


'''simple docstring'''






from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt


def       _snake_case     (  A )		->					bool:
							lowerCAmelCase__      =			int(number**0.5 )
							return number == sq * sq


def       _snake_case     (  A				,					A				,					A				,					A				,					A				,					A )		->					tuple[int, int]:
							lowerCAmelCase__      =			x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
							lowerCAmelCase__      =			x_den * y_den * z_den
							lowerCAmelCase__      =			gcd(A				,					A )
							top //= hcf
							bottom //= hcf
							return top, bottom


def       _snake_case     (  A = 35 )		->					int:
							lowerCAmelCase__      =			set()
							lowerCAmelCase__      =			42
							lowerCAmelCase__      =			Fraction(0 )
							lowerCAmelCase__      =			42

							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
																																			lowerCAmelCase__      =			x_num * y_den + x_den * y_num
																																			lowerCAmelCase__      =			x_den * y_den
																																			lowerCAmelCase__      =			gcd(A				,					A )
																																			z_num //= hcf
																																			z_den //= hcf
																																			if 0 < z_num < z_den <= order:
																																										lowerCAmelCase__      =			add_three(
																																										    A				,					A				,					A				,					A				,					A				,					A )
																																										unique_s.add(A )

																																			# n=2
																																			lowerCAmelCase__      =			(
																																			    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
																																			)
																																			lowerCAmelCase__      =			x_den * x_den * y_den * y_den
																																			if is_sq(A ) and is_sq(A ):
																																										lowerCAmelCase__      =			int(sqrt(A ) )
																																										lowerCAmelCase__      =			int(sqrt(A ) )
																																										lowerCAmelCase__      =			gcd(A				,					A )
																																										z_num //= hcf
																																										z_den //= hcf
																																										if 0 < z_num < z_den <= order:
																																																	lowerCAmelCase__      =			add_three(
																																																	    A				,					A				,					A				,					A				,					A				,					A )
																																																	unique_s.add(A )

                    # n=-1
																																			lowerCAmelCase__      =			x_num * y_num
																																			lowerCAmelCase__      =			x_den * y_num + x_num * y_den
																																			lowerCAmelCase__      =			gcd(A				,					A )
																																			z_num //= hcf
																																			z_den //= hcf
																																			if 0 < z_num < z_den <= order:
																																										lowerCAmelCase__      =			add_three(
																																										    A				,					A				,					A				,					A				,					A				,					A )
																																										unique_s.add(A )

																																			# n=2
																																			lowerCAmelCase__      =			x_num * x_num * y_num * y_num
																																			lowerCAmelCase__      =			(
																																			    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																																			)
																																			if is_sq(A ) and is_sq(A ):
																																										lowerCAmelCase__      =			int(sqrt(A ) )
																																										lowerCAmelCase__      =			int(sqrt(A ) )
																																										lowerCAmelCase__      =			gcd(A				,					A )
																																										z_num //= hcf
																																										z_den //= hcf
																																										if 0 < z_num < z_den <= order:
																																																	lowerCAmelCase__      =			add_three(
																																																	    A				,					A				,					A				,					A				,					A				,					A )
																																																	unique_s.add(A )

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

							return total.denominator + total.numerator


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



'''simple docstring'''






import jax.numpy as jnp

from ...utils import logging
from ..ta.modeling_flax_ta import FlaxTaEncoderModel, FlaxTaForConditionalGeneration, FlaxTaModel
from .configuration_mta import MTaConfig


__UpperCAmelCase					       =							logging.get_logger(__name__)

__UpperCAmelCase					       =							'''T5Config'''


def       _snake_case     (  A				,					A				,					A )		->					jnp.ndarray:
							lowerCAmelCase__      =			jnp.zeros_like(A )
							lowerCAmelCase__      =			shifted_input_ids.at[:, 1:].set(input_ids[:, :-1] )
							lowerCAmelCase__      =			shifted_input_ids.at[:, 0].set(A )

							lowerCAmelCase__      =			jnp.where(shifted_input_ids == -100				,					A				,					A )
							return shifted_input_ids




class 	a__       (							a__						):





							'''simple docstring'''






							lowercase__    :     int					=   "mt5"
							lowercase__    :     Dict					=   MTaConfig




class 	a__       (							a__						):





							'''simple docstring'''






							lowercase__    :     int					=   "mt5"
							lowercase__    :     Any					=   MTaConfig




class 	a__       (							a__						):





							'''simple docstring'''






							lowercase__    :     Union[str, Any]					=   "mt5"
							lowercase__    :     Tuple					=   MTaConfig