


"""simple docstring"""







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


a__				:							List[Any]						=     {
    '''configuration_bigbird_pegasus''': [
        '''BIGBIRD_PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''BigBirdPegasusConfig''',
        '''BigBirdPegasusOnnxConfig''',
    ],
}

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		a__				:							Dict						=     [
		    '''BIGBIRD_PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST''',
		    '''BigBirdPegasusForCausalLM''',
		    '''BigBirdPegasusForConditionalGeneration''',
		    '''BigBirdPegasusForQuestionAnswering''',
		    '''BigBirdPegasusForSequenceClassification''',
		    '''BigBirdPegasusModel''',
		    '''BigBirdPegasusPreTrainedModel''',
		]


if TYPE_CHECKING:
		from .configuration_bigbird_pegasus import (
		    BIGBIRD_PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP,
		    BigBirdPegasusConfig,
		    BigBirdPegasusOnnxConfig,
		)

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_bigbird_pegasus import (
				    BIGBIRD_PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST,
				    BigBirdPegasusForCausalLM,
				    BigBirdPegasusForConditionalGeneration,
				    BigBirdPegasusForQuestionAnswering,
				    BigBirdPegasusForSequenceClassification,
				    BigBirdPegasusModel,
				    BigBirdPegasusPreTrainedModel,
				)


else:
		import sys

		a__				:							Optional[Any]						=     _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)




'''simple docstring'''



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int   ):
					__a			:       int					    =  int(number**0.5   )
					return number == sq * sq






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int   ):
					__a			:       int					    =  x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
					__a			:       int					    =  x_den * y_den * z_den
					__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
					top //= hcf
					bottom //= hcf
					return top, bottom






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int = 35   ):
					__a			:       set					    =  set()
					__a			:       int
					__a			:       Fraction					    =  Fraction(0   )
					__a			:       tuple[int, int]

					for x_num in range(1						,      order + 1   ):
										for x_den in range(x_num + 1						,      order + 1   ):
															for y_num in range(1						,      order + 1   ):
																				for y_den in range(y_num + 1						,      order + 1   ):
																									# n=1
																									__a			:       Union[str, Any]					    =  x_num * y_den + x_den * y_num
																									__a			:       Optional[Any]					    =  x_den * y_den
																									__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														__a			:       Any					    =  add_three(
																														    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														unique_s.add(_SCREAMING_SNAKE_CASE   )

																									# n=2
																									__a			:       Optional[int]					    =  (
																									    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
																									)
																									__a			:       Union[str, Any]					    =  x_den * x_den * y_den * y_den
																									if is_sq(_SCREAMING_SNAKE_CASE   ) and is_sq(_SCREAMING_SNAKE_CASE   ):
																														__a			:       List[Any]					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       Any					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       Optional[int]					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			__a			:       List[Any]					    =  add_three(
																																			    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																																			unique_s.add(_SCREAMING_SNAKE_CASE   )

                    # n=-1
																									__a			:       int					    =  x_num * y_num
																									__a			:       Optional[Any]					    =  x_den * y_num + x_num * y_den
																									__a			:       Tuple					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														__a			:       Any					    =  add_three(
																														    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														unique_s.add(_SCREAMING_SNAKE_CASE   )

																									# n=2
																									__a			:       List[Any]					    =  x_num * x_num * y_num * y_num
																									__a			:       List[Any]					    =  (
																									    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																									)
																									if is_sq(_SCREAMING_SNAKE_CASE   ) and is_sq(_SCREAMING_SNAKE_CASE   ):
																														__a			:       Optional[Any]					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       Union[str, Any]					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			__a			:       List[str]					    =  add_three(
																																			    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																																			unique_s.add(_SCREAMING_SNAKE_CASE   )

					for num, den in unique_s:
										total += Fraction(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )

					return total.denominator + total.numerator


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



