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:
# A - Darker and Darker
from collections import deque

H,W = map(int,input().split())
B = [[-1] * W for _ in range(H)]

queue = deque([])

for i in range(H):
    A = input()
    for j in range(W):
        if A[j]=='#':
            B[i][j] = 0
            queue.append((i,j))

ans = 0

while queue:
    I,J = queue.popleft()
    for di,dj in ((-1,0),(1,0),(0,-1),(0,1)):
        i,j = I+di,J+dj
        if 0<=i<H and 0<=j<W:
            if B[i][j]<0:
                B[i][j] = B[I][J]+1
                ans = max(ans,B[i][j])
                queue.append((i,j))

print(ans)