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mate2code

Tesseract group conjugacy classes

mate2code
Aug 31st, 2019
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  1. # This dictionary shows the 16*24 = 384 permutations of the tesseract in their 20 conjugacy classes.
  2.  
  3. # size: number of permutations in the CC
  4. # mininv: smallest inversion number in the CC
  5. # selfinv: each permutation is self inverse
  6. # selfcomp: the complement (15-m, n) of each permutation (m, n) is in the same CC
  7. # transp: number of transpositions of each permutation
  8. # cycles: cycle type in the form {cycle length: number of such cycles}
  9. # list: dictionary with the inversion number, matrix coordinates and tuple of each permutation
  10.  
  11. # Complementary CC are grouped together. Short separators are between CC that are not complements.
  12. # Long separators are between CC of different sizes.
  13.  
  14.  
  15. tesseract_conjugacy_classes = [
  16.  
  17.     {'size': 1, 'mininv': 0, 'selfinv': True, 'selfcomp': False, 'transp': 0, 'cycles': {1: 16},
  18.      'list': [{'inv': 0, 'pair': (0, 0), 'perm': (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)}]},
  19.  
  20.     {'size': 1, 'mininv': 120, 'selfinv': True, 'selfcomp': False, 'transp': 8, 'cycles': {2: 8},
  21.      'list': [{'inv': 120, 'pair': (15, 0), 'perm': (15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0)}]},
  22.  
  23.     ####################################################################################################################
  24.  
  25.     {'size': 4, 'mininv': 8, 'selfinv': True, 'selfcomp': False, 'transp': 8, 'cycles': {2: 8},
  26.      'list': [{'inv': 8, 'pair': (1, 0), 'perm': (1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14)},
  27.               {'inv': 16, 'pair': (2, 0), 'perm': (2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13)},
  28.               {'inv': 32, 'pair': (4, 0), 'perm': (4, 5, 6, 7, 0, 1, 2, 3, 12, 13, 14, 15, 8, 9, 10, 11)},
  29.               {'inv': 64, 'pair': (8, 0), 'perm': (8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7)}]},
  30.  
  31.     {'size': 4, 'mininv': 56, 'selfinv': True, 'selfcomp': False, 'transp': 8, 'cycles': {2: 8},
  32.      'list': [{'inv': 56, 'pair': (7, 0), 'perm': (7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8)},
  33.               {'inv': 88, 'pair': (11, 0), 'perm': (11, 10, 9, 8, 15, 14, 13, 12, 3, 2, 1, 0, 7, 6, 5, 4)},
  34.               {'inv': 104, 'pair': (13, 0), 'perm': (13, 12, 15, 14, 9, 8, 11, 10, 5, 4, 7, 6, 1, 0, 3, 2)},
  35.               {'inv': 112, 'pair': (14, 0), 'perm': (14, 15, 12, 13, 10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 0, 1)}]},
  36.  
  37.     ####################################################################################################################
  38.  
  39.     {'size': 6, 'mininv': 24, 'selfinv': True, 'selfcomp': True, 'transp': 8, 'cycles': {2: 8},
  40.      'list': [{'inv': 24, 'pair': (3, 0), 'perm': (3, 2, 1, 0, 7, 6, 5, 4, 11, 10, 9, 8, 15, 14, 13, 12)},
  41.               {'inv': 40, 'pair': (5, 0), 'perm': (5, 4, 7, 6, 1, 0, 3, 2, 13, 12, 15, 14, 9, 8, 11, 10)},
  42.               {'inv': 48, 'pair': (6, 0), 'perm': (6, 7, 4, 5, 2, 3, 0, 1, 14, 15, 12, 13, 10, 11, 8, 9)},
  43.               {'inv': 72, 'pair': (9, 0), 'perm': (9, 8, 11, 10, 13, 12, 15, 14, 1, 0, 3, 2, 5, 4, 7, 6)},
  44.               {'inv': 80, 'pair': (10, 0), 'perm': (10, 11, 8, 9, 14, 15, 12, 13, 2, 3, 0, 1, 6, 7, 4, 5)},
  45.               {'inv': 96, 'pair': (12, 0), 'perm': (12, 13, 14, 15, 8, 9, 10, 11, 4, 5, 6, 7, 0, 1, 2, 3)}]},
  46.  
  47.     ####################################################################################################################
  48.  
  49.     {'size': 12, 'mininv': 4, 'selfinv': True, 'selfcomp': False, 'transp': 4, 'cycles': {2: 4, 1: 8},
  50.      'list': [{'inv': 4, 'pair': (0, 1), 'perm': (0, 2, 1, 3, 4, 6, 5, 7, 8, 10, 9, 11, 12, 14, 13, 15)},
  51.               {'inv': 8, 'pair': (0, 2), 'perm': (0, 1, 4, 5, 2, 3, 6, 7, 8, 9, 12, 13, 10, 11, 14, 15)},
  52.               {'inv': 16, 'pair': (0, 5), 'perm': (0, 4, 2, 6, 1, 5, 3, 7, 8, 12, 10, 14, 9, 13, 11, 15)},
  53.               {'inv': 16, 'pair': (0, 6), 'perm': (0, 1, 2, 3, 8, 9, 10, 11, 4, 5, 6, 7, 12, 13, 14, 15)},
  54.               {'inv': 20, 'pair': (3, 1), 'perm': (3, 1, 2, 0, 7, 5, 6, 4, 11, 9, 10, 8, 15, 13, 14, 12)},
  55.               {'inv': 32, 'pair': (0, 14), 'perm': (0, 1, 8, 9, 4, 5, 12, 13, 2, 3, 10, 11, 6, 7, 14, 15)},
  56.               {'inv': 32, 'pair': (5, 5), 'perm': (5, 1, 7, 3, 4, 0, 6, 2, 13, 9, 15, 11, 12, 8, 14, 10)},
  57.               {'inv': 40, 'pair': (0, 21), 'perm': (0, 8, 2, 10, 4, 12, 6, 14, 1, 9, 3, 11, 5, 13, 7, 15)},
  58.               {'inv': 40, 'pair': (6, 2), 'perm': (6, 7, 2, 3, 4, 5, 0, 1, 14, 15, 10, 11, 12, 13, 8, 9)},
  59.               {'inv': 56, 'pair': (9, 21), 'perm': (9, 1, 11, 3, 13, 5, 15, 7, 8, 0, 10, 2, 12, 4, 14, 6)},
  60.               {'inv': 64, 'pair': (10, 14), 'perm': (10, 11, 2, 3, 14, 15, 6, 7, 8, 9, 0, 1, 12, 13, 4, 5)},
  61.               {'inv': 80, 'pair': (12, 6), 'perm': (12, 13, 14, 15, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3)}]},
  62.  
  63.     {'size': 12, 'mininv': 40, 'selfinv': True, 'selfcomp': False, 'transp': 8, 'cycles': {2: 8},
  64.      'list': [{'inv': 40, 'pair': (3, 6), 'perm': (3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 15, 14, 13, 12)},
  65.               {'inv': 56, 'pair': (5, 14), 'perm': (5, 4, 13, 12, 1, 0, 9, 8, 7, 6, 15, 14, 3, 2, 11, 10)},
  66.               {'inv': 64, 'pair': (6, 21), 'perm': (6, 14, 4, 12, 2, 10, 0, 8, 7, 15, 5, 13, 3, 11, 1, 9)},
  67.               {'inv': 80, 'pair': (9, 2), 'perm': (9, 8, 13, 12, 11, 10, 15, 14, 1, 0, 5, 4, 3, 2, 7, 6)},
  68.               {'inv': 80, 'pair': (15, 21), 'perm': (15, 7, 13, 5, 11, 3, 9, 1, 14, 6, 12, 4, 10, 2, 8, 0)},
  69.               {'inv': 88, 'pair': (10, 5), 'perm': (10, 14, 8, 12, 11, 15, 9, 13, 2, 6, 0, 4, 3, 7, 1, 5)},
  70.               {'inv': 88, 'pair': (15, 14), 'perm': (15, 14, 7, 6, 11, 10, 3, 2, 13, 12, 5, 4, 9, 8, 1, 0)},
  71.               {'inv': 100, 'pair': (12, 1), 'perm': (12, 14, 13, 15, 8, 10, 9, 11, 4, 6, 5, 7, 0, 2, 1, 3)},
  72.               {'inv': 104, 'pair': (15, 5), 'perm': (15, 11, 13, 9, 14, 10, 12, 8, 7, 3, 5, 1, 6, 2, 4, 0)},
  73.               {'inv': 104, 'pair': (15, 6), 'perm': (15, 14, 13, 12, 7, 6, 5, 4, 11, 10, 9, 8, 3, 2, 1, 0)},
  74.               {'inv': 112, 'pair': (15, 2), 'perm': (15, 14, 11, 10, 13, 12, 9, 8, 7, 6, 3, 2, 5, 4, 1, 0)},
  75.               {'inv': 116, 'pair': (15, 1), 'perm': (15, 13, 14, 12, 11, 9, 10, 8, 7, 5, 6, 4, 3, 1, 2, 0)}]},
  76.  
  77.     ############################
  78.  
