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 PYTHON):

Solution:
import sys
from collections import deque

H,W=map(int, raw_input().split())
A=[ list( sys.stdin.readline().strip())  for i in range(H) ]


D=[ (-1,0),(1,0),(0,1),(0,-1) ]
K=[ [ float("inf") for j in range(W) ] for i in range(H)  ]  #Kyori

q=deque()

for i in range(H):
	for j in range(W):
		if A[i][j]=="#":
			q.append( (i,j) )
			K[i][j]=0


while q:
	h,w=q.popleft()
	for dx,dy in D:
		if 0<=h+dx<H and 0<=w+dy<W and K[h+dx][w+dy]>K[h][w]+1:
				K[h+dx][w+dy]=K[h][w]+1
				q.append( (h+dx,w+dy) )	

ans=0
for x in K:
	ans=max(ans, max(x) )
print ans