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 = [list(input()) for i in range(H)]
X = [1,0,-1,0]
Y = [0,-1,0,1]
Q = deque()
dist = [[99999]*W for i in range(H)]
for i in range(H):
  for j in range(W):
    if C[i][j] == "#":
      dist[i][j] = 0
      Q.append((i,j))

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