You are given an array of length consisting of positive integers.
Find the number of triples of indices (i, j, k) such that i \ne j, i \ne k, j \ne k, and the equality a_i \cdot a_j = a_k^2 holds.
The first line contains one integer n~(3 \le n \le 10^5). The second line contains positive integers a_1, a_2, \ldots, a_n (1 \le a_i \le 3 \cdot 10^5). It is guaranteed that all elements of the array are distinct.
Print one integer — the number of required triples.
Example 1