#include<bits/stdc++.h>
#define ll long long
#define maxn 200010
using namespace std;
struct data{int x, pos;};
int a[maxn], b[maxn], c[maxn], used[maxn];
data A[maxn];
bool cmp(data a, data b) {return a.x < b.x;}
int main()
{
	int n;
	scanf("%d", &n);
	for (int i = 1; i <= n; i++)
	{
		scanf("%d%d", &a[i], &b[i]);
		A[i] = (data){a[i], i};
		A[i + n] = (data){b[i], i};
	}
	ll res = 0, sum = 0;
	for (int i = 1; i <= n; i++)
		sum += a[i];
	res = sum;
	sum = 0;
	for (int i = 1; i <= n; i++)
		sum += b[i];
	res = min(res, sum);
	sort(A + 1, A + 2 * n + 1, cmp);
	sum = 0;
	for (int i = 1; i <= n; i++)
	{
		used[A[i].pos]++;
		sum += A[i].x;
	}
	for (int i = 1; i <= n; i++)
		if (used[i] == 2) res = min(res, sum);
	for (int i = 1; i <= n; i++)
		if (used[i] == 1)
		{
			ll tmp = sum + max(a[i], b[i]);
			if (A[n].pos == i) tmp -= A[n - 1].x;
			else tmp -= A[n].x;
			res = min(res, tmp);
		}
		else if (used[i] == 0)
		{
			ll tmp = sum + a[i] + b[i] - A[n].x - A[n - 1].x;
			res = min(res, tmp);
		}
	printf("%lld\n", res);
	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 ll long long
#define maxn 200010
using namespace std;
struct data{int x, pos;};
int a[maxn], b[maxn], c[maxn], used[maxn];
data A[maxn];
bool cmp(data a, data b) {return a.x < b.x;}
int main()
{
	int n;
	scanf("%d", &n);
	for (int i = 1; i <= n; i++)
	{
		scanf("%d%d", &a[i], &b[i]);
		A[i] = (data){a[i], i};
		A[i + n] = (data){b[i], i};
	}
	ll res = 0, sum = 0;
	for (int i = 1; i <= n; i++)
		sum += a[i];
	res = sum;
	sum = 0;
	for (int i = 1; i <= n; i++)
		sum += b[i];
	res = min(res, sum);
	sort(A + 1, A + 2 * n + 1, cmp);
	sum = 0;
	for (int i = 1; i <= n; i++)
	{
		used[A[i].pos]++;
		sum += A[i].x;
	}
	for (int i = 1; i <= n; i++)
		if (used[i] == 2) res = min(res, sum);
	for (int i = 1; i <= n; i++)
		if (used[i] == 1)
		{
			ll tmp = sum + max(a[i], b[i]);
			if (A[n].pos == i) tmp -= A[n - 1].x;
			else tmp -= A[n].x;
			res = min(res, tmp);
		}
		else if (used[i] == 0)
		{
			ll tmp = sum + a[i] + b[i] - A[n].x - A[n - 1].x;
			res = min(res, tmp);
		}
	printf("%lld\n", res);
	return 0;
}
```