def 	__lowerCamelCase							(UpperCAmelCase__     :							int  ):
					if upper_limit < 0:
										raise ValueError("Limit for the Catalan sequence must be ≥ 0"  )

					SCREAMING_SNAKE_CASE    			=       [0] * (upper_limit + 1)

					# Base case: C(0) = C(1) = 1
					SCREAMING_SNAKE_CASE    			=       1
					if upper_limit > 0:
										SCREAMING_SNAKE_CASE    			=       1

					# Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
					for i in range(2      , upper_limit + 1  ):
										for j in range(UpperCAmelCase__  ):
															catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]

					return catalan_list


if __name__ == "__main__":
							print('''\n********* Catalan Numbers Using Dynamic Programming ************\n''')
							print('''\n*** Enter -1 at any time to quit ***''')
							print('''\nEnter the upper limit (≥ 0) for the Catalan number sequence: ''', end='''''')
							try:
														while True:
																					_lowerCamelCase					:   str							=		int(input().strip())
																					if N < 0:
																												print('''\n********* Goodbye!! ************''')
																												break
																					else:
																												print(f"""The Catalan numbers from 0 through {N} are:""")
																												print(catalan_numbers(N))
																												print('''Try another upper limit for the sequence: ''', end='''''')
							except (NameError, ValueError):
														print('''\n********* Invalid input, goodbye! ************\n''')

							import doctest

							doctest.testmod()





import torch

from diffusers import KDPMaDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest


class 						lowercase    (     a     ):
							lowercase__						:       Tuple								=							(KDPMaDiscreteScheduler,)
							lowercase__						:       Optional[int]								=							10




							def 	__snake_case(						self   :					Optional[Any]	,							**_UpperCamelCase   :					List[Any]      )					->				Tuple:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE    			=       {
												    "num_train_timesteps": 1_100,
												    "beta_start": 0.0_0_0_1,
												    "beta_end": 0.0_2,
												    "beta_schedule": "linear",
												}

												config.update(**_UpperCamelCase      )
												return config




							def 	__snake_case(						self   :					int      )					->				List[Any]:



												'''simple docstring'''

												for timesteps in [10, 50, 100, 1_000]:
																	self.check_over_configs(num_train_timesteps=_UpperCamelCase      )




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



												'''simple docstring'''

												for beta_start, beta_end in zip([0.0_0_0_0_1, 0.0_0_0_1, 0.0_0_1]	,							[0.0_0_0_2, 0.0_0_2, 0.0_2]      ):
																	self.check_over_configs(beta_start=_UpperCamelCase	,							beta_end=_UpperCamelCase      )




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



												'''simple docstring'''

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




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



												'''simple docstring'''

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




							def 	__snake_case(						self   :					Optional[int]      )					->				Any:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE    			=       self.scheduler_classes[0]
												SCREAMING_SNAKE_CASE    			=       self.get_scheduler_config(prediction_type="v_prediction"      )
												SCREAMING_SNAKE_CASE    			=       scheduler_class(**_UpperCamelCase      )

												scheduler.set_timesteps(self.num_inference_steps      )

												SCREAMING_SNAKE_CASE    			=       self.dummy_model()
												SCREAMING_SNAKE_CASE    			=       self.dummy_sample_deter * scheduler.init_noise_sigma
												SCREAMING_SNAKE_CASE    			=       sample.to(_UpperCamelCase      )

												for i, t in enumerate(scheduler.timesteps      ):
																	SCREAMING_SNAKE_CASE    			=       scheduler.scale_model_input(_UpperCamelCase	,							_UpperCamelCase      )

																	SCREAMING_SNAKE_CASE    			=       model(_UpperCamelCase	,							_UpperCamelCase      )

																	SCREAMING_SNAKE_CASE    			=       scheduler.step(_UpperCamelCase	,							_UpperCamelCase	,							_UpperCamelCase      )
																	SCREAMING_SNAKE_CASE    			=       output.prev_sample

												SCREAMING_SNAKE_CASE    			=       torch.sum(torch.abs(_UpperCamelCase      )      )
												SCREAMING_SNAKE_CASE    			=       torch.mean(torch.abs(_UpperCamelCase      )      )

