k_53P loves to build snowmen. But his favorite type has to be arithmetic snowmen. An arithmetic snowman consists of 3 snowballs whose sizes, when arranged in a non-decreasing order, form an arithmetic sequence. For example, k_53P can make an arithmetic snowman out of snowballs of sizes 1, 3, and 5.
The size of an arithmetic snowman is the sum of the sizes of the snowballs that it's made of. k_53P has made ~N~ snowballs of varying sizes, find the largest arithmetic snowman he can make!
~3 \le N \le 100~
~1 \le size \le 100~
~3 \le N \le 3000~
~1 \le size \le 10^5~
The first line of input will contain ~N~, the number of snowballs.
The second line of input will contain ~N~ space-separated integers, the sizes of the snowballs.
One integer, the size of the largest arithmetic snowman k_53P can build. It is guaranteed that he can build at least one.
7 4 2 8 10 14 3 7
Explanation for Sample Output
k_53P will use the snowballs of sizes 2, 8 and 14 to make the snowman.