Black-and-White Grid

Problem Description

Xiaoyang has a grid of $n$ rows and $m$ columns, where each cell is either white or black. For a sub-rectangle of the grid, Xiaoyang calls it balanced if it contains the same number of black cells as white cells. Xiaoyang wants to know: what is the maximum number of cells contained in a balanced sub-rectangle?

Input Format

The first line contains two positive integers $n$ and $m$, as described. The following $n$ lines each contain a string of length $m$ consisting of 0 and 1, representing the colors of the $i$-th row: 0 means white, 1 means black.

Output Format

Output one integer: the maximum number of cells in a balanced sub-rectangle. If no balanced sub-rectangle exists, output $0$.

Sample Input

4 5
00000
01111
00011
00011

Sample Output

16

Sample Explanation

In the sample, the largest balanced sub-rectangle occupies rows $1$ to $4$ and columns $2$ to $5$ (rows and columns are $1$-indexed). This sub-rectangle has $4 \times 4 = 16$ cells, of which $8$ are black and $8$ are white, so it is balanced. Thus the answer is $16$.

Constraints

For all test data, $1 \le n, m \le 10$.