CF1034B.Little C Loves 3 II

普及/提高-

通过率:0%

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题目描述

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×mn \times m . The cell in the xx -th row and in the yy -th column is called (x,y)(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 33 . The Manhattan distance between two cells (xi,yi)(x_i,y_i) and (xj,yj)(x_j,y_j) is defined as xixj+yiyj|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.

输入格式

A single line contains two integers nn and mm ( 1n,m1091 \leq n,m \leq 10^9 ) — the number of rows and the number of columns of the chessboard.

输出格式

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

输入输出样例

  • 输入#1

    2 2
    

    输出#1

    0
  • 输入#2

    3 3
    

    输出#2

    8

说明/提示

In the first example, the Manhattan distance between any two cells is smaller than 33 , so the answer is 00 .

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

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