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 <map>
#include <algorithm>
using namespace std;

int main(){
   int n, ans=0, t[1000], u[1000];
   bool visited[1000];
   map<int, int> change;
   cin >> n;
   for(int i=0; i<n; i++){
      cin >> t[i];
      change[t[i]]=i; //キーt[i]の値をiに設定
      u[i]=t[i];
      visited[i]=false;
   }
   sort(u, u+n);
   for(int i=0; i<n; i++){
      int w=i, x=0, y=0, z=10000;
      while(!visited[w]){
         z=min(z, t[w]);
         y+=t[w];
         x++;
         visited[w]=true;
         w=change[u[w]];
      }
      if(x>=2)ans+=min(y+z+u[0]*(x+1), y+z*(x-2)); //最小値を使うか
   }
   cout << ans << endl;
   return 0;
}
