#include<bits/stdc++.h>
#define pii pair<int,int>
#define ll long long
#define rep(i,x,y) for(register int i=(x);i<=(y);++i)
using namespace std;
int n;const int mxn=1e5+5;
int a[mxn],b[mxn];
ll sa,sb;
int main(){
	scanf("%d",&n);
	rep(i,0,n-1) scanf("%d%d",a+i,b+i);
	vector<pii>x;
	rep(i,0,n-1){
		x.emplace_back(a[i],i);
		x.emplace_back(b[i],i);
		sa+=a[i],sb+=b[i];
	}
	sort(x.begin(),x.end());
	vector<ll>pre(x.size()+1);
	pre[0]=0;
	rep(i,0,x.size()-1) pre[i+1]=pre[i]+x[i].first;
	vector<vector<int> >pos(n);
	rep(i,0,x.size()-1) pos[x[i].second].push_back(i);
	ll sum=(ll)(2e18);
	rep(i,0,n-1){
		int j=n;
		while(1){
			int tc=(pos[i][0]<j)+(pos[i][1]<j);
			if(tc==j-n) break;
			++j;
		}
		ll cur=pre[j];
		if(pos[i][0]<j) cur-=x[pos[i][0]].first;
		if(pos[i][1]<j) cur-=x[pos[i][1]].first;
		sum=min(sum,cur);
	}
	sum=min(sum,min(sa,sb));
	printf("%lld\n",sum);
}
### Prompt

Please create a solution in cpp to the following problem:

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

### Response

```cpp
#include<bits/stdc++.h>
#define pii pair<int,int>
#define ll long long
#define rep(i,x,y) for(register int i=(x);i<=(y);++i)
using namespace std;
int n;const int mxn=1e5+5;
int a[mxn],b[mxn];
ll sa,sb;
int main(){
	scanf("%d",&n);
	rep(i,0,n-1) scanf("%d%d",a+i,b+i);
	vector<pii>x;
	rep(i,0,n-1){
		x.emplace_back(a[i],i);
		x.emplace_back(b[i],i);
		sa+=a[i],sb+=b[i];
	}
	sort(x.begin(),x.end());
	vector<ll>pre(x.size()+1);
	pre[0]=0;
	rep(i,0,x.size()-1) pre[i+1]=pre[i]+x[i].first;
	vector<vector<int> >pos(n);
	rep(i,0,x.size()-1) pos[x[i].second].push_back(i);
	ll sum=(ll)(2e18);
	rep(i,0,n-1){
		int j=n;
		while(1){
			int tc=(pos[i][0]<j)+(pos[i][1]<j);
			if(tc==j-n) break;
			++j;
		}
		ll cur=pre[j];
		if(pos[i][0]<j) cur-=x[pos[i][0]].first;
		if(pos[i][1]<j) cur-=x[pos[i][1]].first;
		sum=min(sum,cur);
	}
	sum=min(sum,min(sa,sb));
	printf("%lld\n",sum);
}
```