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>
using namespace std;
int main(){
  int n,a[1111],tmp[1111],b[1111]={},mina=10000,ans=0;
  cin>>n;
  for(int i=0;i<n;i++){
    cin>>a[i];
    tmp[i]=a[i];
    mina=min(a[i],mina);
  }
  
  sort(tmp,tmp+n);
  
  for(int i=0;i<n;i++){
    int l=0,r=n,m;
    while(1){
      m=(l+r)/2;
      if(tmp[m]>a[i])r=m;
      else if(tmp[m]<a[i])l=m;
      else {
	a[i]=m;
	break;
      }
    }
  }
  
  for(int i=0;i<n;i++){
    if(a[i]!=i&&b[i]==0){
      int t=i,mint=10000,sum=0,cnt=0;
      while(1){
	cnt++;
	sum+=tmp[a[t]];
	mint=min(mint,tmp[a[t]]);
	b[t]++;
	t=a[t];
	if(t==i){
	  ans+=min(sum+mint*(cnt-2),sum-mint+mina*(cnt-1)+(mina+mint)*2);
	  break;
	}
      }
    }
  }
  cout<<ans<<endl;
  return 0;
}