

"""simple docstring"""



from __future__ import annotations





def 			_snake_case  (     UpperCAmelCase_	:       Optional[Any]      ):
     A__				      =	{1}
     A__				      =	[1]
     for _ in range(2       , depth + 1      ):
          A__				      =	[*previous_coefficients, 0]
          A__				      =	[0, *previous_coefficients]
          A__				      =	[]
          for x, y in zip(UpperCAmelCase_       , UpperCAmelCase_      ):
               coefficients.add(x + y      )
               previous_coefficients.append(x + y      )
     return coefficients





def 			_snake_case  (     UpperCAmelCase_	:       Union[str, Any]      ):
     A__				      =	set()
     for number in unique_coefficients:
          A__				      =	2
          A__				      =	number
          while divisor**2 <= copy_number:
               A__				      =	0
               while copy_number % divisor == 0:
                    copy_number //= divisor
                    multiplicity += 1
               if multiplicity >= 2:
                    non_squarefrees.add(UpperCAmelCase_      )
                    break
               divisor += 1

     return unique_coefficients.difference(UpperCAmelCase_      )





def 			_snake_case  (     UpperCAmelCase_	:       Optional[int] = 51      ):
     A__				      =	get_pascal_triangle_unique_coefficients(UpperCAmelCase_      )
     A__				      =	get_squarefrees(UpperCAmelCase_      )
     return sum(UpperCAmelCase_      )


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












from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCamelCase__						=		{
    'configuration_prophetnet': ['PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP', 'ProphetNetConfig'],
    'tokenization_prophetnet': ['ProphetNetTokenizer'],
}

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCamelCase__						=		[
							    'PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST',
							    'ProphetNetDecoder',
							    'ProphetNetEncoder',
							    'ProphetNetForCausalLM',
							    'ProphetNetForConditionalGeneration',
							    'ProphetNetModel',
							    'ProphetNetPreTrainedModel',
							]


if TYPE_CHECKING:
							from .configuration_prophetnet import PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP, ProphetNetConfig
							from .tokenization_prophetnet import ProphetNetTokenizer

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_prophetnet import (
														    PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST,
														    ProphetNetDecoder,
														    ProphetNetEncoder,
														    ProphetNetForCausalLM,
														    ProphetNetForConditionalGeneration,
														    ProphetNetModel,
														    ProphetNetPreTrainedModel,
														)

else:
							import sys

							UpperCamelCase__						=		_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
