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>
void swap(int *a, int *b) {
  int t = *a;
  *a = *b;
  *b = t;
}
int partition(int *a, int p, int r) {
  int i, j;
  int x;
  x = a[r];
  i = p - 1;
  for (j = p; j < r; j++) {
    if (a[j] <= x) {
      i++;
      swap(&a[i], &a[j]);
    }
  }
  i++;
  swap(&a[i], &a[r]);
  return i;
}
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);
  }
}
int main() {
  int n, w[10000];
  int x[10000];
  int i, j, k;
  int c = 0;
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &w[i]);
    x[i] = w[i];
  }
  quicksort(x, 0, n - 1);
  for (i = (n - 1) / 2, j = i + 1; i >= 0; i--, j++) {
    if (i >= 0) {
      if (x[i] != w[i]) {
        for (k = 0; k < n && (x[i] != w[k]); k++)
          ;
        swap(&w[i], &w[k]);
        c += w[i];
        c += w[k];
      }
    }
    if (j < n) {
      if (x[j] != w[j]) {
        for (k = 0; k < n && (x[j] != w[k]); k++)
          ;
        swap(&w[j], &w[k]);
        c += w[j];
        c += w[k];
      }
    }
  }
  printf("%d\n", c);
  return 0;
}
