1.3 It's A Grid!
(RankList for this Question)
Score: 100pts
Time Limit: 1.00 sec
There is a $$N$$ * $$M$$ grid ( $$N$$ is the number of rows and $$M$$ number of columns). You are given $$N$$ strings $$S_i$$, consisting of ‘O’ indicating empty space and ‘X’ indicating obstacle, each of length $$M$$.

Let us define a function $$f(i,j)$$ for all the cells of the grid ($$i$$ is the row number and $$j$$ is the column number) as count of all the cells in up, down, left and right direction of the cell $$(i,j)$$ until an obstacle is reached in the respective direction. If the the cell $$(i,j)$$ is an obstacle then $$f(i,j)$$ = 0. Read the sample cases for better understanding.

Find the maximum $$f(i,j)$$ possible.

NOTE - Problem has tight time constraints. If you think you have an optimised code but the judge gave you a TLE verdict, you can try resubmitting a couple of times since the judge sometimes gives a higher absolute running time due to server idleness. In case you get a SIGKILL verdict or TLE multiple times, that would mean your approach is most probably not an optimal one.

Constraints
$$1 \leq N, M \leq 500$$
$$1 \leq i \leq N$$
$$1 \leq j \leq M$$
$$S_i$$ has length $$M$$ and consists of only ‘O’ or ‘X’.
There is atleast one empty space ‘O’ in a given grid.

Input Format
$$N M$$
$$S_1$$
$$S_2$$
.
.
.
$$S_n$$

Output Format
Single integer - maximum value of $$f(i,j)$$ possible.

Example 1
Input:
5 5
OOXOO
XXOXX
XOOOO
XOXOO
OXXXO

Output:
6

Explanation:
Here, if we consider 1-based indexing for the 2D grid we can see that maximum value will be of $$f(3,5) = 6$$. It will include all the empty spaces in cardinal directions of $$(3,5) ie (3,2), (3,3),(3,4),(3,5),(4,5),(5,5)$$.

Example 2
Input:
5 4
OOXO
OXOX
XOOO
OOOX
XOXX

Output:
5

Explanation:
Here there are $$2$$ cells present which have the maximum value for $$f(i,j)$$. They are -
$$f(3,3) : (3,3),(3,2),(3,4),(2,3),(4,3)$$ and
$$f(4,3) : (4,1),(4,2),(4,3),(3,4),(2,4)$$