from functools import lru_cache
from functools import cache

@cache
def steps_to(stair):
    if stair == 1:
        # You can reach the first stair with only a single step from the floor.
        return 1

    elif stair == 2:
        # You can reach the second stair by jumping from the floor with a single two-stair hop or by jumping a single stair a couple of times.
        return 2

    elif stair == 3:
        # You can reach the third stair using four possible combinations:
        # 1. Jumping all the way from the floor
        # 2. Jumping two stairs, then one
        # 3. Jumping one stair, then two
        # 4. Jumping one stair three times
        return 4

    else:
        # You can reach your current stair from three different places:
        # 1. From three stairs down
        # 2. From two stairs down
        # 2. From one stair down
        # If you add up the number of ways of getting to those
        # those three positions, then you should have your solution.
        return steps_to(stair - 3) + steps_to(stair - 2) + steps_to(stair - 1)

print(steps_to(35))