There are \(n\) points in the plane, the \(i^{th}\) of which is labeled \(A_i\) and has coordinates \((x_i, y_i)\). How many ordered quadruples of pairwise-distinct indices \((p,q,r,s)\) are there such that \(A_p A_q + A_r A_s = A_q A_r + A_p A_s\)? 

Input Format :

The first line of input contains a single integer \(n\).

The next \(n\) lines of input each contain two space-separated integers \(x_i\) and \(y_i\).

Output Format :

Print a single integer: the number of ordered quadruples satisfying the above condition.

Constraints :

\(4 \le n \le 250\)

\(0 \le x_i, y_i \le 16\)

Note :

\(A_i A_j\) is the euclidean distance between points \(A_i\) and \(A_j\).