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> vec(n);
  vector<pair<int, int> > sorted(n);
  for (int i = 0; i < n; i++) {
    sorted[i].second = i;
    cin >> sorted[i].first;
    vec[i] = sorted[i].first;
  }
  sort(sorted.rbegin(), sorted.rend());
  int count = 0;
  for (int i = 0; i < n - 1; i++) {
    int j;
    for (j = 0; j < n; j++) {
      if (sorted[j].first == vec[n - i - 1]) {
        break;
      }
    }
    int max_ind = sorted[i].second;
    swap(vec[n - i - 1], vec[max_ind]);
    if (vec[n - i - 1] != vec[max_ind]) {
      count = count + vec[n - i - 1] + vec[max_ind];
    }
    sorted[j].second = sorted[i].second;
    sorted[i].second = n - i - 1;
  }
  cout << count << endl;
  return 0;
}
