#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=200005,p=1000000007,inf=0x3f3f3f3f;
int read(){
	int f=1,g=0;char ch=getchar();
	for (;!isdigit(ch);ch=getchar()) if (ch=='-') f=-1;
	for (;isdigit(ch);ch=getchar()) g=g*10+ch-'0';
	return f*g;
}
int n,a[N],b[N],pos[N];
ll sum,ans;
bool cmp(int x,int y){return a[x]<a[y];}
int main(){
	n=read();
	for (int i=1;i<=n;i++) a[i]=read(),a[i+n]=read();
	ans=0;
	for (int i=1;i<=n;i++) ans+=a[i];
	sum=0;
	for (int i=n+1;i<=n*2;i++) sum+=a[i];
	ans=min(ans,sum);
	for (int i=1;i<=n*2;i++) b[i]=i;
	sort(b+1,b+n*2+1,cmp);
	for (int i=1;i<=n*2;i++) pos[b[i]]=i;
	
	sum=0;
	for (int i=1;i<=n-2;i++) sum+=a[b[i]];
	for (int i=1;i<=n;i++){
		ll t=sum;int cnt=n-2;
		if (min(pos[i],pos[i+n])<=cnt) t+=a[b[++cnt]];
		if (max(pos[i],pos[i+n])<=cnt) t+=a[b[++cnt]];
		if (pos[i]>cnt) t+=a[i];
		if (pos[i+n]>cnt) t+=a[i+n];
		ans=min(ans,t);
	}
	printf("%lld\n",ans);
	return 0;
}
### Prompt

In cpp, your task is to solve 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;
typedef long long ll;
const int N=200005,p=1000000007,inf=0x3f3f3f3f;
int read(){
	int f=1,g=0;char ch=getchar();
	for (;!isdigit(ch);ch=getchar()) if (ch=='-') f=-1;
	for (;isdigit(ch);ch=getchar()) g=g*10+ch-'0';
	return f*g;
}
int n,a[N],b[N],pos[N];
ll sum,ans;
bool cmp(int x,int y){return a[x]<a[y];}
int main(){
	n=read();
	for (int i=1;i<=n;i++) a[i]=read(),a[i+n]=read();
	ans=0;
	for (int i=1;i<=n;i++) ans+=a[i];
	sum=0;
	for (int i=n+1;i<=n*2;i++) sum+=a[i];
	ans=min(ans,sum);
	for (int i=1;i<=n*2;i++) b[i]=i;
	sort(b+1,b+n*2+1,cmp);
	for (int i=1;i<=n*2;i++) pos[b[i]]=i;
	
	sum=0;
	for (int i=1;i<=n-2;i++) sum+=a[b[i]];
	for (int i=1;i<=n;i++){
		ll t=sum;int cnt=n-2;
		if (min(pos[i],pos[i+n])<=cnt) t+=a[b[++cnt]];
		if (max(pos[i],pos[i+n])<=cnt) t+=a[b[++cnt]];
		if (pos[i]>cnt) t+=a[i];
		if (pos[i+n]>cnt) t+=a[i+n];
		ans=min(ans,t);
	}
	printf("%lld\n",ans);
	return 0;
}
```