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.*;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.StringJoiner;
import java.util.StringTokenizer;
import java.util.function.Function;

public class Main {

    static int H, W;
    static int[][] A;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        H = sc.nextInt();
        W = sc.nextInt();
        A = new int[H][W];
        for (int i = 0; i < H; i++) {
            String s = sc.next();
            for (int j = 0; j < W; j++) {
                char c = s.charAt(j);
                if( c == '#' ) {
                    A[i][j] = 0;
                } else {
                    A[i][j] = Integer.MAX_VALUE;
                }
            }
        }

        System.out.println(solve());
    }

    static int solve() {
        ArrayDeque<Integer> q = new ArrayDeque<>();

        for (int i = 0; i < H; i++) {
            for (int j = 0; j < W; j++) {
                if( A[i][j] == 0 ) {
                    q.add( i*W + j );
                }
            }
        }

        while(!q.isEmpty()) {
            int s = q.pollFirst();
            int h = s / W;
            int w = s % W;
            int d = A[h][w];

            for (int i = 0; i < 4; i++) {
                int nh = DH[i] + h;
                int nw = DW[i] + w;

                if( inRange(nh, nw) && A[nh][nw] > d + 1 ) {
                    A[nh][nw] = d + 1;
                    q.addLast( nh*W + nw );
                }
            }
        }
        int ans = -1;
        for (int i = 0; i < H; i++) {
            for (int j = 0; j < W; j++) {
                ans = Math.max(ans, A[i][j]);
            }
        }
        return ans;
    }

    static int[] DH = {0, 1, 0, -1};
    static int[] DW = {1, 0, -1, 0};

    static boolean inRange(int h, int w) {
        return 0 <= h && h < H && 0 <= w && w < W;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

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

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

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }

    static <A> void writeLines(A[] as, Function<A, String> f) {
        PrintWriter pw = new PrintWriter(System.out);
        for (A a : as) {
            pw.println(f.apply(a));
        }
        pw.flush();
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }
}