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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(reader.readLine());
		int[] a = new int[n];
		int[] b = new int[n];
		StringTokenizer st = new StringTokenizer(reader.readLine());
		for (int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(st.nextToken());
			b[i] = a[i];
		}
		quickSort(a, 0, n - 1);

		int cost = 0;
		for (int i = 0; i < n; i++) {
			if (a[i] != b[i]) {
				cost += (a[i] + b[i]);
			}
		}
		System.out.println(cost / 2);
	}

	private static void quickSort(int[] a, int p, int r) {
		if (p < r) {
			int q = partition(a, p, r);
			quickSort(a, p, q - 1);
			quickSort(a, q + 1, r);
		}
	}

	private static int partition(int[] a, int p, int r) {
		int x = a[r];
		int i = p - 1;
		for (int j = p; j < r; j++) {
			if (a[j] <= x) {
				i++;
				swap(a, i, j);
			}
		}
		swap(a, i + 1, r);
		return i + 1;
	}

	private static void swap(int[] a, int i, int j) {
		int tmp = a[i];
		a[i] = a[j];
		a[j] = tmp;
	}
}

