Number of Triplets

You are given n points on a plane. All points are different.

Find the number of different groups of three points (A, B, C) such that point B is the middle of segment AC.

The groups of three points are considered unordered, that is, if point B is the middle of segment AC, then groups (A, B, C) and (C, B, A) are considered the same.

Input

The first line contains a single integer n (3 ≤ n ≤ 3000) — the number of points.

Next n lines contain the points. The i-th line contains coordinates of the i-th point: two space-separated integers xi, yi ( - 1000 ≤ xi, yi ≤ 1000).

It is guaranteed that all given points are different.

Output

Print the single number — the answer to the problem.

Examples

Input

3 1 1 2 2 3 3

Output

1

Input

3 0 0 -1 0 0 1

Output

0

inputFormat

Input

The first line contains a single integer n (3 ≤ n ≤ 3000) — the number of points.

Next n lines contain the points. The i-th line contains coordinates of the i-th point: two space-separated integers xi, yi ( - 1000 ≤ xi, yi ≤ 1000).

It is guaranteed that all given points are different.

outputFormat

Output

Print the single number — the answer to the problem.

Examples

Input

3 1 1 2 2 3 3

Output

1

Input

3 0 0 -1 0 0 1

Output

0

样例

3
0 0
-1 0
0 1

0

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