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.Scanner;
public class Main{
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        Node W[] = new Node[n];
        int s = Integer.MAX_VALUE, cost = 0;
        for (int i = 0; i < n; i++) {
            W[i] = new Node();
            W[i].value = scan.nextInt();
            W[i].place = -1;
            if (s > W[i].value)
                s = W[i].value;
        }
        for (int j = 0; j < n; j++) {
            int min = Integer.MAX_VALUE, place = -1;
            for (int i = 0; i < n; i++) {
                if (W[i].place != -1)
                    continue;
                if (min > W[i].value) {
                    min = W[i].value;
                    place = i;
                }
            }
            W[place].place = j;
        }
        for (int i = 0; i < n; i++) {
            int j = W[i].place;
            if (j != -1 && j != i) {
                int cnt = 1, min, sum;
                min = sum = W[i].value;
                while (j != i) {
                    int next = W[j].place;
                    if (min > W[j].value)
                        min = W[j].value;
                    sum += W[j].value;
                    cnt++;
                    W[j].place = -1;
                    j = next;
                }
                if(sum + (cnt - 2) * min < sum + min + (cnt + 1) * s){
                    cost += sum + (cnt - 2) * min;
                }
                else{
                    cost += sum + min + (cnt + 1) * s;
                }
            }
        }
        System.out.println(cost);
    }
}
class Node {
    int value;
    int place;
}
