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   Problem Statement  

 Problem Statement for SpecialClique

Problem Statement

    In this problem we use "AND" to denote the bitwise-and operator. For example, (6 AND 5) = 4.



A collection C is called a clique if and only if it has the following properties:
  • C is non-empty.
  • The elements of C are positive integers. (They are not required to be distinct.)
  • Whenever x and y are two (not necessarily distinct) elements of C, the value (x AND y) is non-zero.
For example, {3}, {1,1,1}, {16,17,18,19}, and {3,6,5} are cliques, but {3,5,20} is not a clique because (3 AND 20) = 0.



A clique is called trivial if the bitwise-and of all its elements is non-zero. A clique that is not trivial is called special.



For example, the cliques {3}, {1,1,1} and {16,17,18,19} are trivial, and the cliques {3,6,5} and {3,3,6,5,6} are special.



You are given a long[] s that contains a collection of positive integers. We want to change s into a special clique by erasing some (possibly none, but not all) of its elements. Return "Possible" if this can be done, or "Impossible" if it cannot be done.
 

Definition

    
Class:SpecialClique
Method:exist
Parameters:long[]
Returns:String
Method signature:String exist(long[] s)
(be sure your method is public)
    
 

Constraints

-s will contain between 1 and 1,000 elements, inclusive.
-Each element in s will be between 1 and 1,000,000,000,000,000,000 (10^18) inclusive.
 

Examples

0)
    
{3,6,5,8,24,56}
Returns: "Possible"
We can erase the last three elements of s, producing the special clique {3,6,5}.
1)
    
{6, 5, 8, 24, 56}
Returns: "Impossible"
Each clique we can produce from this s is a trivial clique.
2)
    
{585858585858585858, 585858585858585858, 585858585858585858, 585858585858585858}
Returns: "Impossible"
Note that s may contain duplicates.
3)
    
{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47}
Returns: "Impossible"
4)
    
{1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597}
Returns: "Possible"

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This problem was used for:
       2016 TCO Algorithm Algo Semifinal 2 - Division I, Level One