#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int a[101010],b[101010];
int c[202020];
int main()
{
	int n,cn,now;
	long long suma=0,sumb=0,sum=0,ans,k;
	scanf("%d",&n);
	cn=0;
	for(int i=1;i<=n;i++)
	{
		scanf("%d%d",&a[i],&b[i]);
		suma+=a[i];
		sumb+=b[i];
		c[++cn]=a[i];
		c[++cn]=b[i];
	}
	ans=min(suma,sumb);
	sort(c+1,c+1+cn);
	for(int i=1;i<=n;i++)
		sum+=c[i];
	for(int i=1;i<=n;i++)
	{
		now=n;
		k=sum;
		if(max(a[i],b[i])>c[now])
		{
			k+=max(a[i],b[i]);
			k-=c[now];
			now--;
		}
		if(min(a[i],b[i])>c[now])
		{
			k+=min(a[i],b[i]);
			k-=c[now];
			now--;
		}
		ans=min(ans,k);
	}
	printf("%lld",ans);
	return 0;
}
### Prompt

Please formulate 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<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int a[101010],b[101010];
int c[202020];
int main()
{
	int n,cn,now;
	long long suma=0,sumb=0,sum=0,ans,k;
	scanf("%d",&n);
	cn=0;
	for(int i=1;i<=n;i++)
	{
		scanf("%d%d",&a[i],&b[i]);
		suma+=a[i];
		sumb+=b[i];
		c[++cn]=a[i];
		c[++cn]=b[i];
	}
	ans=min(suma,sumb);
	sort(c+1,c+1+cn);
	for(int i=1;i<=n;i++)
		sum+=c[i];
	for(int i=1;i<=n;i++)
	{
		now=n;
		k=sum;
		if(max(a[i],b[i])>c[now])
		{
			k+=max(a[i],b[i]);
			k-=c[now];
			now--;
		}
		if(min(a[i],b[i])>c[now])
		{
			k+=min(a[i],b[i]);
			k-=c[now];
			now--;
		}
		ans=min(ans,k);
	}
	printf("%lld",ans);
	return 0;
}
```