
import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging


_A   =			logging.get_logger(__name__)







class 					lowerCamelCase		(  A_  ):
     UpperCAmelCase__    :							Union[str, Any]									=		"encoder-decoder"
     UpperCAmelCase__    :							str									=		True





     def __init__(self				:   Dict    ,   **_A				:   List[Any]       )						->						str:
         super().__init__(**_A       )
         assert (
             "encoder" in kwargs and "decoder" in kwargs
         ), "Config has to be initialized with encoder and decoder config"
         snake_case								= kwargs.pop("encoder"       )
         snake_case								= encoder_config.pop("model_type"       )
         snake_case								= kwargs.pop("decoder"       )
         snake_case								= decoder_config.pop("model_type"       )

         from ..auto.configuration_auto import AutoConfig

         snake_case								= AutoConfig.for_model(_A    ,   **_A       )
         snake_case								= AutoConfig.for_model(_A    ,   **_A       )
         snake_case								= True





     @classmethod
     def 		UpperCAmelCase(cls				:   Dict    ,   _A				:   PretrainedConfig    ,   _A				:   PretrainedConfig    ,   **_A				:   List[str]       )						->						PretrainedConfig:
         logger.info("Set `config.is_decoder=True` and `config.add_cross_attention=True` for decoder_config"       )
         snake_case								= True
         snake_case								= True

         return cls(encoder=encoder_config.to_dict()    ,   decoder=decoder_config.to_dict()    ,   **_A       )





     def 		UpperCAmelCase(self				:   List[Any]       )						->						int:
         snake_case								= copy.deepcopy(self.__dict__       )
         snake_case								= self.encoder.to_dict()
         snake_case								= self.decoder.to_dict()
         snake_case								= self.__class__.model_type
         return output



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt



def 						lowercase_      (       A__		)							->							bool:
    """simple docstring"""

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



def 						lowercase_      (       A__			,		A__			,		A__			,		A__			,		A__			,		A__		)							->							tuple[int, int]:
    """simple docstring"""

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



def 						lowercase_      (       A__ = 35		)							->							int:
    """simple docstring"""

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

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

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

                    # n=2
                    snake_case								= x_num * x_num * y_num * y_num
                    snake_case								= (
                        x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                    )
                    if is_sq(A__		) and is_sq(A__		):
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= int(sqrt(A__		)		)
                        snake_case								= gcd(A__			,		A__		)
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            snake_case								= 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() = }")

