30, 33, 38, 39, 48, 50, 55, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 26, 27, 31, 33, 38, 40, 46, 51, 55, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 20, 24, 29, 31, 33, 38, 40, 48, 49, 55, 57, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17, 18, 30, 35, 38, 40, 42, 46, 48, 50, 51, 53, 54, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17, 18, 24, 26, 30, 38, 40, 42, 50, 51, 53, 55, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 26, 29, 30, 36, 37, 38, 39, 40, 42, 44, 50, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 26, 29, 30, 31, 36, 38, 39, 40, 42, 44, 52, 54, 55, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 26, 28, 29, 31, 36, 38, 39, 40, 42, 46, 51, 54, 55, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 25, 29, 31, 36, 37, 38, 39, 40, 42, 45, 49, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 25, 29, 30, 31, 37, 38, 39, 40, 42, 45, 52, 53, 55, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 25, 26, 29, 31, 36, 38, 39, 40, 42, 48, 49, 54, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 25, 26, 29, 30, 37, 38, 39, 40, 42, 48, 50, 53, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 24, 26, 28, 29, 35, 36, 38, 39, 42, 51, 52, 54, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 23, 26, 30, 35, 36, 37, 38, 39, 42, 50, 51, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 21, 29, 30, 36, 37, 38, 39, 44, 45, 48, 50, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 21, 29, 30, 34, 35, 38, 39, 46, 47, 48, 50, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 21, 29, 30, 31, 36, 38, 39, 44, 45, 48, 52, 54, 55, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 21, 25, 29, 36, 37, 38, 39, 45, 49, 50, 52, 55, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 21, 25, 29, 30, 31, 38, 39, 45, 52, 53, 54, 55, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 21, 25, 26, 29, 36, 38, 39, 48, 49, 50, 52, 54, 55, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 21, 25, 26, 29, 30, 38, 39, 48, 50, 53, 54, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 21, 24, 29, 30, 34, 35, 38, 39, 48, 50, 55, 56, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 29, 31, 36, 37, 38, 40, 44, 45, 48, 49, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 29, 30, 31, 37, 38, 40, 44, 45, 48, 52, 53, 55, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 28, 29, 31, 35, 38, 40, 46, 47, 48, 51, 53, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 26, 29, 36, 37, 38, 40, 44, 49, 50, 52, 55, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 26, 29, 30, 31, 38, 40, 44, 52, 53, 54, 55, 56, 57, 60 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 26, 28, 29, 31, 38, 40, 46, 51, 53, 54, 55, 56, 57, 61 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 26, 27, 31, 34, 35, 38, 40, 46, 51, 55, 56, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 25, 26, 31, 35, 38, 40, 48, 49, 50, 51, 53, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 25, 26, 29, 37, 38, 40, 48, 49, 50, 52, 53, 55, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 25, 26, 29, 31, 38, 40, 48, 49, 53, 54, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 25, 26, 27, 31, 35, 38, 40, 48, 51, 53, 56, 57, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 24, 29, 31, 34, 35, 38, 40, 48, 49, 55, 56, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 24, 28, 29, 31, 35, 38, 40, 48, 51, 53, 56, 57, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 29, 31, 36, 38, 42, 44, 45, 48, 49, 54, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 29, 30, 37, 38, 42, 44, 45, 48, 50, 53, 55, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 26, 29, 36, 38, 42, 44, 49, 50, 52, 54, 55, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 26, 29, 30, 38, 42, 44, 50, 53, 54, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 25, 35, 37, 38, 42, 45, 49, 51, 52, 53, 54, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 25, 33, 35, 37, 38, 42, 45, 49, 51, 52, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 25, 31, 35, 38, 42, 45, 49, 50, 51, 53, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 25, 29, 37, 38, 42, 45, 49, 50, 52, 53, 55, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 25, 29, 31, 38, 42, 45, 49, 53, 54, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 18, 