Triple#12434

Triple

1 second
128 megabytes
Medium

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.

Input

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.

Output

Print one integer — the number of required triples.

Examples

Example 1

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