Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 5
4 2
6 3

Sample Output 1

7

Consider the cycle 1→3→2→1. The weights of those edges are {\rm min}(A_1,B_3)=1, {\rm min}(A_3,B_2)=2 and {\rm min}(A_2,B_1)=4, for a total of 7.
As there is no cycle with a total weight of less than 7, the answer is 7.

Sample Input 2

4
1 5
2 6
3 7
4 8

Sample Output 2

10

Sample Input 3

6
19 92
64 64
78 48
57 33
73 6
95 73

Sample Output 3

227

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define pii pair<int,int>
#define fi first
#define se second

#define ll long long

int n, a[101000], b[101000], ark[101000], brk[101000];
pii pa[101000], pb[101000];

ll ans;

int main(){
    cin>>n;
    for (int i=1;i<=n;++i){
        cin>>a[i]>>b[i];
        pa[i]={a[i],i};
        pb[i]={b[i],i};
    }
    sort(pa+1,pa+n+1);
    sort(pb+1,pb+n+1);
    for (int i=1;i<=n;++i){
        ark[pa[i].se]=i;
        brk[pb[i].se]=i;
    }

    set<int>S;
    int p1=1, p2=1;
    for (int i=1;i<=n;++i)
        if (pa[p1].fi<pb[p2].fi){
            S.insert(pa[p1].se);
            ans+=pa[p1++].fi;
        }else{
            S.insert(pb[p2].se);
            ans+=pb[p2++].fi;
        }
    
    if (p1>n||p2>n||S.size()<n){
        cout<<ans<<endl; return 0;
    }
    ll bas=ans;
    ans=min(bas+pa[p1].fi-pa[p1-1].fi,bas+pb[p2].fi-pb[p2-1].fi);
    for (int i=0;i<2;++i)
        for (int j=1;j<=2;++j)
            if (p1+i<=n&&p2-j>=1)
                if (pa[p1+i].se!=pb[p2-j].se){
                    ans=min(ans,bas+pa[p1+i].fi-pb[p2-j].fi);
                }
    for (int i=0;i<2;++i)
        for (int j=1;j<=2;++j)
            if (p2+i<=n&&p1-j>=1)
                if (pb[p2+i].se!=pa[p1-j].se){
                    ans=min(ans,bas+pb[p2+i].fi-pa[p1-j].fi);
                }
    cout<<ans<<endl;
}