#include <bits/stdc++.h>
using namespace std;
using ll = long long;

int main()
{
	int N;
	cin >> N;
	vector<ll> A(N), B(N);
	vector<pair<ll, int>> vp;
	for (int i = 0; i < N; i++) {
		cin >> A[i] >> B[i];
		vp.emplace_back(A[i], i);
		vp.emplace_back(B[i], i);
	}
	if (*max_element(A.begin(), A.end()) <= *min_element(B.begin(), B.end())) {
		cout << accumulate(A.begin(), A.end(), 0LL) << endl;
		return 0;
	}
	if (*max_element(B.begin(), B.end()) <= *min_element(A.begin(), A.end())) {
		cout << accumulate(B.begin(), B.end(), 0LL) << endl;
		return 0;
	}
	sort(vp.begin(), vp.end());
	ll res = 0;
	int c = 0;
	vector<int> cnt(N);
	for (int i = 0; i < N; i++) {
		res += vp[i].first;
		c += cnt[vp[i].second];
		cnt[vp[i].second] = 1;
	}
	if (c == 0) {
		res += vp[N].second != vp[N - 1].second ? vp[N].first - vp[N - 1].first : min(vp[N + 1].first - vp[N - 1].first, vp[N].first - vp[N - 2].first);
	}
	cout << res << endl;
	return 0;
}

### Prompt

Please formulate 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>
using namespace std;
using ll = long long;

int main()
{
	int N;
	cin >> N;
	vector<ll> A(N), B(N);
	vector<pair<ll, int>> vp;
	for (int i = 0; i < N; i++) {
		cin >> A[i] >> B[i];
		vp.emplace_back(A[i], i);
		vp.emplace_back(B[i], i);
	}
	if (*max_element(A.begin(), A.end()) <= *min_element(B.begin(), B.end())) {
		cout << accumulate(A.begin(), A.end(), 0LL) << endl;
		return 0;
	}
	if (*max_element(B.begin(), B.end()) <= *min_element(A.begin(), A.end())) {
		cout << accumulate(B.begin(), B.end(), 0LL) << endl;
		return 0;
	}
	sort(vp.begin(), vp.end());
	ll res = 0;
	int c = 0;
	vector<int> cnt(N);
	for (int i = 0; i < N; i++) {
		res += vp[i].first;
		c += cnt[vp[i].second];
		cnt[vp[i].second] = 1;
	}
	if (c == 0) {
		res += vp[N].second != vp[N - 1].second ? vp[N].first - vp[N - 1].first : min(vp[N + 1].first - vp[N - 1].first, vp[N].first - vp[N - 2].first);
	}
	cout << res << endl;
	return 0;
}

```