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 <iostream>
#include <limits>
#include <algorithm>
using namespace std;

int main() {
  int n;
  int cost = 0;
  cin >> n;
  int w[n], a[n], b[n];
  int min_val = numeric_limits<int>::max();
  for (int i = 0; i < n; i++) {
    cin >> w[i];
    a[i] = w[i];
    b[i] = 0;
    min_val = min(w[i], min_val);
  }
  sort(a, a+n);
  for (int i = 0; i < n; i++) {
    if (b[i] == 0 && a[i] != w[i]) {
      int index = find(a, a+n, w[i]) - a;
      if (w[index] == a[i]) {
        cost += w[i] + w[index];
        b[index]++;
      } else {
        int first_value = w[i];
        int local_min = w[i];
        int local_cost = w[i];
        int local_n = 1;
        while (w[index] != first_value) {
          local_min = min(local_min, w[index]);
          local_cost += w[index];
          local_n++;
          b[index]++;
          index = find(a, a+n, w[index]) - a;
        }
        int local_cost2 = local_cost;
        local_cost += (local_n - 2) * local_min;
        local_cost2 += local_min + (local_n + 1) * min_val;
        cost += min(local_cost, local_cost2);
      }
    }
  }
  cout << cost << endl;
}

