#include <bits/stdc++.h>
using namespace std;
using i64 = int64_t;
using vi = vector<i64>;
using vvi = vector<vi>;
using ii = pair<i64, i64>;

bool used[101010];

int main() {
    int n;
    cin >> n;
    vector<ii> vs;
    i64 sum = 0, suma = 0, sumb = 0;
    for (int i = 0; i < n; i++) {
        int a, b;
        cin >> a >> b;
        vs.push_back(ii(a, i));
        suma += a;
        vs.push_back(ii(b, i));
        sumb += b;
    }
    sort(vs.begin(), vs.end());
    int ok = false;
    for (int i = 0; i < n; i++) {
        sum += vs[i].first;
        if (used[vs[i].second]) {
            ok = true;
        }
        used[vs[i].second] = 1;
    }

    if (ok) {
        cout << min({suma, sumb, sum}) << endl;
        return 0;
    }

    if (vs[n - 1].second != vs[n].second) {
        cout << min({sum - vs[n - 1].first + vs[n].first, suma, sumb}) << endl;
        return 0;
    }

    cout << min({sum - vs[n - 1].first + vs[n + 1].first, sum - vs[n - 2].first + vs[n].first, suma, sumb}) << endl;
}
### Prompt

In cpp, your task is to solve 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;
using i64 = int64_t;
using vi = vector<i64>;
using vvi = vector<vi>;
using ii = pair<i64, i64>;

bool used[101010];

int main() {
    int n;
    cin >> n;
    vector<ii> vs;
    i64 sum = 0, suma = 0, sumb = 0;
    for (int i = 0; i < n; i++) {
        int a, b;
        cin >> a >> b;
        vs.push_back(ii(a, i));
        suma += a;
        vs.push_back(ii(b, i));
        sumb += b;
    }
    sort(vs.begin(), vs.end());
    int ok = false;
    for (int i = 0; i < n; i++) {
        sum += vs[i].first;
        if (used[vs[i].second]) {
            ok = true;
        }
        used[vs[i].second] = 1;
    }

    if (ok) {
        cout << min({suma, sumb, sum}) << endl;
        return 0;
    }

    if (vs[n - 1].second != vs[n].second) {
        cout << min({sum - vs[n - 1].first + vs[n].first, suma, sumb}) << endl;
        return 0;
    }

    cout << min({sum - vs[n - 1].first + vs[n + 1].first, sum - vs[n - 2].first + vs[n].first, suma, sumb}) << endl;
}
```