


"""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 (							__snake_case				):






		'''simple docstring'''

		def __init__(self				,       a_				,       a_=None				,       a_=None				,       a_=0					):





			'''simple docstring'''

			__snake_case	:						str						=				1.0 if scale is None else scale
			__snake_case	:						List[str]						=				0.0 if loc is None else loc

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



		@property
		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			return self.base_dist.mean * self.scale + self.loc



		@property
		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			return self.base_dist.variance * self.scale**2



		@property
		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			return self.variance.sqrt()



class 			_UpperCAmelCase (							nn.Module				):






		'''simple docstring'''

		def __init__(self				,       a_				,       a_				,       a_				,       **a_					):





			'''simple docstring'''

			super().__init__(**a_					)
			__snake_case	:						Tuple						=				args_dim
			__snake_case	:						Tuple						=				nn.ModuleList([nn.Linear(a_				,       a_					) for dim in args_dim.values()]					)
			__snake_case	:						Any						=				domain_map



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			__snake_case	:						Optional[Any]						=				[proj(a_					) for proj in self.proj]

			return self.domain_map(*a_					)



class 			_UpperCAmelCase (							nn.Module				):






		'''simple docstring'''

		def __init__(self				,       a_					):





			'''simple docstring'''

			super().__init__()
			__snake_case	:						Union[str, Any]						=				function



		def 				SCREAMING_SNAKE_CASE  (self				,       a_				,       *a_					):





			'''simple docstring'''

			return self.function(a_				,       *a_					)



class 			_UpperCAmelCase :






		'''simple docstring'''

		lowerCamelCase__				=42
		lowerCamelCase__				=42
		lowerCamelCase__				=42



		def __init__(self				,       a_ = 1					):





			'''simple docstring'''

			__snake_case	:						Optional[Any]						=				dim
			__snake_case	:						Optional[int]						=				{k: dim * self.args_dim[k] for k in self.args_dim}



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			if self.dim == 1:
				return self.distribution_class(*a_					)
			else:
				return Independent(self.distribution_class(*a_					)				,       1					)



		def 				SCREAMING_SNAKE_CASE  (self				,       a_				,       a_ = None				,       a_ = None				,       ):





			'''simple docstring'''

			__snake_case	:						Tuple						=				self._base_distribution(a_					)
			if loc is None and scale is None:
				return distr
			else:
				return AffineTransformed(a_				,       loc=a_				,       scale=a_				,       event_dim=self.event_dim					)



		@property
		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			return () if self.dim == 1 else (self.dim,)



		@property
		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			return len(self.event_shape					)



		@property
		def 				SCREAMING_SNAKE_CASE  (self					):





			'''simple docstring'''

			return 0.0



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			return ParameterProjection(
			    in_features=a_				,       args_dim=self.args_dim				,       domain_map=LambdaLayer(self.domain_map					)				,       )



		def 				SCREAMING_SNAKE_CASE  (self				,       *a_					):





			'''simple docstring'''

			raise NotImplementedError()



		@staticmethod
		def 				SCREAMING_SNAKE_CASE  (a_					):





			'''simple docstring'''

			return (x + torch.sqrt(torch.square(a_					) + 4.0					)) / 2.0



class 			_UpperCAmelCase (							__snake_case				):






		'''simple docstring'''

		lowerCamelCase__				={"df": 1, "loc": 1, "scale": 1}
		lowerCamelCase__				=StudentT



		@classmethod
		def 				SCREAMING_SNAKE_CASE  (cls				,       a_				,       a_				,       a_					):





			'''simple docstring'''

			__snake_case	:						Optional[int]						=				cls.squareplus(a_					).clamp_min(torch.finfo(scale.dtype					).eps					)
			__snake_case	:						Optional[int]						=				2.0 + cls.squareplus(a_					)
			return df.squeeze(-1					), loc.squeeze(-1					), scale.squeeze(-1					)



class 			_UpperCAmelCase (							__snake_case				):






		'''simple docstring'''

		lowerCamelCase__				={"loc": 1, "scale": 1}
		lowerCamelCase__				=Normal



		@classmethod
		def 				SCREAMING_SNAKE_CASE  (cls				,       a_				,       a_					):





			'''simple docstring'''

			__snake_case	:						Dict						=				cls.squareplus(a_					).clamp_min(torch.finfo(scale.dtype					).eps					)
			return loc.squeeze(-1					), scale.squeeze(-1					)



class 			_UpperCAmelCase (							__snake_case				):






		'''simple docstring'''

		lowerCamelCase__				={"total_count": 1, "logits": 1}
		lowerCamelCase__				=NegativeBinomial



		@classmethod
		def 				SCREAMING_SNAKE_CASE  (cls				,       a_				,       a_					):





			'''simple docstring'''

			__snake_case	:						Dict						=				cls.squareplus(a_					)
			return total_count.squeeze(-1					), logits.squeeze(-1					)



		def 				SCREAMING_SNAKE_CASE  (self				,       a_					):





			'''simple docstring'''

			__snake_case	,							__snake_case	:						List[Any]						=				distr_args
			if self.dim == 1:
				return self.distribution_class(total_count=a_				,       logits=a_					)
			else:
				return Independent(self.distribution_class(total_count=a_				,       logits=a_					)				,       1					)



		def 				SCREAMING_SNAKE_CASE  (self				,       a_				,       a_ = None				,       a_ = None					):





			'''simple docstring'''

			__snake_case	,							__snake_case	:						Tuple						=				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 math






def 		lowercase							(     _snake_case						:      int     )     ->bool:
	"""simple docstring"""





	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(_snake_case     ) + 1     )     ,   6     ):
		if number % i == 0 or number % (i + 2) == 0:
			return False
	return True






def 		lowercase							(     _snake_case						:      float = 0.1     )     ->int:
	"""simple docstring"""





	__snake_case	:						Tuple						=				3
	__snake_case	:						Any						=				3

	while primes / (2 * j - 1) >= ratio:
		for i in range(j * j + j + 1     ,   (j + 2) * (j + 2)     ,   j + 1     ):
			primes += is_prime(_snake_case     )
		j += 2
	return j


if __name__ == "__main__":
			import doctest

			doctest.testmod()





