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
input = sys.stdin.readline

class BIT:
    def __init__(self, size):
        self.bit = [0] * (size + 1)
        self.size = size

    def sum(self, i):
        i += 1
        s = 0
        while i > 0:
            s += self.bit[i]
            i -= i & -i
        return s

    def add(self, i, x):
        i += 1
        while i <= self.size:
            self.bit[i] += x
            i += i & -i

N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
ans = float('inf')
for b in range(1 << N):
    even = []
    odd = []
    for i in range(N):
        if b >> i & 1:  # red
            if i % 2 == 0:
                even.append((A[i], i))
            else:
                odd.append((A[i], i))
        else:  # blue
            if i % 2 == 0:
                odd.append((B[i], i))
            else:
                even.append((B[i], i))
    if len(even) != (N + 1) // 2 or len(odd) != N // 2:
        continue
    even.sort()
    odd.sort()
    num = []
    for i in range(len(odd)):
        num += [even[i], odd[i]]
    if N % 2 == 1:
        num += [even[-1]]
    ok = True
    for i in range(N-1):
        if num[i][0] > num[i+1][0]:
            ok = False
            break
    if not ok:
        continue
    tmp = 0
    bit = BIT(N)
    for i in range(1, N):
        bit.add(i, 1)
    for i in range(N):
        j = num[i][1]
        tmp += bit.sum(j) - i
        bit.add(0, 1)
        bit.add(j, -1)
    ans = min(ans, tmp)
print(ans if ans < float('inf') else -1)