




"""simple docstring"""






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


lowercase__			=		logging.get_logger(__name__)

lowercase__			=		{"""openai-gpt""": """https://huggingface.co/openai-gpt/resolve/main/config.json"""}






class lowerCAmelCase__      (	lowercase		):






			'''simple docstring'''



			lowerCamelCase__ =     """openai-gpt"""
			lowerCamelCase__ =     {
			    """max_position_embeddings""": """n_positions""",
			    """hidden_size""": """n_embd""",
			    """num_attention_heads""": """n_head""",
			    """num_hidden_layers""": """n_layer""",
			}
			def __init__(    self    , lowercase=40478    , lowercase=512    , lowercase=768    , lowercase=12    , lowercase=12    , lowercase="gelu"    , lowercase=0.1    , lowercase=0.1    , lowercase=0.1    , lowercase=1E-5    , lowercase=0.02    , lowercase="cls_index"    , lowercase=True    , lowercase=None    , lowercase=True    , lowercase=0.1    , **lowercase    , ):
							_lowerCamelCase	:     Tuple       =       vocab_size
							_lowerCamelCase	:     List[str]       =       n_positions
							_lowerCamelCase	:     Tuple       =       n_embd
							_lowerCamelCase	:     Optional[int]       =       n_layer
							_lowerCamelCase	:     List[Any]       =       n_head
							_lowerCamelCase	:     Dict       =       afn
							_lowerCamelCase	:     Union[str, Any]       =       resid_pdrop
							_lowerCamelCase	:     Dict       =       embd_pdrop
							_lowerCamelCase	:     List[Any]       =       attn_pdrop
							_lowerCamelCase	:     Any       =       layer_norm_epsilon
							_lowerCamelCase	:     List[Any]       =       initializer_range
							_lowerCamelCase	:     List[Any]       =       summary_type
							_lowerCamelCase	:     List[str]       =       summary_use_proj
							_lowerCamelCase	:     Tuple       =       summary_activation
							_lowerCamelCase	:     int       =       summary_first_dropout
							_lowerCamelCase	:     str       =       summary_proj_to_labels
							super().__init__(**lowercase    )





"""simple docstring"""






from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt







def 	_snake_case     (							lowercase__						):
				_lowerCamelCase	:     int       =       int(number**0.5						)
				return number == sq * sq







def 	_snake_case     (							lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__						):
				_lowerCamelCase	:     int       =       x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
				_lowerCamelCase	:     int       =       x_den * y_den * z_den
				_lowerCamelCase	:     int       =       gcd(lowercase__				,       lowercase__						)
				top //= hcf
				bottom //= hcf
				return top, bottom







def 	_snake_case     (							lowercase__ = 35						):
				_lowerCamelCase	:     set       =       set()
				_lowerCamelCase	:     int
				_lowerCamelCase	:     Fraction       =       Fraction(0						)
				_lowerCamelCase	:     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
																				_lowerCamelCase	:     int       =       x_num * y_den + x_den * y_num
																				_lowerCamelCase	:     List[Any]       =       x_den * y_den
																				_lowerCamelCase	:     int       =       gcd(lowercase__				,       lowercase__						)
																				z_num //= hcf
																				z_den //= hcf
																				if 0 < z_num < z_den <= order:
																								_lowerCamelCase	:     Optional[Any]       =       add_three(
																								    lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__						)
																								unique_s.add(lowercase__						)

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

                    # n=-1
																				_lowerCamelCase	:     List[str]       =       x_num * y_num
																				_lowerCamelCase	:     int       =       x_den * y_num + x_num * y_den
																				_lowerCamelCase	:     Dict       =       gcd(lowercase__				,       lowercase__						)
																				z_num //= hcf
																				z_den //= hcf
																				if 0 < z_num < z_den <= order:
																								_lowerCamelCase	:     List[str]       =       add_three(
																								    lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__						)
																								unique_s.add(lowercase__						)

																				# n=2
																				_lowerCamelCase	:     Tuple       =       x_num * x_num * y_num * y_num
																				_lowerCamelCase	:     List[str]       =       (
																				    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																				)
																				if is_sq(lowercase__						) and is_sq(lowercase__						):
																								_lowerCamelCase	:     Optional[int]       =       int(sqrt(lowercase__						)						)
																								_lowerCamelCase	:     Optional[int]       =       int(sqrt(lowercase__						)						)
																								_lowerCamelCase	:     Dict       =       gcd(lowercase__				,       lowercase__						)
																								z_num //= hcf
																								z_den //= hcf
																								if 0 < z_num < z_den <= order:
																												_lowerCamelCase	:     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() = }")