You are given N integers. Each integer is square free (i.e. it has no divisor which is a square number except 1) and all the prime factors are less than 50.
You have to find out the number of pairs these numbers such that their GCD is 1 or a prime number. Note that (i, j) and (j, i) are different pairs if i and j are different.
Input
The first line contains an integer T (1 ≤ T ≤ 10), the number of tests. Then T test cases follow.
The first line of each test cases contains an integer N (1 ≤ N ≤ 100000). The next line contains N integers.
Output
Print T lines. In each line print the required result.
Sample
| Input | Output |
|---|---|
1 3 2 1 6 | 8 |
In the sample case, the following pairs satisfy the criteria:
gcd(1,2) = 1
gcd(2,1) = 1
gcd(2,6) = 2, a prime number
gcd(6,2) = 2, a prime number
gcd(1,6) = 1
gcd(6,1) = 1
gcd(2,2) = 2, a prime number
gcd(1,1) = 1
This problem was authored for CodeMask Championship 2016 and is being hosted on Toph per organizer’s request.
