Perfect Route Cycles

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"A large bus company recently expanded its fleet to enhance its in-house transportation system. These buses travel to specific stations, numbered from 1 to n. Currently, the company only operates in two regions. All bus routes are designed as a tree structure, meaning buses departing from any station go to a local hub, then travel to a larger hub or one of the company's destinations. Let's represent stations in the first region with the color white, and stations in the second region with the color black. Given a list of stations and their immediate destinations, your task is to add a route between any two stations such that a perfect route cycle is formed. The characteristics of a perfect route cycle are: - The number of destinations in the cycle is greater than or equal to 3. - All stations in the cycle are in the same region. Count the number of distinct ways to form a perfect route cycle by adding a path between any two stations. This will help the bus company decide where to register its buses for regional travel."