CF1034B.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.

小 C 非常喜欢数字「3」，他对一切与之相关的事物都情有独钟。

现在，他正在一个 $n \times m$ 的棋盘上玩游戏。第 $x$ 行第 $y$ 列的格子记为 $(x,y)$。初始时，棋盘为空。每次操作，他将两枚棋子放在两个不同的空格子上，且这两个格子之间的曼哈顿距离恰好为 $3$。两个格子 $(x_i,y_i)$ 与 $(x_j,y_j)$ 之间的曼哈顿距离定义为 $|x_i-x_j|+|y_i-y_j|$。

他希望在棋盘上放置尽可能多的棋子。请帮助他求出最多能放置多少枚棋子。

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.

一行包含两个整数 $n$ 和 $m$（$1 \leq n,m \leq 10^9$）—— 分别表示棋盘的行数和列数。

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

输出一个整数——小C最多能放置的棋子数量。

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

在第一个例子中，任意两个格子之间的曼哈顿距离均小于 $3$，因此答案为 $0$。

在第二个例子中，一种可能的解为 $(1,1)(3,2)$、$(1,2)(3,3)$、$(2,1)(1,3)$、$(3,1)(2,3)$。