Introduction

You've been hired to develop Noble Knots, the hottest new dating app for nobility! With centuries of royal intermarriage, things have gotten… complicated. To avoid any oops-we're-twins situations, your job is to build a system that checks how closely two people are related.

Noble Knots is inspired by Iceland's "Islendinga-App," which is backed up by a database that traces all known family connections between Icelanders from the time of the settlement of Iceland. Your algorithm will determine the degree of separation between two individuals in the royal family tree.

Will your app help crown a perfect match?

Instructions

Your task is to determine the degree of separation between two individuals in a family tree. This is similar to the pop culture idea that every Hollywood actor is within six degrees of Kevin Bacon.

You will be given an input, with all parent names and their children.
Each name is unique, a child can have one or two parents.
The degree of separation is defined as the shortest number of connections from one person to another.
If two individuals are not connected, return a value that represents "no known relationship." Please see the test cases for the actual implementation.

Example

Given the following family tree:

      ┌──────────┐            ┌──────────┐     ┌───────────┐
      │  Helena  │            │  Erdős   ├─────┤  Shusaku  │
      └───┬───┬──┘            └─────┬────┘     └────┬──────┘
      ┌───┘   └───────┐             └───────┬───────┘
┌─────┴────┐     ┌────┴───┐           ┌─────┴────┐
│   Isla   ├─────┤ Tariq  │           │   Kevin  │
└────┬─────┘     └────┬───┘           └──────────┘
     │                │
┌────┴────┐      ┌────┴───┐
│   Uma   │      │ Morphy │
└─────────┘      └────────┘

The degree of separation between Tariq and Uma is 2 (Tariq → Isla → Uma). There's no known relationship between Isla and Kevin, as there is no connection in the given data. The degree of separation between Uma and Isla is 1.

Note

Isla and Tariq are siblings and have a separation of 1. Similarly, this implementation would report a separation of 2 from you to your father's brother.