



import os
import sys

snake_case    :						Any  =						os.path.join(os.path.dirname(__file__), 'src')
sys.path.append(SRC_DIR)


from transformers import (
    AutoConfig,
    AutoModel,
    AutoModelForCausalLM,
    AutoModelForMaskedLM,
    AutoModelForQuestionAnswering,
    AutoModelForSequenceClassification,
    AutoTokenizer,
    add_start_docstrings,
)


snake_case    :						Union[str, Any]  =						[
    'torch',
    'numpy',
    'tokenizers',
    'filelock',
    'requests',
    'tqdm',
    'regex',
    'sentencepiece',
    'sacremoses',
    'importlib_metadata',
    'huggingface_hub',
]
@add_start_docstrings(AutoConfig.__doc__       )
def 	snake_case__       (					*__lowercase							,     **__lowercase       )		->		Optional[Any]:







      """simple docstring"""

      return AutoConfig.from_pretrained(*_snake_case							,     **_snake_case       )
@add_start_docstrings(AutoTokenizer.__doc__       )
def 	snake_case__       (					*__lowercase							,     **__lowercase       )		->		str:







      """simple docstring"""

      return AutoTokenizer.from_pretrained(*_snake_case							,     **_snake_case       )
@add_start_docstrings(AutoModel.__doc__       )
def 	snake_case__       (					*__lowercase							,     **__lowercase       )		->		List[str]:







      """simple docstring"""

      return AutoModel.from_pretrained(*_snake_case							,     **_snake_case       )
@add_start_docstrings(AutoModelForCausalLM.__doc__       )
def 	snake_case__       (					*__lowercase							,     **__lowercase       )		->		Dict:







      """simple docstring"""

      return AutoModelForCausalLM.from_pretrained(*_snake_case							,     **_snake_case       )
@add_start_docstrings(AutoModelForMaskedLM.__doc__       )
def 	snake_case__       (					*__lowercase							,     **__lowercase       )		->		Optional[Any]:







      """simple docstring"""

      return AutoModelForMaskedLM.from_pretrained(*_snake_case							,     **_snake_case       )
@add_start_docstrings(AutoModelForSequenceClassification.__doc__       )
def 	snake_case__       (					*__lowercase							,     **__lowercase       )		->		Union[str, Any]:







      """simple docstring"""

      return AutoModelForSequenceClassification.from_pretrained(*_snake_case							,     **_snake_case       )




@add_start_docstrings(AutoModelForQuestionAnswering.__doc__       )
def 	snake_case__       (					*__lowercase							,     **__lowercase       )		->		Union[str, Any]:







      """simple docstring"""

      return AutoModelForQuestionAnswering.from_pretrained(*_snake_case							,     **_snake_case       )




from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt
def 	snake_case__       (					__lowercase       )		->		bool:







						"""simple docstring"""

						A__	:							int						    = int(number**0.5       )
						return number == sq * sq
def 	snake_case__       (					__lowercase							,     __lowercase							,     __lowercase							,     __lowercase							,     __lowercase							,     __lowercase       )		->		tuple[int, int]:







						"""simple docstring"""

						A__	:							int						    = x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
						A__	:							int						    = x_den * y_den * z_den
						A__	:							int						    = gcd(__lowercase							,     __lowercase       )
						top //= hcf
						bottom //= hcf
						return top, bottom
def 	snake_case__       (					__lowercase = 3_5       )		->		int:







						"""simple docstring"""

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

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

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

																														# n=2
																														A__	:							Any						    = x_num * x_num * y_num * y_num
																														A__	:							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       ):
																																				A__	:							Optional[int]						    = int(sqrt(__lowercase       )       )
																																				A__	:							List[Any]						    = int(sqrt(__lowercase       )       )
																																				A__	:							Union[str, Any]						    = gcd(__lowercase							,     __lowercase       )
																																				z_num //= hcf
																																				z_den //= hcf
																																				if 0 < z_num < z_den <= order:
																																										A__	:							Optional[Any]						    = 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() = }""")