#include<bits/stdc++.h>
#define N 100100
using namespace std;
struct node{int x,w;}a[N+N];
bool in[N+N];
bool cmp(node a,node b){return a.x<b.x;}
int n,t,va[N],vb[N],pd[N];
long long mn=1e18,sm;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i){
		int u,v;scanf("%d %d",&u,&v);
		va[i]=u;vb[i]=v;pd[i]=u>v;
		a[++t]=(node){u,i+i};
		a[++t]=(node){v,i+i+1};
	}
	sort(a+1,a+t+1,cmp);
	for(int i=1;i<=n;++i)sm+=a[i].x,in[a[i].w]=1;
	for(int i=1;i<=n;++i)if(in[i+i]&&in[i+i+1]){
		printf("%lld",sm);return 0;
	}
	for(int i=1;i<=n;++i){
		long long tmp=sm+va[i]+vb[i];
		tmp-=in[i+i]?va[i]:vb[i];
		tmp-=a[n].w/2==i?a[n-1].x:a[n].x;
		mn=min(mn,tmp);
	}
	sm=0;
	for(int i=1;i<=n;++i)sm+=va[i];
	mn=min(mn,sm);
	sm=0;
	for(int i=1;i<=n;++i)sm+=vb[i];
	mn=min(mn,sm);
	printf("%lld",mn);
}
### Prompt

Your challenge is to write 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 N 100100
using namespace std;
struct node{int x,w;}a[N+N];
bool in[N+N];
bool cmp(node a,node b){return a.x<b.x;}
int n,t,va[N],vb[N],pd[N];
long long mn=1e18,sm;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i){
		int u,v;scanf("%d %d",&u,&v);
		va[i]=u;vb[i]=v;pd[i]=u>v;
		a[++t]=(node){u,i+i};
		a[++t]=(node){v,i+i+1};
	}
	sort(a+1,a+t+1,cmp);
	for(int i=1;i<=n;++i)sm+=a[i].x,in[a[i].w]=1;
	for(int i=1;i<=n;++i)if(in[i+i]&&in[i+i+1]){
		printf("%lld",sm);return 0;
	}
	for(int i=1;i<=n;++i){
		long long tmp=sm+va[i]+vb[i];
		tmp-=in[i+i]?va[i]:vb[i];
		tmp-=a[n].w/2==i?a[n-1].x:a[n].x;
		mn=min(mn,tmp);
	}
	sm=0;
	for(int i=1;i<=n;++i)sm+=va[i];
	mn=min(mn,sm);
	sm=0;
	for(int i=1;i<=n;++i)sm+=vb[i];
	mn=min(mn,sm);
	printf("%lld",mn);
}
```