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, c = 0;
  int a[1000], b[1000];
  bool f[1000];
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  memcpy(b, a, sizeof(a));
  sort(b, b + n);
  memset(f, 0, sizeof(f));
  for (int i = 0; i < n; i++) {
    if (a[i] == b[i]) f[i] = 1;
  }
  for (int i = 0; i < n; i++) {
    if (f[i] == 0) {
      while (a[i] != b[i]) {
        int j = i, k = i;
        while (f[j] == 1 || a[j] != b[i]) j++;
        while (f[k] == 1 || a[k] != b[j]) k++;
        swap(a[j], a[k]);
        c += a[j] + a[k];
        f[j] = 1;
      }
      f[i] = 1;
    }
  }
  cout << c << endl;
  return 0;
}
