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 solve(int *w, int n) {
  int g_m = w[0];
  map<int, int> address;
  int *tmp = new int[n];
  bool *T = new bool[n];
  int ans = 0;
  for (int i = 0; i < n; i++) {
    if (w[i] < g_m) {
      g_m = w[i];
    }
    T[i] = false;
    tmp[i] = w[i];
  }
  sort(tmp, tmp + n);
  for (int i = 0; i < n; i++) {
    pair<int, int> pair_map(tmp[i], i);
    address.insert(pair_map);
  }
  for (int i = 0; i < n; i++) {
    if (T[i]) {
      continue;
    }
    int m = w[i];
    int cur = i;
    int S = 0;
    int count = 0;
    while (1) {
      count++;
      int v = w[cur];
      m = min(v, m);
      S += v;
      T[cur] = true;
      cur = address.at(v);
      if (T[cur]) {
        break;
      }
    }
    int r = min(ans + S + (count - 2) * m, ans + S + m + (1 + m) * g_m);
    ans = r;
  }
  return ans;
}
int main() {
  int n;
  cin >> n;
  int *w = new int[n];
  for (int i = 0; i < n; i++) {
    cin >> w[i];
  }
  int ans = solve(w, n);
  cout << ans << endl;
  return 0;
}
