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
dx=[1,0,-1,0]
dy=[0,1,0,-1]

h, w = list(map(int, input().split()))
board = [list(input()) for i in range(h)]
q = deque()
for i in range(h):
    for j in range(w):
        if board[i][j] == "#":
            board[i][j] = True
            q.append((i, j, 0))
        else:
            board[i][j] = False

ans = 0
while q:
    i,j,cnt = q.popleft()
    for x, y in zip(dx,dy):
        if 0<=i+x<h and 0<=j+y<w and not board[i+x][j+y]:
            board[i+x][j+y] = True
            q.append((i+x, j+y, cnt+1))
            ans = max(ans, cnt+1)
print(ans)