List Mutating Operations

Write a function list_mutating_operations(items, item1, item2) that applies the following operations to items in place, in this exact order. Do not build a new list anywhere -- every step must modify items itself.

1. Sort items in ascending order.
2. Append item1 at the end.
3. Insert item2 at index 3.
4. Extend items with the first three elements of items (as it is at that moment).
5. If the list now has at least 5 elements, pop the element at index 4 and keep it in popped_item; otherwise popped_item is None.
6. If item2 is present in the list, remove its first occurrence.
7. If the list has more than 4 elements, set the element at index 4 to None.
8. Set every even index (0, 2, 4, ...) to None.
9. If the list has at least 3 elements, delete the third-last element.
10. Delete every even index.

Return the tuple (items, popped_item).

Example

list_mutating_operations([5, 3, 9, 1, 7], 10, 3)  ->  ([5, 9, None], 7)

Your task

Implement this function:

def list_mutating_operations(items: list, item1, item2) -> tuple:

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

([5, 9, None], 7)