Maximizing Dinner Invitations

Mirko has bought an apartment and wants to invite as many people as possible to dinner with him. To celebrate, he plans to buy a large rectangular wooden table. The number of people a table can accommodate is equal to its perimeter, i.e. in mathematical notation: $$P = 2(\text{length} + \text{width})$$.

The table must be placed such that its edges are parallel to the edges of the apartment. The apartment layout is given as a grid of characters where a dot (.) represents free space and a hash (#) represents an obstacle. Your task is to find the maximum possible perimeter of a rectangle (table) that can be placed entirely in the free space.

inputFormat

The first line contains two integers R and C representing the number of rows and columns of the apartment layout. The next R lines each contain a string of C characters (each either . or #), which describe the layout.

outputFormat

Output a single integer - the maximum number of people that can be accommodated at the table, i.e. the maximum perimeter of any axis‐aligned rectangle that fits completely within free spaces.

sample

2 3
...
...

10