#include <iostream>
#include <algorithm>
#include <set>

using i64 = long long;

const int N = 400000 + 7;

int n;
int a[N], b[N];
i64 u[N], v[N];
i64 x, y, z;

int main() {
//	freopen("code.in", "r", stdin);
//	freopen("code.out", "w", stdout);

	scanf("%d", &n);
	for (int i = 1; i <= n; ++i)
		scanf("%d%d", a + i, b + i),
		x += v[i] = a[i], y += v[i + n] = b[i];
	std::sort(v + 1, v + n * 2 + 1);
	for (int i = 1; i <= n * 2; ++i)
		u[i] = u[i - 1] + v[i];
	z = std::min(x, y);
	for (int i = 1; i <= n; ++i) {
		if (a[i] > b[i]) std::swap(a[i], b[i]);
		if (a[i] > v[n - 2])
			z = std::min(z, u[n - 2] + a[i] + b[i]);
		else {
			if (b[i] > v[n - 1])
				z = std::min(z, u[n - 1] + b[i]);
			else
				z = std::min(z, u[n]);
		}
	}
	printf("%lld", z);
		
	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 <iostream>
#include <algorithm>
#include <set>

using i64 = long long;

const int N = 400000 + 7;

int n;
int a[N], b[N];
i64 u[N], v[N];
i64 x, y, z;

int main() {
//	freopen("code.in", "r", stdin);
//	freopen("code.out", "w", stdout);

	scanf("%d", &n);
	for (int i = 1; i <= n; ++i)
		scanf("%d%d", a + i, b + i),
		x += v[i] = a[i], y += v[i + n] = b[i];
	std::sort(v + 1, v + n * 2 + 1);
	for (int i = 1; i <= n * 2; ++i)
		u[i] = u[i - 1] + v[i];
	z = std::min(x, y);
	for (int i = 1; i <= n; ++i) {
		if (a[i] > b[i]) std::swap(a[i], b[i]);
		if (a[i] > v[n - 2])
			z = std::min(z, u[n - 2] + a[i] + b[i]);
		else {
			if (b[i] > v[n - 1])
				z = std::min(z, u[n - 1] + b[i]);
			else
				z = std::min(z, u[n]);
		}
	}
	printf("%lld", z);
		
	return 0;
}

```