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;
static const int Max =1000;
static const int Vmax=10000;

int n,A[Max],s;
int B[Max],T[Vmax+1];

int solve(){
  int ans=0;
  bool V[Max];

  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 cur=i;
    int S=0;
    int m=Vmax;
    int an=0;
    while(1){
      V[cur]=true;
      an++;
      int v=A[cur];
      m=min(m,v);
      S+=v;
      cur=T[v];
      if(V[cur])break;
    }
    ans+=min(S+(an-2)*m,m+S+(an+1)*s);
  }
  return ans;
}

int main(){
  cin>>n;
  s=Vmax;
  for(int i=0;i<n;i++){
    cin>>A[i];
    s=min(s,A[i]);
  }
  int ans=solve();
  cout<<ans<<endl;

  return 0;
}

