def solution(banana_list):
    fewest_possible_number = len(banana_list)
    for pairs in generate_trainer_pairs(list(range(len(banana_list)))):
        possible_number = len(banana_list)
        for i, j in pairs:
            if check_loop(banana_list[i], banana_list[j]):
                possible_number -= 2
        if possible_number < fewest_possible_number:
            fewest_possible_number = possible_number
    return fewest_possible_number

import copy
def generate_trainer_pairs(trainer_id_list):
    if len(trainer_id_list) < 2:
        yield []
    else:
        first_id = trainer_id_list[0]
        temp_list = copy.deepcopy(trainer_id_list)
        temp_list.remove(first_id)
        for second_id in temp_list:
            tt_list = copy.deepcopy(temp_list)
            tt_list.remove(second_id)
            for pairs in generate_trainer_pairs(tt_list):
                yield [(first_id, second_id)] + pairs

def check_loop(x, y):
    a, b = x, y
    memo = []
    while a != b:
        if a > b:
            a, b = a - b, 2*b
        else:
            a, b = 2*a, b - a
        if (a, b) in memo:
            return True
        else:
            memo += [(a, b)]
    return False

tests = [
        ([1, 1], 2),
        ([1, 7, 3, 21, 13, 19], 0),
        ]

for i, o in tests:
    result = solution(i)
    print(i, result == o, result, o)