  79.     {'size': 12, 'mininv': 12, 'selfinv': False, 'selfcomp': False, 'transp': 12, 'cycles': {4: 4},
  80.      'list': [{'inv': 12, 'pair': (1, 1), 'perm': (1, 3, 0, 2, 5, 7, 4, 6, 9, 11, 8, 10, 13, 15, 12, 14)},
  81.               {'inv': 12, 'pair': (2, 1), 'perm': (2, 0, 3, 1, 6, 4, 7, 5, 10, 8, 11, 9, 14, 12, 15, 13)},
  82.               {'inv': 24, 'pair': (1, 5), 'perm': (1, 5, 3, 7, 0, 4, 2, 6, 9, 13, 11, 15, 8, 12, 10, 14)},
  83.               {'inv': 24, 'pair': (2, 2), 'perm': (2, 3, 6, 7, 0, 1, 4, 5, 10, 11, 14, 15, 8, 9, 12, 13)},
  84.               {'inv': 24, 'pair': (4, 2), 'perm': (4, 5, 0, 1, 6, 7, 2, 3, 12, 13, 8, 9, 14, 15, 10, 11)},
  85.               {'inv': 24, 'pair': (4, 5), 'perm': (4, 0, 6, 2, 5, 1, 7, 3, 12, 8, 14, 10, 13, 9, 15, 11)},
  86.               {'inv': 48, 'pair': (1, 21), 'perm': (1, 9, 3, 11, 5, 13, 7, 15, 0, 8, 2, 10, 4, 12, 6, 14)},
  87.               {'inv': 48, 'pair': (2, 14), 'perm': (2, 3, 10, 11, 6, 7, 14, 15, 0, 1, 8, 9, 4, 5, 12, 13)},
  88.               {'inv': 48, 'pair': (4, 6), 'perm': (4, 5, 6, 7, 12, 13, 14, 15, 0, 1, 2, 3, 8, 9, 10, 11)},
  89.               {'inv': 48, 'pair': (8, 6), 'perm': (8, 9, 10, 11, 0, 1, 2, 3, 12, 13, 14, 15, 4, 5, 6, 7)},
  90.               {'inv': 48, 'pair': (8, 14), 'perm': (8, 9, 0, 1, 12, 13, 4, 5, 10, 11, 2, 3, 14, 15, 6, 7)},
  91.               {'inv': 48, 'pair': (8, 21), 'perm': (8, 0, 10, 2, 12, 4, 14, 6, 9, 1, 11, 3, 13, 5, 15, 7)}]},
  92.  
  93.     {'size': 12, 'mininv': 72, 'selfinv': False, 'selfcomp': False, 'transp': 12, 'cycles': {4: 4},
  94.      'list': [{'inv': 72, 'pair': (7, 6), 'perm': (7, 6, 5, 4, 15, 14, 13, 12, 3, 2, 1, 0, 11, 10, 9, 8)},
  95.               {'inv': 72, 'pair': (7, 14), 'perm': (7, 6, 15, 14, 3, 2, 11, 10, 5, 4, 13, 12, 1, 0, 9, 8)},
  96.               {'inv': 72, 'pair': (7, 21), 'perm': (7, 15, 5, 13, 3, 11, 1, 9, 6, 14, 4, 12, 2, 10, 0, 8)},
  97.               {'inv': 72, 'pair': (11, 6), 'perm': (11, 10, 9, 8, 3, 2, 1, 0, 15, 14, 13, 12, 7, 6, 5, 4)},
  98.               {'inv': 72, 'pair': (13, 14), 'perm': (13, 12, 5, 4, 9, 8, 1, 0, 15, 14, 7, 6, 11, 10, 3, 2)},
  99.               {'inv': 72, 'pair': (14, 21), 'perm': (14, 6, 12, 4, 10, 2, 8, 0, 15, 7, 13, 5, 11, 3, 9, 1)},
  100.               {'inv': 96, 'pair': (11, 2), 'perm': (11, 10, 15, 14, 9, 8, 13, 12, 3, 2, 7, 6, 1, 0, 5, 4)},
  101.               {'inv': 96, 'pair': (11, 5), 'perm': (11, 15, 9, 13, 10, 14, 8, 12, 3, 7, 1, 5, 2, 6, 0, 4)},
  102.               {'inv': 96, 'pair': (13, 2), 'perm': (13, 12, 9, 8, 15, 14, 11, 10, 5, 4, 1, 0, 7, 6, 3, 2)},
  103.               {'inv': 96, 'pair': (14, 5), 'perm': (14, 10, 12, 8, 15, 11, 13, 9, 6, 2, 4, 0, 7, 3, 5, 1)},
  104.               {'inv': 108, 'pair': (13, 1), 'perm': (13, 15, 12, 14, 9, 11, 8, 10, 5, 7, 4, 6, 1, 3, 0, 2)},
  105.               {'inv': 108, 'pair': (14, 1), 'perm': (14, 12, 15, 13, 10, 8, 11, 9, 6, 4, 7, 5, 2, 0, 3, 1)}]},
  106.  
  107.     ############################
  108.  
  109.     {'size': 12, 'mininv': 20, 'selfinv': True, 'selfcomp': True, 'transp': 6, 'cycles': {2: 6, 1: 4},
  110.      'list': [{'inv': 20, 'pair': (0, 7), 'perm': (0, 2, 1, 3, 8, 10, 9, 11, 4, 6, 5, 7, 12, 14, 13, 15)},
  111.               {'inv': 36, 'pair': (0, 16), 'perm': (0, 4, 8, 12, 1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15)},
  112.               {'inv': 36, 'pair': (3, 7), 'perm': (3, 1, 2, 0, 11, 9, 10, 8, 7, 5, 6, 4, 15, 13, 14, 12)},
  113.               {'inv': 44, 'pair': (0, 23), 'perm': (0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15)},
  114.               {'inv': 52, 'pair': (5, 16), 'perm': (5, 1, 13, 9, 4, 0, 12, 8, 7, 3, 15, 11, 6, 2, 14, 10)},
  115.               {'inv': 60, 'pair': (6, 23), 'perm': (6, 14, 2, 10, 4, 12, 0, 8, 7, 15, 3, 11, 5, 13, 1, 9)},
  116.               {'inv': 60, 'pair': (9, 23), 'perm': (9, 1, 13, 5, 11, 3, 15, 7, 8, 0, 12, 4, 10, 2, 14, 6)},
  117.               {'inv': 68, 'pair': (10, 16), 'perm': (10, 14, 2, 6, 11, 15, 3, 7, 8, 12, 0, 4, 9, 13, 1, 5)},
  118.               {'inv': 76, 'pair': (15, 23), 'perm': (15, 7, 11, 3, 13, 5, 9, 1, 14, 6, 10, 2, 12, 4, 8, 0)},
  119.               {'inv': 84, 'pair': (12, 7), 'perm': (12, 14, 13, 15, 4, 6, 5, 7, 8, 10, 9, 11, 0, 2, 1, 3)},
  120.               {'inv': 84, 'pair': (15, 16), 'perm': (15, 11, 7, 3, 14, 10, 6, 2, 13, 9, 5, 1, 12, 8, 4, 0)},
  121.               {'inv': 100, 'pair': (15, 7), 'perm': (15, 13, 14, 12, 7, 5, 6, 4, 11, 9, 10, 8, 3, 1, 2, 0)}]},
  122.  
  123.     ############################
  124.  
  125.     {'size': 12, 'mininv': 60, 'selfinv': False, 'selfcomp': True, 'transp': 12, 'cycles': {4: 4},
  126.      'list': [{'inv': 60, 'pair': (3, 16), 'perm': (3, 7, 11, 15, 2, 6, 10, 14, 1, 5, 9, 13, 0, 4, 8, 12)},
  127.               {'inv': 60, 'pair': (3, 23), 'perm': (3, 11, 7, 15, 1, 9, 5, 13, 2, 10, 6, 14, 0, 8, 4, 12)},
  128.               {'inv': 60, 'pair': (5, 7), 'perm': (5, 7, 4, 6, 13, 15, 12, 14, 1, 3, 0, 2, 9, 11, 8, 10)},
  129.               {'inv': 60, 'pair': (5, 23), 'perm': (5, 13, 1, 9, 7, 15, 3, 11, 4, 12, 0, 8, 6, 14, 2, 10)},
  130.               {'inv': 60, 'pair': (6, 7), 'perm': (6, 4, 7, 5, 14, 12, 15, 13, 2, 0, 3, 1, 10, 8, 11, 9)},
  131.               {'inv': 60, 'pair': (6, 16), 'perm': (6, 2, 14, 10, 7, 3, 15, 11, 4, 0, 12, 8, 5, 1, 13, 9)},
  132.               {'inv': 60, 'pair': (9, 7), 'perm': (9, 11, 8, 10, 1, 3, 0, 2, 13, 15, 12, 14, 5, 7, 4, 6)},
  133.               {'inv': 60, 'pair': (9, 16), 'perm': (9, 13, 1, 5, 8, 12, 0, 4, 11, 15, 3, 7, 10, 14, 2, 6)},
  134.               {'inv': 60, 'pair': (10, 7), 'perm': (10, 8, 11, 9, 2, 0, 3, 1, 14, 12, 15, 13, 6, 4, 7, 5)},
  135.               {'inv': 60, 'pair': (10, 23), 'perm': (10, 2, 14, 6, 8, 0, 12, 4, 11, 3, 15, 7, 9, 1, 13, 5)},
  136.               {'inv': 60, 'pair': (12, 16), 'perm': (12, 8, 4, 0, 13, 9, 5, 1, 14, 10, 6, 2, 15, 11, 7, 3)},
  137.               {'inv': 60, 'pair': (12, 23), 'perm': (12, 4, 8, 0, 14, 6, 10, 2, 13, 5, 9, 1, 15, 7, 11, 3)}]},
  138.  
  139.     ####################################################################################################################
  140.  
