
from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt


def 						UpperCAmelCase			(	a_						)		->	bool:







				"""simple docstring"""



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


def 						UpperCAmelCase			(	a_		,   a_		,   a_		,   a_		,   a_		,   a_						)		->	tuple[int, int]:







				"""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 						UpperCAmelCase			(	a_ = 3_5						)		->	int:







				"""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() = }''')








from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


UpperCAmelCase__				   =		{
    "configuration_groupvit": [
        "GROUPVIT_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "GroupViTConfig",
        "GroupViTOnnxConfig",
        "GroupViTTextConfig",
        "GroupViTVisionConfig",
    ],
}

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     UpperCAmelCase__				   =		[
         "GROUPVIT_PRETRAINED_MODEL_ARCHIVE_LIST",
         "GroupViTModel",
         "GroupViTPreTrainedModel",
         "GroupViTTextModel",
         "GroupViTVisionModel",
     ]

try:
     if not is_tf_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     UpperCAmelCase__				   =		[
         "TF_GROUPVIT_PRETRAINED_MODEL_ARCHIVE_LIST",
         "TFGroupViTModel",
         "TFGroupViTPreTrainedModel",
         "TFGroupViTTextModel",
         "TFGroupViTVisionModel",
     ]

if TYPE_CHECKING:
     from .configuration_groupvit import (
         GROUPVIT_PRETRAINED_CONFIG_ARCHIVE_MAP,
         GroupViTConfig,
         GroupViTOnnxConfig,
         GroupViTTextConfig,
         GroupViTVisionConfig,
     )

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_groupvit import (
              GROUPVIT_PRETRAINED_MODEL_ARCHIVE_LIST,
              GroupViTModel,
              GroupViTPreTrainedModel,
              GroupViTTextModel,
              GroupViTVisionModel,
          )

     try:
          if not is_tf_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_tf_groupvit import (
              TF_GROUPVIT_PRETRAINED_MODEL_ARCHIVE_LIST,
              TFGroupViTModel,
              TFGroupViTPreTrainedModel,
              TFGroupViTTextModel,
              TFGroupViTVisionModel,
          )

else:
     import sys

     UpperCAmelCase__				   =		_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)


