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

state = []
# 初期状態
for h in range(H):
    for w in range(W):
        if field[h][w] == "#":
            state.append([w, h])

tmp = []
ret = 0
while len(state) > 0:
    tmp = list()
    ret += 1
    for x, y in state:
        for nx, ny in ((1,0), (-1,0), (0,1), (0,-1)):
            nx += x
            ny += y
            if nx < 0 or ny < 0 or nx >= W or ny >= H:
                continue

            if field[ny][nx] == ".":
                field[ny][nx] = "#"
                tmp.append([nx, ny])
    state = tmp

print(ret-1)