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>
int solve(int*, int);
int check(int*, int);
int main() {
  int n, i, arr[1000];
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", arr + i);
    arr[i]--;
  }
  printf("%d\n", solve(arr, n));
  return 0;
}
int check(int arr[], int n) {
  int i;
  for (i = 0; i < n; i++) {
    if (arr[i] != i) {
      return 0;
    }
  }
  return 1;
}
int solve(int arr[], int n) {
  int i, j, res = 0, tmp;
  for (i = 0; i < n - 1; i++) {
    if (arr[i] != i) {
      for (j = i + 1; j < n; j++) {
        if (arr[j] != j && arr[i] == j && arr[j] == i) {
          res += arr[i] + arr[j] + 2;
          tmp = arr[i];
          arr[i] = arr[j];
          arr[j] = tmp;
        }
      }
    }
  }
  for (i = 0; i < n - 1; i++) {
    if (arr[i] != i) {
      for (j = i + 1; j < n; j++) {
        if (arr[i] == j) {
          res += arr[i] + arr[j] + 2;
          tmp = arr[i];
          arr[i] = arr[j];
          arr[j] = tmp;
        }
      }
    }
  }
  if (check(arr, n)) {
    return res;
  } else {
    return res += solve(arr, n);
  }
}
