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Byteasar the hacker has qualified for this yearâs IHO, the International Hacking Olympiad. One of the tasks in the Olympiad involves competing against a system operator. There are computers numbered from 1 to , connected in a ring topology, i.e. computers and are connected (for ), and also computers and 1 are connected.
The competition is performed as a game between the hacker and the system operator:
At the beginning of the game none of the computers are hacked or protected.
Every computer has a certain value which specifies the value of the data which is stored on it. For each hacked computer , Byteasar scores its value . Byteasar is quite a good hacker, but has no idea of algorithms. That is why he asks you to write a program that computes his maximum possible score, assuming that the operator plays optimally.
The first line of input contains a positive integer (), specifying the number of computers. The second line contains a sequence of integers (); number specifies the value of the data stored on computer .
In the first and only line of output your program should write one integer: Byteasar's maximum possible score against an optimally playing operator.
For the input data:
4 7 6 8 4
the correct result is:
13
For the input data:
5 1 1 1 1 1
the correct result is:
3
Explanation to the examples: In the first example, Byteasar in his first move should hack computer 2 (scoring 6). The operator's response will be protecting computer 3. In the next move Byteasar can hack computer 1 (scoring 7). Finally, the operator will protect computer 4.
Subtask | Conditions | Points |
1 | 20 | |
2 | 20 | |
3 | , hacking computer 1 is optimal as Byteasar's first move | 20 |
4 | 40 |