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;
const int INF = INT_MAX / 3;
int main() {
  int n;
  cin >> n;
  int input[n];
  for (int i = 0; i < n; i++) {
    cin >> input[i];
  }
  int checked[n];
  for (int i = 0; i < n; i++) {
    checked[i] = 0;
  }
  vector<pair<int, int> > inputSorted;
  for (int i = 0; i < n; i++) {
    inputSorted.push_back(make_pair(input[i], i));
  }
  sort(inputSorted.begin(), inputSorted.end());
  int toMove[n];
  for (int i = 0; i < n; i++) {
    toMove[inputSorted[i].second] = i;
  }
  int result = 0;
  for (int i = 0; i < n; i++) {
    if (checked[i] == 0 and i != toMove[i]) {
      checked[i] = 1;
      int mini = input[i];
      int count = 1;
      int sum = input[i];
      int now = toMove[i];
      while (i != now) {
        checked[now] = 1;
        mini = min(mini, input[now]);
        count++;
        sum += input[now];
        now = toMove[now];
      }
      sum += mini * (count - 2);
      result += sum;
    }
  }
  cout << result << endl;
  return 0;
}
