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, mini;
int A[1000], B[1000], C[1000];
bool V[1000];
int solve() {
  int total = 0;
  for (int i = 0; i < N; i++) {
    B[i] = A[i];
    V[i] = false;
  }
  sort(B, B + N);
  mini = B[0];
  for (int i = 0; i < N; i++) {
    C[B[i]] = i;
    if (B[i] == A[i]) V[i] = true;
  }
  for (int i = 0; i < N; i++) {
    while (V[i] == false) {
      int tmp = A[i];
      int min_tmp;
      int next = C[A[i]];
      int sum = A[i];
      int n = 0;
      V[i] = true;
      min_tmp = min(A[i], A[next]);
      while (!V[next]) {
        n++;
        V[next] = true;
        sum = sum + A[next];
        if (A[next] < min_tmp) min_tmp = A[next];
        next = C[A[next]];
      }
      total =
          total + min(sum + (n - 1) * min_tmp, sum + min_tmp + (n + 2) * mini);
    }
  }
  return total;
}
int main() {
  cin >> N;
  for (int i = 0; i < N; i++) {
    cin >> A[i];
  }
  int s = solve();
  cout << s << endl;
  return 0;
}
