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 collections

h,w = map(int, input().split())
cells = []
for i in range(h):
    row = input()
    cells.append([c == '#' for c in row])

blacks = collections.deque()

for i in range(h):
    for j in range(w):
        if cells[i][j]:
            blacks.append((i,j,0))
res = 0
while blacks:
    y,x,c = blacks.popleft()
    for dy,dx in ((-1, 0), (1, 0), (0, -1), (0,1)):
        if 0<=y+dy<h and 0<=x+dx<w and not cells[y+dy][x+dx]:
            cells[y+dy][x+dx] = True
            blacks.append((y+dy, x+dx, c+1))
            res = c+1
print(c)