Rectangles 2

In the $3 \times 2$ grid shown above, the rectangles whose vertices all lie on grid points and whose sides are vertical or horizontal are: six $1 \times 1$, four $2 \times 1$, three $1 \times 2$, two $2 \times 2$, two $3 \times 1$, and one $3 \times 2$, for a total of 18. A grid point is the intersection of a vertical line and a horizontal line.

You are given a grid of size $n \times m$. Count how many rectangles have all four vertices on grid points, have vertical or horizontal sides, and have perimeter at least $p$. A rectangle of size $w \times h$ has perimeter $2(w + h)$.

The first and only line of standard input contains three integers $n$, $m$, and $p$ separated by spaces ($1 \le n, m \le 5000$, $4 \le p \le 2(n + m)$). Here $n$ and $m$ are the dimensions of the grid, and $p$ is the lower bound on the rectangle perimeter.

On the first line of standard output, print a single integer: the number of rectangles in the $n \times m$ grid whose vertices lie on grid points, whose sides are vertical or horizontal, and whose perimeter is at least $p$.