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() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  pair<int, int> w[1000];
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> w[i].first;
    w[i].second = i;
  }
  sort(w, w + n);
  int c, cost = 0;
  for (int i = 0; i < n; i++) {
    if (w[i].first != -1 && w[i].second != i) {
      c = w[i].second;
      while (c != i) {
        cost += w[i].first;
        cost += w[c].first;
        w[c].first = -1;
        c = w[c].second;
      }
    }
  }
  cout << cost << '\n';
  return 0;
}
