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
using System;

class Program{
    static void Swap(int[] A, int a, int b){
        var tmp=A[a];
        A[a]=A[b];
        A[b]=tmp;
    }

    public static void Main(){
        var n=int.Parse(Console.ReadLine());
        var s=Console.ReadLine().Split(' ');
        var ws=new int[n];
        var positions=new int[10001];
        for(var i=0; i<positions.Length; i++){
            positions[i]=-1;
        }
        for(var i=0; i<n; i++){
            ws[i]=int.Parse(s[i]);
            positions[ws[i]]=i;
        }

        var result=0;
        var acc=0;
        for(var i=positions.Length-1; i>=0; i--){
            if(positions[i]!=-1){
                acc++;
                if(ws[n-acc]!=i){
                    Swap(ws, n-acc, positions[i]);
                    result+=(ws[n-acc]+ws[positions[i]]);
                }
            }
        }

        Console.WriteLine(result);
    }
}