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>
#define MAX 1000
#define VMAX 10000
using namespace std;
int A[MAX],B[MAX],n,s;
int T[VMAX+1];
int solve(){
    bool V[MAX];
    int ans=0;
    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 cur=i;
        int S=0;
        int an=0;
        int m=VMAX;
        while(1){
            V[cur]=true;
            int v=A[cur];
            S+=v;
            an++;
            m=min(m,v);
            cur=T[v];
            if(V[cur])  
                break;
        }
        ans+=min(S+(an-2)*m,S+m+(an+1)*s);
    }
    return ans;
}
int main(){
    cin>>n;
    s=VMAX;
    for(int i=0;i<n;i++){
          cin>>A[i];
          s=min(s,A[i]);
    }
    int ans=solve();
    cout<<ans<<endl;
    return 0;
}
