You are given $n$ integers $w_i (i = 0, 1, ..., n-1)$ to be sorted in ascending order. You can swap two integers $w_i$ and $w_j$. Each swap operation has a cost, which is the sum of the two integers $w_i + w_j$. You can perform the operations any number of times.

Write a program which reports the minimal total cost to sort the given integers.

Constraints

* $1 \leq n \leq 1,000$
* $0 \leq w_i\leq 10^4$
* $w_i$ are all different

Input

In the first line, an integer $n$ is given. In the second line, $n$ integers $w_i (i = 0, 1, 2, ... n-1)$ separated by space characters are given.

Output

Print the minimal cost in a line.

Examples

Input

5
1 5 3 4 2


Output

7


Input

4
4 3 2 1


Output

10
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  vector<int> order = a, p = a;
  sort(order.begin(), order.end());
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (a[i] == order[j]) p[i] = j;
    }
  }
  long long ans = 0;
  vector<bool> use(n, 0);
  for (int i = 0; i < n; i++) {
    if (!use[i]) {
      int cur = i, maxv = 0, sum = 0;
      do {
        use[cur] = 1;
        int cost = a[p[cur]] + a[cur];
        maxv = max(maxv, cost);
        sum += cost;
        cur = p[cur];
      } while (cur != i);
      ans += sum - maxv;
    }
  }
  cout << ans << endl;
}
