#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

int A[101010],B[101010];

int main(){
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  
  int N; cin>>N;
  vector<pair<int,pair<int,int>>> V;
  rep(i,N){
    cin>>A[i]>>B[i];
    V.push_back({A[i],{i,0}});
    V.push_back({B[i],{i,1}});
  }
  sort(V.begin(),V.end());
  int x=V[0].second.second;
  ll sum=V[0].first;
  for(int i=1;i<N;i++){
    sum+=V[i].first;
    if(x!=V[i].second.second) x=-1;
  }
  if(x!=-1){
    cout<<sum<<endl;
    return 0;
  }
  ll ans=1e15;
  rep(i,N){
    ll tmp=sum;
    if(A[i]<=V[N-1].first) tmp-=A[i];
    if(B[i]<=V[N-1].first) tmp-=B[i];
    if((tmp+A[i]+B[i])==sum) ans=min(ans,sum);
    else{
      if(V[N].second.first!=i) ans=min(ans,tmp+1LL*V[N].first);
      else ans=min(ans,tmp+1LL*V[N+1].first);
    }
  }
  cout<<ans<<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;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

int A[101010],B[101010];

int main(){
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  
  int N; cin>>N;
  vector<pair<int,pair<int,int>>> V;
  rep(i,N){
    cin>>A[i]>>B[i];
    V.push_back({A[i],{i,0}});
    V.push_back({B[i],{i,1}});
  }
  sort(V.begin(),V.end());
  int x=V[0].second.second;
  ll sum=V[0].first;
  for(int i=1;i<N;i++){
    sum+=V[i].first;
    if(x!=V[i].second.second) x=-1;
  }
  if(x!=-1){
    cout<<sum<<endl;
    return 0;
  }
  ll ans=1e15;
  rep(i,N){
    ll tmp=sum;
    if(A[i]<=V[N-1].first) tmp-=A[i];
    if(B[i]<=V[N-1].first) tmp-=B[i];
    if((tmp+A[i]+B[i])==sum) ans=min(ans,sum);
    else{
      if(V[N].second.first!=i) ans=min(ans,tmp+1LL*V[N].first);
      else ans=min(ans,tmp+1LL*V[N+1].first);
    }
  }
  cout<<ans<<endl;
  return 0;
}

```