




import mpmath  # for roots of unity
import numpy as np


class     UpperCamelCase_   :

    '''simple docstring'''






    def __init__(      self				:     Union[str, Any] ,			UpperCAmelCase__				:     List[str]=None ,			UpperCAmelCase__				:     List[str]=None)						->List[Any]:





           '''simple docstring'''

           A__							=   list(poly_a or [0])[:]
           A__							=   list(poly_b or [0])[:]

           # Remove leading zero coefficients
           while self.polyA[-1] == 0:
                  self.polyA.pop()
           A__							=   len(self.polyA)

           while self.polyB[-1] == 0:
                  self.polyB.pop()
           A__							=   len(self.polyB)

           # Add 0 to make lengths equal a power of 2
           A__							=   int(
               2 ** np.ceil(np.loga(len(self.polyA) + len(self.polyB) - 1)))

           while len(self.polyA) < self.c_max_length:
                  self.polyA.append(0)
           while len(self.polyB) < self.c_max_length:
                  self.polyB.append(0)
           # A complex root used for the fourier transform
           A__							=   complex(mpmath.root(x=1 ,			n=self.c_max_length ,			k=1))

           # The product
           A__							=   self.__multiply()


    def 	SCREAMING_SNAKE_CASE							(      self				:     List[str] ,			UpperCAmelCase__				:     List[str])						->Dict:





           '''simple docstring'''

           A__							=   [[x] for x in self.polyA] if which == '''A''' else [[x] for x in self.polyB]
           # Corner case
           if len(UpperCAmelCase__) <= 1:
                  return dft[0]
           #
           A__							=   self.c_max_length // 2
           while next_ncol > 0:
                  A__							=   [[] for i in range(UpperCAmelCase__)]
                  A__							=   self.root**next_ncol

                  # First half of next step
                  A__							=   1
                  for j in range(self.c_max_length // (next_ncol * 2)):
                         for i in range(UpperCAmelCase__):
                                new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j])
                         current_root *= root
                  # Second half of next step
                  A__							=   1
                  for j in range(self.c_max_length // (next_ncol * 2)):
                         for i in range(UpperCAmelCase__):
                                new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j])
                         current_root *= root
                  # Update
                  A__							=   new_dft
                  A__							=   next_ncol // 2
           return dft[0]


    def 	SCREAMING_SNAKE_CASE							(      self				:     int)						->Any:





           '''simple docstring'''

           A__							=   self.__dft('''A''')
           A__							=   self.__dft('''B''')
           A__							=   [[dft_a[i] * dft_b[i] for i in range(self.c_max_length)]]
           del dft_a
           del dft_b

           # Corner Case
           if len(inverce_c[0]) <= 1:
                  return inverce_c[0]
           # Inverse DFT
           A__							=   2
           while next_ncol <= self.c_max_length:
                  A__							=   [[] for i in range(UpperCAmelCase__)]
                  A__							=   self.root ** (next_ncol // 2)
                  A__							=   1
                  # First half of next step
                  for j in range(self.c_max_length // next_ncol):
                         for i in range(next_ncol // 2):
                                # Even positions
                                new_inverse_c[i].append(
                                    (
                                        inverce_c[i][j]
                                        + inverce_c[i][j + self.c_max_length // next_ncol]
                                    )
                                    / 2)
                                # Odd positions
                                new_inverse_c[i + next_ncol // 2].append(
                                    (
                                        inverce_c[i][j]
                                        - inverce_c[i][j + self.c_max_length // next_ncol]
                                    )
                                    / (2 * current_root))
                         current_root *= root
                  # Update
                  A__							=   new_inverse_c
                  next_ncol *= 2
           # Unpack
           A__							=   [round(x[0].real ,			8) + round(x[0].imag ,			8) * 1j for x in inverce_c]

           # Remove leading 0's
           while inverce_c[-1] == 0:
                  inverce_c.pop()
           return inverce_c





    def __str__(      self				:     List[str])						->List[str]:





           '''simple docstring'''

           A__							=   '''A = ''' + ''' + '''.join(
               f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]))
           A__							=   '''B = ''' + ''' + '''.join(
               f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]))
           A__							=   '''A*B = ''' + ''' + '''.join(
               f"""{coef}*x^{i}""" for coef, i in enumerate(self.product))

           return f"""{a}\n{b}\n{c}"""


# Unit tests
if __name__ == "__main__":
  import doctest

  doctest.testmod()








from __future__ import annotations

import queue


class     UpperCamelCase_   :

    '''simple docstring'''






    def __init__(      self				:     Optional[Any] ,			UpperCAmelCase__				:     Dict)						->Any:





           '''simple docstring'''

           A__							=   data
           A__							=   None
           A__							=   None







def SCREAMING_SNAKE_CASE    (	)       ->	TreeNode:



       """simple docstring"""

       print('''\n********Press N to stop entering at any point of time********\n'''						)
       A__							=   input('''Enter the value of the root node: '''						).strip().lower()
       A__							=   queue.Queue()
       A__							=   TreeNode(int(lowercase_						)						)
       q.put(lowercase_						)
       while not q.empty():
              A__							=   q.get()
              A__							=   f"""Enter the left node of {node_found.data}: """
              A__							=   input(lowercase_						).strip().lower() or '''n'''
              if check == "n":
                     return tree_node
              A__							=   TreeNode(int(lowercase_						)						)
              A__							=   left_node
              q.put(lowercase_						)
              A__							=   f"""Enter the right node of {node_found.data}: """
              A__							=   input(lowercase_						).strip().lower() or '''n'''
              if check == "n":
                     return tree_node
              A__							=   TreeNode(int(lowercase_						)						)
              A__							=   right_node
              q.put(lowercase_						)
       raise







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	None:



       """simple docstring"""

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







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	None:



       """simple docstring"""

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







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	None:



       """simple docstring"""

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







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	None:



       """simple docstring"""

       if not isinstance(lowercase_			,    lowercase_						) or not node:
              return
       A__							=   queue.Queue()
       q.put(lowercase_						)
       while not q.empty():
              A__							=   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 SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	None:



       """simple docstring"""

       if not isinstance(lowercase_			,    lowercase_						) or not node:
              return
       A__							=   queue.Queue()
       q.put(lowercase_						)
       while not q.empty():
              A__							=   []
              while not q.empty():
                     A__							=   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(lowercase_						)







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	None:



       """simple docstring"""

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







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	None:



       """simple docstring"""

       if not isinstance(lowercase_			,    lowercase_						) or not node:
              return
       A__							=   []
       A__							=   node
       while n or stack:
              while n:
                     stack.append(lowercase_						)
                     A__							=   n.left
              A__							=   stack.pop()
              print(n.data			,    end=''','''						)
              A__							=   n.right







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	None:



       """simple docstring"""

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







def SCREAMING_SNAKE_CASE    (	lowercase_ = ""			,    lowercase_=50			,    lowercase_="*"						)       ->	str:



       """simple docstring"""

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


if __name__ == "__main__":
  import doctest

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

  _lowerCamelCase     :		TreeNode								=       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("""*""" * 50 + """\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())


