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

int main() {
    int n; scanf("%d", &n);
    vector<int> a(n), b(n);
    for (int i = 0; i < n; ++i) scanf("%d%d", &a[i], &b[i]);
    long long ans = min(accumulate(a.begin(), a.end(), 0LL), accumulate(b.begin(), b.end(), 0LL));
    vector<pair<int, int>> v;
    for (int i = 0; i < n; ++i) {
        v.emplace_back(a[i], i);
        v.emplace_back(b[i], i);
    }
    sort(v.begin(), v.end());
    vector<vector<int>> pos(n);
    for (int i = 0; i < n + n; ++i) pos[v[i].second].push_back(i);
    vector<long long> pref(n + n + 1, 0);
    for (int i = 0; i < n + n; ++i) pref[i + 1] = pref[i] + v[i].first;
    for (int i = 0; i < n; ++i) {
        assert(pos[i].size() == 2);
        int l = pos[i][0], r = pos[i][1];
        long long res = a[i] + b[i];
        if (l >= n - 2) {
            res += pref[n - 2];
        } else {
            if (r - 1 >= n - 2) res += pref[n - 1] - v[l].first;
            else res = pref[n];
        }
        ans = min(ans, res);
    }
    printf("%lld\n", ans);
    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;

int main() {
    int n; scanf("%d", &n);
    vector<int> a(n), b(n);
    for (int i = 0; i < n; ++i) scanf("%d%d", &a[i], &b[i]);
    long long ans = min(accumulate(a.begin(), a.end(), 0LL), accumulate(b.begin(), b.end(), 0LL));
    vector<pair<int, int>> v;
    for (int i = 0; i < n; ++i) {
        v.emplace_back(a[i], i);
        v.emplace_back(b[i], i);
    }
    sort(v.begin(), v.end());
    vector<vector<int>> pos(n);
    for (int i = 0; i < n + n; ++i) pos[v[i].second].push_back(i);
    vector<long long> pref(n + n + 1, 0);
    for (int i = 0; i < n + n; ++i) pref[i + 1] = pref[i] + v[i].first;
    for (int i = 0; i < n; ++i) {
        assert(pos[i].size() == 2);
        int l = pos[i][0], r = pos[i][1];
        long long res = a[i] + b[i];
        if (l >= n - 2) {
            res += pref[n - 2];
        } else {
            if (r - 1 >= n - 2) res += pref[n - 1] - v[l].first;
            else res = pref[n];
        }
        ans = min(ans, res);
    }
    printf("%lld\n", ans);
    return 0;
}

```