


from __future__ import annotations
def 				UpperCAmelCase_					(							__snake_case						)     ->			bool:







 """simple docstring"""


 return len(set(__a						)						) == len(__a						)


if __name__ == "__main__":
  import doctest

  doctest.testmod()








from math import ceil, sqrt





def      lowerCAmelCase_ (       __a = 1000000		)     ->		int:







  """simple docstring"""





  lowerCamelCase__:      Optional[int]			  =0

  for outer_width in range(3	,    (limit // 4) + 2		):
    if outer_width**2 > limit:
      lowerCamelCase__:      Dict			  =max(ceil(sqrt(outer_width**2 - limit		)		)	,    1		)
    else:
      lowerCamelCase__:      str			  =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() = }')

