




"""simple docstring"""






from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt





def 							UpperCAmelCase		(		snake_case			:					int    ):
					_lowerCAmelCase:int									=  int(number**0.5    )
					return number == sq * sq





def 							UpperCAmelCase		(		snake_case			:					int      ,       snake_case			:					int      ,       snake_case			:					int      ,       snake_case			:					int      ,       snake_case			:					int      ,       snake_case			:					int    ):
					_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(snake_case      ,       snake_case    )
					top //= hcf
					bottom //= hcf
					return top, bottom





def 							UpperCAmelCase		(		snake_case			:					int = 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:Any									=  x_num * y_den + x_den * y_num
																									_lowerCAmelCase:str									=  x_den * y_den
																									_lowerCAmelCase:List[Any]									=  gcd(snake_case      ,       snake_case    )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														_lowerCAmelCase:str									=  add_three(
																														    snake_case      ,       snake_case      ,       snake_case      ,       snake_case      ,       snake_case      ,       snake_case    )
																														unique_s.add(snake_case    )

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

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

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

					for num, den in unique_s:
										total += Fraction(snake_case      ,       snake_case    )

					return total.denominator + total.numerator


if __name__ == "__main__":
				print(F"{solution() = }")












"""simple docstring"""






import torch

from diffusers import KDPMaDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest




class   a__			(       UpperCamelCase_  ):
						snake_case__             = (KDPMaDiscreteScheduler,)
						snake_case__             = 1_0





						def       __UpperCamelCase     (							self      :	Dict     ,**a__      :	str)						->       int:




											"""simple docstring"""







											_lowerCAmelCase:Optional[int]									=  {
											    '''num_train_timesteps''': 1100,
											    '''beta_start''': 0.0001,
											    '''beta_end''': 0.02,
											    '''beta_schedule''': '''linear''',
											}

											config.update(**a__)
											return config





						def       __UpperCamelCase     (							self      :	Optional[int])						->       Optional[int]:




											"""simple docstring"""







											for timesteps in [10, 50, 100, 1000]:
																self.check_over_configs(num_train_timesteps=a__)





						def       __UpperCamelCase     (							self      :	Union[str, Any])						->       Optional[int]:




											"""simple docstring"""







											for beta_start, beta_end in zip([0.00001, 0.0001, 0.001]     ,[0.0002, 0.002, 0.02]):
																self.check_over_configs(beta_start=a__     ,beta_end=a__)





						def       __UpperCamelCase     (							self      :	Optional[Any])						->       Union[str, Any]:




											"""simple docstring"""







											for schedule in ["linear", "scaled_linear"]:
																self.check_over_configs(beta_schedule=a__)





						def       __UpperCamelCase     (							self      :	str)						->       str:




											"""simple docstring"""







											for prediction_type in ["epsilon", "v_prediction"]:
																self.check_over_configs(prediction_type=a__)





						def       __UpperCamelCase     (							self      :	Tuple)						->       Tuple:




											"""simple docstring"""







											_lowerCAmelCase:Union[str, Any]									=  self.scheduler_classes[0]
											_lowerCAmelCase:Union[str, Any]									=  self.get_scheduler_config(prediction_type='''v_prediction''')
											_lowerCAmelCase:Tuple									=  scheduler_class(**a__)

											scheduler.set_timesteps(self.num_inference_steps)

											_lowerCAmelCase:Optional[Any]									=  self.dummy_model()
											_lowerCAmelCase:List[Any]									=  self.dummy_sample_deter * scheduler.init_noise_sigma
											_lowerCAmelCase:Optional[Any]									=  sample.to(a__)

											for i, t in enumerate(scheduler.timesteps):
																_lowerCAmelCase:Tuple									=  scheduler.scale_model_input(a__     ,a__)

																_lowerCAmelCase:Any									=  model(a__     ,a__)

