C. Coffee Break
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

The members of MaratonUSP were invited by the god Zeos to visit Mount Olympus. May, knowing about the legendary banquets that take place there, quickly agreed.

After a long stroll through the fields of Caieffes, the MaratonUSP members were invited to a banquet. However, to the surprise of almost everyone, the banquet consisted only of cheese balls and coxinhas! Secretly, Thilio, the finicky one, told the gods that this was the only food that MaratonUSP members liked, so he wouldn't have to deal with any ancient Greek food.

May was revolted because she hates coxinhas. The gods served the snacks on a table, organized in $$$n$$$ rows and $$$m$$$ columns. Since May still wants to visit more places before returning to IME, she doesn't have time to feast with her colleagues. She decided to go to the snack table and take all the snacks from a rectangular subsection of the table at once. To make it easier, she will select a rectangular subsection of the table (that is, a contiguous subset of rows and columns) and take all the snacks from this subsection. The following image shows some valid choices for the third test case.

Help May discover the maximum number of cheese balls she can take in this way without taking any coxinhas.

Input

The first line contains two positive integers $$$n$$$ and $$$m$$$ separated by a space, the dimensions of the snack table. It is guaranteed that $$$n \times m \leq 400$$$.

The following $$$n$$$ lines contain $$$m$$$ numbers $$$a_{i, j} \in \{0, 1\}$$$ separated by spaces. If $$$a_{i, j} = 0$$$, it indicates that the snack in row $$$i$$$ and column $$$j$$$ is a coxinha. If $$$a_{i, j} = 1$$$, it's a cheese ball.

Output

An integer, the maximum number of cheese balls that May can take.

Examples
Input
2 2
1 1
1 1
Output
4
Input
4 4
1 1 0 1
1 1 1 1
1 0 1 0
1 1 1 1
Output
4
Input
3 3
1 0 1
0 1 1
0 1 1
Output
4
Note

For the first example, May can select columns 1-2 and rows 1-2.

For the second example, May has several options:

  • Rows 1-2 and columns 1-2;
  • Row 1 and columns 1-4;
  • Row 4 and columns 1-4;
  • Rows 1-4 and column 1.