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

#include<bits/stdc++.h>
using namespace std;
#define int long long
const int maxn=1000001;
int n,a[maxn],b[maxn];
struct asuka{int id,val;}q[maxn];
int cntx,cnty,x,y,ans,cnt[maxn],flag,top;
bool cmp(asuka a,asuka b){if(a.val!=b.val)return a.val<b.val;else return a.id<b.id;}
signed main()
{
    cin>>n;
    for(int i=1;i<=n;i++)
        cin>>a[i]>>b[i],
        cntx+=a[i],cnty+=b[i],
        q[++top]={i,a[i]},q[++top]={i,b[i]};
    ans=min(cntx,cnty);
    cntx=cnty=0;
    sort(q+1,q+1+2*n,cmp);
    for(int i=1;i<=n;i++)
    {
        cnt[q[i].id]++;
        cntx+=q[i].val;
    }
    for(int i=1;i<=n;i++)if(cnt[i]==0)flag=1;
    if(flag)ans=min(ans,cntx);
    else 
    {
        if(q[n].id==q[n+1].id)
        {
            ans=min(ans,cntx-q[n].val+q[n+2].val);
            ans=min(ans,cntx-q[n-1].val+q[n+1].val);
        }
        else ans=min(ans,cntx-q[n].val+q[n+1].val);
    }
    cout<<ans;
}
