from __future__ import annotations

import unittest
from collections.abc import Iterator

class 	_SCREAMING_SNAKE_CASE							:






  """simple docstring"""







  def __init__(			self    :				str  ,					__SCREAMING_SNAKE_CASE    :				Dict  ,					__SCREAMING_SNAKE_CASE    :				Union[str, Any]   ):






     """simple docstring"""
     _snake_case              =      label
     _snake_case              =      parent
     _snake_case              =      None
     _snake_case              =      None

class 	_SCREAMING_SNAKE_CASE							:






  """simple docstring"""







  def __init__(			self    :				List[str]   ):






     """simple docstring"""
     _snake_case              =      None



  def 				_a				(			self    :				Any   ):






     """simple docstring"""
     _snake_case              =      None



  def 				_a				(			self    :				str   ):






     """simple docstring"""
     return self.root is None



  def 				_a				(			self    :				List[Any]  ,					__SCREAMING_SNAKE_CASE    :				Tuple   ):






     """simple docstring"""
     _snake_case              =      self._put(self.root  ,					a_   )



  def 				_a				(			self    :				Any  ,					__SCREAMING_SNAKE_CASE    :				List[str]  ,					__SCREAMING_SNAKE_CASE    :				Any  ,					__SCREAMING_SNAKE_CASE    :				str = None   ):






     """simple docstring"""
     if node is None:
        _snake_case              =      Node(a_  ,					a_   )
     else:
        if label < node.label:
           _snake_case              =      self._put(node.left  ,					a_  ,					a_   )
        elif label > node.label:
           _snake_case              =      self._put(node.right  ,					a_  ,					a_   )
        else:
           _snake_case              =      F'Node with label {label} already exists'
           raise Exception(a_   )

     return node



  def 				_a				(			self    :				Dict  ,					__SCREAMING_SNAKE_CASE    :				Tuple   ):






     """simple docstring"""
     return self._search(self.root  ,					a_   )



  def 				_a				(			self    :				Union[str, Any]  ,					__SCREAMING_SNAKE_CASE    :				str  ,					__SCREAMING_SNAKE_CASE    :				Optional[int]   ):






     """simple docstring"""
     if node is None:
        _snake_case              =      F'Node with label {label} does not exist'
        raise Exception(a_   )
     else:
        if label < node.label:
           _snake_case              =      self._search(node.left  ,					a_   )
        elif label > node.label:
           _snake_case              =      self._search(node.right  ,					a_   )

     return node



  def 				_a				(			self    :				Any  ,					__SCREAMING_SNAKE_CASE    :				Dict   ):






     """simple docstring"""
     _snake_case              =      self.search(a_   )
     if node.right and node.left:
        _snake_case              =      self._get_lowest_node(node.right   )
        _snake_case              =      node.left
        _snake_case              =      node.right
        _snake_case              =      lowest_node
        if node.right:
           _snake_case              =      lowest_node
        self._reassign_nodes(a_  ,					a_   )
     elif not node.right and node.left:
        self._reassign_nodes(a_  ,					node.left   )
     elif node.right and not node.left:
        self._reassign_nodes(a_  ,					node.right   )
     else:
        self._reassign_nodes(a_  ,					a_   )



  def 				_a				(			self    :				List[str]  ,					__SCREAMING_SNAKE_CASE    :				Dict  ,					__SCREAMING_SNAKE_CASE    :				Optional[int]   ):






     """simple docstring"""
     if new_children:
        _snake_case              =      node.parent

     if node.parent:
        if node.parent.right == node:
           _snake_case              =      new_children
        else:
           _snake_case              =      new_children
     else:
        _snake_case              =      new_children



  def 				_a				(			self    :				Tuple  ,					__SCREAMING_SNAKE_CASE    :				Dict   ):






     """simple docstring"""
     if node.left:
        _snake_case              =      self._get_lowest_node(node.left   )
     else:
        _snake_case              =      node
        self._reassign_nodes(a_  ,					node.right   )

     return lowest_node



  def 				_a				(			self    :				int  ,					__SCREAMING_SNAKE_CASE    :				List[str]   ):






     """simple docstring"""
     try:
        self.search(a_   )
        return True
     except Exception:
        return False



  def 				_a				(			self    :				Optional[Any]   ):






     """simple docstring"""
     if self.root is None:
        raise Exception("Binary search tree is empty"   )

     _snake_case              =      self.root
     while node.right is not None:
        _snake_case              =      node.right

     return node.label



  def 				_a				(			self    :				str   ):






     """simple docstring"""
     if self.root is None:
        raise Exception("Binary search tree is empty"   )

