





'''simple docstring'''




from __future__ import annotations

import math
import random
from typing import Any


class 			SCREAMING_SNAKE_CASE   :


     def __init__(						self):

          '''simple docstring'''






          __A						:			list[Any]								=	[]
          __A						:			int								=	0
          __A						:			int								=	0


     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          return self.head == self.tail


     def 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase):

          '''simple docstring'''






          self.data.append(__lowercase)
          __A						:			Tuple								=	self.tail + 1


     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          __A						:			int								=	self.data[self.head]
          __A						:			List[Any]								=	self.head + 1
          return ret


     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          return self.tail - self.head


     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          print(self.data)
          print('**************')
          print(self.data[self.head : self.tail])




class 			SCREAMING_SNAKE_CASE   :


     def __init__(						self						,     _UpperCAmelCase):

          '''simple docstring'''






          __A						:			List[Any]								=	data
          __A						:			MyNode | None								=	None
          __A						:			MyNode | None								=	None
          __A						:			int								=	1


     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          return self.data


     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          return self.left


     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          return self.right


     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          return self.height


     def 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase):

          '''simple docstring'''






          __A						:			str								=	data


     def 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase):

          '''simple docstring'''






          __A						:			str								=	node


     def 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase):

          '''simple docstring'''






          __A						:			Any								=	node


     def 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase):

          '''simple docstring'''






          __A						:			int								=	height






def 	_lowerCAmelCase      (  __snake_case  :			str      )					->					Optional[int]:







     if node is None:
          return 0
     return node.get_height()






def 	_lowerCAmelCase      (  __snake_case  :			int			,							__snake_case  :			List[Any]      )					->					Any:







     if a > b:
          return a
     return b






def 	_lowerCAmelCase      (  __snake_case  :			str      )					->					Union[str, Any]:
     print('left rotation node:'			,							node.get_data()      )
     __A						:			Union[str, Any]								=	node.get_left()
     assert ret is not None
     node.set_left(ret.get_right()      )
     ret.set_right(__snake_case      )
     __A						:			List[Any]								=	my_max(get_height(node.get_right()      )			,							get_height(node.get_left()      )      ) + 1
     node.set_height(__snake_case      )
     __A						:			Any								=	my_max(get_height(ret.get_right()      )			,							get_height(ret.get_left()      )      ) + 1
     ret.set_height(__snake_case      )
     return ret






def 	_lowerCAmelCase      (  __snake_case  :			Optional[Any]      )					->					int:
     print('right rotation node:'			,							node.get_data()      )
     __A						:			Union[str, Any]								=	node.get_right()
     assert ret is not None
     node.set_right(ret.get_left()      )
     ret.set_left(__snake_case      )
     __A						:			Dict								=	my_max(get_height(node.get_right()      )			,							get_height(node.get_left()      )      ) + 1
     node.set_height(__snake_case      )
     __A						:			List[Any]								=	my_max(get_height(ret.get_right()      )			,							get_height(ret.get_left()      )      ) + 1
     ret.set_height(__snake_case      )
     return ret






def 	_lowerCAmelCase      (  __snake_case  :			Union[str, Any]      )					->					Dict:
     __A						:			List[Any]								=	node.get_left()
     assert left_child is not None
     node.set_left(left_rotation(__snake_case      )      )
     return right_rotation(__snake_case      )






def 	_lowerCAmelCase      (  __snake_case  :			str      )					->					Dict:
     __A						:			List[Any]								=	node.get_right()
     assert right_child is not None
     node.set_right(right_rotation(__snake_case      )      )
     return left_rotation(__snake_case      )






def 	_lowerCAmelCase      (  __snake_case  :			Dict			,							__snake_case  :			Tuple      )					->					Optional[int]:







     if node is None:
          return MyNode(__snake_case      )
     if data < node.get_data():
          node.set_left(insert_node(node.get_left()			,							__snake_case      )      )
          if (
              get_height(node.get_left()      ) - get_height(node.get_right()      ) == 2
          ):  # an unbalance detected
               __A						:			Any								=	node.get_left()
               assert left_child is not None
               if (
                   data < left_child.get_data()
               ):  # new node is the left child of the left child
                    __A						:			str								=	right_rotation(__snake_case      )
               else:
                    __A						:			List[str]								=	lr_rotation(__snake_case      )
     else:
          node.set_right(insert_node(node.get_right()			,							__snake_case      )      )
          if get_height(node.get_right()      ) - get_height(node.get_left()      ) == 2:
               __A						:			Union[str, Any]								=	node.get_right()
               assert right_child is not None
               if data < right_child.get_data():
                    __A						:			Optional[Any]								=	rl_rotation(__snake_case      )
               else:
                    __A						:			str								=	left_rotation(__snake_case      )
     __A						:			str								=	my_max(get_height(node.get_right()      )			,							get_height(node.get_left()      )      ) + 1
     node.set_height(__snake_case      )
     return node






def 	_lowerCAmelCase      (  __snake_case  :			int      )					->					List[str]:







     while True:
          __A						:			List[str]								=	root.get_right()
          if right_child is None:
               break
          __A						:			Optional[int]								=	right_child
     return root.get_data()






def 	_lowerCAmelCase      (  __snake_case  :			List[Any]      )					->					int:







