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;
bool comp1(const pair<int, int> &a, const pair<int, int> &b) {
  return a.first < b.first;
}
bool comp2(const pair<int, int> &a, const pair<int, int> &b) {
  return a.second < b.second;
}
int main() {
  int n;
  cin >> n;
  int w[n], x[n];
  for (int i = 0; i < n; i++) {
    cin >> w[i];
    x[i] = w[i];
  }
  sort(x, x + n);
  for (int i = 0; i < n; i++) {
    if (i != 0) cout << " ";
    cout << x[i];
  }
  cout << endl;
  int *p, *q;
  int sum = 0, tmp;
  for (int i = 0; i < n; i++) {
    p = find(w, w + n, x[i]);
    while (i != p - w) {
      q = find(w, w + n, x[p - w]);
      tmp = *p;
      *p = *q;
      *q = tmp;
      sum += *p + *q;
      p = q;
    }
  }
  cout << sum << "\n";
  return 0;
}
