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 1100
#define MAX_W 11000
 
 
int n, mimi = MAX_W;
bool used[MAX];
pair<int,int> w[MAX];
 
int hoge(int x,int sum, int mi,int count){
    if(used[x]){
        return min(sum+mi*(count-2), mi + sum + (count+1)*mimi);
    } else {
        used[x] = true;
        return hoge(w[x].second,sum+w[x].first,min(mi,w[x].first),count+1);
    }
}
 
int main(){
    int W, sum = 0;
     
    cin>>n;
     
    for(int i = 0; i < n; i++){
        cin>>W;
        w[i] = make_pair(W,i);
        mimi = min(W, mimi);
    }
     
    sort(w, w + n);
     
    for(int i = 0; i < n; i++){
        if(!used[i]) sum +=  hoge(i,0,w[i].first,0);
    }
     
    cout<<sum<<endl;
     
    return 0;
}
