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:
#AGC033-A-Darker and Darker
from collections import deque

h,w = map(int,input().split())
grid = [input() for i in range(h)]

#初期の黒('#')の位置からの距離
dist = [[-1]*w for _ in range(h)]

p = deque()
d = 0
for i in range(h):
    for j in range(w):
        if grid[i][j] == '#':
            p.append((i,j))
            dist[i][j] = 0

while p:
    y,x = p.popleft()
    d = dist[y][x]
    for dy,dx in ((1,0),(0,1),(-1,0),(0,-1)):
        if 0<= x+dx < w and 0<= y+dy < h and dist[y+dy][x+dx] == -1:
            dist[y+dy][x+dx] = d+1
            p.append((y+dy,x+dx))

    
print(d)