A chessboard n×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≤n,m≤5000). The second line contains integer x (1≤x≤109).
Print how many squares will be painted exactly x times.
3 3
1
4
3 3
2
1
1 1
1
1