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

const int maxn = 500010, P = 1000000007;
int n, a[maxn][2], st[maxn];

int main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
        scanf("%d %d", &a[i][0], &a[i][1]);
        st[i * 2 - 1] = a[i][0], st[i * 2] = a[i][1];
    }
    sort(st + 1, st + n + n + 1);
    long long ans = 0, sum = 0;
    for (int i = 1; i <= n; i++) {
        ans += a[i][0], sum += a[i][1];
    }
    ans = min(ans, sum), sum = 0;
    for (int i = 1; i <= n; i++) {
        sum += st[i];
    }
    for (int i = 1; i <= n; i++) {
        if (max(a[i][0], a[i][1]) < st[n]) printf("%lld\n", sum), exit(0);
        if (min(a[i][0], a[i][1]) > st[n]) printf("%lld\n", sum), exit(0);
        long long t = sum + max(a[i][0], a[i][1]) - st[n];
        ans = min(ans, t + max(0, min(a[i][0], a[i][1]) - st[n - 1]));
    }
    printf("%lld\n", ans);
    return 0;
}
### Prompt

Your task is to create 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;

const int maxn = 500010, P = 1000000007;
int n, a[maxn][2], st[maxn];

int main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
        scanf("%d %d", &a[i][0], &a[i][1]);
        st[i * 2 - 1] = a[i][0], st[i * 2] = a[i][1];
    }
    sort(st + 1, st + n + n + 1);
    long long ans = 0, sum = 0;
    for (int i = 1; i <= n; i++) {
        ans += a[i][0], sum += a[i][1];
    }
    ans = min(ans, sum), sum = 0;
    for (int i = 1; i <= n; i++) {
        sum += st[i];
    }
    for (int i = 1; i <= n; i++) {
        if (max(a[i][0], a[i][1]) < st[n]) printf("%lld\n", sum), exit(0);
        if (min(a[i][0], a[i][1]) > st[n]) printf("%lld\n", sum), exit(0);
        long long t = sum + max(a[i][0], a[i][1]) - st[n];
        ans = min(ans, t + max(0, min(a[i][0], a[i][1]) - st[n - 1]));
    }
    printf("%lld\n", ans);
    return 0;
}
```