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<map>
#include<algorithm>
using namespace std;
int main(){
  int n,ans=0,t[1000],u[1000];
  bool visited[1000];
  map<int,int> change;
  cin>>n;
  for(int i=0;i<n;i++){
    cin>>t[i];
    change[t[i]]=i;
    u[i]=t[i];
    visited[i]=false;
  }
  sort(u,u+n);
  for(int i=0;i<n;i++){   
    int w=i,x=0,y=0,z=10000;
    while(!visited[w]){
      z=min(z,t[w]);
      y+=t[w];
      x++;
      visited[w]=true;
      w=change[u[w]];
    }
    if(x>=2)ans+=min(y+z+u[0]*(x+1),y+z*(x-2));
  }
  cout<<ans<<endl;
  return 0;
}