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
import queue
bbn=1000000007
	
#+++++

def is_ok(ll):
	for i,next in zip(ll,ll[1:]):
		if i > next:
			return False
	return True
	
def mkhash(al,bl):
	return '_'.join([str(v) for v in al])+'__'+'_'.join([str(v) for v in bl])
	
	
def main():
	n = int(input())
	al = list(map(int, input().split()))
	bl = list(map(int, input().split()))
	if is_ok(al):
		print(0)
		return 
		
	closed_list=set()
	open_list=queue.Queue()
	open_list.put((al,bl,0))
	closed_list.add(mkhash(al,bl))
	
	while not open_list.empty():
		cc, rv, nn = open_list.get()
		for i in range(n-1):
			tcc=cc[:]
			trv=rv[:]
			tcc[i]=rv[i+1]
			tcc[i+1]=rv[i]
			trv[i]=cc[i+1]
			trv[i+1]=cc[i]
			if mkhash(tcc,trv) in closed_list:
				continue
			if is_ok(tcc):
				return nn+1
			open_list.put((tcc,trv,nn+1))
			closed_list.add(mkhash(tcc,trv))
	
	print(-1)
	
	
#+++++
isTest=False

def pa(v):
	if isTest:
		print(v)

if __name__ == "__main__":
	if sys.platform =='ios':
		sys.stdin=open('inputFile.txt')
		isTest=True
	else:
		pass
		#input = sys.stdin.readline
			
	ret = main()
	if ret is not None:
		print(ret)