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:

H, W = map(int, input().split())
maze = [list(input()) for _ in range(H)]
# print(maze)

blacks = []
for i in range(H):
    for j in range(W):
        if maze[i][j] == '#':
            blacks.append((i, j))
# print(blacks)

count = 0
while len(blacks) != 0:
    count += 1
#     print(blacks)
    nexts = []
    for x, y in blacks:
        for nx, ny in [(x-1, y), (x+1,y), (x,y-1),(x,y+1)]:
            if 0<=nx<H and 0<=ny<W and maze[nx][ny] == '.':
                maze[nx][ny] = '#'
                nexts.append((nx, ny))
#     print(maze)
    blacks = nexts
    
print(count-1)