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 <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
using namespace std;
typedef long long int ll;
typedef pair<ll, int> P;

int main()
{
	int n;
	cin>>n;
	ll a[100000], b[100000];
	ll s1=0, s2=0;
	vector<P> v;
	for(int i=0; i<n; i++){
		cin>>a[i]>>b[i];
		s1+=a[i]; s2+=b[i];
		v.push_back(P(a[i], i));
		v.push_back(P(b[i], i));
	}
	sort(v.begin(), v.end());
	ll ans=min(s1, s2);
	set<int> st;
	ll s3=0;
	for(int i=0; i<n; i++){
		st.insert(v[i].second);
		s3+=v[i].first;
	}
	if(st.size()<n){
		cout<<min(s3, ans)<<endl;
		return 0;
	}
	if(v[n-1].second!=v[n].second){
		cout<<min(s3-v[n-1].first+v[n].first, ans)<<endl;
		return 0;
	}
	ll s4=s3-v[n-2].first+v[n].first;
	ll s5=s3-v[n-1].first+v[n+1].first;
	cout<<min(ans, min(s4, s5))<<endl;
	return 0;
}