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 = 0
dp = [None] * H
mat = deque(maxlen=W*H)
for h in range(H):
    s = list(input())
    for w, x in zip(range(W), s):
        if x == "#":
            mat.append((h, w, 0))
    dp[h] = s

while len(mat):
    h, w, cnt = mat.popleft()

    for t, h, w, cnt in ((h > 0, h - 1, w, cnt),(h < H-1, h + 1, w, cnt),(w > 0, h , w - 1, cnt),(w < W-1, h , w + 1, cnt)):
        if t and dp[h][w] == ".":
            mat.append((h, w, cnt+1))
            dp[h][w] = "#"

print(cnt)