Problem:
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.

Sample Input 1

3
3 4 3
3 2 3

Sample Output 1

1

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

Sample Input 2

2
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 3

4
1 2 3 4
5 6 7 8

Sample Output 3

0

No operation may be required.

Sample Input 4

5
28 15 22 43 31
20 22 43 33 32

Sample Output 4

-1

Sample Input 5

5
4 46 6 38 43
33 15 18 27 37

Sample Output 5

3

Solution in PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import sys
from itertools import combinations
input = sys.stdin.readline
n = int(input())
a = [int(x) for x in input().strip().split()]
b = [int(x) for x in input().strip().split()]

all_cards = []
for i, (aa, bb) in enumerate(zip(a, b)):
    all_cards.append((aa, bb, i))

def check(cards):
    pre = -1
    for c in cards:
        print(c)
        if c[0] >= pre:
            pre = c[0]
        else:
            return False
    else:
        return True

def cnt(l):
    ret = 0
    for i in range(len(l)-1):
        for j in range(i+1, len(l)):
            if l[i] > l[j]:
                ret += 1
    return ret

dic = {}
def dp(all_cards, l, p):
    i = len(l) + 1
    if len(l) == n:
        return cnt(l)
    ret = float('inf')
    for card in all_cards:
        if card[2] not in l and card[0] < p and card[1] < p:
            return ret
    for card in all_cards:
        if card[2] in l:
            continue
        if card[(i-(card[2]+1))%2] >= p:
            ret = min(ret, dp(all_cards - set(card), l+[card[2]], card[(i-(card[2]+1))%2]))
    dic[tuple(l)] = ret
    return ret

ans = dp(set(all_cards), [], -float('inf'))
if ans == float('inf'):
    ans = -1
print(ans)