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 -*-
h,w = map(int, input().split())
al = [list(input()) for _ in range(h)]
cnt = 0

q = []
for hi in range(h):
    for wi in range(w):
        if al[hi][wi]=="#":
            q.append((hi,wi))

while len(q)>0:
    nq = []
    cnt += 1
    for hi,wi in q:
        for d in [[1,0],[0,1],[-1,0],[0,-1]]:
            if h>hi+d[0]>=0 and w>wi+d[1]>=0:
                if al[hi+d[0]][wi+d[1]]==".":
                    al[hi+d[0]][wi+d[1]] = "#"
                    nq.append((hi+d[0], wi+d[1]))
    q = nq

print(cnt-1)