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;
using System.Collections.Generic;
using System.Linq;


namespace AtCoder
{
    static class Extensions
    {
        public static int LowerBound<T>(this IList<T> list, T value, IComparer<T> comp=null)
        {
            if (comp == null) comp = Comparer<T>.Default;

            var l = 0;
            var r = list.Count;

            while (l < r)
            {
                var m = (l + r) / 2;
                var c = comp.Compare(value, list[m]);
                if (c > 0) l = m + 1;
                else  r = m;
            }

            return l;
        }
        public static int UpperBound<T>(this IList<T> list, T value, IComparer<T> comp=null)
        {
            if (comp == null) comp = Comparer<T>.Default;

            var l = 0;
            var r = list.Count;

            while (l < r)
            {
                var m = (l + r) / 2;
                var c = comp.Compare(value, list[m]);
                if (c >= 0) l = m + 1;
                else r = m;
            }

            return r;
        }
    }
    class Program
    {
		static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }
        static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }
        static int[] ReadIntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }
        static int[] ReadIntArray(int n)
        {
            var a = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = ReadInt();
            }
            return a;
        }
        static long[] ReadLongArray()
        {
            return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        }
        static long[] ReadLongArray(int n)
        {
            var a = new long[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = ReadLong();
            }
            return a;
        }
		
        public static int[] ZAlgotithm(string s)
        {
            var len = s.Length;

            var a = new int[len];
            a[0] = len;
            var i = 1;
            var j = 0;
            while (i < len)
            {
                while (i + j < len && s[j] == s[i + j]) j++;
                a[i] = j;

                if (j == 0)
                {
                    i++;
                    continue;
                }

                var k = 1;
                while (i + k < len && k + a[k] < j)
                {
                    a[i + k] = a[k];
                    k++;
                }
                i += k;
                j -= k;
            }

            return a;
        }
        public class MaxHeap<T> : IEnumerable<T>
        {
            private List<T> _list;
            private Comparer<T> _comp;
			
            public int Count
            {
                get
                {
                    return _list.Count;
                }
            }
            public MaxHeap() : this(0) { }
            public MaxHeap(int capacity, Comparison<T> comp=null)
            {
                _list = new List<T>(capacity);

                if (comp == null)
                {
                    _comp = Comparer<T>.Default;
                }
                else
                {
                    _comp = Comparer<T>.Create(comp);
                }
            }
            
            public void Push(T elem)
            {
                Upheap(elem);
            }

            public T Pop()
            {
                return Downheap();
            }

            public T Peek()
            {
                return _list[0];
            }

            
            private void Swap(int i, int j)
            {
                var a = _list[j];
                _list[j] = _list[i];
                _list[i] = a;
            }

            private void Upheap(T elem)
            {
                _list.Add(elem);
                var i = _list.Count - 1;

                while (true)
                {
                    if (i == 0) return;
                    var j = (i - 1) / 2;

                    var e = _list[i];
                    var p = _list[j];

                    var c = _comp.Compare(e, p);
                    if (c > 0)
                    {
                        Swap(i, j);
                        i = j;
                        continue;
                    }
                    else
                    {
                        break;
                    }
                }
            }

            private T Downheap()
            {
                var result = _list[0];

                var last = _list.Count - 1;
                Swap(0, last);
                _list.RemoveAt(last);
                if (_list.Count == 0) return result;

                var i = 0;
                while (true)
                {
                    if (i == _list.Count - 1) return result;
                    var p = _list[i];

                    var j = i * 2 + 1;
                    if (j >= _list.Count) return result;

                    if(j+1 < _list.Count && _comp.Compare(_list[j], _list[j+1]) < 0)
                    {
                        j++;
                    }

                    if (_comp.Compare(_list[i], _list[j]) < 0)
                    {
                        Swap(i, j);
                        i = j;
                    }
                    else
                    {
                        return result;
                    }
                }
            }
            public MaxHeap<T> Copy(Comparison<T> comp=null)
            {
                var c = new MaxHeap<T>(0, comp);
                c._list = _list.ToList();

                return c;
            }
            public MaxHeap(List<T> list)
            {
                _list = list;

                _comp = Comparer<T>.Default;
            }

            public List<T> GetList()
            {
                return _list;
            }

            public IEnumerator<T> GetEnumerator()
            {
                return _list.GetEnumerator();
            }

