Bishops on Black

We have a chessboard with dimensions M x N squares, where the bottom-left square is black. Determine the maximum number of bishops that can be placed on the black squares of this board such that no two bishops can attack each other. Remember, bishops attack each other if they are positioned on the same diagonal.

Input

The input consists of natural numbers 1 ≤ M, N ≤ 10^9.

Output

Provide the maximum number of bishops that can be placed under the given conditions.

Examples