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(void) {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  vector<int> w(n);
  vector<int> sorted;
  vector<int> idx(10001, -1);
  for (int i = 0; i < n; i++) {
    cin >> w[i];
  }
  sorted = w;
  sort(sorted.begin(), sorted.end());
  for (int i = 0; i < n; i++) {
    idx[w[i]] = i;
  }
  int ans = 0;
  for (int i = 0; i < n; i++) {
    if (w[i] == sorted[i]) continue;
    int opposite = sorted[idx[sorted[i]]];
    if (w[i] == opposite) {
      ans += w[i] + sorted[i];
      swap(sorted[i], sorted[idx[sorted[i]]]);
    }
  }
  vector<int> chk(w);
  sort(chk.begin(), chk.end());
  for (int i = n - 1; i >= 0; i--) {
    int v = chk[i];
    int sortedind = -1;
    for (int j = 0; j < n; j++) {
      if (sorted[j] == v) {
        sortedind = j;
        break;
      }
    }
    if (sortedind == idx[v]) continue;
    ans += sorted[sortedind] + sorted[idx[v]];
    swap(sorted[sortedind], sorted[idx[v]]);
  }
  cout << ans << endl;
  return 0;
}
