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 $A_j$.