#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <queue>
#define MAXN 100010
int n, m, a[MAXN], b[MAXN], c[MAXN << 1];
typedef long long lnt;
lnt sum[MAXN << 1], suma, sumb, ans;
int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i++) {
		scanf("%d%d", &a[i], &b[i]);
		suma += (c[++m] = a[i]);
		sumb += (c[++m] = b[i]);
	}
	ans = std::min(suma, sumb);
	std::sort(c + 1, c + m + 1);
	for (int i = 1; i <= m; i++) sum[i] = sum[i - 1] + c[i];
	for (int i = 1; i <= n; i++) {
		int pa = std::upper_bound(c + 1, c + m + 1, a[i]) - c - 1;
		int pb = std::upper_bound(c + 1, c + m + 1, b[i]) - c - 1;
		if (pa > n - 2 && pb > n - 2) {
			ans = std::min(ans, sum[n - 2] + a[i] + b[i]);
		} else if (pa > n - 1) {
			ans = std::min(ans, a[i] + sum[n - 1]);
		} else if (pb > n - 1) {
			ans = std::min(ans, b[i] + sum[n - 1]);
		} else {
			ans = std::min(ans, sum[n]);
		}
	}
	printf("%lld\n", ans);
	return 0;
}
### 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 <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <queue>
#define MAXN 100010
int n, m, a[MAXN], b[MAXN], c[MAXN << 1];
typedef long long lnt;
lnt sum[MAXN << 1], suma, sumb, ans;
int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i++) {
		scanf("%d%d", &a[i], &b[i]);
		suma += (c[++m] = a[i]);
		sumb += (c[++m] = b[i]);
	}
	ans = std::min(suma, sumb);
	std::sort(c + 1, c + m + 1);
	for (int i = 1; i <= m; i++) sum[i] = sum[i - 1] + c[i];
	for (int i = 1; i <= n; i++) {
		int pa = std::upper_bound(c + 1, c + m + 1, a[i]) - c - 1;
		int pb = std::upper_bound(c + 1, c + m + 1, b[i]) - c - 1;
		if (pa > n - 2 && pb > n - 2) {
			ans = std::min(ans, sum[n - 2] + a[i] + b[i]);
		} else if (pa > n - 1) {
			ans = std::min(ans, a[i] + sum[n - 1]);
		} else if (pb > n - 1) {
			ans = std::min(ans, b[i] + sum[n - 1]);
		} else {
			ans = std::min(ans, sum[n]);
		}
	}
	printf("%lld\n", ans);
	return 0;
}
```