Problem: You are given a grid of squares with H horizontal rows and W vertical columns, where each square is painted white or black. HW characters from A_{11} to A_{HW} represent the colors of the squares. A_{ij} is `#` if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is `.` if that square is white.

We will repeatedly perform the following operation until all the squares are black:

* Every white square that shares a side with a black square, becomes black.



Find the number of operations that will be performed. The initial grid has at least one black square.

Constraints

* 1 \leq H,W \leq 1000
* A_{ij} is `#` or `.`.
* The given grid has at least one black square.

Input

Input is given from Standard Input in the following format:


H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}


Output

Print the number of operations that will be performed.

Examples

Input

3 3
...
.#.
...


Output

2


Input

6 6
..#..#
......
..#..
......
.#....
....#.


Output

3

Solution (in JAVA):

Solution:
import java.util.*;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int h = Integer.parseInt(sc.next());
        int w = Integer.parseInt(sc.next());
        char[][] matrix = new char[h][w];
        Deque<Point> points = new ArrayDeque<Point>();
        for(int i=0;i<h;i++){
            matrix[i] = sc.next().toCharArray();
            for(int j=0;j<w;j++){
                if(matrix[i][j] == '#'){
                    points.addLast(new Point(i,j));
                }
            }
        }
        sc.close();
        int count = search(matrix, points, h, w, 0);
        System.out.println(count);
        return;
    }
    public static int search(char[][] matrix, Deque<Point> points, int h, int w, int count){
        Point p;
        Deque<Point> new_points = new ArrayDeque<Point>();
        while(true){
            try{
                p = points.removeFirst();
            }catch(NoSuchElementException e){
                break;
            }
            int x = p.x; int y = p.y;
            matrix[y][x] = '%';
            int[] dx = {-1,0,1,0}; int[] dy = {0,-1,0,1};
            for(int i=0;i<4;i++){
                int nx = x + dx[i]; int ny = y + dy[i];
                if(ny<0 || ny>=h || nx<0 || nx>=w || matrix[ny][nx] != '.'){
                    continue;
                }
                matrix[ny][nx] = '#';
                new_points.addLast(new Point(ny,nx));
            }
        }
        try{
            p = new_points.getFirst();
            count++;
            return search(matrix, new_points, h, w, count);
        }catch(NoSuchElementException e){
            return count;
        }
    }
}
class Point{
    int x; int y;
    public Point(int y, int x){
        this.x = x;
        this.y = y;
    }
}