#include <bits/stdc++.h>
#define f first
#define s second
using namespace std;
using ll = long long;
using ii = pair<int, int>;
constexpr int MN = 100001;

ii A[MN];
bitset<MN> used;

int main() {
    if (fopen("in", "r")) freopen("in", "r", stdin), freopen("out", "w", stdout);
    ios_base::sync_with_stdio(0), cin.tie(0);

    int N; cin >> N;
    for (int i = 0; i < N; ++i) cin >> A[i].f >> A[i].s;

    ll x = 0, y = 0;
    for (int i = 0; i < N; ++i) x += A[i].f, y += A[i].s;
    ll ans = min(x, y);

    vector<ii> v;
    for (int i = 0; i < N; ++i) v.emplace_back(A[i].f, i), v.emplace_back(A[i].s, i);
    sort(begin(v), end(v));

    ll sum = 0;
    bool done = 0;
    for (int i = 0; i < N; ++i) {
        sum += v[i].f;
        if (used[v[i].s]) done = 1;
        used[v[i].s] = 1;
    }

    if (done) ans = min(sum, ans);
    else for (int i = 0; i < N; ++i) ans = min(sum+A[v[i].s].f+A[v[i].s].s-v[i].f-(i < N-1 ? v[N-1].f : v[N-2].f), ans);
    cout << ans;
}

### 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>
#define f first
#define s second
using namespace std;
using ll = long long;
using ii = pair<int, int>;
constexpr int MN = 100001;

ii A[MN];
bitset<MN> used;

int main() {
    if (fopen("in", "r")) freopen("in", "r", stdin), freopen("out", "w", stdout);
    ios_base::sync_with_stdio(0), cin.tie(0);

    int N; cin >> N;
    for (int i = 0; i < N; ++i) cin >> A[i].f >> A[i].s;

    ll x = 0, y = 0;
    for (int i = 0; i < N; ++i) x += A[i].f, y += A[i].s;
    ll ans = min(x, y);

    vector<ii> v;
    for (int i = 0; i < N; ++i) v.emplace_back(A[i].f, i), v.emplace_back(A[i].s, i);
    sort(begin(v), end(v));

    ll sum = 0;
    bool done = 0;
    for (int i = 0; i < N; ++i) {
        sum += v[i].f;
        if (used[v[i].s]) done = 1;
        used[v[i].s] = 1;
    }

    if (done) ans = min(sum, ans);
    else for (int i = 0; i < N; ++i) ans = min(sum+A[v[i].s].f+A[v[i].s].s-v[i].f-(i < N-1 ? v[N-1].f : v[N-2].f), ans);
    cout << ans;
}

```