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 const MAX = 1000000000;
int main() {
  int n;
  cin >> n;
  vector<int> vec(n), sorted(n);
  for (int i = 0; i < n; i++) {
    cin >> vec[i];
    sorted[i] = vec[i];
  }
  sort(sorted.begin(), sorted.end());
  int count = 0;
  int min = 0;
  int mini = 0;
  int T;
  while (1) {
    min = MAX;
    for (int i = 0; i < n; i++) {
      if (vec[i] == sorted[i]) {
        T = MAX;
      } else {
        T = vec[i] + sorted[i];
      }
      if (min > T) {
        min = T;
        mini = i;
      }
    }
    if (min == MAX) {
      break;
    }
    int iswap = 0;
    for (int i = 0; i < n; i++) {
      if (sorted[mini] == vec[i]) {
        iswap = i;
      }
    }
    swap(vec[mini], vec[iswap]);
    count += (vec[mini] + vec[iswap]);
  }
  cout << count << endl;
  return 0;
}
