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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std ;

int a[20], b[20] ;
int dp[ (1<<18) ][ 50 ] ;
int n ;
const int inf = 1e8 ;

int go ( int mask, int mx ) {
    if ( __builtin_popcount(mask) == n ) return 0 ;
    auto &rf = dp[mask][mx] ;
    if ( rf!=-1 ) return rf ;
    int cur = 0, v = __builtin_popcount(mask) ;
    rf = inf ;
    for ( int i = 0 ; i < n ; ++i ) {
        if ( mask&(1<<i) ) {
            --v ;
            continue ;
        }
        if ( (cur+v) % 2 && b[i] >= mx ) rf = min(rf, go ( mask|(1<<i), b[i] ) + cur) ;
        if ( (cur+v) % 2 == 0 && a[i] >= mx ) rf = min ( rf, go(mask|(1<<i), a[i])+cur ) ;
        ++cur;
    }
    return rf ;
}

int main() {
  //  freopen("input.txt", "r", stdin ) ;
    memset ( dp, -1, sizeof dp ) ;
    cin >> n ;
    for ( int i = 0 ; i < n ; ++i )
        cin >> a[i] ;
    for ( int i = 0 ; i < n ; ++i )
        cin >> b[i] ;
    if ( go(0,0) >= inf ) cout << "-1\n" ;
    else cout << go(0,0) << '\n' ;
}