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)

#if DEBUG
using Microsoft.VisualStudio.TestTools.UnitTesting;
#endif

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

namespace Contest
{
    class Program
    {
        static long mod = 1000000007;

        static void Main(string[] args)
        {
            var scanner = new IO.StreamScanner(Console.OpenStandardInput());
            var h = scanner.Integer();
            var w = scanner.Integer();
            var map = new List<string>();
            for(int i=0; i<h; i++) map.Add(scanner.ScanLine());

            var ans = GetAns(h, w, map);
            IO.Printer.Out.WriteLine(ans);
            IO.Printer.Out.Flush();
        }

        public static int GetAns(int h, int w, List<string> map)
        {
            var left = new int[h, w];
            var right = new int[h, w];
            var top = new int[h, w];
            var bottom = new int[h, w];

            for (int i = 0; i < h; i++)
            {
                // right
                var lastPos = -1;
                for (int j = w - 1; j >= 0; j--)
                {
                    if (map[i][j] == '#') lastPos = j;
                    right[i, j] = lastPos;
                }

                // left
                lastPos = -1;
                for (int j = 0; j < w; j++)
                {
                    if (map[i][j] == '#') lastPos = j;
                    left[i, j] = lastPos;
                }
            }

            for (int j = 0; j < w; j++)
            {
                // top
                var lastPos = -1;
                for (int i = 0; i < h; i++)
                {
                    if (map[i][j] == '#') lastPos = i;
                    top[i, j] = lastPos;
                }

                // bottom
                lastPos = -1;
                for (int i = h - 1; i >= 0; i--)
                {
                    if (map[i][j] == '#') lastPos = i;
                    bottom[i, j] = lastPos;
                }
            }

            var ret = 0;

            for (int i = 0; i < h; i++)
            {
                for (int j = 0; j < w; j++)
                {
                    if (map[i][j] == '#') continue;

                    var wk = 1;

                    // top
                    wk += top[i, j] == -1 ? i : i - top[i, j] - 1;

                    // bottom
                    wk += bottom[i, j] == -1 ? h - i - 1 : bottom[i, j] - i - 1;

                    // left
                    wk += left[i, j] == -1 ? j : j - left[i, j] - 1;

                    // right
                    wk += right[i, j] == -1 ? w - j - 1 : right[i, j] - j - 1;

                    ret = Math.Max(ret, wk);
                }
            }


            return ret;
        }
    }


#if DEBUG

    [TestClass]
    public class Test
    {
        [TestMethod]
        public void Test1()
        {

        }

        public bool IsEq<T> (List<T> l1, List<T> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for(int i=0; i<l1.Count(); i++)
            {
                if (!l1[i].Equals(l2[i])) return false;
            }
            return true;
        }
    }

#endif
}

namespace IO
{
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer : StreamWriter
    {
        static Printer()
        {
            Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false };
        }

        public static Printer Out { get; set; }

        public override IFormatProvider FormatProvider
        {
            get { return CultureInfo.InvariantCulture; }
        }

        public Printer(Stream stream)
            : base(stream, new UTF8Encoding(false, true))
        {
        }

        public Printer(Stream stream, Encoding encoding)
            : base(stream, encoding)
        {
        }

        public void Write<T>(string format, T[] source)
        {
            base.Write(format, source.OfType<object>().ToArray());
        }

        public void WriteLine<T>(string format, T[] source)
        {
            base.WriteLine(format, source.OfType<object>().ToArray());
        }
    }

    public class StreamScanner
    {
        public StreamScanner(Stream stream)
        {
            str = stream;
        }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof;

        public bool IsEndOfStream
        {
            get { return isEof; }
        }

        private byte read()
        {
            if (isEof) return 0;
            if (ptr < len) return buf[ptr++];
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
            isEof = true;
            return 0;
        }

        public char Char()
        {
            byte b;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }

        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n'; b = (char)read())
                if (b == 0) break;
                else if (b != '\r') sb.Append(b);
            return sb.ToString();
        }

        public long Long()
        {
            if (isEof) return long.MinValue;
            long ret = 0;
            byte b;
            var ng = false;
            do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
            if (b == 0) return long.MinValue;
            if (b == '-')
            {
                ng = true;
                b = read();
            }
            for (; ; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                ret = ret * 10 + b - '0';
            }
        }

        public int Integer()
        {
            return (isEof) ? int.MinValue : (int)Long();
        }

        public double Double()
        {
            var s = Scan();
            return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
        }

        static T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n)
        {
            return enumerate(n, Char);
        }

        public string[] Scan(int n)
        {
            return enumerate(n, Scan);
        }

        public double[] Double(int n)
        {
            return enumerate(n, Double);
        }

        public int[] Integer(int n)
        {
            return enumerate(n, Integer);
        }

        public long[] Long(int n)
        {
            return enumerate(n, Long);
        }
    }
}