Bit permutations by cycle type

Compare: Permutations by cycle type

The following table shows the bit permutations corresponding to the 5!=120 permutations of 5 elements ordered by cycle type.

There are  | 1  | ,  | 10  | ,  | 20  | ,  | 15  | ,  | 30  | ,  | 20  | ,  | 24  (row 5 of  A181897)  permutations of 5 elements

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with cycle type  | 0 | ,  | 1 (2) | ,  | 2 (3) | ,  | 3 (2+2) | ,  | 4 (4) | ,  | 5 (3+2) | ,  | 6 (5).

The violet numbers represent partitions by index numbers of  A194602 (compare this table).

The cycle type of the n-th finite permutation is shown in  A198380.

The bit permutations in natural order can be found here.

* 1 finite permutation with cycle type 0 (only fixed points) and corresponding bit permutation:

0    -->    0 1 2 3 4    -->    0  1  2  3    4  5  6  7    8  9 10 11   12 13 14 15     16 17 18 19   20 21 22 23   24 25 26 27   28 29 30 31

* 10 finite permutations with cycle type 1 (one 2-cycle) and corresponding bit permutations:

1    -->    1 0 2 3 4    -->    0  2  1  3    4  6  5  7    8 10  9 11   12 14 13 15     16 18 17 19   20 22 21 23   24 26 25 27   28 30 29 31
2    -->    0 2 1 3 4    -->    0  1  4  5    2  3  6  7    8  9 12 13   10 11 14 15     16 17 20 21   18 19 22 23   24 25 28 29   26 27 30 31
5    -->    2 1 0 3 4    -->    0  4  2  6    1  5  3  7    8 12 10 14    9 13 11 15     16 20 18 22   17 21 19 23   24 28 26 30   25 29 27 31
6    -->    0 1 3 2 4    -->    0  1  2  3    8  9 10 11    4  5  6  7   12 13 14 15     16 17 18 19   24 25 26 27   20 21 22 23   28 29 30 31
14    -->    0 3 2 1 4    -->    0  1  8  9    4  5 12 13    2  3 10 11    6  7 14 15     16 17 24 25   20 21 28 29   18 19 26 27   22 23 30 31
21    -->    3 1 2 0 4    -->    0  8  2 10    4 12  6 14    1  9  3 11    5 13  7 15     16 24 18 26   20 28 22 30   17 25 19 27   21 29 23 31
24    -->    0 1 2 4 3    -->    0  1  2  3    4  5  6  7   16 17 18 19   20 21 22 23      8  9 10 11   12 13 14 15   24 25 26 27   28 29 30 31
54    -->    0 1 4 3 2    -->    0  1  2  3   16 17 18 19    8  9 10 11   24 25 26 27      4  5  6  7   20 21 22 23   12 13 14 15   28 29 30 31
80    -->    0 4 2 3 1    -->    0  1 16 17    4  5 20 21    8  9 24 25   12 13 28 29      2  3 18 19    6  7 22 23   10 11 26 27   14 15 30 31
105    -->    4 1 2 3 0    -->    0 16  2 18    4 20  6 22    8 24 10 26   12 28 14 30      1 17  3 19    5 21  7 23    9 25 11 27   13 29 15 31

* 10 finite permutations with cycle type 2 (one 3-cycle) and corresponding bit permutations:

