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 = [list(input()) for _ in range(H)]

q = []
for y in range(H) :
    for x in range(W) :
        if A[y][x] == '#' :
            q.append((y, x))

ret = 0
while True :
    r = []
    while q :
        cy, cx = q.pop()
        for dy, dx in ((-1, 0), (1, 0), (0, -1), (0, 1)) :
            ny, nx = cy + dy, cx + dx
            if 0 <= ny < H and 0 <= nx < W and A[ny][nx] == '.' :
                A[ny][nx] = '#'
                r.append((ny, nx))
    ret += 1
    if len(r) == 0 :
        break
    
    q = r
    
print(ret - 1)