#include <bits/stdc++.h>

using namespace std;

int main(int argc, char *argv[]) {
  std::ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  vector<tuple<int, int, int>> a;
  for (int i = 0; i < n; i++) {
    int x, y;
    cin >> x >> y;
    a.emplace_back(x, 0, i);
    a.emplace_back(y, 1, i);
  }
  sort(a.begin(), a.end());
  int mask = 0;
  long long sum = 0;
  vector<bool> vis(n);
  bool ok = false;
  for (int i = 0; i < n; i++) {
    int v, d, x;
    tie(v, d, x) = a[i];
    mask |= (1 << d);
    sum += v;
    if (vis[x]) {
      ok = true;
    }
    vis[x] = true;
  }
  long long ans = sum;
  if (mask == 3 && !ok) {
    ans = sum - get<0>(a[n - 1]) + get<0>(a[n]);
    if (get<2>(a[n - 1]) == get<2>(a[n])) {
      ans = sum - get<0>(a[n - 1]) + get<0>(a[n + 1]);
      for (int i = 0; i + 1 < n; i++) {
        ans = min(ans, sum - get<0>(a[i]) + get<0>(a[n]));
      }
    }
  }
  cout << ans << endl;
  return 0;
}

### 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;

int main(int argc, char *argv[]) {
  std::ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  vector<tuple<int, int, int>> a;
  for (int i = 0; i < n; i++) {
    int x, y;
    cin >> x >> y;
    a.emplace_back(x, 0, i);
    a.emplace_back(y, 1, i);
  }
  sort(a.begin(), a.end());
  int mask = 0;
  long long sum = 0;
  vector<bool> vis(n);
  bool ok = false;
  for (int i = 0; i < n; i++) {
    int v, d, x;
    tie(v, d, x) = a[i];
    mask |= (1 << d);
    sum += v;
    if (vis[x]) {
      ok = true;
    }
    vis[x] = true;
  }
  long long ans = sum;
  if (mask == 3 && !ok) {
    ans = sum - get<0>(a[n - 1]) + get<0>(a[n]);
    if (get<2>(a[n - 1]) == get<2>(a[n])) {
      ans = sum - get<0>(a[n - 1]) + get<0>(a[n + 1]);
      for (int i = 0; i + 1 < n; i++) {
        ans = min(ans, sum - get<0>(a[i]) + get<0>(a[n]));
      }
    }
  }
  cout << ans << endl;
  return 0;
}

```