Triples

Given a sequence of positive integers, you need to find the number of triples in that sequence. For this problem, (x, y, z) constructs a triple if and only if x + y = z. So, (1, 2, 3) is a triple, while (3, 4, 5) is not.

Input Specification

The input consists of several test cases. Each test case starts with a positive integer N (3 ≤ N ≤ 5000). The next few lines contain N positive integers. The input is terminated by EOF.

Output Specification

For each test case, print the number of triples in the sequence in a line by itself.

Sample Input

1. 6
2. 1 2 3 4 5 6
3. 6
4. 1 2 4 8 16 32
5. 3
6. 100000000 200000000 100000000
7. 5
8. 1 1 1 2 2

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Output for Sample Input

1. 6
2. 0
3. 1
4. 6

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