#include <bits/stdc++.h>

using namespace std;

const int MAX_N = 100000;
int n;
int64_t a[MAX_N];
int64_t b[MAX_N];
vector<pair<int64_t, int> > c;

int main()
{
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i] >> b[i];
    c.push_back(make_pair(a[i], i));
    c.push_back(make_pair(b[i], i));
  }

  sort(c.begin(), c.end());

  bool has_typex = false;
  vector<int64_t> seen(n, 0);
  for (int i = 0; i < n; i++) {
    if (seen[c[i].second] > 0) {
      has_typex = true;
      break;
    }
    seen[c[i].second] = c[i].first;
  }

  int64_t a_sum = accumulate(a, a+n, 0LL);
  int64_t b_sum = accumulate(b, b+n, 0LL);
  int64_t c_sum = 0;
  for (int i = 0; i < n; i++) {
    c_sum += c[i].first;
  }
  if (has_typex) {
    cout << min(c_sum, min(a_sum, b_sum)) << endl;
  } else {
    int64_t min_n = min(a_sum, b_sum);
    for (int w = 0; w < n; w++) {
      min_n = min(min_n, c_sum - seen[w] + (c[n].second != w ? c[n].first : c[n+1].first));
    }
    cout << min_n << 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 <bits/stdc++.h>

using namespace std;

const int MAX_N = 100000;
int n;
int64_t a[MAX_N];
int64_t b[MAX_N];
vector<pair<int64_t, int> > c;

int main()
{
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i] >> b[i];
    c.push_back(make_pair(a[i], i));
    c.push_back(make_pair(b[i], i));
  }

  sort(c.begin(), c.end());

  bool has_typex = false;
  vector<int64_t> seen(n, 0);
  for (int i = 0; i < n; i++) {
    if (seen[c[i].second] > 0) {
      has_typex = true;
      break;
    }
    seen[c[i].second] = c[i].first;
  }

  int64_t a_sum = accumulate(a, a+n, 0LL);
  int64_t b_sum = accumulate(b, b+n, 0LL);
  int64_t c_sum = 0;
  for (int i = 0; i < n; i++) {
    c_sum += c[i].first;
  }
  if (has_typex) {
    cout << min(c_sum, min(a_sum, b_sum)) << endl;
  } else {
    int64_t min_n = min(a_sum, b_sum);
    for (int w = 0; w < n; w++) {
      min_n = min(min_n, c_sum - seen[w] + (c[n].second != w ? c[n].first : c[n+1].first));
    }
    cout << min_n << endl;
  }

  return 0;
}

```