Limited Swaps
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Lina is playing with $$$n$$$ cubes placed in a row. Each cube has an integer from $$$1$$$ to $$$n$$$ written on it. Every integer from $$$1$$$ to $$$n$$$ appears on exactly one cube.

Initially, the numbers on the cubes from left to right are $$$a_1, a_2, \ldots, a_n$$$. Lina wants the numbers on the cubes from left to right to be $$$b_1, b_2, \ldots, b_n$$$.

Lina can swap any two adjacent cubes, but only if the difference between the numbers on them is at least $$$2$$$. This operation can be performed at most $$$20\,000$$$ times.

Find any sequence of swaps that transforms the initial configuration of numbers on the cubes into the desired one, or report that it is impossible.

Input

The first line contains a single integer $$$n$$$ — the number of cubes ($$$1 \le n \le 100$$$).

The second line contains $$$n$$$ distinct integers $$$a_1, a_2, \ldots, a_n$$$ — the initial numbers on the cubes from left to right ($$$1 \le a_i \le n$$$).

The third line contains $$$n$$$ distinct integers $$$b_1, b_2, \ldots, b_n$$$ — the desired numbers on the cubes from left to right ($$$1 \le b_i \le n$$$).

Output

If it is impossible to obtain the desired configuration of numbers on the cubes from the initial one, print a single integer $$$-1$$$.

Otherwise, in the first line, print a single integer $$$k$$$ — the number of swaps in your sequence ($$$0 \le k \le 20\,000$$$).

In the second line, print $$$k$$$ integers $$$s_1, s_2, \ldots, s_k$$$ describing the operations in order ($$$1 \le s_i \le n - 1$$$). Integer $$$s_i$$$ stands for "swap the $$$s_i$$$-th cube from the left with the $$$(s_i + 1)$$$-th cube from the left".

You do not have to find the shortest solution. Any solution satisfying the constraints will be accepted.

Examples

Input

    5
    1 3 5 2 4
    3 5 1 4 2

Output

    3
    1 2 4

Input

    4
    1 2 3 4
    4 3 2 1

Output

    -1

Note

In the first example test, the configuration of numbers changes as follows:

$$$1$$$ $$$3$$$ $$$5$$$ $$$2$$$ $$$4$$$   $$$\rightarrow$$$ $$$1$$$ $$$5$$$ $$$3$$$ $$$2$$$ $$$4$$$   $$$\rightarrow$$$   $$$5$$$ $$$1$$$ $$$3$$$ $$$2$$$ $$$4$$$   $$$\rightarrow$$$   $$$5$$$ $$$3$$$ $$$1$$$ $$$2$$$ $$$4$$$ $$$\rightarrow$$$ $$$5$$$ $$$3$$$ $$$1$$$ $$$4$$$ $$$2$$$   $$$\rightarrow$$$   $$$3$$$ $$$5$$$ $$$1$$$ $$$4$$$ $$$2$$$

In the second example test, making even a single swap in the initial configuration is impossible.