Darker and Darker

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

inputFormat

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}

outputFormat

Output

Print the number of operations that will be performed.

Examples

Input

3 3 ... .#. ...

Output

2

Input

6 6 ..#..# ...... ..#.. ...... .#.... ....#.

Output

3

样例

3 3
...
.#.
...

2