Miner
Every miner knows that the likelihood of stepping on a mine greatly depends on how skillfully they are placed.
The popular game "Minesweeper" is played on a rectangular grid consisting of w×h cells. Each cell either contains a mine or displays a number representing the count of mines in the eight surrounding cells (a number from 0 to 8).
Your task is to determine the minimum number of mines needed so that no cell is without a mine in it or in its neighboring cells.
Input
The first line of the input contains two integers w and h (1 ≤ w, h ≤ 1000), separated by a space, representing the width and height of the field, respectively.
Output
Output a single line with the minimum number of mines required so that each cell on the game field either contains a mine or has a number greater than zero.
The second example (a 5×5 field) is illustrated in the following image:
