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())
S=[input() for _ in range(H)]

paint=((1,0),(-1,0),(0,1),(0,-1))
que=deque([])

dark=[[0]*W for _ in range(H)] # 1が黒、0はまだ白

for i in range(H): # 初期化(最初に黒いマスをdarkリストに入れて、キューに入れる。)
    for j in range(W):
        if S[i][j]=='#':
            que.append((i,j,0))
            dark[i][j]=1
ans=0
while len(que)>0:
    di,dj,c=que.popleft()
    
    for pi,pj in paint:
        ni,nj=pi+di,pj+dj # 移動先がni,nj
        if 0<=ni<H and 0<=nj<W and dark[ni][nj]==0:
            dark[ni][nj]=1
            que.append((ni,nj,c+1))
            ans=c+1
print(ans)