Triple

Given many different integers, find out the number of triples (a, b, c) which satisfy a, b, c are co-primed each other or are not co-primed each other. In a triple, (a, b, c) and (b, a, c) are considered as same triple.

The first line contains a single integer T (T <= 15), indicating the number of test cases.
In each case, the first line contains one integer n (3 <= n <= 800), second line contains n different integers d (2 <= d < 10⁵) separated with space.

For each test case, output an integer in one line, indicating the number of triples.

1
6
2 3 5 7 11 13

20

2011 Multi-University Training Contest 7 - Host by ECNU