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:
import sys
input=sys.stdin.readline
from collections import deque
h,w=map(int,input().split())
MAP=[list(input().strip()) for _ in range(h)]
q=deque()
for i,M in enumerate(MAP):
    for j,m in enumerate(M):
        if m=='#':
            q.append((i,j,0))
delta=[(1,0),(-1,0),(0,1),(0,-1)]
ans=0
while q:
    x,y,d=q.popleft()
    ans=max(ans,d)
    for dx,dy in delta:
        if 0<=x+dx<h and 0<=y+dy<w:
            if MAP[x+dx][y+dy]=='.':
                MAP[x+dx][y+dy]='#'
                q.append((x+dx,y+dy,d+1))
print(ans)