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 qsort(int a[], int left, int right) {
  int p = (left + right) / 2;
  int pivot = a[p];
  int i, temp;
  if (left < right) {
    p = left;
    pivot = a[p];
    for (i = left + 1; i <= right; i++) {
      if (a[i] < pivot) {
        p++;
        temp = a[i];
        a[i] = a[p];
        a[p] = temp;
      }
    }
    temp = a[left];
    a[left] = a[p];
    a[p] = temp;
    qsort(a, left, p - 1);
    qsort(a, p + 1, right);
  }
}
int check(int a[], int b[], int n) {
  int i;
  for (i = 0; i < n; i++) {
    if (a[i] != b[i]) return -1;
  }
  return 1;
}
int main(void) {
  int n, i, j, mini, minj, min, cost = 0, w;
  int a[1000], b[1000];
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &a[i]);
  for (i = 0; i < n; i++) b[i] = a[i];
  qsort(b, 0, n - 1);
  while (check(a, b, n) == -1) {
    min = 20000;
    for (i = 0; i < n; i++) {
      for (j = 0; a[i] != b[j] && j < n; j++)
        ;
      if (j == n || j == i) continue;
      w = a[i] + a[j];
      if (min > w) {
        min = w;
        mini = i;
        minj = j;
      }
    }
    cost += (a[mini] + a[minj]);
    int temp = a[mini];
    a[mini] = a[minj];
    a[minj] = temp;
  }
  printf("%d\n", cost);
  return 0;
}
