Problem:
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Minimum Cost Sort

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.

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.

Constraints

$1 \leq n \leq 1,000$

$0 \leq w_i\leq 10^4$

$w_i$ are all different

Sample Input 1

5
1 5 3 4 2

Sample Output 1

7

Sample Input 2

4
4 3 2 1

Sample Output 2

10

Solution in C# (judge verdict: Wrong Answer)

using System;

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

    static void CountingSort(int[] A, int[] B, int k){
        var C=new int[k+1];
        for(var j=0; j<A.Length; j++){
            C[A[j]]++;
        }
        var remain=B.Length-1;
        for(; k>=0; k--){
            while(C[k]>0){
                B[remain]=k;
                remain--;
                C[k]--;
            }
        }
    }

    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;
        }
        var max=0;
        for(var i=0; i<n; i++){
            ws[i]=int.Parse(s[i]);
            positions[ws[i]]=i;
            if(ws[i]>max){
                max=ws[i];
            }
        }

        var wsSorted=new int[n];
        CountingSort(ws, wsSorted,max);
        var result=0;
        for(var i=0; i<positions.Length; i++){
            while (positions[i]!=-1) {
                var srcIdx=positions[i];
                var dstIdx=positions[wsSorted[srcIdx]];
                if(srcIdx==dstIdx){
                    positions[i]=-1;
                } else{
                    positions[wsSorted[srcIdx]]=-1;
                    Swap(ws, srcIdx, dstIdx);
                    result+=(ws[srcIdx]+ws[dstIdx]);
                    positions[i]=dstIdx;
                }
            }
        }

        Console.WriteLine(result);
    }
}