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:
h,w = map(int,input().split())
a = list(list(input())for i in range(h))
stack = []
for i in range(h):
    for j in range(w):
        if a[i][j] == "#":
            stack.append((i,j))
        
vec = ((1,0),(0,1),(-1,0),(0,-1))
move = 0
while stack:
    next = []
    move +=1
    for y,x in stack:
        for ny,nx in vec:
            ty,tx = y+ny,x+nx
            if ty>h-1 or tx>w-1 or ty<0 or tx <0:continue
            if a[ty][tx] == ".":
                a[ty][tx] = move
                next.append((ty,tx))
    stack = next

print(move-1)