201102: [AtCoder]ARC110 C - Exoswap

Problem Statement

We have a permutation $P = P_1, P_2, \ldots, P_N$ of $1, 2, \ldots, N$.

You have to do the following $N - 1$ operations on $P$, each exactly once, in some order:

• Swap $P_1$ and $P_2$.

• Swap $P_2$ and $P_3$.

  $\vdots$

• Swap $P_{N-1}$ and $P_N$.

Your task is to sort $P$ in ascending order by configuring the order of operations. If it is impossible, print -1 instead.

Constraints

• All values in input are integers.
• $2 \leq N \leq 2 \times 10^5$
• $P$ is a permutation of $1, 2, \ldots, N$.

Input

Input is given from Standard Input in the following format:

$N$
$P_1$ $P_2$ $\ldots$ $P_N$

Output

If it is impossible to sort $P$ in ascending order by configuring the order of operations, print -1.

Otherwise, print $N-1$ lines to represent a sequence of operations that sorts $P$ in ascending order. The $i$-th line $(1 \leq i \leq N - 1)$ should contain $j$, where the $i$-th operation swaps $P_j$ and $P_{j + 1}$.

If there are multiple such sequences of operations, any of them will be accepted.

Sample Input 1

5
2 4 1 5 3

Sample Output 1

4
2
3
1

The following sequence of operations sort $P$ in ascending order:

• First, swap $P_4$ and $P_5$, turning $P$ into $2, 4, 1, 3, 5$.
• Then, swap $P_2$ and $P_3$, turning $P$ into $2, 1, 4, 3, 5$.
• Then, swap $P_3$ and $P_4$, turning $P$ into $2, 1, 3, 4, 5$.
• Finally, swap $P_1$ and $P_2$, turning $P$ into $1, 2, 3, 4, 5$.

Sample Input 2

5
5 4 3 2 1

Sample Output 2

-1