#include<bits/stdc++.h>
using namespace std;
int main()
{
	ios::sync_with_stdio(false);
	int n;
	cin>>n;
	vector<int>a(n),b(n);
	for(int i=0;i<n;i++)
		cin>>a[i]>>b[i];
	long long sa=0,sb=0;
	vector<pair<int,int>>x;
	for(int i=0;i<n;i++)
	{
		x.emplace_back(a[i],i);
		x.emplace_back(b[i],i);
		sa+=a[i];
		sb+=b[i];	
	} 
	sort(x.begin(),x.end());
	vector<long long>pref(x.size()+1);
	pref[0]=0;
	for(int i=0;i<(int)x.size();i++)
		pref[i+1]=pref[i]+x[i].first;
	vector<vector<int>>pos(n);
	for(int i=0;i<(int)x.size();i++)
		pos[x[i].second].push_back(i);
	long long sum=(long long)2e18;
	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++;
		}
		long long cur=pref[j];
		if(pos[i][0]<j)
			cur-=x[pos[i][0]].first;
		if(pos[i][1]<j)
			cur-=x[pos[i][1]].first;
		sum=min(sum,cur);
	}
	sum=min(sum,min(sa,sb));
	cout<<sum<<"\n"; 
	return 0;
}

### Prompt

Please formulate 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;
int main()
{
	ios::sync_with_stdio(false);
	int n;
	cin>>n;
	vector<int>a(n),b(n);
	for(int i=0;i<n;i++)
		cin>>a[i]>>b[i];
	long long sa=0,sb=0;
	vector<pair<int,int>>x;
	for(int i=0;i<n;i++)
	{
		x.emplace_back(a[i],i);
		x.emplace_back(b[i],i);
		sa+=a[i];
		sb+=b[i];	
	} 
	sort(x.begin(),x.end());
	vector<long long>pref(x.size()+1);
	pref[0]=0;
	for(int i=0;i<(int)x.size();i++)
		pref[i+1]=pref[i]+x[i].first;
	vector<vector<int>>pos(n);
	for(int i=0;i<(int)x.size();i++)
		pos[x[i].second].push_back(i);
	long long sum=(long long)2e18;
	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++;
		}
		long long cur=pref[j];
		if(pos[i][0]<j)
			cur-=x[pos[i][0]].first;
		if(pos[i][1]<j)
			cur-=x[pos[i][1]].first;
		sum=min(sum,cur);
	}
	sum=min(sum,min(sa,sb));
	cout<<sum<<"\n"; 
	return 0;
}

```