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:
N = int(input())
A = [int(a) for a in input().split()]
B = [int(b) for b in input().split()]

L = [[0]*2 for _ in range(N)]

for i in range(N):
    L[i][i%2] = A[i]
    L[i][(i+1)%2] = B[i]

P = [int(i) for i in range(N)]

ans = 10**10
import itertools
for C in itertools.combinations(P, (N+1)//2):
    C = list(C)
    used = [0]*N
    for i in C:
        used[i] = 1
    B_temp = []
    for i in range(N):
        if used[i] == 0:
            B_temp.append((L[i][1], i))

    temp = [0]*N
    check = [0]*N
    B_temp.sort()
    for i in range(len(C)):
        C[i] = (L[C[i]][0], C[i])
    C.sort()
    j = 0
    k = 0
    for i in range(N):
        if i%2 == 0:
            temp[i] = C[j][1]
            check[i] = C[j][0]
            j += 1
        else:
            temp[i] = B_temp[k][1]
            check[i] = B_temp[k][0]
            k += 1
    if check != sorted(check):
        continue

    cnt = 0
    for i in reversed(range(N)):
        for j in range(i):
            if temp[j] > temp[j + 1]:
                temp[j], temp[j + 1] = temp[j + 1], temp[j]
                cnt += 1

    ans = min(ans, cnt)

if ans == 10**10:
    ans = -1
print(ans)