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())
C = []
Q = deque()
dist = [[-1]*W for i in range(H)]

for i in range(H):
  s = list(input())
  yxidx = [(i,x) for x,v in enumerate(s) if v == "#"]
  for (y, x) in yxidx:
    Q.append((y,x))
    dist[y][x] = 0
  C.append(s)
X = [1,0,-1,0]
Y = [0,-1,0,1]


while Q:
  y,x = Q.popleft()
  for i in range(4):
    nx = x + X[i]
    ny = y + Y[i]
    if (0 <= nx < W) and (0 <= ny < H) and (dist[ny][nx] == -1):
      dist[ny][nx] = dist[y][x] + 1
      Q.append((ny,nx))

ans = 0
for i in range(H):
  ans = max(ans,max(dist[i]))
print(ans)