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())
coords = []
blacks = deque([])
for i in range(H):
    rows = list(input())
    coords.append(rows)
    for j,row in enumerate(rows):
        if row == "#":
            blacks.append((i,j,0))

ans = 0
while len(blacks) > 0: 
    h,w,dist = blacks.popleft()
    ans = max(dist,ans)
    for di, dj in [(1, 0), (0, 1), (-1, 0), (0, -1)]:
        ni = h + di
        nj = w + dj
        if 0 <= ni < H and 0 <= nj < W:
            if coords[ni][nj] == ".":
                blacks.append((ni,nj,dist+1))
                coords[ni][nj] = "#"

print(ans)