msd_fib{0, 1} {0, 1} 

0 1
0 0 0 -> 1
1 0 0 -> 2
0 1 0 -> 3
1 1 0 -> 4

1 1
0 0 0 -> 1
1 0 0 -> 2
0 1 0 -> 3
1 1 0 -> 4
0 0 1 -> 5
1 0 1 -> 6
0 1 1 -> 7
1 1 1 -> 8

2 0
0 0 1 -> 9
0 1 1 -> 10

3 0
0 0 0 -> 11
1 0 0 -> 12
0 1 0 -> 13
1 1 0 -> 14
0 0 1 -> 15
1 0 1 -> 16
0 1 1 -> 17
1 1 1 -> 18

4 1
0 0 0 -> 19
0 1 0 -> 2
0 0 1 -> 20
0 1 1 -> 21

5 0
1 0 0 -> 22
1 1 0 -> 23
0 0 1 -> 24
1 0 1 -> 25
0 1 1 -> 26
1 1 1 -> 27

6 0
0 0 0 -> 28
0 1 0 -> 29
0 0 1 -> 2
0 1 1 -> 30

7 1
1 0 0 -> 31
0 0 1 -> 32
1 0 1 -> 33
0 1 1 -> 34
1 1 1 -> 35

8 0
0 0 0 -> 36
0 1 0 -> 37
0 0 1 -> 38
0 1 1 -> 39

9 0
0 0 0 -> 2
0 1 0 -> 30

10 0
0 0 0 -> 38
0 1 0 -> 39

11 1
0 0 0 -> 13
1 0 0 -> 14
0 1 0 -> 40
1 1 0 -> 41
0 0 1 -> 17
1 0 1 -> 18
0 1 1 -> 42
1 1 1 -> 43

12 0
0 0 0 -> 2
0 1 0 -> 4
0 0 1 -> 21
0 1 1 -> 44

13 0
0 0 0 -> 45
1 0 0 -> 46
0 1 0 -> 47
1 1 0 -> 48
0 0 1 -> 28
1 0 1 -> 49
0 1 1 -> 29
1 1 1 -> 50

14 1
0 0 0 -> 51
0 1 0 -> 52
0 0 1 -> 53
0 1 1 -> 54

15 0
0 1 0 -> 55
0 0 1 -> 34
1 0 1 -> 35
0 1 1 -> 56
1 1 1 -> 57

16 0
0 0 0 -> 37
0 1 0 -> 58
0 0 1 -> 39
0 1 1 -> 59

17 1
0 0 0 -> 9
0 1 0 -> 10
0 0 1 -> 53
1 0 1 -> 60
0 1 1 -> 54
1 1 1 -> 61

18 0
0 0 0 -> 62
0 1 0 -> 63
0 0 1 -> 28
0 1 1 -> 29

19 0
0 1 1 -> 55

20 0
0 0 0 -> 39
0 1 0 -> 59
1 1 0 -> 64
0 1 1 -> 64

21 0
0 0 0 -> 28
1 0 0 -> 2
0 1 0 -> 29
1 1 0 -> 30
0 0 1 -> 2
0 1 1 -> 30

22 0
0 0 0 -> 65
0 1 0 -> 66

23 0
0 0 0 -> 67
0 1 0 -> 68

24 0
0 0 0 -> 5
1 0 0 -> 6
0 1 0 -> 7
1 1 0 -> 8
1 0 1 -> 69
1 1 1 -> 70

25 1
0 0 0 -> 9
0 1 0 -> 10
0 0 1 -> 53
0 1 1 -> 54

26 0
0 0 0 -> 15
1 0 0 -> 16
0 1 0 -> 17
1 1 0 -> 18
1 0 1 -> 71

27 0
0 0 0 -> 20
0 1 0 -> 21
0 0 1 -> 72
0 1 1 -> 65

28 1
0 0 0 -> 21
0 1 0 -> 44
1 1 0 -> 55
0 0 1 -> 65
1 0 1 -> 6
0 1 1 -> 66
1 1 1 -> 8

29 0
0 0 0 -> 53
1 0 0 -> 9
0 1 0 -> 54
1 1 0 -> 10
0 0 1 -> 67
1 0 1 -> 16
0 1 1 -> 68
1 1 1 -> 18

30 1
0 0 1 -> 20
0 1 1 -> 21

31 0
0 0 0 -> 68
0 1 0 -> 73

32 0
0 0 0 -> 17
1 0 0 -> 18
0 1 0 -> 42
1 1 0 -> 43
0 1 1 -> 64

33 1
0 0 0 -> 21
0 1 0 -> 44
0 0 1 -> 65
0 1 1 -> 66

34 0
0 0 0 -> 28
1 0 0 -> 49
0 1 0 -> 29
1 1 0 -> 50
0 0 1 -> 2
0 1 1 -> 30

35 0
0 0 0 -> 53
0 1 0 -> 54
0 0 1 -> 67
0 1 1 -> 68

36 1
0 0 0 -> 54
1 0 0 -> 10
0 1 0 -> 74
1 1 0 -> 75
0 0 1 -> 68
1 0 1 -> 18
0 1 1 -> 73
1 1 1 -> 76

