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 heapq import*
h,w=map(int,input().split())
grid=[["#"]*(w+2)]+[list("#"+input()+"#")for x in range(h)]+[["#"]*(w+2)]

stack=[]
for y in range(1,h+1):
    for x in range(1,w+1):
        if grid[y][x]=="#":
            grid[y][x]=0
            stack.append((y,x))

for i in range(h*w):
    tmp=[]
    for my,mx in stack:
        for y,x in ([0,1],[1,0],[-1,0],[0,-1]):
            if grid[my+y][mx+x]==".":
                grid[my+y][mx+x]=i+1
                tmp.append([my+y,mx+x])
    stack=tmp
    if len(tmp)==0:
        print(i)
        break