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, t[1000], u[1000];
  bool visited[1000];
  map<int, int> change;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> t[i];
    change[t[i]] = i;
    u[i] = t[i];
    visited[i] = false;
  }
  sort(u, u + n);
  for (int i = 0; i < n; i++) {
    int w = i, x = 0, y = 0, z = 10000;
    while (!visited[w]) {
      z = min(z, t[w]);
      y += t[w];
      x++;
      visited[w] = true;
      w = change[u[w]];
    }
    if (x >= 2) ans += min(y + z + u[0] * (x + 1), y + z * (x - 2));
  }
  cout << ans << endl;
  return 0;
}
