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.*;
import java.math.BigInteger;
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_depth = 0;

    while (true) {
      if (q.size() < 1) {
        break;
      }
      XY xy = q.poll();
      int x = xy.x;
      int y = xy.y;
      int depth = xy.depth;
      max_depth = Math.max(max_depth, 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_depth);
  }
}

class XY {
  int y;
  int x;
  int depth;

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