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 N;
int W[11111];
int U[11111];
int R[11111];
int T[11111];
void view() {
  for (int i = 0; i < N; i++) cout << U[i] << " ";
  cout << endl;
}
int main() {
  cin >> N;
  for (int i = 0; i < N; i++) {
    cin >> U[i];
    W[i] = U[i];
    T[U[i]] = i;
  }
  sort(W, W + N);
  for (int i = 0; i < N; i++) {
    R[W[i]] = i;
  }
  int res = 0;
  for (int i = 0; i < N; i++) {
    if (W[i] == U[i]) continue;
    int id = T[W[i]];
    int nd = T[W[id]];
    while (U[id] != U[nd]) {
      swap(U[id], U[nd]);
      T[U[id]] = id;
      T[U[nd]] = nd;
      res += U[id] + U[nd];
      id = nd;
      nd = T[W[id]];
    }
  }
  cout << res << endl;
}