     while True:
          __A						:			Dict								=	root.get_left()
          if left_child is None:
               break
          __A						:			Dict								=	left_child
     return root.get_data()






def 	_lowerCAmelCase      (  __snake_case  :			Any			,							__snake_case  :			int      )					->					str:
     __A						:			Union[str, Any]								=	root.get_left()
     __A						:			Any								=	root.get_right()
     if root.get_data() == data:
          if left_child is not None and right_child is not None:
               __A						:			Tuple								=	get_left_most(__snake_case      )
               root.set_data(__snake_case      )
               root.set_right(del_node(__snake_case			,							__snake_case      )      )
          elif left_child is not None:
               __A						:			Optional[Any]								=	left_child
          elif right_child is not None:
               __A						:			List[Any]								=	right_child
          else:
               return None
     elif root.get_data() > data:
          if left_child is None:
               print('No such data'      )
               return root
          else:
               root.set_left(del_node(__snake_case			,							__snake_case      )      )
     else:  # root.get_data() < data
          if right_child is None:
               return root
          else:
               root.set_right(del_node(__snake_case			,							__snake_case      )      )

     if get_height(__snake_case      ) - get_height(__snake_case      ) == 2:
          assert right_child is not None
          if get_height(right_child.get_right()      ) > get_height(right_child.get_left()      ):
               __A						:			Union[str, Any]								=	left_rotation(__snake_case      )
          else:
               __A						:			Optional[Any]								=	rl_rotation(__snake_case      )
     elif get_height(__snake_case      ) - get_height(__snake_case      ) == -2:
          assert left_child is not None
          if get_height(left_child.get_left()      ) > get_height(left_child.get_right()      ):
               __A						:			List[str]								=	right_rotation(__snake_case      )
          else:
               __A						:			List[Any]								=	lr_rotation(__snake_case      )
     __A						:			Optional[Any]								=	my_max(get_height(root.get_right()      )			,							get_height(root.get_left()      )      ) + 1
     root.set_height(__snake_case      )
     return root


class 			SCREAMING_SNAKE_CASE   :


     def __init__(						self):

          '''simple docstring'''






          __A						:			MyNode | None								=	None


     def 							SCREAMING_SNAKE_CASE  (						self):

          '''simple docstring'''






          return get_height(self.root)


     def 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase):

          '''simple docstring'''






          print('insert:' + str(__lowercase))
          __A						:			Union[str, Any]								=	insert_node(self.root						,     __lowercase)


     def 							SCREAMING_SNAKE_CASE  (						self						,     _UpperCAmelCase):

          '''simple docstring'''






          print('delete:' + str(__lowercase))
          if self.root is None:
               print('Tree is empty!')
               return
          __A						:			List[str]								=	del_node(self.root						,     __lowercase)


     def __str__(						self						,     ):  # a level traversale, gives a more intuitive look on the tree

          '''simple docstring'''






          __A						:			Optional[int]								=	''''''
          __A						:			int								=	MyQueue()
          q.push(self.root)
          __A						:			List[Any]								=	self.get_height()
          if layer == 0:
               return output
          __A						:			Tuple								=	0
          while not q.is_empty():
               __A						:			int								=	q.pop()
               __A						:			List[Any]								=	''' ''' * int(math.pow(2						,     layer - 1))
               output += space
               if node is None:
                    output += "*"
                    q.push(__lowercase)
                    q.push(__lowercase)
               else:
                    output += str(node.get_data())
                    q.push(node.get_left())
                    q.push(node.get_right())
               output += space
               __A						:			Union[str, Any]								=	cnt + 1
               for i in range(100):
                    if cnt == math.pow(2						,     __lowercase) - 1:
                         __A						:			int								=	layer - 1
                         if layer == 0:
                              output += "\n*************************************"
                              return output
                         output += "\n"
                         break
          output += "\n*************************************"
          return output






def 	_lowerCAmelCase      (  )					->					Dict:
     import doctest

     doctest.testmod()


if __name__ == "__main__":
  _test()
  lowercase__   :				Any      =   AVLtree()
  lowercase__   :				Optional[Any]      =   list(range(10))
  random.shuffle(lst)
  for i in lst:
    t.insert(i)
    print(str(t))
  random.shuffle(lst)
  for i in lst:
    t.del_node(i)
    print(str(t))






'''simple docstring'''




from __future__ import annotations






def 	_lowerCAmelCase      (  __snake_case  :			list[int | str]      )					->					None:
     create_state_space_tree(__snake_case			,							[]			,							0			,							[0 for i in range(len(__snake_case      )      )]      )






def 	_lowerCAmelCase      (  __snake_case  :			list[int | str]			,							__snake_case  :			list[int | str]			,							__snake_case  :			int			,							__snake_case  :			list[int]			,							)					->					None:

     if index == len(__snake_case      ):
          print(__snake_case      )
          return

     for i in range(len(__snake_case      )      ):
          if not index_used[i]:
               current_sequence.append(sequence[i]      )
               __A						:			Any								=	True
               create_state_space_tree(__snake_case			,							__snake_case			,							index + 1			,							__snake_case      )
               current_sequence.pop()
               __A						:			Any								=	False
lowercase__   :				list[int | str]      =   [3, 1, 2, 4]
generate_all_permutations(sequence)

lowercase__   :				list[int | str]      =   ["A", "B", "C"]







generate_all_permutations(sequence_a)