There is an infinite grid and an M × N rectangle of stones on it (1 ≤ M, N ≤ 10000). 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.

Given a pair of numbers M and N separated with one space you are to write a program which should determine a minimal number of the stones left on the grid.

Numbers M and N separated by space.

The minimal number of the stones left on the grid.