题目描述
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.
Examples
Input
3
3 4 3
3 2 3
Output
1
Input
2
2 1
1 2
Output
-1
Input
4
1 2 3 4
5 6 7 8
Output
0
Input
5
28 15 22 43 31
20 22 43 33 32
Output
-1
Input
5
4 46 6 38 43
33 15 18 27 37
Output
3
输入格式
见题面
输出格式
见题面