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<iostream>
#include<algorithm>
#include<cstdio>
#include<string>
using namespace std;
const int MAX=1005,VMAX=10005;
int a[1005],b[1005];
int T[10005];
bool v[1005];
int main()
{
    int n;
    cin>>n;
    int s=VMAX+5,ans=0;
    for(int i=0;i<n;i++)cin>>a[i],b[i]=a[i],s=min(s,a[i]);
    sort(b,b+n);
    for(int i=0;i<n;i++)T[b[i]]=i;      //构造Cytle的必要方法
    for(int i=0;i<n;i++)
    {
        if(v[i])continue;
        int an=0;
        int sn=0;
        int m=VMAX+1;
        int cur=i;
        while(1)
        {
            v[cur]=true;
            an++;
            int V=a[cur];
            m=min(m,V);
            sn+=V;
            cur=T[V];
            if(v[cur])break;
        }
        ans+=min(sn+(an-2)*m,m+sn+(an+1)*s);
    }
    cout<<ans<<endl;
    return 0;
}
//4 3 1 2 5

