#include<bits/stdc++.h>
using namespace std;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}

//INSERT ABOVE HERE
signed main(){
  Int n;
  cin>>n;
  vector<Int> a(n),b(n);
  for(Int i=0;i<n;i++) cin>>a[i]>>b[i];
  using P = pair<Int, Int>;
  vector<P> v;
  for(Int i=0;i<n;i++) v.emplace_back(a[i],i);
  for(Int i=0;i<n;i++) v.emplace_back(b[i],n+i);
  sort(v.begin(),v.end());

  Int sum=0;
  vector<Int> used(n*2,0);
  for(Int i=0;i<n;i++){
    sum+=v[i].first;
    used[v[i].second]=1;
  }
  
  for(Int k=0;k<=n;k+=n){
    Int flg=1;
    for(Int i=0;i<n;i++) flg&=used[k+i];
    if(flg){
      cout<<sum<<endl;
      return 0;
    }
  }

  for(Int i=0;i<n;i++){
    if(used[i]&&used[n+i]){
      cout<<sum<<endl;
      return 0;
    }
  }
  
  Int ans=sum+v[n].first;
  for(Int i=0;i<n;i++){
    Int res=sum-v[i].first;
    res+=v[n+((v[i].second%n)==(v[n].second%n))].first;
    chmin(ans,res);
  }
  cout<<ans<<endl;
  return 0;
}

### Prompt

Your challenge is to write 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;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}

//INSERT ABOVE HERE
signed main(){
  Int n;
  cin>>n;
  vector<Int> a(n),b(n);
  for(Int i=0;i<n;i++) cin>>a[i]>>b[i];
  using P = pair<Int, Int>;
  vector<P> v;
  for(Int i=0;i<n;i++) v.emplace_back(a[i],i);
  for(Int i=0;i<n;i++) v.emplace_back(b[i],n+i);
  sort(v.begin(),v.end());

  Int sum=0;
  vector<Int> used(n*2,0);
  for(Int i=0;i<n;i++){
    sum+=v[i].first;
    used[v[i].second]=1;
  }
  
  for(Int k=0;k<=n;k+=n){
    Int flg=1;
    for(Int i=0;i<n;i++) flg&=used[k+i];
    if(flg){
      cout<<sum<<endl;
      return 0;
    }
  }

  for(Int i=0;i<n;i++){
    if(used[i]&&used[n+i]){
      cout<<sum<<endl;
      return 0;
    }
  }
  
  Int ans=sum+v[n].first;
  for(Int i=0;i<n;i++){
    Int res=sum-v[i].first;
    res+=v[n+((v[i].second%n)==(v[n].second%n))].first;
    chmin(ans,res);
  }
  cout<<ans<<endl;
  return 0;
}

```