#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,a[200005],b[100005][2];
long long ans,tmp,sx,sy,sum;
set<int> s;
/*bool cmp(_ x,_ y){
	return x.x>y.x;
}*/
int main(){
	cin>>n;
	rep(i,n){
		cin>>b[i][0]>>b[i][1];
		sx+=b[i][0];sy+=b[i][1];
		a[i*2]=b[i][0];
		a[i*2-1]=b[i][1];
	}
	sum=sx+sy;
	ans=max(sx,sy);
	sort(a+1,a+n+n+1,greater<int>());
	rep(i,n) tmp+=a[i];
	rep(i,n){
		if(max(b[i][0],b[i][1])<a[n]){
			ans=max(ans,tmp);
			break;
		}
		if(min(b[i][0],b[i][1])>a[n]){
			ans=max(ans,tmp);
			break;
		}
		long long tmp2=tmp;
		tmp2-=a[n]-min(b[i][0],b[i][1]);
		tmp2-=max(0,a[n-1]-max(b[i][0],b[i][1]));
		ans=max(ans,tmp2);
	}
	cout<<sum-ans<<endl;
	return 0;
}

### Prompt

Create a solution in cpp for 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 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,a[200005],b[100005][2];
long long ans,tmp,sx,sy,sum;
set<int> s;
/*bool cmp(_ x,_ y){
	return x.x>y.x;
}*/
int main(){
	cin>>n;
	rep(i,n){
		cin>>b[i][0]>>b[i][1];
		sx+=b[i][0];sy+=b[i][1];
		a[i*2]=b[i][0];
		a[i*2-1]=b[i][1];
	}
	sum=sx+sy;
	ans=max(sx,sy);
	sort(a+1,a+n+n+1,greater<int>());
	rep(i,n) tmp+=a[i];
	rep(i,n){
		if(max(b[i][0],b[i][1])<a[n]){
			ans=max(ans,tmp);
			break;
		}
		if(min(b[i][0],b[i][1])>a[n]){
			ans=max(ans,tmp);
			break;
		}
		long long tmp2=tmp;
		tmp2-=a[n]-min(b[i][0],b[i][1]);
		tmp2-=max(0,a[n-1]-max(b[i][0],b[i][1]));
		ans=max(ans,tmp2);
	}
	cout<<sum-ans<<endl;
	return 0;
}

```