#include<bits/stdc++.h>
using namespace std;
const int N=100100;
typedef long long ll;
pair<int,int>a[N],b[N];
ll sumx,sumy,sa[N],sb[N],ans;
int n,ia[N],ib[N];
int main(){
#ifdef ONLINE_JUDGE
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#endif
	cin>>n;
	for(int i=1;i<=n;++i){
		int x,y;cin>>x>>y;
		a[i]=make_pair(x,i);b[i]=make_pair(y,i);
		sumx+=x;sumy+=y;
	}
	ans=min(sumx,sumy);
	sort(a+1,a+n+1);sort(b+1,b+n+1);
	for(int i=1;i<=n;++i){
		ia[a[i].second]=i;ib[b[i].second]=i;
		sa[i]=sa[i-1]+a[i].first;sb[i]=sb[i-1]+b[i].first;
	}
	int rg=n+1;
	for(int i=1;i<n;++i){
		rg=min(rg,ib[a[i].second]);
		if(rg<=n-i)ans=min(ans,sa[i]+sb[n-i]);
		else ans=min(ans,min(sa[i-1]+a[i+1].first+sb[n-i],sa[i]+sb[n-i-1]+b[n-i+1].first));
	}
	cout<<ans<<endl;
	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;
const int N=100100;
typedef long long ll;
pair<int,int>a[N],b[N];
ll sumx,sumy,sa[N],sb[N],ans;
int n,ia[N],ib[N];
int main(){
#ifdef ONLINE_JUDGE
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#endif
	cin>>n;
	for(int i=1;i<=n;++i){
		int x,y;cin>>x>>y;
		a[i]=make_pair(x,i);b[i]=make_pair(y,i);
		sumx+=x;sumy+=y;
	}
	ans=min(sumx,sumy);
	sort(a+1,a+n+1);sort(b+1,b+n+1);
	for(int i=1;i<=n;++i){
		ia[a[i].second]=i;ib[b[i].second]=i;
		sa[i]=sa[i-1]+a[i].first;sb[i]=sb[i-1]+b[i].first;
	}
	int rg=n+1;
	for(int i=1;i<n;++i){
		rg=min(rg,ib[a[i].second]);
		if(rg<=n-i)ans=min(ans,sa[i]+sb[n-i]);
		else ans=min(ans,min(sa[i-1]+a[i+1].first+sb[n-i],sa[i]+sb[n-i-1]+b[n-i+1].first));
	}
	cout<<ans<<endl;
	return 0;
}


```