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 PYTHON):

Solution:
import sys
range = xrange
input = lambda: sys.stdin.readline().rstrip()

h,w = [int(x) for x in input().split()]
A = [list(input()) for _ in range(h)]

found = [False]*(w*h)

cur = []
for y in range(h):
    for x in range(w):
        if A[y][x]=='#':
            cur.append(y*w+x)
            found[y*w+x]=True


counter = 0
while cur:
    counter += 1
    tmp = []
    
    while cur:
        ind = cur.pop()
        y,x = divmod(ind,w)

        if 0<=x-1 and not found[ind-1]:
            tmp.append(ind-1)
            found[ind-1] = True
        if x+1<w and not found[ind+1]:
            tmp.append(ind+1)
            found[ind+1] = True

        if 0<=y-1 and not found[ind - w]:
            tmp.append(ind - w)
            found[ind-w] = True
    
        if y+1<h and not found[ind + w]:
            tmp.append(ind + w)
            found[ind+w] = True
    cur = tmp

print counter-1