






"""simple docstring"""
from __future__ import annotations

import queue






class  _SCREAMING_SNAKE_CASE:




       def __init__(						self		,SCREAMING_SNAKE_CASE__							)      ->				str:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  data
             __SCREAMING_SNAKE_CASE       :List[str]		    =  None
             __SCREAMING_SNAKE_CASE       :Any		    =  None




def 					__lowerCamelCase       (							)      ->				Optional[int]:
      print('''\n********Press N to stop entering at any point of time********\n'''							)
      __SCREAMING_SNAKE_CASE       :Any		    =  input('''Enter the value of the root node: '''							).strip().lower()
      __SCREAMING_SNAKE_CASE       :queue.Queue		    =  queue.Queue()
      __SCREAMING_SNAKE_CASE       :Tuple		    =  TreeNode(int(_a							)							)
      q.put(_a							)
      while not q.empty():
            __SCREAMING_SNAKE_CASE       :Optional[int]		    =  q.get()
            __SCREAMING_SNAKE_CASE       :str		    =  f'''Enter the left node of {node_found.data}: '''
            __SCREAMING_SNAKE_CASE       :Tuple		    =  input(_a							).strip().lower() or """n"""
            if check == "n":
                  return tree_node
            __SCREAMING_SNAKE_CASE       :str		    =  TreeNode(int(_a							)							)
            __SCREAMING_SNAKE_CASE       :List[str]		    =  left_node
            q.put(_a							)
            __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  f'''Enter the right node of {node_found.data}: '''
            __SCREAMING_SNAKE_CASE       :Optional[int]		    =  input(_a							).strip().lower() or """n"""
            if check == "n":
                  return tree_node
            __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  TreeNode(int(_a							)							)
            __SCREAMING_SNAKE_CASE       :Dict		    =  right_node
            q.put(_a							)
      raise



def 					__lowerCamelCase       (							a_					:		TreeNode							)      ->				Dict:




      if not isinstance(_a			,       _a							) or not node:
            return
      print(node.data			,       end=''','''							)
      pre_order(node.left							)
      pre_order(node.right							)



def 					__lowerCamelCase       (							a_					:		TreeNode							)      ->				Union[str, Any]:




      if not isinstance(_a			,       _a							) or not node:
            return
      in_order(node.left							)
      print(node.data			,       end=''','''							)
      in_order(node.right							)



def 					__lowerCamelCase       (							a_					:		TreeNode							)      ->				int:




      if not isinstance(_a			,       _a							) or not node:
            return
      post_order(node.left							)
      post_order(node.right							)
      print(node.data			,       end=''','''							)



def 					__lowerCamelCase       (							a_					:		TreeNode							)      ->				Optional[Any]:




      if not isinstance(_a			,       _a							) or not node:
            return
      __SCREAMING_SNAKE_CASE       :queue.Queue		    =  queue.Queue()
      q.put(_a							)
      while not q.empty():
            __SCREAMING_SNAKE_CASE       :List[str]		    =  q.get()
            print(node_dequeued.data			,       end=''','''							)
            if node_dequeued.left:
                  q.put(node_dequeued.left							)
            if node_dequeued.right:
                  q.put(node_dequeued.right							)



def 					__lowerCamelCase       (							a_					:		TreeNode							)      ->				Dict:




      if not isinstance(_a			,       _a							) or not node:
            return
      __SCREAMING_SNAKE_CASE       :queue.Queue		    =  queue.Queue()
      q.put(_a							)
      while not q.empty():
            __SCREAMING_SNAKE_CASE       :Dict		    =  []
            while not q.empty():
                  __SCREAMING_SNAKE_CASE       :int		    =  q.get()
                  print(node_dequeued.data			,       end=''','''							)
                  if node_dequeued.left:
                        list_.append(node_dequeued.left							)
                  if node_dequeued.right:
                        list_.append(node_dequeued.right							)
            print()
            for node in list_:
                  q.put(_a							)



def 					__lowerCamelCase       (							a_					:		TreeNode							)      ->				List[str]:




      if not isinstance(_a			,       _a							) or not node:
            return
      __SCREAMING_SNAKE_CASE       :list[TreeNode]		    =  []
      __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  node
      while n or stack:
            while n:  # start from root node, find its left child
                  print(n.data			,       end=''','''							)
                  stack.append(_a							)
                  __SCREAMING_SNAKE_CASE       :str		    =  n.left
            # end of while means current node doesn't have left child
            __SCREAMING_SNAKE_CASE       :Tuple		    =  stack.pop()
            # start to traverse its right child
            __SCREAMING_SNAKE_CASE       :Any		    =  n.right



def 					__lowerCamelCase       (							a_					:		TreeNode							)      ->				Union[str, Any]:




      if not isinstance(_a			,       _a							) or not node:
            return
      __SCREAMING_SNAKE_CASE       :list[TreeNode]		    =  []
      __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  node
      while n or stack:
            while n:
                  stack.append(_a							)
                  __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  n.left
            __SCREAMING_SNAKE_CASE       :Dict		    =  stack.pop()
            print(n.data			,       end=''','''							)
            __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  n.right



def 					__lowerCamelCase       (							a_					:		TreeNode							)      ->				str:




