

from collections.abc import Iterable
from typing import Any


class        _SCREAMING_SNAKE_CASE	:







						def __init__(       self			,		_SCREAMING_SNAKE_CASE = None				)->				Optional[int]:
													lowerCamelCase_				     =value
													lowerCamelCase_				     =None  # Added in order to delete a node easier
													lowerCamelCase_				     =None
													lowerCamelCase_				     =None







						def __repr__(       self				)->				str:
													from pprint import pformat

													if self.left is None and self.right is None:
																				return str(self.value				)
													return pformat({f'{self.value}': (self.left, self.right)}			,		indent=1				)


class        _SCREAMING_SNAKE_CASE	:







						def __init__(       self			,		_SCREAMING_SNAKE_CASE = None				)->				Optional[Any]:
													lowerCamelCase_				     =root







						def __str__(       self				)->				str:
													return str(self.root				)







						def     _snake_case							(       self			,		_SCREAMING_SNAKE_CASE			,		_SCREAMING_SNAKE_CASE				)->				None:



													if new_children is not None:  # reset its kids
																				lowerCamelCase_				     =node.parent
													if node.parent is not None:  # reset its parent
																				if self.is_right(_SCREAMING_SNAKE_CASE				):  # If it is the right children
																											lowerCamelCase_				     =new_children
																				else:
																											lowerCamelCase_				     =new_children
													else:
																				lowerCamelCase_				     =new_children







						def     _snake_case							(       self			,		_SCREAMING_SNAKE_CASE				)->				bool:



													if node.parent and node.parent.right:
																				return node == node.parent.right
													return False







						def     _snake_case							(       self				)->				bool:
													return self.root is None







						def     _snake_case							(       self			,		_SCREAMING_SNAKE_CASE				)->				None:
													lowerCamelCase_				     =Node(_SCREAMING_SNAKE_CASE				)  # create a new Node
													if self.empty():  # if Tree is empty
																				lowerCamelCase_				     =new_node  # set its root
													else:  # Tree is not empty
																				lowerCamelCase_				     =self.root  # from root
																				if parent_node is None:
																											return
																				while True:  # While we don't get to a leaf
																											if value < parent_node.value:  # We go left
																																		if parent_node.left is None:
																																									lowerCamelCase_				     =new_node  # We insert the new node in a leaf
																																									break
																																		else:
																																									lowerCamelCase_				     =parent_node.left
																											else:
																																		if parent_node.right is None:
																																									lowerCamelCase_				     =new_node
																																									break
																																		else:
																																									lowerCamelCase_				     =parent_node.right
																				lowerCamelCase_				     =parent_node







						def     _snake_case							(       self			,		*_SCREAMING_SNAKE_CASE				)->				None:



													for value in values:
																				self.__insert(_SCREAMING_SNAKE_CASE				)







						def     _snake_case							(       self			,		_SCREAMING_SNAKE_CASE				)->				Node | None:



													if self.empty():
																				raise IndexError("""Warning: Tree is empty! please use another."""				)
													else:
																				lowerCamelCase_				     =self.root
																				# use lazy evaluation here to avoid NoneType Attribute error
																				while node is not None and node.value is not value:
																											lowerCamelCase_				     =node.left if value < node.value else node.right
																				return node







						def     _snake_case							(       self			,		_SCREAMING_SNAKE_CASE = None				)->				Node | None:



													if node is None:
																				if self.root is None:
																											return None
																				lowerCamelCase_				     =self.root

													if not self.empty():
																				while node.right is not None:
																											lowerCamelCase_				     =node.right
													return node







						def     _snake_case							(       self			,		_SCREAMING_SNAKE_CASE = None				)->				Node | None:



													if node is None:
																				lowerCamelCase_				     =self.root
													if self.root is None:
																				return None
													if not self.empty():
																				lowerCamelCase_				     =self.root
																				while node.left is not None:
																											lowerCamelCase_				     =node.left
													return node







						def     _snake_case							(       self			,		_SCREAMING_SNAKE_CASE				)->				None:
													lowerCamelCase_				     =self.search(_SCREAMING_SNAKE_CASE				)  # Look for the node with that label
													if node is not None:
																				if node.left is None and node.right is None:  # If it has no children
																											self.__reassign_nodes(_SCREAMING_SNAKE_CASE			,		_SCREAMING_SNAKE_CASE				)
																				elif node.left is None:  # Has only right children
																											self.__reassign_nodes(_SCREAMING_SNAKE_CASE			,		node.right				)
																				elif node.right is None:  # Has only left children
																											self.__reassign_nodes(_SCREAMING_SNAKE_CASE			,		node.left				)
																				else:
																											lowerCamelCase_				     =self.get_max(
																											    node.left				)  # Gets the max value of the left branch
																											self.remove(tmp_node.value				)  # type: ignore
																											lowerCamelCase_				     =(
																											    tmp_node.value  # type: ignore
																											)  # Assigns the value to the node to delete and keep tree structure







						def     _snake_case							(       self			,		_SCREAMING_SNAKE_CASE				)->				Iterable:



													if node is not None:
																				yield node  # Preorder Traversal
																				yield from self.preorder_traverse(node.left				)
																				yield from self.preorder_traverse(node.right				)