            IEnumerator IEnumerable.GetEnumerator()
            {
                return GetEnumerator();
            }
        }
        class InputLine
        {
            private string[] _inputs;
            private int _index = 0;

            InputLine(string input)
            {
                _inputs = input.Split();
                _index = 0;
            }

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

            public int NextInt()
            {
                return int.Parse(_inputs[_index++]);
            }
            public long NextLong()
            {
                return long.Parse(_inputs[_index++]);
            }
            public double NextDouble()
            {
                return double.Parse(_inputs[_index++]);
            }
        }
        public static int GCD(int x, int y)
        {
            var a = Math.Max(x, y);
            var b = x + y - a;

            while (b != 0)
            {
                var c = b;
                b = a % b;
                a = c;
            }

            return a;
        }
        public static long GCD(long x, long y)
        {
            var a = Math.Max(x, y);
            var b = x + y - a;

            while (b != 0)
            {
                var c = b;
                b = a % b;
                a = c;
            }

            return a;
        }
        static long ModPower(long x, long y, long mod)
        {
            var bytes = BitConverter.GetBytes(y);
            var bits = new System.Collections.BitArray(bytes);

            var max2 = 0;
            for (int i = bits.Length - 1; i >= 0; i--)
            {
                if (bits[i])
                {
                    max2 = i;
                    break;
                }
            }

            long result = 1;
            for (int i = max2; i >= 0; i--)
            {
                result = (result * result) % mod;
                if (bits[i])
                {
                    result = (result * x) % mod;
                }
            }

            return result;
        }
        
        static long ModFact(long n, long mod)
        {
            long result = 1;

            for (int i = 1; i <= n; i++)
            {
                result = result * i % mod;
            }
            return result;
        }
		
        static long ModAdd(long x, long y, long mod)
        {
            return ((x % mod) + (y % mod)) % mod;
        }
        static long ModMal(long x, long y, long mod)
        {
            return ((x % mod) * (y % mod)) % mod;
        }

        static long ModDiv(long x, long y, long mod)
        {
            //フェルマーの小定理より、a^(-1) = a^(p-2)
            return ModMal(x, ModPower(y, mod - 2, mod), mod);
        }
        static long ModComb(long n, long r, long mod)
        {
            long numerator = 1;
            for (int i = 0; i < r; i++)
            {
                numerator = ModMal(numerator, n - i, mod);
            }

            long denominator = ModFact(r, mod);

            return ModDiv(numerator, denominator, mod);
        }
        class Graph
        {
            private int _size;
            private List<int>[] _map;

            public IEnumerable<int> this[int i]
            {
                get
                {
                    if (_map[i] == null) return Enumerable.Empty<int>();
                    return _map[i];
                }
            }

            public Graph(int size)
            {
                _size = size;
                _map = new List<int>[size];
            }

            public void Add(int from, int to)
            {
                if (_map[from] == null)
                {
                    _map[from] = new List<int>();
                }
                _map[from].Add(to);
            }
        }
        static long p1097 = 1000000007;
        static void Main(string[] args)
        {
			//↓

            var hw = ReadIntArray();
            var h = hw[0];
            var w = hw[1];
            var ss = new string[h];
            for (int i = 0; i < h; i++)
            {
                ss[i] = Console.ReadLine();
            }

            var row = new int[h + 2, w + 2];
            var col = new int[h + 2, w + 2];
            
            for (int i = 1; i < h + 1; i++)
            {
                for (int j = 1; j < w + 1; j++)
                {
                    var s = ss[i - 1][j - 1];
                    if (s == '#')
                    {
                        col[i, j] = 0;
                        row[i, j] = 0;
                    }
                    else
                    {
                        col[i, j] = col[i - 1, j] + 1;
                        row[i, j] = row[i, j - 1] + 1;
                    }
                }
            }

            var max = int.MinValue;
            
            for (int i = h; i >= 1; i--)
            {
                for (int j = w; j >= 1; j--)
                {
                    if (col[i + 1, j] > 0 && col[i, j] > 0) col[i, j] = col[i + 1, j];
                    if (row[i, j + 1] > 0 && row[i, j] > 0) row[i, j] = row[i, j + 1];

                    if(col[i, j] > 0)
                        max = Math.Max(max, row[i, j] + col[i, j] - 1);
                }
            }
            
            Console.WriteLine(max);


			//↑
        }

	}
}