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>
//toriaezu
int sort(int *A,int n){
  int i,j;
  int min=1000,max=0;
  int cost=0;
  
  for(i=1;i<n;i++){
    if(A[i]>max) max=A[i];
    else if(A[i]<min) min=A[i];
  }
  cost+=max+min;
  return cost;
}
int main(){

  int i,n,cost;
  int A[1000];

  scanf("%d",&n);

  for(i=0;i<n;i++) scanf("%d",&A[i]);
  cost=sort(&A[0],n);
  
  printf("%d\n",cost);
return 0;
}