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 main() {
  int n, j = 1;
  cin >> n;
  int a[1010];
  pair<long long, long long> c[1010];
  for (int i = 1; i <= n; cin >> a[i++])
    ;
  a[n + 1] == 1;
  for (int i = 1, m = 0;;) {
    if (a[i] != 0) {
      c[j].first++;
      c[j].second += a[i];
      if (a[i] > m) m = a[i];
      int l = a[i];
      a[i] = 0;
      i = l;
    } else {
      if (c[j].first == 1) {
        c[j].second = 0;
      } else if (c[j].first >= 3) {
        c[j].second -= m;
        c[j].second *= 2;
      }
      m = 0;
      j++;
      int s = 0;
      for (int k = 1; k <= n; k++) {
        s += a[k];
        if (a[k] != 0) i = k;
      }
      if (s == 0) break;
    }
  }
  long long s = 0;
  for (int i = 1; i <= j; i++) {
    s += c[i].second;
  }
  cout << s << endl;
  return 0;
}