3    -->    2 0 1 3 4    -->    0  2  4  6    1  3  5  7    8 10 12 14    9 11 13 15     16 18 20 22   17 19 21 23   24 26 28 30   25 27 29 31
4    -->    1 2 0 3 4    -->    0  4  1  5    2  6  3  7    8 12  9 13   10 14 11 15     16 20 17 21   18 22 19 23   24 28 25 29   26 30 27 31
8    -->    0 3 1 2 4    -->    0  1  4  5    8  9 12 13    2  3  6  7   10 11 14 15     16 17 20 21   24 25 28 29   18 19 22 23   26 27 30 31
11    -->    3 1 0 2 4    -->    0  4  2  6    8 12 10 14    1  5  3  7    9 13 11 15     16 20 18 22   24 28 26 30   17 21 19 23   25 29 27 31
12    -->    0 2 3 1 4    -->    0  1  8  9    2  3 10 11    4  5 12 13    6  7 14 15     16 17 24 25   18 19 26 27   20 21 28 29   22 23 30 31
15    -->    3 0 2 1 4    -->    0  2  8 10    4  6 12 14    1  3  9 11    5  7 13 15     16 18 24 26   20 22 28 30   17 19 25 27   21 23 29 31
19    -->    2 1 3 0 4    -->    0  8  2 10    1  9  3 11    4 12  6 14    5 13  7 15     16 24 18 26   17 25 19 27   20 28 22 30   21 29 23 31
20    -->    1 3 2 0 4    -->    0  8  1  9    4 12  5 13    2 10  3 11    6 14  7 15     16 24 17 25   20 28 21 29   18 26 19 27   22 30 23 31
30    -->    0 1 4 2 3    -->    0  1  2  3    8  9 10 11   16 17 18 19   24 25 26 27      4  5  6  7   12 13 14 15   20 21 22 23   28 29 30 31
38    -->    0 4 2 1 3    -->    0  1  8  9    4  5 12 13   16 17 24 25   20 21 28 29      2  3 10 11    6  7 14 15   18 19 26 27   22 23 30 31
45    -->    4 1 2 0 3    -->    0  8  2 10    4 12  6 14   16 24 18 26   20 28 22 30      1  9  3 11    5 13  7 15   17 25 19 27   21 29 23 31
48    -->    0 1 3 4 2    -->    0  1  2  3   16 17 18 19    4  5  6  7   20 21 22 23      8  9 10 11   24 25 26 27   12 13 14 15   28 29 30 31
56    -->    0 4 1 3 2    -->    0  1  4  5   16 17 20 21    8  9 12 13   24 25 28 29      2  3  6  7   18 19 22 23   10 11 14 15   26 27 30 31
59    -->    4 1 0 3 2    -->    0  4  2  6   16 20 18 22    8 12 10 14   24 28 26 30      1  5  3  7   17 21 19 23    9 13 11 15   25 29 27 31
74    -->    0 3 2 4 1    -->    0  1 16 17    4  5 20 21    2  3 18 19    6  7 22 23      8  9 24 25   12 13 28 29   10 11 26 27   14 15 30 31
78    -->    0 2 4 3 1    -->    0  1 16 17    2  3 18 19    8  9 24 25   10 11 26 27      4  5 20 21    6  7 22 23   12 13 28 29   14 15 30 31
81    -->    4 0 2 3 1    -->    0  2 16 18    4  6 20 22    8 10 24 26   12 14 28 30      1  3 17 19    5  7 21 23    9 11 25 27   13 15 29 31
99    -->    3 1 2 4 0    -->    0 16  2 18    4 20  6 22    1 17  3 19    5 21  7 23      8 24 10 26   12 28 14 30    9 25 11 27   13 29 15 31
103    -->    2 1 4 3 0    -->    0 16  2 18    1 17  3 19    8 24 10 26    9 25 11 27      4 20  6 22    5 21  7 23   12 28 14 30   13 29 15 31
104    -->    1 4 2 3 0    -->    0 16  1 17    4 20  5 21    8 24  9 25   12 28 13 29      2 18  3 19    6 22  7 23   10 26 11 27   14 30 15 31

* 15 finite permutations with cycle type 3 (two 2-cycles) and corresponding bit permutations:

