"""simple docstring"""
from __future__ import annotations

from cmath import sqrt







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->tuple[complex, complex]:

  if a == 0:
    raise ValueError('Coefficient \'a\' must not be zero.'   )
  a__:     List[str]										=	b * b - 4 * a * c

  a__:     Dict										=	(-b + sqrt(_SCREAMING_SNAKE_CASE   )) / (2 * a)
  a__:     str										=	(-b - sqrt(_SCREAMING_SNAKE_CASE   )) / (2 * a)

  return (
      root_a.real if not root_a.imag else root_a,
      root_a.real if not root_a.imag else root_a,
  )







def 						__a   (	)	->int:
  a__							,    a__:     Optional[Any]										=	quadratic_roots(a=5		,     b=6		,     c=1   )
  print(F'The solutions are: {solutiona} and {solutiona}'   )


if __name__ == "__main__":
 main()



"""simple docstring"""
def 						__a   (	_SCREAMING_SNAKE_CASE = 1000000   )	->int:
  a__:     int										=	limit + 1
  a__:     Optional[int]										=	[0] * limit
  for first_term in range(1		,     _SCREAMING_SNAKE_CASE   ):
    for n in range(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   ):
      a__:     List[Any]										=	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

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

  return count


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


