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 fi first
#define se second
#define Mp make_pair
#define pb push_back
#define rep(i, j, k) for (int i = (j); i <= (k); i++)
#define per(i, j, k) for (int i = (j); i >= (k); i--)
using namespace std;

typedef long long ll;
typedef double db;
typedef pair<int, int> PII;
typedef vector<int> VI;

const int N = 1e5+3;
int n,a[N],b[N];
ll nums[N*2],s[N*2];
ll ans,tmp,sa,sb;

int main(){
    scanf("%d",&n);
    rep(i,1,n) scanf("%d %d",&a[i],&b[i]);
    rep(i,1,n) sa+=a[i],sb+=b[i];
    ans=min(sa,sb);
    rep(i,1,n) nums[i]=a[i],nums[i+n]=b[i];
    sort(nums+1,nums+1+n*2);
    rep(i,1,n) s[i]=s[i-1]+nums[i];
    rep(i,1,n){
        if(a[i]>b[i]) swap(a[i],b[i]);
        tmp=a[i]+b[i];
        tmp+=s[n-2];
        if(nums[n-2]>=a[i]) {
            tmp+=-a[i]+nums[n-1];
            if(nums[n-1]>=b[i]) tmp+=-b[i]+nums[n];
        }
        ans=min(ans,tmp);
    }
    printf("%lld\n",ans);
    return 0;
}