After fiddling with numbers for too long, Mr. DeMello has decided to work with spooky arrays! However, he is not very good with them; he has had a question on his mind for a while but cannot solve it, so he asks you for help:

Given an array, find the number of valid solutions for ~A_i + A_j + A_k = A_l~, where ~(i, j, k, l)~ are strictly increasing ~(i < j < k < l)~.

Can you help him?

Constraints

For all subtasks:

~1 \le A_i \le 100~

Subtask 1 [10%]

~1 \le N \le 100~

Subtask 2 [20%]

~1 \le N \le 600~

Subtask 3 [70%]

~1 \le N \le 100\,000~

Input Specification

The first line will contain ~N~, the number of array elements.

The second line will contain ~N~ space-separated integers, ~A_i~, the elements of the array.

Output Specification

Output the number of valid solutions to the given equation ~(A_i + A_j + A_k = A_l)~.

Sample Input

8
1 1 2 3 1 1 2 3

Sample Output

4

Explanation for Sample Output

The valid solutions are ~(i = 1, j = 2, k = 5, l = 8)~, ~(i = 1, j = 2, k = 6, l = 8)~, ~(i = 1, j = 5, k = 6, l = 8)~, ~(i = 2, j = 5, k = 6, l = 8)~.

Note that the indices are 1-indexed.