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())
q = deque()
A = []
for h in range(H):
    r = input()
    for w in range(W):
        if r[w] == "#":
            q.append([h, w])
    A.append([0 if s=="#" else -1 for s in r])

d = [[-1, 0], [0, -1], [0, 1], [1, 0]]
p = 0

while q:
    h, w = q.popleft()
    p = A[h][w]+1
    for dh, dw in d:
        nh = h+dh
        nw = w+dw
        if not (0 <= nh < H):
            continue
        if not (0 <= nw < W):
            continue
        if A[nh][nw] == -1:
            A[nh][nw] = p
            q.append([nh, nw])

print(p-1)