A12007. 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 $n \times m$ . 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.

A single line contains two integers $n$ and $m$ ( $1 \leq n,m \leq 10^9$ ) — the number of rows and the number of columns of the chessboard.

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

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 $(1,1)(3,2)$ , $(1,2)(3,3)$ , $(2,1)(1,3)$ , $(3,1)(2,3)$ .