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>
using namespace std;
#define MAX 1000
int n,x,a[MAX],b[MAX],t[10001];
 
int solve(){
    int ans=0;
    bool v[MAX];
    for(int i=0;i<n;i++){
        b[i]=a[i];  v[i]=false;
    }
    sort(b,b+n);
    for(int i=0;i<n;i++) t[b[i]]=i;
    for(int i=0;i<n;i++){
        if(v[i])    continue;
        int current=i;
        int s=0;
        int m=10000;
        int count=0;
        while(1){
            v[current]=true;
            count++;
            m=min(m,a[current]);
            s+=a[current];
            current=t[a[current]];
            if(v[current])  break;
        }
        ans+=min(s+(count-2)*m,s+m+(count+1)*x);
    }
    return ans;
}
         
 
int main(){
    cin>>n;
    x=10000;
    for(int i=0;i<n;i++){
        cin>>a[i];
        x=min(x,a[i]);
    }
    cout<<solve()<<endl;
    return 0;
}
