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=[list(input()) for _ in range(H)]

q=deque()

#黒マスを探す
for w in range(W):
    for h in range(H):
        if A[h][w]=='#':
            q.append((h,w,0))

#BFS
ans=0
while q:
    h,w,d = q.popleft()
    ans=max(ans,d)
    for dh,dw in [(0,1),(1,0),(0,-1),(-1,0)]:
        nh,nw = h+dh, w+dw
        if nh<0 or nh>=H or nw<0 or nw>=W:
            continue
        if A[nh][nw]=='#':
            continue
        A[nh][nw]='#'
        q.append((nh,nw,d+1))

print(ans)