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:
import collections
H,W=map(int,input().split())
went=[[False]*W for i in range(H)]
queue=collections.deque()
for hoge in range(H):
    for huga,t in enumerate(input()):
        if t=="#":
            went[hoge][huga]=True
            queue.append([hoge,huga,0])
while queue:
    curx,cury,ct=queue.popleft()
    for dx,dy in [[1,0],[-1,0],[0,1],[0,-1]]:
        newx,newy=curx+dx,cury+dy
        newct=ct+1
        if 0<=newx<H and 0<=newy<W and (not went[newx][newy]):
            went[newx][newy]=True
            queue.append([newx,newy,newct])
print(ct)