#include<bits/stdc++.h>
#define F first
#define S second
#define PQ pq.top()
using namespace std;
int a,b,n,k,pas,pss,dd,pss1;
long long ans;
bool p=false;
bitset<100005>BIT;
priority_queue<pair<int,pair<int,int> > >pq;
int main()
{
	//freopen("subtask01-05.txt","r",stdin);
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d %d",&a,&b),pq.push({-a,{0,i}}),pq.push({-b,{1,i}});
	for(int i=1;i<=n;i++)
	{
		if(i==n-1)dd=PQ.F;
		if(i==n)pas=PQ.F,pss=PQ.S.S;
		ans-=PQ.F;
		if(PQ.S.F==0)k++;
		if(BIT[PQ.S.S])p=true;
		BIT[PQ.S.S]=true;
		pq.pop();
	}
	if(k==0||k==n||p)
	{
		printf("%lld",ans);
	}
	else if(pss==PQ.S.S)
	{
		if(k==1&&PQ.S.F==0)
		{
			printf("%lld",ans+pas-PQ.F);
		}
		else if(k==n-1&&PQ.S.F==1)
		{
			printf("%lld",ans+pas-PQ.F);
		}
		else
		{
			pss1=PQ.F;
			//printf("%lld\n",ans+dd-PQ.F);
			pq.pop();
			printf("%lld",min(ans-pss1+dd,ans-PQ.F+pas));
		}
	}
	else
	{
		printf("%lld",ans+pas-PQ.F);
	}
}

### Prompt

Create a solution in Cpp for 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 F first
#define S second
#define PQ pq.top()
using namespace std;
int a,b,n,k,pas,pss,dd,pss1;
long long ans;
bool p=false;
bitset<100005>BIT;
priority_queue<pair<int,pair<int,int> > >pq;
int main()
{
	//freopen("subtask01-05.txt","r",stdin);
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d %d",&a,&b),pq.push({-a,{0,i}}),pq.push({-b,{1,i}});
	for(int i=1;i<=n;i++)
	{
		if(i==n-1)dd=PQ.F;
		if(i==n)pas=PQ.F,pss=PQ.S.S;
		ans-=PQ.F;
		if(PQ.S.F==0)k++;
		if(BIT[PQ.S.S])p=true;
		BIT[PQ.S.S]=true;
		pq.pop();
	}
	if(k==0||k==n||p)
	{
		printf("%lld",ans);
	}
	else if(pss==PQ.S.S)
	{
		if(k==1&&PQ.S.F==0)
		{
			printf("%lld",ans+pas-PQ.F);
		}
		else if(k==n-1&&PQ.S.F==1)
		{
			printf("%lld",ans+pas-PQ.F);
		}
		else
		{
			pss1=PQ.F;
			//printf("%lld\n",ans+dd-PQ.F);
			pq.pop();
			printf("%lld",min(ans-pss1+dd,ans-PQ.F+pas));
		}
	}
	else
	{
		printf("%lld",ans+pas-PQ.F);
	}
}

```