#include <bits/stdc++.h>
#define int long long 
#define inf 1e18
using namespace std;
const int N=1e5+100;
int n,a[N],b[N],w,ans,sh[N*2];
signed main()
{
	scanf("%lld",&n);
	for (int i=1;i<=n;i++)
	{
		scanf("%lld%lld",&a[i],&b[i]);
		sh[++w]=a[i];
		sh[++w]=b[i];
	}
	sort(sh+1,sh+1+n+n);
	int sum=0;ans=inf;
	for (int i=1;i<=n;i++) sum+=a[i];
	ans=min(ans,sum);
	sum=0;
	for (int i=1;i<=n;i++) sum+=b[i];
	ans=min(ans,sum);
	sum=0;
	for (int i=1;i<=n-2;i++) sum+=sh[i];
	for (int i=1;i<=n;i++)
	{
		int tmp=sum+a[i]+b[i],pa,pb;
		pa=lower_bound(sh+1,sh+1+2*n,a[i])-sh;
		pb=lower_bound(sh+1,sh+1+2*n,b[i])-sh;
		if (pa>pb) swap(pa,pb),swap(a[i],b[i]);
		if (pa<=n-2)
		{
			tmp-=a[i];
			if (pb<=n-1)
			{
				tmp-=b[i];
				tmp+=sh[n-1]+sh[n];
			}
			else tmp+=sh[n-1];
		}
		ans=min(ans,tmp);
	}
	printf("%lld\n",ans);
}
### 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>
#define int long long 
#define inf 1e18
using namespace std;
const int N=1e5+100;
int n,a[N],b[N],w,ans,sh[N*2];
signed main()
{
	scanf("%lld",&n);
	for (int i=1;i<=n;i++)
	{
		scanf("%lld%lld",&a[i],&b[i]);
		sh[++w]=a[i];
		sh[++w]=b[i];
	}
	sort(sh+1,sh+1+n+n);
	int sum=0;ans=inf;
	for (int i=1;i<=n;i++) sum+=a[i];
	ans=min(ans,sum);
	sum=0;
	for (int i=1;i<=n;i++) sum+=b[i];
	ans=min(ans,sum);
	sum=0;
	for (int i=1;i<=n-2;i++) sum+=sh[i];
	for (int i=1;i<=n;i++)
	{
		int tmp=sum+a[i]+b[i],pa,pb;
		pa=lower_bound(sh+1,sh+1+2*n,a[i])-sh;
		pb=lower_bound(sh+1,sh+1+2*n,b[i])-sh;
		if (pa>pb) swap(pa,pb),swap(a[i],b[i]);
		if (pa<=n-2)
		{
			tmp-=a[i];
			if (pb<=n-1)
			{
				tmp-=b[i];
				tmp+=sh[n-1]+sh[n];
			}
			else tmp+=sh[n-1];
		}
		ans=min(ans,tmp);
	}
	printf("%lld\n",ans);
}
```