


class 			lowerCamelCase__						:







						def __init__(							self   :    Optional[int]			,			_lowercase   :    int		):
								A					       = size
								A					       = [0] * size
								A					       = [0] * size







						@staticmethod
						def __a						(							_lowercase   :    int		):
								return index | (index + 1)







						@staticmethod
						def __a						(							_lowercase   :    int		):
								return (index & (index + 1)) - 1







						def __a						(							self   :    int			,			_lowercase   :    int			,			_lowercase   :    int		):
								A					       = value
								while index < self.size:
										A					       = self.get_prev(_lowercase		) + 1
										if current_left_border == index:
												A					       = value
										else:
												A					       = max(_lowercase			,			_lowercase			,			_lowercase		)
										A					       = self.get_next(_lowercase		)







						def __a						(							self   :    Dict			,			_lowercase   :    int			,			_lowercase   :    int		):
								right -= 1  # Because of right is exclusive
								A					       = 0
								while left <= right:
										A					       = self.get_prev(_lowercase		)
										if left <= current_left:
												A					       = max(_lowercase			,			self.tree[right]		)
												A					       = current_left
										else:
												A					       = max(_lowercase			,			self.arr[right]		)
												right -= 1
								return result


if __name__ == "__main__":
	import doctest

	doctest.testmod()









"""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))