  141.     {'size': 24, 'mininv': 16, 'selfinv': True, 'selfcomp': True, 'transp': 8, 'cycles': {2: 8},
  142.      'list': [{'inv': 16, 'pair': (1, 2), 'perm': (1, 0, 5, 4, 3, 2, 7, 6, 9, 8, 13, 12, 11, 10, 15, 14)},
  143.               {'inv': 24, 'pair': (1, 6), 'perm': (1, 0, 3, 2, 9, 8, 11, 10, 5, 4, 7, 6, 13, 12, 15, 14)},
  144.               {'inv': 24, 'pair': (2, 5), 'perm': (2, 6, 0, 4, 3, 7, 1, 5, 10, 14, 8, 12, 11, 15, 9, 13)},
  145.               {'inv': 32, 'pair': (2, 6), 'perm': (2, 3, 0, 1, 10, 11, 8, 9, 6, 7, 4, 5, 14, 15, 12, 13)},
  146.               {'inv': 36, 'pair': (4, 1), 'perm': (4, 6, 5, 7, 0, 2, 1, 3, 12, 14, 13, 15, 8, 10, 9, 11)},
  147.               {'inv': 40, 'pair': (1, 14), 'perm': (1, 0, 9, 8, 5, 4, 13, 12, 3, 2, 11, 10, 7, 6, 15, 14)},
  148.               {'inv': 40, 'pair': (7, 5), 'perm': (7, 3, 5, 1, 6, 2, 4, 0, 15, 11, 13, 9, 14, 10, 12, 8)},
  149.               {'inv': 48, 'pair': (2, 21), 'perm': (2, 10, 0, 8, 6, 14, 4, 12, 3, 11, 1, 9, 7, 15, 5, 13)},
  150.               {'inv': 48, 'pair': (4, 14), 'perm': (4, 5, 12, 13, 0, 1, 8, 9, 6, 7, 14, 15, 2, 3, 10, 11)},
  151.               {'inv': 48, 'pair': (7, 2), 'perm': (7, 6, 3, 2, 5, 4, 1, 0, 15, 14, 11, 10, 13, 12, 9, 8)},
  152.               {'inv': 52, 'pair': (7, 1), 'perm': (7, 5, 6, 4, 3, 1, 2, 0, 15, 13, 14, 12, 11, 9, 10, 8)},
  153.               {'inv': 56, 'pair': (4, 21), 'perm': (4, 12, 6, 14, 0, 8, 2, 10, 5, 13, 7, 15, 1, 9, 3, 11)},
  154.               {'inv': 64, 'pair': (11, 21), 'perm': (11, 3, 9, 1, 15, 7, 13, 5, 10, 2, 8, 0, 14, 6, 12, 4)},
  155.               {'inv': 68, 'pair': (8, 1), 'perm': (8, 10, 9, 11, 12, 14, 13, 15, 0, 2, 1, 3, 4, 6, 5, 7)},
  156.               {'inv': 72, 'pair': (8, 2), 'perm': (8, 9, 12, 13, 10, 11, 14, 15, 0, 1, 4, 5, 2, 3, 6, 7)},
  157.               {'inv': 72, 'pair': (11, 14), 'perm': (11, 10, 3, 2, 15, 14, 7, 6, 9, 8, 1, 0, 13, 12, 5, 4)},
  158.               {'inv': 72, 'pair': (13, 21), 'perm': (13, 5, 15, 7, 9, 1, 11, 3, 12, 4, 14, 6, 8, 0, 10, 2)},
  159.               {'inv': 80, 'pair': (8, 5), 'perm': (8, 12, 10, 14, 9, 13, 11, 15, 0, 4, 2, 6, 1, 5, 3, 7)},
  160.               {'inv': 80, 'pair': (14, 14), 'perm': (14, 15, 6, 7, 10, 11, 2, 3, 12, 13, 4, 5, 8, 9, 0, 1)},
  161.               {'inv': 84, 'pair': (11, 1), 'perm': (11, 9, 10, 8, 15, 13, 14, 12, 3, 1, 2, 0, 7, 5, 6, 4)},
  162.               {'inv': 88, 'pair': (13, 6), 'perm': (13, 12, 15, 14, 5, 4, 7, 6, 9, 8, 11, 10, 1, 0, 3, 2)},
  163.               {'inv': 96, 'pair': (13, 5), 'perm': (13, 9, 15, 11, 12, 8, 14, 10, 5, 1, 7, 3, 4, 0, 6, 2)},
  164.               {'inv': 96, 'pair': (14, 6), 'perm': (14, 15, 12, 13, 6, 7, 4, 5, 10, 11, 8, 9, 2, 3, 0, 1)},
  165.               {'inv': 104, 'pair': (14, 2), 'perm': (14, 15, 10, 11, 12, 13, 8, 9, 6, 7, 2, 3, 4, 5, 0, 1)}]},
  166.  
  167.     ############################
  168.  
  169.     {'size': 24, 'mininv': 28, 'selfinv': False, 'selfcomp': True, 'transp': 12, 'cycles': {4: 4},
  170.      'list': [{'inv': 28, 'pair': (1, 7), 'perm': (1, 3, 0, 2, 9, 11, 8, 10, 5, 7, 4, 6, 13, 15, 12, 14)},
  171.               {'inv': 28, 'pair': (2, 7), 'perm': (2, 0, 3, 1, 10, 8, 11, 9, 6, 4, 7, 5, 14, 12, 15, 13)},
  172.               {'inv': 44, 'pair': (1, 16), 'perm': (1, 5, 9, 13, 0, 4, 8, 12, 3, 7, 11, 15, 2, 6, 10, 14)},
  173.               {'inv': 44, 'pair': (4, 16), 'perm': (4, 0, 12, 8, 5, 1, 13, 9, 6, 2, 14, 10, 7, 3, 15, 11)},
  174.               {'inv': 52, 'pair': (1, 23), 'perm': (1, 9, 5, 13, 3, 11, 7, 15, 0, 8, 4, 12, 2, 10, 6, 14)},
  175.               {'inv': 52, 'pair': (2, 16), 'perm': (2, 6, 10, 14, 3, 7, 11, 15, 0, 4, 8, 12, 1, 5, 9, 13)},
  176.               {'inv': 52, 'pair': (2, 23), 'perm': (2, 10, 6, 14, 0, 8, 4, 12, 3, 11, 7, 15, 1, 9, 5, 13)},
  177.               {'inv': 52, 'pair': (4, 7), 'perm': (4, 6, 5, 7, 12, 14, 13, 15, 0, 2, 1, 3, 8, 10, 9, 11)},
  178.               {'inv': 52, 'pair': (4, 23), 'perm': (4, 12, 0, 8, 6, 14, 2, 10, 5, 13, 1, 9, 7, 15, 3, 11)},
  179.               {'inv': 52, 'pair': (8, 7), 'perm': (8, 10, 9, 11, 0, 2, 1, 3, 12, 14, 13, 15, 4, 6, 5, 7)},
  180.               {'inv': 52, 'pair': (8, 16), 'perm': (8, 12, 0, 4, 9, 13, 1, 5, 10, 14, 2, 6, 11, 15, 3, 7)},
  181.               {'inv': 52, 'pair': (8, 23), 'perm': (8, 0, 12, 4, 10, 2, 14, 6, 9, 1, 13, 5, 11, 3, 15, 7)},
  182.               {'inv': 68, 'pair': (7, 7), 'perm': (7, 5, 6, 4, 15, 13, 14, 12, 3, 1, 2, 0, 11, 9, 10, 8)},
  183.               {'inv': 68, 'pair': (7, 16), 'perm': (7, 3, 15, 11, 6, 2, 14, 10, 5, 1, 13, 9, 4, 0, 12, 8)},
  184.               {'inv': 68, 'pair': (7, 23), 'perm': (7, 15, 3, 11, 5, 13, 1, 9, 6, 14, 2, 10, 4, 12, 0, 8)},
  185.               {'inv': 68, 'pair': (11, 7), 'perm': (11, 9, 10, 8, 3, 1, 2, 0, 15, 13, 14, 12, 7, 5, 6, 4)},
  186.               {'inv': 68, 'pair': (11, 23), 'perm': (11, 3, 15, 7, 9, 1, 13, 5, 10, 2, 14, 6, 8, 0, 12, 4)},
  187.               {'inv': 68, 'pair': (13, 16), 'perm': (13, 9, 5, 1, 12, 8, 4, 0, 15, 11, 7, 3, 14, 10, 6, 2)},
  188.               {'inv': 68, 'pair': (13, 23), 'perm': (13, 5, 9, 1, 15, 7, 11, 3, 12, 4, 8, 0, 14, 6, 10, 2)},
  189.               {'inv': 68, 'pair': (14, 23), 'perm': (14, 6, 10, 2, 12, 4, 8, 0, 15, 7, 11, 3, 13, 5, 9, 1)},
  190.               {'inv': 76, 'pair': (11, 16), 'perm': (11, 15, 3, 7, 10, 14, 2, 6, 9, 13, 1, 5, 8, 12, 0, 4)},
  191.               {'inv': 76, 'pair': (14, 16), 'perm': (14, 10, 6, 2, 15, 11, 7, 3, 12, 8, 4, 0, 13, 9, 5, 1)},
  192.               {'inv': 92, 'pair': (13, 7), 'perm': (13, 15, 12, 14, 5, 7, 4, 6, 9, 11, 8, 10, 1, 3, 0, 2)},
  193.               {'inv': 92, 'pair': (14, 7), 'perm': (14, 12, 15, 13, 6, 4, 7, 5, 10, 8, 11, 9, 2, 0, 3, 1)}]},
  194.  
  195.     ############################
  196.  
