Problem Statement  
Consider a hexagonal grid with 6 sides, with the side lengths given by the int[] s (in the clockwise order), as shown in the following picture: Count the number of ways to color each cell with one of two colors, black or white, such that every nonborder black cell has exactly a black neighbors, and every nonborder white cell has exactly b white neighbors (a cell is called nonborder if and only if it has exactly 6 neighbors in the grid).  
Definition  
 
Constraints  
  s will contain exactly 6 elements.  
  Each element of s will be between 2 and 6, inclusive.  
  a and b will each be between 0 and 6, inclusive.  
  s will define a valid hexagonal grid.  
  The answer will always fit into an int.  
Examples  
0)  
 
1)  
 
2)  
 
3)  
