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<stdio.h>
  
int n;
int a[1000];
int b[1000];
int vd[1000];
int cnt,sum,mini;

void swap(int* a,int* b){
  int tmp=*a;
  *a=*b;
  *b=tmp;
}
 
int min(int x,int y){
  if(x<y)return x;
  else return y;
}
  
int search(int x){
  int i;
  for(i=0;i<n;i++)if(a[i]==x)return i;
}
  
int main(){
  int i,j,ans,x;
  
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%d",&a[i]);
    b[i]=a[i];
  }
  
  for(i=n-1;i>0;i--)
    for(j=0;j<i;j++)
      if(B[j]>B[j+1])swap(&b[j],&b[j+1]);
    
  ans=0;
  for(i=0;i<n;i++)vd[i]=0;
  
  for(i=0;i<n;i++){   
    x=i;
    cnt=sum=0;
    mini=(1<<24);
    while(vd[x]==0){
      vd[x]=1;
      cnt++;
      sum+=a[x];
      mini=min(mini,a[x]);
      x=search(b[x]);
    }
    if(cnt<2)continue;
    ans+=min(sum+b[0]*(cnt+1)+mini,sum+mini*(cnt-2));
  
  }
  
  printf("%d\n",ans);
  return 0;
}