


from math import factorial






def   _lowercase(					__a				:						int    ,     __a				:						int    ,     __a				:						float     ):
							if successes > trials:
														raise ValueError('successes must be lower or equal to trials'     )
							if trials < 0 or successes < 0:
														raise ValueError('the function is defined for non-negative integers'     )
							if not isinstance(__a    ,     __a     ) or not isinstance(__a    ,     __a     ):
														raise ValueError('the function is defined for non-negative integers'     )
							if not 0 < prob < 1:
														raise ValueError('prob has to be in range of 1 - 0'     )
							a__      =(prob**successes) * ((1 - prob) ** (trials - successes))
							# Calculate the binomial coefficient: n! / k!(n-k)!
							a__      =float(factorial(__a     )     )
							coefficient /= factorial(__a     ) * factorial(trials - successes     )
							return probability * coefficient


if __name__ == "__main__":
	from doctest import testmod

	testmod()
	print('Probability of 2 successes out of 4 trails')
	print('with probability of 0.75 is:', end=' ')
	print(binomial_distribution(2, 4, 0.75))









"""simple docstring"""
import torch
import torch.nn as nn
from transformers.modeling_utils import ModuleUtilsMixin
from transformers.models.ta.modeling_ta import TaBlock, TaConfig, TaLayerNorm

from ...configuration_utils import ConfigMixin, register_to_config
from ...models import ModelMixin



class   SCREAMING_SNAKE_CASE	(					_SCREAMING_SNAKE_CASE							,							_SCREAMING_SNAKE_CASE							,							_SCREAMING_SNAKE_CASE    ):





	"""simple docstring"""




	@register_to_config
	def __init__(self  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_ = False  ,  ):
		super().__init__()

		A_		:    Tuple						     = nn.Embedding(lowerCAmelCase_  ,  lowerCAmelCase_				)

		A_		:    List[str]						     = nn.Embedding(lowerCAmelCase_  ,  lowerCAmelCase_				)
		A_		:    Any						     = False

		A_		:    Tuple						     = nn.Dropout(p=lowerCAmelCase_				)

		A_		:    List[str]						     = TaConfig(
		    vocab_size=lowerCAmelCase_  ,  d_model=lowerCAmelCase_  ,  num_heads=lowerCAmelCase_  ,  d_kv=lowerCAmelCase_  ,  d_ff=lowerCAmelCase_  ,  dropout_rate=lowerCAmelCase_  ,  feed_forward_proj=lowerCAmelCase_  ,  is_decoder=lowerCAmelCase_  ,  is_encoder_decoder=lowerCAmelCase_  ,  )

		A_		:    Optional[Any]						     = nn.ModuleList()
		for lyr_num in range(lowerCAmelCase_				):
			A_		:    Tuple						     = TaBlock(lowerCAmelCase_				)
			self.encoders.append(lowerCAmelCase_				)

		A_		:    Any						     = TaLayerNorm(lowerCAmelCase_				)
		A_		:    Union[str, Any]						     = nn.Dropout(p=lowerCAmelCase_				)





	def  lowerCamelCase(self  ,  lowerCAmelCase_  ,  lowerCAmelCase_				):
		A_		:    List[Any]						     = self.token_embedder(lowerCAmelCase_				)

		A_		:    Optional[Any]						     = encoder_input_tokens.shape[1]
		A_		:    Any						     = torch.arange(lowerCAmelCase_  ,  device=encoder_input_tokens.device				)
		x += self.position_encoding(lowerCAmelCase_				)

		A_		:    Optional[Any]						     = self.dropout_pre(lowerCAmelCase_				)

		# inverted the attention mask
		A_		:    int						     = encoder_input_tokens.size()
		A_		:    Optional[Any]						     = self.get_extended_attention_mask(lowerCAmelCase_  ,  lowerCAmelCase_				)

		for lyr in self.encoders:
			A_		:    int						     = lyr(lowerCAmelCase_  ,  lowerCAmelCase_				)[0]
		A_		:    List[str]						     = self.layer_norm(lowerCAmelCase_				)

		return self.dropout_post(lowerCAmelCase_				), encoder_inputs_mask