  197.     {'size': 24, 'mininv': 32, 'selfinv': False, 'selfcomp': True, 'transp': 12, 'cycles': {4: 4},
  198.      'list': [{'inv': 32, 'pair': (3, 2), 'perm': (3, 2, 7, 6, 1, 0, 5, 4, 11, 10, 15, 14, 9, 8, 13, 12)},
  199.               {'inv': 32, 'pair': (3, 5), 'perm': (3, 7, 1, 5, 2, 6, 0, 4, 11, 15, 9, 13, 10, 14, 8, 12)},
  200.               {'inv': 32, 'pair': (5, 2), 'perm': (5, 4, 1, 0, 7, 6, 3, 2, 13, 12, 9, 8, 15, 14, 11, 10)},
  201.               {'inv': 32, 'pair': (6, 5), 'perm': (6, 2, 4, 0, 7, 3, 5, 1, 14, 10, 12, 8, 15, 11, 13, 9)},
  202.               {'inv': 44, 'pair': (5, 1), 'perm': (5, 7, 4, 6, 1, 3, 0, 2, 13, 15, 12, 14, 9, 11, 8, 10)},
  203.               {'inv': 44, 'pair': (6, 1), 'perm': (6, 4, 7, 5, 2, 0, 3, 1, 14, 12, 15, 13, 10, 8, 11, 9)},
  204.               {'inv': 56, 'pair': (3, 14), 'perm': (3, 2, 11, 10, 7, 6, 15, 14, 1, 0, 9, 8, 5, 4, 13, 12)},
  205.               {'inv': 56, 'pair': (3, 21), 'perm': (3, 11, 1, 9, 7, 15, 5, 13, 2, 10, 0, 8, 6, 14, 4, 12)},
  206.               {'inv': 56, 'pair': (5, 6), 'perm': (5, 4, 7, 6, 13, 12, 15, 14, 1, 0, 3, 2, 9, 8, 11, 10)},
  207.               {'inv': 56, 'pair': (9, 6), 'perm': (9, 8, 11, 10, 1, 0, 3, 2, 13, 12, 15, 14, 5, 4, 7, 6)},
  208.               {'inv': 56, 'pair': (9, 14), 'perm': (9, 8, 1, 0, 13, 12, 5, 4, 11, 10, 3, 2, 15, 14, 7, 6)},
  209.               {'inv': 56, 'pair': (10, 21), 'perm': (10, 2, 8, 0, 14, 6, 12, 4, 11, 3, 9, 1, 15, 7, 13, 5)},
  210.               {'inv': 64, 'pair': (5, 21), 'perm': (5, 13, 7, 15, 1, 9, 3, 11, 4, 12, 6, 14, 0, 8, 2, 10)},
  211.               {'inv': 64, 'pair': (6, 6), 'perm': (6, 7, 4, 5, 14, 15, 12, 13, 2, 3, 0, 1, 10, 11, 8, 9)},
  212.               {'inv': 64, 'pair': (6, 14), 'perm': (6, 7, 14, 15, 2, 3, 10, 11, 4, 5, 12, 13, 0, 1, 8, 9)},
  213.               {'inv': 64, 'pair': (10, 6), 'perm': (10, 11, 8, 9, 2, 3, 0, 1, 14, 15, 12, 13, 6, 7, 4, 5)},
  214.               {'inv': 64, 'pair': (12, 14), 'perm': (12, 13, 4, 5, 8, 9, 0, 1, 14, 15, 6, 7, 10, 11, 2, 3)},
  215.               {'inv': 64, 'pair': (12, 21), 'perm': (12, 4, 14, 6, 8, 0, 10, 2, 13, 5, 15, 7, 9, 1, 11, 3)},
  216.               {'inv': 76, 'pair': (9, 1), 'perm': (9, 11, 8, 10, 13, 15, 12, 14, 1, 3, 0, 2, 5, 7, 4, 6)},
  217.               {'inv': 76, 'pair': (10, 1), 'perm': (10, 8, 11, 9, 14, 12, 15, 13, 2, 0, 3, 1, 6, 4, 7, 5)},
  218.               {'inv': 88, 'pair': (9, 5), 'perm': (9, 13, 11, 15, 8, 12, 10, 14, 1, 5, 3, 7, 0, 4, 2, 6)},
  219.               {'inv': 88, 'pair': (10, 2), 'perm': (10, 11, 14, 15, 8, 9, 12, 13, 2, 3, 6, 7, 0, 1, 4, 5)},
  220.               {'inv': 88, 'pair': (12, 2), 'perm': (12, 13, 8, 9, 14, 15, 10, 11, 4, 5, 0, 1, 6, 7, 2, 3)},
  221.               {'inv': 88, 'pair': (12, 5), 'perm': (12, 8, 14, 10, 13, 9, 15, 11, 4, 0, 6, 2, 5, 1, 7, 3)}]},
  222.  
  223.     ####################################################################################################################
  224.  
  225.     {'size': 32, 'mininv': 12, 'selfinv': False, 'selfcomp': False, 'transp': 8, 'cycles': {3: 4, 1: 4},
  226.      'list': [{'inv': 12, 'pair': (0, 3), 'perm': (0, 4, 1, 5, 2, 6, 3, 7, 8, 12, 9, 13, 10, 14, 11, 15)},
  227.               {'inv': 12, 'pair': (0, 4), 'perm': (0, 2, 4, 6, 1, 3, 5, 7, 8, 10, 12, 14, 9, 11, 13, 15)},
  228.               {'inv': 24, 'pair': (0, 8), 'perm': (0, 1, 8, 9, 2, 3, 10, 11, 4, 5, 12, 13, 6, 7, 14, 15)},
  229.               {'inv': 24, 'pair': (0, 12), 'perm': (0, 1, 4, 5, 8, 9, 12, 13, 2, 3, 6, 7, 10, 11, 14, 15)},
  230.               {'inv': 28, 'pair': (3, 4), 'perm': (3, 1, 7, 5, 2, 0, 6, 4, 11, 9, 15, 13, 10, 8, 14, 12)},
  231.               {'inv': 28, 'pair': (5, 3), 'perm': (5, 1, 4, 0, 7, 3, 6, 2, 13, 9, 12, 8, 15, 11, 14, 10)},
  232.               {'inv': 32, 'pair': (0, 11), 'perm': (0, 8, 2, 10, 1, 9, 3, 11, 4, 12, 6, 14, 5, 13, 7, 15)},
  233.               {'inv': 32, 'pair': (0, 19), 'perm': (0, 4, 2, 6, 8, 12, 10, 14, 1, 5, 3, 7, 9, 13, 11, 15)},
  234.               {'inv': 36, 'pair': (0, 15), 'perm': (0, 8, 1, 9, 4, 12, 5, 13, 2, 10, 3, 11, 6, 14, 7, 15)},
  235.               {'inv': 36, 'pair': (0, 20), 'perm': (0, 2, 8, 10, 4, 6, 12, 14, 1, 3, 9, 11, 5, 7, 13, 15)},
  236.               {'inv': 36, 'pair': (3, 3), 'perm': (3, 7, 2, 6, 1, 5, 0, 4, 11, 15, 10, 14, 9, 13, 8, 12)},
  237.               {'inv': 36, 'pair': (5, 4), 'perm': (5, 7, 1, 3, 4, 6, 0, 2, 13, 15, 9, 11, 12, 14, 8, 10)},
  238.               {'inv': 36, 'pair': (6, 3), 'perm': (6, 2, 7, 3, 4, 0, 5, 1, 14, 10, 15, 11, 12, 8, 13, 9)},
  239.               {'inv': 36, 'pair': (6, 4), 'perm': (6, 4, 2, 0, 7, 5, 3, 1, 14, 12, 10, 8, 15, 13, 11, 9)},
  240.               {'inv': 48, 'pair': (5, 19), 'perm': (5, 1, 7, 3, 13, 9, 15, 11, 4, 0, 6, 2, 12, 8, 14, 10)},
  241.               {'inv': 48, 'pair': (9, 11), 'perm': (9, 1, 11, 3, 8, 0, 10, 2, 13, 5, 15, 7, 12, 4, 14, 6)},
  242.               {'inv': 52, 'pair': (3, 20), 'perm': (3, 1, 11, 9, 7, 5, 15, 13, 2, 0, 10, 8, 6, 4, 14, 12)},
  243.               {'inv': 52, 'pair': (9, 15), 'perm': (9, 1, 8, 0, 13, 5, 12, 4, 11, 3, 10, 2, 15, 7, 14, 6)},
  244.               {'inv': 56, 'pair': (6, 12), 'perm': (6, 7, 2, 3, 14, 15, 10, 11, 4, 5, 0, 1, 12, 13, 8, 9)},
  245.               {'inv': 56, 'pair': (10, 8), 'perm': (10, 11, 2, 3, 8, 9, 0, 1, 14, 15, 6, 7, 12, 13, 4, 5)},
  246.               {'inv': 60, 'pair': (3, 15), 'perm': (3, 11, 2, 10, 7, 15, 6, 14, 1, 9, 0, 8, 5, 13, 4, 12)},
  247.               {'inv': 60, 'pair': (9, 20), 'perm': (9, 11, 1, 3, 13, 15, 5, 7, 8, 10, 0, 2, 12, 14, 4, 6)},
  248.               {'inv': 60, 'pair': (10, 15), 'perm': (10, 2, 11, 3, 14, 6, 15, 7, 8, 0, 9, 1, 12, 4, 13, 5)},
  249.               {'inv': 60, 'pair': (10, 20), 'perm': (10, 8, 2, 0, 14, 12, 6, 4, 11, 9, 3, 1, 15, 13, 7, 5)},
  250.               {'inv': 72, 'pair': (5, 11), 'perm': (5, 13, 7, 15, 4, 12, 6, 14, 1, 9, 3, 11, 0, 8, 2, 10)},
  251.               {'inv': 72, 'pair': (6, 8), 'perm': (6, 7, 14, 15, 4, 5, 12, 13, 2, 3, 10, 11, 0, 1, 8, 9)},
  252.               {'inv': 72, 'pair': (9, 19), 'perm': (9, 13, 11, 15, 1, 5, 3, 7, 8, 12, 10, 14, 0, 4, 2, 6)},
  253.               {'inv': 72, 'pair': (10, 12), 'perm': (10, 11, 14, 15, 2, 3, 6, 7, 8, 9, 12, 13, 0, 1, 4, 5)},
  254.               {'inv': 72, 'pair': (12, 8), 'perm': (12, 13, 4, 5, 14, 15, 6, 7, 8, 9, 0, 1, 10, 11, 2, 3)},
  255.               {'inv': 72, 'pair': (12, 11), 'perm': (12, 4, 14, 6, 13, 5, 15, 7, 8, 0, 10, 2, 9, 1, 11, 3)},
  256.               {'inv': 72, 'pair': (12, 12), 'perm': (12, 13, 8, 9, 4, 5, 0, 1, 14, 15, 10, 11, 6, 7, 2, 3)},
  257.               {'inv': 72, 'pair': (12, 19), 'perm': (12, 8, 14, 10, 4, 0, 6, 2, 13, 9, 15, 11, 5, 1, 7, 3)}]},
  258.  
