Interesting part of the solution is to see how the look up table is formed
0, 1, 2, 3 0 - 0, 1, 1, 2 -------- GROUP_A(0)
4 - 1, 2, 2, 3 -------- GROUP_A(1)16 - 1, 2, 2, 3 -------- GROUP_A(1)
20 - 2, 3, 3, 4 -------- GROUP_A(2)
8 - 1, 2, 2, 3 -------- GROUP_A(1)
12 - 2, 3, 3, 4 -------- GROUP_A(2)
24 - 2, 3, 3, 4 -------- GROUP_A(2)
28 - 3, 4, 4, 5 -------- GROUP_A(3) ... so on
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