As an experiment the Educational Codeforces Round 33 will be rated for Div. 2.
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A. Worms Evolution

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputProfessor Vasechkin is studying evolution of worms. Recently he put forward hypotheses that all worms evolve by division. There are *n* forms of worms. Worms of these forms have lengths *a*_{1}, *a*_{2}, ..., *a*_{n}. To prove his theory, professor needs to find 3 different forms that the length of the first form is equal to sum of lengths of the other two forms. Help him to do this.

Input

The first line contains integer *n* (3 ≤ *n* ≤ 100) — amount of worm's forms. The second line contains *n* space-separated integers *a*_{i} (1 ≤ *a*_{i} ≤ 1000) — lengths of worms of each form.

Output

Output 3 distinct integers *i* *j* *k* (1 ≤ *i*, *j*, *k* ≤ *n*) — such indexes of worm's forms that *a*_{i} = *a*_{j} + *a*_{k}. If there is no such triple, output -1. If there are several solutions, output any of them. It possible that *a*_{j} = *a*_{k}.

Examples

Input

5

1 2 3 5 7

Output

3 2 1

Input

5

1 8 1 5 1

Output

-1

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

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