Problem Statement

We have a permutation $P = P_0, P_1, \ldots, P_{N - 1}$ of $0, 1, \ldots, N - 1$.

You can do the following operation on $P$ at most $2 \times 10^5$ times:

• Announce an integer $i ~ (0 \leq i \leq N - 1)$. Swap $P_i$ and $P_{(i + P_i) \textrm{ mod } N}$.

Your task is to sort $P$ in ascending order with this operation. If it is impossible, print -1 instead.

Constraints

• All values in input are integers.
• $2 \leq N \leq 100$
• $P$ is a permutation of $0, 1, \ldots, N - 1$.

Input

Input is given from Standard Input in the following format:

N
P_0 P_1 \ldots P_{N - 1}

Output

If it is impossible to sort $P$ in ascending order with at most $2 \times 10^5$ operations, print -1.

Otherwise, print $K + 1$ lines to represent a sequence of operations that sorts $P$ in ascending order, where $K$ is the number of operations done, as follows:

• The first line should contain the integer $K$;
• the $(1 + i)$-the line $(1 \leq i \leq K)$ should contain the integer $j ~ (0 \leq j \leq N - 1)$ announced in the $i$-th operation.

You do not have to minimize the number of operations done. If there are multiple such sequences of at most $2 \times 10^5$ operations, any of them will be accepted.