[요약] N (4 <= N <= 1,000)마리의 소들의 좌표 X,Y (-1,000,000,000 <= X , Y <= 1,000,000,000)가 주어졌을 때, 4마리의 소들을 잡고 180도로 돌렸을 때 기존에 있던 소들의 좌표와 동일한 집합의 수를 찾는 문제이다.

The cows wish to form into groups of four in order to play Bridge, their new favorite card game. Each group must satisfy an important constraint: four cows are allowed to team up if and only if there exists some point X somewhere in the plane (and not coincident with any of the four points of the potential group of four) such that rotating any of the group's cows 180 degrees about that point X gives the position of some other cow in the group.

Please help the cows determine the number of sets of four cows that can form a Bridge group.

By way of example, suppose eight cows are standing at eight points:

                  |
                 f*
                  |             a = (-3, 1)    e = (-1, 1)
           b*     |             b = (-2, 2)    f = ( 0, 3)
        a      e  |             c = (-3, 0)    g = ( 2, 0)
         *     *  |             d = (-2, 0)    h = ( 3, 0)
         c  d     |     g  h
---------*--*-----+-----*--*---------
                  |

The supplied locations of the cows given are all distinct, although they are supplied in no particular order. Furthermore, the answer will fit into a signed 32-bit integer.

입력

• * Line 1: A single integer: N
• * Lines 2..N+1: Line i+1 contains two space-separated integers: X_i and Y_i

출력

입출력 예

입력

8
-3 0
-2 0
-1 1
0 3
2 0
-3 1
3 0
-2 2

출력

3

출처:usaco 2011 MAR silver
요약: pl0892029