#include <iostream>
#include <algorithm>
using namespace std;
int a[1000006], b[1000006], c[1000006];
long long s[1000006];
int main(){
	int n;
	cin >> n;
	long long s1 = 0, s2 = 0;
	for (int i = 1; i <= n; ++ i){
		cin >> a[i] >> b[i];
		s1 += a[i];
		s2 += b[i];
		c[i] = a[i];
		c[i + n] = b[i];
	}
	long long ans = min(s1, s2);
	sort(c + 1, c + 1 + 2 * n);
	for (int i = 1; i <= n; ++ i)
		s[i] = s[i - 1] + c[i];
	for (int i = 1; i <= n; ++ i){
		int x = a[i], y = b[i];
		if (x > y)
			swap(x, y);
		int px = lower_bound(c + 1, c + 1 + 2 * n, x) - c;
		int py = lower_bound(c + 1, c + 1 + 2 * n, y) - c;
		if (px <= n - 2){
			if (py <= n - 1)
				ans = min(ans, s[n]);
			else
				ans = min(ans, y + s[n - 1]);
		}
		else
			ans = min(ans, x + y + s[n - 2]);
	}
	cout << ans << endl;
}

### Prompt

Generate 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 <algorithm>
using namespace std;
int a[1000006], b[1000006], c[1000006];
long long s[1000006];
int main(){
	int n;
	cin >> n;
	long long s1 = 0, s2 = 0;
	for (int i = 1; i <= n; ++ i){
		cin >> a[i] >> b[i];
		s1 += a[i];
		s2 += b[i];
		c[i] = a[i];
		c[i + n] = b[i];
	}
	long long ans = min(s1, s2);
	sort(c + 1, c + 1 + 2 * n);
	for (int i = 1; i <= n; ++ i)
		s[i] = s[i - 1] + c[i];
	for (int i = 1; i <= n; ++ i){
		int x = a[i], y = b[i];
		if (x > y)
			swap(x, y);
		int px = lower_bound(c + 1, c + 1 + 2 * n, x) - c;
		int py = lower_bound(c + 1, c + 1 + 2 * n, y) - c;
		if (px <= n - 2){
			if (py <= n - 1)
				ans = min(ans, s[n]);
			else
				ans = min(ans, y + s[n - 1]);
		}
		else
			ans = min(ans, x + y + s[n - 2]);
	}
	cout << ans << endl;
}

```