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;

bool vis[200001];
int l[100001],r[100001];
int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n;
	cin>>n;
	vector<pair<int,int> > v;
	long long int ans, tot = 0,totl = 0, totr = 0;
	for(int i=0;i<n;i++){
		cin>>l[i]>>r[i];totl+=l[i],totr+=r[i];
		v.emplace_back(l[i],i<<1);
		v.emplace_back(r[i],i<<1|1);
	}
	ans = min(totl,totr);
	sort(v.begin(),v.end());
	for(int i=0;i<n-2;i++)
		vis[v[i].second] = true, tot += v[i].first;
	for(int i=0;i<n;i++){
		int stp = n-2;
		long long int cur = tot;
		if(vis[i<<1]){
			while((v[stp].second>>1) == i)	stp++;
			cur += v[stp++].first;
		}
		else
			cur += l[i];
		if(vis[i<<1|1]){
			while((v[stp].second>>1) == i)	stp++;
			cur += v[stp++].first;
		}
		else
			cur += r[i];
		ans = min(ans,cur);
	}
	cout<<ans<<endl;
}
