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 n;
int A[1001],B[1001];

int getIdx(){
  int idx = n;
  for(int i=0;i<n;i++)if(A[i]!=B[i] && A[idx]>A[i]) idx = i;  
  return idx;
}

int Sort(int pos){
  int sum=0,cnt=0;
  while(A[pos]!=B[pos]){
    cnt++;
    int idx=0;
    while(B[pos]!=A[idx]) idx++;
    sum += A[idx];
    swap(A[pos],A[idx]);
    pos = idx;
  }
  return min(sum+A[pos]*cnt,sum+A[pos]*2+(cnt+2)*B[0]);
}

int main(){
  cin>>n;
  for(int i=0;i<n;i++)cin>>A[i],B[i] = A[i];
  A[n] = B[n] = 1e9;
  sort(B,B+n);

  int ans = 0;  
  for(int i=0;i<n;i++)ans+=Sort(getIdx());
  cout<<ans<<endl;
  
  return 0;
}