





class 		__a							:



       def __init__(     self	:   str					,			UpperCAmelCase	:   Tuple			):
           lowerCAmelCase_					:	Tuple						=   data
           lowerCAmelCase_					:	BinaryTreeNode | None						=   None
           lowerCAmelCase_					:	BinaryTreeNode | None						=   None






def 			__UpperCamelCase				(			lowercase__	:       List[str]		,    lowercase__	:       int		)	->      BinaryTreeNode | None:
    '''simple docstring'''





    if node is None:
        lowerCAmelCase_					:	List[Any]						=   BinaryTreeNode(lowercase__		)
        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:
        lowerCAmelCase_					:	Tuple						=   insert(node.left_child		,    lowercase__		)
    else:
        # if new_value is greater than value of data in node,
        #  add it to right subtree and proceed recursively
        lowerCAmelCase_					:	str						=   insert(node.right_child		,    lowercase__		)
    return node
def 			__UpperCamelCase				(			lowercase__	:       Dict		)	->      list[int]:  # if node is None,return
    '''simple docstring'''





    if node:
        lowerCAmelCase_					:	List[Any]						=   inorder(node.left_child		)
        lowerCAmelCase_					:	int						=   [*inorder_array, node.data]
        lowerCAmelCase_					:	Optional[Any]						=   inorder_array + inorder(node.right_child		)
    else:
        lowerCAmelCase_					:	List[Any]						=   []
    return inorder_array
def 			__UpperCamelCase				(			)	->      BinaryTreeNode | None:
    '''simple docstring'''





    lowerCAmelCase_					:	Tuple						=   insert(lowercase__		,    15		)
    insert(lowercase__		,    10		)
    insert(lowercase__		,    25		)
    insert(lowercase__		,    6		)
    insert(lowercase__		,    14		)
    insert(lowercase__		,    20		)
    insert(lowercase__		,    60		)
    return root
def 			__UpperCamelCase				(			)	->      None:
    '''simple docstring'''





    lowerCAmelCase_					:	Union[str, Any]						=   make_tree()
    print("""Printing values of binary search tree in Inorder Traversal."""		)
    inorder(lowercase__		)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()











import math
def 			__UpperCamelCase				(			lowercase__	:       int		)	->      list:
    '''simple docstring'''





    if n <= 0:
        raise ValueError("""Only positive integers have prime factors"""		)
    lowerCAmelCase_					:	str						=   []
    while n % 2 == 0:
        pf.append(2		)
        lowerCAmelCase_					:	str						=   int(n / 2		)
    for i in range(3		,    int(math.sqrt(lowercase__		)		) + 1		,    2		):
        while n % i == 0:
            pf.append(lowercase__		)
            lowerCAmelCase_					:	List[Any]						=   int(n / i		)
    if n > 2:
        pf.append(lowercase__		)
    return pf
def 			__UpperCamelCase				(			lowercase__	:       int		)	->      int:
    '''simple docstring'''





    if n <= 0:
        raise ValueError("""Only positive numbers are accepted"""		)
    lowerCAmelCase_					:	Union[str, Any]						=   1
    lowerCAmelCase_					:	str						=   1
    while n % 2 == 0:
        temp += 1
        lowerCAmelCase_					:	Optional[Any]						=   int(n / 2		)
    div *= temp
    for i in range(3		,    int(math.sqrt(lowercase__		)		) + 1		,    2		):
        lowerCAmelCase_					:	Tuple						=   1
        while n % i == 0:
            temp += 1
            lowerCAmelCase_					:	Any						=   int(n / i		)
        div *= temp
    if n > 1:
        div *= 2
    return div
def 			__UpperCamelCase				(			lowercase__	:       int		)	->      int:
    '''simple docstring'''





    if n <= 0:
        raise ValueError("""Only positive numbers are accepted"""		)
    lowerCAmelCase_					:	Tuple						=   1
    lowerCAmelCase_					:	str						=   1
    while n % 2 == 0:
        temp += 1
        lowerCAmelCase_					:	Optional[int]						=   int(n / 2		)
    if temp > 1:
        s *= (2**temp - 1) / (2 - 1)
    for i in range(3		,    int(math.sqrt(lowercase__		)		) + 1		,    2		):
        lowerCAmelCase_					:	int						=   1
        while n % i == 0:
            temp += 1
            lowerCAmelCase_					:	Any						=   int(n / i		)
        if temp > 1:
            s *= (i**temp - 1) / (i - 1)
    return int(lowercase__		)
def 			__UpperCamelCase				(			lowercase__	:       int		)	->      int:
    '''simple docstring'''





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


if __name__ == "__main__":
  import doctest

  doctest.testmod()


