Problem Statement

Orion is going to perform a choral piece. For this purpose, he has decided to determine the key of the piece. Analyzing the piece, he found that it uses a major scale and consists of the notes $T_1, T_2, \dots, T_N$. Determine the key of this piece and print the integer at least $0$ and less than $12$ that represents the key. If no such integer exists, or if more than one exists, print $-1$ instead. Here, when the key is $D$, the notes contained in the major scale are $\{ D, D+2, D+4, D+5, D+7, D+9, D+11 \} \pmod{12}$.

(Added 2020/07/10 22:07) When the key is $D$, the only notes that may be used are $D, D+2, D+4, D+5, D+7, D+9, D+11$, and it is possible that not all of them are used.

Input

$N$
$T_1\ T_2\ \dots\ T_N$

All inputs are integers.
$1 \le N \le 12$
$0 \le T_i < 12$
If $i < j$, then $T_i < T_j$

Output

If the key can be uniquely determined, print the integer at least $0$ and less than $12$ that represents the tonic of that key; otherwise, print $-1$. Print a newline at the end.

Sample

5
0 2 6 7 11

7

3
2 6 10

-1

5
0 2 4 7 9

-1