#include<bits/stdc++.h>
#define fo(i,a,b)for(int i=a,_e=b;i<=_e;++i)
#define ll long long
using namespace std;
const int N=1e5+5;
int n,a,b,is[N],c[4];
struct nod{int a,i;}v[N*2];
ll tot,tot2,ansa,ansb;
bool cmp(nod a,nod b){return a.a<b.a;}
int main(){
	ios::sync_with_stdio(false);
	cin>>n;
	fo(i,1,n)cin>>a>>b,v[i*2]=(nod){a,i},v[i*2-1]=(nod){b,-i},ansa+=a,ansb+=b;
	sort(v+1,v+n*2+1,cmp);
	fo(i,1,n){
		tot+=v[i].a;
		is[abs(v[i].i)]|=v[i].i>0?2:1;
	}
	fo(i,1,n)c[is[i]]++;
	if(c[1]+c[2]==n){
		tot2=tot-v[n-1].a;
		tot-=v[n].a;
		is[abs(v[n].i)]=0;
		fo(i,n+1,n*2)
			if(is[abs(v[i].i)]){
				tot+=v[i].a;
				break;
			}
		is[abs(v[n].i)]=1;
		is[abs(v[n-1].i)]=0;
		fo(i,n+1,n*2)
			if(is[abs(v[i].i)]){
				tot2+=v[i].a;
				break;
			}
		tot=min(tot,tot2);
	}
	cout<<min(tot,min(ansa,ansb));
}
### Prompt

Please provide a CPP coded solution 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 fo(i,a,b)for(int i=a,_e=b;i<=_e;++i)
#define ll long long
using namespace std;
const int N=1e5+5;
int n,a,b,is[N],c[4];
struct nod{int a,i;}v[N*2];
ll tot,tot2,ansa,ansb;
bool cmp(nod a,nod b){return a.a<b.a;}
int main(){
	ios::sync_with_stdio(false);
	cin>>n;
	fo(i,1,n)cin>>a>>b,v[i*2]=(nod){a,i},v[i*2-1]=(nod){b,-i},ansa+=a,ansb+=b;
	sort(v+1,v+n*2+1,cmp);
	fo(i,1,n){
		tot+=v[i].a;
		is[abs(v[i].i)]|=v[i].i>0?2:1;
	}
	fo(i,1,n)c[is[i]]++;
	if(c[1]+c[2]==n){
		tot2=tot-v[n-1].a;
		tot-=v[n].a;
		is[abs(v[n].i)]=0;
		fo(i,n+1,n*2)
			if(is[abs(v[i].i)]){
				tot+=v[i].a;
				break;
			}
		is[abs(v[n].i)]=1;
		is[abs(v[n-1].i)]=0;
		fo(i,n+1,n*2)
			if(is[abs(v[i].i)]){
				tot2+=v[i].a;
				break;
			}
		tot=min(tot,tot2);
	}
	cout<<min(tot,min(ansa,ansb));
}
```