The Alchemist's Component Count

An alchemist needs to know how many units of a 'Base' element are required to create a 'Target' compound. You are given a list of recipes where each compound is made of several ingredients (which could be other compounds or base elements). If an ingredient is not defined by a recipe, it is considered a base element. Calculate the total count of the specified Base element needed for one unit of the Target. Input Format: 1. The name of the Target compound. 2. The name of the Base element to count. 3. An integer N, the number of recipes. 4. N lines, each in the format: 'Compound: Qty1 Ingredient1, Qty2 Ingredient2...' Output Format: A single integer representing the total amount of the Base element required. Example: Input: Gold Lead 2 Gold: 2 Mercury, 1 Sulfur Mercury: 3 Lead, 1 Tin Output: 6 (Explanation: 1 Gold needs 2 Mercury. 1 Mercury needs 3 Lead. Total Lead = 2 * 3 = 6.)