7    -->    1 0 3 2 4    -->    0  2  1  3    8 10  9 11    4  6  5  7   12 14 13 15     16 18 17 19   24 26 25 27   20 22 21 23   28 30 29 31
16    -->    2 3 0 1 4    -->    0  4  8 12    1  5  9 13    2  6 10 14    3  7 11 15     16 20 24 28   17 21 25 29   18 22 26 30   19 23 27 31
23    -->    3 2 1 0 4    -->    0  8  4 12    2 10  6 14    1  9  5 13    3 11  7 15     16 24 20 28   18 26 22 30   17 25 21 29   19 27 23 31
25    -->    1 0 2 4 3    -->    0  2  1  3    4  6  5  7   16 18 17 19   20 22 21 23      8 10  9 11   12 14 13 15   24 26 25 27   28 30 29 31
26    -->    0 2 1 4 3    -->    0  1  4  5    2  3  6  7   16 17 20 21   18 19 22 23      8  9 12 13   10 11 14 15   24 25 28 29   26 27 30 31
29    -->    2 1 0 4 3    -->    0  4  2  6    1  5  3  7   16 20 18 22   17 21 19 23      8 12 10 14    9 13 11 15   24 28 26 30   25 29 27 31
55    -->    1 0 4 3 2    -->    0  2  1  3   16 18 17 19    8 10  9 11   24 26 25 27      4  6  5  7   20 22 21 23   12 14 13 15   28 30 29 31
60    -->    0 3 4 1 2    -->    0  1  8  9   16 17 24 25    2  3 10 11   18 19 26 27      4  5 12 13   20 21 28 29    6  7 14 15   22 23 30 31
67    -->    3 1 4 0 2    -->    0  8  2 10   16 24 18 26    1  9  3 11   17 25 19 27      4 12  6 14   20 28 22 30    5 13  7 15   21 29 23 31
82    -->    2 4 0 3 1    -->    0  4 16 20    1  5 17 21    8 12 24 28    9 13 25 29      2  6 18 22    3  7 19 23   10 14 26 30   11 15 27 31
86    -->    0 4 3 2 1    -->    0  1 16 17    8  9 24 25    4  5 20 21   12 13 28 29      2  3 18 19   10 11 26 27    6  7 22 23   14 15 30 31
94    -->    3 4 2 0 1    -->    0  8 16 24    4 12 20 28    1  9 17 25    5 13 21 29      2 10 18 26    6 14 22 30    3 11 19 27    7 15 23 31
107    -->    4 2 1 3 0    -->    0 16  4 20    2 18  6 22    8 24 12 28   10 26 14 30      1 17  5 21    3 19  7 23    9 25 13 29   11 27 15 31
111    -->    4 1 3 2 0    -->    0 16  2 18    8 24 10 26    4 20  6 22   12 28 14 30      1 17  3 19    9 25 11 27    5 21  7 23   13 29 15 31
119    -->    4 3 2 1 0    -->    0 16  8 24    4 20 12 28    2 18 10 26    6 22 14 30      1 17  9 25    5 21 13 29    3 19 11 27    7 23 15 31

* 30 finite permutations with cycle type 4 (one 4-cycle) and corresponding bit permutations:

