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 main(){
  int n;
  cin >> n;

  vector<int> a(n);
  for(int i=0;i<n;i++)cin >> a[i];
  int MinV = *min_element(a.begin(),a.end());

  vector<int> order = a, p = a;
  sort(order.begin(), order.end());

  for(int i=0;i<n;i++){
    for(int j=0;j<n;j++){
      if(a[i] == order[j])p[i] = j;
    }
  }

  long long ans = 0;
  vector<bool> use(n,0);
  for(int i=0;i<n;i++){
    if(!use[i]){
      int cur = i, minv = 1e8, sum = 0, len = 0;
      do{
	use[cur] = 1;
	minv = min(minv, a[cur]);
	sum += a[cur];
	cur = p[cur];
	len++;
      }while(cur!=i);
      ans += min(sum + minv*(len-2), sum + MinV*len + minv + MinV);
    }
  }
  cout << ans << endl;
}