






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() = }')










'''simple docstring'''





from typing import List

from ...processing_utils import ProcessorMixin
from ...utils import is_torch_available


if is_torch_available():
       import torch






class     lowercase  ( UpperCAmelCase_):
      __lowercase					=	['''image_processor''', '''tokenizer''']
      __lowercase					=	'''OneFormerImageProcessor'''
      __lowercase					=	('''CLIPTokenizer''', '''CLIPTokenizerFast''')






      def __init__(self			,	a__=None			,	a__=None			,	a__ = 7_7			,	a__ = 7_7			,	**a__       )							-> str:
         if image_processor is None:
            raise ValueError('''You need to specify an `image_processor`.'''       )
         if tokenizer is None:
            raise ValueError('''You need to specify a `tokenizer`.'''       )

         SCREAMING_SNAKE_CASE__      :					Tuple							    =			max_seq_length
         SCREAMING_SNAKE_CASE__      :					Tuple							    =			task_seq_length

         super().__init__(a__			,	a__       )






      def  A__(self			,	a__=None			,	a__=7_7       )							-> str:
         if text_list is None:
            raise ValueError('''tokens cannot be None.'''       )

         SCREAMING_SNAKE_CASE__      :					int							    =			self.tokenizer(a__			,	padding='''max_length'''			,	max_length=a__			,	truncation=a__       )

         SCREAMING_SNAKE_CASE__    ,					SCREAMING_SNAKE_CASE__      :					Any							    =			tokens['''attention_mask'''], tokens['''input_ids''']

         SCREAMING_SNAKE_CASE__      :					Tuple							    =			[]
         for attn_mask, input_id in zip(a__			,	a__       ):
            SCREAMING_SNAKE_CASE__      :					List[str]							    =			torch.tensor(a__       ) * torch.tensor(a__       )
            token_inputs.append(token.unsqueeze(0       )       )

         SCREAMING_SNAKE_CASE__      :					Dict							    =			torch.cat(a__			,	dim=0       )
         return token_inputs






      def __call__(self			,	a__=None			,	a__=None			,	a__=None			,	**a__       )							-> str:

         if task_inputs is None:
            raise ValueError('''You have to specify the task_input. Found None.'''       )
         elif images is None:
            raise ValueError('''You have to specify the image. Found None.'''       )

         if not all(task in ['''semantic''', '''instance''', '''panoptic'''] for task in task_inputs       ):
            raise ValueError('''task_inputs must be semantic, instance, or panoptic.'''       )

         SCREAMING_SNAKE_CASE__      :					Dict							    =			self.image_processor(a__			,	a__			,	a__			,	**a__       )

         if isinstance(a__			,	a__       ):
            SCREAMING_SNAKE_CASE__      :					List[str]							    =			[task_inputs]

         if isinstance(a__			,	a__       ) and all(isinstance(a__			,	a__       ) for task_input in task_inputs       ):
            SCREAMING_SNAKE_CASE__      :					Any							    =			[]
            for task in task_inputs:
               SCREAMING_SNAKE_CASE__      :					Tuple							    =			f"""the task is {task}"""
               task_token_inputs.append(a__       )
            SCREAMING_SNAKE_CASE__      :					int							    =			self._preprocess_text(a__			,	max_length=self.task_seq_length       )
         else:
            raise TypeError('''Task Inputs should be a string or a list of strings.'''       )

         if hasattr(a__			,	'''text_inputs'''       ):
            SCREAMING_SNAKE_CASE__      :					Tuple							    =			encoded_inputs.text_inputs

            SCREAMING_SNAKE_CASE__      :					int							    =			[]
            for texts in texts_list:
               SCREAMING_SNAKE_CASE__      :					Any							    =			self._preprocess_text(a__			,	max_length=self.max_seq_length       )
               text_inputs.append(text_input_list.unsqueeze(0       )       )

            SCREAMING_SNAKE_CASE__      :					List[str]							    =			torch.cat(a__			,	dim=0       )

         return encoded_inputs






      def  A__(self			,	a__=None			,	a__=None			,	a__=None			,	**a__       )							-> Any:

         if task_inputs is None:
            raise ValueError('''You have to specify the task_input. Found None.'''       )
         elif images is None:
            raise ValueError('''You have to specify the image. Found None.'''       )

         if not all(task in ['''semantic''', '''instance''', '''panoptic'''] for task in task_inputs       ):
            raise ValueError('''task_inputs must be semantic, instance, or panoptic.'''       )

         SCREAMING_SNAKE_CASE__      :					List[str]							    =			self.image_processor.encode_inputs(a__			,	a__			,	a__			,	**a__       )

         if isinstance(a__			,	a__       ):
            SCREAMING_SNAKE_CASE__      :					Optional[Any]							    =			[task_inputs]

         if isinstance(a__			,	a__       ) and all(isinstance(a__			,	a__       ) for task_input in task_inputs       ):
            SCREAMING_SNAKE_CASE__      :					List[Any]							    =			[]
            for task in task_inputs:
               SCREAMING_SNAKE_CASE__      :					Union[str, Any]							    =			f"""the task is {task}"""
               task_token_inputs.append(a__       )
            SCREAMING_SNAKE_CASE__      :					Tuple							    =			self._preprocess_text(a__			,	max_length=self.task_seq_length       )
         else:
            raise TypeError('''Task Inputs should be a string or a list of strings.'''       )

         if hasattr(a__			,	'''text_inputs'''       ):
            SCREAMING_SNAKE_CASE__      :					List[Any]							    =			encoded_inputs.text_inputs

            SCREAMING_SNAKE_CASE__      :					List[Any]							    =			[]
            for texts in texts_list:
               SCREAMING_SNAKE_CASE__      :					Any							    =			self._preprocess_text(a__			,	max_length=self.max_seq_length       )
               text_inputs.append(text_input_list.unsqueeze(0       )       )

            SCREAMING_SNAKE_CASE__      :					Union[str, Any]							    =			torch.cat(a__			,	dim=0       )

         return encoded_inputs






      def  A__(self			,	*a__			,	**a__       )							-> str:
         return self.image_processor.post_process_semantic_segmentation(*a__			,	**a__       )






      def  A__(self			,	*a__			,	**a__       )							-> Optional[Any]:
         return self.image_processor.post_process_instance_segmentation(*a__			,	**a__       )






      def  A__(self			,	*a__			,	**a__       )							-> Tuple:
         return self.image_processor.post_process_panoptic_segmentation(*a__			,	**a__       )

