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 = [input() for i in range(H)]
q = deque()
c = [[-1] * W for i in range(H)]
for i in range(H):
    for j in range(W):
        if A[i][j] == '#':
            q.append((i, j))
            c[i][j] = 0
D = [[0, 1], [1, 0], [0, -1], [-1, 0]]
while q:
    y, x = q.popleft()
    for dy, dx in D:
        ny, nx = y+dy, x+dx
        if 0 <= ny < H and 0 <= nx < W and c[ny][nx] == -1:
            q.append((ny, nx))
            c[ny][nx] = c[y][x]+1
print(max([max(l) for l in c]))