Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3 3
...
.#.
...

Sample Output 1

2

After one operation, all but the corners of the grid will be black. After one more operation, all the squares will be black.

Sample Input 2

6 6
..#..#
......
#..#..
......
.#....
....#.

Sample Output 2

3

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;

namespace agc033
{
    class Program
    {
        static void Main(string[] args)
        {
            /*
            var m2 = Solve(new[,]
            {
                {false, false, true, false, false, true},
                {false, false, false, false, false, false},
                {true, false, false, true, false, false},
                {false, false, false, false, false, false},
                {false, true, false, false, false, false},
                {false, false, false, false, true, false},
            }, 6, 6);
            var m1 = Solve(new[,]
            {
                {false, false, false},
                {false, true, false},
                {false, false, false}
            }, 3, 3);
            */

            var tmp = Console.ReadLine().Split(' ').Select(s => int.Parse((string)s)).ToArray();
            var h = tmp[0];
            var w = tmp[1];

            var matrix = new bool[h, w];

            for (var ir = 0; ir < h; ir++)
            {
                var s = Console.ReadLine();
                for (var ic = 0; ic < w; ic++)
                {
                    matrix[ir, ic] = s[ic] == '#';
                }
            }

            var result = Solve(matrix, h, w);
            Console.WriteLine(result);
        }

        static int Solve(bool[,] matrix, int h, int w)
        {
            var count = 0;

            while (true)
            {
                var cellCount = 0;
                var matrixTmp = new bool[h, w];

                for (var hi = 0; hi < h; hi++)
                {
                    for (var wi = 0; wi < w; wi++)
                    {
                        if (matrix[hi, wi]) cellCount++;
                        matrixTmp[hi, wi] = Check(matrix, h, w, hi, wi);
                    }
                }

                if (cellCount == h * w)
                {
                    return count;
                }

                matrix = matrixTmp;
                count++;
            }
        }

        static bool Check(bool[,] matrix, int h, int w, int hi, int wi)
        {
            if (matrix[hi, wi]) return true;

            if (hi - 1 > 0)
            {
                if (matrix[hi - 1, wi]) return true;
            }
            if (wi - 1 > 0)
            {
                if (matrix[hi, wi - 1]) return true;
            }
            if (hi + 1 < h)
            {
                if (matrix[hi + 1, wi]) return true;
            }
            if (wi + 1 < w)
            {
                if (matrix[hi, wi + 1]) return true;
            }

            return false;
        }
    }
}