from __future__ import annotations

import queue



class  UpperCamelCase				:

     '''simple docstring'''

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






           """simple docstring"""
           _lowerCamelCase			    =				data
           _lowerCamelCase			    =				None
           _lowerCamelCase			    =				None





def       __magic_name__(  )						->    TreeNode:



      '''simple docstring'''

      print('''\n********Press N to stop entering at any point of time********\n'''		)
      _lowerCamelCase			    =				input('''Enter the value of the root node: '''		).strip().lower()
      _lowerCamelCase			    =				queue.Queue()
      _lowerCamelCase			    =				TreeNode(int(__UpperCAmelCase		)		)
      q.put(__UpperCAmelCase		)
      while not q.empty():
            _lowerCamelCase			    =				q.get()
            _lowerCamelCase			    =				F'Enter the left node of {node_found.data}: '
            _lowerCamelCase			    =				input(__UpperCAmelCase		).strip().lower() or '''n'''
            if check == "n":
                  return tree_node
            _lowerCamelCase			    =				TreeNode(int(__UpperCAmelCase		)		)
            _lowerCamelCase			    =				left_node
            q.put(__UpperCAmelCase		)
            _lowerCamelCase			    =				F'Enter the right node of {node_found.data}: '
            _lowerCamelCase			    =				input(__UpperCAmelCase		).strip().lower() or '''n'''
            if check == "n":
                  return tree_node
            _lowerCamelCase			    =				TreeNode(int(__UpperCAmelCase		)		)
            _lowerCamelCase			    =				right_node
            q.put(__UpperCAmelCase		)
      raise
def       __magic_name__(  __UpperCAmelCase		)						->    None:



      '''simple docstring'''

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



      '''simple docstring'''

      if not isinstance(__UpperCAmelCase ,						__UpperCAmelCase		) or not node:
            return
      _lowerCamelCase			    =				[]
      _lowerCamelCase			    =				node
      while n or stack:
            while n:  # start from root node, find its left child
                  print(n.data ,						end=''','''		)
                  stack.append(__UpperCAmelCase		)
                  _lowerCamelCase			    =				n.left
            # end of while means current node doesn't have left child
            _lowerCamelCase			    =				stack.pop()
            # start to traverse its right child
            _lowerCamelCase			    =				n.right
def       __magic_name__(  __UpperCAmelCase		)						->    None:



      '''simple docstring'''

      if not isinstance(__UpperCAmelCase ,						__UpperCAmelCase		) or not node:
            return
      _lowerCamelCase			    =				[]
      _lowerCamelCase			    =				node
      while n or stack:
            while n:
                  stack.append(__UpperCAmelCase		)
                  _lowerCamelCase			    =				n.left
            _lowerCamelCase			    =				stack.pop()
            print(n.data ,						end=''','''		)
            _lowerCamelCase			    =				n.right
def       __magic_name__(  __UpperCAmelCase		)						->    None:



      '''simple docstring'''

      if not isinstance(__UpperCAmelCase ,						__UpperCAmelCase		) or not node:
            return
      _lowerCamelCase    ,					_lowerCamelCase			    =				[], []
      _lowerCamelCase			    =				node
      stacka.append(__UpperCAmelCase		)
      while stacka:  # to find the reversed order of post order, store it in stack2
            _lowerCamelCase			    =				stacka.pop()
            if n.left:
                  stacka.append(n.left		)
            if n.right:
                  stacka.append(n.right		)
            stacka.append(__UpperCAmelCase		)
      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
      _lowerCamelCase    ,					_lowerCamelCase			    =				divmod(width - len(__UpperCAmelCase		) - 2 ,						2		)
      return F'{left * char} {s} {(left + extra) * char}'


if __name__ == "__main__":
     import doctest

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

     snake_case__				= 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())



from typing import List

import numpy as np
def       __magic_name__(  __UpperCAmelCase		)						->    int:



      '''simple docstring'''

      _lowerCamelCase			    =				{key: len(__UpperCAmelCase		) for key, value in gen_kwargs.items() if isinstance(__UpperCAmelCase ,						__UpperCAmelCase		)}
      if len(set(lists_lengths.values()		)		) > 1:
            raise RuntimeError(
                (
                    '''Sharding is ambiguous for this dataset: '''
                    + '''we found several data sources lists of different lengths, and we don\'t know over which list we should parallelize:\n'''
                    + '''\n'''.join(F'\t- key {key} has length {length}' for key, length in lists_lengths.items()		)
                    + '''\nTo fix this, check the \'gen_kwargs\' and make sure to use lists only for data sources, '''
                    + '''and use tuples otherwise. In the end there should only be one single list, or several lists with the same length.'''
                )		)
      _lowerCamelCase			    =				max(lists_lengths.values() ,						default=0		)
      return max(1 ,						__UpperCAmelCase		)
def       __magic_name__(  __UpperCAmelCase ,						__UpperCAmelCase		)						->    List[range]:



      '''simple docstring'''

      _lowerCamelCase			    =				[]
      for group_idx in range(__UpperCAmelCase		):
            _lowerCamelCase			    =				num_shards // max_num_jobs + (group_idx < (num_shards % max_num_jobs))
            if num_shards_to_add == 0:
                  break
            _lowerCamelCase			    =				shards_indices_per_group[-1].stop if shards_indices_per_group else 0
            _lowerCamelCase			    =				range(__UpperCAmelCase ,						start + num_shards_to_add		)
            shards_indices_per_group.append(__UpperCAmelCase		)
      return shards_indices_per_group
def       __magic_name__(  __UpperCAmelCase ,						__UpperCAmelCase		)						->    List[dict]:



      '''simple docstring'''

      _lowerCamelCase			    =				_number_of_shards_in_gen_kwargs(__UpperCAmelCase		)
      if num_shards == 1:
            return [dict(__UpperCAmelCase		)]
      else:
            _lowerCamelCase			    =				_distribute_shards(num_shards=__UpperCAmelCase ,						max_num_jobs=__UpperCAmelCase		)
            return [
                {
                    key: [value[shard_idx] for shard_idx in shard_indices_per_group[group_idx]]
                    if isinstance(__UpperCAmelCase ,						__UpperCAmelCase		)
                    else value
                    for key, value in gen_kwargs.items()
                }
                for group_idx in range(len(__UpperCAmelCase		)		)
            ]
def       __magic_name__(  __UpperCAmelCase		)						->    dict:



      '''simple docstring'''

      return {
          key: [value for gen_kwargs in gen_kwargs_list for value in gen_kwargs[key]]
          if isinstance(gen_kwargs_list[0][key] ,						__UpperCAmelCase		)
          else gen_kwargs_list[0][key]
          for key in gen_kwargs_list[0]
      }




def       __magic_name__(  __UpperCAmelCase ,						__UpperCAmelCase		)						->    dict:



      '''simple docstring'''

      _lowerCamelCase			    =				{len(__UpperCAmelCase		) for value in gen_kwargs.values() if isinstance(__UpperCAmelCase ,						__UpperCAmelCase		)}
      _lowerCamelCase			    =				{}
      for size in list_sizes:
            _lowerCamelCase			    =				list(range(__UpperCAmelCase		)		)
            rng.shuffle(indices_per_size[size]		)
      # Now let's copy the gen_kwargs and shuffle the lists based on their sizes
      _lowerCamelCase			    =				dict(__UpperCAmelCase		)
      for key, value in shuffled_kwargs.items():
            if isinstance(__UpperCAmelCase ,						__UpperCAmelCase		):
                  _lowerCamelCase			    =				[value[i] for i in indices_per_size[len(__UpperCAmelCase		)]]
      return shuffled_kwargs