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문제

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.

입력

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).

출력

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

제한

  • 0 ≤ A(i,j) ≤ 109
  • 1 ≤ N, M ≤ 103

예제 입력 1

2 3
2 4 3
5 7 5

예제 출력 1

2

힌트

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).