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 <iostream>
#include <vector>
#include <algorithm>

using namespace std;

const int Inf = 1e9;

int main(int argc, char const *argv[]) {
  int n;  cin >> n;
  int ans = 0;
  int mini = Inf;
  vector<int> w, b, t(10001);
  vector<bool> visit(n, false);
  for (int i = 0; i < n; ++i) {
    int a;  cin >> a;
    mini = min(mini, a);
    w.push_back(a);
    b.push_back(a);
  }
  sort(b.begin(), b.end());
  for (int i = 0; i < n; ++i) {
    t[b[i]] = i;
  }
  for (int i = 0; i < n; ++i) {
    if (visit[i]) continue;
    int current = i;
    int sum = 0;
    int e = 0;
    int m = Inf;
    while (1) {
      visit[current] = true;
      e++;
      int value = w[current];
      sum += value;
      m = min(m, value);
      current = t[value];
      if (visit[current]) break;
    }
    ans += min(sum + m + (e + 1) * mini, sum + (e - 2) * m);
  }
  cout << ans << endl;

  return 0;
}

