Problem Statement  
You are arranging a weird game for a team building exercise. In this game there are certain locations that people can stand at, and from each location there are paths that lead to other locations, but there are not necessarily paths that lead directly back. You want the paths set up such that regardless of where someone starts, there will be at least one path they can take that will return to their starting location. You already have the locations set up, and some paths connecting them. You want to know the fewest paths that you have to add such that everything is set up the way you need it. Create a class TeamBuilding with a method fewestPaths that takes a String[] paths that describes the way the locations are currently connected, and returns an int that is the fewest number of paths that must be added. Each element of paths will be a String containing as many characters as there are elements in paths. The ith element of paths (beginning with the 0th element) will contain a '1' (all quotes are for clarity only) in position j if there is a path that leads directly from i to j, and a '0' if there is not a path that leads directly from i to j.  
Definition  
 
Notes  
  There may be paths that leads directly from one location to that same location.  
Constraints  
  paths will contain between 2 and 20 elements, inclusive.  
  Each element of paths will contain only the characters '0' and '1'.  
  Each element of paths will contain as many characters as there are elements in paths.  
Examples  
0)  
 
1)  
 
2)  
 
3)  
