



"""simple docstring"""






from typing import Callable, Dict, Optional, Tuple

import torch
from torch import nn
from torch.distributions import (
    AffineTransform,
    Distribution,
    Independent,
    NegativeBinomial,
    Normal,
    StudentT,
    TransformedDistribution,
)

class  __SCREAMING_SNAKE_CASE			(   lowerCAmelCase_     ):


					'''simple docstring'''





					def __init__( self							:						Dict,						lowerCamelCase							:						Distribution,						lowerCamelCase							:						int=None,						lowerCamelCase							:						Tuple=None,						lowerCamelCase							:						Tuple=0  )->      int:
								lowerCamelCase__	:	Tuple				=1.0 if scale is None else scale
								lowerCamelCase__	:	Union[str, Any]				=0.0 if loc is None else loc

								super().__init__(lowerCamelCase,						[AffineTransform(loc=self.loc,						scale=self.scale,						event_dim=lowerCamelCase  )]  )



					@property
					def 	snake_case ( self							:						Optional[int]  )->      Any:
								return self.base_dist.mean * self.scale + self.loc



					@property
					def 	snake_case ( self							:						Optional[Any]  )->      Tuple:
								return self.base_dist.variance * self.scale**2




					@property
					def 	snake_case ( self							:						List[str]  )->      Dict:
								return self.variance.sqrt()





class  __SCREAMING_SNAKE_CASE			(   nn.Module     ):


					'''simple docstring'''





					def __init__( self							:						Union[str, Any],						lowerCamelCase							:						int,						lowerCamelCase							:						Dict[str, int],						lowerCamelCase							:						Callable[..., Tuple[torch.Tensor]],						**lowerCamelCase							:						List[str]  )->      None:
								super().__init__(**lowerCamelCase  )
								lowerCamelCase__	:	Any				=args_dim
								lowerCamelCase__	:	int				=nn.ModuleList([nn.Linear(lowerCamelCase,						lowerCamelCase  ) for dim in args_dim.values()]  )
								lowerCamelCase__	:	Optional[Any]				=domain_map




					def 	snake_case ( self							:						Optional[Any],						lowerCamelCase							:						torch.Tensor  )->      Tuple[torch.Tensor]:
								lowerCamelCase__	:	int				=[proj(lowerCamelCase  ) for proj in self.proj]

								return self.domain_map(*lowerCamelCase  )





class  __SCREAMING_SNAKE_CASE			(   nn.Module     ):


					'''simple docstring'''





					def __init__( self							:						Optional[Any],						lowerCamelCase							:						Tuple  )->      Optional[int]:
								super().__init__()
								lowerCamelCase__	:	Tuple				=function




					def 	snake_case ( self							:						Dict,						lowerCamelCase							:						Tuple,						*lowerCamelCase							:						Union[str, Any]  )->      List[str]:
								return self.function(lowerCamelCase,						*lowerCamelCase  )





class  __SCREAMING_SNAKE_CASE			:


					'''simple docstring'''





					_a         =							4_2
					_a         =							4_2
					_a         =							4_2



					def __init__( self							:						int,						lowerCamelCase							:						int = 1  )->      None:
								lowerCamelCase__	:	str				=dim
								lowerCamelCase__	:	Any				={k: dim * self.args_dim[k] for k in self.args_dim}



					def 	snake_case ( self							:						Any,						lowerCamelCase							:						List[Any]  )->      Dict:
								if self.dim == 1:
											return self.distribution_class(*lowerCamelCase  )
								else:
											return Independent(self.distribution_class(*lowerCamelCase  ),						1  )



					def 	snake_case ( self							:						Any,						lowerCamelCase							:						List[Any],						lowerCamelCase							:						Optional[torch.Tensor] = None,						lowerCamelCase							:						Optional[torch.Tensor] = None,						)->      Distribution:
								lowerCamelCase__	:	Tuple				=self._base_distribution(lowerCamelCase  )
								if loc is None and scale is None:
											return distr
								else:
											return AffineTransformed(lowerCamelCase,						loc=lowerCamelCase,						scale=lowerCamelCase,						event_dim=self.event_dim  )



					@property
					def 	snake_case ( self							:						str  )->      Tuple:
								return () if self.dim == 1 else (self.dim,)



					@property
					def 	snake_case ( self							:						str  )->      int:
								return len(self.event_shape  )



					@property
					def 	snake_case ( self							:						List[Any]  )->      float:
								return 0.0



					def 	snake_case ( self							:						List[Any],						lowerCamelCase							:						int  )->      nn.Module:
								return ParameterProjection(
								    in_features=lowerCamelCase,						args_dim=self.args_dim,						domain_map=LambdaLayer(self.domain_map  ),						)



					def 	snake_case ( self							:						str,						*lowerCamelCase							:						torch.Tensor  )->      List[Any]:
								raise NotImplementedError()




