VTRI - Triangles

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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 


hide comments
neha: 2011-07-08 10:36:40

i got result as 0..wat does dis mean?

martin richardt: 2010-02-07 08:43:38

how to interpret result?


Added by:Duc
Date:2008-04-19
Time limit:0.349s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:VNOI Marathon '08 - Round 1/DivA
Problem Setter: Ngô Minh Đức