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.

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.

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.

Sample Input 1

4
3 4 8 6
5 3 1 3
3 4 2 1

Sample Output 1

3
3 4
1 3
4 2

Initially, People 1, 2, 3, 4 has pieces of baggage with weights 1, 3, 3, 5, respectively, so no one is tired.
First, we do the operation choosing Person 3 and 4. Now, people 1, 2, 3, 4 has pieces of baggage with weights 1, 3, 5, 3, so no one is tired yet.
Second, we do the operation choosing Person 1 and 3. Now, people 1, 2, 3, 4 has pieces of baggage with weights 5, 3, 1, 3, so Person 1 gets tired.
Lastly, we do the operation choosing Person 4 and 2. Now, people 1, 2, 3, 4 has pieces of baggage with weights 5, 3, 1, 3, so no one gets tired.
This sequence of operations has made everyone have the right piece of baggage, with the minimum possible number of operations, so it is valid.

Sample Input 2

4
1 2 3 4
4 3 2 1
4 3 2 1

Sample Output 2

-1

No sequence of operations achieves the objective.

Sample Input 3

1
58
998244353
1

Sample Output 3

0

The objective is already achieved in the initial state.

见题面 Input 部分

见题面 Output 部分