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 {
	
	static int MAX = 1000;
	static int VMAX = 10000;
	
	static int s;
	static int[] A = new int[MAX];
	static int[] B = new int[MAX];
	static int[] T = new int[VMAX + 1];
	
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		s = VMAX;
		for (int i=0; i<n; i++){
			A[i] = sc.nextInt();
			s = Math.min(s, A[i]);
		}
		int ans = solve(n);
		System.out.println(ans);
	}
	
	static int solve(int n){
		int ans = 0;
		
		int[] V = new int[MAX];
		for(int i=0; i<n; i++){
			B[i] = A[i];
			V[i] = 1;
		}
		Arrays.sort(B, 0, n);
		for(int i=0; i<n; i++) T[B[i]] = i;
		for(int i=0; i<n; i++){
			if (V[i] == 0) continue;
			int cur = i;
			int S = 0;
			int  m = VMAX;
			int an = 0;
			for (;;) {
				V[cur] = 0;
				an++;
				int v = A[cur];
				m = Math.min(m,v);
				S += v;
				cur = T[v];
				if (V[cur] == 0) break;
			}
			ans += Math.min(S + (an - 2) * m, m + S + (an + 1) * s);
		}
		return ans;
	}
}