      if not isinstance(_a			,       _a							) or not node:
            return
      __SCREAMING_SNAKE_CASE       :str		    =  [], []
      __SCREAMING_SNAKE_CASE       :List[str]		    =  node
      stacka.append(_a							)
      while stacka:  # to find the reversed order of post order, store it in stack2
            __SCREAMING_SNAKE_CASE       :Any		    =  stacka.pop()
            if n.left:
                  stacka.append(n.left							)
            if n.right:
                  stacka.append(n.right							)
            stacka.append(_a							)
      while stacka:  # pop up from stack2 will be the post order
            print(stacka.pop().data			,       end=''','''							)



def 					__lowerCamelCase       (							a_					:		str = ""			,       a_					:		str=50			,       a_					:		str="*"							)      ->				List[Any]:




      if not s:
            return "\n" + width * char
      __SCREAMING_SNAKE_CASE       :str		    =  divmod(width - len(_a							) - 2			,       2							)
      return f'''{left * char} {s} {(left + extra) * char}'''


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(prompt("Binary Tree Traversals"))

  lowerCamelCase_       =		build_tree()
  print(prompt("Pre Order Traversal"))
  pre_order(node)
  print(prompt() + "\n")

  print(prompt("In Order Traversal"))
  in_order(node)
  print(prompt() + "\n")

  print(prompt("Post Order Traversal"))
  post_order(node)
  print(prompt() + "\n")

  print(prompt("Level Order Traversal"))
  level_order(node)
  print(prompt() + "\n")

  print(prompt("Actual Level Order Traversal"))
  level_order_actual(node)
  print("*" * 5_0 + "\n")

  print(prompt("Pre Order Traversal - Iteration Version"))
  pre_order_iter(node)
  print(prompt() + "\n")

  print(prompt("In Order Traversal - Iteration Version"))
  in_order_iter(node)
  print(prompt() + "\n")

  print(prompt("Post Order Traversal - Iteration Version"))
  post_order_iter(node)
  print(prompt())






"""simple docstring"""
import colorsys

from PIL import Image  # type: ignore



def 					__lowerCamelCase       (							a_					:		float			,       a_					:		float			,       a_					:		int							)      ->				float:
      __SCREAMING_SNAKE_CASE       :List[Any]		    =  x
      __SCREAMING_SNAKE_CASE       :List[Any]		    =  y
      for step in range(a_							):  # noqa: B007
            __SCREAMING_SNAKE_CASE       :Dict		    =  a * a - b * b + x
            __SCREAMING_SNAKE_CASE       :Tuple		    =  2 * a * b + y
            __SCREAMING_SNAKE_CASE       :Dict		    =  a_new

            # divergence happens for all complex number with an absolute value
            # greater than 4
            if a * a + b * b > 4:
                  break
      return step / (max_step - 1)



def 					__lowerCamelCase       (							a_					:		float							)      ->				tuple:
      if distance == 1:
            return (0, 0, 0)
      else:
            return (2_55, 2_55, 2_55)



def 					__lowerCamelCase       (							a_					:		float							)      ->				tuple:
      if distance == 1:
            return (0, 0, 0)
      else:
            return tuple(round(i * 2_55							) for i in colorsys.hsv_to_rgb(a_			,       1			,       1							)							)



def 					__lowerCamelCase       (							a_					:		int = 8_00			,       a_					:		int = 6_00			,       a_					:		float = -0.6			,       a_					:		float = 0			,       a_					:		float = 3.2			,       a_					:		int = 50			,       a_					:		bool = True			,       )      ->				Image.Image:
      __SCREAMING_SNAKE_CASE       :Optional[int]		    =  Image.new('''RGB'''			,       (image_width, image_height)							)
      __SCREAMING_SNAKE_CASE       :Tuple		    =  img.load()

      # loop through the image-coordinates
      for image_x in range(a_							):
            for image_y in range(a_							):
                  # determine the figure-coordinates based on the image-coordinates
                  __SCREAMING_SNAKE_CASE       :Dict		    =  figure_width / image_width * image_height
                  __SCREAMING_SNAKE_CASE       :str		    =  figure_center_x + (image_x / image_width - 0.5) * figure_width
                  __SCREAMING_SNAKE_CASE       :Tuple		    =  figure_center_y + (image_y / image_height - 0.5) * figure_height

                  __SCREAMING_SNAKE_CASE       :List[Any]		    =  get_distance(a_			,       a_			,       a_							)

                  # color the corresponding pixel based on the selected coloring-function
                  if use_distance_color_coding:
                        __SCREAMING_SNAKE_CASE       :Optional[int]		    =  get_color_coded_rgb(a_							)
                  else:
                        __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  get_black_and_white_rgb(a_							)

      return img


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  # colored version, full figure
  lowerCamelCase_       =		get_image()

  # uncomment for colored version, different section, zoomed in
  # img = get_image(figure_center_x = -0.6, figure_center_y = -0.4,
  # figure_width = 0.8)

  # uncomment for black and white version, full figure
  # img = get_image(use_distance_color_coding = False)

  # uncomment to save the image
  # img.save("mandelbrot.png")

  img.show()