9    -->    3 0 1 2 4    -->    0  2  4  6    8 10 12 14    1  3  5  7    9 11 13 15     16 18 20 22   24 26 28 30   17 19 21 23   25 27 29 31
10    -->    1 3 0 2 4    -->    0  4  1  5    8 12  9 13    2  6  3  7   10 14 11 15     16 20 17 21   24 28 25 29   18 22 19 23   26 30 27 31
13    -->    2 0 3 1 4    -->    0  2  8 10    1  3  9 11    4  6 12 14    5  7 13 15     16 18 24 26   17 19 25 27   20 22 28 30   21 23 29 31
17    -->    3 2 0 1 4    -->    0  4  8 12    2  6 10 14    1  5  9 13    3  7 11 15     16 20 24 28   18 22 26 30   17 21 25 29   19 23 27 31
18    -->    1 2 3 0 4    -->    0  8  1  9    2 10  3 11    4 12  5 13    6 14  7 15     16 24 17 25   18 26 19 27   20 28 21 29   22 30 23 31
22    -->    2 3 1 0 4    -->    0  8  4 12    1  9  5 13    2 10  6 14    3 11  7 15     16 24 20 28   17 25 21 29   18 26 22 30   19 27 23 31
32    -->    0 4 1 2 3    -->    0  1  4  5    8  9 12 13   16 17 20 21   24 25 28 29      2  3  6  7   10 11 14 15   18 19 22 23   26 27 30 31
35    -->    4 1 0 2 3    -->    0  4  2  6    8 12 10 14   16 20 18 22   24 28 26 30      1  5  3  7    9 13 11 15   17 21 19 23   25 29 27 31
36    -->    0 2 4 1 3    -->    0  1  8  9    2  3 10 11   16 17 24 25   18 19 26 27      4  5 12 13    6  7 14 15   20 21 28 29   22 23 30 31
39    -->    4 0 2 1 3    -->    0  2  8 10    4  6 12 14   16 18 24 26   20 22 28 30      1  3  9 11    5  7 13 15   17 19 25 27   21 23 29 31
43    -->    2 1 4 0 3    -->    0  8  2 10    1  9  3 11   16 24 18 26   17 25 19 27      4 12  6 14    5 13  7 15   20 28 22 30   21 29 23 31
44    -->    1 4 2 0 3    -->    0  8  1  9    4 12  5 13   16 24 17 25   20 28 21 29      2 10  3 11    6 14  7 15   18 26 19 27   22 30 23 31
50    -->    0 3 1 4 2    -->    0  1  4  5   16 17 20 21    2  3  6  7   18 19 22 23      8  9 12 13   24 25 28 29   10 11 14 15   26 27 30 31
53    -->    3 1 0 4 2    -->    0  4  2  6   16 20 18 22    1  5  3  7   17 21 19 23      8 12 10 14   24 28 26 30    9 13 11 15   25 29 27 31
57    -->    4 0 1 3 2    -->    0  2  4  6   16 18 20 22    8 10 12 14   24 26 28 30      1  3  5  7   17 19 21 23    9 11 13 15   25 27 29 31
58    -->    1 4 0 3 2    -->    0  4  1  5   16 20 17 21    8 12  9 13   24 28 25 29      2  6  3  7   18 22 19 23   10 14 11 15   26 30 27 31
62    -->    0 4 3 1 2    -->    0  1  8  9   16 17 24 25    4  5 12 13   20 21 28 29      2  3 10 11   18 19 26 27    6  7 14 15   22 23 30 31
69    -->    4 1 3 0 2    -->    0  8  2 10   16 24 18 26    4 12  6 14   20 28 22 30      1  9  3 11   17 25 19 27    5 13  7 15   21 29 23 31
72    -->    0 2 3 4 1    -->    0  1 16 17    2  3 18 19    4  5 20 21    6  7 22 23      8  9 24 25   10 11 26 27   12 13 28 29   14 15 30 31
75    -->    3 0 2 4 1    -->    0  2 16 18    4  6 20 22    1  3 17 19    5  7 21 23      8 10 24 26   12 14 28 30    9 11 25 27   13 15 29 31
79    -->    2 0 4 3 1    -->    0  2 16 18    1  3 17 19    8 10 24 26    9 11 25 27      4  6 20 22    5  7 21 23   12 14 28 30   13 15 29 31
83    -->    4 2 0 3 1    -->    0  4 16 20    2  6 18 22    8 12 24 28   10 14 26 30      1  5 17 21    3  7 19 23    9 13 25 29   11 15 27 31
84    -->    0 3 4 2 1    -->    0  1 16 17    8  9 24 25    2  3 18 19   10 11 26 27      4  5 20 21   12 13 28 29    6  7 22 23   14 15 30 31
95    -->    4 3 2 0 1    -->    0  8 16 24    4 12 20 28    2 10 18 26    6 14 22 30      1  9 17 25    5 13 21 29    3 11 19 27    7 15 23 31
97    -->    2 1 3 4 0    -->    0 16  2 18    1 17  3 19    4 20  6 22    5 21  7 23      8 24 10 26    9 25 11 27   12 28 14 30   13 29 15 31
98    -->    1 3 2 4 0    -->    0 16  1 17    4 20  5 21    2 18  3 19    6 22  7 23      8 24  9 25   12 28 13 29   10 26 11 27   14 30 15 31
102    -->    1 2 4 3 0    -->    0 16  1 17    2 18  3 19    8 24  9 25   10 26 11 27      4 20  5 21    6 22  7 23   12 28 13 29   14 30 15 31
106    -->    2 4 1 3 0    -->    0 16  4 20    1 17  5 21    8 24 12 28    9 25 13 29      2 18  6 22    3 19  7 23   10 26 14 30   11 27 15 31
109    -->    3 1 4 2 0    -->    0 16  2 18    8 24 10 26    1 17  3 19    9 25 11 27      4 20  6 22   12 28 14 30    5 21  7 23   13 29 15 31
118    -->    3 4 2 1 0    -->    0 16  8 24    4 20 12 28    1 17  9 25    5 21 13 29      2 18 10 26    6 22 14 30    3 19 11 27    7 23 15 31

* 20 finite permutations with cycle type 5 (one 3-cycle and one 2-cycle) and corresponding bit permutations:

