题目描述
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
输入格式
见题面
输出格式
见题面