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 = [int(i) for i in input().split()]
A = [input() for _ in range(H)]
seen = [[False]*W for _ in range(H)]
ans = 0
dq = deque([])
for i in range(H):
    for j in range(W):
        if A[i][j] == "#":
            dq.append((i, j, 0))
            seen[i][j] = True
while len(dq):
    x, y, d = dq.popleft()
    ans = max(ans, d)
    for nx, ny in [(x-1, y), (x+1, y), (x, y+1), (x, y-1)]:
        if 0 <= nx < H and 0 <= ny < W:
            if not seen[nx][ny]:
                dq.append((nx, ny, d+1))
                seen[nx][ny] = True
print(ans)