#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int main()
{
  do {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
  } while (false);
  int n;
  cin >> n;
  vector<int> a(n), b(n), vec;
  for (int i = 0; i < n; i++) {
    cin >> a[i] >> b[i];
    vec.push_back(a[i]);
    vec.push_back(b[i]);
  }
  sort(vec.begin(), vec.end());
  ll A = 0, B = 0, sum = 0;
  for (int i = 0; i < n; i++) {
    A += a[i];
    B += b[i];
    sum += vec[i];
  }
  ll ans = min(A, B);
  for (int i = 0; i < n; i++) {
    int x = n - 1;
    ll val = sum;
    if (a[i] < b[i]) {
      swap(a[i], b[i]);
    }
    if (a[i] > vec[x]) {
      val += a[i] - vec[x--];
    }
    if (b[i] > vec[x]) {
      val += b[i] - vec[x--];
    }
    ans = min(ans, val);
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Your challenge is to write 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;
typedef long long ll;
int main()
{
  do {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
  } while (false);
  int n;
  cin >> n;
  vector<int> a(n), b(n), vec;
  for (int i = 0; i < n; i++) {
    cin >> a[i] >> b[i];
    vec.push_back(a[i]);
    vec.push_back(b[i]);
  }
  sort(vec.begin(), vec.end());
  ll A = 0, B = 0, sum = 0;
  for (int i = 0; i < n; i++) {
    A += a[i];
    B += b[i];
    sum += vec[i];
  }
  ll ans = min(A, B);
  for (int i = 0; i < n; i++) {
    int x = n - 1;
    ll val = sum;
    if (a[i] < b[i]) {
      swap(a[i], b[i]);
    }
    if (a[i] > vec[x]) {
      val += a[i] - vec[x--];
    }
    if (b[i] > vec[x]) {
      val += b[i] - vec[x--];
    }
    ans = min(ans, val);
  }
  cout << ans << endl;
  return 0;
}

```