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 = sc.nextInt();
      int w = sc.nextInt();
      char[][] masu = new char[h][w];
      Deque<XY> q = new ArrayDeque<>();
      for(int i = 0; i < h; i++) {
        masu[i] = sc.next().toCharArray();
        for (int j = 0; j < w; j++) {
             if (masu[i][j]=='#') {
               q.add(new XY(i, j, 0));
             }
        }
      }
      int max = 0;
      for (;;) {
        if (q.size() < 1){
          break;
        }
        XY xy = q.poll();
        int x = xy.x;
        int y = xy.y;
        int depth = xy.depth;
        if (depth >= max) {
          max = depth;
        }
        if (x + 1 < w && masu[y][x + 1] == '.') {
          masu[y][x + 1] = '#';
          q.add(new XY(y, x + 1, depth + 1));
        }
        if (x - 1 >= 0 && masu[y][x - 1] == '.') {
          masu[y][x - 1] = '#';
          q.add(new XY(y, x - 1, depth + 1));
        }
        if (y + 1 < h && masu[y + 1][x] == '.') {
          masu[y + 1][x] = '#';
          q.add(new XY(y + 1, x, depth + 1));
        }
        if (y - 1 >= 0 && masu[y - 1][x] == '.') {
          masu[y - 1][x] = '#';
          q.add(new XY(y - 1, x, depth + 1));
        }

      }
        System.out.println(max);
    }
}

class XY {
    int y;
    int x;

    int depth;

    XY(int y, int x, int d) {
        this.x = x;
        this.y = y;
        depth = d;
    }
}