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.io.InputStream;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.math.BigDecimal;
import java.math.MathContext;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;

import static java.util.Comparator.*;

public class Main {
    public static void main(String[] args) {
        PrintWriter out = new PrintWriter(System.out);
        Solver solver = new Solver(System.in, out);
        solver.solve();
        out.close();
    }
}
class Solver {
	Scanner sc;
	PrintWriter out;
    public Solver(InputStream in, PrintWriter out) {
    	sc = new Scanner(in);
    	this.out = out;
    }
    // ==================================================================
    public void solve() {
    	int H = ni();
    	int W = ni();
    	char[][] D = new char[H][];
    	D = ndc(H);
    	List<PP> list = new ArrayList<>();
    	for (int i = 0; i < H; i++) {		// 最初の黒をリストに追加する
			for (int j = 0; j < W; j++) {
				if(D[i][j] == '#')	list.add(new PP(i, j));
			}
		}
    	int ans = 0, x, y;
    	boolean f;
    	Queue<PP> que = new ArrayDeque<>();
    	PP p;
    	while(true) {
    		if(list.isEmpty())	break;		// リストが空で終了
    		for(PP pp : list) {
//    			out.println("キューに追加する　 y = " + pp.y + "  x = " + pp.x);
    			que.add(pp);
    		}
//    		out.println("");
    		list.clear();
    		while(!que.isEmpty()) {
    			p = que.poll();
    			y = p.y;
    			x = p.x;
				if(y > 0 && D[y-1][x] == '.') {
					D[y-1][x] = '#';
					list.add(new PP(y-1, x));
				}
				if(x > 0 && D[y][x-1] == '.') {
					D[y][x-1] = '#';
					list.add(new PP(y, x-1));
				}
				if(x < W-1 && D[y][x+1] == '.') {
					D[y][x+1] = '#';
					list.add(new PP(y, x+1));
				}
				if(y < H-1 && D[y+1][x] == '.') {
					D[y+1][x] = '#';
					list.add(new PP(y+1, x));
				}
			}
	    	ans++;
		}
    	out.println(ans-1);
    }
    class PP {
    	int x, y;
    	public PP(int y, int x) {
    		this.x = x;
    		this.y = y;
    	}
    }
    // ------------------------------------------
    // 入力
    // ------------------------------------------
    public int ni() {
    	return Integer.parseInt(sc.next());
    }
    public long nl() {
    	return Long.parseLong(sc.next());
    }
    public String ns() {
    	return sc.next();
    }
    public char[] nc() {
    	return sc.next().toCharArray();
    }
    public int[] ndi(int N) {
    	int[] ans = new int[N];
    	for (int i = 0; i < N; i++) {
			ans[i] = ni();
		}
    	return ans;
    }
    public long[] ndl(int N) {
    	long[] ans = new long[N];
    	for (int i = 0; i < N; i++) {
			ans[i] = nl();
		}
    	return ans;
    }
    public String[] nds(int N) {
    	String[] ans = new String[N];
    	for (int i = 0; i < N; i++) {
			ans[i] = ns();
		}
    	return ans;
    }
    public char[][] ndc(int N) {
    	char[][] ans = new char[N][];
    	for (int i = 0; i < N; i++) {
			ans[i] = nc();
		}
    	return ans;
    }
    public int[][] ndii(int N, int S) {
    	int[][] ans = new int[N][S];
    	for (int i = 0; i < N; i++) {
			for (int j = 0; j < S; j++) {
				ans[i][j] = ni();
			}
		}
    	return ans;
    }
}