One day while going across the topic GCD Adi came across a very simple question.

You are given an array consisting of N integers.

You have to find the number of pairs in the array such that GCD(A[ i ],A[ j ])

INPUT

First line contains an integer N denoting the size of the array.

Next line contain N space separated integers dentoing the array.

OUTPUT

Find the number of pairs such that GCD(A[ i ],A[ j ])

CONSTRAINT

\(2 \leq N \leq 10^{5}\)

\(0 \leq A[i] \leq 10^{5}\)