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;
typedef long long ll;
const int INF = (1<<28);
const ll INFLL = (1ll<<60);
const ll MOD = (ll)(1e9+7);

#define l_ength size

void mul_mod(ll& a, ll b){
	a *= b;
	a %= MOD;
}

void add_mod(ll& a, ll b){
	a = (a<MOD)?a:(a-MOD);
	b = (b<MOD)?b:(b-MOD);
	a += b;
	a = (a<MOD)?a:(a-MOD);
}

int a[18][2],dp[1<<18][18],b[18];

int main(void){
	int n,i,j,mask,k,t,ans=-INF;
	fill(dp[0],dp[1<<18],-INF);
	cin >> n; b[n] = (1<<n);
	for(i=0; i<n; ++i){
		cin >> a[i][0];
		b[i] = (1<<i);
	}
	for(i=0; i<n; ++i){
		cin >> a[i][1];
		dp[b[i]][i] = 0;
	}
	for(mask=1; mask<b[n]; ++mask){
		k = __builtin_popcount(mask);
		for(i=0; i<n; ++i){
			if(!(mask&b[i])){
				continue;
			}
			t = a[i][abs(i-k+1)%2];
			for(j=0; j<n; ++j){
				if(mask&b[j]){
					continue;
				}
				if(t>a[j][abs(j-k)%2]){
					continue;
				}
				dp[mask+b[j]][j] = max(dp[mask+b[j]][j],dp[mask][i]+__builtin_popcount(mask&(b[j]-1)));
			}
		}
	}
	for(i=0; i<n; ++i){
		ans = max(ans,dp[b[n]-1][i]);
	}
	cout << ((ans<0)?(-1):(n*(n-1)/2-ans)) << endl;
	return 0;
}