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;
  cin >> n;
  vector<int> inp(n);
  vector<pair<int, int> > input(n);
  for (int i = 0; i < n; i++) {
    input[i].second = i;
    cin >> input[i].first;
    inp[i] = input[i].first;
  }
  sort(input.rbegin(), input.rend());
  int count = 0;
  for (int i = 0; i < n - 1; i++) {
    if (input[i].second > n - i - 1) {
      swap(inp[input[i].second], inp[n - i - 1]);
      count += (inp[input[i].second] + inp[n - i - 1]);
      swap(input[input[i].second].second, input[n - i - 1].second);
    }
  }
  cout << count;
  return 0;
}
