Laboratory

A virus that is lethal to humans leaked inside a laboratory. The virus has not spread yet, so you are going to build walls in the laboratory to stop it.

The laboratory is an $N \times M$ rectangle divided into squares of size $1 \times 1$. Every square is either an empty cell or a wall, and a wall fills one whole cell.

Some cells hold the virus. The virus spreads to every empty cell next to it, up, down, left, or right. You can build 3 new walls, and you must build all 3 of them.

For example, take a laboratory that looks like this.

2 0 0 0 1 1 0
0 0 1 0 1 2 0
0 1 1 0 1 0 0
0 1 0 0 0 0 0
0 0 0 0 0 1 1
0 1 0 0 0 0 0
0 1 0 0 0 0 0

Here 0 is an empty cell, 1 is a wall, and 2 is a cell that holds the virus. If you build no wall at all, the virus reaches every empty cell.

If you build walls at row 2 column 1, row 1 column 2, and row 4 column 6, the map becomes this.

2 1 0 0 1 1 0
1 0 1 0 1 2 0
0 1 1 0 1 0 0
0 1 0 0 0 1 0
0 0 0 0 0 1 1
0 1 0 0 0 0 0
0 1 0 0 0 0 0

After the virus spreads, the map looks like this.

2 1 0 0 1 1 2
1 0 1 0 1 2 2
0 1 1 0 1 2 2
0 1 0 0 0 1 2
0 0 0 0 0 1 1
0 1 0 0 0 0 0
0 1 0 0 0 0 0

Once the 3 walls are built, the cells the virus cannot reach form the safe area. The safe area of the map above has size 27.

Given the map of the laboratory, write a program that finds the largest safe area you can obtain.

The first line has the height $N$ and the width $M$ of the map. ($3 \le N, M \le 8$)

Each of the next $N$ lines has one row of the map. 0 is an empty cell, 1 is a wall, and 2 is a cell that holds the virus. The number of 2s is at least 2 and at most 10.

The map has at least 3 empty cells.

Print the largest size of the safe area on the first line.