
from __future__ import annotations

from fractions import Fraction







def     A__   (  lowerCamelCase       ,      lowerCamelCase  )					->		bool:
				return (
				    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
				)







def     A__   (  lowerCamelCase  )					->		list[str]:
				UpperCamelCase_:							int		=  []
				UpperCamelCase_:							Dict		=  11
				UpperCamelCase_:							Union[str, Any]		=  int("""1""" + """0""" * digit_len  )
				for num in range(lowerCamelCase       ,      lowerCamelCase  ):
								while den <= 99:
												if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
																if is_digit_cancelling(lowerCamelCase       ,      lowerCamelCase  ):
																				solutions.append(F'''{num}/{den}'''  )
												den += 1
								num += 1
								UpperCamelCase_:							Optional[int]		=  10
				return solutions







def     A__   (  lowerCamelCase = 2  )					->		int:
				UpperCamelCase_:							Optional[int]		=  1.0
				for fraction in fraction_list(lowerCamelCase  ):
								UpperCamelCase_:							List[str]		=  Fraction(lowerCamelCase  )
								result *= frac.denominator / frac.numerator
				return int(lowerCamelCase  )


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








from ...configuration_utils import PretrainedConfig
from ...utils import logging


lowerCamelCase_  :	Optional[int] 				=					logging.get_logger(__name__)

lowerCamelCase_  :	Optional[int] 				=					{"""ctrl""": """https://huggingface.co/ctrl/resolve/main/config.json"""}

class     _UpperCamelCase			(   _A					):






			'''simple docstring'''

			__UpperCamelCase :  int    =	"""ctrl"""
			__UpperCamelCase :  Dict    =	["""past_key_values"""]
			__UpperCamelCase :  List[str]    =	{
			    """max_position_embeddings""": """n_positions""",
			    """hidden_size""": """n_embd""",
			    """num_attention_heads""": """n_head""",
			    """num_hidden_layers""": """n_layer""",
			}

			def __init__(    self	:    Dict  ,		snake_case_	:    Any=24_6534  ,		snake_case_	:    Dict=256  ,		snake_case_	:    str=1280  ,		snake_case_	:    Optional[int]=8192  ,		snake_case_	:    Union[str, Any]=48  ,		snake_case_	:    Any=16  ,		snake_case_	:    Optional[int]=0.1  ,		snake_case_	:    Any=0.1  ,		snake_case_	:    Any=1e-6  ,		snake_case_	:    Optional[Any]=0.02  ,		snake_case_	:    Optional[int]=True  ,		**snake_case_	:    Union[str, Any]  ,		):
							UpperCamelCase_:							Union[str, Any]		=  vocab_size
							UpperCamelCase_:							Union[str, Any]		=  n_positions
							UpperCamelCase_:							Optional[int]		=  n_embd
							UpperCamelCase_:							int		=  n_layer
							UpperCamelCase_:							str		=  n_head
							UpperCamelCase_:							Optional[int]		=  dff
							UpperCamelCase_:							Optional[Any]		=  resid_pdrop
							UpperCamelCase_:							Union[str, Any]		=  embd_pdrop
							UpperCamelCase_:							List[str]		=  layer_norm_epsilon
							UpperCamelCase_:							Optional[Any]		=  initializer_range

							UpperCamelCase_:							Optional[Any]		=  use_cache

							super().__init__(**snake_case_ )






