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
input=sys.stdin.readline
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
ans=10**9
def bubble_sort(arr):
    change = True
    num=0
    while change:
        change = False
        for i in range(len(arr) - 1):
            if arr[i] > arr[i + 1]:
                arr[i], arr[i + 1] = arr[i + 1], arr[i]
                change = True
                num+=1
    return num
for i in range(2**n):
    even=[]
    odd=[]
    for j in range(n):
        x=(i>>j)%2
        if j%2==0:
            if x==0:
                even.append((a[j],j))
            else:
                odd.append((b[j],j))
        else:
            if x==0:
                odd.append((a[j],j))
            else:
                even.append((b[j],j))
    if len(odd)!=n//2:
        continue
    even.sort()
    odd.sort()
    check=True
    order=[]
    new=[]
    for j in range(n//2):
        order.append(even[j][1])
        order.append(odd[j][1])
        new.append(even[j][0])
        new.append(odd[j][0])
    if n%2!=0:
        new.append(even[-1][0])
        order.append(even[-1][1])
    for j in range(n-1):
        if new[j]>new[j+1]:
            check=False
    if not check:
        continue
    x=bubble_sort(order)
    ans=min(ans,x)
if ans==10**9:
    print(-1)
else:
    print(ans)