27    -->    2 0 1 4 3    -->    0  2  4  6    1  3  5  7   16 18 20 22   17 19 21 23      8 10 12 14    9 11 13 15   24 26 28 30   25 27 29 31
28    -->    1 2 0 4 3    -->    0  4  1  5    2  6  3  7   16 20 17 21   18 22 19 23      8 12  9 13   10 14 11 15   24 28 25 29   26 30 27 31
31    -->    1 0 4 2 3    -->    0  2  1  3    8 10  9 11   16 18 17 19   24 26 25 27      4  6  5  7   12 14 13 15   20 22 21 23   28 30 29 31
40    -->    2 4 0 1 3    -->    0  4  8 12    1  5  9 13   16 20 24 28   17 21 25 29      2  6 10 14    3  7 11 15   18 22 26 30   19 23 27 31
47    -->    4 2 1 0 3    -->    0  8  4 12    2 10  6 14   16 24 20 28   18 26 22 30      1  9  5 13    3 11  7 15   17 25 21 29   19 27 23 31
49    -->    1 0 3 4 2    -->    0  2  1  3   16 18 17 19    4  6  5  7   20 22 21 23      8 10  9 11   24 26 25 27   12 14 13 15   28 30 29 31
61    -->    3 0 4 1 2    -->    0  2  8 10   16 18 24 26    1  3  9 11   17 19 25 27      4  6 12 14   20 22 28 30    5  7 13 15   21 23 29 31
65    -->    4 3 0 1 2    -->    0  4  8 12   16 20 24 28    2  6 10 14   18 22 26 30      1  5  9 13   17 21 25 29    3  7 11 15   19 23 27 31
66    -->    1 3 4 0 2    -->    0  8  1  9   16 24 17 25    2 10  3 11   18 26 19 27      4 12  5 13   20 28 21 29    6 14  7 15   22 30 23 31
70    -->    3 4 1 0 2    -->    0  8  4 12   16 24 20 28    1  9  5 13   17 25 21 29      2 10  6 14   18 26 22 30    3 11  7 15   19 27 23 31
76    -->    2 3 0 4 1    -->    0  4 16 20    1  5 17 21    2  6 18 22    3  7 19 23      8 12 24 28    9 13 25 29   10 14 26 30   11 15 27 31
87    -->    4 0 3 2 1    -->    0  2 16 18    8 10 24 26    4  6 20 22   12 14 28 30      1  3 17 19    9 11 25 27    5  7 21 23   13 15 29 31
88    -->    3 4 0 2 1    -->    0  4 16 20    8 12 24 28    1  5 17 21    9 13 25 29      2  6 18 22   10 14 26 30    3  7 19 23   11 15 27 31
91    -->    3 2 4 0 1    -->    0  8 16 24    2 10 18 26    1  9 17 25    3 11 19 27      4 12 20 28    6 14 22 30    5 13 21 29    7 15 23 31
92    -->    2 4 3 0 1    -->    0  8 16 24    1  9 17 25    4 12 20 28    5 13 21 29      2 10 18 26    3 11 19 27    6 14 22 30    7 15 23 31
101    -->    3 2 1 4 0    -->    0 16  4 20    2 18  6 22    1 17  5 21    3 19  7 23      8 24 12 28   10 26 14 30    9 25 13 29   11 27 15 31
110    -->    1 4 3 2 0    -->    0 16  1 17    8 24  9 25    4 20  5 21   12 28 13 29      2 18  3 19   10 26 11 27    6 22  7 23   14 30 15 31
113    -->    4 3 1 2 0    -->    0 16  4 20    8 24 12 28    2 18  6 22   10 26 14 30      1 17  5 21    9 25 13 29    3 19  7 23   11 27 15 31
114    -->    2 3 4 1 0    -->    0 16  8 24    1 17  9 25    2 18 10 26    3 19 11 27      4 20 12 28    5 21 13 29    6 22 14 30    7 23 15 31
117    -->    4 2 3 1 0    -->    0 16  8 24    2 18 10 26    4 20 12 28    6 22 14 30      1 17  9 25    3 19 11 27    5 21 13 29    7 23 15 31

* 24 finite permutations with cycle type 6 (one 5-cycle) and corresponding bit permutations:

