





import torch
from torch import nn

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


class   A      (SCREAMING_SNAKE_CASE       ,					SCREAMING_SNAKE_CASE   ):
			'''simple docstring'''




			@register_to_config
			def __init__(      self       :   Any							,     *,
			    __lowerCAmelCase       :   int = 4							,     __lowerCAmelCase       :   int = 7_68							,     __lowerCAmelCase       :   int							,     __lowerCAmelCase       :   Optional[int]							,     )     ->     Dict:







					"""simple docstring"""






					super().__init__()

					A__  				=       nn.Parameter(torch.zeros(__lowerCAmelCase       )       )

					# parameters for additional clip time embeddings
					A__  				=       nn.Linear(__lowerCAmelCase							,     __lowerCAmelCase       )
					A__  				=       nn.Linear(__lowerCAmelCase							,     __lowerCAmelCase       )

					# parameters for encoder hidden states
					A__  				=       clip_extra_context_tokens
					A__  				=       nn.Linear(
					    __lowerCAmelCase							,     self.clip_extra_context_tokens * cross_attention_dim       )
					A__  				=       nn.Linear(__lowerCAmelCase							,     __lowerCAmelCase       )
					A__  				=       nn.LayerNorm(__lowerCAmelCase       )







			def        a_	(      self       :   Tuple							,     *, __lowerCAmelCase       :   str							,     __lowerCAmelCase       :   Union[str, Any]							,     __lowerCAmelCase       :   List[str]							,     __lowerCAmelCase       :   Tuple       )     ->     Optional[Any]:







					"""simple docstring"""






					if do_classifier_free_guidance:
							# Add the classifier free guidance embeddings to the image embeddings
							A__  				=       image_embeddings.shape[0]
							A__  				=       self.learned_classifier_free_guidance_embeddings.unsqueeze(0       )
							A__  				=       classifier_free_guidance_embeddings.expand(
							    __lowerCAmelCase							,     -1       )
							A__  				=       torch.cat([classifier_free_guidance_embeddings, image_embeddings]							,     dim=0       )

					# The image embeddings batch size and the text embeddings batch size are equal
					assert image_embeddings.shape[0] == prompt_embeds.shape[0]

					A__  				=       prompt_embeds.shape[0]

					# "Specifically, we modify the architecture described in Nichol et al. (2021) by projecting and
					# adding CLIP embeddings to the existing timestep embedding, ...
					A__  				=       self.embedding_proj(__lowerCAmelCase       )
					A__  				=       self.clip_image_embeddings_project_to_time_embeddings(__lowerCAmelCase       )
					A__  				=       time_projected_image_embeddings + time_projected_prompt_embeds

					# ... and by projecting CLIP embeddings into four
					# extra tokens of context that are concatenated to the sequence of outputs from the GLIDE text encoder"
					A__  				=       self.clip_extra_context_tokens_proj(__lowerCAmelCase       )
					A__  				=       clip_extra_context_tokens.reshape(__lowerCAmelCase							,     -1							,     self.clip_extra_context_tokens       )
					A__  				=       clip_extra_context_tokens.permute(0							,     2							,     1       )

					A__  				=       self.encoder_hidden_states_proj(__lowerCAmelCase       )
					A__  				=       self.text_encoder_hidden_states_norm(__lowerCAmelCase       )
					A__  				=       torch.cat([clip_extra_context_tokens, text_encoder_hidden_states]							,     dim=1       )

					return text_encoder_hidden_states, additive_clip_time_embeddings










import math







def        __lowerCamelCase (							__a       :int   )		->    bool:






		"""simple docstring"""

		A__  				=       math.loga(math.sqrt(4 * positive_integer + 1   ) / 2 + 1 / 2   )

		return exponent == int(__a   )







def        __lowerCamelCase (							__a       :float = 1 / 1_2_3_4_5   )		->    int:






		"""simple docstring"""

		A__  				=       0
		A__  				=       0

		A__  				=       3
		while True:
				A__  				=       (integer**2 - 1) / 4
				# if candidate is an integer, then there is a partition for k
				if partition_candidate == int(__a   ):
						A__  				=       int(__a   )
						total_partitions += 1
						if check_partition_perfect(__a   ):
								perfect_partitions += 1
				if perfect_partitions > 0:
						if perfect_partitions / total_partitions < max_proportion:
								return int(__a   )
				integer += 1


if __name__ == "__main__":
					print(F'''{solution() = }''')



