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())
a = []
d = []
que = deque()
for i in range(h):
    a.append(list(input()))
    d.append([1e100]*w)
    for j in range(w):
        if a[i][j] == '#':
            que.append([i,j])
            d[i][j] = 0
di = [-1,0,1,0]
dj = [0,1,0,-1]
ans = 0

while que:
    i,j = que.popleft()
    for k in range(4):
        ni = i + di[k]
        nj = j + dj[k]
        if 0 <= ni < h and 0 <= nj < w and d[ni][nj] == 1e100:
            d[ni][nj] = d[i][j] + 1
            ans = max(ans, d[ni][nj])
            que.append([ni,nj])
print(ans)