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 main(void) {
  int n, i, j, k, min, cost = 0;
  int a[1000];
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &a[i]);
  for (i = 0; i < n; i++) {
    min = a[i];
    k = i;
    for (j = i + 1; j < n; j++) {
      if (min > a[j]) {
        min = a[j];
        k = j;
      }
    }
    if (i != k) {
      cost += (a[i] + a[k]);
      int temp = a[i];
      a[i] = a[k];
      a[k] = temp;
    }
  }
  printf("%d\n", cost);
  return 0;
}
