Troubled Witch

The Witch’s Grimoire of Shadows has been torn apart, scattering its pages. Myregietha Frost possesses crates of ingredients, bundles of candles, piles of tools, and ritual diagrams—but she doesn't know how to combine them back into spells. Your task is to help her restore the book by organizing her inventory.

Myregietha needs your assistance! She has a list of all items in her witches hut, but it’s currently disorganized. The item details are provided in the witch_input.txt file, formatted as (item type):(item).

To help Myregietha calculate her inventory coefficient, you need to determine the quantity of each item type and multiply them together.

For Example:
Input:
candle:candle_green
candle:candle_red
tool:mortar
ingredient:spider_leg
diagram:bone_script

Solution: 2 (candles) * 1 (tool) * 1 (ingredient) * 1 (diagram) = 2

Your solution is the product of the quantities of each of the four item types: candles, tools, ingredients, and diagrams.