Problem E
Exchange Students

Silhouettes via Freepik

Determine the minimum number of exchanges needed to arrange the students in the photographer’s preferred order, and find a suitable sequence of exchanges of this minimal length. The photographer only has time for at most $2\cdot 10^5$ exchanges. If more are needed, you only need to determine the first $2\cdot 10^5$ exchanges.

Input

The input consists of:

• One line with an integer $n$ ($1\leq n \leq 3\cdot 10^5$), the number of students.

• One line with $n$ integers $g_1, g_2, \ldots , g_ n$ ($1\leq g_ i\leq 10^9$), the heights of the students.

• One line with $n$ integers $h_1, h_2, \ldots , h_ n$ ($1\leq h_ i\leq 10^9$), the order of heights the photographer prefers.

It is guaranteed that $(h_1, \ldots , h_ n)$ is a permutation of $(g_1, \ldots , g_ n)$.

Output

First output an integer $s$, the minimum number of exchanges needed. Then print $\min (s, 2\cdot 10^5)$ exchanges, each consisting of two integers $i$ and $j$, the one-based positions of the students that must be exchanged in this step.

If there are multiple valid solutions, you may print any one of them.

3
2 1 3
3 1 2

1
1 3

5
6 7 5 9 6
9 6 7 6 5

4
3 4
4 5
1 2
1 3