


"""simple docstring"""



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt







def 						__lowerCAmelCase		(		lowercase						:						int				)			->		bool:


    """simple docstring"""





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







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


    """simple docstring"""





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







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


    """simple docstring"""





    snake_case					:   set         =					set()
    snake_case					:   int
    snake_case					:   Fraction         =					Fraction(0				)
    snake_case					:   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
                    snake_case					:   Dict         =					x_num * y_den + x_den * y_num
                    snake_case					:   List[str]         =					x_den * y_den
                    snake_case					:   Optional[Any]         =					gcd(lowercase		,							lowercase				)
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        snake_case					:   Dict         =					add_three(
                            lowercase		,							lowercase		,							lowercase		,							lowercase		,							lowercase		,							lowercase				)
                        unique_s.add(lowercase				)

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

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

                    # n=2
                    snake_case					:   Union[str, Any]         =					x_num * x_num * y_num * y_num
                    snake_case					:   Optional[Any]         =					(
                        x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                    )
                    if is_sq(lowercase				) and is_sq(lowercase				):
                        snake_case					:   Optional[Any]         =					int(sqrt(lowercase				)				)
                        snake_case					:   List[Any]         =					int(sqrt(lowercase				)				)
                        snake_case					:   str         =					gcd(lowercase		,							lowercase				)
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            snake_case					:   int         =					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"""



from collections import OrderedDict
from typing import Mapping

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import logging


__snake_case         =					logging.get_logger(__name__)

__snake_case         =					{
    """facebook/xmod-base""": """https://huggingface.co/facebook/xmod-base/resolve/main/config.json""",
    """facebook/xmod-large-prenorm""": """https://huggingface.co/facebook/xmod-large-prenorm/resolve/main/config.json""",
    """facebook/xmod-base-13-125k""": """https://huggingface.co/facebook/xmod-base-13-125k/resolve/main/config.json""",
    """facebook/xmod-base-30-125k""": """https://huggingface.co/facebook/xmod-base-30-125k/resolve/main/config.json""",
    """facebook/xmod-base-30-195k""": """https://huggingface.co/facebook/xmod-base-30-195k/resolve/main/config.json""",
    """facebook/xmod-base-60-125k""": """https://huggingface.co/facebook/xmod-base-60-125k/resolve/main/config.json""",
    """facebook/xmod-base-60-265k""": """https://huggingface.co/facebook/xmod-base-60-265k/resolve/main/config.json""",
    """facebook/xmod-base-75-125k""": """https://huggingface.co/facebook/xmod-base-75-125k/resolve/main/config.json""",
    """facebook/xmod-base-75-269k""": """https://huggingface.co/facebook/xmod-base-75-269k/resolve/main/config.json""",
}







class _lowerCAmelCase       (   snake_case_			):
   __UpperCAmelCase				: Union[str, Any]													=						'''xmod'''







   def __init__(			self		,			UpperCamelCase__=3_0522		,			UpperCamelCase__=768		,			UpperCamelCase__=12		,			UpperCamelCase__=12		,			UpperCamelCase__=3072		,			UpperCamelCase__="gelu"		,			UpperCamelCase__=0.1		,			UpperCamelCase__=0.1		,			UpperCamelCase__=512		,			UpperCamelCase__=2		,			UpperCamelCase__=0.02		,			UpperCamelCase__=1e-12		,			UpperCamelCase__=1		,			UpperCamelCase__=0		,			UpperCamelCase__=2		,			UpperCamelCase__="absolute"		,			UpperCamelCase__=True		,			UpperCamelCase__=None		,			UpperCamelCase__=False		,			UpperCamelCase__=2		,			UpperCamelCase__=False		,			UpperCamelCase__=True		,			UpperCamelCase__=True		,			UpperCamelCase__=("en_XX",)		,			UpperCamelCase__=None		,			**UpperCamelCase__		,			)			->	List[str]:

       '''simple docstring'''




       super().__init__(pad_token_id=UpperCamelCase__		,			bos_token_id=UpperCamelCase__		,			eos_token_id=UpperCamelCase__		,			**UpperCamelCase__		)

       snake_case					:   Optional[int]         =					vocab_size
       snake_case					:   Optional[Any]         =					hidden_size
       snake_case					:   Union[str, Any]         =					num_hidden_layers
       snake_case					:   int         =					num_attention_heads
       snake_case					:   Dict         =					hidden_act
       snake_case					:   Union[str, Any]         =					intermediate_size
       snake_case					:   str         =					hidden_dropout_prob
       snake_case					:   List[str]         =					attention_probs_dropout_prob
       snake_case					:   Dict         =					max_position_embeddings
       snake_case					:   Union[str, Any]         =					type_vocab_size
       snake_case					:   Union[str, Any]         =					initializer_range
       snake_case					:   str         =					layer_norm_eps
       snake_case					:   Dict         =					position_embedding_type
       snake_case					:   Any         =					use_cache
       snake_case					:   str         =					classifier_dropout
       snake_case					:   Any         =					pre_norm
       snake_case					:   Union[str, Any]         =					adapter_reduction_factor
       snake_case					:   Optional[int]         =					adapter_layer_norm
       snake_case					:   int         =					adapter_reuse_layer_norm
       snake_case					:   List[Any]         =					ln_before_adapter
       snake_case					:   Tuple         =					list(UpperCamelCase__		)
       snake_case					:   Tuple         =					default_language







class _lowerCAmelCase       (   snake_case_			):







   @property
   def 				lowerCamelCase	(			self		)			->	Mapping[str, Mapping[int, str]]:

       '''simple docstring'''




       if self.task == "multiple-choice":
           snake_case					:   str         =					{0: "batch", 1: "choice", 2: "sequence"}
       else:
           snake_case					:   Tuple         =					{0: "batch", 1: "sequence"}
       return OrderedDict(
           [
               ("input_ids", dynamic_axis),
               ("attention_mask", dynamic_axis),
           ]		)





