You are given a sequence of n distinct integers a1, a2, ..., an. Zero quintuple is any five numbers ai, aj, ak, ap, aq (i < j < k < p < q) which sum to zero (ai + aj + ak + ap + aq = 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 a1, a2, ..., an (-10000 ≤ ai ≤ 10000) - elements of the sequence.

Output

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