Problem Statement

A Kadomatsu sequence is defined as follows: when 3 integers are arranged as A, B, C from the left,
they form a Kadomatsu sequence if all the values are distinct and the second largest integer among A, B, C is either A or C.

D and E play the Kadomatsu game using these Kadomatsu sequences.
Initially, N positive integers are arranged in a horizontal row.
First, among the N integers, choose the a-th integer X, the b-th integer Y, and the c-th integer Z from the left $(a \lt b \lt c)$.
If X, Y, Z form a Kadomatsu sequence, D can erase these 3 integers.
The 3 integers erased in this way cannot be used afterwards.
This operation is repeated in the same way alternately, with D moving first, in the order E, D, ...
In the Kadomatsu game, the player who cannot form a Kadomatsu sequence and thus cannot erase integers loses.

Both D and E make the best choices in order to win.
What first move should D, the first player, choose in order to win for certain?
Answer with the positions from the left of the three integers (0-indexed).
If there are multiple answers, output the lexicographically smallest one among them.
If D cannot win, output -1.

Input

$N$
$K_0\ K_1\ \dots\ K_{N-1}$

N is the number of positive integers. $3\le N \le 12$.
$K_i$ is the value of the i-th positive integer from the left. $1\le K_i \le 20$.

Output

When the lexicographically smallest first move with which D wins is the a-th, b-th, and c-th integers from the left $(a< b < c)$,
output the answer on one line in the form "a b c", with a half-width space between the numbers.
If D cannot win no matter what, output "-1" on one line.
Do not forget the newline at the end.

Sample

6
2 3 5 7 4 1

0 4 5

5
1 2 3 4 5

-1

12
5 1 13 10 12 12 12 3 9 13 17 18

-1