#include <vector>
#include <cstdio>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;

const int N=2e5+5;
ll ans;
int n,cnt,a[N],b[N],sum[2],tot[N];
struct Node {int pos,val,type;} tmp[N<<1];
bool cmp(Node a,Node b) {return a.val<b.val;}

template <typename _Tp> inline void IN(_Tp&x) {
	char ch;bool flag=0;x=0;
	while(ch=getchar(),!isdigit(ch)) if(ch=='-') flag=1;
	while(isdigit(ch)) x=x*10+ch-'0',ch=getchar();
	if(flag) x=-x;
}

int main() {
	IN(n);
	for(int i=1;i<=n;++i)
		IN(a[i]),tmp[++cnt]=(Node){i,a[i],0},
		IN(b[i]),tmp[++cnt]=(Node){i,b[i],1};
	sort(tmp+1,tmp+1+cnt,cmp);
	bool flag=false;
	for(int i=1;i<=n;++i)
		sum[tmp[i].type]++,ans+=tmp[i].val,
		flag|=(bool)(++tot[tmp[i].pos]==2);
	if(flag||max(sum[0],sum[1])==n)
		return printf("%lld\n",ans),0;
	sum[tmp[n].type]--,sum[tmp[n+1].type]++,ans+=tmp[n+1].val-tmp[n].val;
	if(tmp[n].pos!=tmp[n+1].pos||max(sum[0],sum[1])==n)
		return printf("%lld\n",ans),0;
	printf("%lld\n",ans+min(tmp[n+2].val-tmp[n+1].val,tmp[n].val-tmp[n-1].val));
	return 0;
}
### Prompt

Your task is to create 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 <vector>
#include <cstdio>
#include <string>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;

const int N=2e5+5;
ll ans;
int n,cnt,a[N],b[N],sum[2],tot[N];
struct Node {int pos,val,type;} tmp[N<<1];
bool cmp(Node a,Node b) {return a.val<b.val;}

template <typename _Tp> inline void IN(_Tp&x) {
	char ch;bool flag=0;x=0;
	while(ch=getchar(),!isdigit(ch)) if(ch=='-') flag=1;
	while(isdigit(ch)) x=x*10+ch-'0',ch=getchar();
	if(flag) x=-x;
}

int main() {
	IN(n);
	for(int i=1;i<=n;++i)
		IN(a[i]),tmp[++cnt]=(Node){i,a[i],0},
		IN(b[i]),tmp[++cnt]=(Node){i,b[i],1};
	sort(tmp+1,tmp+1+cnt,cmp);
	bool flag=false;
	for(int i=1;i<=n;++i)
		sum[tmp[i].type]++,ans+=tmp[i].val,
		flag|=(bool)(++tot[tmp[i].pos]==2);
	if(flag||max(sum[0],sum[1])==n)
		return printf("%lld\n",ans),0;
	sum[tmp[n].type]--,sum[tmp[n+1].type]++,ans+=tmp[n+1].val-tmp[n].val;
	if(tmp[n].pos!=tmp[n+1].pos||max(sum[0],sum[1])==n)
		return printf("%lld\n",ans),0;
	printf("%lld\n",ans+min(tmp[n+2].val-tmp[n+1].val,tmp[n].val-tmp[n-1].val));
	return 0;
}
```