Migrated from Lutece 1142 Meet-in-the-middle

All parts of this problem, including description, images, samples, data and checker, might be broken. If you find bugs in this problem, please contact the admins.

Description

Given S, a set of integers, find the largest $d$ such that $a + b + c = d$ where $a, b, c,$ and $d$ are distinct elements of S.

Input

Several S, each consisting of a line containing an integer $1 ≤ n ≤ 1000$ indicating the number of elements in S, followed by the elements of S, in a line. Each element of S is a distinct integer between $-536870912$ and $+536870911$ inclusive. The last line of input contains $0$.

Output

For each S, a single line containing $d$, or a single line containing no solution.

Samples

5
2 3 5 7 12
5
2 16 64 256 1024
0

12
no solution

Resources

peterpan