






"""simple docstring"""
from __future__ import annotations

from random import random







class     UpperCamelCase_ :





	def __init__(   self      :				int			,			lowerCAmelCase_      :				int | None = None		)		->    Union[str, Any]:
				UpperCAmelCase_  :				Union[str, Any]      =      value
				UpperCAmelCase_  :				Tuple      =      random()
				UpperCAmelCase_  :				Node | None      =      None
				UpperCAmelCase_  :				Node | None      =      None





	def __repr__(   self      :				int		)		->    str:
				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      :				str		)		->    str:
				UpperCAmelCase_  :				int      =      str(self.value		) + " "
				UpperCAmelCase_  :				Tuple      =      str(self.left or ""		)
				UpperCAmelCase_  :				List[Any]      =      str(self.right or ""		)
				return value + left + right





def        snake_case   (     A__			,A__		):
			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:
									UpperCAmelCase_  ,			UpperCAmelCase_  :				str      =      split(root.left			,A__		)
									return left, root
						else:
									UpperCAmelCase_  ,			UpperCAmelCase_  :				str      =      split(root.right			,A__		)
									return root, right

def        snake_case   (     A__			,A__		):
			if (not left) or (not right):  # If one node is None, return the other
						return left or right
			elif left.prior < right.prior:
						UpperCAmelCase_  :				Tuple      =      merge(left.right			,A__		)
						return left
			else:
						UpperCAmelCase_  :				Any      =      merge(A__			,right.left		)
						return right

def        snake_case   (     A__			,A__		):
			UpperCAmelCase_  :				Any      =      Node(A__		)
			UpperCAmelCase_  ,			UpperCAmelCase_  :				Optional[int]      =      split(A__			,A__		)
			return merge(merge(A__			,A__		)			,A__		)

def        snake_case   (     A__			,A__		):
			UpperCAmelCase_  ,			UpperCAmelCase_  :				Tuple      =      split(A__			,value - 1		)
			UpperCAmelCase_  ,			UpperCAmelCase_  :				Tuple      =      split(A__			,A__		)
			return merge(A__			,A__		)

def        snake_case   (     A__		):
			if not root:  # None
						return
			else:
						inorder(root.left		)
						print(root.value			,end=","		)
						inorder(root.right		)

def        snake_case   (     A__			,A__		):
			for arg in args.split():
						if arg[0] == "+":
									UpperCAmelCase_  :				List[Any]      =      insert(A__			,int(arg[1:]		)		)

						elif arg[0] == "-":
									UpperCAmelCase_  :				Optional[Any]      =      erase(A__			,int(arg[1:]		)		)

						else:
									print("Unknown command"		)

			return root

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

			UpperCAmelCase_  :				List[str]      =      input()
			while args != "q":
						UpperCAmelCase_  :				List[Any]      =      interact_treap(A__			,A__		)
						print(A__		)
						UpperCAmelCase_  :				Tuple      =      input()

			print("good by!"		)


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			main()











"""simple docstring"""
lowerCamelCase_       			=   {
    '''a''': '''AAAAA''',
    '''b''': '''AAAAB''',
    '''c''': '''AAABA''',
    '''d''': '''AAABB''',
    '''e''': '''AABAA''',
    '''f''': '''AABAB''',
    '''g''': '''AABBA''',
    '''h''': '''AABBB''',
    '''i''': '''ABAAA''',
    '''j''': '''BBBAA''',
    '''k''': '''ABAAB''',
    '''l''': '''ABABA''',
    '''m''': '''ABABB''',
    '''n''': '''ABBAA''',
    '''o''': '''ABBAB''',
    '''p''': '''ABBBA''',
    '''q''': '''ABBBB''',
    '''r''': '''BAAAA''',
    '''s''': '''BAAAB''',
    '''t''': '''BAABA''',
    '''u''': '''BAABB''',
    '''v''': '''BBBAB''',
    '''w''': '''BABAA''',
    '''x''': '''BABAB''',
    '''y''': '''BABBA''',
    '''z''': '''BABBB''',
    ''' ''': ''' ''',
}


lowerCamelCase_       			=   {value: key for key, value in encode_dict.items()}

def        snake_case   (     A__		):
			UpperCAmelCase_  :				Union[str, Any]      =      ""
			for letter in word.lower():
						if letter.isalpha() or letter == " ":
									encoded += encode_dict[letter]
						else:
									raise Exception("encode() accepts only letters of the alphabet and spaces"		)
			return encoded

def        snake_case   (     A__		):
			if set(A__		) - {"A", "B", " "} != set():
						raise Exception("decode() accepts only 'A', 'B' and spaces"		)
			UpperCAmelCase_  :				Dict      =      ""
			for word in coded.split():
						while len(A__		) != 0:
									decoded += decode_dict[word[:5]]
									UpperCAmelCase_  :				str      =      word[5:]
						decoded += " "
			return decoded.strip()


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

			testmod()



