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 Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(defparameter *h* (read))
(defparameter *w* (read))

(defun black-white-positions (h w)
  (let ((black-positions '())
        (white-positions '()))
    (dotimes (i h)
      (let ((row (remove #\ (coerce (read-line) 'list))))
        (dotimes (j w)
          (let ((a_ij (nth j row)))
            (if (char= #\# a_ij)
                (push (cons i j) black-positions)
                (push (cons i j) white-positions))))))
    (values black-positions
            white-positions)))

(multiple-value-bind (b-poss w-poss)
  (black-white-positions *h* *w*)
  (defparameter *black-positions* b-poss)
  (defparameter *white-positions* w-poss))

(defun f (b-poss w-poss)
  (reduce #'max
          (mapcar (lambda (w-pos)
                    (reduce #'min
                            (mapcar (lambda (b-pos) (+ (abs (- (car b-pos) (car w-pos)))
                                                       (abs (- (cdr b-pos) (cdr w-pos)))))
                                    b-poss)))
                  w-poss)))

(princ (f *black-positions* *white-positions*))