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())
a=[list(input()) for _ in range(h)]
 
q=deque()
 
for i in range(h):
    for j in range(w):
        if a[i][j]=='#':
            q.append((i,j))
 
dx=[1,0,-1,0]            
dy=[0,1,0,-1]
ans=0
 
while q:
    nq=deque()
    while True:
        y,x=q.popleft()    
        for i in range(4):
            ny=y+dy[i]
            nx=x+dx[i]
            if 0<=ny<h and 0<=nx<w and a[ny][nx]!='#':
                a[ny][nx]='#'
                nq.append((ny,nx))

        if not q:
            ans+=1
            q=nq
            break
print(ans-1)