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
#include<bits/stdc++.h>

using namespace std;

const int INF=1e9;

int main()
{
    int n;
    int a[1010];
    int b[1010];
    bool visit[1010];

    while(cin>>n)
    {
        int mi=INF;
        for(int i=0;i<n;i++)
        {
            cin>>a[i];
            b[i]=a[i];
            mi=min(mi,a[i]);
        }

        int ans=0;

        sort(b,b+n);

        map<int,int> mp;
        for(int i=0;i<n;i++)
        {
            mp[b[i]]=i;
        }

        memset(visit,0,sizeof(visit));

        for(int i=0;i<n;i++)
        {
            if(visit[i])
                continue;

            int cur=i;
            int sum=0,s=INF;
            int cnt=0;
            while(true)
            {
                visit[cur]=true;
                s=min(s,a[cur]);
                sum+=a[cur];
                cnt++;

                cur=mp[a[cur]];

                if(visit[cur])
                    break;
            }
            ans+=min(sum+(cnt-2)*s,sum+s+(cnt+1)*mi);
        }
        cout<<ans<<endl;
    }


    return 0;
}

