with python set[tuple[int, ...]]that takes an integer n> 0 and returns a set containing all the permutations of 1,2,3,..., n. Each per-mutation must be represented as a tuple. For example:•...

with python

Extracted text: In this task, you will implement a recursive function all_perm(n: int) -> set[tuple[int, ...]] that takes an integer n> 0 and returns a set containing all the permutations of 1,2,3,..., n. Each per- mutation must be represented as a tuple. For example: • all_perm(1) • all_perm(2) • all_perm(3) {(1,)} {(1,2), (2,1)} == {(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1)} %3D%3D Restrictions: Do not write a helper function. Your function must be recursive, and must work with sets and tuples directly. You are not allowed to import anything. Hints: Consider how we can use all_perm(2) to create the answer for all_perm(3). Perhaps the following diagram will help (pay close attention to the color coding and numbers in boldface fonts): all_perm(2) == {(1,2), (2,1)} all_perm(3) == {(3,1,2), (1,3,2), (1,2,3), (3,2,1), (2,3, 1), (2,1,3)} all_perm(4) == {(4,3,1,2), (3,4, 1,2), (3, 1, 4, 2), (3, 1,2, 4), (4, 1,3,2), (1,4,3, 2), (1,3,4,2), (1,3,2,4), (4, 1,2,3), (1,4,2,3), (1,2,4,3), (1,2,3,4), (4,3,2, 1), (3, 4, 2, 1), (3,2, 4, 1), (3,2, 1,4), (4,2,3, 1), (2, 4, 3, 1), (2,3, 4, 1), (2,3,1,4), (4,2, 1,3), (2,4, 1,3), (2,1,4, 3), (2,1,3,4)}