






'''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 _lowercase			(       _lowercase	):




							def __init__(							self:       Optional[int]    ,							UpperCamelCase__:       Distribution    ,							UpperCamelCase__:       Dict=None    ,							UpperCamelCase__:       Dict=None    ,							UpperCamelCase__:       Optional[int]=0  ):
														lowerCamelCase__      :			List[str] 						= 1.0 if scale is None else scale
														lowerCamelCase__      :			List[str] 						= 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:       Optional[int]  ):
														return self.base_dist.mean * self.scale + self.loc




							@property
							def 	lowerCamelCase_       (							self:       int  ):
														return self.base_dist.variance * self.scale**2




							@property
							def 	lowerCamelCase_       (							self:       str  ):
														return self.variance.sqrt()



class _lowercase			(       nn.Module	):




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




							def 	lowerCamelCase_       (							self:       List[Any]    ,							UpperCamelCase__:       torch.Tensor  ):
														lowerCamelCase__      :			str 						= [proj(UpperCamelCase__  ) for proj in self.proj]

														return self.domain_map(*UpperCamelCase__  )



class _lowercase			(       nn.Module	):




							def __init__(							self:       Dict    ,							UpperCamelCase__:       Optional[Any]  ):
														super().__init__()
														lowerCamelCase__      :			List[str] 						= function




							def 	lowerCamelCase_       (							self:       Any    ,							UpperCamelCase__:       int    ,							*UpperCamelCase__:       Optional[Any]  ):
														return self.function(UpperCamelCase__    ,							*UpperCamelCase__  )



class _lowercase			:
							a          = 42
							a          = 42
							a          = 42




							def __init__(							self:       Any    ,							UpperCamelCase__:       int = 1  ):
														lowerCamelCase__      :			List[str] 						= dim
														lowerCamelCase__      :			List[str] 						= {k: dim * self.args_dim[k] for k in self.args_dim}




							def 	lowerCamelCase_       (							self:       Optional[int]    ,							UpperCamelCase__:       Dict  ):
														if self.dim == 1:
																					return self.distribution_class(*UpperCamelCase__  )
														else:
																					return Independent(self.distribution_class(*UpperCamelCase__  )    ,							1  )




							def 	lowerCamelCase_       (							self:       Any    ,							UpperCamelCase__:       Optional[Any]    ,							UpperCamelCase__:       Optional[torch.Tensor] = None    ,							UpperCamelCase__:       Optional[torch.Tensor] = None    ,							):
														lowerCamelCase__      :			str 						= 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:       Union[str, Any]  ):
														return len(self.event_shape  )




							@property
							def 	lowerCamelCase_       (							self:       str  ):
														return 0.0




							def 	lowerCamelCase_       (							self:       Tuple    ,							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 _lowercase			(       _lowercase	):
							a          = {"df": 1, "loc": 1, "scale": 1}
							a          = StudentT




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



class _lowercase			(       _lowercase	):
							a          = {"loc": 1, "scale": 1}
							a          = Normal




							@classmethod
							def 	lowerCamelCase_       (							cls:       Dict    ,							UpperCamelCase__:       torch.Tensor    ,							UpperCamelCase__:       torch.Tensor  ):
														lowerCamelCase__      :			List[Any] 						= cls.squareplus(UpperCamelCase__  ).clamp_min(torch.finfo(scale.dtype  ).eps  )
														return loc.squeeze(-1  ), scale.squeeze(-1  )



class _lowercase			(       _lowercase	):
							a          = {"total_count": 1, "logits": 1}
							a          = NegativeBinomial




							@classmethod
							def 	lowerCamelCase_       (							cls:       Union[str, Any]    ,							UpperCamelCase__:       torch.Tensor    ,							UpperCamelCase__:       torch.Tensor  ):
														lowerCamelCase__      :			List[Any] 						= cls.squareplus(UpperCamelCase__  )
														return total_count.squeeze(-1  ), logits.squeeze(-1  )




							def 	lowerCamelCase_       (							self:       Dict    ,							UpperCamelCase__:       Dict  ):
														lowerCamelCase__						,	lowerCamelCase__      :			Optional[int] 						= 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__:       List[str]    ,							UpperCamelCase__:       Optional[torch.Tensor] = None    ,							UpperCamelCase__:       Optional[torch.Tensor] = None  ):
														lowerCamelCase__						,	lowerCamelCase__      :			List[str] 						= distr_args

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

														return self._base_distribution((total_count, logits)  )









'''simple docstring'''







import sys
import turtle





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase   )   -> tuple[float, float]:
							return (pa[0] + pa[0]) / 2, (pa[1] + pa[1]) / 2





def 				SCREAMING_SNAKE_CASE_ (UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase       ,    UpperCamelCase       ,    )   -> None:
							my_pen.up()
							my_pen.goto(vertexa[0]       ,    vertexa[1]   )
							my_pen.down()
							my_pen.goto(vertexa[0]       ,    vertexa[1]   )
							my_pen.goto(vertexa[0]       ,    vertexa[1]   )
							my_pen.goto(vertexa[0]       ,    vertexa[1]   )

							if depth == 0:
														return

							triangle(UpperCamelCase       ,    get_mid(UpperCamelCase       ,    UpperCamelCase   )       ,    get_mid(UpperCamelCase       ,    UpperCamelCase   )       ,    depth - 1   )
							triangle(UpperCamelCase       ,    get_mid(UpperCamelCase       ,    UpperCamelCase   )       ,    get_mid(UpperCamelCase       ,    UpperCamelCase   )       ,    depth - 1   )
							triangle(UpperCamelCase       ,    get_mid(UpperCamelCase       ,    UpperCamelCase   )       ,    get_mid(UpperCamelCase       ,    UpperCamelCase   )       ,    depth - 1   )


if __name__ == "__main__":
			if len(sys.argv) != 2:
						raise ValueError(
						    '''Correct format for using this script: '''
						    '''python fractals.py <int:depth_for_fractal>'''
						)
			_A			:    Any					  =turtle.Turtle()
			my_pen.ht()
			my_pen.speed(5)
			my_pen.pencolor('''red''')

			_A			:    Dict					  =[(-175, -125), (0, 175), (175, -125)]  # vertices of triangle
			triangle(vertices[0], vertices[1], vertices[2], int(sys.argv[1]))

