#include<bits/stdc++.h>
using namespace std;
const int maxn=2e5;
int n,cnt[maxn];
long long ans=1e15,Ans,tot[2];
bool flag=false;
struct point{
	long long bel,val;
}p[2*maxn];
inline long long read(){
	long long x=0,f=1;
	char c;
	do{c=getchar();if(c=='-') f*=-1;}while(!isdigit(c));
	while(isdigit(c)){x=(x<<3)+(x<<1)+c-'0';c=getchar();}
	return x*f;
}
bool cmp(const point a,const point b){return a.val<b.val;}

int main(){
	n=read();
	for(int i=1;i<=n;i++){
		p[2*i].val=read();p[2*i-1].bel=i;
		p[2*i-1].val=read();p[2*i].bel=i;
		tot[0]+=p[2*i].val;tot[1]+=p[2*i-1].val;
	}
	ans=min(tot[0],tot[1]);
	sort(p+1,p+2*n+1,cmp);
	for(int i=1;i<=n;i++){
		cnt[p[i].bel]++;Ans+=p[i].val;
		if(cnt[p[i].bel]==2) flag=true;
	}
	if(flag){ans=min(ans,Ans);}
	else{
		ans=min(ans,(p[n].bel==p[n+1].bel)?min(Ans-p[n].val+p[n+2].val,Ans-p[n-1].val+p[n+1].val):Ans-p[n].val+p[n+1].val);
	}
	printf("%lld\n",ans);
	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;
const int maxn=2e5;
int n,cnt[maxn];
long long ans=1e15,Ans,tot[2];
bool flag=false;
struct point{
	long long bel,val;
}p[2*maxn];
inline long long read(){
	long long x=0,f=1;
	char c;
	do{c=getchar();if(c=='-') f*=-1;}while(!isdigit(c));
	while(isdigit(c)){x=(x<<3)+(x<<1)+c-'0';c=getchar();}
	return x*f;
}
bool cmp(const point a,const point b){return a.val<b.val;}

int main(){
	n=read();
	for(int i=1;i<=n;i++){
		p[2*i].val=read();p[2*i-1].bel=i;
		p[2*i-1].val=read();p[2*i].bel=i;
		tot[0]+=p[2*i].val;tot[1]+=p[2*i-1].val;
	}
	ans=min(tot[0],tot[1]);
	sort(p+1,p+2*n+1,cmp);
	for(int i=1;i<=n;i++){
		cnt[p[i].bel]++;Ans+=p[i].val;
		if(cnt[p[i].bel]==2) flag=true;
	}
	if(flag){ans=min(ans,Ans);}
	else{
		ans=min(ans,(p[n].bel==p[n+1].bel)?min(Ans-p[n].val+p[n+2].val,Ans-p[n-1].val+p[n+1].val):Ans-p[n].val+p[n+1].val);
	}
	printf("%lld\n",ans);
	return 0;
}
```