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.ArrayDeque;
import java.util.Queue;
import java.util.Scanner;

public class Main {

    private static int H = 0;
    private static int W = 0;
    private static char[][] AHW;

    public static void main(String[] args) {
        Main main = new Main();

        Scanner sc = new Scanner(System.in);

        String[] HW = sc.nextLine().split(" ");
        H = Integer.parseInt(HW[0]);
        W = Integer.parseInt(HW[1]);

        AHW = new char[H][W];
        Queue<Cell> queue = new ArrayDeque<>();

        for (int i = 0; i < H; i++) {
            String A = sc.nextLine();
            AHW[i] = A.toCharArray();
            for (int j = 0; j < W; j++) {
                if (AHW[i][j] == '#') {
                    queue.add(main.new Cell(i, j, 0));
                }
            }
        }

        int times = 0;
        while (!queue.isEmpty()) {

            Cell cell = queue.poll();
            int row = cell.row;
            int col = cell.col;
            int layer = cell.layer;

            if (row > 0 && AHW[row - 1][col] == '.') {
                // 上のセルが白だった場合
                AHW[row - 1][col] = '#';
                queue.add(main.new Cell(row - 1, col, layer + 1));
            }

            if (row < H - 1 && AHW[row + 1][col] == '.') {
                // 下のセルが白だった場合
                AHW[row + 1][col] = '#';
                queue.add(main.new Cell(row + 1, col, layer + 1));
            }

            if (col > 0 && AHW[row][col - 1] == '.') {
                // 左のセルが白だった場合
                AHW[row][col - 1] = '#';
                queue.add(main.new Cell(row, col - 1, layer + 1));
            }

            if (col < W - 1 && AHW[row][col + 1] == '.') {
                // 右のセルが白だった場合
                AHW[row][col + 1] = '#';
                queue.add(main.new Cell(row, col + 1, layer + 1));
            }
            times = layer;
        }

        System.out.println(times);
    }

    private class Cell {
        int row;
        int col;
        int layer;

        Cell(int row, int col, int layer) {
            this.row = row;
            this.col = col;
            this.layer = layer;
        }
    }
}