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=list(map(int,input().split()))
a=[[c for c in input()] for _ in range(h)]
visit=[[0]*w for _ in range(h)]
q=deque()

for i in range(h):
    for j in range(w):
        if a[i][j]=='#':
            deque.appendleft(q,(i,j,0))
            visit[i][j]=1
ans=0
while len(q)>0:
    i,j,cnt=deque.pop(q)

    ans=max(ans,cnt)

    for di,dj in [(-1,0),(1,0),(0,-1),(0,1)]:
        ni=i+di
        nj=j+dj
        if 0<=ni<h and 0<=nj<w and visit[ni][nj]==0:
            visit[ni][nj]=1
            deque.appendleft(q,(ni,nj,cnt+1))

print(ans)