## On the Subject of Decay

Everything falls apart...

The module displays 3 pressable symbols. In order to solve the module, press the symbols in the correct order. Any confusing terminology will be explained at the end of the manual.

### Step 1: Over-Complicated Prime Factorisation

...the numbers...

#### Step 1.1: Decrypting the display

The module displays 3 encrypted symbols. To decrypt each symbol individually, interpret the vertical bars as binary, where a vertical connected to the base is a 1 and a vertical disconnected from the base is a 0. Then add 2^{k}-1 to this value, where k is the amount of vertical bars on the character. Interpret the three values as base-15 and convert it in its entirety to decimal. This number will be called n.

#### Step 1.2: Constructing the tree

Construct a tree consisting of nodes and branches. To construct the tree start with a node with [V_{p}=0; V_{r}=n]. For each unique prime factor P of V_{r}, create a child node with [V_{p}=P; V_{r}=(V_{r,parent}/P)+1]. Order the children in each node from lowest to highest V_{p}. This function should be applied to each node with V_{r} not being prime. This set of nodes will be called T