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;
const int VMAX=10001;
int T[VMAX+1];
int solve(int A[],int n,int Min){
  int ans=0;
  int *B=new int[n];
  bool *v=new bool[n];
  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 an = 0;
	int m = VMAX;//
	int cur = i;
	int s = 0;
	if(i!=T[A[i]]){
	while(1){
	  	  an++;
	      v[cur]=true;
	      int t=A[cur];
	      m=min(m,t);
	      s+=t;
	      cur=T[t];
	      if(v[cur])break;
	   }

	   ans+=min(s+(an-2)*m,s+m+(an+1)*Min);    

  	}
  }
   return ans;
}
int main(){
	int n;
	int Min=VMAX;//
	cin>>n;
	int *A=new int[n];
	for(int i=0;i<n;i++){
		cin>>A[i];
		Min=min(Min,A[i]);
	}
	int ans=solve(A,n,Min);
	cout<<ans<<endl;
	return 0;
}
