    #include <bits/stdc++.h>
    using namespace std;
    #define int long long
    #define N 100010
    struct node{
    	int x,id;
    	bool operator<(const node &a) const{
    		return x<a.x;
    	}
    	node(int x=0,int id=0):x(x),id(id){}
    }P[N<<1];
    bool vis[N];
    int n,x,y,M1=0,M2=0,tot=0;
    signed main(){
    	scanf("%lld",&n);
    	for (int i=1;i<=n;i++){
    		scanf("%lld%lld",&x,&y);
    		M1+=x; M2+=y;
    		P[++tot]=node(x,i);
    		P[++tot]=node(y,i);
    	}
    	sort(P+1,P+1+tot);
    	bool flag=0; int Mn=0;
    	for (int i=1;i<=n;i++){
    		Mn+=P[i].x;
    		if (vis[P[i].id]) flag=1;
    		vis[P[i].id]=1;
    	}
    	if (!flag) {
    		if (P[n+1].id==P[n].id) Mn=min(Mn-P[n].x+P[n+2].x,Mn-P[n-1].x+P[n+1].x);
    		else Mn=Mn-P[n].x+P[n+1].x;
    	}
    	printf("%lld\n",min(min(Mn,M1),M2));
    	return 0;
    }
### 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>
    using namespace std;
    #define int long long
    #define N 100010
    struct node{
    	int x,id;
    	bool operator<(const node &a) const{
    		return x<a.x;
    	}
    	node(int x=0,int id=0):x(x),id(id){}
    }P[N<<1];
    bool vis[N];
    int n,x,y,M1=0,M2=0,tot=0;
    signed main(){
    	scanf("%lld",&n);
    	for (int i=1;i<=n;i++){
    		scanf("%lld%lld",&x,&y);
    		M1+=x; M2+=y;
    		P[++tot]=node(x,i);
    		P[++tot]=node(y,i);
    	}
    	sort(P+1,P+1+tot);
    	bool flag=0; int Mn=0;
    	for (int i=1;i<=n;i++){
    		Mn+=P[i].x;
    		if (vis[P[i].id]) flag=1;
    		vis[P[i].id]=1;
    	}
    	if (!flag) {
    		if (P[n+1].id==P[n].id) Mn=min(Mn-P[n].x+P[n+2].x,Mn-P[n-1].x+P[n+1].x);
    		else Mn=Mn-P[n].x+P[n+1].x;
    	}
    	printf("%lld\n",min(min(Mn,M1),M2));
    	return 0;
    }
```