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())
m = [list(input()) for _ in range(h)]

flag = [[True] * w for _ in range(h)]

q = deque()

for i in range(h):
    for j in range(w):
        if m[i][j] == "#":
            q.appendleft((i, j, 0))
            flag[i][j] = False

ans = 0
while q:
    (i, j, n) = q.pop()
    ans = n
    for dx, dy in zip([1,0, -1, 0], [0, 1, 0, -1]):
        ni = i + dx
        nj = j + dy
        if (0 <= ni < h and 0 <= nj < w and flag[ni][nj]):
            flag[ni][nj] = False
            q.appendleft((ni, nj, n + 1))

print(ans)