有这样一个游戏：

There is an infinite grid and an m* n rectangle of stones on it (1 <= m,n <= 1000). The stones are located in the knots of the grid.

A following game for a single player is being played. One stone can jump over another along a vertical or a horizontal line. A stone which had been overjumped is taken away. The purpose of the game is to minimize number of stones on a grid.

现在要你做的是证明对于给定的m，n（m＜＝n)，则剩余的最少石头数a为

若m=1                  =>  a= (m+1)/2 的整数部分

若m或n为3的倍数 => a=2

其他情况              =>  a=1

（是URAL上的题，把问题改了，成为数学题）