Chocolate Bar

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}.

Constraints

• 2 ≤ H, W ≤ 10^5

Input

Input is given from Standard Input in the following format:

H W

Output

Print the minimum possible value of S_{max} - S_{min}.

Examples

Input

3 5

Output

0

Input

4 5

Output

2

Input

5 5

Output

4

Input

100000 2

Output

1

Input

100000 100000

Output

50000

inputFormat

Input

Input is given from Standard Input in the following format:

H W

outputFormat

Output

Print the minimum possible value of S_{max} - S_{min}.

Examples

Input

3 5

Output

0

Input

4 5

Output

2

Input

5 5

Output

4

Input

100000 2

Output

1

Input

100000 100000

Output

50000

样例

3 5

0