/// 

      /// Permutation.
      /// 
      /// 
      /// n         n!
      ///  P      = __________
      ///    r    (n-r)!
      /// 
      /// n * (n-1) * (n-2) * (n-3) * ..... * (lower+1) * lower.
      /// 
      /// 
      /// 
      /// 
      /// 
      private long nPr(long upper,long lower)
      {
         long output = 1;
         if(lower<1) lower = 1;        
         for(long i=upper;i>=lower;i--)
            output *= i;
         return output;
      }