题目链接

Description

Little C loves number «3» very much. He loves all things about it.

Now he is playing a game on a chessboard of size n×m. The cell in the x-th row and in the y-th column is called (x,y). Initially, The chessboard is empty. Each time, he places two chessmen on two different empty cells, the Manhattan distance between which is exactly 3. The Manhattan distance between two cells (xi,yi) and (xj,yj) is defined as |xi−xj|+|yi−yj|.

He want to place as many chessmen as possible on the chessboard. Please help him find the maximum number of chessmen he can place.

Input

A single line contains two integers n and m (1≤n,m≤109) — the number of rows and the number of columns of the chessboard.

Output

Print one integer — the maximum number of chessmen Little C can place.

Examples

Input

2 2

Output

0

Input

3 3

Output

8

Note

In the first example, the Manhattan distance between any two cells is smaller than 3, so the answer is 0.

In the second example, a possible solution is (1,1)(3,2), (1,2)(3,3), (2,1)(1,3), (3,1)(2,3).

---

#include<cstdio>
#include<algorithm>
using namespace std;
int main()
{
	int n,m;
	scanf("%d%d",&n,&m);
	if(n>m)swap(n,m);
	if(n==1)printf("%d\n",m/6*6+2*max(m%6-3,0));
	else if(n==2)printf("%d\n",m==2?0:m==3?4:m==7?12:m*2);
	else printf("%lld\n",1ll*n*m/2*2);
	return 0;
}

总结

很巧妙的构造小的情况，再数学归纳法归纳出通解。拿到这题我也尝试画图找规律，找半天屁都没找出来。所以找规律也需要方法，先考虑很小的情况，再通过小情况推导出大范围的解。