
'''simple docstring'''






from typing import Optional

from torch import nn

from .transformer_ad import TransformeraDModel, TransformeraDModelOutput

class  UpperCAmelCase__						(       nn.Module ):



    def __init__(	self      :       Tuple,__A      :       int = 1_6,__A      :       int = 8_8,__A      :       Optional[int] = None,__A      :       int = 1,__A      :       float = 0.0,__A      :       int = 3_2,__A      :       Optional[int] = None,__A      :       bool = False,__A      :       Optional[int] = None,__A      :       Optional[int] = None,__A      :       str = "geglu",__A      :       Optional[int] = None,):
          super().__init__()
          _lowerCamelCase				:   List[Any]								=   nn.ModuleList(
              [
                  TransformeraDModel(
                      num_attention_heads=__A,attention_head_dim=__A,in_channels=__A,num_layers=__A,dropout=__A,norm_num_groups=__A,cross_attention_dim=__A,attention_bias=__A,sample_size=__A,num_vector_embeds=__A,activation_fn=__A,num_embeds_ada_norm=__A,)
                  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
          _lowerCamelCase				:   Dict								=   0.5

          # The shape of `encoder_hidden_states` is expected to be
          # `(batch_size, condition_lengths[0]+condition_lengths[1], num_features)`
          _lowerCamelCase				:   Dict								=   [7_7, 2_5_7]

          # 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])`
          _lowerCamelCase				:   int								=   [1, 0]



    def   lowerCamelCase_  (	self      :       List[Any],__A      :       Dict,__A      :       List[str],__A      :       Dict=None,__A      :       Dict=None,__A      :       Tuple=None,__A      :       bool = True,):
          _lowerCamelCase				:   Optional[Any]								=   hidden_states

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

          _lowerCamelCase				:   List[Any]								=   encoded_states[0] * self.mix_ratio + encoded_states[1] * (1 - self.mix_ratio)
          _lowerCamelCase				:   Dict								=   output_states + input_states

          if not return_dict:
                return (output_states,)

          return TransformeraDModelOutput(sample=__A     )

'''simple docstring'''






from math import sqrt







def 		A_       (	_lowerCAmelCase   :    int = 1000000							):



      """simple docstring"""




      _lowerCamelCase				:   int								=   0
      _lowerCamelCase				:   int								=   0
      _lowerCamelCase				:   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(_lowerCAmelCase				,	sum_shortest_sides // 2							)
                            - max(1				,	sum_shortest_sides - max_cuboid_size							)
                            + 1
                        )

      return max_cuboid_size


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