#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
#include <map>
using namespace std;

typedef long long ll;

ll mod = 1000000007;



int main() {
	ll n;
	cin >> n;
	vector<pair<ll, ll> > v;
	ll lval = 0;
	ll rval = 0;
	vector<ll> all;
	for(int i=0; i<n; i++){
		ll x, y;
		cin >> x >> y;
		v.push_back(make_pair(x, y));
		all.push_back(x);
		all.push_back(y);
		lval+=x;
		rval+=y;
	}
	sort(all.begin(), all.end());
	ll cutoff = all[n-1];
	ll sum = 0;
	for(int i=0; i<n; i++){
		sum += all[i];
	}
	ll mn = sum + 2000000000;
	for(int i=0; i<n; i++){
		if(v[i].first <= cutoff && v[i].second <= cutoff){
			cout << sum << endl;
			return 0;
		}
		else if(v[i].first <= all[n-2]){
			mn = min(mn, v[i].second + sum - all[n-1]);
		}
		else if(v[i].second <= all[n-2]){
			mn = min(mn, v[i].first + sum - all[n-1]);
		} else{
			mn = min(mn, v[i].first + v[i].second + sum - all[n-1] - all[n-2]);
		}
	}
	cout << min(min(lval, rval), mn) << endl;
	
	return 0;
}
### Prompt

Please formulate 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 <iostream>
#include <vector>
#include <algorithm>
#include <set>
#include <map>
using namespace std;

typedef long long ll;

ll mod = 1000000007;



int main() {
	ll n;
	cin >> n;
	vector<pair<ll, ll> > v;
	ll lval = 0;
	ll rval = 0;
	vector<ll> all;
	for(int i=0; i<n; i++){
		ll x, y;
		cin >> x >> y;
		v.push_back(make_pair(x, y));
		all.push_back(x);
		all.push_back(y);
		lval+=x;
		rval+=y;
	}
	sort(all.begin(), all.end());
	ll cutoff = all[n-1];
	ll sum = 0;
	for(int i=0; i<n; i++){
		sum += all[i];
	}
	ll mn = sum + 2000000000;
	for(int i=0; i<n; i++){
		if(v[i].first <= cutoff && v[i].second <= cutoff){
			cout << sum << endl;
			return 0;
		}
		else if(v[i].first <= all[n-2]){
			mn = min(mn, v[i].second + sum - all[n-1]);
		}
		else if(v[i].second <= all[n-2]){
			mn = min(mn, v[i].first + sum - all[n-1]);
		} else{
			mn = min(mn, v[i].first + v[i].second + sum - all[n-1] - all[n-2]);
		}
	}
	cout << min(min(lval, rval), mn) << endl;
	
	return 0;
}
```