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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Windows;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{
    public class Program
    {
        static void Main(string[] args)
        {
            var r = ReadSplit();
            var h = r[0].Int();
            var w = r[1].Int();
            var hDic = new Dictionary<int, int[]>();
            var wDic = new Dictionary<int, int[]>();
            for (int i = 0; i < h; i++)
            {
                var r2 = Read();
                var hl = new int[w];
                var wl = new int[w];
                wDic.Add(i, wl);
                var hCount = 0;
                for (int j = 0; j < w; j++)
                {
                    if (r2[j] == '.')
                    {
                        hCount++;
                        hl[j] = hCount;
                        wl[j] = 1;
                        if (i > 0)
                        {
                            wDic[i][j] = wDic[i - 1][j] + 1;
                        }
                    }
                    
                    if(r2[j] == '#' || j == w - 1 || i == h - 1) 
                    {
                        var tmp = j - 1;
                        while (tmp >= 0)
                        {
                            if (r2[tmp] == '#') break;
                            if (tmp < 0) break;
                            hl[tmp] = hCount;
                            tmp -= 1;
                        }
                        hCount = 0;

                        var startIndex = i - 1;
                        if (i == h - 1) startIndex = i;

                        for (int k = startIndex; k >= 0; k--)
                        {
                            if (wDic[k][j] == 0) break;
                            if (k - 1 < 0) break;
                            wDic[k - 1][j] = wDic[k][j];
                        }
                    }
                }
                hDic.Add(i, hl);
                //wDic.Add(i, wl);
            }
            var ans = 0;
            for (int i = 0; i < h; i++)
            {
                for (int j = 0; j < w; j++)
                {
                    ans = Math.Max(hDic[i][j] + wDic[i][j] - 1, ans);
                }
            }
            WriteRead(ans);
        }

        public static string Read()
        {
            return Console.ReadLine();
        }

        public static string[] ReadSplit()
        {
            return Console.ReadLine().Split(' ');
        }

        public static void WriteRead(object str)
        {
            Console.WriteLine(str);
            Read();
        }

        public static void Write(object str)
        {
            Console.WriteLine(str);
        }

        private static bool ChangeMin<T>(ref T a, T b) where T : IComparable
        {
            if (a.CompareTo(b) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }

        private static bool ChangekMax<T>(ref T a, T b) where T : IComparable
        {
            if (b.CompareTo(a) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }
    }
}


public static class Extentions
{
    public static int Int(this object obj)
    {
        return int.Parse(obj.ToString());
    }

    public static long Long(this object obj)
    {
        return long.Parse(obj.ToString());
    }

    public static decimal Decimal(this object obj)
    {
        return decimal.Parse(obj.ToString());
    }

    public static double Double(this object obj)
    {
        return double.Parse(obj.ToString());
    }

    public static T2 GetValueZero<T1, T2>(this Dictionary<T1, T2> d, T1 key) where T2 : struct
    {
        T2 value;
        if (d.TryGetValue(key, out value))
        {
            return value;
        }
        return new T2();
    }
}