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())
graph = []
finished = [[False for _ in range(w)] for _ in range(h)]
y = [0, 0, 1,-1]
x = [1,-1, 0, 0]
q = deque([])
for i in range(h):
    a = input()
    graph.append(a)
    for j in range(w):
        if a[j] == "#":
            q.append((i,j,0))
while q:
    c = q.popleft()
    for i in range(4):
        nh = c[0]+y[i]
        nw = c[1]+x[i]
        if nh < 0 or nh >= h or nw < 0 or nw >= w or graph[nh][nw] == "#" or finished[nh][nw]:continue
        finished[nh][nw] = True
        q.append((nh,nw,c[2]+1))
print(c[2])