You've gotten an $*n* × *m*$ sheet of squared paper. Some of its squares are painted. Let's mark the set of all painted squares as $*A*$. Set $*A*$ is connected. Your task is to find the minimum number of squares that we can delete from set $*A*$ to make it not connected.

A set of painted squares is called connected, if for every two squares $*a*$ and $*b*$ from this set there is a sequence of squares from the set, beginning in $*a*$ and ending in $*b*$, such that in this sequence any square, except for the last one, shares a common side with the square that follows next in the sequence. An empty set and a set consisting of exactly one square are connected by definition.

Input

The first input line contains two space-separated integers $*n*$ and $*m*$ ($1 ≤ *n*, *m* ≤ 50$) — the sizes of the sheet of paper.

Each of the next $*n*$ lines contains $*m*$ characters — the description of the sheet of paper: the $*j*$-th character of the $*i*$-th line equals either "#", if the corresponding square is painted (belongs to set $*A*$), or equals "." if the corresponding square is not painted (does not belong to set $*A*$). It is guaranteed that the set of all painted squares $*A*$ is connected and isn't empty.

Output

On the first line print the minimum number of squares that need to be deleted to make set $*A*$ not connected. If it is impossible, print -1.

Note

In the first sample you can delete any two squares that do not share a side. After that the set of painted squares is not connected anymore.

The note to the second sample is shown on the figure below. To the left there is a picture of the initial set of squares. To the right there is a set with deleted squares. The deleted squares are marked with crosses.