#include<bits/stdc++.h>
using namespace std;
#define int long long
const int N=200005;
int n,a[N],to[N],b[N],c[N];
int cmp(int x,int y){
	return a[x]<a[y];
}
signed main(){
	scanf("%lld",&n);
	int sum1=0,sum2=0;
	for (int i=0;i<n;i++)scanf("%lld%lld",&a[i],&a[i+n]),sum1+=a[i],sum2+=a[i+n];
	if (n==2){
		printf("%lld\n",min(a[0],a[3])+min(a[1],a[2]));
		return 0; 
	}
	int ans=min(sum1,sum2);
	for (int i=0;i<2*n;i++)b[i]=i;
	sort(b,b+2*n,cmp);
	c[0]=a[b[0]];
	for (int i=1;i<2*n;i++)c[i]=a[b[i]]+c[i-1];
	for (int i=0;i<2*n;i++)to[b[i]]=i;
	for (int i=0;i<n;i++){
		int now=n-3,v=a[i]+a[i+n];
		if (to[i]<=now|to[i+n]<=now){
			if (to[i]<=now+1)now++,v-=a[i];
			if (to[i+n]<=now+1)now++,v-=a[i+n];
		}
		ans=min(ans,c[now]+v);
	}
	printf("%lld\n",ans);
}
### 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;
#define int long long
const int N=200005;
int n,a[N],to[N],b[N],c[N];
int cmp(int x,int y){
	return a[x]<a[y];
}
signed main(){
	scanf("%lld",&n);
	int sum1=0,sum2=0;
	for (int i=0;i<n;i++)scanf("%lld%lld",&a[i],&a[i+n]),sum1+=a[i],sum2+=a[i+n];
	if (n==2){
		printf("%lld\n",min(a[0],a[3])+min(a[1],a[2]));
		return 0; 
	}
	int ans=min(sum1,sum2);
	for (int i=0;i<2*n;i++)b[i]=i;
	sort(b,b+2*n,cmp);
	c[0]=a[b[0]];
	for (int i=1;i<2*n;i++)c[i]=a[b[i]]+c[i-1];
	for (int i=0;i<2*n;i++)to[b[i]]=i;
	for (int i=0;i<n;i++){
		int now=n-3,v=a[i]+a[i+n];
		if (to[i]<=now|to[i+n]<=now){
			if (to[i]<=now+1)now++,v-=a[i];
			if (to[i+n]<=now+1)now++,v-=a[i+n];
		}
		ans=min(ans,c[now]+v);
	}
	printf("%lld\n",ans);
}
```