Best Pile

There is a \(n*m\) grid with square cells. There are blocks with a sqaure base and an arbitrary integer height \(h\) on some cells.

Pile of blocks is a set of blocks in which, every block shares a grid cell wall with at least one other block of the set. Therefore, each block must be a part of only one pile.

Output the open surface area of the pile with the highest open surface area.

Notes:

• A part of a surface is considered hidden if it’s covered by another block.
• Underside of a block is considered hidden
• Consider the width of a cell as 1 unit and height is also given in this unit

subtasks:

• each pile fills only 1 cell - 5 pts
• there is only one pile in the whole grid - 45 pts
• No extra constraints - 50 pts

Input Format

first line contains two integers \(n\) and \(m\) each of next \(n\) lines contains \(m\) integers, height \(h\) of the block in that cell. (0 if the cell is empty)

Output Format

single integer - maximum found surface area

Constraints

\[n<10^2\] \[m<10^2\] \[h<10^6\]