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:
H, W = map(int, input().split())


HW=[ [-1 for w in range(W)] for h in range(H) ]

#print(HW)
from collections import deque
Q = deque()

for h in range(H):
  S = input()
  for w in range(W):
    if S[w]=="#":
      Q.append([h,w])
      HW[h][w]=0

X = [0,0,-1,1]
Y = [-1,1,0,0]
ans=0

while Q:
  h,w = Q.popleft()

  for i in range(len(X)):
    ih,iw = h + Y[i], w + X[i]

    if not ((0 <= ih < H) and (0 <= iw < W)): continue
    if HW[ih][iw] >= 0: continue

    HW[ih][iw] = HW[h][w]+1
    ans = max(ans, HW[ih][iw])
    Q.append([ih,iw])

print(ans)