Problem Statement

There are $N$ people numbered $1$ to $N$ and $N$ pieces of baggage numbered numbered $1$ to $N$. Person $i$ has a weight of $a_i$, and Baggage $j$ has a weight of $b_j$. Initially, Person $i$ has Baggage $p_i$. We want to do the operation below zero or more times so that each Person $i$ will have Baggage $i$.

• Choose $i,j (i \neq j)$, and swap the baggages of Person $i$ and Person $j$.

However, when a person has a piece of baggage with a weight greater than or equal to his/her own weight, the person gets tired and becomes unable to take part in a future operation (that is, we cannot choose him/her as Person $i$ or $j$). Particularly, if $a_i \leq b_{p_i}$, Person $i$ cannot take part in any operation.

Determine whether there is a sequence of operations that achieves the objective, and if so, construct one such sequence with the minimum possible number of operations.

Constraints

• $1 \leq N \leq 200000$
• $1 \leq a_i,b_i \leq 10^9$
• $p$ is a permutation of $1, \ldots, N$.
• All numbers in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 \ldots a_N
b_1 b_2 \ldots b_N
p_1 p_2 \ldots p_N

Output

If no sequence of operations achieves the objective, print -1. Otherwise, print a sequence of operations in the following format:

K
i_1 j_1
i_2 j_2
:
i_K j_K

Here, $K$ is the number of operations, and $i_t, j_t$ represent the people chosen in the $t$-th operation.

If there are multiple solutions, any of them will be accepted.