





'''simple docstring'''

from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt







def    a__							(							lowercase   :	int )						->						bool:





     """simple docstring"""

     _UpperCamelCase							       =			int(number**0.5 )
     return number == sq * sq







def    a__							(							lowercase   :	int,   lowercase   :	int,   lowercase   :	int,   lowercase   :	int,   lowercase   :	int,   lowercase   :	int )						->						tuple[int, int]:





     """simple docstring"""

     _UpperCamelCase							       =			x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
     _UpperCamelCase							       =			x_den * y_den * z_den
     _UpperCamelCase							       =			gcd(lowercase,   lowercase )
     top //= hcf
     bottom //= hcf
     return top, bottom







def    a__							(							lowercase   :	int = 35 )						->						int:





     """simple docstring"""

     _UpperCamelCase							       =			set()
     _UpperCamelCase							       =			42
     _UpperCamelCase							       =			Fraction(0 )
     _UpperCamelCase							       =			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
                         _UpperCamelCase							       =			x_num * y_den + x_den * y_num
                         _UpperCamelCase							       =			x_den * y_den
                         _UpperCamelCase							       =			gcd(lowercase,   lowercase )
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              _UpperCamelCase							       =			add_three(
                                  lowercase,   lowercase,   lowercase,   lowercase,   lowercase,   lowercase )
                              unique_s.add(lowercase )

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

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

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

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

     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


lowercase__		:     int			=							logging.get_logger(__name__)

lowercase__		:     Any			=							'T5Config'







def    a__							(							lowercase   :	jnp.array,   lowercase   :	int,   lowercase   :	int )						->						jnp.ndarray:





     """simple docstring"""

     _UpperCamelCase							       =			jnp.zeros_like(lowercase )
     _UpperCamelCase							       =			shifted_input_ids.at[:, 1:].set(input_ids[:, :-1] )
     _UpperCamelCase							       =			shifted_input_ids.at[:, 0].set(lowercase )

     _UpperCamelCase							       =			jnp.where(shifted_input_ids == -100,   lowercase,   lowercase )
     return shifted_input_ids
class 							__lowerCAmelCase	(       __magic_name__					):






       """simple docstring"""
       _snake_case      :	Optional[Any]									=       'mt5'
       _snake_case      :	Union[str, Any]									=       MTaConfig

class 							__lowerCAmelCase	(       __magic_name__					):






       """simple docstring"""
       _snake_case      :	Tuple									=       'mt5'
       _snake_case      :	int									=       MTaConfig

class 							__lowerCAmelCase	(       __magic_name__					):






       """simple docstring"""
       _snake_case      :	Optional[int]									=       'mt5'
       _snake_case      :	Optional[Any]									=       MTaConfig



