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
#include <bits/stdc++.h>
#define for1(a,b,i) for(int i=a;i<=b;++i)
#define FOR2(a,b,i) for(int i=a;i>=b;--i)
using namespace std;
typedef long long ll;
inline int read() {
	int f=1,sum=0;
	char x=getchar();
	for(;(x<'0'||x>'9');x=getchar()) if(x=='-') f=-1;
	for(;x>='0'&&x<='9';x=getchar()) sum=sum*10+x-'0';
	return f*sum;
}

#define M 500005
int n;
int a[M][2],sta[M];

int main () {
	//freopen("a.in","r",stdin);
	n=read();
	for1(1,n,i) {
		a[i][0]=read();
		a[i][1]=read();
		sta[i*2]=a[i][1];
		sta[i*2-1]=a[i][0];
	}
	sort(sta+1,sta+2*n+1);
	
	ll ans=0,sum=0;
	for1(1,n,i) ans+=a[i][0],sum+=a[i][1];
	ans=min(ans,sum),sum=0;
	for1(1,n,i) sum+=sta[i];
	for1(1,n,i) {
		if(max(a[i][0],a[i][1])<sta[n]) return printf("%lld\n",sum),0;
		if(min(a[i][0],a[i][1])>sta[n]) return printf("%lld\n",sum),0;
		
		ll now=sum;
		now+=max(a[i][0],a[i][1])-sta[n];
		now+=max(0,min(a[i][0],a[i][1])-sta[n-1]);
		ans=min(ans,now);
	}
	printf("%lld\n",ans);
}