There are n points in the plane, the ith of which is labeled Pi and has coordinates (xi,yi).
We know that the formula of Euclidean distance ( https://en.wikipedia.org/wiki/Euclidean_distance ) of two points which is denoted fun(P,Q) = ((p1 - q1)^2 + (p2 - q2)^2)^(1/2)
Now find how many ordered quadruples of pairwise-distinct indices (p,q,r,s) are there such that fun(p,q)+fun(r,s) is equal to fun(q,r) +fun(p,s) ?
Double precision should be 1e-6 (EPS = 1e-6)
Input
The first line of input contains a single integer (4<=n<=250).
The next n lines of input each contain two space-separated integers (0<=xi,yi<=16).
Output
Print a single integer: the number of ordered quadruples which is satisfied the condition.
Sample
| Input | Output |
|---|---|
4 3 0 0 4 7 3 4 7 | 8 |
Explanation:
The eight quadruples are
(0,1,3,2),
(0,2,3,1),
(1,0,2,3),
(1,3,2,0),
(2,0,1,3),
(2,3,1,0) ,
(3,1,0,2) ,
(3,2,0,1)
