from functools import cache


def euler_092():
    count = 0

    square_dict = {str(i): i * i for i in range(10)}
    square_lookup = lambda s: square_dict[s]

    @cache
    def number_chain(n):
        if n == 1 or n == 89:
            return n
        squared_digits = map(square_lookup, str(n))
        new_n = sum(squared_digits)
        n = number_chain(new_n)
        return n

    for n in range(1, 10**7 + 1):
        if number_chain(n) == 89:
            count += 1
    return count


if __name__ == "__main__":
    solution = euler_092()
    print("e092.py: " + str(solution))
    assert(solution == 8581146)