Problem:
Score : 400 points

Problem Statement

There is a grid with H horizontal rows and W vertical columns, and there are obstacles on some of the squares.

Snuke is going to choose one of the squares not occupied by an obstacle and place a lamp on it.
The lamp placed on the square will emit straight beams of light in four cardinal directions: up, down, left, and right.
In each direction, the beam will continue traveling until it hits a square occupied by an obstacle or it hits the border of the grid. It will light all the squares on the way, including the square on which the lamp is placed, but not the square occupied by an obstacle.

Snuke wants to maximize the number of squares lighted by the lamp.

You are given H strings S_i (1 \leq i \leq H), each of length W. If the j-th character (1 \leq j \leq W) of S_i is #, there is an obstacle on the square at the i-th row from the top and the j-th column from the left; if that character is ., there is no obstacle on that square.

Find the maximum possible number of squares lighted by the lamp.

Constraints

1 \leq H \leq 2,000

1 \leq W \leq 2,000

S_i is a string of length W consisting of # and ..

. occurs at least once in one of the strings S_i (1 \leq i \leq H).

Input

Input is given from Standard Input in the following format:

H W
S_1
:
S_H

Output

Print the maximum possible number of squares lighted by the lamp.

Sample Input 1

4 6
#..#..
.....#
....#.
#.#...

Sample Output 1

8

If Snuke places the lamp on the square at the second row from the top and the second column from the left, it will light the following squares: the first through fifth squares from the left in the second row, and the first through fourth squares from the top in the second column, for a total of eight squares.

Sample Input 2

8 8
..#...#.
....#...
##......
..###..#
...#..#.
##....#.
#...#...
###.#..#

Sample Output 2

13

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Data.List
import Control.Monad
import Data.Array.Unboxed
import Data.Array.MArray
import Data.Array.ST
import Control.Monad.ST
import Data.Maybe (fromJust)
import qualified Data.ByteString.Lazy.Char8 as B

--import Debug.Trace

type Field s = STUArray s (Int,Int) Int

modifyArray :: (MArray a e m ,Ix i) => a i e -> i -> (e -> e) -> m ()
modifyArray arr i f =  readArray arr i >>= writeArray arr i . f

f :: Field s -> Int -> [[Char]] -> ST s ()
f arr' y [] = return ()
f arr' y (s:field) = do
  sub arr' 1 $ group s
  f arr' (y+1) field
  where
    sub :: Field s -> Int -> [[Char]] -> ST s ()
    sub arr i [] = return ()
    sub arr i (a:bs) = if head a == '.' then do
        --traceShowM (i,length a)
        forM [i..i+(length a)-1] $ \i' -> modifyArray arr (y,i') (+(length a))
        sub arr (i+(length a)) bs
      else do
        sub arr (i+(length a)) bs

g :: Field s -> Int -> [[Char]] -> ST s ()
g arr' x [] = return ()
g arr' x (s:field) = do
  sub arr' 1 $ group s
  g arr' (x+1) field
  where
    sub :: Field s -> Int -> [[Char]] -> ST s ()
    sub arr i [] = return ()
    sub arr i (a:bs) = if head a == '.' then do
        --traceShowM (i,length a)
        forM [i..i+(length a)-1] $ \i' -> modifyArray arr (i',x) (+(length a))
        sub arr (i+(length a)) bs
      else do
        sub arr (i+(length a)) bs

solve :: Int -> Int -> [[Char]] -> ST s Int
solve h w field = do
  arr <- newListArray ((1,1),(h,w)) $ repeat (-1)
  --fileld <- newlistArray ((1,1),(h,w)) $ concat list
  f arr 1 field
  --traceShowM $ show "---------------------"
  g arr 1 (transpose field)
  list <- forM [1..h] $ \y -> do
    forM [1..w] $ \x -> do
      readArray arr (y,x)

  return $ maximum $ concat list

readBInt :: B.ByteString -> Int
readBInt = fst . fromJust . B.readInt

main0 :: B.ByteString -> Int
main0 cont =
   let remLines0 = map B.words (B.lines cont)
       [h',w']:remLines1 = remLines0
       h = readBInt h'
       w = readBInt w'
       hs = map (B.unpack . head) (take h (remLines1))
   in runST $ solve h w hs

main :: IO ()
main = print . main0 =<< B.getContents