Pacific knights P27960

Given an $n \times m$ chess board, how many knights can we place on it so that no two knights threaten each other? For instance, we can place six knights on a $2 \times 5$ board:

Input

Input consists of several cases, each with $n$ and $m$, both between 1 and $10^4$.

Output

For every case, print the maximum number of knights that we can place on an $n \times m$ chess board without any threats.