#include <cstdio>
#include <cstring>
#include <algorithm>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define fd(i,a,b) for(int i=a;i>=b;i--)
using namespace std;

typedef long long ll;

int read() {
	char ch;
	for(ch=getchar();ch<'0'||ch>'9';ch=getchar());
	int x=ch-'0';
	for(ch=getchar();ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
	return x;
}

const int N=2e5+5;

int n,a[N],b[N],c[N];
ll ans,suma,sumb,sum[N];

int main() {
	n=read();
	fo(i,1,n) {
		a[i]=read();b[i]=read();
		c[i*2-1]=a[i];c[i*2]=b[i];
		suma+=a[i];sumb+=b[i];
	}
	sort(c+1,c+n*2+1);
	ans=min(suma,sumb);
	fo(i,1,2*n) sum[i]=sum[i-1]+c[i];
	fo(i,1,n) {
		int boder=n,tmp=0;
		if (a[i]>=c[boder]) tmp+=a[i],boder--;
		if (b[i]>=c[boder]) tmp+=b[i],boder--;
		ans=min(ans,sum[boder]+tmp);
	}
	printf("%lld\n",ans);
	return 0;
}
### Prompt

Your challenge is to write a cpp solution 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 <cstdio>
#include <cstring>
#include <algorithm>
#define fo(i,a,b) for(int i=a;i<=b;i++)
#define fd(i,a,b) for(int i=a;i>=b;i--)
using namespace std;

typedef long long ll;

int read() {
	char ch;
	for(ch=getchar();ch<'0'||ch>'9';ch=getchar());
	int x=ch-'0';
	for(ch=getchar();ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0';
	return x;
}

const int N=2e5+5;

int n,a[N],b[N],c[N];
ll ans,suma,sumb,sum[N];

int main() {
	n=read();
	fo(i,1,n) {
		a[i]=read();b[i]=read();
		c[i*2-1]=a[i];c[i*2]=b[i];
		suma+=a[i];sumb+=b[i];
	}
	sort(c+1,c+n*2+1);
	ans=min(suma,sumb);
	fo(i,1,2*n) sum[i]=sum[i-1]+c[i];
	fo(i,1,n) {
		int boder=n,tmp=0;
		if (a[i]>=c[boder]) tmp+=a[i],boder--;
		if (b[i]>=c[boder]) tmp+=b[i],boder--;
		ans=min(ans,sum[boder]+tmp);
	}
	printf("%lld\n",ans);
	return 0;
}
```