#include <algorithm>
#include <iostream>
#include <vector>
#include <numeric>
using namespace std;
const long long INF = 1LL << 60;    // 1.15x10^18
template<class T> inline bool chmin(T &a, T b) { return a > b ? (a = b, 1) : 0; }

int main() {
    int n; cin >> n;
    vector<pair<int, int>> ps;
    for (int i = 0; i < n; i++) {
        int a, b; cin >> a >> b;
        ps.emplace_back(a, i);
        ps.emplace_back(b, i + n);
    }
    sort(begin(ps), end(ps));
    long long sum = 0;
    vector<bool> used(n * 2);
    for (int i = 0; i < n; i++) sum += ps[i].first, used[ps[i].second] = true;
    int cnt = accumulate(begin(used), begin(used) + n, 0);
    if (cnt % n == 0) return !(cout << sum << endl);
    for (int i = 0; i < n; i++) {
        if (used[i] == used[i + n]) return !(cout << sum << endl);
    }
    long long mi = INF;
    for (int i = 0; i < n; i++) {
        bool eq = ps[i].second % n == ps[n].second % n;
        chmin(mi, sum - ps[i].first + ps[n + eq].first);
    }
    cout << mi << endl;
    return 0;
}

### Prompt

Please create a solution in CPP 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 <algorithm>
#include <iostream>
#include <vector>
#include <numeric>
using namespace std;
const long long INF = 1LL << 60;    // 1.15x10^18
template<class T> inline bool chmin(T &a, T b) { return a > b ? (a = b, 1) : 0; }

int main() {
    int n; cin >> n;
    vector<pair<int, int>> ps;
    for (int i = 0; i < n; i++) {
        int a, b; cin >> a >> b;
        ps.emplace_back(a, i);
        ps.emplace_back(b, i + n);
    }
    sort(begin(ps), end(ps));
    long long sum = 0;
    vector<bool> used(n * 2);
    for (int i = 0; i < n; i++) sum += ps[i].first, used[ps[i].second] = true;
    int cnt = accumulate(begin(used), begin(used) + n, 0);
    if (cnt % n == 0) return !(cout << sum << endl);
    for (int i = 0; i < n; i++) {
        if (used[i] == used[i + n]) return !(cout << sum << endl);
    }
    long long mi = INF;
    for (int i = 0; i < n; i++) {
        bool eq = ps[i].second % n == ps[n].second % n;
        chmin(mi, sum - ps[i].first + ps[n + eq].first);
    }
    cout << mi << endl;
    return 0;
}

```