

"""simple docstring"""
class        _UpperCamelCase	:


  """simple docstring"""





  def __init__( self					: Dict       ,       snake_case					: int      )	->			None:


         '''simple docstring'''





         __magic_name__			:		Tuple        =     data
         __magic_name__			:		BinaryTreeNode | None        =     None
         __magic_name__			:		BinaryTreeNode | None        =     None







def       UpperCamelCase_					(     lowerCamelCase							:					BinaryTreeNode | None     , lowerCamelCase							:					int   )						->     BinaryTreeNode | None:



       """simple docstring"""







       if node is None:
              __magic_name__			:		str        =     BinaryTreeNode(lowerCamelCase   )
              return node

       # binary search tree is not empty,
       # so we will insert it into the tree
       # if new_value is less than value of data in node,
       #  add it to left subtree and proceed recursively
       if new_value < node.data:
              __magic_name__			:		int        =     insert(node.left_child     , lowerCamelCase   )
       else:
              # if new_value is greater than value of data in node,
              #  add it to right subtree and proceed recursively
              __magic_name__			:		Any        =     insert(node.right_child     , lowerCamelCase   )
       return node







def       UpperCamelCase_					(     lowerCamelCase							:					None | BinaryTreeNode   )						->     list[int]:  # if node is None,return



       """simple docstring"""







       if node:
              __magic_name__			:		Dict        =     inorder(node.left_child   )
              __magic_name__			:		str        =     [*inorder_array, node.data]
              __magic_name__			:		str        =     inorder_array + inorder(node.right_child   )
       else:
              __magic_name__			:		Tuple        =     []
       return inorder_array







def       UpperCamelCase_					(     )						->     BinaryTreeNode | None:



       """simple docstring"""







       __magic_name__			:		Dict        =     insert(lowerCamelCase     , 15   )
       insert(lowerCamelCase     , 10   )
       insert(lowerCamelCase     , 25   )
       insert(lowerCamelCase     , 6   )
       insert(lowerCamelCase     , 14   )
       insert(lowerCamelCase     , 20   )
       insert(lowerCamelCase     , 60   )
       return root







def       UpperCamelCase_					(     )						->     None:



       """simple docstring"""







       __magic_name__			:		Any        =     make_tree()
       print('''Printing values of binary search tree in Inorder Traversal.'''   )
       inorder(lowerCamelCase   )


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()



"""simple docstring"""
import math







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     list:



       """simple docstring"""







       if n <= 0:
              raise ValueError('''Only positive integers have prime factors'''   )
       __magic_name__			:		Union[str, Any]        =     []
       while n % 2 == 0:
              pf.append(2   )
              __magic_name__			:		Union[str, Any]        =     int(n / 2   )
       for i in range(3     , int(math.sqrt(lowerCamelCase   )   ) + 1     , 2   ):
              while n % i == 0:
                     pf.append(lowerCamelCase   )
                     __magic_name__			:		Any        =     int(n / i   )
       if n > 2:
              pf.append(lowerCamelCase   )
       return pf







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     int:



       """simple docstring"""







       if n <= 0:
              raise ValueError('''Only positive numbers are accepted'''   )
       __magic_name__			:		List[Any]        =     1
       __magic_name__			:		Dict        =     1
       while n % 2 == 0:
              temp += 1
              __magic_name__			:		Dict        =     int(n / 2   )
       div *= temp
       for i in range(3     , int(math.sqrt(lowerCamelCase   )   ) + 1     , 2   ):
              __magic_name__			:		Dict        =     1
              while n % i == 0:
                     temp += 1
                     __magic_name__			:		Union[str, Any]        =     int(n / i   )
              div *= temp
       if n > 1:
              div *= 2
       return div







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     int:



       """simple docstring"""







       if n <= 0:
              raise ValueError('''Only positive numbers are accepted'''   )
       __magic_name__			:		int        =     1
       __magic_name__			:		Dict        =     1
       while n % 2 == 0:
              temp += 1
              __magic_name__			:		List[Any]        =     int(n / 2   )
       if temp > 1:
              s *= (2**temp - 1) / (2 - 1)
       for i in range(3     , int(math.sqrt(lowerCamelCase   )   ) + 1     , 2   ):
              __magic_name__			:		Any        =     1
              while n % i == 0:
                     temp += 1
                     __magic_name__			:		Any        =     int(n / i   )
              if temp > 1:
                     s *= (i**temp - 1) / (i - 1)
       return int(lowerCamelCase   )







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     int:



       """simple docstring"""







       __magic_name__			:		str        =     n
       for x in set(prime_factors(lowerCamelCase   )   ):
              s *= (x - 1) / x
       return int(lowerCamelCase   )


if __name__ == "__main__":
 import doctest

 doctest.testmod()
