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)]
V = [[-1]*w for _ in range(h)]
que = deque([])
for i,a in enumerate(A):
    for j,_a in enumerate(a):
        if _a == '#':
            que.append([i,j])
            V[i][j] = 0
dhdw = [[-1,0],[1,0],[0,-1],[0,1]]
while que:
    nwh,nww = que.popleft()
    for dh, dw in dhdw:
        if not (0<=nwh+dh<h and 0<=nww+dw<w): continue
        if V[nwh+dh][nww+dw] != -1: continue
        V[nwh+dh][nww+dw] = V[nwh][nww]+1
        que.append([nwh+dh, nww+dw])
print(max(map(max, V)))