





from __future__ import annotations


def 							__snake_case							(    lowerCAmelCase_ ,							lowerCAmelCase_ ,							lowerCAmelCase_ ,							lowerCAmelCase_	)				->						list:
    SCREAMING_SNAKE_CASE__											=			[]
    SCREAMING_SNAKE_CASE__				,		SCREAMING_SNAKE_CASE__											=			input_list[low:mid], input_list[mid : high + 1]
    while left and right:
        result.append((left if left[0] <= right[0] else right).pop(0	)	)
    SCREAMING_SNAKE_CASE__											=			result + left + right
    return input_list


def 							__snake_case							(    lowerCAmelCase_	)				->						list:
    if len(lowerCAmelCase_	) <= 1:
        return input_list
    SCREAMING_SNAKE_CASE__											=			list(lowerCAmelCase_	)

    # iteration for two-way merging
    SCREAMING_SNAKE_CASE__											=			2
    while p <= len(lowerCAmelCase_	):
        # getting low, high and middle value for merge-sort of single list
        for i in range(0 ,							len(lowerCAmelCase_	) ,							lowerCAmelCase_	):
            SCREAMING_SNAKE_CASE__											=			i
            SCREAMING_SNAKE_CASE__											=			i + p - 1
            SCREAMING_SNAKE_CASE__											=			(low + high + 1) // 2
            SCREAMING_SNAKE_CASE__											=			merge(lowerCAmelCase_ ,							lowerCAmelCase_ ,							lowerCAmelCase_ ,							lowerCAmelCase_	)
        # final merge of last two parts
        if p * 2 >= len(lowerCAmelCase_	):
            SCREAMING_SNAKE_CASE__											=			i
            SCREAMING_SNAKE_CASE__											=			merge(lowerCAmelCase_ ,							0 ,							lowerCAmelCase_ ,							len(lowerCAmelCase_	) - 1	)
            break
        p *= 2

    return input_list


if __name__ == "__main__":
  _A					:				List[str]				=			input("""Enter numbers separated by a comma:\n""").strip()
  if user_input == "":
    _A					:				Dict				=			[]
  else:
    _A					:				Any				=			[int(item.strip()) for item in user_input.split(""",""")]
  print(iter_merge_sort(unsorted))



import torch

from diffusers import KDPMaDiscreteScheduler
from diffusers.utils import torch_device

from .test_schedulers import SchedulerCommonTest






class 						__magic_name__					(							snake_case				):
     UpperCamelCase_	:Dict										=      (KDPMaDiscreteScheduler,)
     UpperCamelCase_	:str										=      1_0






     def 	UpperCAmelCase_				(				self		,						**_lowercase	)->     str:
         UpperCamelCase_			  =						{
             "num_train_timesteps": 1_100,
             "beta_start": 0.0_001,
             "beta_end": 0.02,
             "beta_schedule": "linear",
         }

         config.update(**_lowercase	)
         return config






     def 	UpperCAmelCase_				(				self	)->     Union[str, Any]:
         for timesteps in [10, 50, 100, 1_000]:
             self.check_over_configs(num_train_timesteps=_lowercase	)






     def 	UpperCAmelCase_				(				self	)->     int:
         for beta_start, beta_end in zip([0.00_001, 0.0_001, 0.001]		,						[0.0_002, 0.002, 0.02]	):
             self.check_over_configs(beta_start=_lowercase		,						beta_end=_lowercase	)






     def 	UpperCAmelCase_				(				self	)->     str:
         for schedule in ["linear", "scaled_linear"]:
             self.check_over_configs(beta_schedule=_lowercase	)






     def 	UpperCAmelCase_				(				self	)->     Any:
         for prediction_type in ["epsilon", "v_prediction"]:
             self.check_over_configs(prediction_type=_lowercase	)






     def 	UpperCAmelCase_				(				self	)->     Optional[int]:
         UpperCamelCase_			  =						self.scheduler_classes[0]
         UpperCamelCase_			  =						self.get_scheduler_config(prediction_type="v_prediction"	)
         UpperCamelCase_			  =						scheduler_class(**_lowercase	)

         scheduler.set_timesteps(self.num_inference_steps	)

