Points

On the plane are given N distinct points. Required to find many ways to choose three of them, so that the area of ​​a triangle with vertices at these points was an integer. We assume that three points on one line, form a triangle.

Input

The first line contains the number N (1 ≤ N ≤ 10000). Followed by N pairs of non-negative integers that define thethe coordinates of the the points . All coordinates does not exceed 1000.

Output

Bring out one number - the required number of triple points.

Examples