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 {
	final int INF = Integer.MAX_VALUE;
	int cost = 0;

	void run() {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[] m = new int[n];
		int[] q = new int[n];
		int[] s = new int[n];
		for (int i = 0; i < n; i++)
			s[i] = m[i] = q[i] = scan.nextInt();

		selectionSort(s, n);
		System.out.println(cost);
	}
	
	void selectionSort(int[] a, int n) {
		for (int i = 0; i < n; i++) {
			int min_j = i;
			for (int j = i; j < n; j++) {
				if (a[j] < a[min_j])
					min_j = j;
			}
			if (i == min_j)
				continue;
			cost += a[i] + a[min_j];
			int tmp = a[i];
			a[i] = a[min_j];
			a[min_j] = tmp;
		}
	}

	public static void main(String[] args) {
		new Main().run();
	}
}

