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:
#!/usr/bin/env python3
import sys, math, itertools, collections, bisect
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8')
inf = float('inf') ;mod = 10**9+7
mans = inf ;ans = 0 ;count = 0 ;pro = 1

def f(n):
    count=0
    while n:
        count+=n%2
        n//=2
    return count

n=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
for bit in range(2**n):
    # if f(bit)%2!=0:
    #     continue
    arr=[]
    for i in range(n):
        if bit >> i & 1:
            arr.append((B[i],i))
        else:
            arr.append((A[i],i))
    i=0;flug=1;tmp=0
    while flug:
        flug=0
        for j in range(n-1,i,-1):
            if arr[j-1][0]>arr[j][0]:
                arr[j-1],arr[j]=arr[j],arr[j-1]
                tmp+=1; flug=1
        i+=1
    stack=[]
    for i in range(n):
        if (abs(arr[i][1]-i)) % 2 != bit >> arr[i][1] & 1:
            stack.append(arr[i][0]*1000+i)
    # if bit == 3:
        # print(tmp,stack,arr,bin(bit))
        # print((abs(arr[1][1]-1)) % 2 , bit >> arr[1][1])
    if len(stack) & 1:
        tmp=1000; stack.pop()
    while stack:
        p=stack.pop(); q=stack.pop()
        if (p-q) & 1:
            tmp+=p-q
            # if bit==3:
                # print(p,q,tmp,mans)
                # print(arr)
        else:
            tmp+=1000
    mans=min(mans,tmp)

print(-1 if mans > 999 else mans)