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;
const double EPS = 1e-10;
const double PI = acos(-1.0);
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  int N;
  cin >> N;
  vector<int> ws(N), tmp(N);
  for (int i = (0); i < (N); ++i) {
    cin >> ws[i];
    tmp[i] = ws[i];
  }
  sort((tmp).begin(), (tmp).end());
  int ans = 0;
  for (int i = N - 1; i >= 0; --i) {
    for (int j = (0); j < (i); ++j) {
      if (ws[j] == tmp[i]) {
        ans += ws[j] + ws[i];
        swap(ws[j], ws[i]);
      }
    }
  }
  cout << ans << endl;
  return 0;
}
