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

def clamp(a,b,c):
  return min(max(a,b),c)

H,W = map(int,input().split())
A = [input() for _ in range(H)]

D = [[-1]*W for _ in range(H)]
dd = [(1,0),(-1,0),(0,1),(0,-1)]
Q = deque()
res = 0

for i in range(H):
  for j in range(W):
    if A[i][j] == "#":
      D[i][j] = 0
      Q.append([i,j,0])
      
while len(Q)>0:
  x,y,n = Q.popleft()
  for dx,dy in dd:
    xx = clamp(x+dx,0,H-1)
    yy = clamp(y+dy,0,W-1)
    if D[xx][yy] == -1:
      D[xx][yy] = n+1
      Q.append([xx,yy,n+1])
      res = n+1
      
print(res)