In the plane, given a rectangular grid with sides parallel to the axes of coordinates. The coordinates of the bottom-left corner is (0, 0) and the top-right corner is (X, Y).

Your task is to count the number of triangles with integer coordinates lying inside the given grid and having areas equal to an integer S.

Input

A single line consisting of three integers: X, Y, S (1 ≤ X, Y ≤ 30, 1 ≤ S ≤ X*Y/2).

Output

A single integer: the number of triangles with integer coordinates lying inside the rectanglular grid and having areas equal to S.

Constraint

There are 50% of the test cases, corresponding to 50% of the grades, in which 1≤X, Y≤10.

Example

Input
2 1 1	

Output
6