#include <bits/stdc++.h>
using namespace std;

int main(){
    int64_t i, j, k;
    int N;
    vector<vector<int64_t>> weight;
    cin >> N;
    for(i=0; i<N; i++){
        int64_t a, b;
        scanf("%lld %lld", &a, &b);
        weight.push_back({a, 0LL, i});
        weight.push_back({b, 1LL, i});
    }
    sort(weight.begin(), weight.end());
    int use_side[2] = {0, 0};
    bool dub = false;
    bool use_num[100000];
    for(i=0; i<N; i++) use_num[i] = false;

    int64_t ans = 0;
    for(i=0; i<N; i++){
        auto v = weight[i];
        ans += v[0];
        use_side[v[1]]++;
        if(use_num[v[2]]) dub = true;
        use_num[v[2]] = true;
    }

    if(use_side[0]>0 && use_side[1]>0 && !dub){
        int64_t loss;
        if(weight[N-1][2] == weight[N][2] && use_side[weight[N-1][1]] > 1){
            loss = min(weight[N+1][0] - weight[N-1][0], weight[N][0] - weight[N-2][0]);
        }else{
            loss = weight[N][0] - weight[N-1][0];
        }
        ans += loss;
    }
    cout << ans << endl;
    return 0;
}
### Prompt

Generate 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 <bits/stdc++.h>
using namespace std;

int main(){
    int64_t i, j, k;
    int N;
    vector<vector<int64_t>> weight;
    cin >> N;
    for(i=0; i<N; i++){
        int64_t a, b;
        scanf("%lld %lld", &a, &b);
        weight.push_back({a, 0LL, i});
        weight.push_back({b, 1LL, i});
    }
    sort(weight.begin(), weight.end());
    int use_side[2] = {0, 0};
    bool dub = false;
    bool use_num[100000];
    for(i=0; i<N; i++) use_num[i] = false;

    int64_t ans = 0;
    for(i=0; i<N; i++){
        auto v = weight[i];
        ans += v[0];
        use_side[v[1]]++;
        if(use_num[v[2]]) dub = true;
        use_num[v[2]] = true;
    }

    if(use_side[0]>0 && use_side[1]>0 && !dub){
        int64_t loss;
        if(weight[N-1][2] == weight[N][2] && use_side[weight[N-1][1]] > 1){
            loss = min(weight[N+1][0] - weight[N-1][0], weight[N][0] - weight[N-2][0]);
        }else{
            loss = weight[N][0] - weight[N-1][0];
        }
        ans += loss;
    }
    cout << ans << endl;
    return 0;
}
```