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B. Number of Triplets

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 *x*_{i}, *y*_{i} ( - 1000 ≤ *x*_{i}, *y*_{i} ≤ 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

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