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
def mbfs(S,H,W):
    dxy=[[1,0],[0,1],[-1,0],[0,-1]]
    while(len(d)!=0):
        h,w,x=d.popleft()
        for t,y in dxy:
            if(0<=h+t<=H-1 and 0<=w+y<=W-1 and S[h+t][w+y]!='#'):
                S[h+t][w+y]='#'
                d.append([h+t,w+y,x+1])
    return x
H,W=map(int,input().split())
A=[list(input()) for i in range(H)]
d=deque()
for i in range(H):
    for j in range(W):
        if(A[i][j]=='#'):
            d.append([i,j,0])
print(mbfs(A,H,W))