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())
A = [input() for i in range(H)]
X = [1,0,-1,0]
Y = [0,-1,0,1]

INF = 99999
dp = [[-1]*W for i in range(H)]
q = deque()
for y, row in enumerate(A):
  for x,c in enumerate(row):
    if c == "#":
      dp[y][x] = 0
      q.append((y,x))
while q:
  y,x = q.popleft()
  d = dp[y][x]
  for i in range(4):
    nx = x + X[i]
    ny = y + Y[i]
    if (0 <= nx < W) and (0 <= ny < H) and (dp[ny][nx] == -1):
      dp[ny][nx] = d + 1
      q.append((ny,nx))
print(max(max(row) for row in dp))