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())
d=[]
for i in range(H):    
    d.append([0 if c=='#' else -1 for c in input()])
#print(d)
q=deque()
for i in range(H):
    for j in range(W):
        if not d[i][j]:
            q.append((i,j))
#print(q)
while q:
    u=q.popleft()
    ui,uj=u
    for v in [(ui-1,uj),(ui+1,uj),(ui,uj-1),(ui,uj+1)]:
        vi,vj=v
        if 0<=vi<=H-1 and 0<=vj<=W-1 and d[vi][vj]==-1:
            d[vi][vj]=d[ui][uj]+1
            q.append(v)
#print(d)
print(max(max(di) for di in d))