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 itertools import combinations

def solve():
    INF = 10**5

    def getNumInversion(odrAs):
        def makeBIT(numEle):
            numPow2 = 2 ** (numEle-1).bit_length()
            data = [0] * (numPow2+1)
            return data, numPow2
        def addValue(iA, A):
            iB = iA + 1
            while iB <= numPow2:
                data[iB] += A
                iB += iB & -iB
        def getSum(iA):
            iB = iA + 1
            ans = 0
            while iB > 0:
                ans += data[iB]
                iB -= iB & -iB
            return ans
        lenA = len(odrAs)
        data, numPow2 = makeBIT(lenA)
        ans = 0
        for odrA in reversed(odrAs):
            ans += getSum(odrA)
            addValue(odrA, 1)
        return ans

    N = int(input())
    As = list(map(int, input().split()))
    Bs = list(map(int, input().split()))

    ans = INF
    for iEvens in combinations(range(N), r=N//2):
        iEvens = set(iEvens)
        COdds, CEvens = [], []
        for i in range(N):
            if i in iEvens:
                if i % 2:
                    CEvens.append((As[i], i))
                else:
                    CEvens.append((Bs[i], i))
            else:
                if i % 2:
                    COdds.append((Bs[i], i))
                else:
                    COdds.append((As[i], i))
        COdds.sort()
        CEvens.sort()

        Cs = []
        for COdd, CEven in zip(COdds, CEvens):
            Cs += [COdd, CEven]
        if N % 2:
            Cs += [COdds[-1]]

        for i in range(N-1):
            if Cs[i][0] > Cs[i+1][0]:
                break
        else:
            odrAs = [i for C, i in Cs]
            num = getNumInversion(odrAs)
            ans = min(ans, num)
            if ans == 0:
                break

    if ans == INF:
        print(-1)
    else:
        print(ans)


solve()