  259.     {'size': 32, 'mininv': 48, 'selfinv': False, 'selfcomp': False, 'transp': 12, 'cycles': {6: 2, 2: 2},
  260.      'list': [{'inv': 48, 'pair': (3, 8), 'perm': (3, 2, 11, 10, 1, 0, 9, 8, 7, 6, 15, 14, 5, 4, 13, 12)},
  261.               {'inv': 48, 'pair': (3, 11), 'perm': (3, 11, 1, 9, 2, 10, 0, 8, 7, 15, 5, 13, 6, 14, 4, 12)},
  262.               {'inv': 48, 'pair': (3, 12), 'perm': (3, 2, 7, 6, 11, 10, 15, 14, 1, 0, 5, 4, 9, 8, 13, 12)},
  263.               {'inv': 48, 'pair': (3, 19), 'perm': (3, 7, 1, 5, 11, 15, 9, 13, 2, 6, 0, 4, 10, 14, 8, 12)},
  264.               {'inv': 48, 'pair': (5, 12), 'perm': (5, 4, 1, 0, 13, 12, 9, 8, 7, 6, 3, 2, 15, 14, 11, 10)},
  265.               {'inv': 48, 'pair': (6, 19), 'perm': (6, 2, 4, 0, 14, 10, 12, 8, 7, 3, 5, 1, 15, 11, 13, 9)},
  266.               {'inv': 48, 'pair': (9, 8), 'perm': (9, 8, 1, 0, 11, 10, 3, 2, 13, 12, 5, 4, 15, 14, 7, 6)},
  267.               {'inv': 48, 'pair': (10, 11), 'perm': (10, 2, 8, 0, 11, 3, 9, 1, 14, 6, 12, 4, 15, 7, 13, 5)},
  268.               {'inv': 60, 'pair': (5, 15), 'perm': (5, 13, 4, 12, 1, 9, 0, 8, 7, 15, 6, 14, 3, 11, 2, 10)},
  269.               {'inv': 60, 'pair': (5, 20), 'perm': (5, 7, 13, 15, 1, 3, 9, 11, 4, 6, 12, 14, 0, 2, 8, 10)},
  270.               {'inv': 60, 'pair': (6, 20), 'perm': (6, 4, 14, 12, 2, 0, 10, 8, 7, 5, 15, 13, 3, 1, 11, 9)},
  271.               {'inv': 60, 'pair': (12, 15), 'perm': (12, 4, 13, 5, 8, 0, 9, 1, 14, 6, 15, 7, 10, 2, 11, 3)},
  272.               {'inv': 64, 'pair': (5, 8), 'perm': (5, 4, 13, 12, 7, 6, 15, 14, 1, 0, 9, 8, 3, 2, 11, 10)},
  273.               {'inv': 64, 'pair': (9, 12), 'perm': (9, 8, 13, 12, 1, 0, 5, 4, 11, 10, 15, 14, 3, 2, 7, 6)},
  274.               {'inv': 68, 'pair': (6, 15), 'perm': (6, 14, 7, 15, 2, 10, 3, 11, 4, 12, 5, 13, 0, 8, 1, 9)},
  275.               {'inv': 68, 'pair': (12, 20), 'perm': (12, 14, 4, 6, 8, 10, 0, 2, 13, 15, 5, 7, 9, 11, 1, 3)},
  276.               {'inv': 72, 'pair': (6, 11), 'perm': (6, 14, 4, 12, 7, 15, 5, 13, 2, 10, 0, 8, 3, 11, 1, 9)},
  277.               {'inv': 72, 'pair': (10, 19), 'perm': (10, 14, 8, 12, 2, 6, 0, 4, 11, 15, 9, 13, 3, 7, 1, 5)},
  278.               {'inv': 84, 'pair': (9, 3), 'perm': (9, 13, 8, 12, 11, 15, 10, 14, 1, 5, 0, 4, 3, 7, 2, 6)},
  279.               {'inv': 84, 'pair': (9, 4), 'perm': (9, 11, 13, 15, 8, 10, 12, 14, 1, 3, 5, 7, 0, 2, 4, 6)},
  280.               {'inv': 84, 'pair': (10, 4), 'perm': (10, 8, 14, 12, 11, 9, 15, 13, 2, 0, 6, 4, 3, 1, 7, 5)},
  281.               {'inv': 84, 'pair': (12, 3), 'perm': (12, 8, 13, 9, 14, 10, 15, 11, 4, 0, 5, 1, 6, 2, 7, 3)},
  282.               {'inv': 84, 'pair': (15, 15), 'perm': (15, 7, 14, 6, 11, 3, 10, 2, 13, 5, 12, 4, 9, 1, 8, 0)},
  283.               {'inv': 84, 'pair': (15, 20), 'perm': (15, 13, 7, 5, 11, 9, 3, 1, 14, 12, 6, 4, 10, 8, 2, 0)},
  284.               {'inv': 88, 'pair': (15, 11), 'perm': (15, 7, 13, 5, 14, 6, 12, 4, 11, 3, 9, 1, 10, 2, 8, 0)},
  285.               {'inv': 88, 'pair': (15, 19), 'perm': (15, 11, 13, 9, 7, 3, 5, 1, 14, 10, 12, 8, 6, 2, 4, 0)},
  286.               {'inv': 92, 'pair': (10, 3), 'perm': (10, 14, 11, 15, 8, 12, 9, 13, 2, 6, 3, 7, 0, 4, 1, 5)},
  287.               {'inv': 92, 'pair': (12, 4), 'perm': (12, 14, 8, 10, 13, 15, 9, 11, 4, 6, 0, 2, 5, 7, 1, 3)},
  288.               {'inv': 96, 'pair': (15, 8), 'perm': (15, 14, 7, 6, 13, 12, 5, 4, 11, 10, 3, 2, 9, 8, 1, 0)},
  289.               {'inv': 96, 'pair': (15, 12), 'perm': (15, 14, 11, 10, 7, 6, 3, 2, 13, 12, 9, 8, 5, 4, 1, 0)},
  290.               {'inv': 108, 'pair': (15, 3), 'perm': (15, 11, 14, 10, 13, 9, 12, 8, 7, 3, 6, 2, 5, 1, 4, 0)},
  291.               {'inv': 108, 'pair': (15, 4), 'perm': (15, 13, 11, 9, 14, 12, 10, 8, 7, 5, 3, 1, 6, 4, 2, 0)}]},
  292.  
  293.     ############################
  294.  
