A chessboard n \times m in size is given. During the zero minute we repaint all the black squares to the 0 color. During the i-th minute we repaint to the i color the initially black squares that have exactly four corner-adjacent squares painted i-1 (all such squares are repainted simultaneously). This process continues ad infinitum. You have to figure out how many squares we repainted exactly x times.

The upper left square of the board has to be assumed to be always black. Two squares are called corner-adjacent, if they have exactly one common point.

The first line contains integers n and m (1 \le n,m \le 5000). The second line contains integer x (1 \le x \le 109).

Print how many squares will be painted exactly x times.