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;
					}
				}
			}
		}
			
		for (int i = 0; i < lim; i++) {
			if (a[i] != b[i]) {
				
				for (int j = (i + 1); j < lim; j++) {
					if (a[j] != b[j]) {
						int small = -1;
						int large = -1;
						
						for (int k = 0; k < lim; k++) {
							
							if (a[k] == b[i]) {
								small = k;
							} else if (a[k] == b[j]) {
								large = k;
							}
							
							if ((small != -1) && (large != -1)) {
								break;
							}
						}
						
						if (small == j) {
							a[large] = a[small];
							a[small] = b[j];
							
							ans = ans + a[small] + a[large];
							break;
						}
						if (large == i) {
							a[small] = a[large];
							a[large] = b[i];
							
							ans = ans + a[small] + a[large];
							break;
						}
					}
				}
			}
			if (a[i] != b[i]) i--;
		}
		
		System.out.println(ans);
	}
}