Flood Fill (Painting)

Problem Statement

JOI-kun is playing with a drawing software.

In the drawing software, you can draw pictures on a rectangular grid of H rows and W columns. Each cell has a color, represented by an integer between 1 and 10⁹ (inclusive).

The cell in the i-th row from the top (1 \leq i \leq H) and the j-th column from the left (1 \leq j \leq W) is called cell (i,j). Currently, the color of cell (i,j) is A_i,j.

The set of cells reachable from cell (i,j) by repeatedly moving to cells sharing an edge, without entering any cell with a color different from that of cell (i,j), is called the region of cell (i,j).

The drawing software has a feature called flood fill. When you specify a cell (x,y) (1 \leq x \leq H, 1 \leq y \leq W) and a color c (1 \leq c \leq 10⁹), the colors of all cells in the region of cell (x,y) change to c.

JOI-kun chooses a cell (x,y) and a color c, and uses the flood fill feature exactly once with that cell and color. JOI-kun's score is the number of cells in the region of cell (x,y) after using the flood fill.

Write a program to find the maximum possible value of JOI-kun's score.

Constraints

• 1 \leq H \leq 500.
• 1 \leq W \leq 500.
• 1 \leq A_i,j \leq 10⁹ (1 \leq i \leq H, 1 \leq j \leq W).
• All input values are integers.

Input

The input is given in the following format.
H W
A_1,1 A_1,2 ... A_1,W
A_2,1 A_2,2 ... A_2,W
:
A_H,1 A_H,2 ... A_H,W

Output

Output the maximum possible value of JOI-kun's score in one line.

Sample Input and Output

Sample Input 1

4 4
1 2 3 1
2 2 3 1
1 2 3 1
3 3 2 2

Sample Output 1

9

Initially, the region of cell (2,2) contains the 4 cells (1,2), (2,1), (2,2), (3,2). Therefore, if you use the flood fill feature with cell (2,2) and color 3, the colors of these 4 cells change to 3, as shown in the figure below.

After using the flood fill, the region of cell (2,2) contains the 9 cells (1,2), (1,3), (2,1), (2,2), (2,3), (3,2), (3,3), (4,1), (4,2). Thus, JOI-kun's score is 9.

It is not possible to achieve a score of 10 or higher, so output 9.

Sample Input 2

2 10
1 2 2 1 3 3 3 3 1 1
1 1 1 1 1 1 1 3 3 3

Sample Output 2

18

Sample Input 3

5 5
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1

Sample Output 3

25

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