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.*;
import java.util.Arrays;
import java.util.StringTokenizer;

class Main{

static final PrintWriter out=new PrintWriter(System.out);

public static void main(Stirng[] args) throws IOException{
BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
String line="";
while((line=br.readLine())!=null&&!line.isEmpty()){
int n=Integer.parseInt(line);
int[] w=new int[n];
StringTokenizer st=new StringTokenizer(br.readLine());
for(int i=0;i<n;i++) w[i]=Integer.parseInt(st.nextToken());
int[] wd=w.clone();
Arrays.sort(wd);
int ans=0;
for(int i=0;i<=n/2;i++){
if(w[i]!=wd[i]) ans+=w[i]+wd[i];
}
out.println(ans);
}
out.flush();
}
}