#include <bits/stdc++.h>
using namespace std;
#define all(V) V.begin(),V.end()
using ll = long long;
const ll MOD = 1000000007;

int main() {
	ll N, a, b;
	cin >> N;

	vector<pair<ll, ll>> VP(N);
	vector<ll> scr(2 * N);
	ll LS = 0, RS = 0;
	for (int i = 0;i < N;i++) {
		cin >> a >> b;
		LS += a;
		RS += b;
		VP[i] = { a,b };
		scr[i * 2] = a;
		scr[i * 2 + 1] = b;
	}
	sort(all(scr));

	ll C, CR = 0, CRR, ans = min(LS, RS);
	for (int i = 0;i < N;i++)CR += scr[i];
	CRR = CR;
	for (int i = 0;i < N;i++) {
		tie(a, b) = VP[i];
		if (a > b)swap(a, b);
		C = scr[N - 1];
		if (a < C) {
			if (b > C)CR += b - C;
		}
		else if (a == C) {
			C = scr[N - 2];
			if (b > C) {
				CR += b - C;
			}
		}
		else {
			CR += a - C;
			C = scr[N - 2];
			CR += b - C;
		}
		ans = min(ans, CR);
		CR = CRR;
	}
	cout << ans << endl;
}
### 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>
using namespace std;
#define all(V) V.begin(),V.end()
using ll = long long;
const ll MOD = 1000000007;

int main() {
	ll N, a, b;
	cin >> N;

	vector<pair<ll, ll>> VP(N);
	vector<ll> scr(2 * N);
	ll LS = 0, RS = 0;
	for (int i = 0;i < N;i++) {
		cin >> a >> b;
		LS += a;
		RS += b;
		VP[i] = { a,b };
		scr[i * 2] = a;
		scr[i * 2 + 1] = b;
	}
	sort(all(scr));

	ll C, CR = 0, CRR, ans = min(LS, RS);
	for (int i = 0;i < N;i++)CR += scr[i];
	CRR = CR;
	for (int i = 0;i < N;i++) {
		tie(a, b) = VP[i];
		if (a > b)swap(a, b);
		C = scr[N - 1];
		if (a < C) {
			if (b > C)CR += b - C;
		}
		else if (a == C) {
			C = scr[N - 2];
			if (b > C) {
				CR += b - C;
			}
		}
		else {
			CR += a - C;
			C = scr[N - 2];
			CR += b - C;
		}
		ans = min(ans, CR);
		CR = CRR;
	}
	cout << ans << endl;
}
```