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.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int h = scanner.nextInt();
		int w = scanner.nextInt();

		int[][] map = new int[h][w];


		for (int i=0; i<h; i++){
			char[] as = scanner.next().toCharArray();
			for (int j=0; j<w; j++){
				boolean isB = (as[j]=='#');
				if(isB){
					for (int k=1; k<=j && map[i][j-k]>k; k++){
						map[i][j-k]=k;
						for(int l=1; l<=i && map[i-l][j-k]>k+l; l++){
							map[i-l][j-k]=k+l;
						}
					}
					for (int k=1; k<=i && map[i-k][j]>k; k++){
						map[i-k][j]=k;
						for (int l=1; j+l<w && map[i-k][j+l]>k+l; l++){
							map[i-k][j+l]=k+l;
						}
					}
				}else if (i==0 && j==0) map[i][j] = Integer.MAX_VALUE;
				else if (map[0][0]==Integer.MAX_VALUE) map[i][j] = Integer.MAX_VALUE;
				else if (i==0) map[i][j] = map[i][j-1]+1;
				else if (j==0) map[i][j] = map[i-1][j]+1;
				else map[i][j] = Math.min(map[i][j-1], map[i-1][j])+1;
			}
		}

		int ans = 0;

		for (int i=0; i<h; i++) for (int j=0; j<w; j++) {
			ans = Math.max(ans, map[i][j]);
		}

		System.out.println(ans);
	}
}