Problem: 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.

Examples

Input

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


Output

8


Input

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


Output

8


Input

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


Output

13

Solution (in JAVA):

Solution:
import java.util.*; import java.io.*; import java.math.*;
public class Main{
	//Don't have to see. start------------------------------------------
	static class InputIterator{
		ArrayList<String> inputLine = new ArrayList<String>(1024);
		int index = 0; int max; String read;
		InputIterator(){
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			try{
				while((read = br.readLine()) != null){
					inputLine.add(read);
				}
			}catch(IOException e){}
			max = inputLine.size();
		}
		boolean hasNext(){return (index < max);}
		String next(){
			if(hasNext()){
				return inputLine.get(index++);
			}else{
				throw new IndexOutOfBoundsException("There is no more input");
			}
		}
	}
	static HashMap<Integer, String> CONVSTR = new HashMap<Integer, String>();
	static InputIterator ii = new InputIterator();//This class cannot be used in reactive problem.
	static PrintWriter out = new PrintWriter(System.out);
	static void flush(){out.flush();}
	static void myout(Object t){out.println(t);}
	static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
	static String next(){return ii.next();}
	static boolean hasNext(){return ii.hasNext();}
	static int nextInt(){return Integer.parseInt(next());}
	static long nextLong(){return Long.parseLong(next());}
	static double nextDouble(){return Double.parseDouble(next());}
	static ArrayList<String> nextStrArray(){return myconv(next(), 8);}
	static ArrayList<String> nextCharArray(){return myconv(next(), 0);}
	static ArrayList<Integer> nextIntArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Integer> ret = new ArrayList<Integer>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Integer.parseInt(input.get(i)));
		}
		return ret;
	}
	static ArrayList<Long> nextLongArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Long> ret = new ArrayList<Long>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Long.parseLong(input.get(i)));
		}
		return ret;
	}
	static String myconv(Object list, int no){//only join
		String joinString = CONVSTR.get(no);
		if(list instanceof String[]){
			return String.join(joinString, (String[])list);
		}else if(list instanceof ArrayList){
			return String.join(joinString, (ArrayList)list);
		}else{
			throw new ClassCastException("Don't join");
		}
	}
	static ArrayList<String> myconv(String str, int no){//only split
		String splitString = CONVSTR.get(no);
		return new ArrayList<String>(Arrays.asList(str.split(splitString)));
	}
	public static void main(String[] args){
		CONVSTR.put(8, " "); CONVSTR.put(9, "\n"); CONVSTR.put(0, "");
		solve();flush();
	}
	//Don't have to see. end------------------------------------------
	static void solve(){//Here is the main function
	ArrayList<Integer> one = nextIntArray();
	int H = one.get(0);
	int W = one.get(1);
	String[][] list = new String[H][W];
	Node[][] xy = new Node[H][W];
	for(int i = 0; i < H; i++){
      	ArrayList<String> tmp = nextCharArray();
		for(var j = 0; j < W; j++){
          	list[i][j] = tmp.get(j);
          	int add = (list[i][j].equals(".")) ? 1 : 0;
          	xy[i][j] = new Node(add, add);
		}
	}
	for(int i = 0; i < H; i++){
		for(int j = 0; j < W; j++){
			if(i == 0 && j == 0){continue;}
			if(j != 0){
				if(xy[i][j].x != 0){
					xy[i][j].x += xy[i][j - 1].x;
				}
			}
			if(i != 0){
				if(xy[i][j].y != 0){
					xy[i][j].y += xy[i - 1][j].y;
				}
			}
		}
	}
	for(int i = H - 1; i >= 0; i--){
		for(int j = W - 1; j >= 0; j--){
			if(list[i][j].equals("#")){continue;}
			if(i - 1 != -1 && list[i - 1][j].equals(".")){
				xy[i - 1][j].y = xy[i][j].y;
			}
			if(j - 1 != -1 && list[i][j - 1].equals(".")){
				xy[i][j - 1].x = xy[i][j].x;
			}
		}
	}
	int max = 0;
	for(int i = 0; i < H; i++){
		for(int j = 0; j < W; j++){
			max = Math.max(max, xy[i][j].x + xy[i][j].y - 1);
		}
	}
	myout(max);
	}
	//Method addition frame start

static class Node{
  int x;
  int y;
  Node(int x, int y){
    this.x = x;
    this.y = y;
  }
}

	//Method addition frame end
}