         UpperCamelCase_			  =						self.dummy_model()
         UpperCamelCase_			  =						self.dummy_sample_deter * scheduler.init_noise_sigma
         UpperCamelCase_			  =						sample.to(_lowercase	)

         for i, t in enumerate(scheduler.timesteps	):
             UpperCamelCase_			  =						scheduler.scale_model_input(_lowercase		,						_lowercase	)

             UpperCamelCase_			  =						model(_lowercase		,						_lowercase	)

             UpperCamelCase_			  =						scheduler.step(_lowercase		,						_lowercase		,						_lowercase	)
             UpperCamelCase_			  =						output.prev_sample

         UpperCamelCase_			  =						torch.sum(torch.abs(_lowercase	)	)
         UpperCamelCase_			  =						torch.mean(torch.abs(_lowercase	)	)

         if torch_device in ["cpu", "mps"]:
             assert abs(result_sum.item() - 4.6_9_3_4e-0_7	) < 1e-2
             assert abs(result_mean.item() - 6.1_1_1_2e-1_0	) < 1e-3
         else:
             # CUDA
             assert abs(result_sum.item() - 4.6_9_3_4_2_8_6_5_0_1_7_0_9_7_2e-0_7	) < 1e-2
             assert abs(result_mean.item() - 0.0_002	) < 1e-3






     def 	UpperCAmelCase_				(				self	)->     Dict:
         if torch_device == "mps":
             return
         UpperCamelCase_			  =						self.scheduler_classes[0]
         UpperCamelCase_			  =						self.get_scheduler_config()
         UpperCamelCase_			  =						scheduler_class(**_lowercase	)

         scheduler.set_timesteps(self.num_inference_steps	)

         UpperCamelCase_			  =						self.dummy_model()
         UpperCamelCase_			  =						self.dummy_sample_deter * scheduler.init_noise_sigma
         UpperCamelCase_			  =						sample.to(_lowercase	)

         for i, t in enumerate(scheduler.timesteps	):
             UpperCamelCase_			  =						scheduler.scale_model_input(_lowercase		,						_lowercase	)

             UpperCamelCase_			  =						model(_lowercase		,						_lowercase	)

             UpperCamelCase_			  =						scheduler.step(_lowercase		,						_lowercase		,						_lowercase	)
             UpperCamelCase_			  =						output.prev_sample

         UpperCamelCase_			  =						torch.sum(torch.abs(_lowercase	)	)
         UpperCamelCase_			  =						torch.mean(torch.abs(_lowercase	)	)

         if torch_device in ["cpu", "mps"]:
             assert abs(result_sum.item() - 20.4_125	) < 1e-2
             assert abs(result_mean.item() - 0.0_266	) < 1e-3
         else:
             # CUDA
             assert abs(result_sum.item() - 20.4_125	) < 1e-2
             assert abs(result_mean.item() - 0.0_266	) < 1e-3






     def 	UpperCAmelCase_				(				self	)->     Optional[int]:
         if torch_device == "mps":
             return
         UpperCamelCase_			  =						self.scheduler_classes[0]
         UpperCamelCase_			  =						self.get_scheduler_config()
         UpperCamelCase_			  =						scheduler_class(**_lowercase	)

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

         UpperCamelCase_			  =						self.dummy_model()
         UpperCamelCase_			  =						self.dummy_sample_deter.to(_lowercase	) * scheduler.init_noise_sigma

         for t in scheduler.timesteps:
             UpperCamelCase_			  =						scheduler.scale_model_input(_lowercase		,						_lowercase	)

             UpperCamelCase_			  =						model(_lowercase		,						_lowercase	)

             UpperCamelCase_			  =						scheduler.step(_lowercase		,						_lowercase		,						_lowercase	)
             UpperCamelCase_			  =						output.prev_sample

         UpperCamelCase_			  =						torch.sum(torch.abs(_lowercase	)	)
         UpperCamelCase_			  =						torch.mean(torch.abs(_lowercase	)	)

         if str(_lowercase	).startswith("cpu"	):
             # The following sum varies between 148 and 156 on mps. Why?
             assert abs(result_sum.item() - 20.4_125	) < 1e-2
             assert abs(result_mean.item() - 0.0_266	) < 1e-3
         else:
             # CUDA
             assert abs(result_sum.item() - 20.4_125	) < 1e-2
             assert abs(result_mean.item() - 0.0_266	) < 1e-3