     _snake_case              =      self.root
     while node.left is not None:
        _snake_case              =      node.left

     return node.label



  def 				_a				(			self    :				Tuple   ):






     """simple docstring"""
     return self._inorder_traversal(self.root   )



  def 				_a				(			self    :				Union[str, Any]  ,					__SCREAMING_SNAKE_CASE    :				List[str]   ):






     """simple docstring"""
     if node is not None:
        yield from self._inorder_traversal(node.left   )
        yield node
        yield from self._inorder_traversal(node.right   )



  def 				_a				(			self    :				Tuple   ):






     """simple docstring"""
     return self._preorder_traversal(self.root   )







  def 				_a				(			self    :				int  ,					__SCREAMING_SNAKE_CASE    :				Any   ):






     """simple docstring"""
     if node is not None:
        yield node
        yield from self._preorder_traversal(node.left   )
        yield from self._preorder_traversal(node.right   )

class 	_SCREAMING_SNAKE_CASE							(     unittest.TestCase							):






  """simple docstring"""







  @staticmethod
  def 				_a				(			):






     """simple docstring"""
     _snake_case              =      BinarySearchTree()
     t.put(8   )
     t.put(3   )
     t.put(6   )
     t.put(1   )
     t.put(10   )
     t.put(14   )
     t.put(13   )
     t.put(4   )
     t.put(7   )
     t.put(5   )

     return t



  def 				_a				(			self    :				Dict   ):






     """simple docstring"""
     _snake_case              =      BinarySearchTree()
     assert t.is_empty()

     t.put(8   )
     assert t.root is not None
     assert t.root.parent is None
     assert t.root.label == 8

     t.put(10   )
     assert t.root.right is not None
     assert t.root.right.parent == t.root
     assert t.root.right.label == 10

     t.put(3   )
     assert t.root.left is not None
     assert t.root.left.parent == t.root
     assert t.root.left.label == 3

     t.put(6   )
     assert t.root.left.right is not None
     assert t.root.left.right.parent == t.root.left
     assert t.root.left.right.label == 6

     t.put(1   )
     assert t.root.left.left is not None
     assert t.root.left.left.parent == t.root.left
     assert t.root.left.left.label == 1

     with self.assertRaises(a_   ):  # noqa: B017
        t.put(1   )



  def 				_a				(			self    :				List[str]   ):






     """simple docstring"""
     _snake_case              =      self._get_binary_search_tree()

     _snake_case              =      t.search(6   )
     assert node.label == 6

     _snake_case              =      t.search(13   )
     assert node.label == 13

     with self.assertRaises(a_   ):  # noqa: B017
        t.search(2   )



  def 				_a				(			self    :				Union[str, Any]   ):






     """simple docstring"""
     _snake_case              =      self._get_binary_search_tree()

     t.remove(13   )
     assert t.root is not None
     assert t.root.right is not None
     assert t.root.right.right is not None
     assert t.root.right.right.right is None
     assert t.root.right.right.left is None

     t.remove(7   )
     assert t.root.left is not None
     assert t.root.left.right is not None
     assert t.root.left.right.left is not None
     assert t.root.left.right.right is None
     assert t.root.left.right.left.label == 4

     t.remove(6   )
     assert t.root.left.left is not None
     assert t.root.left.right.right is not None
     assert t.root.left.left.label == 1
     assert t.root.left.right.label == 4
     assert t.root.left.right.right.label == 5
     assert t.root.left.right.left is None
     assert t.root.left.left.parent == t.root.left
     assert t.root.left.right.parent == t.root.left

     t.remove(3   )
     assert t.root is not None
     assert t.root.left.label == 4
     assert t.root.left.right.label == 5
     assert t.root.left.left.label == 1
     assert t.root.left.parent == t.root
     assert t.root.left.left.parent == t.root.left
     assert t.root.left.right.parent == t.root.left

     t.remove(4   )
     assert t.root.left is not None
     assert t.root.left.left is not None
     assert t.root.left.label == 5
     assert t.root.left.right is None
     assert t.root.left.left.label == 1
     assert t.root.left.parent == t.root
     assert t.root.left.left.parent == t.root.left



  def 				_a				(			self    :				int   ):






     """simple docstring"""
     _snake_case              =      self._get_binary_search_tree()

     t.remove(3   )
     assert t.root is not None
     assert t.root.left is not None
     assert t.root.left.left is not None
     assert t.root.left.right is not None
     assert t.root.left.right.left is not None
     assert t.root.left.right.right is not None
     assert t.root.left.label == 4
     assert t.root.left.right.label == 6
     assert t.root.left.left.label == 1
     assert t.root.left.right.right.label == 7
     assert t.root.left.right.left.label == 5
     assert t.root.left.parent == t.root
     assert t.root.left.right.parent == t.root.left
     assert t.root.left.left.parent == t.root.left
     assert t.root.left.right.left.parent == t.root.left.right



  def 				_a				(			self    :				Tuple   ):






