#include<bits/stdc++.h>
#define to edge[i].v
#define mp make_pair
#define rint register int
#define debug(x) cerr<<#x<<"="<<x<<endl
#define fgx cerr<<"-------------"<<endl
#define N 1000000
using namespace std;
typedef long long ll;
typedef long double db;
typedef pair<int,int> pii;
int a[N],b[N],c[N]; ll s[N];
int main()
{	int n,t=0; ll s1=0,s2=0,ans; cin>>n;
	for(rint i=1;i<=n;i++)
	scanf("%d%d",&a[i],&b[i]),c[++t]=a[i],c[++t]=b[i],s1+=a[i],s2+=b[i];
	ans=min(s1,s2); sort(c+1,c+t+1);
	for(rint i=1;i<=n;s[i]=s[i-1]+c[i],i++)
	a[i]=lower_bound(c+1,c+t+1,a[i])-c,b[i]=lower_bound(c+1,c+t+1,b[i])-c;
	for(rint i=1;i<=n;i++)
	{	if(a[i]>b[i]) swap(a[i],b[i]);
		if(a[i]<=n-2&&b[i]<=n-1) ans=min(ans,s[n]);
		else if(a[i]<=n-1) ans=min(ans,c[b[i]]+s[n-1]);
		else ans=min(ans,c[a[i]]+c[b[i]]+s[n-2]);
	}
	cout<<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<bits/stdc++.h>
#define to edge[i].v
#define mp make_pair
#define rint register int
#define debug(x) cerr<<#x<<"="<<x<<endl
#define fgx cerr<<"-------------"<<endl
#define N 1000000
using namespace std;
typedef long long ll;
typedef long double db;
typedef pair<int,int> pii;
int a[N],b[N],c[N]; ll s[N];
int main()
{	int n,t=0; ll s1=0,s2=0,ans; cin>>n;
	for(rint i=1;i<=n;i++)
	scanf("%d%d",&a[i],&b[i]),c[++t]=a[i],c[++t]=b[i],s1+=a[i],s2+=b[i];
	ans=min(s1,s2); sort(c+1,c+t+1);
	for(rint i=1;i<=n;s[i]=s[i-1]+c[i],i++)
	a[i]=lower_bound(c+1,c+t+1,a[i])-c,b[i]=lower_bound(c+1,c+t+1,b[i])-c;
	for(rint i=1;i<=n;i++)
	{	if(a[i]>b[i]) swap(a[i],b[i]);
		if(a[i]<=n-2&&b[i]<=n-1) ans=min(ans,s[n]);
		else if(a[i]<=n-1) ans=min(ans,c[b[i]]+s[n-1]);
		else ans=min(ans,c[a[i]]+c[b[i]]+s[n-2]);
	}
	cout<<ans;
	return 0;
}

```