  295.     {'size': 32, 'mininv': 20, 'selfinv': False, 'selfcomp': False, 'transp': 12, 'cycles': {6: 2, 2: 2},
  296.      'list': [{'inv': 20, 'pair': (1, 3), 'perm': (1, 5, 0, 4, 3, 7, 2, 6, 9, 13, 8, 12, 11, 15, 10, 14)},
  297.               {'inv': 20, 'pair': (1, 4), 'perm': (1, 3, 5, 7, 0, 2, 4, 6, 9, 11, 13, 15, 8, 10, 12, 14)},
  298.               {'inv': 20, 'pair': (2, 4), 'perm': (2, 0, 6, 4, 3, 1, 7, 5, 10, 8, 14, 12, 11, 9, 15, 13)},
  299.               {'inv': 20, 'pair': (4, 3), 'perm': (4, 0, 5, 1, 6, 2, 7, 3, 12, 8, 13, 9, 14, 10, 15, 11)},
  300.               {'inv': 28, 'pair': (2, 3), 'perm': (2, 6, 3, 7, 0, 4, 1, 5, 10, 14, 11, 15, 8, 12, 9, 13)},
  301.               {'inv': 28, 'pair': (4, 4), 'perm': (4, 6, 0, 2, 5, 7, 1, 3, 12, 14, 8, 10, 13, 15, 9, 11)},
  302.               {'inv': 40, 'pair': (1, 11), 'perm': (1, 9, 3, 11, 0, 8, 2, 10, 5, 13, 7, 15, 4, 12, 6, 14)},
  303.               {'inv': 40, 'pair': (1, 19), 'perm': (1, 5, 3, 7, 9, 13, 11, 15, 0, 4, 2, 6, 8, 12, 10, 14)},
  304.               {'inv': 40, 'pair': (2, 8), 'perm': (2, 3, 10, 11, 0, 1, 8, 9, 6, 7, 14, 15, 4, 5, 12, 13)},
  305.               {'inv': 40, 'pair': (2, 12), 'perm': (2, 3, 6, 7, 10, 11, 14, 15, 0, 1, 4, 5, 8, 9, 12, 13)},
  306.               {'inv': 40, 'pair': (4, 12), 'perm': (4, 5, 0, 1, 12, 13, 8, 9, 6, 7, 2, 3, 14, 15, 10, 11)},
  307.               {'inv': 40, 'pair': (4, 19), 'perm': (4, 0, 6, 2, 12, 8, 14, 10, 5, 1, 7, 3, 13, 9, 15, 11)},
  308.               {'inv': 40, 'pair': (8, 8), 'perm': (8, 9, 0, 1, 10, 11, 2, 3, 12, 13, 4, 5, 14, 15, 6, 7)},
  309.               {'inv': 40, 'pair': (8, 11), 'perm': (8, 0, 10, 2, 9, 1, 11, 3, 12, 4, 14, 6, 13, 5, 15, 7)},
  310.               {'inv': 44, 'pair': (1, 15), 'perm': (1, 9, 0, 8, 5, 13, 4, 12, 3, 11, 2, 10, 7, 15, 6, 14)},
  311.               {'inv': 44, 'pair': (1, 20), 'perm': (1, 3, 9, 11, 5, 7, 13, 15, 0, 2, 8, 10, 4, 6, 12, 14)},
  312.               {'inv': 44, 'pair': (2, 20), 'perm': (2, 0, 10, 8, 6, 4, 14, 12, 3, 1, 11, 9, 7, 5, 15, 13)},
  313.               {'inv': 44, 'pair': (7, 3), 'perm': (7, 3, 6, 2, 5, 1, 4, 0, 15, 11, 14, 10, 13, 9, 12, 8)},
  314.               {'inv': 44, 'pair': (7, 4), 'perm': (7, 5, 3, 1, 6, 4, 2, 0, 15, 13, 11, 9, 14, 12, 10, 8)},
  315.               {'inv': 44, 'pair': (8, 15), 'perm': (8, 0, 9, 1, 12, 4, 13, 5, 10, 2, 11, 3, 14, 6, 15, 7)},
  316.               {'inv': 52, 'pair': (2, 15), 'perm': (2, 10, 3, 11, 6, 14, 7, 15, 0, 8, 1, 9, 4, 12, 5, 13)},
  317.               {'inv': 52, 'pair': (8, 20), 'perm': (8, 10, 0, 2, 12, 14, 4, 6, 9, 11, 1, 3, 13, 15, 5, 7)},
  318.               {'inv': 56, 'pair': (4, 8), 'perm': (4, 5, 12, 13, 6, 7, 14, 15, 0, 1, 8, 9, 2, 3, 10, 11)},
  319.               {'inv': 56, 'pair': (8, 12), 'perm': (8, 9, 12, 13, 0, 1, 4, 5, 10, 11, 14, 15, 2, 3, 6, 7)},
  320.               {'inv': 64, 'pair': (4, 11), 'perm': (4, 12, 6, 14, 5, 13, 7, 15, 0, 8, 2, 10, 1, 9, 3, 11)},
  321.               {'inv': 64, 'pair': (8, 19), 'perm': (8, 12, 10, 14, 0, 4, 2, 6, 9, 13, 11, 15, 1, 5, 3, 7)},
  322.               {'inv': 68, 'pair': (11, 15), 'perm': (11, 3, 10, 2, 15, 7, 14, 6, 9, 1, 8, 0, 13, 5, 12, 4)},
  323.               {'inv': 68, 'pair': (11, 20), 'perm': (11, 9, 3, 1, 15, 13, 7, 5, 10, 8, 2, 0, 14, 12, 6, 4)},
  324.               {'inv': 80, 'pair': (13, 11), 'perm': (13, 5, 15, 7, 12, 4, 14, 6, 9, 1, 11, 3, 8, 0, 10, 2)},
  325.               {'inv': 80, 'pair': (13, 19), 'perm': (13, 9, 15, 11, 5, 1, 7, 3, 12, 8, 14, 10, 4, 0, 6, 2)},
  326.               {'inv': 88, 'pair': (14, 8), 'perm': (14, 15, 6, 7, 12, 13, 4, 5, 10, 11, 2, 3, 8, 9, 0, 1)},
  327.               {'inv': 88, 'pair': (14, 12), 'perm': (14, 15, 10, 11, 6, 7, 2, 3, 12, 13, 8, 9, 4, 5, 0, 1)}]},
  328.  
  329.     {'size': 32, 'mininv': 32, 'selfinv': False, 'selfcomp': False, 'transp': 12, 'cycles': {6: 2, 2: 2},
  330.      'list': [{'inv': 32, 'pair': (1, 8), 'perm': (1, 0, 9, 8, 3, 2, 11, 10, 5, 4, 13, 12, 7, 6, 15, 14)},
  331.               {'inv': 32, 'pair': (1, 12), 'perm': (1, 0, 5, 4, 9, 8, 13, 12, 3, 2, 7, 6, 11, 10, 15, 14)},
  332.               {'inv': 40, 'pair': (2, 11), 'perm': (2, 10, 0, 8, 3, 11, 1, 9, 6, 14, 4, 12, 7, 15, 5, 13)},
  333.               {'inv': 40, 'pair': (2, 19), 'perm': (2, 6, 0, 4, 10, 14, 8, 12, 3, 7, 1, 5, 11, 15, 9, 13)},
  334.               {'inv': 52, 'pair': (4, 15), 'perm': (4, 12, 5, 13, 0, 8, 1, 9, 6, 14, 7, 15, 2, 10, 3, 11)},
  335.               {'inv': 52, 'pair': (4, 20), 'perm': (4, 6, 12, 14, 0, 2, 8, 10, 5, 7, 13, 15, 1, 3, 9, 11)},
  336.               {'inv': 56, 'pair': (7, 19), 'perm': (7, 3, 5, 1, 15, 11, 13, 9, 6, 2, 4, 0, 14, 10, 12, 8)},
  337.               {'inv': 56, 'pair': (11, 11), 'perm': (11, 3, 9, 1, 10, 2, 8, 0, 15, 7, 13, 5, 14, 6, 12, 4)},
  338.               {'inv': 64, 'pair': (7, 12), 'perm': (7, 6, 3, 2, 15, 14, 11, 10, 5, 4, 1, 0, 13, 12, 9, 8)},
  339.               {'inv': 64, 'pair': (11, 8), 'perm': (11, 10, 3, 2, 9, 8, 1, 0, 15, 14, 7, 6, 13, 12, 5, 4)},
  340.               {'inv': 68, 'pair': (7, 20), 'perm': (7, 5, 15, 13, 3, 1, 11, 9, 6, 4, 14, 12, 2, 0, 10, 8)},
  341.               {'inv': 68, 'pair': (13, 15), 'perm': (13, 5, 12, 4, 9, 1, 8, 0, 15, 7, 14, 6, 11, 3, 10, 2)},
  342.               {'inv': 76, 'pair': (7, 15), 'perm': (7, 15, 6, 14, 3, 11, 2, 10, 5, 13, 4, 12, 1, 9, 0, 8)},
  343.               {'inv': 76, 'pair': (8, 3), 'perm': (8, 12, 9, 13, 10, 14, 11, 15, 0, 4, 1, 5, 2, 6, 3, 7)},
  344.               {'inv': 76, 'pair': (8, 4), 'perm': (8, 10, 12, 14, 9, 11, 13, 15, 0, 2, 4, 6, 1, 3, 5, 7)},
  345.               {'inv': 76, 'pair': (13, 20), 'perm': (13, 15, 5, 7, 9, 11, 1, 3, 12, 14, 4, 6, 8, 10, 0, 2)},
  346.               {'inv': 76, 'pair': (14, 15), 'perm': (14, 6, 15, 7, 10, 2, 11, 3, 12, 4, 13, 5, 8, 0, 9, 1)},
  347.               {'inv': 76, 'pair': (14, 20), 'perm': (14, 12, 6, 4, 10, 8, 2, 0, 15, 13, 7, 5, 11, 9, 3, 1)},
  348.               {'inv': 80, 'pair': (7, 8), 'perm': (7, 6, 15, 14, 5, 4, 13, 12, 3, 2, 11, 10, 1, 0, 9, 8)},
  349.               {'inv': 80, 'pair': (7, 11), 'perm': (7, 15, 5, 13, 6, 14, 4, 12, 3, 11, 1, 9, 2, 10, 0, 8)},
  350.               {'inv': 80, 'pair': (11, 12), 'perm': (11, 10, 15, 14, 3, 2, 7, 6, 9, 8, 13, 12, 1, 0, 5, 4)},
  351.               {'inv': 80, 'pair': (11, 19), 'perm': (11, 15, 9, 13, 3, 7, 1, 5, 10, 14, 8, 12, 2, 6, 0, 4)},
  352.               {'inv': 80, 'pair': (13, 8), 'perm': (13, 12, 5, 4, 15, 14, 7, 6, 9, 8, 1, 0, 11, 10, 3, 2)},
  353.               {'inv': 80, 'pair': (13, 12), 'perm': (13, 12, 9, 8, 5, 4, 1, 0, 15, 14, 11, 10, 7, 6, 3, 2)},
  354.               {'inv': 80, 'pair': (14, 11), 'perm': (14, 6, 12, 4, 15, 7, 13, 5, 10, 2, 8, 0, 11, 3, 9, 1)},
  355.               {'inv': 80, 'pair': (14, 19), 'perm': (14, 10, 12, 8, 6, 2, 4, 0, 15, 11, 13, 9, 7, 3, 5, 1)},
  356.               {'inv': 92, 'pair': (11, 4), 'perm': (11, 9, 15, 13, 10, 8, 14, 12, 3, 1, 7, 5, 2, 0, 6, 4)},
  357.               {'inv': 92, 'pair': (13, 3), 'perm': (13, 9, 12, 8, 15, 11, 14, 10, 5, 1, 4, 0, 7, 3, 6, 2)},
  358.               {'inv': 100, 'pair': (11, 3), 'perm': (11, 15, 10, 14, 9, 13, 8, 12, 3, 7, 2, 6, 1, 5, 0, 4)},
  359.               {'inv': 100, 'pair': (13, 4), 'perm': (13, 15, 9, 11, 12, 14, 8, 10, 5, 7, 1, 3, 4, 6, 0, 2)},
  360.               {'inv': 100, 'pair': (14, 3), 'perm': (14, 10, 15, 11, 12, 8, 13, 9, 6, 2, 7, 3, 4, 0, 5, 1)},
  361.               {'inv': 100, 'pair': (14, 4), 'perm': (14, 12, 10, 8, 15, 13, 11, 9, 6, 4, 2, 0, 7, 5, 3, 1)}]},
  362.  
