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[1111];
int U[1111];
int main() {
  cin >> N;
  for (int i = 0; i < N; i++) {
    cin >> W[i];
    U[i] = W[i];
  }
  sort(W, W + N);
  int res = 0;
  for (int i = N - 1; i > -1; i--) {
    if (W[i] == U[i]) continue;
    for (int j = i - 1; j > -1; j--) {
      if (W[i] == U[j]) {
        swap(U[i], U[j]);
        res += U[i] + U[j];
        break;
      }
    }
  }
  cout << res << endl;
}
