#include <iostream>
#include <algorithm>

using namespace std;

typedef long long ll;
const ll inf = 1e16;
ll n, vis[200005], ans, cnt1, cnt2, a[100005], b[100005], dif1, dif2, cmp;
struct node
{
	ll v, id;
	friend bool operator < (node a, node b)
	{
		return a.v < b.v;
	}
}e[200005];

int main()
{
	cin >> n;
	for (ll i = 1; i <= n; i++)
	{
		cin >> e[i].v >> e[i + n].v;
		a[i] = e[i].v, b[i] = e[i + n].v;
		e[i].id = i, e[i + n].id = i + n;
	}
	sort(e + 1, e + n * 2 + 1);
	for (ll i = 1; i <= n; i++) vis[e[i].id] = 1, ans += e[i].v;
	for (ll i = 1; i <= n; i++)
	{
		if (vis[i] && vis[i + n])
		{
			cout << ans << endl;
			return 0;
		}
		if (vis[i]) cnt1++, dif1 += b[i] - a[i];
		if (vis[i + n]) cnt2++, dif2 += a[i] - b[i];
	}
	if (cnt1 == 0 || cnt2 == 0)
	{
		cout << ans << endl;
		return 0;
	}
	cmp = inf;
	cmp = min(cmp, ans + dif1);
	cmp = min(cmp, ans + dif2);
	for (int i = 1; i <= n; i++)
	{
		int tar = n + 1;
		if (e[tar].id == e[i].id + n || e[tar].id + n == e[i].id) tar++;
		cmp = min(cmp, ans + e[tar].v - e[i].v);
	}
	cout << cmp << endl;
	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 <iostream>
#include <algorithm>

using namespace std;

typedef long long ll;
const ll inf = 1e16;
ll n, vis[200005], ans, cnt1, cnt2, a[100005], b[100005], dif1, dif2, cmp;
struct node
{
	ll v, id;
	friend bool operator < (node a, node b)
	{
		return a.v < b.v;
	}
}e[200005];

int main()
{
	cin >> n;
	for (ll i = 1; i <= n; i++)
	{
		cin >> e[i].v >> e[i + n].v;
		a[i] = e[i].v, b[i] = e[i + n].v;
		e[i].id = i, e[i + n].id = i + n;
	}
	sort(e + 1, e + n * 2 + 1);
	for (ll i = 1; i <= n; i++) vis[e[i].id] = 1, ans += e[i].v;
	for (ll i = 1; i <= n; i++)
	{
		if (vis[i] && vis[i + n])
		{
			cout << ans << endl;
			return 0;
		}
		if (vis[i]) cnt1++, dif1 += b[i] - a[i];
		if (vis[i + n]) cnt2++, dif2 += a[i] - b[i];
	}
	if (cnt1 == 0 || cnt2 == 0)
	{
		cout << ans << endl;
		return 0;
	}
	cmp = inf;
	cmp = min(cmp, ans + dif1);
	cmp = min(cmp, ans + dif2);
	for (int i = 1; i <= n; i++)
	{
		int tar = n + 1;
		if (e[tar].id == e[i].id + n || e[tar].id + n == e[i].id) tar++;
		cmp = min(cmp, ans + e[tar].v - e[i].v);
	}
	cout << cmp << endl;
	return 0;
}

```