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

o=N//2
e=N-o

import itertools
E=[]
O=[]
for i in range(N):
    if i%2==0:
        E.append(i)
    else:
        O.append(i)
ANS=10000

def mergecount(Z):
    cnt1 = 0
    z = len(Z)
    if z>1:
        A1 = Z[:z>>1]
        A2 = Z[z>>1:]
        cnt1 += mergecount(A1)
        cnt1 += mergecount(A2)
        i1=0
        i2=0
        for i in range(z):
            if i2 == len(A2):
                Z[i] = A1[i1]
                i1 += 1
            elif i1 == len(A1):
                Z[i] = A2[i2]
                i2 += 1
            elif A1[i1] <= A2[i2]:
                Z[i] = A1[i1]
                i1 += 1
            else:
                Z[i] = A2[i2]
                i2 += 1
                cnt1 += z//2 - i1
    return cnt1

for i in range(o+1):
    X=list(itertools.combinations(E,i))
    Y=list(itertools.combinations(O,i))
    for j in range(len(X)):
        for k in range(len(Y)):
            ev=[]
            od=[]
            for n in range(N):
                if n%2==0:
                    if n in X[j]:
                        od.append([B[n],n])
                    else:
                        ev.append([A[n],n])
                else:
                    if n in Y[k]:
                        ev.append([B[n],n])
                    else:
                        od.append([A[n],n])
            ev.sort()
            od.sort()
            #print(ev,od)
            Z=[]
            Num=0
            F=0
            for x in range(N):
                if x%2==0:
                    if Num>ev[x//2][0]:
                        F=1
                        break
                    else:
                        Num=ev[x//2][0]
                        Z.append(ev[x//2][1])
                else:
                    if Num>od[x//2][0]:
                        F=1
                        break
                    else:
                        Num=od[x//2][0]
                        Z.append(od[x//2][1])
            if F==0:
                #print(Z)
                tcnt=mergecount(Z)
            if F==0 and tcnt<ANS:
                ANS=tcnt
                
if ANS==10000:
    print(-1)
else:
    print(ANS)