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 w[1000], a[1000], n, i, j, cost;
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> w[i];
    a[i] = w[i];
  }
  sort(a, a + n);
  cost = 0;
  for (i = 0; i < n - 1; i++) {
    if (a[i] != w[i]) {
      for (j = i + 1; j < n; j++) {
        if (a[i] == w[j]) {
          int t = w[j];
          w[j] = w[i];
          w[i] = t;
          cost += w[i] + w[j];
          break;
        }
      }
    }
  }
  cout << cost << endl;
  return 0;
}
