




'''simple docstring'''





from __future__ import annotations

from collections import defaultdict
from dataclasses import dataclass

@dataclass
class    _a				:
     SCREAMING_SNAKE_CASE_							:    int    				=						42
     SCREAMING_SNAKE_CASE_							:    Union[str, Any]    				=						None
     SCREAMING_SNAKE_CASE_							:    Union[str, Any]    				=						None







def 	__a	(   )						-> TreeNode:

     """simple docstring"""




     return TreeNode(3					,						TreeNode(9    )					,						TreeNode(20					,						TreeNode(15    )					,						TreeNode(7    )    )    )





def 	__a	(   _UpperCamelCase:    str    )						-> list[int]:

     """simple docstring"""




     def depth_first_search(
         _UpperCamelCase:    Optional[Any]					,						_UpperCamelCase:    Union[str, Any]					,						_UpperCamelCase:    Optional[int]    ) -> None:
          if not root:
               return

          if depth == len(__lowercase    ):
               right_view.append(root.val    )

          depth_first_search(root.right					,						depth + 1					,						__lowercase    )
          depth_first_search(root.left					,						depth + 1					,						__lowercase    )

     _snake_case							=      []
     if not root:
          return right_view

     depth_first_search(__lowercase					,						0					,						__lowercase    )
     return right_view





def 	__a	(   _UpperCamelCase:    Any    )						-> list[int]:

     """simple docstring"""




     def depth_first_search(
         _UpperCamelCase:    int					,						_UpperCamelCase:    Dict					,						_UpperCamelCase:    Optional[Any]    ) -> None:
          if not root:
               return

          if depth == len(__lowercase    ):
               left_view.append(root.val    )

          depth_first_search(root.left					,						depth + 1					,						__lowercase    )
          depth_first_search(root.right					,						depth + 1					,						__lowercase    )

     _snake_case							=      []
     if not root:
          return left_view

     depth_first_search(__lowercase					,						0					,						__lowercase    )
     return left_view





def 	__a	(   _UpperCamelCase:    Dict    )						-> list[int]:

     """simple docstring"""




     def breadth_first_search(_UpperCamelCase:    Optional[Any]					,						_UpperCamelCase:    Tuple    ) -> None:
          _snake_case							=      [(root, 0)]
          _snake_case							=      defaultdict(__lowercase    )

          while queue:
               _snake_case							=      queue.pop(0    )
               _snake_case							,					_snake_case							=      first

               lookup[hd].append(node.val    )

               if node.left:
                    queue.append((node.left, hd - 1)    )
               if node.right:
                    queue.append((node.right, hd + 1)    )

          for pair in sorted(lookup.items()					,						key=lambda _UpperCamelCase    : each[0]    ):
               top_view.append(pair[1][0]    )

     _snake_case							=      []
     if not root:
          return top_view

     breadth_first_search(__lowercase					,						__lowercase    )
     return top_view





def 	__a	(   _UpperCamelCase:    Union[str, Any]    )						-> list[int]:

     """simple docstring"""




     from collections import defaultdict

     def breadth_first_search(_UpperCamelCase:    List[str]					,						_UpperCamelCase:    int    ) -> None:
          _snake_case							=      [(root, 0)]
          _snake_case							=      defaultdict(__lowercase    )

          while queue:
               _snake_case							=      queue.pop(0    )
               _snake_case							,					_snake_case							=      first
               lookup[hd].append(node.val    )

               if node.left:
                    queue.append((node.left, hd - 1)    )
               if node.right:
                    queue.append((node.right, hd + 1)    )

          for pair in sorted(lookup.items()					,						key=lambda _UpperCamelCase    : each[0]    ):
               bottom_view.append(pair[1][-1]    )

     _snake_case							=      []
     if not root:
          return bottom_view

     breadth_first_search(__lowercase					,						__lowercase    )
     return bottom_view


if __name__ == "__main__":
   import doctest

   doctest.testmod()






"""simple docstring"""


import math
from decimal import Decimal, getcontext






def    a__       ( __lowercase = 400_0000      )		->		int:

				try:
								_A         =	int(__lowercase      )
				except (TypeError, ValueError):
								raise TypeError("Parameter n must be int or castable to int."      )
				if n <= 0:
								raise ValueError("Parameter n must be greater than or equal to one."      )
				_A         =	100
				_A         =	(Decimal(5      ) ** Decimal(0.5      ) + 1) / Decimal(2      )

				_A         =	(math.floor(math.log(n * (phi + 2)   ,	__lowercase      ) - 1      ) // 3) * 3 + 2
				_A         =	Decimal(round(phi ** Decimal(index + 1      )      )      ) / (phi + 2)
				_A         =	num // 2
				return int(__lowercase      )


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