




from __future__ import annotations

from random import random

class 						__lowerCAmelCase      :
							def __init__(		self		:Optional[int]						, __magic_name__		:int | None = None							):







								'''simple docstring'''







								a									=				value
								a									=				random()
								a									=				None
								a									=				None
							def __repr__(		self		:List[Any]							):







								'''simple docstring'''







								from pprint import pformat

								if self.left is None and self.right is None:
									return F'\'{self.value}: {self.prior:.5}\''
								else:
									return pformat(
									    {F'{self.value}: {self.prior:.5}': (self.left, self.right)}						, indent=1							)





							def __str__(		self		:Dict							):







								'''simple docstring'''







								a									=				str(self.value							) + """ """
								a									=				str(self.left or """"""							)
								a									=				str(self.right or """"""							)
								return value + left + right







def 						__A						(      __lowerCamelCase				,     __lowerCamelCase       ) ->			tuple[Node | None, Node | None]:
	if root is None:  # None tree is split into 2 Nones
		return None, None
	elif root.value is None:
		return None, None
	else:
		if value < root.value:
			a							,					a									=				split(root.left				,     __lowerCamelCase       )
			return left, root
		else:
			a							,					a									=				split(root.right				,     __lowerCamelCase       )
			return root, right





def 						__A						(      __lowerCamelCase				,     __lowerCamelCase       ) ->			Node | None:
	if (not left) or (not right):  # If one node is None, return the other
		return left or right
	elif left.prior < right.prior:
		a									=				merge(left.right				,     __lowerCamelCase       )
		return left
	else:
		a									=				merge(__lowerCamelCase				,     right.left       )
		return right





def 						__A						(      __lowerCamelCase				,     __lowerCamelCase       ) ->			Node | None:
	a									=				Node(__lowerCamelCase       )
	a							,					a									=				split(__lowerCamelCase				,     __lowerCamelCase       )
	return merge(merge(__lowerCamelCase				,     __lowerCamelCase       )				,     __lowerCamelCase       )





def 						__A						(      __lowerCamelCase				,     __lowerCamelCase       ) ->			Node | None:
	a							,					a									=				split(__lowerCamelCase				,     value - 1       )
	a							,					a									=				split(__lowerCamelCase				,     __lowerCamelCase       )
	return merge(__lowerCamelCase				,     __lowerCamelCase       )





def 						__A						(      __lowerCamelCase       ) ->			None:
	if not root:  # None
		return
	else:
		inorder(root.left       )
		print(root.value				,     end=""","""       )
		inorder(root.right       )





def 						__A						(      __lowerCamelCase				,     __lowerCamelCase       ) ->			Node | None:
	for arg in args.split():
		if arg[0] == "+":
			a									=				insert(__lowerCamelCase				,     int(arg[1:]       )       )

		elif arg[0] == "-":
			a									=				erase(__lowerCamelCase				,     int(arg[1:]       )       )

		else:
			print("""Unknown command"""       )

	return root





def 						__A						(      ) ->			None:
	a									=				None
	print(
	    """enter numbers to create a tree, + value to add value into treap, """
	    """- value to erase all nodes with value. 'q' to quit. """       )

	a									=				input()
	while args != "q":
		a									=				interact_treap(__lowerCamelCase				,     __lowerCamelCase       )
		print(__lowerCamelCase       )
		a									=				input()

	print("""good by!"""       )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		main()







from math import factorial, radians





def 						__A						(      __lowerCamelCase				,     __lowerCamelCase = 18				,     __lowerCamelCase = 10       ) ->			float:
	a									=				angle_in_degrees - ((angle_in_degrees // 360.0) * 360.0)

	# Converting from degrees to radians
	a									=				radians(__lowerCamelCase       )

	a									=				angle_in_radians
	a									=				3
	a									=				-1

	for _ in range(__lowerCamelCase       ):
		result += (b * (angle_in_radians**a)) / factorial(__lowerCamelCase       )

		a									=				-b  # One positive term and the next will be negative and so on...
		a += 2  # Increased by 2 for every term.

	return round(__lowerCamelCase				,     __lowerCamelCase       )


if __name__ == "__main__":
		__import__("doctest").testmod()

