Migrated from Lutece 386 Largest Submatrix of All 1’s

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Description

Given a $m$-by-$n$ $(0,1)$-matrix, of all its submatrixes of all $1$’s which is the largest? By largest we mean that the submatrix has the most elements.

Input

The input contains multiple test cases. Each test case begins with $m$ and $n$ ($1\leq m, n\leq 2000$) on line. Then come the elements of a $(0,1)$-matrix in row-major order on $m$ lines each with $n$ numbers. The input ends once EOF is met.

Output

For each test case, output one line containing the number of elements of the largest submatrix of all $1$’s. If the given matrix is of all $0$’s, output $0$.

Samples

2 2
0 0
0 0
4 4
0 0 0 0
0 1 1 0
0 1 1 0
0 0 0 0

0
4

Note

The data used in this problem is unofficial data prepared by pfctgeorge. So any mistake here does not imply mistake in the offcial judge data.

Resources

POJ Founder Monthly Contest – 2008.01.31