#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <queue>
using namespace std;
typedef long long int ll;

int main(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	int n; cin >> n;
	vector<int> a(n),b(n);
	ll sa=0,sb=0;
	for(int i=0;i<n;i++){
		cin >> a[i] >> b[i];
		sa+=a[i],sb+=b[i];
	}
	ll ans=min(sa,sb);
	vector<pair<int,int>> v;
	for(int i=0;i<n;i++){
		v.push_back({a[i],i});
		v.push_back({b[i],i});
	}
	sort(v.begin(),v.end());
	vector<ll> cnt(2*n+1,0);
	for(int i=0;i<2*n;i++){
		cnt[i+1]=cnt[i]+v[i].first;
	}
	vector<vector<int>> pos(n);
	for(int i=0;i<2*n;i++){
		pos[v[i].second].push_back(i);
	}
	for(int i=0;i<n;i++){
		int j=n;
		while(1){
			int cc=(pos[i][0]<j)+(pos[i][1]<j);
			if(cc==j-n)break;
			j++;
		}
		ll cur=cnt[j];
		if(pos[i][0]<j){
			cur-=v[pos[i][0]].first;
		}
		if(pos[i][1]<j){
			cur-=v[pos[i][1]].first;
		}
		ans=min(ans,cur);
	}
	cout << ans << endl;
}
### 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 <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <queue>
using namespace std;
typedef long long int ll;

int main(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	int n; cin >> n;
	vector<int> a(n),b(n);
	ll sa=0,sb=0;
	for(int i=0;i<n;i++){
		cin >> a[i] >> b[i];
		sa+=a[i],sb+=b[i];
	}
	ll ans=min(sa,sb);
	vector<pair<int,int>> v;
	for(int i=0;i<n;i++){
		v.push_back({a[i],i});
		v.push_back({b[i],i});
	}
	sort(v.begin(),v.end());
	vector<ll> cnt(2*n+1,0);
	for(int i=0;i<2*n;i++){
		cnt[i+1]=cnt[i]+v[i].first;
	}
	vector<vector<int>> pos(n);
	for(int i=0;i<2*n;i++){
		pos[v[i].second].push_back(i);
	}
	for(int i=0;i<n;i++){
		int j=n;
		while(1){
			int cc=(pos[i][0]<j)+(pos[i][1]<j);
			if(cc==j-n)break;
			j++;
		}
		ll cur=cnt[j];
		if(pos[i][0]<j){
			cur-=v[pos[i][0]].first;
		}
		if(pos[i][1]<j){
			cur-=v[pos[i][1]].first;
		}
		ans=min(ans,cur);
	}
	cout << ans << endl;
}
```