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Ali-Amir wrote N numbers in a row. A row is called beautiful if any two of the neighbour numbers in the row have got the same amount of ones in binary or ternary notations.
Ali-Amir wants to count the number of ways the all given numbers can be written in a beautiful row.
The first line of input file contains integer N (2 ≤ N ≤ 20). The next line contains N non-negative integers not exceeding 109 each.
Output the number of ways the all given numbers can be placed in a beautiful row.
3 5 1 6
In the sample 5 = 123 and 1 = 13, 5 = 1012 and 6 = 1102, thus rows 1 5 6 and 6 5 1 are beautiful.