402921: GYM100947 I What a Mess

Alex is a very clever boy, after all he is the son of the greatest watchmaker in Odin.

One day, Alex was playing with some old watches and he found n gears, each gear has a_i teeth in it. Alex likes to make beautiful pairs of gears, he thinks a pair of gears is beautiful if we attach the two gears together and spin the first gear exactly one rotation, then the other gear spins an integer number of rotations. For example a pair of 8 and 4 is beautiful, whereas a pair of 8 and 5 isn't, neither is pair of 4 and 8.

Now Alex is curious, he wants to know how many beautiful pairs are there. Counting is not Alex's thing, so he asked you to help him.

The first line of input contains one integer T: The number of test cases you need to process.

Each test case consists of two lines. The first line is a single integer n: the number of gears Alex has. The second line contains n space separated integers a_i: the number if teeth in the i^th gear.

1 ≤ n ≤ 10⁴

2 ≤ a_i ≤ 10⁶

For each testcase print a single integer: the number of distinct pairs that satisfy the problem statement.

2
5
4 6 7 8 12
6
2 2 2 3 3 4

3
7

note that we consider two pair distinct when they differ by at least one gear.

In the first sample the pairs are: (4,8) , (4,12) , (6,12)