




'''simple docstring'''





from __future__ import annotations


def   UpperCamelCase_(			snake_case							: int  ):

							'''simple docstring'''






							snake_case_			      =   {1}
							snake_case_			      =   [1]
							for _ in range(2							,       depth + 1  ):
														snake_case_			      =   [*previous_coefficients, 0]
														snake_case_			      =   [0, *previous_coefficients]
														snake_case_			      =   []
														for x, y in zip(snake_case							,       snake_case  ):
																					coefficients.add(x + y  )
																					previous_coefficients.append(x + y  )
							return coefficients


def   UpperCamelCase_(			snake_case							: set[int]  ):

							'''simple docstring'''






							snake_case_			      =   set()
							for number in unique_coefficients:
														snake_case_			      =   2
														snake_case_			      =   number
														while divisor**2 <= copy_number:
																					snake_case_			      =   0
																					while copy_number % divisor == 0:
																												copy_number //= divisor
																												multiplicity += 1
																					if multiplicity >= 2:
																												non_squarefrees.add(snake_case  )
																												break
																					divisor += 1

							return unique_coefficients.difference(snake_case  )


def   UpperCamelCase_(			snake_case							: int = 5_1  ):

							'''simple docstring'''






							snake_case_			      =   get_pascal_triangle_unique_coefficients(snake_case  )
							snake_case_			      =   get_squarefrees(snake_case  )
							return sum(snake_case  )


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










'''simple docstring'''





import tempfile

import torch

from diffusers import (
    DEISMultistepScheduler,
    DPMSolverMultistepScheduler,
    DPMSolverSinglestepScheduler,
    UniPCMultistepScheduler,
)

from .test_schedulers import SchedulerCommonTest




class 				_snake_case	(			lowercase_							):
			lowerCAmelCase_  :   Optional[int]		 =					(DPMSolverMultistepScheduler,)
			lowerCAmelCase_  :   int		 =					(("num_inference_steps", 25),)




			def      lowerCAmelCase__       (      self       ,							**a__							)       ->       Optional[int]:

										'''simple docstring'''




										snake_case_			      =   {
										    "num_train_timesteps": 1_000,
										    "beta_start": 0.0_0_0_1,
										    "beta_end": 0.0_2,
										    "beta_schedule": "linear",
										    "solver_order": 2,
										    "prediction_type": "epsilon",
										    "thresholding": False,
										    "sample_max_value": 1.0,
										    "algorithm_type": "dpmsolver++",
										    "solver_type": "midpoint",
										    "lower_order_final": False,
										    "lambda_min_clipped": -float("inf"							),
										    "variance_type": None,
										}

										config.update(**a__							)
										return config




			def      lowerCAmelCase__       (      self       ,							a__=0       ,							**a__							)       ->       Dict:

										'''simple docstring'''




										snake_case_			      =   dict(self.forward_default_kwargs							)
										snake_case_			      =   kwargs.pop("num_inference_steps"       ,							a__							)
										snake_case_			      =   self.dummy_sample
										snake_case_			      =   0.1 * sample
										snake_case_			      =   [residual + 0.2, residual + 0.1_5, residual + 0.1_0]

										for scheduler_class in self.scheduler_classes:
																	snake_case_			      =   self.get_scheduler_config(**a__							)
																	snake_case_			      =   scheduler_class(**a__							)
																	scheduler.set_timesteps(a__							)
																	# copy over dummy past residuals
																	snake_case_			      =   dummy_past_residuals[: scheduler.config.solver_order]

																	with tempfile.TemporaryDirectory() as tmpdirname:
																								scheduler.save_config(a__							)
																								snake_case_			      =   scheduler_class.from_pretrained(a__							)
																								new_scheduler.set_timesteps(a__							)
																								# copy over dummy past residuals
																								snake_case_			      =   dummy_past_residuals[: new_scheduler.config.solver_order]

																	snake_case_      ,   snake_case_			      =   sample, sample
																	for t in range(a__       ,							time_step + scheduler.config.solver_order + 1							):
																								snake_case_			      =   scheduler.step(a__       ,							a__       ,							a__       ,							**a__							).prev_sample
																								snake_case_			      =   new_scheduler.step(a__       ,							a__       ,							a__       ,							**a__							).prev_sample

																								assert torch.sum(torch.abs(output - new_output							)							) < 1e-5, "Scheduler outputs are not identical"




			def      lowerCAmelCase__       (      self							)       ->       Dict:

										'''simple docstring'''




										pass




			def      lowerCAmelCase__       (      self       ,							a__=0       ,							**a__							)       ->       Optional[int]:

