




from math import ceil, sqrt







def 			lowerCamelCase_		(       UpperCamelCase__				:      int = 100_0000      )     ->       int:





				"""simple docstring"""


				__lowerCamelCase		       =    0

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




"""simple docstring"""



def 					_UpperCAmelCase      ( __lowerCamelCase   :       int = 1_00_00_00		)     ->					int:
  _snake_case					     =       limit + 1
  _snake_case					     =       [0] * limit
  for first_term in range(1 ,					__lowerCamelCase		):
    for n in range(__lowerCamelCase ,					__lowerCamelCase ,					__lowerCamelCase		):
      _snake_case					     =       first_term + n / first_term
      if common_difference % 4:  # d must be divisble by 4
        continue
      else:
        common_difference /= 4
        if (
            first_term > common_difference
            and first_term < 4 * common_difference
        ):  # since x,y,z are positive integers
          frequency[n] += 1  # so z>0 and a>d ,also 4d<a

  _snake_case					     =       sum(1 for x in frequency[1:limit] if x == 10		)

  return count


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



