Problem: 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

Solution (in PYTHON3):

Solution:
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)):
    if i % 2:
        aa, bb = bb, aa
    all_cards.append([aa, bb, i])

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

ans = float('inf')
for cards in combinations(all_cards, (n + 1)// 2):
    acards = []
    for card in cards:
        acards.append([card[0],card[2]])
    bcards = []
    for card in all_cards:
        if [card[0],card[2]] not in acards:
            bcards.append([card[1],card[2]])

    acards.sort()
    bcards.sort()
    abcards = []
    # print(acards, bcards)
    for i in range(len(bcards)):
        abcards.extend([acards[i], bcards[i]])
    else:
        if n % 2:
            abcards.append(acards[-1])
    # print(abcards)
    if abcards != sorted(abcards, key=lambda x: x[0]):
        continue
    ans = min(ans, cnt(abcards))

if ans == float('inf'):
    ans = -1
print(ans)