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:
h,w=map(int,input().split())
G=[input() for _ in range(h)]

from collections import deque
move=[(0,1),(0,-1),(1,0),(-1,0)]

que=deque([])

for i in range(h):
    for j in range(w):
        if G[i][j]=='#':
            que.append((i,j,0))

c=0
visit=[[0]*w for _ in range(h)]
while len(que)>0:
    ni,nj,c=que.popleft()
    for di,dj in move:
        mi,mj=ni+di,nj+dj
        if 0<=mi<h and 0<=mj<w and G[mi][mj]=='.' and visit[mi][mj]==0:
            visit[mi][mj]=1
            que.append((mi,mj,c+1))
print(c)