

'''simple docstring'''



from math import sqrt







def   a__			(    a__ = 1_00_00_00		):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE      = 0
     __SCREAMING_SNAKE_CASE      = 0
     __SCREAMING_SNAKE_CASE      = 42

     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(a__ ,       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, Union

import torch
from torch import nn

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







class 		lowerCAmelCase__  ( a					,   a   ):



 """simple docstring"""



 @register_to_config
 def __init__(						self   :			int   ,				__SCREAMING_SNAKE_CASE   :			int = 768   ,				)    ->					int:


      """simple docstring"""




      super().__init__()

      __SCREAMING_SNAKE_CASE      = nn.Parameter(torch.zeros(1   ,				__SCREAMING_SNAKE_CASE     )     )
      __SCREAMING_SNAKE_CASE      = nn.Parameter(torch.ones(1   ,				__SCREAMING_SNAKE_CASE     )     )
 def  UpperCAmelCase__						(						self   :			Any   ,				__SCREAMING_SNAKE_CASE   :			Optional[Union[str, torch.device]] = None   ,				__SCREAMING_SNAKE_CASE   :			Optional[torch.dtype] = None   ,				)    ->					List[str]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE      = nn.Parameter(self.mean.to(__SCREAMING_SNAKE_CASE     ).to(__SCREAMING_SNAKE_CASE     )     )
      __SCREAMING_SNAKE_CASE      = nn.Parameter(self.std.to(__SCREAMING_SNAKE_CASE     ).to(__SCREAMING_SNAKE_CASE     )     )
      return self
 def  UpperCAmelCase__						(						self   :			Optional[Any]   ,				__SCREAMING_SNAKE_CASE   :			Optional[int]     )    ->					Optional[int]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE      = (embeds - self.mean) * 1.0 / self.std
      return embeds


 def  UpperCAmelCase__						(						self   :			Tuple   ,				__SCREAMING_SNAKE_CASE   :			Any     )    ->					Optional[int]:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE      = (embeds * self.std) + self.mean
      return embeds






