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;
#define int long long

const int N = 1e5;
int a[N],b[N],check[N];
map<int,int> mp;

signed main(){

  int n; cin >> n;
  for(int i = 0; i < n; i++){
    cin >> a[i];
    b[i] = a[i];
    mp[a[i]] = i;
  }

  sort(b,b+n);
  int ans = 0;
  for(int i = 0; i < n; i++){
    int cost = 0,u = i,m = 1e9;
    int j = 0;
    for(; !check[u]; j++){
      m = min(m,a[u]);
      cost += a[u];
      check[u] = 1;
      u = mp[b[u]];
    }
    if(j >= 2){
      ans += min(cost+m+(j+1)*b[0],cost+(j-2)*m);
    }
  }
  cout << ans << endl;

  return 0;
}

