List Non-Mutating Operations

Write a function list_non_mutating_operations(items, item1, item2) that computes the result of nine list operations without ever modifying items. Each operation starts again from the original items.

Return a list holding the nine results, in this order:

1. items sorted in ascending order.
2. items with item1 appended at the end.
3. items with item2 inserted at index 3.
4. items followed by the first three elements of items.
5. items with the element at index 4 removed (if items has fewer than 5 elements, an unchanged copy of items).
6. items with the first occurrence of item2 removed (if item2 is not present, an unchanged copy of items).
7. items with the element at index 3 replaced by None (if items has 3 or fewer elements, an unchanged copy of items).
8. items with every even index (0, 2, 4, ...) replaced by None.
9. items with every even index removed.

Example

list_non_mutating_operations([3, 1, 2], 9, 1)
->  [[1, 2, 3], [3, 1, 2, 9], [3, 1, 2, 1], [3, 1, 2, 3, 1, 2],
     [3, 1, 2], [3, 2], [3, 1, 2], [None, 1, None], [1]]

Your task

Implement this function:

def list_non_mutating_operations(items: list, item1, item2) -> list:

Write the function only — the arguments are read for you and the return value is printed automatically.

Arguments arrive as one Python literal per line, in this order: items, item1, item2.

Example

Input

[5, 3, 9, 1, 7]
10
3

Output

[[1, 3, 5, 7, 9], [5, 3, 9, 1, 7, 10], [5, 3, 9, 3, 1, 7], [5, 3, 9, 1, 7, 5, 3, 9], [5, 3, 9, 1], [5, 9, 1, 7], [5, 3, 9, None, 7], [None, 3, None, 1, None], [3, 1]]