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

ll solve() {
    ll N, a, b, sa = 0, sb = 0;
    cin >> N;
    vector<pii> C;
    for ( int i = 0; i < N; i++ ) {
        cin >> a >> b;
        C.push_back(pii(a, i));
        C.push_back(pii(b, i));
        sa += a;
        sb += b;
    }
    sort(C.begin(), C.end());
    ll ans = min(sa,sb);
    ll s = 0;
    vector<int> cc(N);
    for ( int i = 0; i < N; i++ ) {
        s += C[i].first;
        cc[C[i].second]++;
    }
    bool con = false;
    for ( int i = 0; i < N; i++ ) {
        if ( cc[i] != 1 ) {
            con = true;
        }
    }
    if ( !con ) {
        if ( C[N-1].second != C[N].second ) {
            s += C[N].first - C[N-1].first;
        } else {
            s += min( C[N+1].first - C[N-1].first, C[N].first - C[N-2].first);
        }
    }
    ans = min(ans, s);
    return ans;
}

int main() {
    auto ans = solve();
    cout << ans << "\n";
    return 0;
}
### Prompt

In cpp, your task is to solve 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;
using pii = pair<ll,ll>;

ll solve() {
    ll N, a, b, sa = 0, sb = 0;
    cin >> N;
    vector<pii> C;
    for ( int i = 0; i < N; i++ ) {
        cin >> a >> b;
        C.push_back(pii(a, i));
        C.push_back(pii(b, i));
        sa += a;
        sb += b;
    }
    sort(C.begin(), C.end());
    ll ans = min(sa,sb);
    ll s = 0;
    vector<int> cc(N);
    for ( int i = 0; i < N; i++ ) {
        s += C[i].first;
        cc[C[i].second]++;
    }
    bool con = false;
    for ( int i = 0; i < N; i++ ) {
        if ( cc[i] != 1 ) {
            con = true;
        }
    }
    if ( !con ) {
        if ( C[N-1].second != C[N].second ) {
            s += C[N].first - C[N-1].first;
        } else {
            s += min( C[N+1].first - C[N-1].first, C[N].first - C[N-2].first);
        }
    }
    ans = min(ans, s);
    return ans;
}

int main() {
    auto ans = solve();
    cout << ans << "\n";
    return 0;
}
```