
Score : 700 points
Problem StatementWe 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.
InputInput is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
OutputIf 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.
Sample Input 13
3 4 3
3 2 3
Sample Output 11
By doing the operation once with i = 1, we have a sequence [2, 3, 3] facing up, which is non-decreasing.
Sample Input 22
2 1
1 2
Sample Output 2-1
After any number of operations, we have the sequence [2, 1] facing up, which is not non-decreasing.
Sample Input 34
1 2 3 4
5 6 7 8
Sample Output 30
No operation may be required.
Sample Input 45
28 15 22 43 31
20 22 43 33 32
Sample Output 4-1
Sample Input 55
4 46 6 38 43
33 15 18 27 37
Sample Output 53
