
import math


def 						UpperCAmelCase			(	a_		,   a_ = 0		,   a_ = 0						)		->	list:







				"""simple docstring"""



				__A   			= end or len(a_						)
				for i in range(a_		,   a_						):
								__A   			= i
								__A   			= array[i]
								while temp_index != start and temp_index_value < array[temp_index - 1]:
												__A   			= array[temp_index - 1]
												temp_index -= 1
								__A   			= temp_index_value
				return array


def 						UpperCAmelCase			(	a_		,   a_		,   a_						)		->	None:  # Max Heap







				"""simple docstring"""



				__A   			= index
				__A   			= 2 * index + 1  # Left Node
				__A   			= 2 * index + 2  # Right Node

				if left_index < heap_size and array[largest] < array[left_index]:
								__A   			= left_index

				if right_index < heap_size and array[largest] < array[right_index]:
								__A   			= right_index

				if largest != index:
								__A			,							__A   			= array[largest], array[index]
								heapify(a_		,   a_		,   a_						)


def 						UpperCAmelCase			(	a_						)		->	list:







				"""simple docstring"""



				__A   			= len(a_						)

				for i in range(n // 2		,   -1		,   -1						):
								heapify(a_		,   a_		,   a_						)

				for i in range(n - 1		,   0		,   -1						):
								__A			,							__A   			= array[0], array[i]
								heapify(a_		,   0		,   a_						)

				return array


def 						UpperCAmelCase			(	a_		,   a_		,   a_		,   a_						)		->	int:







				"""simple docstring"""



				if (array[first_index] > array[middle_index]) != (
				    array[first_index] > array[last_index]
				):
								return array[first_index]
				elif (array[middle_index] > array[first_index]) != (
				    array[middle_index] > array[last_index]
				):
								return array[middle_index]
				else:
								return array[last_index]


def 						UpperCAmelCase			(	a_		,   a_		,   a_		,   a_						)		->	int:







				"""simple docstring"""



				__A   			= low
				__A   			= high
				while True:
								while array[i] < pivot:
												i += 1
								j -= 1
								while pivot < array[j]:
												j -= 1
								if i >= j:
												return i
								__A			,							__A   			= array[j], array[i]
								i += 1


def 						UpperCAmelCase			(	a_						)		->	list:







				"""simple docstring"""



				if len(a_						) == 0:
								return array
				__A   			= 2 * math.ceil(math.loga(len(a_						)						)						)
				__A   			= 1_6
				return intro_sort(a_		,   0		,   len(a_						)		,   a_		,   a_						)


def 						UpperCAmelCase			(	a_		,   a_		,   a_		,   a_		,   a_						)		->	list:







				"""simple docstring"""



				while end - start > size_threshold:
								if max_depth == 0:
												return heap_sort(a_						)
								max_depth -= 1
								__A   			= median_of_a(a_		,   a_		,   start + ((end - start) // 2) + 1		,   end - 1						)
								__A   			= partition(a_		,   a_		,   a_		,   a_						)
								intro_sort(a_		,   a_		,   a_		,   a_		,   a_						)
								__A   			= p
				return insertion_sort(a_		,   a_		,   a_						)


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					SCREAMING_SNAKE_CASE							:List[Any]							 =				input('Enter numbers separated by a comma : ').strip()
					SCREAMING_SNAKE_CASE							:str							 =				[float(item) for item in user_input.split(',')]
					print(sort(unsorted))







"""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 					_UpperCAmelCase   (	lowercase_ ):


					def __init__(					self			:int     ,       __UpperCamelCase			:Distribution     ,       __UpperCamelCase			:Dict=None     ,       __UpperCamelCase			:Optional[int]=None     ,       __UpperCamelCase			:List[str]=0		):
												A		=  1.0 if scale is None else scale
												A		=  0.0 if loc is None else loc

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


					@property
					def 	lowerCamelCase       (					self			:Any		):
												return self.base_dist.mean * self.scale + self.loc


					@property
					def 	lowerCamelCase       (					self			:Optional[int]		):
												return self.base_dist.variance * self.scale**2


					@property
					def 	lowerCamelCase       (					self			:Dict		):
												return self.variance.sqrt()







class 					_UpperCAmelCase   (	nn.Module ):


					def __init__(					self			:Dict     ,       __UpperCamelCase			:int     ,       __UpperCamelCase			:Dict[str, int]     ,       __UpperCamelCase			:Callable[..., Tuple[torch.Tensor]]     ,       **__UpperCamelCase			:str		):
												super().__init__(**__UpperCamelCase		)
												A		=  args_dim
												A		=  nn.ModuleList([nn.Linear(__UpperCamelCase     ,       __UpperCamelCase		) for dim in args_dim.values()]		)
												A		=  domain_map


