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
import java.util.*;

public class Main{
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int size = scan.nextInt(), r = 0;
        int arr[][] = new int[size][2];
        for(int i = 0; i < size; i++){
            arr[i][0] = scan.nextInt(); arr[i][1] = i;
        }
        int arrsorted[][] = arr.clone();
        Arrays.sort(arrsorted, Comparator.comparing((int[] iarr) -> iarr[0]));
        for(int i = size - 1; 0 <= i; i--)
            if(arr[i][1] != arrsorted[i][1]){
                r += arr[i][0] + arr[arrsorted[i][1]][0];
                arr[arrsorted[i][1]] = arr[i];
                arr[i][1] = arrsorted[i][1];
                arr[i] = arrsorted[i];
                arr[i][1] = i;
            }
        System.out.println(r);
    }
}