


"""simple docstring"""







from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt
def _A						(						lowercase		):







    """simple docstring"""
    a					=int(number**0.5		)
    return number == sq * sq
def _A						(						lowercase	,   lowercase	,   lowercase	,   lowercase	,   lowercase	,   lowercase		):







    """simple docstring"""
    a					=x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
    a					=x_den * y_den * z_den
    a					=gcd(A__	,   A__		)
    top //= hcf
    bottom //= hcf
    return top, bottom
def _A						(						lowercase = 35		):







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

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

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

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

from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ..auto.configuration_auto import CONFIG_MAPPING


lowerCamelCase_       :       int      						=  logging.get_logger(__name__)






class 				__A    (	_SCREAMING_SNAKE_CASE      ):






 """simple docstring"""




 __lowerCAmelCase			 =  "upernet"


 def __init__(		self			,   __A=None			,   __A=512			,   __A=0.02			,   __A=[1, 2, 3, 6]			,   __A=True			,   __A=0.4			,   __A=384			,   __A=256			,   __A=1			,   __A=False			,   __A=255			,   **__A			,   ) ->					Tuple:
     super().__init__(**__A						)

     if backbone_config is None:
         logger.info('''`backbone_config` is `None`. Initializing the config with the default `ResNet` backbone.'''						)
         a					=CONFIG_MAPPING['''resnet'''](out_features=['''stage1''', '''stage2''', '''stage3''', '''stage4''']						)
     elif isinstance(__A			,   __A						):
         a					=backbone_config.get('''model_type'''						)
         a					=CONFIG_MAPPING[backbone_model_type]
         a					=config_class.from_dict(__A						)

     a					=backbone_config
     a					=hidden_size
     a					=initializer_range
     a					=pool_scales
     a					=use_auxiliary_head
     a					=auxiliary_loss_weight
     a					=auxiliary_in_channels
     a					=auxiliary_channels
     a					=auxiliary_num_convs
     a					=auxiliary_concat_input
     a					=loss_ignore_index





 def 				SCREAMING_SNAKE_CASE							(		self						) ->					Dict:
     a					=copy.deepcopy(self.__dict__						)
     a					=self.backbone_config.to_dict()
     a					=self.__class__.model_type
     return output