Problem Statement  
Gogo has been hired by the newly founded TopCoder Security Agency (TSA) and has been tasked to encrypt a signal code generated by a radar.
The signal will consist of several positive integers. The order of integers within the signal is not important and therefore should not be preserved during encryption. However, there may be duplicate integers, and the number of occurrences of each integer is important and must be preserved during encryption. Gogo's idea is to encrypt these integers into a String that consists only of digits '1' and '0'. The encryption scheme is as follows:
Given integers to encrypt in int[] numbers, return the length of the shortest string that encrypts them and can be obtained according to the scheme described above. It is guaranteed that this length will not exceed 2^62.  
Definition  
 
Constraints  
  numbers will contain between 1 and 50 elements, inclusive.  
  Each element of numbers will be between 1 and 1,000,000,000, inclusive.  
  The answer will not exceed 2^62.  
Examples  
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