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)]
dxy = [(0,1),(1,0),(0,-1),(-1,0)]

INF = 99999
dp = [[INF]*W for i in range(H)]
q = deque()
for y,row in enumerate(A):
    for x,c in enumerate(row):
        if c=='#':
            dp[y][x] = 0
            q.append((x,y))

while q:
    x,y = q.popleft()
    d = dp[y][x]
    for dx,dy in dxy:
        nx,ny = x+dx,y+dy
        if not 0 <= nx < W: continue
        if not 0 <= ny < H: continue
        if dp[ny][nx] <= d+1: continue
        dp[ny][nx] = d+1
        q.append((nx,ny))
print(max(max(row) for row in dp))