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
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

import itertools

N = int(readline())
A = list(map(int,readline().split()))
B = list(map(int,readline().split()))

class BinaryIndexedTree():
    def __init__(self, seq):
        self.size = len(seq)
        self.depth = self.size.bit_length()
        self.build(seq)
        
    def build(self,seq):
        data = seq
        size = self.size
        for i,x in enumerate(data):
            j = i+(i&(-i))
            if j < size:
                data[j] += data[i]
        self.data = data
        
    def __repr__(self):
        return self.data.__repr__()
        
    def get_sum(self,i):
        data = self.data
        s = 0
        while i:
            s += data[i]
            i -= i & -i
        return s
 
    def add(self, i, x):
        data = self.data
        size = self.size
        while i < size:
            data[i] += x
            i += i & -i
    
    def find_kth_element(self,k):
        data = self.data; size = self.size
        x,sx = 0,0
        dx = 1 << (self.depth)
        for i in range(self.depth - 1, -1, -1):
            dx = (1 << i)
            if x + dx >= size:
                continue
            y = x + dx
            sy = sx + data[y]
            if sy < k:
                x,sx = y,sy
        return x + 1

def Inversion(seq):
    # seqは、1,2,...,Nの順列
    N = len(seq)
    bit = BinaryIndexedTree([0] * (N+1))
    inv = N*(N-1)//2
    for x in seq:
        inv -= bit.get_sum(x)
        bit.add(x,1)
    return inv

INF = 10 ** 9
answer = INF
for I in itertools.combinations(range(N),(N+1)//2):
    J = [j for j in range(N) if j not in I]
    ODD = [(B[i] if i&1 else A[i],i) for i in I]
    EV = [(A[i] if i&1 else B[i],i) for i in J]
    ODD.sort()
    EV.sort()
    ind = [0] * N
    seq = [0] * N
    for i in range(0,N,2):
        seq[i], ind[i] = ODD[i//2]
    for i in range(1,N,2):
        seq[i], ind[i] = EV[i//2]
    if not all(x<= y for x,y in zip(seq,seq[1:])):
        continue
    ind = [x+1 for x in ind]
    n = Inversion(ind)
    if answer > n:
        answer = n

if answer == INF:
    answer = -1
print(answer)