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.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;

class Main {
  public static void main(String[] args) throws IOException {
	//System.setIn(new FileInputStream("./input2.txt"));
		
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	int n = Integer.parseInt(br.readLine());

	int[] a = new int[n];
	String[] s = br.readLine().split(" ");
    for(int i = 0; i < n; ++i){
        a[i] = Integer.parseInt(s[i]);
    }
    
    int cost = 0;
    for(int i = 0; i < n; ++i){
        int maxj = i;
        for(int j = i; j < n; ++j){
            if(a[maxj] > a[j]){
                maxj = j;
            }
        }
        if(maxj != i){
            int tmp = a[maxj];
            a[maxj] = a[i];
            a[i] = tmp;
            cost += a[maxj] + a[i];
        }   
    }
    /*
    for(int i = 0; i < n; ++i){
    	System.out.print(" " + a[i]);
    }
    System.out.println();*/
    System.out.println(cost);
  }
}