Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
3 4 3
3 2 3

Sample Output 1

1

By doing the operation once with i = 1, we have a sequence [2, 3, 3] facing up, which is non-decreasing.

Sample Input 2

2
2 1
1 2

Sample Output 2

-1

After any number of operations, we have the sequence [2, 1] facing up, which is not non-decreasing.

Sample Input 3

4
1 2 3 4
5 6 7 8

Sample Output 3

0

No operation may be required.

Sample Input 4

5
28 15 22 43 31
20 22 43 33 32

Sample Output 4

-1

Sample Input 5

5
4 46 6 38 43
33 15 18 27 37

Sample Output 5

3

Solution in C++14 (Clang 3.8.0) (judge verdict: Runtime Error)

#include<iostream>
#include<iomanip>
#include<cstdio>
#include<cstdlib>
#include<cassert>

#include<cmath>
#include<functional>
#include<algorithm>

#include<vector>
#include<string>
#include<queue>
#include<stack>
#include<set>
#include<unordered_set>
#include<map>
#include<unordered_map>
#include<bitset>
#include<tuple>

#define TEST {IS_TEST=true;}
#define fi first
#define se second
#define pb(x) {push_back(x);}

using namespace std;
using ll = int_fast64_t;
using v_b = vector <bool>;
using v_ll = vector <ll>;
using str = string;
using v_str = vector <string>;
using p_ll = pair < ll,ll >;
using vv_b = vector < v_b >;
using vv_ll = vector < v_ll >;
using vp_ll = vector < p_ll >;
using vvv_ll = vector < vv_ll >;
using vvp_ll = vector < vp_ll >;

using ld = long double;
using v_ld = vector <ld>;
using vv_ld = vector<v_ld>;

bool IS_TEST=false;
ll ll_min64=1LL<<63;
ll ll_max64=~ll_min64;
ll ll_min32=1LL<<31;
ll ll_max32=~ll_min32;

ll MOD = 1000000007;

/*displaying functions for debug*/
template<class T> void show2(const T &x){cout << x;}
template<class T1,class T2> void show2(const pair<T1,T2> &x){
  cout << "{" << show2(x.first) << "," << show2(x.second) << "}";
}
template<class T> void show(const T &x){
  if (!IS_TEST) return;
  show2(x); cout <<endl;
}
template<class T> void v_show(const T &v, ll n=-1){
  if (!IS_TEST) return;
  auto itr=v.begin(); ll m=n;
  while(itr!=v.end() && m!=0 ){ show2(*itr); cout << " "; itr++; m--;}
  cout << endl;
}
template<class T> void vv_show(const T &v, ll n=-1){
  if (!IS_TEST) return;
  cout << "--------------------------------\n";
  auto itr=v.begin(); ll m=n;
  while(itr!=v.end() && m!=0 ){ v_show(*itr,n); itr++; m--;}
  cout << "--------------------------------" << endl;
}
/*--------------------------------*/

/*loading integers*/
void load(ll& x1){ cin >> x1; }
void load(ll& x1,ll& x2){ cin >> x1 >> x2; }
void load(ll& x1,ll& x2,ll& x3){ cin >> x1 >> x2 >> x3; }
void load(ll& x1,ll& x2,ll& x3,ll& x4){ cin >> x1 >> x2 >> x3 >> x4; }
void v_load(ll n, v_ll& v1, ll head=0, ll tail=0, ll init=0){
    ll m=n+head+tail; v1.assign(m,init);
    for (ll i=0;i<n;i++){ cin >> v1[i+head]; }
}
void v_load(ll n, v_ll& v1 ,v_ll& v2, ll head=0, ll tail=0, ll init=0){
    ll m=n+head+tail; v1.assign(m,init); v2.assign(m,init);
    for (ll i=0;i<n;i++){ cin >> v1[i+head] >> v2[i+head]; }
}
void v_load(ll n, v_ll& v1 ,v_ll& v2, v_ll& v3, ll head=0, ll tail=0, ll init=0){
    ll m=n+head+tail; v1.assign(m,init); v2.assign(m,init); v3.assign(m,init);
    for (ll i=0;i<n;i++){ cin >> v1[i+head] >> v2[i+head] >> v3[i+head]; }
}
void v_load(ll n, v_ll& v1 ,v_ll& v2, v_ll& v3, v_ll& v4, ll head=0, ll tail=0, ll init=0){
    ll m=n+head+tail; v1.assign(m,init); v2.assign(m,init); v3.assign(m,init); v4.assign(m,init);
    for (ll i=0;i<n;i++){ cin >> v1[i+head] >> v2[i+head] >> v3[i+head] >> v4[i+head]; }
}
/*--------------------------------*/

