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 itertools
n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))

odds = []
evens = []
for i in range(n):
    if i%2 == 0:
        odds.append([a[i],i])
        evens.append([b[i],i])
    else:
        odds.append([b[i],i])
        evens.append([a[i],i])

odds = sorted(odds)
evens = sorted(evens)
#print("odss =",odds)
#print("evens =",evens)

inds = [i for i in range(n)]

ans = 10000000000
exist = 0
#print("開始")
half = (n-1)//2 + 1
for v in  itertools.combinations(inds,half):
    #print("start")

    #print(v)
    real_v = [odds[i][1] for i in v]
    #vに入らなかった方を生成する
    real_nokori = []

    for i in range(n):
        if not (evens[i][1] in real_v):
            real_nokori.append(evens[i][1])
    
    nokori = []
    for i in range(n):
        if evens[i][1] in real_nokori:
            nokori.append(i)

    #print(v,nokori)


    moge = 1
    if n%2 == 0:
        for i in range(half):
                if evens[nokori[i]][0] < odds[v[i]][0]:
                    moge = 0
    else:
        for i in range(n-half):
                if evens[nokori[i]][0] < odds[v[i]][0]:
                    moge = 0

    for i in range(half-1):
        if evens[nokori[i]][0] > odds[v[i+1]][0]:
            moge = 0

    if moge != 1:
        continue
    else:
        exist = 1

    tar = []
    for i in range(n):
        if i%2 == 0:
            tar.append(real_v[i//2])
        else:
            tar.append(real_nokori[(i-1)//2])
    dist = 0
    for i in range(n):
        for mo in range(i+1,n):
            if tar[mo] < tar[i]:
                dist += 1
    if dist < ans:
        ans = dist
if exist:
    print(ans)
else:
    print(-1)