

"""simple docstring"""




from __future__ import annotations







class      __lowercase			:

  def __init__(  self		:			Dict					,A		:			int    ):






   '''simple docstring'''
   UpperCAmelCase__					:  Any					   =					data
   UpperCAmelCase__					:  Node | None					   =					None
   UpperCAmelCase__					:  Node | None					   =					None







def   lowerCAmelCase						(					__UpperCamelCase      ):  # In Order traversal of the tree
 '''simple docstring'''





 if tree:
  display(tree.left      )
  print(tree.data      )
  display(tree.right      )
def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 return 1 + max(depth_of_tree(tree.left      )							,    depth_of_tree(tree.right      )      ) if tree else 0
def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 if not tree:
  return True
 if tree.left and tree.right:
  return is_full_binary_tree(tree.left      ) and is_full_binary_tree(tree.right      )
 else:
  return not tree.left and not tree.right
def   lowerCAmelCase						(					):  # Main function for testing.
 '''simple docstring'''





 UpperCAmelCase__					:  Union[str, Any]					   =					Node(1      )
 UpperCAmelCase__					:  Any					   =					Node(2      )
 UpperCAmelCase__					:  Optional[Any]					   =					Node(3      )
 UpperCAmelCase__					:  str					   =					Node(4      )
 UpperCAmelCase__					:  List[str]					   =					Node(5      )
 UpperCAmelCase__					:  Union[str, Any]					   =					Node(6      )
 UpperCAmelCase__					:  Union[str, Any]					   =					Node(7      )
 UpperCAmelCase__					:  int					   =					Node(8      )
 UpperCAmelCase__					:  Optional[Any]					   =					Node(9      )

 print(is_full_binary_tree(__UpperCamelCase      )      )
 print(depth_of_tree(__UpperCamelCase      )      )
 print("""Tree is: """      )
 display(__UpperCamelCase      )


if __name__ == "__main__":
      main()








"""simple docstring"""




def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 UpperCAmelCase__					:  str					   =					[]
 if len(__UpperCamelCase      ) == 1:
  return [nums.copy()]
 for _ in range(len(__UpperCamelCase      )      ):
  UpperCAmelCase__					:  Tuple					   =					nums.pop(0      )
  UpperCAmelCase__					:  List[str]					   =					permute(__UpperCamelCase      )
  for perm in permutations:
   perm.append(__UpperCamelCase      )
  result.extend(__UpperCamelCase      )
  nums.append(__UpperCamelCase      )
 return result
def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 def backtrack(__UpperCamelCase      ):
  if start == len(__UpperCamelCase      ) - 1:
   output.append(nums[:]      )
  else:
   for i in range(__UpperCamelCase							,    len(__UpperCamelCase      )      ):
    UpperCAmelCase__   ,      UpperCAmelCase__					:  Union[str, Any]					   =					nums[i], nums[start]
    backtrack(start + 1      )
    UpperCAmelCase__   ,      UpperCAmelCase__					:  Union[str, Any]					   =					nums[i], nums[start]  # backtrack

 UpperCAmelCase__					:  List[str]					   =					[]
 backtrack(0      )
 return output


if __name__ == "__main__":
      import doctest

      # use res to print the data in permute2 function
      __UpperCAmelCase =				permutea([1, 2, 3])
      print(res)
      doctest.testmod()





