Tile Filling 4

Find the maximum number of 2x1 and 1x2 dominoes that fit on an N by M wall without overlap.

Easy3MathGreedyImplementationNo attempts yetTime limit0.1sMemory limit512 MB

Description

Examples4

Problem

You want to fill an N×M wall with tiles of size 2×1 and 1×2. No two tiles may overlap, and no tile may stick out of the wall. Find the largest number of tiles you can place.

Input

The first line contains N and M. (1 ≤ N, M ≤ 1,000,000,000)

Output

Print the maximum number of tiles that can be placed on the first line.