33    -->    4 0 1 2 3    -->    0  2  4  6    8 10 12 14   16 18 20 22   24 26 28 30      1  3  5  7    9 11 13 15   17 19 21 23   25 27 29 31
34    -->    1 4 0 2 3    -->    0  4  1  5    8 12  9 13   16 20 17 21   24 28 25 29      2  6  3  7   10 14 11 15   18 22 19 23   26 30 27 31
37    -->    2 0 4 1 3    -->    0  2  8 10    1  3  9 11   16 18 24 26   17 19 25 27      4  6 12 14    5  7 13 15   20 22 28 30   21 23 29 31
41    -->    4 2 0 1 3    -->    0  4  8 12    2  6 10 14   16 20 24 28   18 22 26 30      1  5  9 13    3  7 11 15   17 21 25 29   19 23 27 31
42    -->    1 2 4 0 3    -->    0  8  1  9    2 10  3 11   16 24 17 25   18 26 19 27      4 12  5 13    6 14  7 15   20 28 21 29   22 30 23 31
46    -->    2 4 1 0 3    -->    0  8  4 12    1  9  5 13   16 24 20 28   17 25 21 29      2 10  6 14    3 11  7 15   18 26 22 30   19 27 23 31
51    -->    3 0 1 4 2    -->    0  2  4  6   16 18 20 22    1  3  5  7   17 19 21 23      8 10 12 14   24 26 28 30    9 11 13 15   25 27 29 31
52    -->    1 3 0 4 2    -->    0  4  1  5   16 20 17 21    2  6  3  7   18 22 19 23      8 12  9 13   24 28 25 29   10 14 11 15   26 30 27 31
63    -->    4 0 3 1 2    -->    0  2  8 10   16 18 24 26    4  6 12 14   20 22 28 30      1  3  9 11   17 19 25 27    5  7 13 15   21 23 29 31
64    -->    3 4 0 1 2    -->    0  4  8 12   16 20 24 28    1  5  9 13   17 21 25 29      2  6 10 14   18 22 26 30    3  7 11 15   19 23 27 31
68    -->    1 4 3 0 2    -->    0  8  1  9   16 24 17 25    4 12  5 13   20 28 21 29      2 10  3 11   18 26 19 27    6 14  7 15   22 30 23 31
71    -->    4 3 1 0 2    -->    0  8  4 12   16 24 20 28    2 10  6 14   18 26 22 30      1  9  5 13   17 25 21 29    3 11  7 15   19 27 23 31
73    -->    2 0 3 4 1    -->    0  2 16 18    1  3 17 19    4  6 20 22    5  7 21 23      8 10 24 26    9 11 25 27   12 14 28 30   13 15 29 31
77    -->    3 2 0 4 1    -->    0  4 16 20    2  6 18 22    1  5 17 21    3  7 19 23      8 12 24 28   10 14 26 30    9 13 25 29   11 15 27 31
85    -->    3 0 4 2 1    -->    0  2 16 18    8 10 24 26    1  3 17 19    9 11 25 27      4  6 20 22   12 14 28 30    5  7 21 23   13 15 29 31
89    -->    4 3 0 2 1    -->    0  4 16 20    8 12 24 28    2  6 18 22   10 14 26 30      1  5 17 21    9 13 25 29    3  7 19 23   11 15 27 31
90    -->    2 3 4 0 1    -->    0  8 16 24    1  9 17 25    2 10 18 26    3 11 19 27      4 12 20 28    5 13 21 29    6 14 22 30    7 15 23 31
93    -->    4 2 3 0 1    -->    0  8 16 24    2 10 18 26    4 12 20 28    6 14 22 30      1  9 17 25    3 11 19 27    5 13 21 29    7 15 23 31
96    -->    1 2 3 4 0    -->    0 16  1 17    2 18  3 19    4 20  5 21    6 22  7 23      8 24  9 25   10 26 11 27   12 28 13 29   14 30 15 31
100    -->    2 3 1 4 0    -->    0 16  4 20    1 17  5 21    2 18  6 22    3 19  7 23      8 24 12 28    9 25 13 29   10 26 14 30   11 27 15 31
108    -->    1 3 4 2 0    -->    0 16  1 17    8 24  9 25    2 18  3 19   10 26 11 27      4 20  5 21   12 28 13 29    6 22  7 23   14 30 15 31
112    -->    3 4 1 2 0    -->    0 16  4 20    8 24 12 28    1 17  5 21    9 25 13 29      2 18  6 22   10 26 14 30    3 19  7 23   11 27 15 31
115    -->    3 2 4 1 0    -->    0 16  8 24    2 18 10 26    1 17  9 25    3 19 11 27      4 20 12 28    6 22 14 30    5 21 13 29    7 23 15 31
116    -->    2 4 3 1 0    -->    0 16  8 24    1 17  9 25    4 20 12 28    5 21 13 29      2 18 10 26    3 19 11 27    6 22 14 30    7 23 15 31