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;
void printarray(int n, int a[]) {
  for (int i = 0; i < n; i++) {
    cout << a[i] << " ";
  }
  cout << endl;
}
void swap(int a[], int i, int j) {
  int tmp;
  tmp = a[i];
  a[i] = a[j];
  a[j] = tmp;
}
int partition(int a[], int p, int r) {
  int x;
  x = a[r];
  int i;
  i = p - 1;
  for (int j = p; j < r; j++) {
    if (a[j] <= x) {
      i++;
      swap(a, i, j);
    }
  }
  swap(a, i + 1, r);
  return i + 1;
}
void quicksort(int a[], int p, int r) {
  if (p < r) {
    int q;
    q = partition(a, p, r);
    quicksort(a, p, q - 1);
    quicksort(a, q + 1, r);
  }
}
int main() {
  int n;
  cin >> n;
  int a[n];
  int b[n];
  int tmp;
  for (int i = 0; i < n; i++) {
    cin >> tmp;
    a[i] = tmp;
    b[i] = tmp;
  }
  quicksort(a, 0, n - 1);
  int ans = 0;
  for (int i = n - 1; i >= 0; i--) {
    for (int j = 0; j < n; j++) {
      if (a[i] == b[j] && i != j) {
        ans += b[i] + b[j];
        swap(b, i, j);
      }
    }
  }
  cout << ans << endl;
  return 0;
}
