#include <bits/stdc++.h>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;
typedef pair<int,int>P;

int a[200000],b[200000];
int used[200000];

int main(){
	int n;scanf("%d",&n);
	vector<P>v;
	ll sumA=0,sumB=0;
	rep(i,n){
		scanf("%d%d",&a[i],&b[i]);
		v.push_back(P(a[i],i));
		v.push_back(P(b[i],i+n));
		sumA+=a[i];
		sumB+=b[i];
	}
	sort(v.begin(),v.end());
	ll sum=0;
	bool flag=false;
	rep(i,n){
		if(used[v[i].second%n]){
			flag=true;
		}
		sum+=v[i].first;
		used[v[i].second%n]++;
	}
	ll Min=min(sumA,sumB);
	if(flag)Min=min(Min,sum);
	else{
		sum=0;
		set<int>se;
		rep(i,n-2)sum+=v[i].first,se.insert(v[i].second);
		rep(i,n){
			int cnt=0;
			ll sum2=sum;
			if(!se.count(i))sum2+=a[i],cnt++;
			if(!se.count(i+n))sum2+=b[i],cnt++;
			rep(j,2-cnt){
				sum2+=v[n-2+j].first;
			}
			Min=min(Min,sum2);
		}
	}
	cout<<Min<<endl;
}
### Prompt

Develop a solution in cpp to the problem described below:

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>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;
typedef pair<int,int>P;

int a[200000],b[200000];
int used[200000];

int main(){
	int n;scanf("%d",&n);
	vector<P>v;
	ll sumA=0,sumB=0;
	rep(i,n){
		scanf("%d%d",&a[i],&b[i]);
		v.push_back(P(a[i],i));
		v.push_back(P(b[i],i+n));
		sumA+=a[i];
		sumB+=b[i];
	}
	sort(v.begin(),v.end());
	ll sum=0;
	bool flag=false;
	rep(i,n){
		if(used[v[i].second%n]){
			flag=true;
		}
		sum+=v[i].first;
		used[v[i].second%n]++;
	}
	ll Min=min(sumA,sumB);
	if(flag)Min=min(Min,sum);
	else{
		sum=0;
		set<int>se;
		rep(i,n-2)sum+=v[i].first,se.insert(v[i].second);
		rep(i,n){
			int cnt=0;
			ll sum2=sum;
			if(!se.count(i))sum2+=a[i],cnt++;
			if(!se.count(i+n))sum2+=b[i],cnt++;
			rep(j,2-cnt){
				sum2+=v[n-2+j].first;
			}
			Min=min(Min,sum2);
		}
	}
	cout<<Min<<endl;
}
```