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.

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