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

def main():

    n = int(input())
    a = list(map(int, input().split()))
    b = list(map(int, input().split()))

    if all(a[0] == a[i] for i in range(n)):
        print(0)
        exit()

    pre = [1<<i for i in range(n)]
    bitcnt = [0]*(1<<n)
    bitcnt[1] = 1
    for i in range(1<<(n-1)):
        bitcnt[2*i] = bitcnt[i]
        bitcnt[2*i+1] = bitcnt[i]+1

    DP = [defaultdict(lambda : float("inf")) for i in range(n)]

    for i in range(n):
        DP[i][1<<i] = 0
    s = defaultdict(lambda : float("inf"))
    for i in range(n-1):
        nxt = [defaultdict(lambda : float("inf")) for i in range(n)]
        for j in range(n):
            last = a[j] if (i-j)%2 == 0 else b[j]
            for state, cost in DP[j].items():
                for to in range(n):
                    if state>>to&1:
                        continue
                    nlast = a[to] if (i+1-to)%2 == 0 else b[to]
                    if last > nlast:
                        continue
                    nstate = state|pre[to]
                    ncost = cost
                    ncost += bitcnt[state>>to]
                    if s[(nstate, nlast)] <= ncost:
                        continue
                    s[(nstate, nlast)] = ncost
                    if nxt[to][nstate] > ncost:
                        nxt[to][nstate] = ncost
        DP = nxt
    mask = (1<<n)-1
    ans = float("inf")
    for i in range(n):
        ans = min(ans, DP[i][mask])
    if ans == float("inf"):
        print(-1)
    else:
        print(ans)

if __name__ == "__main__":
    main()