implement a bidirectional linked list :)

API

You are given a node that is the beginning of a linked list. This list always contains a tail and a loop.

Your objective is to determine the length of the loop.

in the following example the tail's size is 3 and the loop size is 11.

nodes=[node() for i in range(14)]
for node, next_node in enumerate(nodes,nodes[1:]):
  node.next=next_node
nodes[13].next=nodes[11]

Use the next attribute to get the following node
node.next

Note: do NOT mutate the nodes!

A perfect power is a classification of positive integers:

In mathematics, a perfect power is a positive integer that can be expressed as an integer power of another positive integer. More formally, n is a perfect power if there exist natural numbers m > 1, and k > 1 such that m**k = n.

Your task is to check wheter a given integer is a perfect power. If it is a perfect power, return a pair m and k with mk = n as a proof. Otherwise return None.

Note: For a perfect power, there might be several pairs. For example 81 = 3^4 = 9^2, so (3,4) and (9,2) are valid solutions. However, the tests take care of this, so if a number is a perfect power, return any pair that proves it.

Examples
isPP(4) => [2,2]
isPP(9) => [3,2]
isPP(5) => None