Score : $700$ points

Problem Statement

We have $N$ cards numbered $1, 2, ..., N$. Card $i$ ($1 \leq i \leq N$) has an integer $A_i$ written in red ink on one side and an integer $B_i$ written in blue ink on the other side. Initially, these cards are arranged from left to right in the order from Card $1$ to Card $N$, with the red numbers facing up.

Determine whether it is possible to have a non-decreasing sequence facing up from left to right (that is, for each $i$ ($1 \leq i \leq N - 1$), the integer facing up on the $(i+1)$-th card from the left is not less than the integer facing up on the $i$-th card from the left) by repeating the operation below. If the answer is yes, find the minimum number of operations required to achieve it.

• Choose an integer $i$ ($1 \leq i \leq N - 1$). Swap the $i$-th and $(i+1)$-th cards from the left, then flip these two cards.

Constraints

• $1 \leq N \leq 18$
• $1 \leq A_i, B_i \leq 50$ ($1 \leq i \leq N$)
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $...$ $A_N$

$B_1$ $B_2$ $...$ $B_N$

Output

If it is impossible to have a non-decreasing sequence, print -1. If it is possible, print the minimum number of operations required to achieve it.

3
3 4 3
3 2 3

1

By doing the operation once with $i = 1$, we have a sequence $[2, 3, 3]$ facing up, which is non-decreasing.

2
2 1
1 2

-1

After any number of operations, we have the sequence $[2, 1]$ facing up, which is not non-decreasing.

4
1 2 3 4
5 6 7 8

0

No operation may be required.

5
28 15 22 43 31
20 22 43 33 32

-1

5
4 46 6 38 43
33 15 18 27 37

3