





'''simple docstring'''




from __future__ import annotations

from collections import deque
from collections.abc import Sequence
from dataclasses import dataclass
from typing import Any


@dataclass
class 			SCREAMING_SNAKE_CASE   :
     lowerCAmelCase		      =	42
     lowerCAmelCase		      =	None
     lowerCAmelCase		      =	None






def 	_lowerCAmelCase      (  )					->					Node | None:
     __A						:			List[Any]								=	Node(1      )
     __A						:			Dict								=	Node(2      )
     __A						:			Optional[int]								=	Node(3      )
     __A						:			str								=	Node(4      )
     __A						:			Optional[Any]								=	Node(5      )
     return tree






def 	_lowerCAmelCase      (  __snake_case  :			Node | None      )					->					list[int]:
     return [root.data, *preorder(root.left      ), *preorder(root.right      )] if root else []






def 	_lowerCAmelCase      (  __snake_case  :			Node | None      )					->					list[int]:
     return postorder(root.left      ) + postorder(root.right      ) + [root.data] if root else []






def 	_lowerCAmelCase      (  __snake_case  :			Node | None      )					->					list[int]:
     return [*inorder(root.left      ), root.data, *inorder(root.right      )] if root else []






def 	_lowerCAmelCase      (  __snake_case  :			Node | None      )					->					int:
     return (max(height(root.left      )			,							height(root.right      )      ) + 1) if root else 0






def 	_lowerCAmelCase      (  __snake_case  :			Node | None      )					->					Sequence[Node | None]:
     __A						:			list[Any]								=	[]

     if root is None:
          return output

     __A						:			Union[str, Any]								=	deque([root]      )

     while process_queue:
          __A						:			List[str]								=	process_queue.popleft()
          output.append(node.data      )

          if node.left:
               process_queue.append(node.left      )
          if node.right:
               process_queue.append(node.right      )
     return output






def 	_lowerCAmelCase      (  __snake_case  :			Node | None			,							__snake_case  :			int      )					->					Sequence[Node | None]:
     __A						:			list[Any]								=	[]

     def populate_output(__snake_case  :			Node | None			,							__snake_case  :			int      ) -> None:
          if not root:
               return
          if level == 1:
               output.append(root.data      )
          elif level > 1:
               populate_output(root.left			,							level - 1      )
               populate_output(root.right			,							level - 1      )

     populate_output(snake_case__			,							snake_case__      )
     return output






def 	_lowerCAmelCase      (  __snake_case  :			Node | None			,							__snake_case  :			int      )					->					Sequence[Node | None]:
     __A						:			list[Any]								=	[]

     def populate_output(__snake_case  :			Node | None			,							__snake_case  :			int      ) -> None:
          if root is None:
               return
          if level == 1:
               output.append(root.data      )
          elif level > 1:
               populate_output(root.right			,							level - 1      )
               populate_output(root.left			,							level - 1      )

     populate_output(snake_case__			,							snake_case__      )
     return output






def 	_lowerCAmelCase      (  __snake_case  :			Node | None      )					->					Sequence[Node | None] | list[Any]:
     if root is None:
          return []

     __A						:			list[Sequence[Node | None]]								=	[]

     __A						:			Union[str, Any]								=	0
     __A						:			List[str]								=	height(snake_case__      )

     for h in range(1			,							height_tree + 1      ):
          if not flag:
               output.append(get_nodes_from_left_to_right(snake_case__			,							snake_case__      )      )
               __A						:			Tuple								=	1
          else:
               output.append(get_nodes_from_right_to_left(snake_case__			,							snake_case__      )      )
               __A						:			Dict								=	0

     return output






def 	_lowerCAmelCase      (  )					->					None:  # Main function for testing.
     __A						:			List[str]								=	make_tree()
     print(f'In-order Traversal: {inorder(snake_case__      )}'      )
     print(f'Pre-order Traversal: {preorder(snake_case__      )}'      )
     print(f'Post-order Traversal: {postorder(snake_case__      )}'			,							'\n'      )

     print(f'Height of Tree: {height(snake_case__      )}'			,							'\n'      )

     print('Complete Level Order Traversal: '      )
     print(level_order(snake_case__      )			,							'\n'      )

     print('Level-wise order Traversal: '      )

     for level in range(1			,							height(snake_case__      ) + 1      ):
          print(f'Level {level}:'			,							get_nodes_from_left_to_right(snake_case__			,							level=snake_case__      )      )

     print('\nZigZag order Traversal: '      )
     print(zigzag(snake_case__      )      )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()






'''simple docstring'''




import itertools
import math






def 	_lowerCAmelCase      (  __snake_case  :			int      )					->					bool:

     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5			,							int(math.sqrt(__snake_case      ) + 1      )			,							6      ):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True






def 	_lowerCAmelCase      (  )					->					List[Any]:
     __A						:			Optional[Any]								=	2
     while True:
          if is_prime(__snake_case      ):
               yield num
          num += 1






def 	_lowerCAmelCase      (  __snake_case  :			int = 1_00_01      )					->					int:
     return next(itertools.islice(prime_generator()			,							nth - 1			,							__snake_case      )      )


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