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EXAMPLE
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In case of n = 2.
| | b(1),b(2)
-----+--------------+----------
1 | [2, 2, 1, 1] | [0, 0]
2 | [2, 1, 2, 1] | [1, 1]
3 | [1, 2, 2, 1] | [2, 0]
4 | [1, 2, 1, 2] | [1, 1]
5 | [1, 1, 2, 2] | [0, 0]
In case of n = 3.
| | b(1),b(2),b(3)
-----+-----------------------------+---------------
1 | [3, 3, 3, 2, 2, 2, 1, 1, 1] | [0, 0, 0]
2 | [3, 3, 3, 2, 1, 2, 1, 2, 1] | [1, 1, 0]
3 | [3, 3, 3, 1, 2, 1, 2, 1, 2] | [1, 1, 0]
4 | [3, 3, 3, 1, 1, 1, 2, 2, 2] | [0, 0, 0]
5 | [3, 2, 1, 3, 2, 1, 3, 2, 1] | [2, 2, 2]
6 | [3, 1, 2, 3, 1, 2, 3, 1, 2] | [2, 2, 2]
7 | [1, 3, 3, 3, 1, 2, 2, 2, 1] | [3, 0, 0]
8 | [2, 3, 1, 2, 3, 1, 2, 3, 1] | [2, 2, 2]
9 | [1, 3, 2, 1, 3, 2, 1, 3, 2] | [2, 2, 2]
10 | [2, 1, 3, 2, 1, 3, 2, 1, 3] | [2, 2, 2]
11 | [1, 2, 3, 1, 2, 3, 1, 2, 3] | [2, 2, 2]
12 | [2, 2, 2, 3, 3, 3, 1, 1, 1] | [0, 0, 0]
13 | [1, 1, 1, 3, 3, 3, 2, 2, 2] | [0, 0, 0]
14 | [1, 2, 2, 2, 1, 3, 3, 3, 1] | [3, 0, 0]
15 | [2, 2, 2, 1, 1, 1, 3, 3, 3] | [0, 0, 0]
16 | [2, 1, 2, 1, 2, 1, 3, 3, 3] | [1, 1, 0]
17 | [1, 2, 1, 2, 1, 2, 3, 3, 3] | [1, 1, 0]
18 | [1, 1, 1, 2, 2, 2, 3, 3, 3] | [0, 0, 0]
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