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:
# -*- coding: utf-8 -*-
from collections import deque
h,w = map(int, input().split())
al = [input() for _ in range(h)]

inf = 10**9
m = [[inf]*w for _ in range(h)]
q = deque([])
for hi in range(h):
    for wi in range(w):
        if al[hi][wi]=="#":
            m[hi][wi] = 0
            q.append((hi,wi))

while len(q)>0:
    ch,cw = q.popleft()
    c = m[ch][cw]
    for hi,wi in [[ch+1,cw],[ch,cw+1],[ch-1,cw],[ch,cw-1]]:
        if h>hi>=0 and w>wi>=0 and m[hi][wi]>c+1:
            m[hi][wi] = c+1
            q.append((hi,wi))

res = max([max(m[i]) for i in range(h)])
print(res)