#include <bits/stdc++.h>
#define LL long long
#define MEM(x,y) memset(x,y,sizeof(x))
#define MOD(x) ((x)%1000000007)

using namespace std;
const int maxn = 1e5+7;
LL a[maxn],b[maxn],c[2*maxn],sum[2*maxn],suma,sumb;
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL);
    int tot=0,n;cin>>n;
    suma=sumb=0;
    for (int i=1;i<=n;i++)
    {
        cin>>a[i]>>b[i];
        suma+=a[i];sumb+=b[i];
        c[++tot]=a[i];c[++tot]=b[i];
    }
    sort(c+1,c+1+tot);
    for (int i=1;i<=n;i++) sum[i]=c[i]+sum[i-1];
    LL ans=min(suma,sumb);
    for (int i=1;i<=n;i++)
    {
        int bound=n;
        LL tmp=0;
        if (a[i]>=c[bound]) tmp+=a[i],bound--;
        if (b[i]>=c[bound]) tmp+=b[i],bound--;
        ans=min(ans,sum[bound]+tmp);
    }
    cout<<ans;
    return 0;
}

### Prompt

Please formulate 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 LL long long
#define MEM(x,y) memset(x,y,sizeof(x))
#define MOD(x) ((x)%1000000007)

using namespace std;
const int maxn = 1e5+7;
LL a[maxn],b[maxn],c[2*maxn],sum[2*maxn],suma,sumb;
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL);
    int tot=0,n;cin>>n;
    suma=sumb=0;
    for (int i=1;i<=n;i++)
    {
        cin>>a[i]>>b[i];
        suma+=a[i];sumb+=b[i];
        c[++tot]=a[i];c[++tot]=b[i];
    }
    sort(c+1,c+1+tot);
    for (int i=1;i<=n;i++) sum[i]=c[i]+sum[i-1];
    LL ans=min(suma,sumb);
    for (int i=1;i<=n;i++)
    {
        int bound=n;
        LL tmp=0;
        if (a[i]>=c[bound]) tmp+=a[i],bound--;
        if (b[i]>=c[bound]) tmp+=b[i],bound--;
        ans=min(ans,sum[bound]+tmp);
    }
    cout<<ans;
    return 0;
}

```