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 PYTHON3):

Solution:
from collections import deque
h,w=map(int,input().split())
l=[]
l.append('@'*(w+2))
for i in range(h):
    l.append('@'+input()+'@')
l.append('@'*(w+2))
q=deque()
p=[[-1 for i in j] for j in l]
for i in range(1,h+1):
    for j in range(1,w+1):
        if l[i][j]=='#':
            q.append([i,j])
            p[i][j]=0
while len(q)>0:
    x,y=q.popleft()
    for i,j in [[1,0],[-1,0],[0,-1],[0,1]]:
        if l[x+i][y+j]=='.' and p[x+i][y+j]==-1:
            q.append([x+i,y+j])
            p[x+i][y+j]=p[x][y]+1
a=0
for i in p:
    for j in i:
        a=max(a,j)
print(a)
#print(*p,sep='\n')