#include<bits/stdc++.h>
#define inf 0x3f3f3f3f
using namespace std;
typedef long long ll;
const int N=1e5+5;
int n,a[N],b[N],c[N<<1];
ll sum[N<<1];
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%d%d",&a[i],&b[i]);
    ll ans=1e18,res=0;
    for(int i=1;i<=n;i++) res+=a[i];
    ans=min(ans,res);
    res=0;
    for(int i=1;i<=n;i++) res+=b[i];
    ans=min(ans,res);
    for(int i=1;i<=n;i++) c[i]=a[i],c[i+n]=b[i];
    sort(c+1,c+1+n+n);
    for(int i=1;i<=n+n;i++) sum[i]=sum[i-1]+c[i];
    for(int i=1;i<=n;i++)
    {
        if(a[i]<=c[n]&&b[i]<=c[n]) res=sum[n];
        else if(a[i]<=c[n-1]||b[i]<=c[n-1]) res=sum[n-1]+max(a[i],b[i]);
        else res=sum[n-2]+a[i]+b[i];
        ans=min(ans,res);
    }
    printf("%lld\n",ans);
}

### 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>
#define inf 0x3f3f3f3f
using namespace std;
typedef long long ll;
const int N=1e5+5;
int n,a[N],b[N],c[N<<1];
ll sum[N<<1];
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%d%d",&a[i],&b[i]);
    ll ans=1e18,res=0;
    for(int i=1;i<=n;i++) res+=a[i];
    ans=min(ans,res);
    res=0;
    for(int i=1;i<=n;i++) res+=b[i];
    ans=min(ans,res);
    for(int i=1;i<=n;i++) c[i]=a[i],c[i+n]=b[i];
    sort(c+1,c+1+n+n);
    for(int i=1;i<=n+n;i++) sum[i]=sum[i-1]+c[i];
    for(int i=1;i<=n;i++)
    {
        if(a[i]<=c[n]&&b[i]<=c[n]) res=sum[n];
        else if(a[i]<=c[n-1]||b[i]<=c[n-1]) res=sum[n-1]+max(a[i],b[i]);
        else res=sum[n-2]+a[i]+b[i];
        ans=min(ans,res);
    }
    printf("%lld\n",ans);
}

```