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-----
5
2 4 1 5 3

-----Sample Output-----
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.

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