Two positive integers are said to be coprime if 1 is their only common divisor. Given a sequence of positive integers a₁, a₂, ..., a_n, find the number of pairs of its terms which are coprime.

입력 형식

The first line of input contains one integer n (1 ≤ n ≤ 1,000,000) denoting the length of the sequence. The second line contains n integers a_i (1 ≤ a_i ≤ 3,000,000).

출력 형식

Your program should output one integer representing the number of pairs (i, j) such that 1 ≤ i < j ≤ n and a_i is coprime with a_j.

예제 입력

5
3 6 4 7 3

예제 출력

6