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.

Given a pair of numbers m and n separated with one space in an input file 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.

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