#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
#define fi first
#define se second
int n;
pair<ll,pair<int,int> >c[200001];
int ch[100001][2];
int cnt[4];
int main(){
	ios::sync_with_stdio(false);
	cin >> n;
	for(int i=1; i<=n ;i++){
		int a,b;cin >> a >> b;
		c[i*2-1]={a,{i,0}};
		c[i*2]={b,{i,1}};
	}
	sort(c+1,c+2*n+1);
	ll sum=0;
	for(int i=1; i<=n ;i++){
		ch[c[i].se.fi][c[i].se.se]=1;
		sum+=c[i].fi;
	}
	for(int i=1; i<=n ;i++){
		cnt[ch[i][0]*2+ch[i][1]]++;
	}
	if(cnt[3]!=0 || cnt[2]==n || cnt[2]==0) return cout << sum << endl,0;
	ch[c[n].se.fi][c[n].se.se]=0;ch[c[n+1].se.fi][c[n+1].se.se]=1;
	cnt[0]=cnt[1]=cnt[2]=cnt[3]=0;
	for(int i=1; i<=n ;i++){
		cnt[ch[i][0]*2+ch[i][1]]++;
	}
	if(cnt[3]!=0 || cnt[2]==n || cnt[2]==0) cout << sum-c[n].fi+c[n+1].fi << endl;
	else cout << min(sum-c[n].fi+c[n+2].fi,sum-c[n-1].fi+c[n+1].fi) << 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<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
#define fi first
#define se second
int n;
pair<ll,pair<int,int> >c[200001];
int ch[100001][2];
int cnt[4];
int main(){
	ios::sync_with_stdio(false);
	cin >> n;
	for(int i=1; i<=n ;i++){
		int a,b;cin >> a >> b;
		c[i*2-1]={a,{i,0}};
		c[i*2]={b,{i,1}};
	}
	sort(c+1,c+2*n+1);
	ll sum=0;
	for(int i=1; i<=n ;i++){
		ch[c[i].se.fi][c[i].se.se]=1;
		sum+=c[i].fi;
	}
	for(int i=1; i<=n ;i++){
		cnt[ch[i][0]*2+ch[i][1]]++;
	}
	if(cnt[3]!=0 || cnt[2]==n || cnt[2]==0) return cout << sum << endl,0;
	ch[c[n].se.fi][c[n].se.se]=0;ch[c[n+1].se.fi][c[n+1].se.se]=1;
	cnt[0]=cnt[1]=cnt[2]=cnt[3]=0;
	for(int i=1; i<=n ;i++){
		cnt[ch[i][0]*2+ch[i][1]]++;
	}
	if(cnt[3]!=0 || cnt[2]==n || cnt[2]==0) cout << sum-c[n].fi+c[n+1].fi << endl;
	else cout << min(sum-c[n].fi+c[n+2].fi,sum-c[n-1].fi+c[n+1].fi) << endl;
}
```