#include<bits/stdc++.h>
using namespace std;
using ll=long long;
#define fr(i,n) for(int i=0;i<(n);++i)
#define Fr(i,n) for(int i=1;i<=(n);++i)
#define ifr(i,n) for(int i=(n)-1;i>=0;--i)
#define iFr(i,n) for(int i=(n);i>0;--i)

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    istream& in(cin);
    ostream& out(cout);
    int n;
    in>>n;
    ll A{},B{};
    vector<pair<ll,int>> a(n),b(n),c;
    c.reserve(2*n);
    fr(i,n){
        in>>a[i].first>>b[i].first;
        A+=a[i].first;
        B+=b[i].first;
        a[i].second=b[i].second=i;
        c.emplace_back(a[i]);
        c.emplace_back(b[i]);
    }
    ll ans=min(A,B),ns{};
    vector<bool> v(n);
    sort(c.begin(),c.end());
    bool f{};
    fr(i,n){
        ns+=c[i].first;
        if(v[c[i].second]) f=true;
        v[c[i].second]=true;
    }
    if(f) return cout<<min(ans,ns)<<'\n',0;
    fr(i,n){
        f=c[i].second==c[n].second;
        ans=min(ans,ns-c[i].first+c[f?n+1:n].first);
    }
    cout<<ans<<'\n';
}
### Prompt

In CPP, your task is to solve 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;
using ll=long long;
#define fr(i,n) for(int i=0;i<(n);++i)
#define Fr(i,n) for(int i=1;i<=(n);++i)
#define ifr(i,n) for(int i=(n)-1;i>=0;--i)
#define iFr(i,n) for(int i=(n);i>0;--i)

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    istream& in(cin);
    ostream& out(cout);
    int n;
    in>>n;
    ll A{},B{};
    vector<pair<ll,int>> a(n),b(n),c;
    c.reserve(2*n);
    fr(i,n){
        in>>a[i].first>>b[i].first;
        A+=a[i].first;
        B+=b[i].first;
        a[i].second=b[i].second=i;
        c.emplace_back(a[i]);
        c.emplace_back(b[i]);
    }
    ll ans=min(A,B),ns{};
    vector<bool> v(n);
    sort(c.begin(),c.end());
    bool f{};
    fr(i,n){
        ns+=c[i].first;
        if(v[c[i].second]) f=true;
        v[c[i].second]=true;
    }
    if(f) return cout<<min(ans,ns)<<'\n',0;
    fr(i,n){
        f=c[i].second==c[n].second;
        ans=min(ans,ns-c[i].first+c[f?n+1:n].first);
    }
    cout<<ans<<'\n';
}
```