




from math import ceil, sqrt



def      __lowerCAmelCase			(					UpperCamelCase = 1000000      )     ->	int:
		lowerCAmelCase__				:  Dict		       =     0

		for outer_width in range(3	,      (limit // 4) + 2      ):
				if outer_width**2 > limit:
						lowerCAmelCase__				:  Optional[int]		       =     max(ceil(sqrt(outer_width**2 - limit      )      )	,      1      )
				else:
						lowerCAmelCase__				:  List[Any]		       =     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() = }""")







from datetime import datetime

import matplotlib.pyplot as plt
import torch



def      __lowerCAmelCase			(					UpperCamelCase      )     ->	str:
  for param in module.parameters():
    lowerCAmelCase__				:  int		       =     False



def      __lowerCAmelCase			(					)     ->	Optional[Any]:
  lowerCAmelCase__				:  List[Any]		       =     '''cuda''' if torch.cuda.is_available() else '''cpu'''
  if torch.backends.mps.is_available() and torch.backends.mps.is_built():
    lowerCAmelCase__				:  Optional[Any]		       =     '''mps'''
  if device == "mps":
    print(
        '''WARNING: MPS currently doesn\'t seem to work, and messes up backpropagation without any visible torch'''
        ''' errors. I recommend using CUDA on a colab notebook or CPU instead if you\'re facing inexplicable issues'''
        ''' with generations.'''      )
  return device



def      __lowerCAmelCase			(					UpperCamelCase      )     ->	List[Any]:
  lowerCAmelCase__				:  str		       =     plt.imshow(UpperCamelCase      )
  fig.axes.get_xaxis().set_visible(UpperCamelCase      )
  fig.axes.get_yaxis().set_visible(UpperCamelCase      )
  plt.show()



def      __lowerCAmelCase			(					)     ->	str:
  lowerCAmelCase__				:  Dict		       =     datetime.now()
  lowerCAmelCase__				:  Optional[int]		       =     current_time.strftime('''%H:%M:%S'''      )
  return timestamp

