#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
#define REP(i,n) for(int i=(0);i<(n);i++)
#define fi first
#define se second
#define pb push_back
#define mp make_pair
using namespace std;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef long long ll;
 
template<class T> inline void read(T &x){
	int f=0;x=0;char ch=getchar();
	for(;!isdigit(ch);ch=getchar())f|=(ch=='-');
	for(;isdigit(ch);ch=getchar())x=x*10+ch-'0';
	if(f)x=-x;
}
 
const int N=200005;
int a[N],b[N],c[N],n;
ll A,B,S,ans;
 
int main(){
	read(n);
	rep(i,1,n){
		read(a[i]),read(b[i]);
		A+=a[i],B+=b[i];
		if(a[i]>b[i])swap(a[i],b[i]);
		c[i*2-1]=a[i],c[i<<1]=b[i];
	}
	ans=min(A,B);
	sort(c+1,c+n*2+1);
	rep(i,1,n-2)S+=c[i];
	rep(i,1,n){
		ll s=S+a[i]+b[i]; int k=n-2;
		if(a[i]<=c[k]) s=s-a[i]+c[++k];
		if(b[i]<=c[k]) s=s-b[i]+c[++k];
		ans=min(ans,s);
	}
	cout<<ans<<endl;
	return 0;
}
### Prompt

Your task is to create 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 rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
#define REP(i,n) for(int i=(0);i<(n);i++)
#define fi first
#define se second
#define pb push_back
#define mp make_pair
using namespace std;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef long long ll;
 
template<class T> inline void read(T &x){
	int f=0;x=0;char ch=getchar();
	for(;!isdigit(ch);ch=getchar())f|=(ch=='-');
	for(;isdigit(ch);ch=getchar())x=x*10+ch-'0';
	if(f)x=-x;
}
 
const int N=200005;
int a[N],b[N],c[N],n;
ll A,B,S,ans;
 
int main(){
	read(n);
	rep(i,1,n){
		read(a[i]),read(b[i]);
		A+=a[i],B+=b[i];
		if(a[i]>b[i])swap(a[i],b[i]);
		c[i*2-1]=a[i],c[i<<1]=b[i];
	}
	ans=min(A,B);
	sort(c+1,c+n*2+1);
	rep(i,1,n-2)S+=c[i];
	rep(i,1,n){
		ll s=S+a[i]+b[i]; int k=n-2;
		if(a[i]<=c[k]) s=s-a[i]+c[++k];
		if(b[i]<=c[k]) s=s-b[i]+c[++k];
		ans=min(ans,s);
	}
	cout<<ans<<endl;
	return 0;
}
```