Zero quintuples

You are given a sequence of n distinct integers a[1], a[2], ..., a[n]. Zero quintuple is any five numbers a[i], a[j], a[k], a[p], a[q] (i < j < k < p < q) which sum to zero (a[i] + a[j] + a[k] + a[p] + a[q] = 0). Find the number of distinct zero quintuples from the given sequence.

Input

The first line contains n (5 ≤ n ≤ 2000) - number of elements in a sequence. The next line contains n distinct integers a[1], a[2], ..., a[n] (-10000 ≤ a[i] ≤ 10000) - elements of the sequence.

Output

Print one integer - the number of zero quintuples in a given sequence.

Examples