						def     _snake_case							(       self			,		_SCREAMING_SNAKE_CASE=None				)->				Any:



													if traversal_function is None:
																				return self.preorder_traverse(self.root				)
													else:
																				return traversal_function(self.root				)







						def     _snake_case							(       self			,		_SCREAMING_SNAKE_CASE			,		_SCREAMING_SNAKE_CASE				)->				None:



													if node:
																				self.inorder(_SCREAMING_SNAKE_CASE			,		node.left				)
																				arr.append(node.value				)
																				self.inorder(_SCREAMING_SNAKE_CASE			,		node.right				)







						def     _snake_case							(       self			,		_SCREAMING_SNAKE_CASE			,		_SCREAMING_SNAKE_CASE				)->				int:
													lowerCamelCase_				     =[]
													self.inorder(_SCREAMING_SNAKE_CASE			,		_SCREAMING_SNAKE_CASE				)  # append all values to list using inorder traversal
													return arr[k - 1]




def     __UpperCamelCase			(	_A :				Optional[int]						)							->Optional[Any]:



							"""simple docstring"""
							lowerCamelCase_				     =[]
							if curr_node is not None:
														lowerCamelCase_				     =postorder(curr_node.left						) + postorder(curr_node.right						) + [curr_node]
							return node_list




def     __UpperCamelCase			(	)							->int:



							"""simple docstring"""
							lowerCamelCase_				     =(8, 3, 6, 1, 10, 14, 13, 4, 7)
							lowerCamelCase_				     =BinarySearchTree()
							for i in testlist:
														t.insert(__A						)

							# Prints all the elements of the list in order traversal
							print(__A						)

							if t.search(6						) is not None:
														print("""The value 6 exists"""						)
							else:
														print("""The value 6 doesn\'t exist"""						)

							if t.search(-1						) is not None:
														print("""The value -1 exists"""						)
							else:
														print("""The value -1 doesn\'t exist"""						)

							if not t.empty():
														print("""Max Value: """	,   t.get_max().value						)  # type: ignore
														print("""Min Value: """	,   t.get_min().value						)  # type: ignore

							for i in testlist:
														t.remove(__A						)
														print(__A						)


if __name__ == "__main__":
	import doctest

	doctest.testmod(verbose=True)





'''simple docstring'''





import random




def lowerCAmelCase  (__A):



     """simple docstring"""



     _a      =  num - 1
     _a      =  0

     while s % 2 == 0:
          _a      =  s // 2
          t += 1

     for _ in range(5):
          _a      =  random.randrange(2  ,	num - 1)
          _a      =  pow(__A  ,	__A  ,	__A)
          if v != 1:
               _a      =  0
               while v != (num - 1):
                    if i == t - 1:
                         return False
                    else:
                         _a      =  i + 1
                         _a      =  (v**2) % num
     return True




def lowerCAmelCase  (__A):



     """simple docstring"""



     if num < 2:
          return False

     _a      =  [
         2,
         3,
         5,
         7,
         11,
         13,
         17,
         19,
         23,
         29,
         31,
         37,
         41,
         43,
         47,
         53,
         59,
         61,
         67,
         71,
         73,
         79,
         83,
         89,
         97,
         101,
         103,
         107,
         109,
         113,
         127,
         131,
         137,
         139,
         149,
         151,
         157,
         163,
         167,
         173,
         179,
         181,
         191,
         193,
         197,
         199,
         211,
         223,
         227,
         229,
         233,
         239,
         241,
         251,
         257,
         263,
         269,
         271,
         277,
         281,
         283,
         293,
         307,
         311,
         313,
         317,
         331,
         337,
         347,
         349,
         353,
         359,
         367,
         373,
         379,
         383,
         389,
         397,
         401,
         409,
         419,
         421,
         431,
         433,
         439,
         443,
         449,
         457,
         461,
         463,
         467,
         479,
         487,
         491,
         499,
         503,
         509,
         521,
         523,
         541,
         547,
         557,
         563,
         569,
         571,
         577,
         587,
         593,
         599,
         601,
         607,
         613,
         617,
         619,
         631,
         641,
         643,
         647,
         653,
         659,
         661,
         673,
         677,
         683,
         691,
         701,
         709,
         719,
         727,
         733,
         739,
         743,
         751,
         757,
         761,
         769,
         773,
         787,
         797,
         809,
         811,
         821,
         823,
         827,
         829,
         839,
         853,
         857,
         859,
         863,
         877,
         881,
         883,
         887,
         907,
         911,
         919,
         929,
         937,
         941,
         947,
         953,
         967,
         971,
         977,
         983,
         991,
         997,
     ]

     if num in low_primes:
          return True

     for prime in low_primes:
          if (num % prime) == 0:
               return False

     return rabin_miller(__A)




def lowerCAmelCase  (__A = 1_024):



     """simple docstring"""



     while True:
          _a      =  random.randrange(2 ** (keysize - 1)  ,	2 ** (keysize))
          if is_prime_low_num(__A):
               return num


if __name__ == "__main__":
  lowercase_		       =  generate_large_prime()
  print(("Prime number:", num))
  print(("is_prime_low_num:", is_prime_low_num(num)))