										'''simple docstring'''




										snake_case_			      =   dict(self.forward_default_kwargs							)
										snake_case_			      =   kwargs.pop("num_inference_steps"       ,							a__							)
										snake_case_			      =   self.dummy_sample
										snake_case_			      =   0.1 * sample
										snake_case_			      =   [residual + 0.2, residual + 0.1_5, residual + 0.1_0]

										for scheduler_class in self.scheduler_classes:
																	snake_case_			      =   self.get_scheduler_config()
																	snake_case_			      =   scheduler_class(**a__							)
																	scheduler.set_timesteps(a__							)

																	# copy over dummy past residuals (must be after setting timesteps)
																	snake_case_			      =   dummy_past_residuals[: scheduler.config.solver_order]

																	with tempfile.TemporaryDirectory() as tmpdirname:
																								scheduler.save_config(a__							)
																								snake_case_			      =   scheduler_class.from_pretrained(a__							)
																								# copy over dummy past residuals
																								new_scheduler.set_timesteps(a__							)

																								# copy over dummy past residual (must be after setting timesteps)
																								snake_case_			      =   dummy_past_residuals[: new_scheduler.config.solver_order]

																	snake_case_			      =   scheduler.step(a__       ,							a__       ,							a__       ,							**a__							).prev_sample
																	snake_case_			      =   new_scheduler.step(a__       ,							a__       ,							a__       ,							**a__							).prev_sample

																	assert torch.sum(torch.abs(output - new_output							)							) < 1e-5, "Scheduler outputs are not identical"




			def      lowerCAmelCase__       (      self       ,							a__=None       ,							**a__							)       ->       Tuple:

										'''simple docstring'''




										if scheduler is None:
																	snake_case_			      =   self.scheduler_classes[0]
																	snake_case_			      =   self.get_scheduler_config(**a__							)
																	snake_case_			      =   scheduler_class(**a__							)

										snake_case_			      =   10
										snake_case_			      =   self.dummy_model()
										snake_case_			      =   self.dummy_sample_deter
										scheduler.set_timesteps(a__							)

										for i, t in enumerate(scheduler.timesteps							):
																	snake_case_			      =   model(a__       ,							a__							)
																	snake_case_			      =   scheduler.step(a__       ,							a__       ,							a__							).prev_sample

										return sample




			def      lowerCAmelCase__       (      self							)       ->       Dict:

										'''simple docstring'''




										snake_case_			      =   dict(self.forward_default_kwargs							)

										snake_case_			      =   kwargs.pop("num_inference_steps"       ,							a__							)

										for scheduler_class in self.scheduler_classes:
																	snake_case_			      =   self.get_scheduler_config()
																	snake_case_			      =   scheduler_class(**a__							)

																	snake_case_			      =   self.dummy_sample
																	snake_case_			      =   0.1 * sample

																	if num_inference_steps is not None and hasattr(a__       ,							"set_timesteps"							):
																								scheduler.set_timesteps(a__							)
																	elif num_inference_steps is not None and not hasattr(a__       ,							"set_timesteps"							):
																								snake_case_			      =   num_inference_steps

																	# copy over dummy past residuals (must be done after set_timesteps)
																	snake_case_			      =   [residual + 0.2, residual + 0.1_5, residual + 0.1_0]
																	snake_case_			      =   dummy_past_residuals[: scheduler.config.solver_order]

																	snake_case_			      =   scheduler.timesteps[5]
																	snake_case_			      =   scheduler.timesteps[6]

																	snake_case_			      =   scheduler.step(a__       ,							a__       ,							a__       ,							**a__							).prev_sample
																	snake_case_			      =   scheduler.step(a__       ,							a__       ,							a__       ,							**a__							).prev_sample

																	self.assertEqual(output_a.shape       ,							sample.shape							)
																	self.assertEqual(output_a.shape       ,							output_a.shape							)




			def      lowerCAmelCase__       (      self							)       ->       List[str]:

										'''simple docstring'''




										for timesteps in [25, 50, 100, 999, 1_000]:
																	self.check_over_configs(num_train_timesteps=a__							)




			def      lowerCAmelCase__       (      self							)       ->       str:

										'''simple docstring'''




										self.check_over_configs(thresholding=a__							)
										for order in [1, 2, 3]:
																	for solver_type in ["midpoint", "heun"]:
																								for threshold in [0.5, 1.0, 2.0]:
																															for prediction_type in ["epsilon", "sample"]:
																																						self.check_over_configs(
																																						    thresholding=a__       ,							prediction_type=a__       ,							sample_max_value=a__       ,							algorithm_type="dpmsolver++"       ,							solver_order=a__       ,							solver_type=a__       ,							)




			def      lowerCAmelCase__       (      self							)       ->       int:

										'''simple docstring'''




