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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
	H,W,i,j,ans,X,Y:Longint;
	D:Array[0..1001,0..1001]of Longint;
	S:String;
begin
	readln(H,W);
	for i:=0 to 1001 do begin
		D[0,i]:=1000000000;
		D[i,0]:=1000000000;
		D[H+1,i]:=1000000000;
		D[i,W+1]:=1000000000;
	end;
	for i:=1 to H do begin
		readln(S);
		for j:=1 to W do begin
			if S[j]='#'then D[i,j]:=0 else begin
				X:=D[i-1,j];
				Y:=D[i,j-1];
				if X<Y then D[i,j]:=X+1 else D[i,j]:=Y+1;
			end;
		end;
	end;
	for i:=H downto 1 do for j:=W downto 1 do begin
		X:=D[i+1,j];
		Y:=D[i,j+1];
		if X<Y then inc(X)else X:=Y+1;
		if D[i,j]>X then D[i,j]:=X;
		if ans<D[i,j]then ans:=D[i,j];
	end;
	writeln(ans);
end.