#include<bits/stdc++.h>
#define max(a,b) (((a)>(b))?(a):(b))
#define min(a,b) (((a)<(b))?(a):(b))
#define LL long long
using namespace std;
template<typename T>void read(T &x){
	x=0;int f=1;
	char c=getchar();
	for(;!isdigit(c);c=getchar()) if (c=='-') f=-1;
	for(;isdigit(c);c=getchar()) x=x*10+c-48;
	x*=f;
}
int n,a[100010],b[100010],c[200010];
LL s[200010];
LL ans,s1,s2;
int main(){
	read(n);
	for(int i=1;i<=n;++i) {read(a[i]),s1+=a[i],c[i]=a[i];read(b[i]),s2+=b[i],c[i+n]=b[i];}
	ans=min(s1,s2);
	sort(c+1,c+1+n+n);
	for(int i=1;i<=n+n;++i) s[i]=s[i-1]+c[i];
	for(int i=1;i<=n;++i){
		int nw=n;
		LL cnt=0;
		if(a[i]>=c[nw]) --nw,cnt+=a[i];
		if(b[i]>=c[nw]) --nw,cnt+=b[i];
		ans=min(ans,cnt+s[nw]);
	}
	cout<<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 max(a,b) (((a)>(b))?(a):(b))
#define min(a,b) (((a)<(b))?(a):(b))
#define LL long long
using namespace std;
template<typename T>void read(T &x){
	x=0;int f=1;
	char c=getchar();
	for(;!isdigit(c);c=getchar()) if (c=='-') f=-1;
	for(;isdigit(c);c=getchar()) x=x*10+c-48;
	x*=f;
}
int n,a[100010],b[100010],c[200010];
LL s[200010];
LL ans,s1,s2;
int main(){
	read(n);
	for(int i=1;i<=n;++i) {read(a[i]),s1+=a[i],c[i]=a[i];read(b[i]),s2+=b[i],c[i+n]=b[i];}
	ans=min(s1,s2);
	sort(c+1,c+1+n+n);
	for(int i=1;i<=n+n;++i) s[i]=s[i-1]+c[i];
	for(int i=1;i<=n;++i){
		int nw=n;
		LL cnt=0;
		if(a[i]>=c[nw]) --nw,cnt+=a[i];
		if(b[i]>=c[nw]) --nw,cnt+=b[i];
		ans=min(ans,cnt+s[nw]);
	}
	cout<<ans<<endl;
	return 0;
}

```