Problem Statement 
 An undirected graph is said to be a wheel if there exists a "center" vertex which is adjacent to all other vertices in the graph, and the subgraph induced by taking all other vertices of the graph is precisely a cycle. Additionally, any wheel must have at least 3 vertices in the cycle surrounding the center vertex. The span of a wheel is the degree of the center vertex. For example, the graph below is a wheel with span 4 (the center vertex is colored black).
We define a fractal wheel with depth d and span h as follows: a fractal wheel with depth 0 and span h is simply a wheel with span h.
To obtain a fractal wheel with depth d > 0 and span h, we first take a fractal wheel with depth d1 and span h. Let V be the set of all vertices at distance d from the center vertex of this fractal wheel. For each vertex u in V, add to the graph a new wheel with span h such that its center vertex is u. Each added wheel must be vertexdisjoint from the other added wheels. The resulting graph is a fractal wheel with depth d and span h, and the center vertex of the resulting fractal wheel is the same as the center vertex of the initial fractal wheel with depth d1.
For example, the graph below is a fractal wheel with depth 1 and span 4 (note that adding or removing any edges from this graph would result in a graph which is not a fractal wheel):
Given a graph G with N vertices numbered 0 to N1, inclusive, you must determine if G is a fractal wheel. Concatenate the elements of edges to get a String containing a commaseparated list of edges describing G. Each edge is formatted (quotes for clarity) "u v", which denotes that there is an edge between vertices u and v in G.
If G is not a fractal wheel, then return an empty int[]. Otherwise, return a int[] with two elements: the depth and span of the fractal wheel, respectively. 

Definition 
 Class:  FractalWheels  Method:  describeWheel  Parameters:  int, String[]  Returns:  int[]  Method signature:  int[] describeWheel(int N, String[] edges)  (be sure your method is public) 




Notes 
  The distance between two vertices in a graph is the length of the shortest path between them (or infinity if there is no path). 
  The degree of a vertex v in a graph G is the total number of vertices in G which are adjacent to v. 

Constraints 
  N will be between 2 and 1000, inclusive. 
  edges will contain between 1 and 50 elements, inclusive. 
  Each element of edges will contain between 0 and 50 characters, inclusive. 
  The elements of edges, when concatenated together, will contain a commaseparated list of edges. Let's call the concatenated string E. 
  Each edge in E will be formatted "u v" (quotes for clarity), where u and v are integers between 0 and N1, inclusive, with no extra leading zeroes, and u is strictly less than v. 
  All edges in E will be distinct. 
  E will contain at least one edge. 

Examples 
0)  
 5  {
"","0 1,0 2,0 3,0 4,",
"1 2,2 3,3 4,1 4"
} 
 Returns: {0, 4 }  The first graph from the problem statement. 


1)  
 21  {
"0 1,0 2,0 3,0 4,1 2,1 4,1 5,1 6,1 7,1 8,2 3,2 9,2 ",
"10,2 11,2 12,3 4,3 13,3 14,3 15,3 16,4 17,4 18,4 1","",
"9,4 20,5 6,5 8,6 7,7 8,9 10,9 12,10 11,11 12,13 14",
",13 16,14 15,15 16,17 18,17 20,18 19,19 20",""
} 
 Returns: {1, 4 }  The second graph from the problem statement. 


2)  
 13  {
"0 1,0 2,0 3,1 2,1 3,1 4,1 5,1 6,2 3,2 7,2 8,2 9,3 ",
"10,3 11,3 12,4 5,4 6,5 6,7 8,7 9,8 9,10 11,10 12,1",
"1 12,0 7"
} 
 Returns: { }  Here we have a fractal wheel with depth 1 and span 3, but with an extra edge from the center vertex to an outerlayer vertex. 


3)  
 11  {
"0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,1 2,1 10,",
"2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10"
} 
 Returns: { }  A fractal wheel with depth 0 and span 10, but with a missing edge that should be incident to the center. 


4)  
  Returns: { }  A fractal wheel must have at least 4 vertices. 

