#include<bits/stdc++.h>
#define lowbit(i) ((i)&(-(i)))
#define lson(i) ((i)<<1)
#define rson(i) ((i)<<1|1)
#define sqr(x) ((x)*(x))
#define fi first
#define se second
#define mp(x,y) make_pair((x),(y))
#define pb push_back
using namespace std;

typedef long long ll;
typedef unsigned long long ul;
typedef pair<int,int> pii;
typedef vector<int> vii;
typedef vector<pii> vpi;
typedef queue<int> qii;

const int inf=0x3f3f3f3f;
const int maxn=100007;

int n;
long long a[maxn],b[maxn],c[2*maxn],s[2*maxn],ans;

int main(){
	scanf("%d",&n);
	long long ta=0,tb=0;
	for(int i=1;i<=n;i++){
		scanf("%d%d",&a[i],&b[i]);
		c[i]=a[i];
		c[i+n]=b[i];
		ta+=a[i];
		tb+=b[i];
	}
	ans=min(ta,tb);
	sort(c+1,c+2*n+1);
	for(int i=1;i<=n;i++){
		s[i]=s[i-1]+c[i];
	}
	for(int i=1;i<=n;i++){
		long long x=a[i],y=b[i];
		if(x>y){
			swap(x,y);
		}
		if(lower_bound(c+1,c+2*n+1,x)-c<=n-2){
			if(lower_bound(c+1,c+2*n+1,y)-c<=n-1){
				ans=min(ans,s[n]);
			}
			else{
				ans=min(ans,y+s[n-1]);
			}
		}
		else{
			ans=min(ans,x+y+s[n-2]);
		}
	}
	printf("%lld\n",ans);
	return 0;
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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 lowbit(i) ((i)&(-(i)))
#define lson(i) ((i)<<1)
#define rson(i) ((i)<<1|1)
#define sqr(x) ((x)*(x))
#define fi first
#define se second
#define mp(x,y) make_pair((x),(y))
#define pb push_back
using namespace std;

typedef long long ll;
typedef unsigned long long ul;
typedef pair<int,int> pii;
typedef vector<int> vii;
typedef vector<pii> vpi;
typedef queue<int> qii;

const int inf=0x3f3f3f3f;
const int maxn=100007;

int n;
long long a[maxn],b[maxn],c[2*maxn],s[2*maxn],ans;

int main(){
	scanf("%d",&n);
	long long ta=0,tb=0;
	for(int i=1;i<=n;i++){
		scanf("%d%d",&a[i],&b[i]);
		c[i]=a[i];
		c[i+n]=b[i];
		ta+=a[i];
		tb+=b[i];
	}
	ans=min(ta,tb);
	sort(c+1,c+2*n+1);
	for(int i=1;i<=n;i++){
		s[i]=s[i-1]+c[i];
	}
	for(int i=1;i<=n;i++){
		long long x=a[i],y=b[i];
		if(x>y){
			swap(x,y);
		}
		if(lower_bound(c+1,c+2*n+1,x)-c<=n-2){
			if(lower_bound(c+1,c+2*n+1,y)-c<=n-1){
				ans=min(ans,s[n]);
			}
			else{
				ans=min(ans,y+s[n-1]);
			}
		}
		else{
			ans=min(ans,x+y+s[n-2]);
		}
	}
	printf("%lld\n",ans);
	return 0;
}
```