
"""simple docstring"""




from math import sqrt

def lowercase_						(     _snake_case = 1_000_000		):
							SCREAMING_SNAKE_CASE__		: int     =     0
							SCREAMING_SNAKE_CASE__		: int     =     0
							SCREAMING_SNAKE_CASE__		: int

							while num_cuboids <= limit:
														max_cuboid_size += 1
														for sum_shortest_sides in range(2     ,2 * max_cuboid_size + 1		):
																					if sqrt(sum_shortest_sides**2 + max_cuboid_size**2		).is_integer():
																												num_cuboids += (
																												    min(_snake_case     ,sum_shortest_sides // 2		)
																												    - max(1     ,sum_shortest_sides - max_cuboid_size		)
																												    + 1
																												)

							return max_cuboid_size


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






"""simple docstring"""




from typing import Optional

from torch import nn

from .transformer_ad import TransformeraDModel, TransformeraDModelOutput



class 			lowerCAmelCase_		(nn.Module						):


				"""simple docstring"""



				def __init__(self     , SCREAMING_SNAKE_CASE__ = 16     , SCREAMING_SNAKE_CASE__ = 88     , SCREAMING_SNAKE_CASE__ = None     , SCREAMING_SNAKE_CASE__ = 1     , SCREAMING_SNAKE_CASE__ = 0.0     , SCREAMING_SNAKE_CASE__ = 32     , SCREAMING_SNAKE_CASE__ = None     , SCREAMING_SNAKE_CASE__ = False     , SCREAMING_SNAKE_CASE__ = None     , SCREAMING_SNAKE_CASE__ = None     , SCREAMING_SNAKE_CASE__ = "geglu"     , SCREAMING_SNAKE_CASE__ = None     , )      ->	Optional[Any]:



											"""simple docstring"""




											super().__init__()
											SCREAMING_SNAKE_CASE__		: Union[str, Any]     =     nn.ModuleList(
											    [
											        TransformeraDModel(
											            num_attention_heads=SCREAMING_SNAKE_CASE__     , attention_head_dim=SCREAMING_SNAKE_CASE__     , in_channels=SCREAMING_SNAKE_CASE__     , num_layers=SCREAMING_SNAKE_CASE__     , dropout=SCREAMING_SNAKE_CASE__     , norm_num_groups=SCREAMING_SNAKE_CASE__     , cross_attention_dim=SCREAMING_SNAKE_CASE__     , attention_bias=SCREAMING_SNAKE_CASE__     , sample_size=SCREAMING_SNAKE_CASE__     , num_vector_embeds=SCREAMING_SNAKE_CASE__     , activation_fn=SCREAMING_SNAKE_CASE__     , num_embeds_ada_norm=SCREAMING_SNAKE_CASE__     , )
											        for _ in range(2					)
											    ]					)

											# Variables that can be set by a pipeline:

											# The ratio of transformer1 to transformer2's output states to be combined during inference
											SCREAMING_SNAKE_CASE__		: Tuple     =     0.5

											# The shape of `encoder_hidden_states` is expected to be
											# `(batch_size, condition_lengths[0]+condition_lengths[1], num_features)`
											SCREAMING_SNAKE_CASE__		: Union[str, Any]     =     [77, 2_57]

											# Which transformer to use to encode which condition.
											# E.g. `(1, 0)` means that we'll use `transformers[1](conditions[0])` and `transformers[0](conditions[1])`
											SCREAMING_SNAKE_CASE__		: int     =     [1, 0]



				def 			__magic_name__					(self     , SCREAMING_SNAKE_CASE__     , SCREAMING_SNAKE_CASE__     , SCREAMING_SNAKE_CASE__=None     , SCREAMING_SNAKE_CASE__=None     , SCREAMING_SNAKE_CASE__=None     , SCREAMING_SNAKE_CASE__ = True     , )      ->	Optional[int]:



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__		: Any     =     hidden_states

											SCREAMING_SNAKE_CASE__		: Tuple     =     []
											SCREAMING_SNAKE_CASE__		: List[str]     =     0
											# attention_mask is not used yet
											for i in range(2					):
																		# for each of the two transformers, pass the corresponding condition tokens
																		SCREAMING_SNAKE_CASE__		: str     =     encoder_hidden_states[:, tokens_start : tokens_start + self.condition_lengths[i]]
																		SCREAMING_SNAKE_CASE__		: Any     =     self.transformer_index_for_condition[i]
																		SCREAMING_SNAKE_CASE__		: Union[str, Any]     =     self.transformers[transformer_index](
																		    SCREAMING_SNAKE_CASE__     , encoder_hidden_states=SCREAMING_SNAKE_CASE__     , timestep=SCREAMING_SNAKE_CASE__     , cross_attention_kwargs=SCREAMING_SNAKE_CASE__     , return_dict=SCREAMING_SNAKE_CASE__     , )[0]
																		encoded_states.append(encoded_state - input_states					)
																		tokens_start += self.condition_lengths[i]

											SCREAMING_SNAKE_CASE__		: Tuple     =     encoded_states[0] * self.mix_ratio + encoded_states[1] * (1 - self.mix_ratio)
											SCREAMING_SNAKE_CASE__		: Union[str, Any]     =     output_states + input_states

											if not return_dict:
																		return (output_states,)

											return TransformeraDModelOutput(sample=SCREAMING_SNAKE_CASE__					)




