Set Operations

Write a function do_set_operation(set1, set2, set3, item1, item2) that performs a series of set operations and returns a list of eight results. set1 is updated in place as you go; set2 and set3 are never modified.

Perform these steps in order, appending the stated value to the result list after each:

1. Add item1 to set1, then record sorted(set1).
2. Remove item2 from set1 if it is there (do nothing if it is not), then record sorted(set1).
3. Add every element of set2 to set1, then record sorted(set1).
4. Remove from set1 every element that is also in set3, then record sorted(set1).
5. Record the elements common to set2 and set3, as a sorted list.
6. Record every distinct element present in set1, set2 or set3, as a sorted list.
7. Record the elements in set2 but not in set3, as a sorted list.
8. Record the elements that are in exactly one of set2 and set3, as a sorted list.

Every result is a sorted list, so the output does not depend on set iteration order.

Example

do_set_operation({1, 2, 3}, {3, 4, 5}, {5, 6, 7}, 9, 2)
->  [[1, 2, 3, 9], [1, 3, 9], [1, 3, 4, 5, 9], [1, 3, 4, 9],
     [5], [1, 3, 4, 5, 6, 7, 9], [3, 4], [3, 4, 6, 7]]

Your task

Implement this function:

def do_set_operation(set1: set, set2: set, set3: set, 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: set1, set2, set3, item1, item2.

Example

Input

{1, 2, 3}
{3, 4, 5}
{5, 6, 7}
9
2

Output

[[1, 2, 3, 9], [1, 3, 9], [1, 3, 4, 5, 9], [1, 3, 4, 9], [5], [1, 3, 4, 5, 6, 7, 9], [3, 4], [3, 4, 6, 7]]