37 0
0 0 0 -> 65
1 0 0 -> 6
0 1 0 -> 66
1 1 0 -> 8
1 0 1 -> 69
1 1 1 -> 70

38 0
0 1 0 -> 55
0 0 1 -> 21
0 1 1 -> 44
1 1 1 -> 55

39 1
0 0 0 -> 9
0 1 0 -> 10
0 0 1 -> 53
1 0 1 -> 9
0 1 1 -> 54
1 1 1 -> 10

40 0
0 0 0 -> 77
1 0 0 -> 78
0 1 0 -> 68
1 1 0 -> 79
0 0 1 -> 36
1 0 1 -> 80
0 1 1 -> 37
1 1 1 -> 25

41 0
0 0 0 -> 81
0 1 0 -> 1
0 0 1 -> 82
0 1 1 -> 5

42 0
0 0 0 -> 20
0 1 0 -> 21
0 0 1 -> 72
1 0 1 -> 83
0 1 1 -> 65
1 1 1 -> 6

43 1
0 0 0 -> 84
0 0 1 -> 85
0 1 1 -> 24

44 0
0 0 0 -> 36
1 0 0 -> 86
0 1 0 -> 37
1 1 0 -> 25
0 0 1 -> 38
0 1 1 -> 39

45 0
0 0 0 -> 68
1 0 0 -> 79
0 1 0 -> 73
1 1 0 -> 87
0 0 1 -> 37
1 0 1 -> 25
0 1 1 -> 58
1 1 1 -> 27

46 1
0 0 0 -> 1
0 1 0 -> 3
0 0 1 -> 5
0 1 1 -> 7

47 0
1 0 0 -> 88
1 1 0 -> 70
0 0 1 -> 62
1 0 1 -> 33
0 1 1 -> 63
1 1 1 -> 35

48 0
0 0 0 -> 11
0 1 0 -> 13
0 0 1 -> 15
0 1 1 -> 17

49 0
0 0 1 -> 24
0 1 1 -> 26

50 1
0 0 1 -> 32
0 1 1 -> 34

51 0
0 0 0 -> 2
0 1 0 -> 4
0 0 1 -> 21
0 1 1 -> 44
1 1 1 -> 55

52 1
0 0 0 -> 51
0 1 0 -> 52
0 0 1 -> 53
1 0 1 -> 9
0 1 1 -> 54
1 1 1 -> 10

53 0
0 0 0 -> 37
1 0 0 -> 25
0 1 0 -> 58
1 1 0 -> 27
0 0 1 -> 39
0 1 1 -> 59
1 1 1 -> 64

54 0
0 0 0 -> 62
1 0 0 -> 33
0 1 0 -> 63
1 1 0 -> 35
0 0 1 -> 28
1 0 1 -> 2
0 1 1 -> 29
1 1 1 -> 30

55 0
0 0 0 -> 19
0 1 0 -> 2

56 0
0 0 0 -> 36
1 0 0 -> 80
0 1 0 -> 37
1 1 0 -> 25
0 0 1 -> 38
0 1 1 -> 39

57 0
0 0 0 -> 82
0 1 0 -> 5
0 0 1 -> 89

58 0
0 0 0 -> 67
1 0 0 -> 16
0 1 0 -> 68
1 1 0 -> 18
1 0 1 -> 71

59 0
0 0 0 -> 20
0 1 0 -> 21
0 0 1 -> 72
1 0 1 -> 90
0 1 1 -> 65
1 1 1 -> 6

60 0
0 0 0 -> 5
0 1 0 -> 7

61 0
0 0 0 -> 15
0 1 0 -> 17

62 0
0 0 0 -> 68
1 0 0 -> 18
0 1 0 -> 73
1 1 0 -> 76

63 0
1 0 0 -> 69
1 1 0 -> 70

64 1
0 0 1 -> 91
0 1 1 -> 9

65 0
1 0 0 -> 22
1 1 0 -> 23
0 0 1 -> 37
1 0 1 -> 25
0 1 1 -> 58
1 1 1 -> 27

66 0
1 0 0 -> 31
0 0 1 -> 62
1 0 1 -> 33
0 1 1 -> 63
1 1 1 -> 35

67 0
0 0 1 -> 63
1 0 1 -> 35
0 1 1 -> 92
1 1 1 -> 93

68 0
1 0 1 -> 22
1 1 1 -> 23

69 0
0 0 1 -> 37
0 1 1 -> 58

70 0
0 0 1 -> 62
0 1 1 -> 63

71 0
0 0 1 -> 63
0 1 1 -> 92

72 0
0 0 0 -> 63
1 0 0 -> 35
0 1 0 -> 92
1 1 0 -> 93
0 0 1 -> 29
1 0 1 -> 30
0 1 1 -> 94
1 1 1 -> 95

