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<cstdio>
#include<iostream>
#include<algorithm> 
using namespace std;
int a[1000],b[1000],c[10000],min1=100000,min2=100000,x[1000];
int main(){
	int n,sum=0,s,n1;
	cin>>n;
	for(int i=0;i<n;i++)
	  {cin>>a[i];
	  if(min1>a[i]) min1=a[i];
	  b[i]=a[i];
	  }
	  sort(b,b+n);
	  for(int i=0;i<n;i++)
	  c[b[i]]=i;
	  for(int i=0;i<n;i++){
	  	s=0;min2=100000;n1=0;
	  	   while(a[i]!=b[i]&&x[i]==0)
	  	     { x[i]=1;n1++;
			   s+=a[i];
	  	    min2=min(a[i],min2);
			   i=c[a[i]];
	  	      if(x[i]) sum+=min(s+(n1-2)*min2,s+min2+(n1+1)*min1);
	  	    }  	    	  
	  }
	  cout<<sum<<endl;
} 
