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 (true) {
      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;
  ans = solve();
  cout<<ans<<endl;
  return 0;
}

