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())
al = list(map(int,input().split()))
bl = list(map(int,input().split()))

def bubble_sort(lst):
    a = 0
    for i in range(len(lst)-1):
        for j in range(len(lst)-1, i, -1):
            if lst[j-1] > lst[j]:
                tmp = lst[j]
                lst[j] = lst[j-1]
                lst[j-1] = tmp
                a += 1
    return a

anss = float("inf")
for i in range(2 ** n):
    bits = [0] * n
    for j in range(n):
        if ((i >> j) & 1):
            bits[j] = 1
    even_odd = [[], []]
    for idx, bit in enumerate(bits):
        if bit == 0:
            even_odd[(idx + bit) % 2].append((al[idx], idx))
        else:
            even_odd[(idx + bit) % 2].append((bl[idx], idx))
    if len(even_odd[0]) - len(even_odd[1]) != n % 2:
        continue
    aal = sorted(even_odd[0])
    bbl = sorted(even_odd[1])
    goto = []
    now = 0
    for k in range(n):
        if k % 2 == 0:
            tmp, idx = aal.pop(0)
            if now <= tmp:
                goto+= [idx]
                now = tmp
            else:
                break
        else:
            tmp, idx = bbl.pop(0)
            if now <= tmp:
                goto+= [idx]
                now = tmp
            else:
                break
    else:
        ans = bubble_sort(goto)
        anss = min(anss, ans)

if anss == float('inf'):
    print(-1)
else:
    print(anss)