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 {
	public static void main(String[] args) {
		new Main().solve();
	}

	void solve() {
		Scanner sc =  new Scanner(System.in);

		//上下左右
		int[] dx = {1, 0, -1, 0};
		int[] dy = {0, 1, 0, -1};

		int H = sc.nextInt();
		int W = sc.nextInt();

		char[][] charMap = new char[H][W];
		boolean[][] map = new boolean[H][W];

		Queue<Place> que = new ArrayDeque<Place>();

		// 入力文字列の抽出
		for (int i = 0; i < H; i++) {
			String s =  sc.next();
			charMap[i] = s.toCharArray();
			for (int j = 0; j < W; j++) {
				if (charMap[i][j] == '#') {
					que.add(new Place(i, j, 0));
					map[i][j] = true;
				}
			}
		}
		int max = 0;
		while (que.size() != 0){
			Place place = que.remove();

			for (int i = 0; i < 4; i++) {
				int x = place.getX() + dx[i];
				int y = place.getY() + dy[i];
				if (x < 0 || x >= H || y < 0 || y >= W) {
					continue;
				}
				if (! map[x][y]) {
					que.add(new Place(x,y, place.getCount() + 1));
					map[x][y] = true;
					max = place.getCount() + 1;
				}
			}
		}
		System.out.println(max);
	}

	// 場所を記憶
	class Place {
		private int x;
		private int y;
		private int count;

		public Place(int x, int y, int count) {
			this.x = x;
			this.y = y;
			this.count = count;
		}
		public int getX() {
			return this.x;
		}

		public int getY() {
			return this.y;
		}
		public int getCount() {
			return this.count;
		}
	}
}