#include <bits/stdc++.h>
typedef long long ll;
int a[100005], b[100005], app[200005];
int main()
{
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		scanf("%d%d", a + i, b + i);
		app[i << 1] = a[i];
		app[i << 1 | 1] = b[i];
	}
	std::sort(app, app + (n << 1));
	ll sa = 0, sb = 0, sum = 0;
	for (int i = 0; i < n; i++) {
		sa += a[i];
		sb += b[i];
		sum += app[i];
	}
	ll ans = std::min(sa, sb);
	for (int i = 0; i < n; i++) {
		int cur = n - 1;
		ll res = sum;
		if (a[i] < b[i]) {
			std::swap(a[i], b[i]);
		}
		if (a[i] > app[cur]) {
			res += a[i] - app[cur--];
		}
		if (b[i] > app[cur]) {
			res += b[i] - app[cur--];
		}
		ans = std::min(ans, res);
	}
	printf("%lld\n", ans);
	return 0;
}

### Prompt

Your challenge is to write 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>
typedef long long ll;
int a[100005], b[100005], app[200005];
int main()
{
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		scanf("%d%d", a + i, b + i);
		app[i << 1] = a[i];
		app[i << 1 | 1] = b[i];
	}
	std::sort(app, app + (n << 1));
	ll sa = 0, sb = 0, sum = 0;
	for (int i = 0; i < n; i++) {
		sa += a[i];
		sb += b[i];
		sum += app[i];
	}
	ll ans = std::min(sa, sb);
	for (int i = 0; i < n; i++) {
		int cur = n - 1;
		ll res = sum;
		if (a[i] < b[i]) {
			std::swap(a[i], b[i]);
		}
		if (a[i] > app[cur]) {
			res += a[i] - app[cur--];
		}
		if (b[i] > app[cur]) {
			res += b[i] - app[cur--];
		}
		ans = std::min(ans, res);
	}
	printf("%lld\n", ans);
	return 0;
}

```