					def 	lowerCamelCase       (					self			:int     ,       __UpperCamelCase			:torch.Tensor		):
												A		=  [proj(__UpperCamelCase		) for proj in self.proj]

												return self.domain_map(*__UpperCamelCase		)







class 					_UpperCAmelCase   (	nn.Module ):


					def __init__(					self			:Dict     ,       __UpperCamelCase			:int		):
												super().__init__()
												A		=  function


					def 	lowerCamelCase       (					self			:List[str]     ,       __UpperCamelCase			:Any     ,       *__UpperCamelCase			:Any		):
												return self.function(__UpperCamelCase     ,       *__UpperCamelCase		)







class 					_UpperCAmelCase   :
					UpperCamelCase      =							42
					UpperCamelCase      =							42
					UpperCamelCase      =							42


					def __init__(					self			:Any     ,       __UpperCamelCase			:int = 1		):
												A		=  dim
												A		=  {k: dim * self.args_dim[k] for k in self.args_dim}


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


					def 	lowerCamelCase       (					self			:int     ,       __UpperCamelCase			:List[str]     ,       __UpperCamelCase			:Optional[torch.Tensor] = None     ,       __UpperCamelCase			:Optional[torch.Tensor] = None     ,       ):
												A		=  self._base_distribution(__UpperCamelCase		)
												if loc is None and scale is None:
																			return distr
												else:
																			return AffineTransformed(__UpperCamelCase     ,       loc=__UpperCamelCase     ,       scale=__UpperCamelCase     ,       event_dim=self.event_dim		)


					@property
					def 	lowerCamelCase       (					self			:List[Any]		):
												return () if self.dim == 1 else (self.dim,)


					@property
					def 	lowerCamelCase       (					self			:Tuple		):
												return len(self.event_shape		)


					@property
					def 	lowerCamelCase       (					self			:int		):
												return 0.0


					def 	lowerCamelCase       (					self			:str     ,       __UpperCamelCase			:int		):
												return ParameterProjection(
												    in_features=__UpperCamelCase     ,       args_dim=self.args_dim     ,       domain_map=LambdaLayer(self.domain_map		)     ,       )


					def 	lowerCamelCase       (					self			:List[Any]     ,       *__UpperCamelCase			:torch.Tensor		):
												raise NotImplementedError()


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







class 					_UpperCAmelCase   (	lowercase_ ):
					UpperCamelCase      =							{"df": 1, "loc": 1, "scale": 1}
					UpperCamelCase      =							StudentT


					@classmethod
					def 	lowerCamelCase       (					cls			:List[str]     ,       __UpperCamelCase			:torch.Tensor     ,       __UpperCamelCase			:torch.Tensor     ,       __UpperCamelCase			:torch.Tensor		):
												A		=  cls.squareplus(__UpperCamelCase		).clamp_min(torch.finfo(scale.dtype		).eps		)
												A		=  2.0 + cls.squareplus(__UpperCamelCase		)
												return df.squeeze(-1		), loc.squeeze(-1		), scale.squeeze(-1		)







class 					_UpperCAmelCase   (	lowercase_ ):
					UpperCamelCase      =							{"loc": 1, "scale": 1}
					UpperCamelCase      =							Normal


					@classmethod
					def 	lowerCamelCase       (					cls			:List[Any]     ,       __UpperCamelCase			:torch.Tensor     ,       __UpperCamelCase			:torch.Tensor		):
												A		=  cls.squareplus(__UpperCamelCase		).clamp_min(torch.finfo(scale.dtype		).eps		)
												return loc.squeeze(-1		), scale.squeeze(-1		)







class 					_UpperCAmelCase   (	lowercase_ ):
					UpperCamelCase      =							{"total_count": 1, "logits": 1}
					UpperCamelCase      =							NegativeBinomial


					@classmethod
					def 	lowerCamelCase       (					cls			:str     ,       __UpperCamelCase			:torch.Tensor     ,       __UpperCamelCase			:torch.Tensor		):
												A		=  cls.squareplus(__UpperCamelCase		)
												return total_count.squeeze(-1		), logits.squeeze(-1		)


					def 	lowerCamelCase       (					self			:Tuple     ,       __UpperCamelCase			:List[str]		):
												A,	A		=  distr_args
												if self.dim == 1:
																			return self.distribution_class(total_count=__UpperCamelCase     ,       logits=__UpperCamelCase		)
												else:
																			return Independent(self.distribution_class(total_count=__UpperCamelCase     ,       logits=__UpperCamelCase		)     ,       1		)


					def 	lowerCamelCase       (					self			:List[str]     ,       __UpperCamelCase			:str     ,       __UpperCamelCase			:Optional[torch.Tensor] = None     ,       __UpperCamelCase			:Optional[torch.Tensor] = None		):
												A,	A		=  distr_args

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

												return self._base_distribution((total_count, logits)		)


