For a matrix, let’s call a subset of cells, S, connected if there is a path between any two cells of S which consists only of cells from S. A path is a sequence of cells u1, u2, ..., uk where ui and ui+1 are adjacent for any i=1,k-1

Given a matrix A with N rows and M columns, we define the following formula for a connected subset S of A: weight(S) = (max{A(s)|s∈S} - min{A(s)|s∈S} - |S|). where |*| represents the cardinality of a set and A(s) represents the value of the cell s in A.

Input

The first line of input contains two number N and M representing the dimensions of the matrix A.

The following N lines describe the matrix. The i-th line contains M integers where the j-th value represents A(i,j).

Output

Print the maximum value of weight(S) between all connected components S of the given matrix.

General constraints

0 ≤ A(i,j) ≤ 1091 ≤ N , M ≤ 103

Subtasks

• For 15 points: 1 ≤ N*M ≤ 20
• For other 15 points: N = 1
• For other 30 points: N,M ≤ 20

Explanation

One of the optimal connected subsets is {(1,1),(1,2),(2,2)}. {(1,1),(2,2)} is not a solution because there is no path between (1,1) and (2,2).