



from torch import nn


class       a							(			nn.Module				):



		def __init__(     self     :Tuple   ,__lowercase     :Optional[int]   ,__lowercase     :int  ):
						super().__init__()
						snake_case__	:      Optional[Any]     		=	class_size
						snake_case__	:      Dict     		=	embed_size
						# self.mlp1 = nn.Linear(embed_size, embed_size)
						# self.mlp2 = (nn.Linear(embed_size, class_size))
						snake_case__	:      Dict     		=	nn.Linear(__lowercase   ,__lowercase  )






		def 	__lowerCamelCase			(     self     :str   ,__lowercase     :int  ):
						# hidden_state = nn.functional.relu(self.mlp1(hidden_state))
						# hidden_state = self.mlp2(hidden_state)
						snake_case__	:      Optional[Any]     		=	self.mlp(__lowercase  )
						return logits






from math import ceil, sqrt



def 			_lowerCAmelCase       (					__lowerCAmelCase = 1000000      )   ->					int:


				"""simple docstring"""

				snake_case__	:      Dict     		=	0

				for outer_width in range(3  ,  (limit // 4) + 2      ):
								if outer_width**2 > limit:
												snake_case__	:      Any     		=	max(ceil(sqrt(outer_width**2 - limit      )      )  ,  1      )
								else:
												snake_case__	:      int     		=	1
								if (outer_width - hole_width_lower_bound) % 2:
												hole_width_lower_bound += 1

								answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

				return answer


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

