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:
import sys
#import numpy as np
import math
#from fractions import Fraction
#import itertools
from collections import deque
#import heapq
#from fractions  import gcd
input=sys.stdin.readline
h,w=map(int,input().split())
a=[list(map(str,input())) for _ in range(h)]
b=deque()
n=[-1]*(h*w)
p=((1,0),(-1,0),(0,1),(0,-1))
for x in range(h):
  for y in range(w):
    if a[x][y]=="#":
      b.append((x,y))
      n[x*w+y]=0
while b:
  x,y=b.popleft()
  for idx in p:
    s,t=idx
    if 0<=x+s<h and 0<=y+t<w:
      if n[(x+s)*w+(y+t)]==-1:
        n[(x+s)*w+(y+t)]=n[x*w+y]+1
        b.append((x+s,y+t))
print(max(n))