#include<cstdio>
#include<algorithm>
using namespace std;
const int N=600002;
typedef long long ll;
int n,i,x,y,m,cnt[N],p;
struct Uzi{
    int val,id,tmp;
}a[N];
ll s[N];
bool cmp(Uzi u,Uzi v){
    return u.val<v.val;
}
void init(){
    scanf("%d",&n);
    for(i=1;i<=n;i++){
        scanf("%d%d",&x,&y);
        a[++m]=(Uzi){x,i,0};
        a[++m]=(Uzi){y,i,1};
    }
    sort(a+1,a+m+1,cmp);
}
void work(){
    for(i=1;i<=m;i++)
        s[i]=s[i-1]+a[i].val;
    for(i=1;i<=n;i++){
        cnt[a[i].id]++;
        if(cnt[a[i].id]>1){
            printf("%lld\n",s[n]);
            return;
        }
        p+=a[i].tmp==0;
    }
    if(p%n==0){
        printf("%lld\n",s[n]);
        return;
    }
    cnt[a[n].id]--;
    cnt[a[n+1].id]++;
    if(cnt[a[n+1].id]>1){
        printf("%lld\n",s[n-1]+a[n+1].val);
        return;
    }    
    printf("%lld",s[n-2]+min(a[n-1].val+a[n+2].val,a[n].val+a[n+1].val));
}
int main(){
    init();
    work();
    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<cstdio>
#include<algorithm>
using namespace std;
const int N=600002;
typedef long long ll;
int n,i,x,y,m,cnt[N],p;
struct Uzi{
    int val,id,tmp;
}a[N];
ll s[N];
bool cmp(Uzi u,Uzi v){
    return u.val<v.val;
}
void init(){
    scanf("%d",&n);
    for(i=1;i<=n;i++){
        scanf("%d%d",&x,&y);
        a[++m]=(Uzi){x,i,0};
        a[++m]=(Uzi){y,i,1};
    }
    sort(a+1,a+m+1,cmp);
}
void work(){
    for(i=1;i<=m;i++)
        s[i]=s[i-1]+a[i].val;
    for(i=1;i<=n;i++){
        cnt[a[i].id]++;
        if(cnt[a[i].id]>1){
            printf("%lld\n",s[n]);
            return;
        }
        p+=a[i].tmp==0;
    }
    if(p%n==0){
        printf("%lld\n",s[n]);
        return;
    }
    cnt[a[n].id]--;
    cnt[a[n+1].id]++;
    if(cnt[a[n+1].id]>1){
        printf("%lld\n",s[n-1]+a[n+1].val);
        return;
    }    
    printf("%lld",s[n-2]+min(a[n-1].val+a[n+2].val,a[n].val+a[n+1].val));
}
int main(){
    init();
    work();
    return 0;
}
```