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.Arrays;
import java.util.Scanner;

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

        final int[][] table = new int[h][w];
        for (int i = 0; i < h; i++) {
            final String s = scanner.next();
            for (int j = 0; j < w; j++) {
                table[i][j] = s.charAt(j) == '#' ? 1 : Integer.MAX_VALUE - 1;
            }
        }

        for (int i = 1; i < h; i++) {
            for (int j = 0; j < w; j++) {
                table[i][j] = Math.min(table[i][j], table[i - 1][j] + 1);
            }
        }

        for (int i = h - 2; i >= 0; i--) {
            for (int j = 0; j < w; j++) {
                table[i][j] = Math.min(table[i][j], table[i + 1][j] + 1);
            }
        }

        for (int i = 0; i < h; i++) {
            for (int j = 1; j < w; j++) {
                table[i][j] = Math.min(table[i][j], table[i][j - 1] + 1);
            }
        }

        for (int i = 0; i < h; i++) {
            for (int j = w - 2; j >= 0; j--) {
                table[i][j] = Math.min(table[i][j], table[i][j + 1] + 1);
            }
        }

        final int answer = Arrays.stream(table)
                .flatMapToInt(Arrays::stream)
                .max()
                .getAsInt() - 1;

        System.out.println(answer);
    }
}