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.

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) $ .