20, 21, 25, 27, 31, 35, 38, 42, 45, 51, 53, 56, 60, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 17, 18, 21, 30, 35, 36, 37, 38, 44, 48, 50, 51, 56, 57, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 17, 18, 21, 30, 34, 35, 37, 38, 46, 48, 50, 51, 55, 57, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 18, 23, 30, 36, 37, 39, 42, 45, 48, 50, 51, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 18, 23, 30, 31, 36, 39, 42, 45, 48, 51, 52, 54, 55, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 18, 21, 30, 34, 35, 39, 40, 46, 48, 50, 51, 55, 56, 61, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 18, 21, 28, 29, 36, 39, 40, 46, 48, 51, 52, 54, 55, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 18, 20, 25, 26, 33, 40, 48, 49, 51, 52, 54, 55, 56, 57, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 18, 20, 25, 26, 27, 40, 48, 50, 51, 52, 53, 55, 56, 57, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 18, 20, 21, 25, 33, 42, 45, 49, 51, 52, 54, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 18, 20, 21, 25, 27, 42, 45, 50, 51, 52, 53, 55, 56, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 30, 36, 37, 40, 42, 44, 48, 50, 51, 55, 56, 60, 62 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 30, 31, 36, 40, 42, 44, 48, 51, 52, 54, 55, 60, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 15, 19, 21, 22, 26, 32, 33, 34, 37, 49, 50, 51, 52, 53, 56, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 19, 21, 22, 26, 32, 34, 36, 49, 50, 51, 52, 54, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 22, 29, 31, 34, 36, 41, 42, 48, 49, 54, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 22, 29, 31, 34, 36, 41, 42, 43, 48, 49, 54, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 22, 26, 34, 36, 41, 42, 43, 49, 51, 52, 54, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 22, 26, 27, 34, 36, 41, 42, 50, 51, 52, 54, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 19, 21, 22, 23, 26, 28, 30, 33, 38, 46, 47, 50, 58, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 19, 21, 22, 23, 24, 26, 28, 30, 33, 38, 50, 58, 60, 61, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 22, 23, 24, 26, 28, 30, 41, 42, 43, 50, 53, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 22, 23, 24, 26, 28, 30, 33, 41, 42, 50, 54, 58, 60, 61, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 21, 22, 23, 28, 33, 41, 43, 45, 47, 48, 49, 52, 58, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 21, 22, 23, 24, 28, 33, 41, 45, 46, 48, 49, 52, 59, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 22, 23, 26, 28, 33, 42, 43, 47, 49, 52, 58, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 22, 23, 24, 26, 28, 33, 42, 46, 49, 52, 59, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 24, 25, 27, 28, 45, 52, 53, 58, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 28, 43, 47, 48, 49, 50, 52, 53, 58, 60, 61, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 28, 30, 43, 46, 47, 48, 50, 53, 60, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 28, 46, 48, 49, 50, 52, 53, 59, 60, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 19, 21, 22, 23, 24, 28, 30, 48, 50, 53, 58, 59, 60, 61, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 22, 28, 31, 35, 36, 41, 42, 43, 48, 49, 53, 55, 56, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 19, 21, 22, 26, 27, 28, 33, 35, 36, 37, 52, 55, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 22, 27, 28, 31, 34, 36, 41, 42, 43, 48, 50, 54, 55, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 22, 28, 31, 33, 35, 37, 41, 42, 48, 49, 54, 55, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 22, 28, 31, 33, 35, 37, 41, 42, 43, 48, 49, 54, 55, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 19, 21, 22, 26, 27, 28, 35, 52, 53, 54, 55, 56, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 21, 22, 26, 28, 33, 35, 37, 38, 41, 49, 52, 53, 56, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 21, 22, 26, 28, 33, 37, 38, 49, 50, 52, 53, 55, 56, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 21, 22, 26, 28, 30, 33, 36, 37, 38, 50, 55, 58, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 22, 28, 31, 33, 35, 37, 41, 42, 48, 49, 53, 56, 58, 59, 62 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 22, 28, 31, 33, 35, 37, 41, 42, 