v_ll local_sort(ll x1=ll_max64, ll x2=ll_max64, ll x3=ll_max64, ll x4=ll_max64){
    v_ll x{x1,x2,x3,x4};
    sort(x.begin(),x.end());
    return x;
}

ll max(ll x,ll y){return x>y?x:y;}
ll max(v_ll::iterator b,v_ll::iterator e){
    ll ans=*b;
    while (b<e) {ans=max(ans,*b);b++;}
    return ans;
}
ll argmax(v_ll::iterator b,v_ll::iterator e){
    ll ans=0, cnt=0, val=*b;
    while (b<e) { if (val<*b) {ans=cnt; val=*b;} cnt++; b++;}
    return ans;
}

ll min(ll x,ll y){return x<y?x:y;}
ll min(v_ll::iterator b,v_ll::iterator e){
    ll ans=*b;
    while (b<e) {ans=min(ans,*b);b++;}
    return ans;
}
ll argmin(v_ll::iterator b,v_ll::iterator e){
    ll ans=0, cnt=0, val=*b;
    while (b<e) { if (val>*b) {ans=cnt; val=*b;} cnt++; b++;}
    return ans;
}

ll sum(v_ll::iterator b,v_ll::iterator e){
    ll ans=0;
    while (b<e) {ans+=*b;b++;}
    return ans;
}

template<class T> void chmax(T& x,const T& y){ if (x>=y) return; x=y; }
template<class T> void chmin(T& x,const T& y){ if (x<=y) return; x=y; }
template<class T,class S> void chmax(T& x,S& xx,const T& y,const S& yy){
  if (x>=y) return; x=y; xx=yy;
}
template<class T,class S> void chmin(T& x,S& xx,const T& y,const S& yy){
  if (x<=y) return; x=y; xx=yy;
}

template<class T> void quit(T x){cout << x << endl; exit(0);}

ll rem(ll x,ll y){ ll z=x%y; return z>=0?z:z+y; }

//setprecision(digit)



ll N,M,K,H,W,ans;
v_ll A,B,C;
int main(){
    load(N);
    A.assign(N,0);
    B.assign(N,0);
    for (ll i=0;i<N;i++){
      scanf("%lld",&A[i]);
    }
    for (ll i=0;i<N;i++){
      scanf("%lld",&B[i]);
    }
    for (ll i=1;i<N;i+=2){
      swap(A[i],B[i]);
    }
    
    v_ll S(N/2,0);
    for (ll i=0;i<N/2;i++){
      S[i]=i;
    }
    bool flag=true;
    ans=-1;
    while (flag){
      v_ll T1(N-N/2,0);
      v_ll T2(N/2,0);
      ll k=0;
      bool good=true;
      for (ll i=0;i<N;i++){
        if (k<N/2&&i==S[k]){
          T2[k]=i;
          k++;
        }else{
          T1.push_back(i);
        }
      }
      
      sort(T1.begin(),T1.end(),[&](const ll &x,const ll &y){
        if (A[x]<A[y])return true;
        if (A[x]==A[y] && x<y)return true;
        return false;
      });
      sort(T2.begin(),T2.end(),[&](const ll &x,const ll &y){
        if (B[x]<B[y])return true;
        if (B[x]==B[y] && x<y)return true;
        return false;
      });

      
      for (ll i=0;i<T2.size();i++){
        if (B[T2[i]]<A[T1[i]]) good = false;
      }
      for (ll i=1;i<T1.size();i++){
        if (A[T1[i]]<B[T2[i-1]]) good = false;
      }
      v_ll U;
      if (good){
        for (ll i=0;i<T1.size();i++){
          U.push_back(T1[i]);
          if (i<T2.size()){
            U.push_back(T2[i]);
          }
        }
        ll a=0;
        for (ll i=0;i<N;i++){
          for (ll j=i+1;j<N;j++){
            if (U[i]>U[j])a++;
            if (ans>=0&&a>=ans)goto AAA;
          }
        }
        if (ans<0||a<ans) ans=a;
      }
AAA:
      ll i=0;
      for (i=N/2-1;i>=0;i--){
        S[i]++;
        if (S[i]<=N-(N/2)+i){i++;break;}
        if (i==0) flag=false;
      }
      for (;i<N/2;i++){
        if (i>0)S[i]=S[i-1]+1;
      }
    }
    cout << ans << endl;
}