





'''simple docstring'''

from __future__ import annotations

import queue


class __a :





   def __init__(					self				:			Optional[int]				,lowerCamelCase				:			List[str]    ):

      '''simple docstring'''

      __SCREAMING_SNAKE_CASE      							=       data
      __SCREAMING_SNAKE_CASE      							=       None
      __SCREAMING_SNAKE_CASE      							=       None





def 						__magic_name__       (							)						->					TreeNode:

   '''simple docstring'''







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

def 						__magic_name__       (							__UpperCAmelCase      )						->					None:

   '''simple docstring'''







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

def 						__magic_name__       (							__UpperCAmelCase      )						->					None:

   '''simple docstring'''







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

def 						__magic_name__       (							__UpperCAmelCase      )						->					None:

   '''simple docstring'''







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

def 						__magic_name__       (							__UpperCAmelCase      )						->					None:

   '''simple docstring'''







   if not isinstance(__A							,	__A      ) or not node:
      return
   __SCREAMING_SNAKE_CASE      							=       queue.Queue()
   q.put(__A      )
   while not q.empty():
      __SCREAMING_SNAKE_CASE      							=       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 						__magic_name__       (							__UpperCAmelCase      )						->					None:

   '''simple docstring'''







   if not isinstance(__A							,	__A      ) or not node:
      return
   __SCREAMING_SNAKE_CASE      							=       queue.Queue()
   q.put(__A      )
   while not q.empty():
      __SCREAMING_SNAKE_CASE      							=       []
      while not q.empty():
         __SCREAMING_SNAKE_CASE      							=       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 						__magic_name__       (							__UpperCAmelCase      )						->					None:

   '''simple docstring'''







   if not isinstance(__A							,	__A      ) or not node:
      return
   __SCREAMING_SNAKE_CASE      							=       []
   __SCREAMING_SNAKE_CASE      							=       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      							=       n.left
      # end of while means current node doesn't have left child
      __SCREAMING_SNAKE_CASE      							=       stack.pop()
      # start to traverse its right child
      __SCREAMING_SNAKE_CASE      							=       n.right

def 						__magic_name__       (							__UpperCAmelCase      )						->					None:

   '''simple docstring'''







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

def 						__magic_name__       (							__UpperCAmelCase      )						->					None:

   '''simple docstring'''







   if not isinstance(__A							,	__A      ) or not node:
      return
   __SCREAMING_SNAKE_CASE      							=       [], []
   __SCREAMING_SNAKE_CASE      							=       node
   stacka.append(__A      )
   while stacka:  # to find the reversed order of post order, store it in stack2
      __SCREAMING_SNAKE_CASE      							=       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 						__magic_name__       (							__UpperCAmelCase = ""							,	__UpperCAmelCase=50							,	__UpperCAmelCase="*"      )						->					str:

   '''simple docstring'''







   if not s:
      return "\n" + width * char
   __SCREAMING_SNAKE_CASE      							=       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"))

    a        =						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())












'''simple docstring'''

from __future__ import annotations

from collections.abc import Callable

a        =						list[list[float | int]]

def 						__magic_name__       (							__UpperCAmelCase							,	__UpperCAmelCase      )						->					Matrix:

   '''simple docstring'''







   __SCREAMING_SNAKE_CASE      							=       len(__UpperCAmelCase      )
   __SCREAMING_SNAKE_CASE      							=       [[0 for _ in range(size + 1      )] for _ in range(__UpperCAmelCase      )]
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42

   for row in range(__UpperCAmelCase      ):
      for col in range(__UpperCAmelCase      ):
         __SCREAMING_SNAKE_CASE      							=       matrix[row][col]

      __SCREAMING_SNAKE_CASE      							=       vector[row][0]

   __SCREAMING_SNAKE_CASE      							=       0
   __SCREAMING_SNAKE_CASE      							=       0
   while row < size and col < size:
      # pivoting
      __SCREAMING_SNAKE_CASE      							=       max((abs(augmented[rowa][col]      ), rowa) for rowa in range(__UpperCAmelCase							,	__UpperCAmelCase      )      )[
          1
      ]
      if augmented[pivot_row][col] == 0:
         col += 1
         continue
      else:
         __SCREAMING_SNAKE_CASE							,     __SCREAMING_SNAKE_CASE      							=       augmented[pivot_row], augmented[row]

      for rowa in range(row + 1							,	__UpperCAmelCase      ):
         __SCREAMING_SNAKE_CASE      							=       augmented[rowa][col] / augmented[row][col]
         __SCREAMING_SNAKE_CASE      							=       0
         for cola in range(col + 1							,	size + 1      ):
            augmented[rowa][cola] -= augmented[row][cola] * ratio

      row += 1
      col += 1

   # back substitution
   for col in range(1							,	__UpperCAmelCase      ):
      for row in range(__UpperCAmelCase      ):
         __SCREAMING_SNAKE_CASE      							=       augmented[row][col] / augmented[col][col]
         for cola in range(__UpperCAmelCase							,	size + 1      ):
            augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
   return [
       [round(augmented[row][size] / augmented[row][row]							,	10      )] for row in range(__UpperCAmelCase      )
   ]

def 						__magic_name__       (							__UpperCAmelCase      )						->					Callable[[int], int]:

   '''simple docstring'''







   __SCREAMING_SNAKE_CASE      							=       len(__UpperCAmelCase      )
   __SCREAMING_SNAKE_CASE      							=       [[0 for _ in range(__UpperCAmelCase      )] for _ in range(__UpperCAmelCase      )]
   __SCREAMING_SNAKE_CASE      							=       [[0] for _ in range(__UpperCAmelCase      )]
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42

   for x_val, y_val in enumerate(__UpperCAmelCase      ):
      for col in range(__UpperCAmelCase      ):
         __SCREAMING_SNAKE_CASE      							=       (x_val + 1) ** (size - col - 1)
      __SCREAMING_SNAKE_CASE      							=       y_val

   __SCREAMING_SNAKE_CASE      							=       solve(__UpperCAmelCase							,	__UpperCAmelCase      )

   def interpolated_func(__UpperCAmelCase      ) -> int:
      return sum(
          round(coeffs[x_val][0]      ) * (var ** (size - x_val - 1))
          for x_val in range(__UpperCAmelCase      )      )

   return interpolated_func

def 						__magic_name__       (							__UpperCAmelCase      )						->					int:

   '''simple docstring'''







   return (
       1
       - variable
       + variable**2
       - variable**3
       + variable**4
       - variable**5
       + variable**6
       - variable**7
       + variable**8
       - variable**9
       + variable**10
   )

def 						__magic_name__       (							__UpperCAmelCase = question_function							,	__UpperCAmelCase = 10      )						->					int:

   '''simple docstring'''







   __SCREAMING_SNAKE_CASE      							=       [func(__UpperCAmelCase      ) for x_val in range(1							,	order + 1      )]

   __SCREAMING_SNAKE_CASE      							=       [
       interpolate(data_points[:max_coeff]      ) for max_coeff in range(1							,	order + 1      )
   ]

   __SCREAMING_SNAKE_CASE      							=       0
   __SCREAMING_SNAKE_CASE      							=       42
   __SCREAMING_SNAKE_CASE      							=       42

   for poly in polynomials:
      __SCREAMING_SNAKE_CASE      							=       1
      while func(__UpperCAmelCase      ) == poly(__UpperCAmelCase      ):
         x_val += 1

      ret += poly(__UpperCAmelCase      )

   return ret


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





