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;
  cin >> n;
  int A[n];
  int B[n];
  for (int i = 0; i < n; i++) {
    cin >> A[i];
    B[i] = A[i];
  }
  sort(B, B + n);
  int cnt = 0;
  int i = 0;
  while (i < n) {
    if (A[i] == B[i]) {
      i++;
      continue;
    }
    int tgt_idx = find(A, A + n, B[i]) - A;
    int n_cycle = 1;
    while (tgt_idx != i) {
      int dst_idx = find(A, A + n, B[tgt_idx]) - A;
      cnt += A[tgt_idx] + A[dst_idx];
      swap(A[tgt_idx], A[dst_idx]);
      tgt_idx = dst_idx;
      n_cycle++;
    }
    if ((n - 3) * B[i] > (n + 1) * B[0]) {
      cnt -= (n - 3) * B[i] - (n + 1) * B[0];
    }
  }
  cout << cnt << endl;
  return 0;
}
