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: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i,n) for ((i)=1;(i)<=(n);(i)++)
#define foreach(c,itr) for (__typeof((c).begin()) itr=(c).begin();itr!=(c).end();++itr)
using namespace std;
int n,i;
long long ans,tmp,sx,sy,sum;
set<int> s;
struct _{
	int x,id;
}a[200005];
bool cmp(_ x,_ y){
	return x.x>y.x;
}
int main(){
	cin>>n;
	rep(i,n){
		int x,y;
		cin>>x>>y;
		a[i+i-1]=(_){x,i};
		a[i+i]=(_){y,i};
		sx+=x;sy+=y;
	}
	sum=sx+sy;
	ans=max(sx,sy);
	sort(a+1,a+n+n+1,cmp);
	
	tmp=0;s.clear();
	rep(i,n){
		tmp+=a[i].x;
		s.insert(a[i].id);
	}ans=max(ans,tmp);
	cout<<sum-ans<<endl;
	return 0;
}