73 0
1 0 1 -> 31

74 0
0 0 0 -> 84
1 0 0 -> 96
1 1 0 -> 22
0 0 1 -> 36
1 0 1 -> 86
0 1 1 -> 37
1 1 1 -> 25

75 0
0 0 0 -> 97
0 1 0 -> 28
0 0 1 -> 19
0 1 1 -> 2

76 0
0 0 0 -> 84
0 0 1 -> 36
0 1 1 -> 37

77 0
1 0 0 -> 70
1 1 0 -> 98
0 0 1 -> 63
1 0 1 -> 35
0 1 1 -> 92
1 1 1 -> 93

78 1
0 0 0 -> 13
0 1 0 -> 40
0 0 1 -> 17
0 1 1 -> 42

79 0
0 0 0 -> 45
0 1 0 -> 47
0 0 1 -> 28
0 1 1 -> 29

80 0
0 1 0 -> 55
0 0 1 -> 34
0 1 1 -> 56

81 0
0 0 0 -> 52
0 1 0 -> 99
1 1 0 -> 64
0 0 1 -> 54
1 0 1 -> 10
0 1 1 -> 100
1 1 1 -> 75

82 0
0 0 0 -> 63
1 0 0 -> 35
0 1 0 -> 92
1 1 0 -> 93
0 0 1 -> 29
1 0 1 -> 30
0 1 1 -> 101
1 1 1 -> 95

83 0
0 0 0 -> 17
0 1 0 -> 42
0 1 1 -> 64

84 0
1 0 0 -> 70
1 1 0 -> 98

85 1
0 0 0 -> 54
1 0 0 -> 10
0 1 0 -> 100
1 1 0 -> 75
0 0 1 -> 68
1 0 1 -> 18
0 1 1 -> 73
1 1 1 -> 76

86 0
0 1 0 -> 55
0 0 1 -> 21
0 1 1 -> 44

87 0
0 0 0 -> 77
0 1 0 -> 68
0 0 1 -> 36
0 1 1 -> 37

88 0
0 0 0 -> 68
0 1 0 -> 73
0 0 1 -> 37
0 1 1 -> 58

89 0
1 0 1 -> 23
1 1 1 -> 102

90 0
0 0 0 -> 39
0 1 0 -> 59
0 1 1 -> 64

91 0
0 1 0 -> 64

92 0
1 0 0 -> 71

93 0
0 0 0 -> 72
0 1 0 -> 65
0 0 1 -> 89

94 0
0 0 0 -> 72
1 0 0 -> 90
0 1 0 -> 65
1 1 0 -> 6
0 0 1 -> 89
1 0 1 -> 103
1 1 1 -> 69

95 0
0 0 0 -> 91
0 1 0 -> 9
0 0 1 -> 104
0 1 1 -> 53

96 1
0 0 0 -> 54
0 1 0 -> 74
0 0 1 -> 68
0 1 1 -> 73

97 0
0 0 0 -> 10
0 1 0 -> 105
0 0 1 -> 54
1 0 1 -> 10
0 1 1 -> 74
1 1 1 -> 75

98 0
0 0 1 -> 84

99 0
0 0 0 -> 81
1 0 0 -> 19
0 1 0 -> 1
1 1 0 -> 2
0 0 1 -> 82
1 0 1 -> 90
0 1 1 -> 5
1 1 1 -> 6

100 1
0 0 0 -> 84
1 0 0 -> 96
1 1 0 -> 22
0 0 1 -> 85
1 0 1 -> 86
0 1 1 -> 24
1 1 1 -> 25

101 0
0 0 0 -> 82
1 0 0 -> 90
0 1 0 -> 5
1 1 0 -> 6
0 0 1 -> 89
1 0 1 -> 103
1 1 1 -> 69

102 0
0 0 0 -> 89

103 0
0 0 0 -> 63
0 1 0 -> 92
0 0 1 -> 29
0 1 1 -> 94

104 0
0 0 0 -> 29
1 0 0 -> 30
0 1 0 -> 94
1 1 0 -> 95
0 0 1 -> 30
0 1 1 -> 106
1 1 1 -> 107

105 0
0 0 0 -> 97
1 0 0 -> 19
0 1 0 -> 28
1 1 0 -> 2
0 0 1 -> 19
0 1 1 -> 2

106 0
0 0 0 -> 91
0 1 0 -> 9
0 0 1 -> 104
1 0 1 -> 91
0 1 1 -> 53
1 1 1 -> 9

107 1
