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, ans = 0, amin = 10000;
  cin >> n;
  int a[n], b[n], T[n];
  bool V[n];
  for (int i = 0; i < n; i++) V[i] = true;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    b[i] = a[i];
    amin = min(a[i], amin);
  }
  sort(b, b + n);
  for (int i = 0; i < n; i++) T[b[i]] = i;
  for (int i = 0; i < n; i++) {
    if (!V[i]) continue;
    int j = i, tmpmin = a[i], c = 0;
    while (V[j]) {
      c++;
      tmpmin = min(tmpmin, a[j]);
      ans += a[j];
      V[j] = false;
      j = T[a[j]];
    }
    ans += min((c - 2) * tmpmin, tmpmin + (c + 1) * amin);
  }
  cout << ans << endl;
  return 0;
}
