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北京大学《ACM-ICPC竞赛训练》暑期课面向全球招生。容量有限,报名从速!
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Simple game on a grid
Time Limit: 1000MSMemory Limit: 65536K
Total Submissions: 959Accepted: 490

Description

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.

Input

Numbers m and n separated by space.

Output

The minimal number of the stones left on the grid.

Sample Input

3 4

Sample Output

2

Source

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