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>

#define M_PI       3.14159265358979323846   // pi

using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> VI;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> t3;

#define rep(a,n) for(int a = 0;a < n;a++)
#define repi(a,b,n) for(int a = b;a < n;a++)

const ull mod = (ull)1e9 + 7;
ll n;
vector<vector<ll>> as;
ll ans = 1e15;

void swapLine(int i) {
	ll a1 = as[i][0];
	ll a2 = as[i+1][0];
	ll b1 = as[i][1];
	ll b2 = as[i+1][1];
	as[i][0] = b2;
	as[i+1][0] = b1;
	as[i][1] = a2;
	as[i+1][1] = a1;
}

void dfs(int index, ll c, ll sum) {
	if (index == n - 1) {
		if (as[index][0] >= c) {
			ans = min(ans, sum);
		}
		return;
	}
	for (int i = index; i < n; i++) {
		if (as[i][(i - index) % 2] >= c) {
			for (int j = i - 1; j >= index; j--) {
				swapLine(j);
			}
			int dist = i - index;
			if (dist + sum < ans) {
				dfs(index + 1, as[index][0], dist + sum);
			}
			for (int j = index; j < i; j++) {
				swapLine(j);
			}
		}
	}
}

int main(void)
{
	cin >> n;
	as.resize(n, vector<ll>(2));
	rep(i, n) {
		cin >> as[i][0];
	}
	rep(i, n) {
		cin >> as[i][1];
	}
	dfs(0, -1, 0);
	if (ans == 1e15) {
		cout << -1 << endl;
	}
	else {
		cout << ans << endl;
	}
	return 0;
}