Score : 400 points
There is a bar of chocolate with a height of H blocks and a width of W blocks. Snuke is dividing this bar into exactly three pieces. He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.
Snuke is trying to divide the bar as evenly as possible. More specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece. Find the minimum possible value of S_{max} - S_{min}.
Input is given from Standard Input in the following format:
H W
Print the minimum possible value of S_{max} - S_{min}.
3 5
0
In the division below, S_{max} - S_{min} = 5 - 5 = 0.
4 5
2
In the division below, S_{max} - S_{min} = 8 - 6 = 2.
5 5
4
In the division below, S_{max} - S_{min} = 10 - 6 = 4.
100000 2
1
100000 100000
50000