#include <bits/stdc++.h>
using namespace std;
#define modulo 1000000007
#define mod(mod_x) ((((long long)mod_x+modulo))%modulo)
#define Inf 10000000000000002


int main(){

	int N;
	cin>>N;
	
	vector<long long> A(N),B(N);
	
	for(int i=0;i<N;i++)cin>>A[i]>>B[i];
	
	long long ans = Inf;
	
	{
		long long s = 0;
		for(int i=0;i<N;i++)s+=A[i];
		ans = min(ans,s);
		
		s=0;
		for(int i=0;i<N;i++)s+=B[i];
		ans = min(ans,s);
	}
	
	vector<pair<long long,int>> P;
	for(int i=0;i<N;i++){
		P.emplace_back(A[i],i);
		P.emplace_back(B[i],i);
	}
	
	sort(P.begin(),P.end());
	set<int> S;
	long long s = 0;
	for(int i=0;i<N;i++){
		s += P[i].first;
		S.insert(P[i].second);
	}
	
	if(S.size()!=N){
		ans = min(ans,s);
	}
	else{
		for(int i=0;i<N;i++){
			long long t = s;
			t -= P[i].first;
			t += A[P[i].second]+B[P[i].second];
			if(i!=N-1){
				t -= P[N-1].first;
			}
			else{
				t -= P[N-2].first;
			}
			ans = min(ans,t);
		}
	}
	
	cout<<ans<<endl;
	
	return 0;
}
### Prompt

Please create a solution in CPP 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;
#define modulo 1000000007
#define mod(mod_x) ((((long long)mod_x+modulo))%modulo)
#define Inf 10000000000000002


int main(){

	int N;
	cin>>N;
	
	vector<long long> A(N),B(N);
	
	for(int i=0;i<N;i++)cin>>A[i]>>B[i];
	
	long long ans = Inf;
	
	{
		long long s = 0;
		for(int i=0;i<N;i++)s+=A[i];
		ans = min(ans,s);
		
		s=0;
		for(int i=0;i<N;i++)s+=B[i];
		ans = min(ans,s);
	}
	
	vector<pair<long long,int>> P;
	for(int i=0;i<N;i++){
		P.emplace_back(A[i],i);
		P.emplace_back(B[i],i);
	}
	
	sort(P.begin(),P.end());
	set<int> S;
	long long s = 0;
	for(int i=0;i<N;i++){
		s += P[i].first;
		S.insert(P[i].second);
	}
	
	if(S.size()!=N){
		ans = min(ans,s);
	}
	else{
		for(int i=0;i<N;i++){
			long long t = s;
			t -= P[i].first;
			t += A[P[i].second]+B[P[i].second];
			if(i!=N-1){
				t -= P[N-1].first;
			}
			else{
				t -= P[N-2].first;
			}
			ans = min(ans,t);
		}
	}
	
	cout<<ans<<endl;
	
	return 0;
}
```