


'''simple docstring'''




from __future__ import annotations

from collections import defaultdict
from dataclasses import dataclass




@dataclass
class  _lowercase   :
   _SCREAMING_SNAKE_CASE     :     int
   _SCREAMING_SNAKE_CASE     :     TreeNode | None									=  None
   _SCREAMING_SNAKE_CASE     :     TreeNode | None									=  None





def      _a		() -> TreeNode:






     """simple docstring"""
     return TreeNode(3       ,      TreeNode(9	)       ,      TreeNode(2_0       ,      TreeNode(1_5	)       ,      TreeNode(7	)	)	)





def      _a		(lowercase__ :      TreeNode	) -> list[int]:






     """simple docstring"""

     def depth_first_search(
         lowercase__ :      TreeNode | None       ,      lowercase__ :      int       ,      lowercase__ :      list[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		(lowercase__ :      TreeNode	) -> list[int]:






     """simple docstring"""

     def depth_first_search(
         lowercase__ :      TreeNode | None       ,      lowercase__ :      int       ,      lowercase__ :      list[int]	) -> 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		(lowercase__ :      TreeNode	) -> list[int]:






     """simple docstring"""

     def breadth_first_search(lowercase__ :      TreeNode       ,      lowercase__ :      list[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 lowercase__	: 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		(lowercase__ :      TreeNode	) -> list[int]:






     """simple docstring"""
     from collections import defaultdict

     def breadth_first_search(lowercase__ :      TreeNode       ,      lowercase__ :      list[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 lowercase__	: 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'''




_a      :      List[Any]       				=      [0.33, 0.44, 0.55, 0.44, 0.33]
_a      :      Union[str, Any]       				=      3
_a      :      Optional[Any]       				=      5

# Buffer Space (with Parameters Space)
_a      :      list[float]       				=      []
_a      :      list[float]       				=      []

# Machine Time
_a      :      str       				=      0





def      _a		(lowercase__ :      Optional[int]	) -> List[str]:






     """simple docstring"""
     global buffer_space, params_space, machine_time, K, m, t

     # Choosing Dynamical Systems (All)
     for key, value in enumerate(lowercase__	):
          # Evolution Parameter
          __snake_case    			=	float(seed / value	)

          # Control Theory: Orbit Change
          __snake_case    			=	(buffer_space[(key + 1) % m] + e) % 1

          # Control Theory: Trajectory Change
          __snake_case    			=	(params_space[key] + e) % 1 + 3

          # Modification (Transition Function) - Jumps
          __snake_case    			=	round(float(r * value * (1 - value)	)       ,      1_0	)
          __snake_case    			=	r  # Saving to Parameters Space

     # Logistic Map
     assert max(lowercase__	) < 1
     assert max(lowercase__	) < 4

     # Machine Time
     machine_time += 1





def      _a		() -> Tuple:






     """simple docstring"""
     global buffer_space, params_space, machine_time, K, m, t

     # PRNG (Xorshift by George Marsaglia)
     def xorshift(lowercase__ :      Tuple       ,      lowercase__ :      int	):
          x ^= y >> 1_3
          y ^= x << 1_7
          x ^= y >> 5
          return x

     # Choosing Dynamical Systems (Increment)
     __snake_case    			=	machine_time % m

     # Evolution (Time Length)
     for _ in range(0       ,      lowercase__	):
          # Variables (Position + Parameters)
          __snake_case    			=	params_space[key]
          __snake_case    			=	buffer_space[key]

          # Modification (Transition Function) - Flow
          __snake_case    			=	round(float(r * value * (1 - value)	)       ,      1_0	)
          __snake_case    			=	(machine_time * 0.01 + r * 1.01) % 1 + 3

     # Choosing Chaotic Data
     __snake_case    			=	int(buffer_space[(key + 2) % m] * (1_0**1_0)	)
     __snake_case    			=	int(buffer_space[(key - 2) % m] * (1_0**1_0)	)

     # Machine Time
     machine_time += 1

     return xorshift(lowercase__       ,      lowercase__	) % 0xF_F_F_F_F_F_F_F





def      _a		() -> List[str]:






     """simple docstring"""
     global buffer_space, params_space, machine_time, K, m, t

     __snake_case    			=	K
     __snake_case    			=	[0] * m
     __snake_case    			=	0


if __name__ == "__main__":
       # Initialization
       reset()

       # Pushing Data (Input)
       import random

       _a      :      Tuple       				=      random.sample(range(0xFFFF_FFFF), 100)
       for chunk in message:
              push(chunk)

       # for controlling
       _a      :      List[Any]       				=      ""

       # Pulling Data (Output)
       while inp in ("e", "E"):
              print(f'''{format(pull(), "#04x")}''')
              print(buffer_space)
              print(params_space)
              _a      :      List[str]       				=      input("(e)exit? ").strip()




