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 = [list(input()) for _ in range(H)]
p = deque()
for i, Ai in enumerate(A):
    for j, Aij in enumerate(Ai):
        if Aij == "#":
            p.append([i, j, 0])

while p:
    y, x, cnt = p.popleft()
    for dx, dy in [[1, 0], [-1, 0], [0, 1], [0, -1]]:
        if 0 <= y + dy < H and 0 <= x + dx < W and A[y + dy][x + dx] == ".":
            p.append([y + dy, x + dx, cnt + 1])
            A[y + dy][x + dx] = "#"
print(cnt)