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 Counter,defaultdict,deque
from heapq import heappop,heappush,heapify
import sys,bisect,math,itertools,fractions,pprint
sys.setrecursionlimit(10**8)
mod = 10**9+7
mod2 = 998244353
INF = float('inf')
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def inpln(n): return list(int(sys.stdin.readline()) for i in range(n))

def swap(l):
    cnt = 0
    for i in range(n):
        for j in range(i,n):
            if l[i]>l[j]:
                cnt += 1
    return cnt
n = inp()
a = inpl()
b = inpl()
card = []
res = INF
for i in range(n):
    card.append([a[i],b[i],i])
for flag in itertools.combinations(range(n),(n+1)//2):
    f = True
    odd_li = []
    odd_ind = [False] * n
    for i,bit in enumerate(flag):
        c = 1 if bit%2 else 0
        odd_li.append([card[bit][c],bit])
        odd_ind[bit] = True
    if not f:
        continue
    odd_li.sort()
    even_li = []
    for i in range(n):
        c = 0 if i%2 else 1
        if not odd_ind[i]:
            even_li.append([card[i][c],i])
    even_li.sort()
    if n%2:
        for i in range(n//2):
            if odd_li[i][0] <= even_li[i][0] <= odd_li[i+1][0]:
                continue
            else:
                f = False; break
    else:
        for i in range(n//2):
            if i != n//2-1:
                if odd_li[i][0] <= even_li[i][0] <= odd_li[i+1][0]:
                    continue
                else:
                    f = False; break
            else:
                if odd_li[-1][0] <= even_li[-1][0]:
                    continue
                else:
                    f = False; break
    if f:
        after_ind = []
        for i in range(n//2):
            after_ind.append(odd_li[i][1])
            after_ind.append(even_li[i][1])
        if n%2:
            after_ind.append(odd_li[-1][1])
        res = min(res,swap(after_ind))
print(-1 if res == INF else res)