


'''simple docstring'''



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




def      _a     (						_lowercase :     int      , _lowercase :     int      , _lowercase :     int  ):





     '''simple docstring'''






     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
     __UpperCAmelCase     :			Tuple  							=      (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
     __UpperCAmelCase     :			Dict  							=      _calculate(days - 1      , _lowercase      , late + 1  )

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

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

     __UpperCAmelCase     :			List[str]  							=      state_late + state_absent + state_ontime

     __UpperCAmelCase     :			str  							=      prizestrings
     return prizestrings




def      _a     (						_lowercase :     int = 30  ):





     '''simple docstring'''






     return _calculate(_lowercase      , absent=0      , late=0  )


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



'''simple docstring'''



import os
import sys
import unittest


__UpperCAmelCase      :Optional[int]			    =       os.path.abspath(os.path.dirname(os.path.dirname(os.path.dirname(__file__))))
sys.path.append(os.path.join(git_repo_path, "utils"))

import check_dummies  # noqa: E402
from check_dummies import create_dummy_files, create_dummy_object, find_backend, read_init  # noqa: E402


# Align TRANSFORMERS_PATH in check_dummies with the current path
__UpperCAmelCase      :Dict			    =       os.path.join(git_repo_path, "src", "diffusers")



class      a    (		unittest.TestCase	):


     """simple docstring"""






     def 			lowerCamelCase__			(    self					:		Any      )						->							int:
          __UpperCAmelCase     :			Optional[Any]  							=      find_backend('''    if not is_torch_available():'''      )
          self.assertEqual(snake_case							,			'''torch'''      )

          # backend_with_underscore = find_backend("    if not is_tensorflow_text_available():")
          # self.assertEqual(backend_with_underscore, "tensorflow_text")

          __UpperCAmelCase     :			Union[str, Any]  							=      find_backend('''    if not (is_torch_available() and is_transformers_available()):'''      )
          self.assertEqual(snake_case							,			'''torch_and_transformers'''      )

          # double_backend_with_underscore = find_backend(
          #    "    if not (is_sentencepiece_available() and is_tensorflow_text_available()):"
          # )
          # self.assertEqual(double_backend_with_underscore, "sentencepiece_and_tensorflow_text")

          __UpperCAmelCase     :			List[str]  							=      find_backend(
              '''    if not (is_torch_available() and is_transformers_available() and is_onnx_available()):'''      )
          self.assertEqual(snake_case							,			'''torch_and_transformers_and_onnx'''      )

     def 			lowerCamelCase__			(    self					:		Optional[int]      )						->							int:
          __UpperCAmelCase     :			Tuple  							=      read_init()
          # We don't assert on the exact list of keys to allow for smooth grow of backend-specific objects
          self.assertIn('''torch'''							,			snake_case      )
          self.assertIn('''torch_and_transformers'''							,			snake_case      )
          self.assertIn('''flax_and_transformers'''							,			snake_case      )
          self.assertIn('''torch_and_transformers_and_onnx'''							,			snake_case      )

          # Likewise, we can't assert on the exact content of a key
          self.assertIn('''UNet2DModel'''							,			objects['''torch''']      )
          self.assertIn('''FlaxUNet2DConditionModel'''							,			objects['''flax''']      )
          self.assertIn('''StableDiffusionPipeline'''							,			objects['''torch_and_transformers''']      )
          self.assertIn('''FlaxStableDiffusionPipeline'''							,			objects['''flax_and_transformers''']      )
          self.assertIn('''LMSDiscreteScheduler'''							,			objects['''torch_and_scipy''']      )
          self.assertIn('''OnnxStableDiffusionPipeline'''							,			objects['''torch_and_transformers_and_onnx''']      )

     def 			lowerCamelCase__			(    self					:		Optional[int]      )						->							List[Any]:
          __UpperCAmelCase     :			str  							=      create_dummy_object('''CONSTANT'''							,			'''\'torch\''''      )
          self.assertEqual(snake_case							,			'''\nCONSTANT = None\n'''      )

          __UpperCAmelCase     :			Union[str, Any]  							=      create_dummy_object('''function'''							,			'''\'torch\''''      )
          self.assertEqual(
              snake_case							,			'''\ndef function(*args, **kwargs):\n    requires_backends(function, \'torch\')\n'''      )

          __UpperCAmelCase     :			Optional[int]  							=      '''
class FakeClass(metaclass=DummyObject):
    _backends = \'torch\'

    def __init__(self, *args, **kwargs):
        requires_backends(self, \'torch\')

    @classmethod
    def from_config(cls, *args, **kwargs):
        requires_backends(cls, \'torch\')

    @classmethod
    def from_pretrained(cls, *args, **kwargs):
        requires_backends(cls, \'torch\')
'''
          __UpperCAmelCase     :			Optional[Any]  							=      create_dummy_object('''FakeClass'''							,			'''\'torch\''''      )
          self.assertEqual(snake_case							,			snake_case      )






     def 			lowerCamelCase__			(    self					:		int      )						->							List[Any]:
          __UpperCAmelCase     :			List[str]  							=      '''# This file is autogenerated by the command `make fix-copies`, do not edit.
from ..utils import DummyObject, requires_backends


CONSTANT = None


def function(*args, **kwargs):
    requires_backends(function, ["torch"])


class FakeClass(metaclass=DummyObject):
    _backends = ["torch"]

    def __init__(self, *args, **kwargs):
        requires_backends(self, ["torch"])

    @classmethod
    def from_config(cls, *args, **kwargs):
        requires_backends(cls, ["torch"])

    @classmethod
    def from_pretrained(cls, *args, **kwargs):
        requires_backends(cls, ["torch"])
'''
          __UpperCAmelCase     :			Optional[int]  							=      create_dummy_files({'''torch''': ['''CONSTANT''', '''function''', '''FakeClass''']}      )
          self.assertEqual(dummy_files['''torch''']							,			snake_case      )