#include<cstdio>
#include<algorithm>
#include<iostream>
#define RI register int
#define CI const int&
using namespace std;
const int N=100005;
struct element
{
	int v,p;
	friend inline bool operator < (const element& A,const element& B)
	{
		return A.v<B.v;
	}
}d[N<<1]; int n,a[N],b[N],p[N],q[N]; long long ans,sa,sb,ret;
int main()
{
	RI i; for (scanf("%d",&n),i=1;i<=n;++i)
	scanf("%d%d",&a[i],&b[i]),d[i].v=a[i],d[i].p=i,
	d[n+i].v=b[i],d[n+i].p=n+i,sa+=a[i],sb+=b[i];
	for (sort(d+1,d+(n<<1)+1),i=1;i<=(n<<1);++i)
	if (d[i].p<=n) p[d[i].p]=i; else q[d[i].p-n]=i;
	for (i=1;i<=n;++i) ret+=d[i].v;
	for (ans=min(sa,sb),i=1;i<=n;++i)
	if (p[i]<=n&&q[i]<=n) ans=min(ans,ret); else
	if (p[i]<=n&&q[i]>n) ans=min(ans,ret+d[q[i]].v-(p[i]!=n?d[n].v:d[n-1].v)); else
	if (p[i]>n&&q[i]<=n) ans=min(ans,ret+d[p[i]].v-(q[i]!=n?d[n].v:d[n-1].v)); else
	ans=min(ans,ret+d[p[i]].v+d[q[i]].v-d[n].v-d[n-1].v);
	return printf("%lld",ans),0;
}
### 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<cstdio>
#include<algorithm>
#include<iostream>
#define RI register int
#define CI const int&
using namespace std;
const int N=100005;
struct element
{
	int v,p;
	friend inline bool operator < (const element& A,const element& B)
	{
		return A.v<B.v;
	}
}d[N<<1]; int n,a[N],b[N],p[N],q[N]; long long ans,sa,sb,ret;
int main()
{
	RI i; for (scanf("%d",&n),i=1;i<=n;++i)
	scanf("%d%d",&a[i],&b[i]),d[i].v=a[i],d[i].p=i,
	d[n+i].v=b[i],d[n+i].p=n+i,sa+=a[i],sb+=b[i];
	for (sort(d+1,d+(n<<1)+1),i=1;i<=(n<<1);++i)
	if (d[i].p<=n) p[d[i].p]=i; else q[d[i].p-n]=i;
	for (i=1;i<=n;++i) ret+=d[i].v;
	for (ans=min(sa,sb),i=1;i<=n;++i)
	if (p[i]<=n&&q[i]<=n) ans=min(ans,ret); else
	if (p[i]<=n&&q[i]>n) ans=min(ans,ret+d[q[i]].v-(p[i]!=n?d[n].v:d[n-1].v)); else
	if (p[i]>n&&q[i]<=n) ans=min(ans,ret+d[p[i]].v-(q[i]!=n?d[n].v:d[n-1].v)); else
	ans=min(ans,ret+d[p[i]].v+d[q[i]].v-d[n].v-d[n-1].v);
	return printf("%lld",ans),0;
}
```