#include<bits/stdc++.h>

#define maxn 100005

using namespace std;
typedef long long ll;

int main(){
  ios_base::sync_with_stdio(0);

  vector < pair < int, int > > ret;
  
  int n;
  cin >> n;
  
  ll suma(0), sumb(0);
  
  for (int i = 0; i < n; ++i) {
  	int a, b;
	cin >> a >> b;
	
	suma += a;
	sumb += b;
	
	ret.push_back({a, i});
	ret.push_back({b, i});	
  }
  
  sort(ret.begin(), ret.end());
  
  vector < int > cnt(n);
  
  ll ans = 0, flag = 0;
  
  for (int i = 0; i < n; ++i) {
  	ans += ret[i].first;
  	cnt[ret[i].second] ++;
  	if (cnt[ret[i].second] == 2) flag = 1;
  }
  
  if (flag) {
    cout << ans;
    return 0;
  }
    
  if (ret[n - 1].second == ret[n].second) 
  	ans += min(ret[n].first - ret[n - 2].first, ret[n + 1].first - ret[n - 1].first);
  else
  	ans += ret[n].first - ret[n - 1].first;
  	
  cout << min(ans, min(suma, sumb));
  
  return 0;
}
### Prompt

Create a solution in CPP for 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>

#define maxn 100005

using namespace std;
typedef long long ll;

int main(){
  ios_base::sync_with_stdio(0);

  vector < pair < int, int > > ret;
  
  int n;
  cin >> n;
  
  ll suma(0), sumb(0);
  
  for (int i = 0; i < n; ++i) {
  	int a, b;
	cin >> a >> b;
	
	suma += a;
	sumb += b;
	
	ret.push_back({a, i});
	ret.push_back({b, i});	
  }
  
  sort(ret.begin(), ret.end());
  
  vector < int > cnt(n);
  
  ll ans = 0, flag = 0;
  
  for (int i = 0; i < n; ++i) {
  	ans += ret[i].first;
  	cnt[ret[i].second] ++;
  	if (cnt[ret[i].second] == 2) flag = 1;
  }
  
  if (flag) {
    cout << ans;
    return 0;
  }
    
  if (ret[n - 1].second == ret[n].second) 
  	ans += min(ret[n].first - ret[n - 2].first, ret[n + 1].first - ret[n - 1].first);
  else
  	ans += ret[n].first - ret[n - 1].first;
  	
  cout << min(ans, min(suma, sumb));
  
  return 0;
}
```