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
import itertools
INF = float("INF")

N = int(input())
AA = list(map(int, sys.stdin.readline().split()))
BB = list(map(int, sys.stdin.readline().split()))

cards = set()
for i,(a,b) in enumerate(zip(AA,BB)):
    if i%2 == 0:
        cards.add((a, b, i))
    else:
        cards.add((b, a, i))

def solve(ii):
    tmp = 0
    for i in range(N):
        for j in range(i+1,N):
            if ii[i] > ii[j]:
                tmp += 1
    return tmp

ans = INF
for Acards in itertools.combinations(cards, (N+1)//2):
    Bcards = cards - set(Acards)

    Ais = sorted([(card[0], card[2]) for card in Acards])
    Bis = sorted([(card[1], card[2]) for card in Bcards])

    bn = -1
    ii = []
    flag = False
    for i in range(N):
        if i%2 == 0:
            n,i = Ais[i//2]
        else:
            n,i = Bis[i//2]
        if bn > n: # 組み合わせた時広義単調増加になってない
            flag = True
            break
        bn = n
        ii.append(i)

    if flag: continue

    ans = min(ans,solve(ii))


if ans == INF:
    print(-1)
else:
    print(ans)