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:
/*
String[]の初期化、整数の型がlongになっているか
関数（splitとかcontainsとか）内では"+"とかは正規表現となされるので"\\+"とする
'+'とかは問題ない
配列のコピーはarr1=arr.clone()
HashSet<>[]はおのおの初期化した？？？？？
負の数の割り算は絶対値が小さいほうに切り捨てられるex.-1/2=0ので、ある値>kみたいな式だとバグらせやすいので注意
ある値>=kとして、切り上げた値をとるべき
toLowerCase()はアルファベット以外に対して行ってもエラーにはならない
ArrayDequeではpopとpushはStackと同じ操作になる
//import static java.lang.System.*; はしばらく使わなそう(使うとしてもexit(0)のためだけ)←return;でよさそう
最後にout.flush()またはout.close()をするのを忘れずに！
Point2D p2d=new Point2D.Double(d1,d2);
Line2D l2d=new Line2D.Double(x1,y1,x2,y2);
Line2D l2d_0=new Line2D.Double(x11,y11,x22,y22);
if(l2d.intersectsLine(l2d_0))
next_Permutationを使うときはソート済み配列かどうか確認！！
参照型の比較するときはプリミティブ型にキャストするか.compare,.equalsを使う！
ex.map.get(0)=100,map.get(1)=100でもmap.get(0)==map.get(1)がfalseになりうる
*/
//入力終了→Ctrl+D
import java.io.*;
import java.awt.*;
import java.util.*;
import java.awt.geom.*;
import static java.lang.Math.*;
public class Main {
    public static void main(String[] $) {
        int h=sc.nextInt(),w=sc.nextInt();
        char[][] a=new char[h][w];
        int[][] dist=new int[h][w];
        for (int i = 0; i < h; i++) {
            String s=sc.next();
            for (int j = 0; j < w; j++) {
                a[i][j]=s.charAt(j);
                dist[i][j]=Integer.MAX_VALUE;
            }
        }
        int[] dr={0,-1,0,1};
        int[] dc={-1,0,1,0};
        Queue<Point> q=new ArrayDeque<>();
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                if(a[i][j]=='#'){
                    q.add(new Point(i,j));
                    dist[i][j]=0;
                }
            }
        }
        while (!q.isEmpty()){
            Point now=q.poll();
            for (int i = 0; i < 4; i++) {
                int r=dr[i]+now.x;
                int c=dc[i]+now.y;
                if(0<=r&&r<h&&0<=c&&c<w){
                    if(dist[r][c]>dist[now.x][now.y]+1){
                        dist[r][c]=dist[now.x][now.y]+1;
                        q.add(new Point(r,c));
                    }
                }
            }
        }
        int ans=0;
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                ans=max(ans,dist[i][j]);
            }
        }
        out.println(ans);
        out.close();
    }

    //aはソート済みでなければならない！
    static boolean nextPermutation(int[] a) {
        int t = a.length - 1;
        int tt = t + 1;
        for (int i = t; i > 0; --i) {
            if (a[i - 1] < a[i]) {
                int swapIndex = Find(a[i - 1], a, i, t);
                int temp = a[swapIndex];
                a[swapIndex] = a[i - 1];
                a[i - 1] = temp;
                Arrays.sort(a, i, tt);
                return true;
            }
        }
        return false;
    }

    static int Find(int dest, int[] a, int s, int e) {
        if (s == e) {
            return s;
        }
        int m = (s + e + 1) / 2;
        return a[m] <= dest ? Find(dest, a, s, m - 1) : Find(dest, a, m, e);
    }

    static long power(long x, long n) {
        if (n == 0) return 1;
        if (n % 2 == 0) {
            long e = power(x, n / 2);
            return (e * e) % mod;
        }
        return (x * power(x, n - 1)) % mod;
    }

    static long mod = (long) 1e9 + 7;

    //クラスカル法(0-indexed) n頂点m辺
    static HashSet<Integer> Kruskal(int[] u, int[] v, long[] cost, int n) {
        int m = u.length;
        UF.Init(n);
        PriorityQueue<Integer> S = new PriorityQueue<>((p1, p2) -> Long.compare(cost[p1], cost[p2]));
        for (int i = 0; i < m; i++) {
            S.add(i);
        }
        //最小全域木をなす辺
        HashSet<Integer> F = new HashSet<>();
        while (!S.isEmpty()) {
            int e = S.poll();
            if (!UF.same(u[e], v[e])) {
                F.add(e);
                UF.unite(u[e], v[e]);
            }
        }
        return F;
    }

