#include<bits/stdc++.h>
#define int long long
using namespace std;
int n, a[100007], b[100007], s[200007], sum[100007], sa, sb, res;
int read()
{
	int num = 0;
	char c = getchar();
	while (c < '0' || c>'9')c = getchar();
	while (c >= '0' && c <= '9')num = num * 10 + c - '0', c = getchar();
	return num;
}
signed main()
{
	n = read();
	for (int i = 1; i <= n; i++)
	{
		a[i] = s[2 * i - 1] = read();
		b[i] = s[2 * i] = read();
		sa += a[i];
		sb += b[i];
	}
	res = min(sa, sb);
	sort(s + 1, s + 2 * n + 1);
	for (int i = 1; i <= n; i++)
		sum[i] = sum[i - 1] + s[i];
	for (int i = 1; i <= n; i++)
	{
		int x = a[i], y = b[i];
		if (x > y)swap(x, y);
		if (lower_bound(s + 1, s + 2 * n + 1, x) - s <= n - 2)
			if (lower_bound(s + 1, s + 2 * n + 1, y) - s <= n - 1)
				res = min(res, sum[n]);
			else res = min(res, sum[n - 1] + y);
		else res = min(res, sum[n - 2] + x + y);
	}
	cout << res << endl;
	return 0;
}
### Prompt

Your task is to create 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<bits/stdc++.h>
#define int long long
using namespace std;
int n, a[100007], b[100007], s[200007], sum[100007], sa, sb, res;
int read()
{
	int num = 0;
	char c = getchar();
	while (c < '0' || c>'9')c = getchar();
	while (c >= '0' && c <= '9')num = num * 10 + c - '0', c = getchar();
	return num;
}
signed main()
{
	n = read();
	for (int i = 1; i <= n; i++)
	{
		a[i] = s[2 * i - 1] = read();
		b[i] = s[2 * i] = read();
		sa += a[i];
		sb += b[i];
	}
	res = min(sa, sb);
	sort(s + 1, s + 2 * n + 1);
	for (int i = 1; i <= n; i++)
		sum[i] = sum[i - 1] + s[i];
	for (int i = 1; i <= n; i++)
	{
		int x = a[i], y = b[i];
		if (x > y)swap(x, y);
		if (lower_bound(s + 1, s + 2 * n + 1, x) - s <= n - 2)
			if (lower_bound(s + 1, s + 2 * n + 1, y) - s <= n - 1)
				res = min(res, sum[n]);
			else res = min(res, sum[n - 1] + y);
		else res = min(res, sum[n - 2] + x + y);
	}
	cout << res << endl;
	return 0;
}
```