Mike likes to draw triangles, but he does it in an unusual way. First he draws an arbitrary triangle, then divides each side into n equal parts and draws through the partition points the lines parallel to sides of triangle. As a result he gets a number of triangles equal to each other. Help Mike to find the maximum number of identical triangles in his final picture.

Input

One integer n (0 < n < 2 * 109).

Output

The maximum number of triangles equal to each other.