You are given N (1 <= N <= 100000) integers. Each integer is square free (meaning 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 are there 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 tests follows. First line of each tests contain an integer N. The next line follows N integers.

Output

Print T lines. In each line print the required result.

Example

Input:
1
3
2 1 6

Output:
8

Explanation

• 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

So, total of 8 pairs.

Problem Setter: Nafis Sadique, Jahangirnagar University