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 collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,copy,time
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def inpl_str(): return list(sys.stdin.readline().split())


N = inp()
AA = inpl()
BB = inpl()

# In[]:
# N = 3
# AA = [3, 4, 3]
# BB = [3, 2, 3]

cards = []
for i,(a,b) in enumerate(zip(AA,BB)):
    if i%2 == 0:
        cards.append((a, b, i))
    else:
        cards.append((b, a, i))


n = (N+1)//2

# In[]:
def solve(ii):
    tmp = 0
    # print(ii)
    for _ in range(N):
        next = []
        for k, i in enumerate(ii):
            if i == 0:
                tmp += k
            else:
                next.append(i-1)
        ii = next[:]
    # print(tmp)
    return tmp



# In[]:
ans = INF
for Acards in itertools.combinations(cards, n):
    Ais = sorted([(Acard[0], Acard[2]) for Acard in Acards])

    ii = set([i for A,i in Ais])
    Bis = []
    for a,b,i in cards:
        if i not in ii:
            Bis.append((b,i))
    Bis.sort()

    nums = []
    ii = []
    for i in range(N):
        if i%2 == 0:
            n,i = Ais[i//2]
        else:
            n,i = Bis[i//2]
        nums.append(n)
        ii.append(i)

    # print(nums,ii)
    if nums != sorted(nums):
        continue
    else:
        ans = min(ans,solve(ii))
        if ans == 0:
          print(0)
          sys.exit()


if ans == INF:
    print(-1)
else:
    print(ans)