#include<bits/stdc++.h>
#define ll long long
using namespace std;
template<typename tn> void read(tn &a){
	tn x=0,f=1; char c=' ';
	for(;!isdigit(c);c=getchar()) if(c=='-') f=-1;
	for(;isdigit(c);c=getchar()) x=x*10+c-'0';
	a=x*f;
}
ll s[201000],p[201000],a[101000],b[101000],n,cnt;
int main(){
	read(n);
	ll s1=0,s2=0;
	for(int i=1;i<=n;i++)
		read(a[i]),read(b[i]),s1+=a[i],s2+=b[i],p[++cnt]=a[i],p[++cnt]=b[i];
	sort(p+1,p+cnt+1);
	for(int i=1;i<=cnt;i++) s[i]=s[i-1]+p[i];
	ll ans=min(s1,s2);
	for(int i=1;i<=n;i++){
		int now=n;ll tag=0;
		if(min(a[i],b[i])<=p[now]) now++,tag-=min(a[i],b[i]);
		if(max(b[i],a[i])<=p[now]) now++,tag-=max(a[i],b[i]);
		ans=min(ans,s[now]+tag);
	}
	cout<<ans<<'\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>
#define ll long long
using namespace std;
template<typename tn> void read(tn &a){
	tn x=0,f=1; char c=' ';
	for(;!isdigit(c);c=getchar()) if(c=='-') f=-1;
	for(;isdigit(c);c=getchar()) x=x*10+c-'0';
	a=x*f;
}
ll s[201000],p[201000],a[101000],b[101000],n,cnt;
int main(){
	read(n);
	ll s1=0,s2=0;
	for(int i=1;i<=n;i++)
		read(a[i]),read(b[i]),s1+=a[i],s2+=b[i],p[++cnt]=a[i],p[++cnt]=b[i];
	sort(p+1,p+cnt+1);
	for(int i=1;i<=cnt;i++) s[i]=s[i-1]+p[i];
	ll ans=min(s1,s2);
	for(int i=1;i<=n;i++){
		int now=n;ll tag=0;
		if(min(a[i],b[i])<=p[now]) now++,tag-=min(a[i],b[i]);
		if(max(b[i],a[i])<=p[now]) now++,tag-=max(a[i],b[i]);
		ans=min(ans,s[now]+tag);
	}
	cout<<ans<<'\n';
	return 0;
}

```