Count Coprime Pairs

You are given several test cases. In each test case, you are given a collection of integers representing the magical power of gemstones. Your task is to count the number of unordered pairs \((i, j)\) such that \(0 \leq i < j < n\) and the greatest common divisor (gcd) of the two numbers is 1.

In mathematical terms, two numbers \(a\) and \(b\) are considered coprime if \(\gcd(a, b) = 1\). For each test case, print the total number of such coprime pairs.

inputFormat

The input is read from standard input (stdin) and has the following format:

• The first line contains a single integer \(T\) representing the number of test cases.
• For each test case:
  • The first line contains an integer \(n\), the number of gemstones.
  • The second line contains \(n\) space-separated integers, each representing the magical power of a gemstone.

outputFormat

For each test case, output a single line to standard output (stdout) containing the number of coprime pairs found in that test case.

## sample

1
3
2 3 4

2

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