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 i₁, j₁, i₂, j₂ (1 ≤ i₁ ≤ i₂ ≤ n; 1 ≤ j₁ ≤ j₂ ≤ m) such elements a_ij of the given matrix that i₁ ≤ i ≤ i₂ AND j₁ ≤ j ≤ j₂. We'll call the area of the submatrix number (i₂ - i₁ + 1)·(j₂ - j₁ + 1). We'll call a submatrix inhomogeneous, if all its elements are distinct.

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

Input

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.

Output

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

Largest Submatrix 3

Examples