In geometry class, Vadim was given the task of drawing a triangle with an integer area S. There is only one problem: Vadim loves integers, so he does not intend to draw sides with non-integer lengths. How many different triangles can Vadim draw?

Two triangles are considered different if the sets of side lengths of these triangles are different.

The input consists of a single line containing one integer S — the given area of the triangle (1 ≤ S ≤ 10⁹).

Output the number of different triangles with the given area that have integer sides.

A triangle with integer sides 3, 4, and 5 has an area of 6. There are no more triangles with that area.