					@staticmethod
					def 	snake_case ( lowerCamelCase							:						torch.Tensor  )->      torch.Tensor:
								return (x + torch.sqrt(torch.square(lowerCamelCase  ) + 4.0  )) / 2.0





class  __SCREAMING_SNAKE_CASE			(   lowerCAmelCase_     ):


					'''simple docstring'''





					_a         =							{'df': 1, 'loc': 1, 'scale': 1}
					_a         =							StudentT



					@classmethod
					def 	snake_case ( cls							:						List[str],						lowerCamelCase							:						torch.Tensor,						lowerCamelCase							:						torch.Tensor,						lowerCamelCase							:						torch.Tensor  )->      List[Any]:
								lowerCamelCase__	:	Tuple				=cls.squareplus(lowerCamelCase  ).clamp_min(torch.finfo(scale.dtype  ).eps  )
								lowerCamelCase__	:	Union[str, Any]				=2.0 + cls.squareplus(lowerCamelCase  )
								return df.squeeze(-1  ), loc.squeeze(-1  ), scale.squeeze(-1  )





class  __SCREAMING_SNAKE_CASE			(   lowerCAmelCase_     ):


					'''simple docstring'''





					_a         =							{'loc': 1, 'scale': 1}
					_a         =							Normal



					@classmethod
					def 	snake_case ( cls							:						Dict,						lowerCamelCase							:						torch.Tensor,						lowerCamelCase							:						torch.Tensor  )->      Any:
								lowerCamelCase__	:	Dict				=cls.squareplus(lowerCamelCase  ).clamp_min(torch.finfo(scale.dtype  ).eps  )
								return loc.squeeze(-1  ), scale.squeeze(-1  )





class  __SCREAMING_SNAKE_CASE			(   lowerCAmelCase_     ):


					'''simple docstring'''





					_a         =							{'total_count': 1, 'logits': 1}
					_a         =							NegativeBinomial



					@classmethod
					def 	snake_case ( cls							:						Optional[Any],						lowerCamelCase							:						torch.Tensor,						lowerCamelCase							:						torch.Tensor  )->      Optional[int]:
								lowerCamelCase__	:	int				=cls.squareplus(lowerCamelCase  )
								return total_count.squeeze(-1  ), logits.squeeze(-1  )



					def 	snake_case ( self							:						int,						lowerCamelCase							:						Optional[Any]  )->      Distribution:
								lowerCamelCase__	:	List[Any]				=distr_args
								if self.dim == 1:
											return self.distribution_class(total_count=lowerCamelCase,						logits=lowerCamelCase  )
								else:
											return Independent(self.distribution_class(total_count=lowerCamelCase,						logits=lowerCamelCase  ),						1  )




					def 	snake_case ( self							:						List[str],						lowerCamelCase							:						Tuple,						lowerCamelCase							:						Optional[torch.Tensor] = None,						lowerCamelCase							:						Optional[torch.Tensor] = None  )->      Distribution:
								lowerCamelCase__	:	int				=distr_args

								if scale is not None:
											# See scaling property of Gamma.
											logits += scale.log()

								return self._base_distribution((total_count, logits)  )









"""simple docstring"""






_lowercase				:				str   		=		0  # The first color of the flag.
_lowercase				:				Dict   		=		1  # The second color of the flag.
_lowercase				:				Tuple   		=		2  # The third color of the flag.
_lowercase				:				Optional[int]   		=		(red, white, blue)






def   snake_case__     (	__lowerCamelCase       :					list			):
			"""simple docstring"""
			if not sequence:
						return []
			if len(__lowerCamelCase			) == 1:
						return list(__lowerCamelCase			)
			lowerCamelCase__	:	List[Any]				=0
			lowerCamelCase__	:	Dict				=len(__lowerCamelCase			) - 1
			lowerCamelCase__	:	Tuple				=0
			while mid <= high:
						if sequence[mid] == colors[0]:
									lowerCamelCase__			,     lowerCamelCase__	:	Optional[Any]				=sequence[mid], sequence[low]
									low += 1
									mid += 1
						elif sequence[mid] == colors[1]:
									mid += 1
						elif sequence[mid] == colors[2]:
									lowerCamelCase__			,     lowerCamelCase__	:	Union[str, Any]				=sequence[high], sequence[mid]
									high -= 1
						else:
									lowerCamelCase__	:	Dict				=f'''The elements inside the sequence must contains only {colors} values'''
									raise ValueError(__lowerCamelCase			)
			return sequence


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		_lowercase				:				Optional[Any]   		=		input("Enter numbers separated by commas:\n").strip()
		_lowercase				:				int   		=		[int(item.strip()) for item in user_input.split(",")]
		print(f'{dutch_national_flag_sort(unsorted)}')




