"""simple docstring"""




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







def 							_UpperCAmelCase		(       lowerCamelCase__			,  lowerCamelCase__			,  lowerCamelCase__     ):





		"""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
		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			,  lowerCamelCase__			,  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			,  lowerCamelCase__			,  0     )

		lowerCAmelCase__        =   state_late + state_absent + state_ontime

		lowerCAmelCase__        =   prizestrings
		return prizestrings







def 							_UpperCAmelCase		(       lowerCamelCase__ = 30     ):





		"""simple docstring"""




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


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





"""simple docstring"""




import io
import json
import unittest

from parameterized import parameterized

from transformers import FSMTForConditionalGeneration, FSMTTokenizer
from transformers.testing_utils import get_tests_dir, require_torch, slow, torch_device
from utils import calculate_bleu


__lowerCAmelCase    :							Union[str, Any]													=						get_tests_dir() + "/test_data/fsmt/fsmt_val_data.json"
with io.open(filename, "r", encoding="utf-8") as f:
			__lowerCAmelCase    :							Optional[int]													=						json.load(f)

@require_torch
class       a_      (     unittest.TestCase			):




					def 						_SCREAMING_SNAKE_CASE						(	self						:     Optional[Any]  ,						snake_case__						:     Dict     ):
							return FSMTTokenizer.from_pretrained(snake_case__     )




					def 						_SCREAMING_SNAKE_CASE						(	self						:     List[str]  ,						snake_case__						:     Any     ):
							lowerCAmelCase__        =   FSMTForConditionalGeneration.from_pretrained(snake_case__     ).to(snake_case__     )
							if torch_device == "cuda":
									model.half()
							return model




					@parameterized.expand(
					    [
					        ["""en-ru""", 26.0],
					        ["""ru-en""", 22.0],
					        ["""en-de""", 22.0],
					        ["""de-en""", 29.0],
					    ]     )
					@slow
					def 						_SCREAMING_SNAKE_CASE						(	self						:     Dict  ,						snake_case__						:     Any  ,						snake_case__						:     int     ):
							# note: this test is not testing the best performance since it only evals a small batch
							# but it should be enough to detect a regression in the output quality
							lowerCAmelCase__        =   F"""facebook/wmt19-{pair}"""
							lowerCAmelCase__        =   self.get_tokenizer(snake_case__     )
							lowerCAmelCase__        =   self.get_model(snake_case__     )

							lowerCAmelCase__        =   bleu_data[pair]["""src"""]
							lowerCAmelCase__        =   bleu_data[pair]["""tgt"""]

							lowerCAmelCase__        =   tokenizer(snake_case__  ,						return_tensors="""pt"""  ,						truncation=snake_case__  ,						padding="""longest"""     ).to(snake_case__     )
							lowerCAmelCase__        =   model.generate(
							    input_ids=batch.input_ids  ,						num_beams=8  ,						)
							lowerCAmelCase__        =   tokenizer.batch_decode(
							    snake_case__  ,						skip_special_tokens=snake_case__  ,						clean_up_tokenization_spaces=snake_case__     )
							lowerCAmelCase__        =   calculate_bleu(snake_case__  ,						snake_case__     )
							print(snake_case__     )
							self.assertGreaterEqual(scores["""bleu"""]  ,						snake_case__     )