     """simple docstring"""
     _snake_case              =      self._get_binary_search_tree()
     t.empty()
     assert t.root is None



  def 				_a				(			self    :				List[str]   ):






     """simple docstring"""
     _snake_case              =      self._get_binary_search_tree()
     assert not t.is_empty()

     t.empty()
     assert t.is_empty()



  def 				_a				(			self    :				Any   ):






     """simple docstring"""
     _snake_case              =      self._get_binary_search_tree()

     assert t.exists(6   )
     assert not t.exists(-1   )



  def 				_a				(			self    :				Union[str, Any]   ):






     """simple docstring"""
     _snake_case              =      self._get_binary_search_tree()

     assert t.get_max_label() == 14

     t.empty()
     with self.assertRaises(a_   ):  # noqa: B017
        t.get_max_label()



  def 				_a				(			self    :				Any   ):






     """simple docstring"""
     _snake_case              =      self._get_binary_search_tree()

     assert t.get_min_label() == 1

     t.empty()
     with self.assertRaises(a_   ):  # noqa: B017
        t.get_min_label()



  def 				_a				(			self    :				List[Any]   ):






     """simple docstring"""
     _snake_case              =      self._get_binary_search_tree()

     _snake_case              =      [i.label for i in t.inorder_traversal()]
     assert inorder_traversal_nodes == [1, 3, 4, 5, 6, 7, 8, 10, 13, 14]







  def 				_a				(			self    :				str   ):






     """simple docstring"""
     _snake_case              =      self._get_binary_search_tree()

     _snake_case              =      [i.label for i in t.preorder_traversal()]
     assert preorder_traversal_nodes == [8, 3, 1, 6, 4, 5, 7, 10, 14, 13]






def    UpperCAmelCase__(						):



   """simple docstring"""





   _snake_case              =      BinarySearchTree()
   t.put(8  )
   t.put(3  )
   t.put(6  )
   t.put(1  )
   t.put(10  )
   t.put(14  )
   t.put(13  )
   t.put(4  )
   t.put(7  )
   t.put(5  )

   print(
       "\n            8\n           / \\\n          3   10\n         / \\    \\\n        1   6    14\n           / \\   /\n          4   7 13\n           \\\n            5\n        "  )

   print("Label 6 exists:"							,	t.exists(6  )  )
   print("Label 13 exists:"							,	t.exists(13  )  )
   print("Label -1 exists:"							,	t.exists(-1  )  )
   print("Label 12 exists:"							,	t.exists(12  )  )

   # Prints all the elements of the list in inorder traversal
   _snake_case              =      [i.label for i in t.inorder_traversal()]
   print("Inorder traversal:"							,	UpperCamelCase__  )

   # Prints all the elements of the list in preorder traversal
   _snake_case              =      [i.label for i in t.preorder_traversal()]
   print("Preorder traversal:"							,	UpperCamelCase__  )

   print("Max. label:"							,	t.get_max_label()  )
   print("Min. label:"							,	t.get_min_label()  )

   # Delete elements
   print("\nDeleting elements 13, 10, 8, 3, 6, 14"  )
   print(
       "\n          4\n         / \\\n        1   7\n             \\\n              5\n        "  )
   t.remove(13  )
   t.remove(10  )
   t.remove(8  )
   t.remove(3  )
   t.remove(6  )
   t.remove(14  )

   # Prints all the elements of the list in inorder traversal after delete
   _snake_case              =      [i.label for i in t.inorder_traversal()]
   print("Inorder traversal after delete:"							,	UpperCamelCase__  )

   # Prints all the elements of the list in preorder traversal after delete
   _snake_case              =      [i.label for i in t.preorder_traversal()]
   print("Preorder traversal after delete:"							,	UpperCamelCase__  )

   print("Max. label:"							,	t.get_max_label()  )
   print("Min. label:"							,	t.get_min_label()  )


if __name__ == "__main__":
   binary_search_tree_example()


from math import gcd






def    UpperCAmelCase__(						lowerCamelCase_ = 12000  ):



			"""simple docstring"""





			_snake_case              =      0
			for d in range(max_d + 1  ):
						for n in range(d // 3 + 1							,	(d + 1) // 2  ):
									if gcd(lowerCamelCase_							,	lowerCamelCase_  ) == 1:
												fractions_number += 1
			return fractions_number


if __name__ == "__main__":
			print(F"{solution() = }")

