


"""simple docstring"""


UpperCamelCase						:				List[str]             =      [0, 2, 4, 6, 8]
UpperCamelCase						:				Tuple             =      [1, 3, 5, 7, 9]







def  __snake_case       (   UpperCamelCase__ ,			UpperCamelCase__ ,			UpperCamelCase__ ,			UpperCamelCase__	)      ->		int:







		"""simple docstring"""





		if remaining_length == 0:
				if digits[0] == 0 or digits[-1] == 0:
						return 0

				for i in range(length // 2 - 1 ,			-1 ,			-1	):
						remainder += digits[i] + digits[length - i - 1]

						if remainder % 2 == 0:
								return 0

						remainder //= 10

				return 1

		if remaining_length == 1:
				if remainder % 2 == 0:
						return 0

				A					       = 0
				for digit in range(10	):
						A					       = digit
						result += reversible_numbers(
						    0 ,			(remainder + 2 * digit) // 10 ,			UpperCamelCase__ ,			UpperCamelCase__	)
				return result

		A					       = 0
		for digita in range(10	):
				A					       = digita

				if (remainder + digita) % 2 == 0:
						A					       = ODD_DIGITS
				else:
						A					       = EVEN_DIGITS

				for digita in other_parity_digits:
						A					       = digita
						result += reversible_numbers(
						    remaining_length - 2 ,			(remainder + digita + digita) // 10 ,			UpperCamelCase__ ,			UpperCamelCase__ ,			)
		return result







def  __snake_case       (   UpperCamelCase__ = 9	)      ->		int:







		"""simple docstring"""





		A					       = 0
		for length in range(1 ,			max_power + 1	):
				result += reversible_numbers(UpperCamelCase__ ,			0 ,			[0] * length ,			UpperCamelCase__	)
		return result


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









"""simple docstring"""


from math import factorial







def  __snake_case       (   UpperCamelCase__ ,			UpperCamelCase__ ,			UpperCamelCase__	)      ->		float:







		"""simple docstring"""





		if successes > trials:
				raise ValueError('successes must be lower or equal to trials'	)
		if trials < 0 or successes < 0:
				raise ValueError('the function is defined for non-negative integers'	)
		if not isinstance(UpperCamelCase__ ,			UpperCamelCase__	) or not isinstance(UpperCamelCase__ ,			UpperCamelCase__	):
				raise ValueError('the function is defined for non-negative integers'	)
		if not 0 < prob < 1:
				raise ValueError('prob has to be in range of 1 - 0'	)
		A					       = (prob**successes) * ((1 - prob) ** (trials - successes))
		# Calculate the binomial coefficient: n! / k!(n-k)!
		A					       = float(factorial(UpperCamelCase__	)	)
		coefficient /= factorial(UpperCamelCase__	) * factorial(trials - successes	)
		return probability * coefficient


if __name__ == "__main__":
	from doctest import testmod

	testmod()
	print("Probability of 2 successes out of 4 trails")
	print("with probability of 0.75 is:", end=" ")
	print(binomial_distribution(2, 4, 0.75))





