


"""simple docstring"""


from __future__ import annotations

from collections import deque
from collections.abc import Sequence
from dataclasses import dataclass
from typing import Any
@dataclass
class   _UpperCamelCase  :
							'''simple docstring'''







							__UpperCAmelCase						:    int
							__UpperCAmelCase						:    Node | None				      =None
							__UpperCAmelCase						:    Node | None				      =None


def _lowerCamelCase	(		):

			'''simple docstring'''




			__lowerCAmelCase				    =			Node(1      )
			__lowerCAmelCase				    =			Node(2      )
			__lowerCAmelCase				    =			Node(3      )
			__lowerCAmelCase				    =			Node(4      )
			__lowerCAmelCase				    =			Node(5      )
			return tree


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




			return [root.data, *preorder(root.left      ), *preorder(root.right      )] if root else []


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




			return postorder(root.left      ) + postorder(root.right      ) + [root.data] if root else []


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




			return [*inorder(root.left      ), root.data, *inorder(root.right      )] if root else []


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




			return (max(height(root.left      )    , height(root.right      )      ) + 1) if root else 0


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




			__lowerCAmelCase				    =			[]

			if root is None:
						return output

			__lowerCAmelCase				    =			deque([root]      )

			while process_queue:
						__lowerCAmelCase				    =			process_queue.popleft()
						output.append(node.data      )

						if node.left:
									process_queue.append(node.left      )
						if node.right:
									process_queue.append(node.right      )
			return output


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




			__lowerCAmelCase				    =			[]

			def populate_output(_UpperCamelCase    , _UpperCamelCase      ) -> None:
						if not root:
									return
						if level == 1:
									output.append(root.data      )
						elif level > 1:
									populate_output(root.left    , level - 1      )
									populate_output(root.right    , level - 1      )

			populate_output(_UpperCamelCase    , _UpperCamelCase      )
			return output


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




			__lowerCAmelCase				    =			[]

			def populate_output(_UpperCamelCase    , _UpperCamelCase      ) -> None:
						if root is None:
									return
						if level == 1:
									output.append(root.data      )
						elif level > 1:
									populate_output(root.right    , level - 1      )
									populate_output(root.left    , level - 1      )

			populate_output(_UpperCamelCase    , _UpperCamelCase      )
			return output


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




			if root is None:
						return []

			__lowerCAmelCase				    =			[]

			__lowerCAmelCase				    =			0
			__lowerCAmelCase				    =			height(_UpperCamelCase      )

			for h in range(1    , height_tree + 1      ):
						if not flag:
									output.append(get_nodes_from_left_to_right(_UpperCamelCase    , _UpperCamelCase      )      )
									__lowerCAmelCase				    =			1
						else:
									output.append(get_nodes_from_right_to_left(_UpperCamelCase    , _UpperCamelCase      )      )
									__lowerCAmelCase				    =			0

			return output


def _lowerCamelCase	(		):  # Main function for testing.

			'''simple docstring'''




			__lowerCAmelCase				    =			make_tree()
			print(f"In-order Traversal: {inorder(_UpperCamelCase      )}"      )
			print(f"Pre-order Traversal: {preorder(_UpperCamelCase      )}"      )
			print(f"Post-order Traversal: {postorder(_UpperCamelCase      )}"    , "\n"      )

			print(f"Height of Tree: {height(_UpperCamelCase      )}"    , "\n"      )

			print("Complete Level Order Traversal: "      )
			print(level_order(_UpperCamelCase      )    , "\n"      )

			print("Level-wise order Traversal: "      )

			for level in range(1    , height(_UpperCamelCase      ) + 1      ):
						print(f"Level {level}:"    , get_nodes_from_left_to_right(_UpperCamelCase    , level=_UpperCamelCase      )      )

			print("\nZigZag order Traversal: "      )
			print(zigzag(_UpperCamelCase      )      )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()








from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt



def 				UpperCamelCase_(      lowerCamelCase_ )    ->						bool:
    _lowercase       :							int      		=		int(number**0.5 )
    return number == sq * sq



def 				UpperCamelCase_(      lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_ )    ->						tuple[int, int]:
    _lowercase       :							int      		=		x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
    _lowercase       :							int      		=		x_den * y_den * z_den
    _lowercase       :							int      		=		gcd(lowerCamelCase_							, lowerCamelCase_ )
    top //= hcf
    bottom //= hcf
    return top, bottom



def 				UpperCamelCase_(      lowerCamelCase_ = 35 )    ->						int:
    _lowercase       :							set      		=		set()
    _lowercase       :							int
    _lowercase       :							Fraction      		=		Fraction(0 )
    _lowercase       :							tuple[int, int]

    for x_num in range(1							, order + 1 ):
        for x_den in range(x_num + 1							, order + 1 ):
            for y_num in range(1							, order + 1 ):
                for y_den in range(y_num + 1							, order + 1 ):
                    # n=1
                    _lowercase       :							int      		=		x_num * y_den + x_den * y_num
                    _lowercase       :							int      		=		x_den * y_den
                    _lowercase       :							str      		=		gcd(lowerCamelCase_							, lowerCamelCase_ )
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        _lowercase       :							List[Any]      		=		add_three(
                            lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_ )
                        unique_s.add(lowerCamelCase_ )

                    # n=2
                    _lowercase       :							Dict      		=		(
                        x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
                    )
                    _lowercase       :							List[Any]      		=		x_den * x_den * y_den * y_den
                    if is_sq(lowerCamelCase_ ) and is_sq(lowerCamelCase_ ):
                        _lowercase       :							Tuple      		=		int(sqrt(lowerCamelCase_ ) )
                        _lowercase       :							int      		=		int(sqrt(lowerCamelCase_ ) )
                        _lowercase       :							Any      		=		gcd(lowerCamelCase_							, lowerCamelCase_ )
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            _lowercase       :							Optional[int]      		=		add_three(
                                lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_ )
                            unique_s.add(lowerCamelCase_ )

                    # n=-1
                    _lowercase       :							Any      		=		x_num * y_num
                    _lowercase       :							str      		=		x_den * y_num + x_num * y_den
                    _lowercase       :							Any      		=		gcd(lowerCamelCase_							, lowerCamelCase_ )
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        _lowercase       :							int      		=		add_three(
                            lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_ )
                        unique_s.add(lowerCamelCase_ )

                    # n=2
                    _lowercase       :							str      		=		x_num * x_num * y_num * y_num
                    _lowercase       :							Optional[Any]      		=		(
                        x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                    )
                    if is_sq(lowerCamelCase_ ) and is_sq(lowerCamelCase_ ):
                        _lowercase       :							Tuple      		=		int(sqrt(lowerCamelCase_ ) )
                        _lowercase       :							List[str]      		=		int(sqrt(lowerCamelCase_ ) )
                        _lowercase       :							Union[str, Any]      		=		gcd(lowerCamelCase_							, lowerCamelCase_ )
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            _lowercase       :							Tuple      		=		add_three(
                                lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_ )
                            unique_s.add(lowerCamelCase_ )

    for num, den in unique_s:
        total += Fraction(lowerCamelCase_							, lowerCamelCase_ )

    return total.denominator + total.numerator


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


