def solution(l):
    remain = sum(l) % 3
    if remain == 0:
        largest_number = get_largest_number(l)
        return largest_number

    (category_0, category_1, category_2) = split_digits_by_remain_of_three(l)
    if remain == 1:
        category_1, category_2 = remove_one_or_two_digits(category_1, category_2)
    else:
        category_2, category_1 = remove_one_or_two_digits(category_2, category_1)
    if (category_1 == False) or (category_2 == False):
        return 0
    largest_number = get_largest_number(category_0 + category_1 + category_2)
    return largest_number

def split_digits_by_remain_of_three(nums):
    result = ([], [], [])
    for n in nums:
        result[n%3].append(n)
    return result

def remove_one_or_two_digits(list1, list2):
    if len(list1) >= 1:
        return sorted(list1)[1:], list2
    if len(list2) >= 2:
        return list1, sorted(list2)[2:]
    return False, False

def get_largest_number(nums):
    if len(nums) == 0:
        return 0
    return int(''.join([str(x) for x in sorted(nums, reverse=True)]))

test_cases=[
    [3, 1, 4, 1],
    [3, 1, 4, 1, 5, 9],
    [5, 5],
    [0, 0, 9,9,9,9,9,9,9,9,7],
    [0, 0, 0,0,0,0],
    [0, 0, 0,0,0,0, 1, 1, 1],
    [1],
    [1, 1],
    [1, 2],
    [1, 1, 1],
    [],
    [0],
    [1, 2, 3],
    [1, 2, 3, 4],
    [1, 2, 3, 4, 5],
    [3, 3, 3, 0, 1, 1, 2, 2],
    [3, 3, 3, 0, 1, 2, 2],
    [3, 3, 3, 0, 1, 1, 2],
    [1, 0, 0, 0],
    [2, 0, 0, 0],
    [3, 0, 0, 0, 6],
    [1, 2, 3, 4, 5, 6, 7, 8, 9, 0]
        ]
for test in test_cases:
    print(test, solution(test))