Problem Statement  
N checkers are placed on an infinitely large board. The ith checker is in the cell at row x[i], column y[i]. There can be more than one checker in the same cell. A move consists of taking one checker and moving it one cell up, down, left or right. Return a int[] containing exactly N elements, where the ith element (0based) is the minimum number of moves necessary to end up with at least i+1 checkers in the same cell.  
Definition  
 
Constraints  
  x will contain between 1 and 50 elements, inclusive.  
  y will contain the same number of elements as x.  
  Each element of x will be between 1 and 1,000,000, inclusive.  
  Each element of y will be between 1 and 1,000,000, inclusive.  
Examples  
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