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:
def iter_bit(k, LIMIT):
    v = (1 << k) - 1

    while v < LIMIT:
        yield v
        x = v & -v
        y = v + x
        v = (v & ~y) // x >> 1 | y


def solve(n, cards):
    dp = [{} for _ in range(1 << n)]
    dp[-1][0] = 0
    LIMIT = 1 << n

    for d in range(n):
        for state in iter_bit(n - d, LIMIT):
            scores = dp[state]
            k = state
            curr = 0
            while k:
                b = k & -k
                i = b.bit_length() - 1
                num = cards[i][(d - i) % 2]
                next_dp = dp[state ^ b]
                for left_num, score in scores.items():
                    if left_num > num:
                        continue
                    ns = score + curr
                    if num not in next_dp or next_dp[num] > ns:
                        next_dp[num] = ns
                k ^= b
                curr += 1

    if len(dp[0]) > 0:
        return min(dp[0].values())
    else:
        return -1


n = int(input())
aaa = list(map(int, input().split()))
bbb = list(map(int, input().split()))
cards = list(zip(aaa, bbb))
print(solve(n, cards))