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 i in range(H)]
q=deque([])
dist=[[-1 for j in range(W)] for i in range(H)]
for i in range(H):
    for j in range(W):
        if A[i][j]=="#":
            q.append((i,j))
            dist[i][j]=0
dx=[-1,1,0,0]
dy=[0,0,1,-1]
while(len(q)>0):
    x,y=q.popleft()
    for k in range(4):
        nx=x+dx[k]
        ny=y+dy[k]
        if not(0<=nx<H and 0<=ny<W):
            continue
        if dist[nx][ny]==-1:
            dist[nx][ny]=dist[x][y]+1
            q.append((nx,ny))
print(max([max(i) for i in dist]))