Restoring a Permutation

Today Christopher studied sequences and permutations at school. A permutation of the numbers 1 to $n$ is a sequence $a_1, \ldots, a_n$ in which each of these numbers appears exactly once.

Christopher especially liked these definitions:

• A descent at position $i$ in a permutation $\langle a_1, a_2, \ldots, a_n \rangle$ is a case where $a_i > a_{i+1}$.
• A fixed point at position $i$ in a permutation $\langle a_1, a_2, \ldots, a_n \rangle$ is an element $a_i$ such that $a_i = i$.

Christopher made up his own permutation and called it a Robin permutation. A permutation $A = \langle a_1, a_2, \ldots, a_{2n} \rangle$ of the numbers 1 to $2n$ is a Robin permutation if both of the following hold:

• $A$ has exactly $n$ descents, and all of them are at odd positions. That is, $a_{2i-1} > a_{2i} < a_{2i+1}$ for every $i$.
• $A$ has exactly $n$ fixed points.

For example, $\langle 3, 2, 6, 4, 5, 1 \rangle$ is a Robin permutation.

Christopher shared his discovery with Rabbit. After learning about Robin permutations, Rabbit came up with this transformation: remove all fixed points from the sequence, then replace each remaining number with the count of numbers in the remaining sequence that are not greater than it. For example, $\langle 3, 2, 6, 4, 5, 1 \rangle \to \langle 3, 6, 1 \rangle \to \langle 2, 3, 1 \rangle$.

Christopher now wants to take a transformed permutation and find a Robin permutation that transforms into it.

The first line contains $n$, the number of elements in the transformed permutation ($1 \le n \le 100\,000$). The second line contains $n$ natural numbers, the transformed permutation.

If no solution exists, print $-1$ on the first line. If a Robin permutation exists, print one. If there are several, print any Robin permutation.