																_lowerCAmelCase:Union[str, Any]									=  scheduler.step(a__     ,a__     ,a__)
																_lowerCAmelCase:Optional[int]									=  output.prev_sample

											_lowerCAmelCase:str									=  torch.sum(torch.abs(a__))
											_lowerCAmelCase:Union[str, Any]									=  torch.mean(torch.abs(a__))

											if torch_device in ["cpu", "mps"]:
																assert abs(result_sum.item() - 4.6_934E-07) < 1E-2
																assert abs(result_mean.item() - 6.1_112E-10) < 1E-3
											else:
																# CUDA
																assert abs(result_sum.item() - 4.693_428_650_170_972E-07) < 1E-2
																assert abs(result_mean.item() - 0.0002) < 1E-3





						def       __UpperCamelCase     (							self      :	Tuple)						->       Dict:




											"""simple docstring"""







											if torch_device == "mps":
																return
											_lowerCAmelCase:Tuple									=  self.scheduler_classes[0]
											_lowerCAmelCase:List[str]									=  self.get_scheduler_config()
											_lowerCAmelCase:Union[str, Any]									=  scheduler_class(**a__)

											scheduler.set_timesteps(self.num_inference_steps)

											_lowerCAmelCase:Any									=  self.dummy_model()
											_lowerCAmelCase:str									=  self.dummy_sample_deter * scheduler.init_noise_sigma
											_lowerCAmelCase:List[str]									=  sample.to(a__)

											for i, t in enumerate(scheduler.timesteps):
																_lowerCAmelCase:Tuple									=  scheduler.scale_model_input(a__     ,a__)

																_lowerCAmelCase:List[str]									=  model(a__     ,a__)

																_lowerCAmelCase:int									=  scheduler.step(a__     ,a__     ,a__)
																_lowerCAmelCase:List[Any]									=  output.prev_sample

											_lowerCAmelCase:Tuple									=  torch.sum(torch.abs(a__))
											_lowerCAmelCase:Dict									=  torch.mean(torch.abs(a__))

											if torch_device in ["cpu", "mps"]:
																assert abs(result_sum.item() - 20.4125) < 1E-2
																assert abs(result_mean.item() - 0.0266) < 1E-3
											else:
																# CUDA
																assert abs(result_sum.item() - 20.4125) < 1E-2
																assert abs(result_mean.item() - 0.0266) < 1E-3







						def       __UpperCamelCase     (							self      :	Union[str, Any])						->       List[Any]:




											"""simple docstring"""







											if torch_device == "mps":
																return
											_lowerCAmelCase:str									=  self.scheduler_classes[0]
											_lowerCAmelCase:Optional[Any]									=  self.get_scheduler_config()
											_lowerCAmelCase:Any									=  scheduler_class(**a__)

											scheduler.set_timesteps(self.num_inference_steps     ,device=a__)

											_lowerCAmelCase:Optional[int]									=  self.dummy_model()
											_lowerCAmelCase:Optional[Any]									=  self.dummy_sample_deter.to(a__) * scheduler.init_noise_sigma

											for t in scheduler.timesteps:
																_lowerCAmelCase:Union[str, Any]									=  scheduler.scale_model_input(a__     ,a__)

																_lowerCAmelCase:Tuple									=  model(a__     ,a__)

																_lowerCAmelCase:str									=  scheduler.step(a__     ,a__     ,a__)
																_lowerCAmelCase:Dict									=  output.prev_sample

											_lowerCAmelCase:Any									=  torch.sum(torch.abs(a__))
											_lowerCAmelCase:str									=  torch.mean(torch.abs(a__))

											if str(a__).startswith('''cpu'''):
																# The following sum varies between 148 and 156 on mps. Why?
																assert abs(result_sum.item() - 20.4125) < 1E-2
																assert abs(result_mean.item() - 0.0266) < 1E-3
											else:
																# CUDA
																assert abs(result_sum.item() - 20.4125) < 1E-2
																assert abs(result_mean.item() - 0.0266) < 1E-3






