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.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分