Binary Casino is a very special skyscraper building consisting of
The floor connections are designed in a way that if there is an escalator going from floor
Your manager decided to organize a promotion game to attract more customers. The game has the following rules:
- The game is played in one or more rounds.
- In each round, a customer can choose a floor
on which that round starts. At this moment he earns some fixed number of tokens associated with floor . Then he may move to other floors using escalators. - If a customer decides to take an escalator from floor
to floor and has tokens he has to pay tokens to enter floor , whereAND
is a bitwise AND operator, is a standard minus operator on numbers, and is a number of tokens associated with floor . - A customer can decide to stop the round on any floor (including
) and keep the tokens from that round. Then he can start a new round from any floor if it is possible. - No two rounds may have the same pair of starting and ending floors, not even in the opposite direction, i.e. when considering exchanged starting and ending floors.
Your manager is curious about the maximum number of tokens a customer can earn in the game.
Input Specification
The first line of input contains an integer
Output Specification
Output a single number – the maximum number of tokens a customer can earn.
Sample Input 1
4
1 2 2 1
0 1
1 2
2 3
Sample Output 1
8
Sample Input 2
5
7 3 5 6 7
0 1
1 2
2 3
2 4
Sample Output 2
48
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