CF1047D Little C Loves 3 II

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原题链接：http://codeforces.com/contest/1047/problem/D

Little C Loves 3 II

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 $(x_i,y_i)$ and $(x_j,y_j)$ is defined as $|x_i−x_j|+|y_i−y_j|$.

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 $m (1≤n,m≤10^9)$ — 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 $(1,1)(3,2), (1,2)(3,3), (2,1)(1,3), (3,1)(2,3)$.

题解

这位老哥找规律实在是太强辣，甘拜下风 $\%\%\%$。

代码

#include<bits/stdc++.h>
using namespace std;
int n,m,x[]={0,0,0,0,2,4};
void in(){scanf("%d%d",&n,&m);}
void ac()
{
	if(n>m)swap(n,m);
	if(n==1)printf("%d",m/6*6+x[m%6]);
	else if(n==2)
	{
		if(m==2)puts("0");
		else if(m==3)puts("4");
		else if(m==7)puts("12");
		else printf("%lld",1ll*n*m);
	}
	else printf("%lld",n%2&&m%2?1ll*n*m-1:1ll*n*m);
}
int main(){in();ac();}