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 PYTHON):

Solution:
# ANSHUL GAUTAM
# IIIT-D

'''

'''

def solve(grid):
	H,W = len(grid),len(grid[0])
	q = []
	dist = [0]*H
	for i in range(H):
		dist[i] = []
	for i in range(H):
		for j in range(W):
			if(grid[i][j] == '#'):
				q.append([i,j])
				grid[i][j] = 0
	maxx = 0
	while(q):
		qq = []
		for i,j in q:
			for r,c in [[i+1,j],[i-1,j],[i,j+1],[i,j-1]]:
				if(0 <= r < H and 0 <= c < W and grid[r][c] == '.'):
					grid[r][c] = grid[i][j] + 1
					maxx = max(maxx,grid[r][c])
					qq.append([r,c])
		q = qq
	return maxx

H,W = map(int, raw_input().split())
grid = []
for h in range(H):
	s = list(raw_input())
	grid.append(s)
ans = solve(grid)
print(ans)