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:
from itertools import combinations
import sys
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
a2=list()
b2=list()

if n==1:
    print(0)
    sys.exit()
    
for i in range(n):
    if i%2:
        b2.append(a[i])
        a2.append(b[i])
    else:
        a2.append(a[i])
        b2.append(b[i])

ans=10**9
for idx in combinations(range(0,n), (n+1)//2):
    a3=list()
    b3=list()
    flag=True
    for i in range(n):
        if i in idx:
            a3.append([a2[i], i])
        else:
            b3.append([b2[i], i])
    a3.sort(key=lambda x:x[0])
    b3.sort(key=lambda x:x[0])

    for i in range(len(b3)-1):
        if a3[i][0]>b3[i][0] or a3[i+1][0]<b3[i][0]:
            flag=False
    if len(a3)>len(b3):
        if a3[-1][0]<b3[-1][0] or a3[-2][0]>b3[-1][0]:
            flag=False
    elif a3[-1][0]>b3[-1][0]:
        flag=False

    if flag:
        ansidx = list()
        for i in range(len(b3)):
            ansidx.append(a3[i][1])
            ansidx.append(b3[i][1])
        if len(a3)>len(b3):
            ansidx.append(a3[-1][1])

        swap=0
        for i in range(n):
            for j in range(i,n):
                if ansidx[i]>ansidx[j]:
                    swap+=1
        ans= min(ans, swap)

if ans==10**9:
    print('-1')
else:
    print(ans)