






from __future__ import annotations





def 						A_					(						lowercase_			)				->set[int]:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		{1}
 SCREAMING_SNAKE_CASE				    =		[1]
 for _ in range(2	,  depth + 1			):
  SCREAMING_SNAKE_CASE				    =		[*previous_coefficients, 0]
  SCREAMING_SNAKE_CASE				    =		[0, *previous_coefficients]
  SCREAMING_SNAKE_CASE				    =		[]
  for x, y in zip(lowercase_	,  lowercase_			):
   coefficients.add(x + y			)
   previous_coefficients.append(x + y			)
 return coefficients





def 						A_					(						lowercase_			)				->set[int]:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		set()
 for number in unique_coefficients:
  SCREAMING_SNAKE_CASE				    =		2
  SCREAMING_SNAKE_CASE				    =		number
  while divisor**2 <= copy_number:
   SCREAMING_SNAKE_CASE				    =		0
   while copy_number % divisor == 0:
    copy_number //= divisor
    multiplicity += 1
   if multiplicity >= 2:
    non_squarefrees.add(lowercase_			)
    break
   divisor += 1

 return unique_coefficients.difference(lowercase_			)





def 						A_					(						lowercase_ = 5_1			)				->int:







 """simple docstring"""

 SCREAMING_SNAKE_CASE				    =		get_pascal_triangle_unique_coefficients(lowercase_			)
 SCREAMING_SNAKE_CASE				    =		get_squarefrees(lowercase_			)
 return sum(lowercase_			)


if __name__ == "__main__":
      print(f'{solution() = }')












import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ..auto.configuration_auto import AutoConfig


__UpperCAmelCase      =				logging.get_logger(__name__)
class 	a_(		lowercase__	):



     """simple docstring"""



     __snake_case		:				Union[str, Any]  					='''speech-encoder-decoder'''
     __snake_case		:				List[Any]  					=True





     def __init__(		self					:	Any  ,  **lowerCAmelCase__					:	List[Any])							->	Tuple:

      """simple docstring"""
      super().__init__(**lowerCAmelCase__)
      if "encoder" not in kwargs or "decoder" not in kwargs:
       raise ValueError(
           f'''A configuraton of type {self.model_type} cannot be instantiated because not both `encoder` and'''
           f''' `decoder` sub-configurations are passed, but only {kwargs}''')

      SCREAMING_SNAKE_CASE				    =		kwargs.pop('encoder')
      SCREAMING_SNAKE_CASE				    =		encoder_config.pop('model_type')
      SCREAMING_SNAKE_CASE				    =		kwargs.pop('decoder')
      SCREAMING_SNAKE_CASE				    =		decoder_config.pop('model_type')

      SCREAMING_SNAKE_CASE				    =		AutoConfig.for_model(lowerCAmelCase__  ,  **lowerCAmelCase__)
      SCREAMING_SNAKE_CASE				    =		AutoConfig.for_model(lowerCAmelCase__  ,  **lowerCAmelCase__)
      SCREAMING_SNAKE_CASE				    =		True





     @classmethod
     def     __UpperCamelCase						(		cls					:	str  ,  lowerCAmelCase__					:	PretrainedConfig  ,  lowerCAmelCase__					:	PretrainedConfig  ,  **lowerCAmelCase__					:	List[str])							->	PretrainedConfig:

      """simple docstring"""
      logger.info('Setting `config.is_decoder=True` and `config.add_cross_attention=True` for decoder_config')
      SCREAMING_SNAKE_CASE				    =		True
      SCREAMING_SNAKE_CASE				    =		True

      return cls(encoder=encoder_config.to_dict()  ,  decoder=decoder_config.to_dict()  ,  **lowerCAmelCase__)





     def     __UpperCamelCase						(		self					:	str)							->	Union[str, Any]:

      """simple docstring"""
      SCREAMING_SNAKE_CASE				    =		copy.deepcopy(self.__dict__)
      SCREAMING_SNAKE_CASE				    =		self.encoder.to_dict()
      SCREAMING_SNAKE_CASE				    =		self.decoder.to_dict()
      SCREAMING_SNAKE_CASE				    =		self.__class__.model_type
      return output




