





UpperCAmelCase__  :     dict[tuple[int, int, int], int]   			= {}





def        _lowercase   (  _UpperCAmelCase     , _UpperCAmelCase     , _UpperCAmelCase			)  ->					int:

				# if we are absent twice, or late 3 consecutive days,
				# no further prize strings are possible
				if late == 3 or absent == 2:
								return 0

				# if we have no days left, and have not failed any other rules,
				# we have a prize string
				if days == 0:
								return 1

				# No easy solution, so now we need to do the recursive calculation

				# First, check if the combination is already in the cache, and
				# if yes, return the stored value from there since we already
				# know the number of possible prize strings from this point on
				lowerCamelCase			=(days, absent, late)
				if key in cache:
								return cache[key]

				# now we calculate the three possible ways that can unfold from
				# this point on, depending on our attendance today

				# 1) if we are late (but not absent), the "absent" counter stays as
				# it is, but the "late" counter increases by one
				lowerCamelCase			=_calculate(days - 1     , _UpperCAmelCase     , late + 1			)

				# 2) if we are absent, the "absent" counter increases by 1, and the
				# "late" counter resets to 0
				lowerCamelCase			=_calculate(days - 1     , absent + 1     , 0			)

				# 3) if we are on time, this resets the "late" counter and keeps the
				# absent counter
				lowerCamelCase			=_calculate(days - 1     , _UpperCAmelCase     , 0			)

				lowerCamelCase			=state_late + state_absent + state_ontime

				lowerCamelCase			=prizestrings
				return prizestrings





def        _lowercase   (  _UpperCAmelCase = 30			)  ->					int:
				return _calculate(_UpperCAmelCase     , absent=0     , late=0			)


if __name__ == "__main__":
							print(solution())












import inspect
import unittest

class  __A       (  unittest.TestCase      ):


				def _snake_case    (						self							):
								try:
												import diffusers  # noqa: F401
								except ImportError:
												assert False


				def _snake_case    (						self							):
								import diffusers
								from diffusers.dependency_versions_table import deps

								lowerCamelCase			=inspect.getmembers(UpperCAmelCase_				,	inspect.isclass							)

								for cls_name, cls_module in all_classes:
												if "dummy_" in cls_module.__module__:
																for backend in cls_module._backends:
																				if backend == "k_diffusion":
																								lowerCamelCase			="""k-diffusion"""
																				elif backend == "invisible_watermark":
																								lowerCamelCase			="""invisible-watermark"""
																				assert backend in deps, f"""{backend} is not in the deps table!"""





