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.Arrays;
import java.util.Scanner;

public class Main {
	private int[] a;
	private int[] b;
	
	private Scanner sc;

	public static void main(String[] args) {
		new Main();
	}
	
	public Main() {
		sc = new Scanner(System.in);
		int lim = Integer.parseInt(sc.nextLine());
		
		a = new int[lim];		
		b = new int[lim];
		for (int i = 0; i < lim; i++) {
			a[i] = Integer.parseInt(sc.next());
			b[i] = a[i];
		}
		Arrays.sort(b);
		
		int ans = 0;
		/*for (int i = 0; i < lim; i++) {
			if (a[i] != b[i]) {
				for (int j = (i + 1); j < lim; j++) {
					if ((a[j] == b[i]) && (a[i] == b[j])) {
						a[i] = b[i];
						a[j] = b[j];
						
						ans = ans + a[i] + a[j];
						break;
					}
				}
			}
		}*/
		
		boolean judge = false;
		while (judge == false) {
			judge = true;
			
			for (int i = 0; i < lim; i++) {
				if (a[i] != b[i]) {
					judge = false;
					for (int j = (i + 1); j < lim; j++) {
						if (a[j] == b[i]) {
							a[i] = b[i];
							a[j] = b[j];
							
							ans = ans + a[i] + a[j];
							judge = true;
							break;
						}
					}
				}
			}
		}
		
		System.out.println(ans);
	}
}