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.*;

class Main {
  static int H, W;
  static String[][] map;
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    H = sc.nextInt();
    W = sc.nextInt();
    map = new String[H][W];
    Deque<Integer[]> que = new ArrayDeque<>();
    for (int i = 0; i < H; i++) {
      map[i] = sc.next().split("");
      for (int j = 0; j < W; j++) {
        if (map[i][j].equals("#")) que.add(new Integer[]{i, j}); 
      }
    }
    int ans = 0;
    while (true) {
      int n = que.size();
      for (int i = 0; i < n; i++) {
        Integer[] p = que.poll();
        change(que, p[0]-1, p[1]);
        change(que, p[0], p[1]+1);
        change(que, p[0], p[1]-1);
        change(que, p[0]+1, p[1]);
      }
      if (que.isEmpty()) break;
      ans++;
    }
    System.out.println(ans);
  }
  
  static void change(Deque<Integer[]> que, int h, int w) {
    if (h < 0 | h >= H | w < 0 | w >= W) return;
    if (map[h][w].equals("#")) return;
    que.add(new Integer[]{h, w});
    map[h][w] = "#";
  }
}