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.*;

public class Main{

	public static void main(String[] args){

		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[] W = new int[n];
		for(int i = 0; i < n; i++){
			W[i] = scan.nextInt();
		}

		System.out.printf("%d\n", minCostSort(W));
	}

	private static int indexOf(int[] A, int x){
		for(int i = 0; i < A.length; i++){
			if(A[i] == x){
				return i;
			}
		}
		return -1;
	}

	private static int minCostSort(int[] W){
		int[] sorted = W.clone();
		Arrays.sort(sorted);
		int cost = 0;
		for(int i = 0; i < W.length; i++){
			int a = indexOf(W, sorted[i]); // ??\??????????????????
			int change = 0;
			while(i < a){ // ????????????????????????????????\???????????????????????§?????????
				int b = indexOf(W, sorted[a]); // ?????????????????????????????\??????????????????????????????????????\?????????
				cost += W[b]; // ??????????????????????¶????
				int work = W[a]; // ???????????¨??´??\????????????
				W[a] = W[b];
				W[b] = work;
				change++;
				a = b;
			}
			cost += Math.min(sorted[i] * change, // ?§????????????????????¶????
								sorted[i] * change + (sorted[i]  + sorted[0] * 3));
								// ?§??????????????????¨?????????????????????????????????
		}
		return cost;
	}
}