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