A9423 | Largest Submatrix 3

You are given matrix $a$ of size $n×m$ , its elements are integers. We will assume that the rows of the matrix are numbered from top to bottom from 1 to $n$ , the columns are numbered from left to right from 1 to $m$ . We will denote the element on the intersecting of the $i$ -th row and the $j$ -th column as $a_{ij}$ .

We'll call submatrix $i_{1},j_{1},i_{2},j_{2}$ $(1<=i_{1}<=i_{2}<=n; 1<=j_{1}<=j_{2}<=m)$ such elements $a_{ij}$ of the given matrix that $i_{1}<=i<=i_{2}$ AND $j_{1}<=j<=j_{2}$ . We'll call the area of the submatrix number $(i_{2}-i_{1}+1)·(j_{2}-j_{1}+1)$ . We'll call a submatrix inhomogeneous, if all its elements are distinct.

Find the largest (in area) inhomogenous submatrix of the given matrix.

The first line contains two integers $n$ , $m$ ( $1<=n,m<=400$ ) — the number of rows and columns of the matrix, correspondingly.

Each of the next $n$ lines contains $m$ integers $a_{ij}$ ( $1<=a_{ij}<=160000$ ) — the elements of the matrix.

Print a single integer — the area of the optimal inhomogenous submatrix.