Given an array a of N numbers , you have to find the number of pair of indices i and j that satisfy the following relation:

  1. i < j
  2. ai > aj
  3. gcd( ai , aj )=1

Input
The first line of the input contains a single integer N - denoting the size of the array.
The next line contains N space separated integers denoting the array a.

Output
Output a single integer - the answer to the problem stated above.

Constraints
1<=N<=105
1<=ai<=105