#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int Maxn=100005;
int rk[Maxn][2];
struct node{
    int type,val,id;
}w[2*Maxn];
int main(){
    int n;scanf("%d",&n);
    for(int i=1;i<=n;i++){
        int a,b;scanf("%d%d",&a,&b);
        w[2*i-1]=(node){0,a,i};
        w[2*i]=(node){1,b,i};
    }
    sort(w+1,w+2*n+1,[](const node&a,const node&b){
        return a.val<b.val;
    });
    bool succ=true;
    ll sum=0,ans=LLONG_MAX;
    for(int i=1;i<=2*n;i++)
        rk[w[i].id][w[i].type]=i;
    for(int i=1;i<=n;i++)
        sum+=w[i].val;
    for(int i=2;i<=n;i++)
        if(w[i].type!=w[i-1].type)
            succ=false;
    if(succ){
        cout<<sum<<"\n";
        return 0;
    }
    for(int i=1;i<=n;i++){
        if(rk[i][0]<=n&&rk[i][1]<=n)ans=min(ans,sum);
        else if(rk[i][0]<=n)ans=min(ans,sum+w[rk[i][1]].val-w[rk[i][0]==n?n-1:n].val);
        else if(rk[i][1]<=n)ans=min(ans,sum+w[rk[i][0]].val-w[rk[i][1]==n?n-1:n].val);
    }
    cout<<ans<<"\n";
    return 0;
}
### Prompt

Please provide a CPP coded solution 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;
typedef long long ll;
const int Maxn=100005;
int rk[Maxn][2];
struct node{
    int type,val,id;
}w[2*Maxn];
int main(){
    int n;scanf("%d",&n);
    for(int i=1;i<=n;i++){
        int a,b;scanf("%d%d",&a,&b);
        w[2*i-1]=(node){0,a,i};
        w[2*i]=(node){1,b,i};
    }
    sort(w+1,w+2*n+1,[](const node&a,const node&b){
        return a.val<b.val;
    });
    bool succ=true;
    ll sum=0,ans=LLONG_MAX;
    for(int i=1;i<=2*n;i++)
        rk[w[i].id][w[i].type]=i;
    for(int i=1;i<=n;i++)
        sum+=w[i].val;
    for(int i=2;i<=n;i++)
        if(w[i].type!=w[i-1].type)
            succ=false;
    if(succ){
        cout<<sum<<"\n";
        return 0;
    }
    for(int i=1;i<=n;i++){
        if(rk[i][0]<=n&&rk[i][1]<=n)ans=min(ans,sum);
        else if(rk[i][0]<=n)ans=min(ans,sum+w[rk[i][1]].val-w[rk[i][0]==n?n-1:n].val);
        else if(rk[i][1]<=n)ans=min(ans,sum+w[rk[i][0]].val-w[rk[i][1]==n?n-1:n].val);
    }
    cout<<ans<<"\n";
    return 0;
}
```