#include<bits/stdc++.h>
using namespace std;
#define MN 100000
struct P{int x,y;}p[MN*2+5];
bool cmp(const P&a,const P&b){return a.x<b.x;}
int u[MN+5];
int main()
{
	int n,i,x=0,y=0;long long ans=0;
	scanf("%d",&n);
	for(i=1;i<=n;++i)scanf("%d%d",&p[i].x,&p[i+n].x),p[i].y=i,p[i+n].y=-i;
	sort(p+1,p+n+n+1,cmp);
	for(i=1;i<=n;++i)ans+=p[i].x,x|=u[abs(p[i].y)]++,y|=1LL*p[i].y*p[i-1].y<0;
	printf("%lld",x||!y?ans:p[n].y==-p[n+1].y?ans+min(p[n+2].x-p[n].x,p[n+1].x-p[n-1].x):ans-p[n].x+p[n+1].x);
}
### Prompt

Develop a solution in CPP to the problem described below:

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>
using namespace std;
#define MN 100000
struct P{int x,y;}p[MN*2+5];
bool cmp(const P&a,const P&b){return a.x<b.x;}
int u[MN+5];
int main()
{
	int n,i,x=0,y=0;long long ans=0;
	scanf("%d",&n);
	for(i=1;i<=n;++i)scanf("%d%d",&p[i].x,&p[i+n].x),p[i].y=i,p[i+n].y=-i;
	sort(p+1,p+n+n+1,cmp);
	for(i=1;i<=n;++i)ans+=p[i].x,x|=u[abs(p[i].y)]++,y|=1LL*p[i].y*p[i-1].y<0;
	printf("%lld",x||!y?ans:p[n].y==-p[n+1].y?ans+min(p[n+2].x-p[n].x,p[n+1].x-p[n-1].x):ans-p[n].x+p[n+1].x);
}
```