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 partition(int[], int, int);
void quicksort(int[], int, int);
int main() {
  int n, i, j, sum = 0, temp;
  int w[1000], v[1000];
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &w[i]);
    v[i] = w[i];
  }
  quicksort(w, 0, n - 1);
  for (i = 0; i < n; i++) {
    if (v[i] != w[i]) {
      for (j = i + 1; j < n; j++) {
        if (v[j] == w[i]) {
          temp = v[i];
          v[i] = v[j];
          v[j] = temp;
          sum += v[i] + v[j];
          break;
        }
      }
    }
  }
  printf("%d\n", sum);
  return 0;
}
int partition(int A[], int p, int r) {
  int x, i, j;
  int temp;
  x = A[r];
  i = p - 1;
  for (j = p; j < r; j++) {
    if (A[j] <= x) {
      i++;
      temp = A[i];
      A[i] = A[j];
      A[j] = temp;
    }
  }
  temp = A[i + 1];
  A[i + 1] = A[r];
  A[r] = temp;
  return i + 1;
}
void quicksort(int A[], int p, int r) {
  int q;
  if (p < r) {
    q = partition(A, p, r);
    quicksort(A, p, q - 1);
    quicksort(A, q + 1, r);
  }
}
