## On the Subject of Decaying Decay

Everything falls apart.

This module displays three pressable symbols.

### Step 1

#### Step 1.1: Decrypting the display

For each symbol, interpret each vertical bar as:

- 0 if it’s disconnected to the base
- 1 if it’s connected to the base

Treat each number as binary and convert them into base 10.

Then, add 2^{k}-1 to the number, where k is the number of vertical bars on the character.

Your base number (hereby referred as *n*) is (First number * 225) + (Second number * 15) + Third number.

#### Step 1.2: Constructing the tree

Construct a tree consisting of nodes and branches. Each node consists of three values: Prime Value, Remainder Value, and Binary Value.

In this step we will only consider the Prime and Remainder Values.

Start by constructing a node with n as the Remainder Value and 0 as the Prime Value. This node is also known as **the base node**.

Then for each node:

- For each unique prime factor of the Remainder Value, construct a child node connecting to the node where Prime Value = the prime factor and Remainder Value = [Remainder Value of the parent] / [Prime Value] + 1.
- Order these children nodes from lowest to highest based on the Prime Value.

Apply these steps above for each node, with the exception when the Remainder Value of that node is prime.

Example: 284

(Each node is presented as [Prime Value, Remainder Value])

0, 284

- 2, 143

- - 11, 14

- - - 2, 8

- - - - 2, 5*

- - 13, 12

- - - 2, 7*

- - - 3, 5*

- 71, 5*

*cases where Remainder Value is prime