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:
# Enter your code here. Read input from STDIN. Print output to STDOUT
def parse(A):
    R=len(A)
    C=len(A[0])
    grid=[[1 for j in xrange(C)]  for i in xrange(R)]
    for i in xrange(R):
        for j in xrange(C):
            if A[i][j]=='.':
                grid[i][j]=0
                
    return grid

def find(grid):
    black={}
    R=len(grid)
    C=len(grid[0])
    new=[]
    for i in xrange(R):
        for j in xrange(C):
            if grid[i][j]==1:
                black[(i,j)]=0
                new+=[(i,j)]
    time=0        
    
    while len(black)<R*C:
        
        time+=1
        new_black=set([])
        
        for X in new:
            x,y=X
            check=[(x-1,y),(x+1,y),(x,y-1),(x,y+1)]
            for Y in check:
                y1,y2=Y[0],Y[1]
                if y1>R-1 or y1<0 or y2>C-1 or y2<0:
                    continue
                if grid[y1][y2]==0:
                    new_black.add((y1,y2))
                    
                    black[(y1,y2)]=1
                else:
                    continue
        for X in new_black:
            grid[X[0]][X[1]]=1
        new=[]
        new=new_black
        #print(new_black)
    return time    

H,W=list(map(int,raw_input().strip().split(' ')))
A=[]
for _ in xrange(H):
    A+=[raw_input()]
grid=parse(A)
print(find(grid))