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




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

										'''simple docstring'''




										for algorithm_type in ["dpmsolver", "dpmsolver++", "sde-dpmsolver", "sde-dpmsolver++"]:
																	for solver_type in ["midpoint", "heun"]:
																								for order in [1, 2, 3]:
																															for prediction_type in ["epsilon", "sample"]:
																																						if algorithm_type in ["sde-dpmsolver", "sde-dpmsolver++"]:
																																													if order == 3:
																																																				continue
																																						else:
																																													self.check_over_configs(
																																													    solver_order=a__       ,							solver_type=a__       ,							prediction_type=a__       ,							algorithm_type=a__       ,							)
																																						snake_case_			      =   self.full_loop(
																																						    solver_order=a__       ,							solver_type=a__       ,							prediction_type=a__       ,							algorithm_type=a__       ,							)
																																						assert not torch.isnan(a__							).any(), "Samples have nan numbers"




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

										'''simple docstring'''




										self.check_over_configs(lower_order_final=a__							)
										self.check_over_configs(lower_order_final=a__							)




			def      lowerCAmelCase__       (      self							)       ->       Optional[Any]:

										'''simple docstring'''




										self.check_over_configs(lambda_min_clipped=-float("inf"							)							)
										self.check_over_configs(lambda_min_clipped=-5.1							)




			def      lowerCAmelCase__       (      self							)       ->       Any:

										'''simple docstring'''




										self.check_over_configs(variance_type=a__							)
										self.check_over_configs(variance_type="learned_range"							)




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

										'''simple docstring'''




										for num_inference_steps in [1, 2, 3, 5, 10, 50, 100, 999, 1_000]:
																	self.check_over_forward(num_inference_steps=a__       ,							time_step=0							)




			def      lowerCAmelCase__       (      self							)       ->       List[str]:

										'''simple docstring'''




										snake_case_			      =   self.full_loop()
										snake_case_			      =   torch.mean(torch.abs(a__							)							)

										assert abs(result_mean.item() - 0.3_3_0_1							) < 1e-3




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

										'''simple docstring'''




										snake_case_			      =   self.full_loop(thresholding=a__       ,							dynamic_thresholding_ratio=0.8_7       ,							sample_max_value=0.5							)
										snake_case_			      =   torch.mean(torch.abs(a__							)							)

										assert abs(result_mean.item() - 1.1_3_6_4							) < 1e-3




			def      lowerCAmelCase__       (      self							)       ->       List[str]:

										'''simple docstring'''




										snake_case_			      =   self.full_loop(prediction_type="v_prediction"							)
										snake_case_			      =   torch.mean(torch.abs(a__							)							)

										assert abs(result_mean.item() - 0.2_2_5_1							) < 1e-3




			def      lowerCAmelCase__       (      self							)       ->       List[str]:

										'''simple docstring'''




										snake_case_			      =   self.full_loop(prediction_type="v_prediction"       ,							use_karras_sigmas=a__							)
										snake_case_			      =   torch.mean(torch.abs(a__							)							)

										assert abs(result_mean.item() - 0.2_0_9_6							) < 1e-3




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

										'''simple docstring'''




										snake_case_			      =   DPMSolverMultistepScheduler(**self.get_scheduler_config()							)
										snake_case_			      =   self.full_loop(scheduler=a__							)
										snake_case_			      =   torch.mean(torch.abs(a__							)							)

										assert abs(result_mean.item() - 0.3_3_0_1							) < 1e-3

										snake_case_			      =   DPMSolverSinglestepScheduler.from_config(scheduler.config							)
										snake_case_			      =   UniPCMultistepScheduler.from_config(scheduler.config							)
										snake_case_			      =   DEISMultistepScheduler.from_config(scheduler.config							)
										snake_case_			      =   DPMSolverMultistepScheduler.from_config(scheduler.config							)

										snake_case_			      =   self.full_loop(scheduler=a__							)
										snake_case_			      =   torch.mean(torch.abs(a__							)							)

										assert abs(result_mean.item() - 0.3_3_0_1							) < 1e-3




			def      lowerCAmelCase__       (      self							)       ->       int:

										'''simple docstring'''




										snake_case_			      =   self.scheduler_classes[0]
										snake_case_			      =   self.get_scheduler_config(thresholding=a__       ,							dynamic_thresholding_ratio=0							)
										snake_case_			      =   scheduler_class(**a__							)

										snake_case_			      =   10
										snake_case_			      =   self.dummy_model()
										snake_case_			      =   self.dummy_sample_deter.half()
										scheduler.set_timesteps(a__							)

										for i, t in enumerate(scheduler.timesteps							):
																	snake_case_			      =   model(a__       ,							a__							)
																	snake_case_			      =   scheduler.step(a__       ,							a__       ,							a__							).prev_sample

										assert sample.dtype == torch.floataa




			def      lowerCAmelCase__       (      self       ,							**a__							)       ->       Dict:

										'''simple docstring'''




										for scheduler_class in self.scheduler_classes:
																	snake_case_			      =   self.get_scheduler_config(**a__							)
																	snake_case_			      =   scheduler_class(**a__							)

																	scheduler.set_timesteps(scheduler.config.num_train_timesteps							)
																	assert len(scheduler.timesteps.unique()							) == scheduler.num_inference_steps




