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

tx = [1, 0, -1, 0]
ty = [0, 1, 0, -1]

H, W = map(int,input().split())

MAP = []

for _ in range(H):
    MAP.append(list(input()))

d = deque()

for i in range(H):
    for j in range(W):
        if MAP[i][j] == '#':
            d.append([i, j, 0])

ans = 0

while len(d) != 0:
    x, y, cnt = d.popleft()
    for i in range(4):
        nx = x + tx[i]
        ny = y + ty[i]
        if 0 <= nx < H and 0 <= ny < W and MAP[nx][ny] == '.':
            MAP[nx][ny] = '#'
            d.append([nx, ny, cnt + 1])
            ans = max(ans, cnt + 1)

print(ans)