Limak is a little polar bear, who isn't afraid of geometry. He has n 2-dimensional non-zero vectors \(\vec{a_1}, \vec{a_2}, \ldots, \vec{a_n}\), each described by two integers \(x_i, y_i\). Show him that you can count ways to choose an ordered triple of distinct indices \(i, j, k\) satisfying the two conditions:

• \(\vec{a_i}\) is perpendicular to \(\vec{a_j} + \vec{a_k}\)
• \(\vec{a_j}+\vec{a_k} \ne 0\)

If you don't know vectors (so you don't understand what is written above) then you can use the following three conditions, equivalent to those given above:

• For fixed \(i, j, k\) let \(A, B, S\) denote points \((x_i, y_i), (x_j + x_k, y_j + y_k), (0, 0)\) respectively.
• \(\measuredangle ASB = 90^{\circ}\)
• \(B \ne S\)

Input format

The first line contains one integer n — the number of vectors.

The i-th of next n lines contains two integers \(x_i, y_i\) — coordinates of \(\vec{a_i}\).

Some of n vectors may be equal to each other but none of them is equal to \(\vec{(0, 0)}\).

Output format

In one line print the number of ordered triples of distinct indices \(i, j, k\) satisfying the given conditions.

Constraints

• \(3 \le n \le 3000\)
• \(|x_i|, |y_i| \le 10^9\)

Subtasks