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 = [input() for _ in range(h)]
memo = [[-1 if j=="." else 0 for j in list(i)] for i in a]

q = []
for i in range(h):
    for j in range(w):
        if a[i][j]=="#":
            q.append([i, j])
q = deque(q)
while q:
    x, y = q.popleft()
    for s, t in [[1,0],[-1,0],[0,1],[0,-1]]:
        if 0<=x+s and 0<=y+t and x+s<h and y+t<w:
            if memo[x+s][y+t]<0:
                memo[x+s][y+t]=memo[x][y]+1
                q.append([x+s,y+t])
print(max(max(i) for i in memo))