												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() - 0.0_0_0_2      ) < 1e-3




							def 	__snake_case(						self   :					Dict      )					->				int:



												'''simple docstring'''

												if torch_device == "mps":
																	return
												SCREAMING_SNAKE_CASE    			=       self.scheduler_classes[0]
												SCREAMING_SNAKE_CASE    			=       self.get_scheduler_config()
												SCREAMING_SNAKE_CASE    			=       scheduler_class(**_UpperCamelCase      )

												scheduler.set_timesteps(self.num_inference_steps      )

												SCREAMING_SNAKE_CASE    			=       self.dummy_model()
												SCREAMING_SNAKE_CASE    			=       self.dummy_sample_deter * scheduler.init_noise_sigma
												SCREAMING_SNAKE_CASE    			=       sample.to(_UpperCamelCase      )

												for i, t in enumerate(scheduler.timesteps      ):
																	SCREAMING_SNAKE_CASE    			=       scheduler.scale_model_input(_UpperCamelCase	,							_UpperCamelCase      )

																	SCREAMING_SNAKE_CASE    			=       model(_UpperCamelCase	,							_UpperCamelCase      )

																	SCREAMING_SNAKE_CASE    			=       scheduler.step(_UpperCamelCase	,							_UpperCamelCase	,							_UpperCamelCase      )
																	SCREAMING_SNAKE_CASE    			=       output.prev_sample

												SCREAMING_SNAKE_CASE    			=       torch.sum(torch.abs(_UpperCamelCase      )      )
												SCREAMING_SNAKE_CASE    			=       torch.mean(torch.abs(_UpperCamelCase      )      )

												if torch_device in ["cpu", "mps"]:
																	assert abs(result_sum.item() - 2_0.4_1_2_5      ) < 1e-2
																	assert abs(result_mean.item() - 0.0_2_6_6      ) < 1e-3
												else:
																	# CUDA
																	assert abs(result_sum.item() - 2_0.4_1_2_5      ) < 1e-2
																	assert abs(result_mean.item() - 0.0_2_6_6      ) < 1e-3





							def 	__snake_case(						self   :					Tuple      )					->				str:



												'''simple docstring'''

												if torch_device == "mps":
																	return
												SCREAMING_SNAKE_CASE    			=       self.scheduler_classes[0]
												SCREAMING_SNAKE_CASE    			=       self.get_scheduler_config()
												SCREAMING_SNAKE_CASE    			=       scheduler_class(**_UpperCamelCase      )

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

												SCREAMING_SNAKE_CASE    			=       self.dummy_model()
												SCREAMING_SNAKE_CASE    			=       self.dummy_sample_deter.to(_UpperCamelCase      ) * scheduler.init_noise_sigma

												for t in scheduler.timesteps:
																	SCREAMING_SNAKE_CASE    			=       scheduler.scale_model_input(_UpperCamelCase	,							_UpperCamelCase      )

																	SCREAMING_SNAKE_CASE    			=       model(_UpperCamelCase	,							_UpperCamelCase      )

																	SCREAMING_SNAKE_CASE    			=       scheduler.step(_UpperCamelCase	,							_UpperCamelCase	,							_UpperCamelCase      )
																	SCREAMING_SNAKE_CASE    			=       output.prev_sample

												SCREAMING_SNAKE_CASE    			=       torch.sum(torch.abs(_UpperCamelCase      )      )
												SCREAMING_SNAKE_CASE    			=       torch.mean(torch.abs(_UpperCamelCase      )      )

												if str(_UpperCamelCase      ).startswith("cpu"      ):
																	# The following sum varies between 148 and 156 on mps. Why?
																	assert abs(result_sum.item() - 2_0.4_1_2_5      ) < 1e-2
																	assert abs(result_mean.item() - 0.0_2_6_6      ) < 1e-3
												else:
																	# CUDA
																	assert abs(result_sum.item() - 2_0.4_1_2_5      ) < 1e-2
																	assert abs(result_mean.item() - 0.0_2_6_6      ) < 1e-3