  363.     ####################################################################################################################
  364.  
  365.     {'size': 48, 'mininv': 28, 'selfinv': False, 'selfcomp': True, 'transp': 10, 'cycles': {2: 1, 4: 3, 1: 2},
  366.      'list': [{'inv': 28, 'pair': (0, 9), 'perm': (0, 8, 1, 9, 2, 10, 3, 11, 4, 12, 5, 13, 6, 14, 7, 15)},
  367.               {'inv': 28, 'pair': (0, 10), 'perm': (0, 2, 8, 10, 1, 3, 9, 11, 4, 6, 12, 14, 5, 7, 13, 15)},
  368.               {'inv': 28, 'pair': (0, 13), 'perm': (0, 4, 1, 5, 8, 12, 9, 13, 2, 6, 3, 7, 10, 14, 11, 15)},
  369.               {'inv': 28, 'pair': (0, 18), 'perm': (0, 2, 4, 6, 8, 10, 12, 14, 1, 3, 5, 7, 9, 11, 13, 15)},
  370.               {'inv': 40, 'pair': (0, 17), 'perm': (0, 8, 4, 12, 1, 9, 5, 13, 2, 10, 6, 14, 3, 11, 7, 15)},
  371.               {'inv': 40, 'pair': (0, 22), 'perm': (0, 4, 8, 12, 2, 6, 10, 14, 1, 5, 9, 13, 3, 7, 11, 15)},
  372.               {'inv': 44, 'pair': (3, 10), 'perm': (3, 1, 11, 9, 2, 0, 10, 8, 7, 5, 15, 13, 6, 4, 14, 12)},
  373.               {'inv': 44, 'pair': (3, 18), 'perm': (3, 1, 7, 5, 11, 9, 15, 13, 2, 0, 6, 4, 10, 8, 14, 12)},
  374.               {'inv': 44, 'pair': (5, 13), 'perm': (5, 1, 4, 0, 13, 9, 12, 8, 7, 3, 6, 2, 15, 11, 14, 10)},
  375.               {'inv': 44, 'pair': (9, 9), 'perm': (9, 1, 8, 0, 11, 3, 10, 2, 13, 5, 12, 4, 15, 7, 14, 6)},
  376.               {'inv': 52, 'pair': (3, 9), 'perm': (3, 11, 2, 10, 1, 9, 0, 8, 7, 15, 6, 14, 5, 13, 4, 12)},
  377.               {'inv': 52, 'pair': (3, 13), 'perm': (3, 7, 2, 6, 11, 15, 10, 14, 1, 5, 0, 4, 9, 13, 8, 12)},
  378.               {'inv': 52, 'pair': (5, 18), 'perm': (5, 7, 1, 3, 13, 15, 9, 11, 4, 6, 0, 2, 12, 14, 8, 10)},
  379.               {'inv': 52, 'pair': (6, 13), 'perm': (6, 2, 7, 3, 14, 10, 15, 11, 4, 0, 5, 1, 12, 8, 13, 9)},
  380.               {'inv': 52, 'pair': (6, 18), 'perm': (6, 4, 2, 0, 14, 12, 10, 8, 7, 5, 3, 1, 15, 13, 11, 9)},
  381.               {'inv': 52, 'pair': (9, 10), 'perm': (9, 11, 1, 3, 8, 10, 0, 2, 13, 15, 5, 7, 12, 14, 4, 6)},
  382.               {'inv': 52, 'pair': (10, 9), 'perm': (10, 2, 11, 3, 8, 0, 9, 1, 14, 6, 15, 7, 12, 4, 13, 5)},
  383.               {'inv': 52, 'pair': (10, 10), 'perm': (10, 8, 2, 0, 11, 9, 3, 1, 14, 12, 6, 4, 15, 13, 7, 5)},
  384.               {'inv': 56, 'pair': (3, 22), 'perm': (3, 7, 11, 15, 1, 5, 9, 13, 2, 6, 10, 14, 0, 4, 8, 12)},
  385.               {'inv': 56, 'pair': (5, 17), 'perm': (5, 13, 1, 9, 4, 12, 0, 8, 7, 15, 3, 11, 6, 14, 2, 10)},
  386.               {'inv': 56, 'pair': (5, 22), 'perm': (5, 1, 13, 9, 7, 3, 15, 11, 4, 0, 12, 8, 6, 2, 14, 10)},
  387.               {'inv': 56, 'pair': (6, 22), 'perm': (6, 2, 14, 10, 4, 0, 12, 8, 7, 3, 15, 11, 5, 1, 13, 9)},
  388.               {'inv': 56, 'pair': (9, 17), 'perm': (9, 1, 13, 5, 8, 0, 12, 4, 11, 3, 15, 7, 10, 2, 14, 6)},
  389.               {'inv': 56, 'pair': (12, 17), 'perm': (12, 4, 8, 0, 13, 5, 9, 1, 14, 6, 10, 2, 15, 7, 11, 3)},
  390.               {'inv': 64, 'pair': (3, 17), 'perm': (3, 11, 7, 15, 2, 10, 6, 14, 1, 9, 5, 13, 0, 8, 4, 12)},
  391.               {'inv': 64, 'pair': (6, 17), 'perm': (6, 14, 2, 10, 7, 15, 3, 11, 4, 12, 0, 8, 5, 13, 1, 9)},
  392.               {'inv': 64, 'pair': (9, 22), 'perm': (9, 13, 1, 5, 11, 15, 3, 7, 8, 12, 0, 4, 10, 14, 2, 6)},
  393.               {'inv': 64, 'pair': (10, 17), 'perm': (10, 2, 14, 6, 11, 3, 15, 7, 8, 0, 12, 4, 9, 1, 13, 5)},
  394.               {'inv': 64, 'pair': (10, 22), 'perm': (10, 14, 2, 6, 8, 12, 0, 4, 11, 15, 3, 7, 9, 13, 1, 5)},
  395.               {'inv': 64, 'pair': (12, 22), 'perm': (12, 8, 4, 0, 14, 10, 6, 2, 13, 9, 5, 1, 15, 11, 7, 3)},
  396.               {'inv': 68, 'pair': (5, 9), 'perm': (5, 13, 4, 12, 7, 15, 6, 14, 1, 9, 0, 8, 3, 11, 2, 10)},
  397.               {'inv': 68, 'pair': (5, 10), 'perm': (5, 7, 13, 15, 4, 6, 12, 14, 1, 3, 9, 11, 0, 2, 8, 10)},
  398.               {'inv': 68, 'pair': (6, 10), 'perm': (6, 4, 14, 12, 7, 5, 15, 13, 2, 0, 10, 8, 3, 1, 11, 9)},
  399.               {'inv': 68, 'pair': (9, 13), 'perm': (9, 13, 8, 12, 1, 5, 0, 4, 11, 15, 10, 14, 3, 7, 2, 6)},
  400.               {'inv': 68, 'pair': (9, 18), 'perm': (9, 11, 13, 15, 1, 3, 5, 7, 8, 10, 12, 14, 0, 2, 4, 6)},
  401.               {'inv': 68, 'pair': (10, 18), 'perm': (10, 8, 14, 12, 2, 0, 6, 4, 11, 9, 15, 13, 3, 1, 7, 5)},
  402.               {'inv': 68, 'pair': (12, 9), 'perm': (12, 4, 13, 5, 14, 6, 15, 7, 8, 0, 9, 1, 10, 2, 11, 3)},
  403.               {'inv': 68, 'pair': (12, 13), 'perm': (12, 8, 13, 9, 4, 0, 5, 1, 14, 10, 15, 11, 6, 2, 7, 3)},
  404.               {'inv': 76, 'pair': (6, 9), 'perm': (6, 14, 7, 15, 4, 12, 5, 13, 2, 10, 3, 11, 0, 8, 1, 9)},
  405.               {'inv': 76, 'pair': (10, 13), 'perm': (10, 14, 11, 15, 2, 6, 3, 7, 8, 12, 9, 13, 0, 4, 1, 5)},
  406.               {'inv': 76, 'pair': (12, 10), 'perm': (12, 14, 4, 6, 13, 15, 5, 7, 8, 10, 0, 2, 9, 11, 1, 3)},
  407.               {'inv': 76, 'pair': (12, 18), 'perm': (12, 14, 8, 10, 4, 6, 0, 2, 13, 15, 9, 11, 5, 7, 1, 3)},
  408.               {'inv': 80, 'pair': (15, 17), 'perm': (15, 7, 11, 3, 14, 6, 10, 2, 13, 5, 9, 1, 12, 4, 8, 0)},
  409.               {'inv': 80, 'pair': (15, 22), 'perm': (15, 11, 7, 3, 13, 9, 5, 1, 14, 10, 6, 2, 12, 8, 4, 0)},
  410.               {'inv': 92, 'pair': (15, 9), 'perm': (15, 7, 14, 6, 13, 5, 12, 4, 11, 3, 10, 2, 9, 1, 8, 0)},
  411.               {'inv': 92, 'pair': (15, 10), 'perm': (15, 13, 7, 5, 14, 12, 6, 4, 11, 9, 3, 1, 10, 8, 2, 0)},
  412.               {'inv': 92, 'pair': (15, 13), 'perm': (15, 11, 14, 10, 7, 3, 6, 2, 13, 9, 12, 8, 5, 1, 4, 0)},
  413.               {'inv': 92, 'pair': (15, 18), 'perm': (15, 13, 11, 9, 7, 5, 3, 1, 14, 12, 10, 8, 6, 4, 2, 0)}]},
  414.  
