#include<bits/stdc++.h>
using namespace std;

#define rep(i,n) for(int i=0;i<(n);i++)
#define REP(i,n) for(int i=1;i<=(n);i++)
#define mp make_pair
#define pb push_back
#define fst first
#define snd second
typedef long long ll;
typedef pair<int,int> pii;

const int maxn=100005;
int n;
int a[maxn],b[maxn];
pii val[maxn*2];
bool occ[maxn];

int main(){
	scanf("%d",&n);
	ll suma=0,sumb=0;
	REP(i,n){
		scanf("%d%d",&a[i],&b[i]);
		val[i]=mp(a[i],i);
		val[i+n]=mp(b[i],i);
		suma+=a[i];
		sumb+=b[i];
	}
	sort(val+1,val+1+2*n);
	ll ans=0;
	int tot=0,cnt=0,spe=0;
	REP(i,2*n){
		int id=val[i].snd;
		if(tot==n-1&&cnt==n-1&&!occ[id]){
			spe=id;
			continue;
		}
		if(!occ[id]){
			cnt++;
			occ[id]=true;
		}
		ans+=val[i].fst;
		tot++;
		if(tot==n)break;
	}
	if(spe){
		ll ans2=a[spe]+b[spe];
		REP(i,n-2)ans2+=val[i].fst;
		ans=min(ans,ans2);
	}
	printf("%lld\n",min(ans,min(suma,sumb)));
	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>
using namespace std;

#define rep(i,n) for(int i=0;i<(n);i++)
#define REP(i,n) for(int i=1;i<=(n);i++)
#define mp make_pair
#define pb push_back
#define fst first
#define snd second
typedef long long ll;
typedef pair<int,int> pii;

const int maxn=100005;
int n;
int a[maxn],b[maxn];
pii val[maxn*2];
bool occ[maxn];

int main(){
	scanf("%d",&n);
	ll suma=0,sumb=0;
	REP(i,n){
		scanf("%d%d",&a[i],&b[i]);
		val[i]=mp(a[i],i);
		val[i+n]=mp(b[i],i);
		suma+=a[i];
		sumb+=b[i];
	}
	sort(val+1,val+1+2*n);
	ll ans=0;
	int tot=0,cnt=0,spe=0;
	REP(i,2*n){
		int id=val[i].snd;
		if(tot==n-1&&cnt==n-1&&!occ[id]){
			spe=id;
			continue;
		}
		if(!occ[id]){
			cnt++;
			occ[id]=true;
		}
		ans+=val[i].fst;
		tot++;
		if(tot==n)break;
	}
	if(spe){
		ll ans2=a[spe]+b[spe];
		REP(i,n-2)ans2+=val[i].fst;
		ans=min(ans,ans2);
	}
	printf("%lld\n",min(ans,min(suma,sumb)));
	return 0;
}
```