from __future__ import annotations

import math





def 	__lowerCamelCase							(UpperCAmelCase__     :							int  ):

     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5      , int(math.sqrt(UpperCAmelCase__  ) + 1  )      , 6  ):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True


_lowerCamelCase					:   Tuple							=		[num for num in range(3, 10_00_01, 2) if not is_prime(num)]





def 	__lowerCamelCase							(UpperCAmelCase__     :							int  ):
     if not isinstance(UpperCAmelCase__      , UpperCAmelCase__  ):
          raise ValueError("n must be an integer"  )
     if n <= 0:
          raise ValueError("n must be >= 0"  )

     SCREAMING_SNAKE_CASE    			=       []
     for num in range(len(UpperCAmelCase__  )  ):
          SCREAMING_SNAKE_CASE    			=       0
          while 2 * i * i <= odd_composites[num]:
               SCREAMING_SNAKE_CASE    			=       odd_composites[num] - 2 * i * i
               if is_prime(UpperCAmelCase__  ):
                    break
               i += 1
          else:
               list_nums.append(odd_composites[num]  )
               if len(UpperCAmelCase__  ) == n:
                    return list_nums

     return []





def 	__lowerCamelCase							():
     return compute_nums(1  )[0]


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





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




