import numpy as np

def calculate_gems_and_experience(experience_sapphire, experience_emerald, experience_ruby, new_total_experience, bonus_multiplier=None):
    if bonus_multiplier:
        experience_sapphire_bonus = experience_sapphire * bonus_multiplier
        experience_emerald_bonus = experience_emerald * bonus_multiplier
        experience_ruby_bonus = experience_ruby * bonus_multiplier
    else:
        experience_sapphire_bonus = experience_sapphire
        experience_emerald_bonus = experience_emerald
        experience_ruby_bonus = experience_ruby

    # Ratios based on probabilities: Sapphire 50%, Emerald 30.03%, Ruby 20%
    gem_ratios = np.array([2.5, 1.5015, 1])  # Scaled to match the smallest ratio (Ruby = 1)

    # Recalculate the weighted experience per unit with the ratios
    experience_per_unit = sum(
        gem_ratios * [experience_sapphire_bonus, experience_emerald_bonus, experience_ruby_bonus]
    )

    # Calculate the multiplier to determine the number of gems needed
    multiplier = new_total_experience / experience_per_unit

    # Calculate the approximate number of gems of each type using the ratios
    required_sapphires = round(gem_ratios[0] * multiplier)
    required_emeralds = round(gem_ratios[1] * multiplier)
    required_rubies = round(gem_ratios[2] * multiplier)

    # Calculate the total experience from this combination
    total_experience_gained = (
            required_sapphires * experience_sapphire_bonus +
            required_emeralds * experience_emerald_bonus +
            required_rubies * experience_ruby_bonus
    )

    return required_sapphires, required_emeralds, required_rubies, total_experience_gained

def main():
    # Constants for experience per action for each gem
    experience_sapphire = 50
    experience_emerald = 67.5
    experience_ruby = 85

    # Total experience needed
    new_total_experience = 1462010

    # Adjusted experience per gem with 2.5% bonus
    bonus_multiplier = 1.025

    # Calculate with bonus multiplier
    sapphires_with_bonus, emeralds_with_bonus, rubies_with_bonus, experience_with_bonus = calculate_gems_and_experience(
        experience_sapphire, experience_emerald, experience_ruby, new_total_experience, bonus_multiplier
    )

    # Calculate without bonus multiplier
    sapphires_without_bonus, emeralds_without_bonus, rubies_without_bonus, experience_without_bonus = calculate_gems_and_experience(
        experience_sapphire, experience_emerald, experience_ruby, new_total_experience
    )

    print(f'With Wisdom Aura:\n Sapphires Needed: {sapphires_with_bonus:,}\n Emeralds Needed: {emeralds_with_bonus:,}\n Rubies Needed: {rubies_with_bonus:,}\n Total Experience Gained: {experience_with_bonus:,}\n')
    print(f'Without Wisdom Aura:\n Sapphires Needed: {sapphires_without_bonus:,}\n Emeralds Needed: {emeralds_without_bonus:,}\n Rubies Needed: {rubies_without_bonus:,}\n Total Experience Gained: {experience_without_bonus:,}')


main()