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())
field=[]
dist=[[-1]*W for _ in range(H)]
que=deque()

for i in range(H):
    tmp=list(input())
    for j in range(W):
        if tmp[j]=="#":
            dist[i][j]=0
            que.append([i,j])
    field.append(tmp)

DX=[1,0,-1,0]
DY=[0,1,0,-1]
ans=0
while que:
    y,x=map(int,que.popleft())
    ans=dist[y][x]
    for dx,dy in zip(DX,DY):
        nx=x+dx
        ny=y+dy
        if nx<0 or nx>=W or ny<0 or ny>=H: continue
        if dist[ny][nx]==-1:
            dist[ny][nx]=dist[y][x]+1
            que.append([ny,nx])

print(ans)