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())
INF = 10**9
sheet = []
log = [[True]*W for i in range(H)]
step = [(-1,0),(1,0),(0,-1),(0,1)]
stuck = deque()
ans = 0

for i in range(H):
  line = input()
  for j in range(W):
    if line[j]=='#':
      stuck += [(i,j,0)]
      log[i][j] = False
      
while stuck:
  y, x, m = stuck.popleft()
  for s in step:
    dx, dy = s
    if x+dx<0 or x+dx>W-1 or y+dy<0 or y+dy>H-1:
      continue
    if log[y+dy][x+dx]:
      log[y+dy][x+dx]=False
      stuck += [(y+dy, x+dx, m+1)]
      if ans<m+1:
        ans = m+1
      
print(ans)