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;
void trace(vector<int> v) {
  for (auto it = v.begin(); it != v.end(); ++it) {
    cout << setw(3) << *it << " ";
  }
  cout << endl;
}
int main() {
  int const N_MAX = 1000;
  int const W_MAX = 10000;
  int n = 0;
  cin >> n;
  vector<int> W, S, T;
  vector<bool> C;
  W.resize(n, 0);
  S.resize(n, 0);
  T.resize(W_MAX, 0);
  C.resize(n, false);
  int g_min = W_MAX;
  for (int i = 0; i < n; i++) {
    cin >> W[i];
    g_min = (W[i] < g_min) ? W[i] : g_min;
  }
  for (int i = 0; i < n; i++) {
    T[W[i]] = i;
  }
  S = W;
  stable_sort(S.begin(), S.end());
  int score = 0;
  for (int i = 0; i < n; i++) {
    if (!C[T[S[i]]]) {
      int l_min = W_MAX;
      int sum = 0;
      int cnt = 0;
      for (int j = S[i]; !C[T[j]]; j = S[T[j]]) {
        C[T[j]] = true;
        cnt++;
        sum += j;
        l_min = (j < l_min) ? j : l_min;
      }
      score += min(sum + l_min * (cnt - 2), sum + g_min * (cnt + 1) + l_min);
    }
  }
  cout << score << endl;
  return 0;
}
