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

using ll = long long;
using pii = pair<ll, ll>;

int main() {
    int n; cin >> n;
    vector<ll> a(n), b(n);
    vector<pii> vs;
    for(int i = 0; i < n; ++i) {
        cin >> a[i] >> b[i];
        vs.emplace_back(a[i], i);
        vs.emplace_back(b[i], i);
    }
    ll ans = min(accumulate(begin(a), end(a), 0LL), accumulate(begin(b), end(b), 0LL));
    sort(begin(vs), end(vs));
    vector<bool> used(n);
    bool ok = false;
    ll sum = 0;
    for(int i = 0; i < n; ++i) {
        sum += vs[i].first;
        ok |= used[vs[i].second];
        used[vs[i].second] = true;
    }
    if(ok) {
        ans = sum;
    }
    for(int i = 0; i < n; ++i) {
        if(vs[i].second == vs[n].second) {
            ans = min(ans, sum - vs[i].first + vs[n + 1].first);
        } else {
            ans = min(ans, sum - vs[i].first + vs[n].first);
        }
    }

    cout << ans << endl;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;
using pii = pair<ll, ll>;

int main() {
    int n; cin >> n;
    vector<ll> a(n), b(n);
    vector<pii> vs;
    for(int i = 0; i < n; ++i) {
        cin >> a[i] >> b[i];
        vs.emplace_back(a[i], i);
        vs.emplace_back(b[i], i);
    }
    ll ans = min(accumulate(begin(a), end(a), 0LL), accumulate(begin(b), end(b), 0LL));
    sort(begin(vs), end(vs));
    vector<bool> used(n);
    bool ok = false;
    ll sum = 0;
    for(int i = 0; i < n; ++i) {
        sum += vs[i].first;
        ok |= used[vs[i].second];
        used[vs[i].second] = true;
    }
    if(ok) {
        ans = sum;
    }
    for(int i = 0; i < n; ++i) {
        if(vs[i].second == vs[n].second) {
            ans = min(ans, sum - vs[i].first + vs[n + 1].first);
        } else {
            ans = min(ans, sum - vs[i].first + vs[n].first);
        }
    }

    cout << ans << endl;
}

```