Problem:
Score : 400 points

Problem Statement

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}.

Sample Input 1

3 5

Sample Output 1

0

In the division below, S_{max} - S_{min} = 5 - 5 = 0.

Sample Input 2

4 5

Sample Output 2

2

In the division below, S_{max} - S_{min} = 8 - 6 = 2.

Sample Input 3

5 5

Sample Output 3

4

In the division below, S_{max} - S_{min} = 10 - 6 = 4.

Sample Input 4

100000 2

Sample Output 4

1

Sample Input 5

100000 100000

Sample Output 5

50000

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

func max(a, b int) int {
	if a >= b {
		return a
	}
	return b
}
func abs(a int) int {
	if a >= 0 {
		return a
	}
	return -a
}
func min(a, b int) int {
	if a >= b {
		return b
	}
	return a
}

func main() {
	var h, w, ans int
	fmt.Scan(&h, &w)
	ans = h * w
	if (h*w)%3 != 0 {

        if h > w {
			h, w = w, h
		}

        for x := 1; x <= w; x++ {
			y1 := h / 2
			y2 := h - y1
			s1 := (w - x) * y1
			s2 := (w - x) * y2
			s3 := x * h
			smax := max(s1, max(s2, s3))
			smin := min(s1, min(s2, s3))
			ans = min(ans, smax-smin)
		}
	} else {
		ans = 0
	}
	fmt.Println(ans)
}