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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static Input;

public class Prog
{
    private const int INF = 1000000007;
    private struct Pair { public long x, y; public Pair(long x, long y) { this.x = x; this.y = y; } }
    public static void Solve()
    {
        int H = NextInt();
        int W = NextInt();
        string[] S = new string[H];
        for (int i = 0; i < H; i++) S[i] = NextString();
        //全てのマスに対して各方向の評価
        int[,] data = new int[2010, 2010];
        //左から
        for (int i = 0; i < H; i++)
        {
            int sum = 0;
            for (int j = 0; j < W; j++)
            {
                if (S[i][j] == '.') sum++;
                else sum = 0;
                data[i, j] = sum;
            }
        }
        //右から
        for (int i = 0; i < H; i++)
        {
            int sum = 0;
            for (int j = W - 1; j != -1; j--)
            {
                if (S[i][j] == '.') sum++;
                else sum = 0;
                data[i, j] += sum;
            }
        }
        //↑から
        for (int i = 0; i < W; i++)
        {
            int sum = 0;
            for (int j = 0; j < H; j++)
            {
                if (S[j][i] == '.') sum++;
                else sum = 0;
                data[j, i] += sum;
            }
        }
        //sita から
        for (int i = 0; i < W; i++)
        {
            int sum = 0;
            for (int j = H - 1; j != -1; j--)
            {
                if (S[j][i] == '.') sum++;
                else sum = 0;
                data[j, i] += sum;
            }
        }

        int ans = 0;
        for (int i = 0; i < H; i++)
            for (int j = 0; j < W; j++)
                if (S[i][j] == '.') ans = Math.Max(ans, data[i, j]);


        Console.WriteLine(ans - 3);
    }
    public static void Main()
    {
        var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
    }
}
public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static char NextChar() { Confirm(); return char.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}