


"""simple docstring"""







from __future__ import annotations


def 					lowercase      (    A_  ,       A_  ,       A_	)->				float:
  '''simple docstring'''







  if days_between_payments <= 0:
    raise ValueError("days_between_payments must be > 0"	)
  if daily_interest_rate < 0:
    raise ValueError("daily_interest_rate must be >= 0"	)
  if principal <= 0:
    raise ValueError("principal must be > 0"	)
  return principal * daily_interest_rate * days_between_payments


def 					lowercase      (    A_  ,       A_  ,       A_  ,       )->				float:
  '''simple docstring'''







  if number_of_compounding_periods <= 0:
    raise ValueError("number_of_compounding_periods must be > 0"	)
  if nominal_annual_interest_rate_percentage < 0:
    raise ValueError("nominal_annual_interest_rate_percentage must be >= 0"	)
  if principal <= 0:
    raise ValueError("principal must be > 0"	)

  return principal * (
      (1 + nominal_annual_interest_rate_percentage) ** number_of_compounding_periods
      - 1
  )


def 					lowercase      (    A_  ,       A_  ,       A_  ,       )->				float:
  '''simple docstring'''







  if number_of_years <= 0:
    raise ValueError("number_of_years must be > 0"	)
  if nominal_annual_percentage_rate < 0:
    raise ValueError("nominal_annual_percentage_rate must be >= 0"	)
  if principal <= 0:
    raise ValueError("principal must be > 0"	)

  return compound_interest(
      A_  ,       nominal_annual_percentage_rate / 365  ,       number_of_years * 365	)


if __name__ == "__main__":
 import doctest

 doctest.testmod()










"""simple docstring"""







from math import ceil, sqrt


def 					lowercase      (    A_ = 1_000_000	)->				int:
  '''simple docstring'''







  a						:		Tuple											=      0

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






