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;

int main(){
        int n, ans=0, amin=10000;
        cin>>n;
        int a[n], b[n], T[10000];
        bool V[n];
        for(int i=0;i<n;i++) V[i] = true;
        for(int i=0;i<n;i++) {
                cin>>a[i];
                b[i]=a[i];
                amin=min(a[i], amin);
        }
        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 j = i, tmpmin = a[i], c=0;
                int S = 0;
                while(V[j]){
                        c++;
                        tmpmin = min(tmpmin, a[j]);
                        S += a[j];
                        V[j] = false;
                        j = T[a[j]];
                }
                ans += min(S+(c-2)*tmpmin, S+tmpmin+(c+1)*amin);
        }

        cout<<ans<<endl;
        return 0;
}
