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())
l = [list(input()) for i in range(h)]

dis = [[10000]*w for i in range(h)]
q = deque([])

for i in range(h):
    for j in range(w):
        if l[i][j] == "#":
            q.append([i,j,0])
            dis[i][j] = 0
dx = [0,0,1,-1]
dy = [1,-1,0,0]
while q:
    x,y,d = q.popleft()

    for i in range(4):
        nx = x + dx[i]
        ny = y + dy[i]
        if 0 <= nx < h and 0 <= ny < w and dis[nx][ny] > d+1:
            dis[nx][ny] = d + 1
            q.append([nx,ny,d+1])

ans = 0
for i in dis:
    ans = max(ans,max(i))
print(ans)