The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Round 122 (Div. 1) |
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Finished |

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constructive algorithms

graphs

trees

*1700

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A. Cutting Figure

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou'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.

Examples

Input

5 4

####

#..#

#..#

#..#

####

Output

2

Input

5 5

#####

#...#

#####

#...#

#####

Output

2

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.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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