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())
a=[list(input()) for i in range(h)]

from collections import deque

v=[[0]*w for i in range(h)]
m=[[-1,0],[0,-1],[1,0],[0,1]]
que=deque([])
for i in range(h):
    for  j in range(w):
        if a[i][j]=='#':
            v[i][j]=1
            que.append([i,j,0])
            #print(que)

while len(que)>0:
    n=que.popleft()
    for i in m:
        ni,nj=i[0]+n[0],i[1]+n[1]
        if ni>=0 and nj>=0 and ni<h and nj<w:
            if v[ni][nj]==0:
                v[ni][nj]=1
                que.append([ni,nj,n[2]+1])
print(n[2])