def is_non_bouncy(n: int):
    digits = list(map(int, list(str(n))))
    decreasing = True
    increasing = True
    for i in range(len(digits) - 1):
        increasing = increasing and digits[i] <= digits[i + 1]
        decreasing = decreasing and digits[i] >= digits[i + 1]
    return increasing or decreasing


def non_bouncy_below_naiv(digits: int):
    threshold = 10 ** digits
    non_bouncy = sum([1 for i in range(1, threshold) if is_non_bouncy(i)])
    return non_bouncy


def non_bouncy_below(digits: int):
    # increasing
    s = [1 for _ in range(1, 10)]
    result = sum(s)
    for _ in range(digits - 1):
        s = [sum(s[i:]) for i in range(9)]
        result += sum(s) - 9
    # The -9 is to avoid double counting 11, 22, 33 for increasing and
    # decreasing.

    # decreasing
    decreasing_count = 0
    s = [i + 1 for i in range(1, 10)]
    for _ in range(digits - 1):
        # print(s)
        decreasing_count += sum(s)
        s = [sum(s[:i]) + 1 for i in range(1, 10)]
    result += decreasing_count
    return result


def euler_113():
    assert non_bouncy_below_naiv(6) == 12951
    assert non_bouncy_below(6) == 12951
    assert non_bouncy_below(10) == 277032
    assert is_non_bouncy(134468)
    assert is_non_bouncy(66420)
    assert (not is_non_bouncy(155349))
    return non_bouncy_below(100)


if __name__ == "__main__":
    solution = euler_113()
    print("e113.py: " + str(solution))
    assert(solution == 51161058134250)