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())
que = deque()
A = [input() for i in range(H)]

dy = [0,1,0,-1]
dx = [1,0,-1,0]
Field = [[-1]*W for i in range(H)]
for i in range(H):
    for j in range(W):
        if A[i][j] == '#':
            Field[i][j] = 0
            que.append((i, j))

d = 0
while que:
    y,x = que.popleft()
    d = Field[y][x]
    for i in range(4):
        nx = x + dx[i]
        ny = y + dy[i]
        if not 0 <= nx < W or not 0 <= ny < H or Field[ny][nx] != -1:
            continue
        Field[ny][nx] = d+1
        que.append((ny, nx))
print(d)