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.*;
import java.io.*;

class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] w = new int[n];
		for (int i = 0; i < n; i++) {
			w[i] = sc.nextInt();
		}
		System.out.println(doSort(w));
	}
	
	public static int getIndex(int[] l, int x){
		for (int i = 0; i < l.length; i++) {
			if(l[i]==x) return i;
		}
		return -1;
	}
	
	public static int doSort(int[] w){
		int[] sortedList = w.clone();
		Arrays.sort(sortedList);
		
		int cost = 0;
		
		for (int i = 0; i < w.length; i++) {
			int x = getIndex(w, sortedList[i]);
			int y = 0;
			while (x>i) {
				y++;
				int k = getIndex(w, sortedList[x]);
				cost = cost + w[k];
				int comp = w[x];
				w[x] = w[k];
				w[k] = comp;
				x = k;
			}
			cost = cost + Math.min(sortedList[i]*y, sortedList[i]*2+sortedList[0]*(y+2));
		
		}
		return cost;
	}
	
}
