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();
        sc.nextLine();

        boolean A[][] = new boolean[H][W];
        List<Pos> posSet = new ArrayList<>();
        int numOfBlack = 0;

        for (int i = 0; i < H; i++) {
            String line = sc.nextLine();
            for (int j = 0; j < W; j++) {
                boolean b = (line.charAt(j) == '#');
                A[i][j] = b;
                if (b) {
                    numOfBlack++;
                    posSet.add(new Pos(i, j));
                }
            }
        }

        int SIZE = H * W;
        int count = 0;
        while(numOfBlack < SIZE) {
            count++;
            List<Pos> nextPosSet = new ArrayList<>();

            Iterator<Pos> iterator = posSet.iterator();
            while(iterator.hasNext()) {
                Pos next = iterator.next();
                if (next.i > 0 && !A[next.i - 1][next.j]) {
                    nextPosSet.add(new Pos(next.i - 1, next.j));
                    A[next.i - 1][next.j] = true;
                    numOfBlack++;
                }
                if (next.j > 0 && !A[next.i][next.j - 1]) {
                    nextPosSet.add(new Pos(next.i, next.j - 1));
                    A[next.i][next.j - 1] = true;
                    numOfBlack++;
                }
                if (next.i < H - 1 && !A[next.i + 1][next.j]) {
                    nextPosSet.add(new Pos(next.i + 1, next.j));
                    A[next.i + 1][next.j] = true;
                    numOfBlack++;
                }
                if (next.j < W - 1 && !A[next.i][next.j + 1]) {
                    nextPosSet.add(new Pos(next.i, next.j + 1));
                    A[next.i][next.j + 1] = true;
                    numOfBlack++;
                }
            }

            posSet = nextPosSet;
        }

        System.out.println(count);
    }

    public static class Pos {
        public int i;
        public int j;

        public Pos(int i, int j) {
            this.i = i;
            this.j = j;
        }
    }
}