  415.     ############################
  416.  
  417.     {'size': 48, 'mininv': 36, 'selfinv': False, 'selfcomp': True, 'transp': 14, 'cycles': {8: 2},
  418.      'list': [{'inv': 36, 'pair': (1, 9), 'perm': (1, 9, 0, 8, 3, 11, 2, 10, 5, 13, 4, 12, 7, 15, 6, 14)},
  419.               {'inv': 36, 'pair': (1, 10), 'perm': (1, 3, 9, 11, 0, 2, 8, 10, 5, 7, 13, 15, 4, 6, 12, 14)},
  420.               {'inv': 36, 'pair': (1, 13), 'perm': (1, 5, 0, 4, 9, 13, 8, 12, 3, 7, 2, 6, 11, 15, 10, 14)},
  421.               {'inv': 36, 'pair': (1, 18), 'perm': (1, 3, 5, 7, 9, 11, 13, 15, 0, 2, 4, 6, 8, 10, 12, 14)},
  422.               {'inv': 36, 'pair': (2, 10), 'perm': (2, 0, 10, 8, 3, 1, 11, 9, 6, 4, 14, 12, 7, 5, 15, 13)},
  423.               {'inv': 36, 'pair': (2, 18), 'perm': (2, 0, 6, 4, 10, 8, 14, 12, 3, 1, 7, 5, 11, 9, 15, 13)},
  424.               {'inv': 36, 'pair': (4, 13), 'perm': (4, 0, 5, 1, 12, 8, 13, 9, 6, 2, 7, 3, 14, 10, 15, 11)},
  425.               {'inv': 36, 'pair': (8, 9), 'perm': (8, 0, 9, 1, 10, 2, 11, 3, 12, 4, 13, 5, 14, 6, 15, 7)},
  426.               {'inv': 44, 'pair': (2, 9), 'perm': (2, 10, 3, 11, 0, 8, 1, 9, 6, 14, 7, 15, 4, 12, 5, 13)},
  427.               {'inv': 44, 'pair': (2, 13), 'perm': (2, 6, 3, 7, 10, 14, 11, 15, 0, 4, 1, 5, 8, 12, 9, 13)},
  428.               {'inv': 44, 'pair': (4, 18), 'perm': (4, 6, 0, 2, 12, 14, 8, 10, 5, 7, 1, 3, 13, 15, 9, 11)},
  429.               {'inv': 44, 'pair': (8, 10), 'perm': (8, 10, 0, 2, 9, 11, 1, 3, 12, 14, 4, 6, 13, 15, 5, 7)},
  430.               {'inv': 48, 'pair': (1, 17), 'perm': (1, 9, 5, 13, 0, 8, 4, 12, 3, 11, 7, 15, 2, 10, 6, 14)},
  431.               {'inv': 48, 'pair': (1, 22), 'perm': (1, 5, 9, 13, 3, 7, 11, 15, 0, 4, 8, 12, 2, 6, 10, 14)},
  432.               {'inv': 48, 'pair': (2, 22), 'perm': (2, 6, 10, 14, 0, 4, 8, 12, 3, 7, 11, 15, 1, 5, 9, 13)},
  433.               {'inv': 48, 'pair': (4, 17), 'perm': (4, 12, 0, 8, 5, 13, 1, 9, 6, 14, 2, 10, 7, 15, 3, 11)},
  434.               {'inv': 48, 'pair': (4, 22), 'perm': (4, 0, 12, 8, 6, 2, 14, 10, 5, 1, 13, 9, 7, 3, 15, 11)},
  435.               {'inv': 48, 'pair': (8, 17), 'perm': (8, 0, 12, 4, 9, 1, 13, 5, 10, 2, 14, 6, 11, 3, 15, 7)},
  436.               {'inv': 56, 'pair': (2, 17), 'perm': (2, 10, 6, 14, 3, 11, 7, 15, 0, 8, 4, 12, 1, 9, 5, 13)},
  437.               {'inv': 56, 'pair': (8, 22), 'perm': (8, 12, 0, 4, 10, 14, 2, 6, 9, 13, 1, 5, 11, 15, 3, 7)},
  438.               {'inv': 60, 'pair': (4, 9), 'perm': (4, 12, 5, 13, 6, 14, 7, 15, 0, 8, 1, 9, 2, 10, 3, 11)},
  439.               {'inv': 60, 'pair': (4, 10), 'perm': (4, 6, 12, 14, 5, 7, 13, 15, 0, 2, 8, 10, 1, 3, 9, 11)},
  440.               {'inv': 60, 'pair': (7, 13), 'perm': (7, 3, 6, 2, 15, 11, 14, 10, 5, 1, 4, 0, 13, 9, 12, 8)},
  441.               {'inv': 60, 'pair': (7, 18), 'perm': (7, 5, 3, 1, 15, 13, 11, 9, 6, 4, 2, 0, 14, 12, 10, 8)},
  442.               {'inv': 60, 'pair': (8, 13), 'perm': (8, 12, 9, 13, 0, 4, 1, 5, 10, 14, 11, 15, 2, 6, 3, 7)},
  443.               {'inv': 60, 'pair': (8, 18), 'perm': (8, 10, 12, 14, 0, 2, 4, 6, 9, 11, 13, 15, 1, 3, 5, 7)},
  444.               {'inv': 60, 'pair': (11, 9), 'perm': (11, 3, 10, 2, 9, 1, 8, 0, 15, 7, 14, 6, 13, 5, 12, 4)},
  445.               {'inv': 60, 'pair': (11, 10), 'perm': (11, 9, 3, 1, 10, 8, 2, 0, 15, 13, 7, 5, 14, 12, 6, 4)},
  446.               {'inv': 64, 'pair': (7, 22), 'perm': (7, 3, 15, 11, 5, 1, 13, 9, 6, 2, 14, 10, 4, 0, 12, 8)},
  447.               {'inv': 64, 'pair': (13, 17), 'perm': (13, 5, 9, 1, 12, 4, 8, 0, 15, 7, 11, 3, 14, 6, 10, 2)},
  448.               {'inv': 72, 'pair': (7, 17), 'perm': (7, 15, 3, 11, 6, 14, 2, 10, 5, 13, 1, 9, 4, 12, 0, 8)},
  449.               {'inv': 72, 'pair': (11, 17), 'perm': (11, 3, 15, 7, 10, 2, 14, 6, 9, 1, 13, 5, 8, 0, 12, 4)},
  450.               {'inv': 72, 'pair': (11, 22), 'perm': (11, 15, 3, 7, 9, 13, 1, 5, 10, 14, 2, 6, 8, 12, 0, 4)},
  451.               {'inv': 72, 'pair': (13, 22), 'perm': (13, 9, 5, 1, 15, 11, 7, 3, 12, 8, 4, 0, 14, 10, 6, 2)},
  452.               {'inv': 72, 'pair': (14, 17), 'perm': (14, 6, 10, 2, 15, 7, 11, 3, 12, 4, 8, 0, 13, 5, 9, 1)},
  453.               {'inv': 72, 'pair': (14, 22), 'perm': (14, 10, 6, 2, 12, 8, 4, 0, 15, 11, 7, 3, 13, 9, 5, 1)},
  454.               {'inv': 76, 'pair': (7, 10), 'perm': (7, 5, 15, 13, 6, 4, 14, 12, 3, 1, 11, 9, 2, 0, 10, 8)},
  455.               {'inv': 76, 'pair': (11, 18), 'perm': (11, 9, 15, 13, 3, 1, 7, 5, 10, 8, 14, 12, 2, 0, 6, 4)},
  456.               {'inv': 76, 'pair': (13, 9), 'perm': (13, 5, 12, 4, 15, 7, 14, 6, 9, 1, 8, 0, 11, 3, 10, 2)},
  457.               {'inv': 76, 'pair': (13, 13), 'perm': (13, 9, 12, 8, 5, 1, 4, 0, 15, 11, 14, 10, 7, 3, 6, 2)},
  458.               {'inv': 84, 'pair': (7, 9), 'perm': (7, 15, 6, 14, 5, 13, 4, 12, 3, 11, 2, 10, 1, 9, 0, 8)},
  459.               {'inv': 84, 'pair': (11, 13), 'perm': (11, 15, 10, 14, 3, 7, 2, 6, 9, 13, 8, 12, 1, 5, 0, 4)},
  460.               {'inv': 84, 'pair': (13, 10), 'perm': (13, 15, 5, 7, 12, 14, 4, 6, 9, 11, 1, 3, 8, 10, 0, 2)},
  461.               {'inv': 84, 'pair': (13, 18), 'perm': (13, 15, 9, 11, 5, 7, 1, 3, 12, 14, 8, 10, 4, 6, 0, 2)},
  462.               {'inv': 84, 'pair': (14, 9), 'perm': (14, 6, 15, 7, 12, 4, 13, 5, 10, 2, 11, 3, 8, 0, 9, 1)},
  463.               {'inv': 84, 'pair': (14, 10), 'perm': (14, 12, 6, 4, 15, 13, 7, 5, 10, 8, 2, 0, 11, 9, 3, 1)},
  464.               {'inv': 84, 'pair': (14, 13), 'perm': (14, 10, 15, 11, 6, 2, 7, 3, 12, 8, 13, 9, 4, 0, 5, 1)},
  465.               {'inv': 84, 'pair': (14, 18), 'perm': (14, 12, 10, 8, 6, 4, 2, 0, 15, 13, 11, 9, 7, 5, 3, 1)}]},
  466.  
  467. ]
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