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())
mz = []
q = deque()
for i in range(h):
    mz.append(list(input()))
    ls = [[i,j,0] for j, a in enumerate(mz[-1]) if a == '#'] #i黒のところのindexをqueに追加
    q.extend(ls)


delta = [[-1,0],[0,-1],[1,0],[0,1]]
while q:
    y,x,c = q.popleft()
    for dy,dx in delta:
        if (0<= y+dy <h) and (0<=x+dx <w):
            if mz[y+dy][x+dx] == ".":
                mz[y+dy][x+dx]="#" #黒に置き換え
                q.append([y+dy,x+dx,c+1])

            else: #すでに黒なら訪問しなくてよい
                pass

print(c)#cは最後にpopされたcost