Problem Statement

Koboshi has decided to prepare a mattress futon and a pillow on the coordinate plane and go to sleep.

The mattress futon is the rectangle $\{(x,y)\in\mathbb{R}^2\mid 0\le x\le A, 0\le y\le B\}$.

A pillow is a rectangle whose vertices are lattice points and whose sides are parallel to the $x$-axis or the $y$-axis.

How many pillows satisfy the following conditions?

• The area of the pillow is at least $1$ and at most $S$.
• The pillow is on the mattress futon (that is, the region represented by the pillow is a subset of the region represented by the mattress futon).

It can be proved that the answer is at most $9\times 10^{18}$ under the constraints of this problem.

Constraints

• $1\le A,B,S\le 5\times 10^5$
• All inputs are integers.

Input

$A$ $B$ $S$

Output

Output the answer.

Sample

Sample 1

Input

3 4 2

Output

29

Here is an example of a pillow satisfying the conditions. The blue rectangle represents the mattress futon, and the red rectangle represents the pillow.

1 1 100

1

100000 200000 300000

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