43, 48, 49, 53, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 22, 28, 30, 33, 35, 36, 41, 42, 43, 48, 50, 54, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 22, 28, 31, 33, 37, 42, 48, 49, 50, 53, 55, 56, 58, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 19, 22, 26, 28, 33, 37, 42, 43, 49, 52, 53, 55, 56, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 21, 22, 26, 28, 35, 36, 38, 41, 49, 52, 54, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 21, 22, 26, 28, 36, 38, 49, 50, 52, 54, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 19, 21, 22, 26, 28, 30, 38, 50, 53, 54, 55, 56, 58, 62, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 22, 28, 31, 35, 36, 41, 42, 48, 49, 54, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 22, 28, 31, 35, 36, 41, 42, 43, 48, 49, 54, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 22, 28, 30, 35, 37, 41, 42, 43, 48, 50, 53, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 21, 22, 28, 36, 41, 43, 48, 49, 52, 54, 55, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 21, 22, 27, 28, 36, 41, 48, 50, 52, 54, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 22, 28, 31, 36, 42, 48, 49, 50, 54, 55, 58, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 22, 26, 28, 36, 42, 43, 49, 52, 54, 55, 62, 63, 64 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 21, 22, 28, 30, 48, 50, 53, 55, 56, 58, 59, 62, 63 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 19, 21, 22, 28, 30, 43, 48, 50, 53, 55, 56, 62, 63, 64 ] ]; ### The number of nonisomorphic symmetric (64,28,12) designs that rise from these DSs is 209 ### These nonisomorphic symmetric (64,28,12) designs are the ones that rise from the following DSs: ### DS107[1], DS107[6], DS107[7], DS107[8], DS107[9], DS107[10], DS107[11], DS107[12], DS107[13], DS107[15], DS107[17], DS107[18], DS107[19], DS107[20], DS107[22], DS107[23], DS107[24], DS107[28], DS107[29], DS107[31], DS107[32], DS107[33], DS107[34], DS107[35], DS107[36], DS107[37], DS107[38], DS107[40], DS107[45], DS107[46], DS107[47], DS107[48], DS107[50], DS107[51], DS107[54], DS107[55], DS107[56], DS107[58], DS107[59], DS107[60], DS107[65], DS107[66], DS107[67], DS107[68], DS107[71], DS107[72], DS107[74], DS107[76], DS107[77], DS107[78], DS107[79], DS107[81], DS107[82], DS107[84], DS107[85], DS107[87], DS107[90], DS107[91], DS107[93], DS107[97], DS107[98], DS107[99], DS107[100], DS107[105], DS107[106], DS107[107], DS107[109], DS107[111], DS107[113], DS107[114], DS107[115], DS107[117], DS107[118], DS107[119], DS107[120], DS107[121], DS107[122], DS107[125], DS107[127], DS107[130], DS107[131], DS107[132], DS107[133], DS107[136], DS107[137], DS107[139], DS107[140], DS107[141], DS107[143], DS107[144], DS107[149], DS107[150], DS107[151], DS107[153], DS107[156], DS107[158], DS107[159], DS107[160], DS107[162], DS107[164], DS107[165], DS107[166], DS107[168], DS107[171], DS107[172], DS107[176], DS107[177], DS107[179], DS107[180], DS107[182], DS107[184], DS107[185], DS107[187], DS107[188], DS107[192], DS107[193], DS107[194], DS107[196], DS107[198], DS107[199], DS107[201], DS107[202], DS107[204], DS107[205], DS107[206], DS107[207], DS107[208], DS107[209], DS107[210], DS107[211], DS107[212], DS107[213], DS107[214], DS107[215], DS107[216], DS107[217], DS107[219], DS107[224], DS107[225], DS107[226], DS107[228], DS107[229], DS107[233], DS107[234], DS107[235], DS107[236], DS107[237], DS107[240], DS107[241], DS107[243], DS107[245], DS107[246], DS107[247], DS107[248], DS107[249], DS107[250], DS107[252], DS107[253], DS107[254], DS107[255], DS107[258], DS107[259], DS107[260], DS107[261], DS107[262], DS107[263], DS107[264], DS107[265], DS107[266], DS107[267], DS107[268], DS107[269], DS107[270], DS107[272], DS107[273], DS107[274], DS107[275], DS107[276], DS107[277], DS107[278], DS107[279], DS107[280], DS107[281], DS107[282], DS107[283], DS107[284], DS107[285], DS107[288], DS107[289], DS107[291], DS107[292], DS107[293], DS107[295], DS107[298], DS107[299], DS107[300], DS107[301], DS107[302], DS107[303], DS107[304], DS107[306], DS107[307], DS107[308], DS107[309], DS107[310], DS107[311], DS107[312], DS107[313], DS107[314]. # Note that there is no reversible (64,28,12) difference sets in # group [64,107]. ########################### ########################### ###########################