import numpy as np

lines = sorted(int(x.strip()) for x in open("input.txt"))

lines.append(lines[-1]+3)
lines.insert(0, 0)
lines = np.array(lines)

diff = lines[1:] - lines[:-1]

one_count = 0
possibilities = 1

one_cache = {}


def count_one_possibilities(one_cnt: int):
    if one_cnt not in one_cache:
        if one_cnt <= 1:
            one_cache[one_cnt] = 1
        else:
            one_cache[one_cnt] = sum(count_one_possibilities(less) for less in range(max(0, one_cnt - 3), one_cnt))
    return one_cache[one_cnt]


# only 3 and 1 differences are available
# 3 has to be taken / calculate possibilities for 1 hops
for num in diff:
    if num == 1:
        one_count += 1
    elif num == 3:
        possibilities *= count_one_possibilities(one_count)
        one_count = 0

print(possibilities)  # 64793042714624
print(one_cache)  # {0: 1, 1: 1, 2: 2, 3: 4, 4: 7}