#include <bits/stdc++.h>
using namespace std;
using LL = long long;
constexpr int N = 1E5;
int n;
int a[N], b[N], c[2 * N];
LL s[N + 1];
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cin >> n;
    for (int i = 0; i < n; ++i) {
        cin >> a[i] >> b[i];
        c[2 * i] = a[i];
        c[2 * i + 1] = b[i];
    }
    sort(c, c + 2 * n);
    for (int i = 0; i < n; ++i)
        s[i + 1] = s[i] + c[i];
    LL ans = min(accumulate(a, a + n, 0LL), accumulate(b, b + n, 0LL));
    for (int i = 0; i < n; ++i) {
        int x = lower_bound(c, c + 2 * n, a[i]) - c;
        int y = lower_bound(c, c + 2 * n, b[i]) - c;
        if (x > y)
            swap(x, y);
        if (x < n - 2 && y < n - 1)
            ans = min(ans, s[n]);
        else if (x < n - 2)
            ans = min(ans, s[n - 1] + c[y]);
        else
            ans = min(ans, s[n - 2] + a[i] + b[i]);
    }
    cout << ans << endl;
    return 0;
}
### Prompt

Develop a solution in cpp to the problem described below:

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 LL = long long;
constexpr int N = 1E5;
int n;
int a[N], b[N], c[2 * N];
LL s[N + 1];
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cin >> n;
    for (int i = 0; i < n; ++i) {
        cin >> a[i] >> b[i];
        c[2 * i] = a[i];
        c[2 * i + 1] = b[i];
    }
    sort(c, c + 2 * n);
    for (int i = 0; i < n; ++i)
        s[i + 1] = s[i] + c[i];
    LL ans = min(accumulate(a, a + n, 0LL), accumulate(b, b + n, 0LL));
    for (int i = 0; i < n; ++i) {
        int x = lower_bound(c, c + 2 * n, a[i]) - c;
        int y = lower_bound(c, c + 2 * n, b[i]) - c;
        if (x > y)
            swap(x, y);
        if (x < n - 2 && y < n - 1)
            ans = min(ans, s[n]);
        else if (x < n - 2)
            ans = min(ans, s[n - 1] + c[y]);
        else
            ans = min(ans, s[n - 2] + a[i] + b[i]);
    }
    cout << ans << endl;
    return 0;
}
```