Troop Deployment

Problem Description

As a general, you naturally need to deploy your troops sensibly. The map can be viewed as an $n \times m$ grid; a cell suitable for deploying troops is marked 1, and an unsuitable cell is marked 0. Now you must choose a rectangular region on the map to deploy troops, and this rectangle must not contain any unsuitable cell. What is the maximum number of cells such a rectangle can contain?

Input Format

The first line contains two positive integers $n$ and $m$, the numbers of rows and columns of the map grid. The following $n$ lines each contain $m$ integers $a_{i,1}, a_{i,2}, \ldots, a_{i,m}$, indicating whether each cell is suitable for deploying troops.

Output Format

One line: one integer, the maximum number of cells in a troop-deployment rectangle.

Sample Input

Sample Input 1

4 3
0 1 1
1 0 1
0 1 1
1 1 1

Sample Input 2

3 5
1 0 1 0 1
0 1 0 1 0
0 1 1 1 0

Sample Output

Sample Output 1

4

Sample Output 2

3

Sample Explanation

For sample 1, the map is:

0 1 1
1 0 1
0 1 1
1 1 1

You can choose the rectangle from row $3$ to row $4$ and column $2$ to column $3$. All cells in it are 1, and its area is $2 \times 2 = 4$. So the maximum is $4$ cells.

Constraints

For all test points, $1 \le n, m \le 12$, $0 \le a_{i,j} \le 1$.