


from __future__ import annotations

from cmath import sqrt
def       _a			(				SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		if a == 0:
				raise ValueError('''Coefficient \'a\' must not be zero.'''					)
		lowercase__						=				b * b - 4 * a * c

		lowercase__						=				(-b + sqrt(SCREAMING_SNAKE_CASE					)) / (2 * a)
		lowercase__						=				(-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			(				):


		"""simple docstring"""




		lowercase__					,		lowercase__						=				quadratic_roots(a=5						,    b=6						,    c=1					)
		print(f'The solutions are: {solutiona} and {solutiona}'					)


if __name__ == "__main__":
			main()






lowerCAmelCase	=							[sum(int(c, 10) ** 2 for c in i.__str__()) for i in range(10_0000)]
def       _a			(				SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		lowercase__						=				0
		while number:
				# Increased Speed Slightly by checking every 5 digits together.
				sum_of_digits_squared += DIGITS_SQUARED[number % 10_00_00]
				number //= 10_00_00

		return sum_of_digits_squared


# There are 2 Chains made,
# One ends with 89 with the chain member 58 being the one which when declared first,
# there will be the least number of iterations for all the members to be checked.

# The other one ends with 1 and has only one element 1.

# So 58 and 1 are chosen to be declared at the starting.

# Changed dictionary to an array to quicken the solution
lowerCAmelCase	=							[None] * 1000_0000
lowerCAmelCase	=							True
lowerCAmelCase	=							False
def       _a			(				SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		if CHAINS[number - 1] is not None:
				return CHAINS[number - 1]  # type: ignore

		lowercase__						=				chain(next_number(SCREAMING_SNAKE_CASE					)					)
		lowercase__						=				number_chain

		while number < 10_00_00_00:
				lowercase__						=				number_chain
				number *= 10

		return number_chain
def       _a			(				SCREAMING_SNAKE_CASE = 10_00_00_00					):


		"""simple docstring"""




		for i in range(1						,    SCREAMING_SNAKE_CASE					):
				if CHAINS[i] is None:
						chain(i + 1					)

		return CHAINS[:number].count(SCREAMING_SNAKE_CASE					)


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			print(f"""{solution() = }""")


