Triangles

n points are given on the plane with integer coordinates. No three points lie on one line. Find k - the number of triangles with vertices in these points and integer area.

Input

The first line contains number n. Next n lines contain the pairs of integers - the points coordinates (x_i, y_i). It is known that 0 < n, |x_i|,|y_i| ≤ 5000. Output

The value of k.

Examples