    //ワーシャルフロイド(0-indexed)
    static void WF(long[][] d, int[] a, int[] b, long[] c) {
        int n = d[0].length;
        long INF = 100000000000l;
        for (int i = 0; i < n; i++) {
            for (int j = i; j < n; j++) {
                d[i][j] = d[j][i] = INF;
            }
        }
        int m = a.length;
        for (int i = 0; i < m; i++) {
            d[a[i]][b[i]] = d[b[i]][a[i]] = c[i];
        }
        for (int k = 0; k < n; k++) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    d[i][j] = d[i][j] > d[i][k] + d[k][j] ? d[i][k] + d[k][j] : d[i][j];
                }
            }
        }
    }

    //Segment Tree
    static class ST {
        //0-indexed
        //親:(n-1)/2,子:2*n+1,2*n+2
        //i番目のindex→n+i-1
        static int INF = Integer.MAX_VALUE;
        static int n = 1048576 / 2;
        static int[] d = new int[n * 2 - 1];

        static void Init() {
            for (int i = 0; i < n * 2 - 1; i++) d[i] = 0;
        }

        //i番目の要素をxに変更（この関数はnが2の累乗でないと機能しない）
        static void update(int i, int x) {
            i += n - 1;
            d[i] = x;
            while (i > 0) {
                i = (i - 1) / 2;
                d[i] = d[i * 2 + 1] + d[i * 2 + 2];
            }
        }

        //[a,b)の最小値,l,rにはノードkに対応付く区間を与える
        static int query(int a, int b, int k, int l, int r) {
            if (r <= a || b <= l) return 0;
            if (a <= l && r <= b) return d[k];
            int vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
            int vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
            return vl + vr;
        }
        /*
        ex.[a,b)のmin→query(a,b,0,0,ST.n)
         */
    }

    static class COM {
        static long[] fact;
        static long[] inv;

        static void Init(int n) {
            fact = new long[n];
            inv = new long[n];
            fact[0] = inv[0] = 1;
            for (int i = 1; i < n; i++) {
                fact[i] = (fact[i - 1] * i) % mod;
                inv[i] = power(fact[i], mod - 2);
            }
        }

        static long C(int n, int k) {
            if (k > n) return 0;
            return ((fact[n] * inv[n - k]) % mod * inv[k]) % mod;
        }
    }

    //Union Find木(0-indexed)
    static class UF {
        static int[] d;

        static void Init(int size) {
            d = new int[size];
            for (int i = 0; i < size; i++) {
                d[i] = -1;
            }
        }

        static boolean unite(int x, int y) {
            x = find(x);
            y = find(y);
            if (x == y) return false;
            if (d[x] > d[y]) {
                int t = d[y];
                d[y] = d[x];
                d[x] = t;
            }
            d[x] += d[y];
            d[y] = x;
            return true;
        }

        static boolean same(int x, int y) {
            return find(x) == find(y);
        }

        static int find(int k) {
            return d[k] < 0 ? k : (d[k] = find(d[k]));
        }

        static int size(int k) {
            return -d[find(k)];
        }
    }

    static long gcd(long a, long b) {
        return a % b == 0 ? b : gcd(b, a % b);
    }

    static PrintWriter out = new PrintWriter(System.out);

    static class sc {
        static Scanner scanner = new Scanner(System.in);

        static String next() {
            return scanner.next();
        }

        static String nextLine() {
            return scanner.nextLine();
        }

        static int nextInt() {
            return Integer.parseInt(scanner.next());
        }

        static long nextLong() {
            return Long.parseLong(scanner.next());
        }

        static double nextDouble() {
            return Double.parseDouble(scanner.next());
        }

        static boolean hasNext() {
            return scanner.hasNext();
        }

        static boolean hasNextInt() {
            return scanner.hasNextInt();
        }

        static boolean hasNext(String str) {
            return scanner.hasNext(str);
        }
    }

}