# from fractions import Fraction
# from functools import reduce
# from operator import add
# import math

# CREATOR_FEE = ...  # Add appropriate value
# LIQUIDITY_FEE = ...  # Add appropriate value
# PLATFORM_FEE = ...  # Add appropriate value
# EPSILON = 0.00000001  # Add appropriate value

# class LimitBet:
#     ...

# class LiquidityProvision:
#     ...

# class Answer:
#     ...


# def get_cpmm_probability(pool, p):
#     YES, NO = pool['YES'], pool['NO']
#     return (p * NO) / ((1 - p) * YES + p * NO)


# def get_cpmm_probability_after_bet_before_fees(state, outcome, bet):
#     pool, p = state['pool'], state['p']
#     shares = calculate_cpmm_shares(pool, p, bet, outcome)
#     y, n = pool['YES'], pool['NO']

#     if outcome == 'YES':
#         newY, newN = y - shares + bet, n + bet
#     else:
#         newY, newN = y + bet, n - shares + bet

#     return get_cpmm_probability({'YES': newY, 'NO': newN}, p)


# def get_cpmm_outcome_probability_after_bet(state, outcome, bet):
#     new_pool = calculate_cpmm_purchase(state, bet, outcome)['newPool']
#     p = get_cpmm_probability(new_pool, state['p'])
#     return 1 - p if outcome == 'NO' else p


# def calculate_cpmm_shares(pool, p, bet, bet_choice):
#     if bet == 0:
#         return 0

#     y, n = pool['YES'], pool['NO']
#     k = y ** p * n ** (1 - p)

#     if bet_choice == 'YES':
#         return y + bet - (k * (bet + n) ** (p - 1)) ** (1 / p)
#     else:
#         return n + bet - (k * (bet + y) ** -p) ** (1 / (1 - p))


# def get_cpmm_fees(state, bet, outcome):
#     prob = get_cpmm_probability_after_bet_before_fees(state, outcome, bet)
#     bet_p = 1 - prob if outcome == 'YES' else prob

#     liquidity_fee = LIQUIDITY_FEE * bet_p * bet
#     platform_fee = PLATFORM_FEE * bet_p * bet
#     creator_fee = CREATOR_FEE * bet_p * bet
#     fees = {'liquidityFee': liquidity_fee, 'platformFee': platform_fee, 'creatorFee': creator_fee}

#     total_fees = liquidity_fee + platform_fee + creator_fee
#     remaining_bet = bet - total_fees

#     return {'remainingBet': remaining_bet, 'totalFees': total_fees, 'fees': fees}

# # ... [Continue for the rest of the functions]

# # Note: Python lacks direct translations for some JavaScript functions such as `mapValues` and `sumBy` from lodash.
# #       You might need to implement those utility functions yourself or use Pythonic methods to achieve the same result.
