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

typedef long long ll;
typedef unsigned long long ull;

int main(){
    vector<pair<ll,ll>> p;
    ll N;
    cin >> N;
    for(ll i=0;i<N;i++){
        ll A,B;
        cin >> A >> B;
        p.push_back(make_pair(A,i*2+0));
        p.push_back(make_pair(B,i*2+1));
    }
    sort(p.begin(),p.end());

    bool allsame=true;
    bool checked[100000];
    ll sum=0;
    for(int i=0;i<N;i++) checked[i]=false;
    for(ll i=0;i<N;i++){
        allsame=(allsame && (p[0].second%2)==(p[i].second%2));
        checked[p[i].second/2]=true;
        sum+=p[i].first;
    }
    for(int i=0;i<N;i++){
        if(checked[i]==false){
            cout << sum << endl;
            return 0;
        }
    }
    if(allsame){
        cout << sum << endl;
        return 0;
    }
    if(p[N-1].second/2!=p[N].second/2){
        cout << sum-p[N-1].first+p[N].first << endl;
    }else{
        cout << min(sum-p[N-1].first+p[N+1].first,sum-p[N-2].first+p[N].first) << endl;
    }

    
    return 0;
}
### Prompt

Your task is to create a CPP solution to the following problem:

We have a directed weighted graph with N vertices. Each vertex has two integers written on it, and the integers written on Vertex i are A_i and B_i.

In this graph, there is an edge from Vertex x to Vertex y for all pairs 1 \leq x,y \leq N, and its weight is {\rm min}(A_x,B_y).

We will consider a directed cycle in this graph that visits every vertex exactly once. Find the minimum total weight of the edges in such a cycle.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq B_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 B_1
A_2 B_2
:
A_N B_N


Output

Print the minimum total weight of the edges in such a cycle.

Examples

Input

3
1 5
4 2
6 3


Output

7


Input

4
1 5
2 6
3 7
4 8


Output

10


Input

6
19 92
64 64
78 48
57 33
73 6
95 73


Output

227

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;

int main(){
    vector<pair<ll,ll>> p;
    ll N;
    cin >> N;
    for(ll i=0;i<N;i++){
        ll A,B;
        cin >> A >> B;
        p.push_back(make_pair(A,i*2+0));
        p.push_back(make_pair(B,i*2+1));
    }
    sort(p.begin(),p.end());

    bool allsame=true;
    bool checked[100000];
    ll sum=0;
    for(int i=0;i<N;i++) checked[i]=false;
    for(ll i=0;i<N;i++){
        allsame=(allsame && (p[0].second%2)==(p[i].second%2));
        checked[p[i].second/2]=true;
        sum+=p[i].first;
    }
    for(int i=0;i<N;i++){
        if(checked[i]==false){
            cout << sum << endl;
            return 0;
        }
    }
    if(allsame){
        cout << sum << endl;
        return 0;
    }
    if(p[N-1].second/2!=p[N].second/2){
        cout << sum-p[N-1].first+p[N].first << endl;
    }else{
        cout << min(sum-p[N-1].first+p[N+1].first,sum-p[N-2].first+p[N].first) << endl;
    }

    
    return 0;
}
```