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You are given a set S of integers between -30000 and 30000 (inclusive).

Find the total number of sixtuples (a, b, c, d, e, f) : a, b, c, d, e, f S, d ≠ 0 that satisfy:

(a * b + c) / d - e = f

Input

The first line contains integer n (1 ≤ n ≤ 100), the size of a set S. Elements of S are given in the second line. Given numbers will be distinct.

Output

Print the total number of plausible sixtuples.

Examples