def num_of_swaps(arr):
    """Calculates min swaps to sort an array."""
    # Create a dictionary to store the original indices of elements
    ori_idx = {val: i for i, val in enumerate(arr)}
    # Sort the array and store the sorted version
    sorted_arr = sorted(arr)
    swap_num = 0  # Initialize swap counter

    # Iterate over the array
    for i in range(len(arr)):
        # If the element is out of place
        if arr[i] != sorted_arr[i]:
            # Find the index of the corresponding element in the original array
            j = ori_idx[sorted_arr[i]]
            # Swap the elements
            arr[i], arr[j] = arr[j], arr[i]
            # Update the indices in the ori_idx dictionary
            ori_idx[arr[i]], ori_idx[arr[j]] = i, j
            swap_num += 1  # Increment swap counter

    return swap_num  # Return total swaps

def lilysHomework(arr):
    """Calculates min swaps for ascending/descending sort."""
    # Calculate the minimum number of swaps needed for both ascending and descending orders
    return min(num_of_swaps(arr[:]), num_of_swaps(arr[::-1]))