Cluster Tier Classifier

A fleet-management system scales server clusters by doubling their node count during scale-out events. A cluster size n is called:

• a quad tier if n is an exact power of four (n = 4^k for some integer k \ge 0),
• a binary tier if n is an exact power of two but is not a power of four,
• irregular otherwise.

Note every power of four is automatically also a power of two, so quad tier takes priority.

Given n, print its classification.

Input format

Line 1: an integer n.

Output format

Print exactly one of the following strings: power-of-four, power-of-two, or neither.

Constraints

• 1 ≤ n ≤ 1,000,000,000