Problem Statement

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.