
'''simple docstring'''

from __future__ import annotations







class 	__lowerCAmelCase    :



     def __init__(self						,	lowerCAmelCase__ = 0	):
          _UpperCAmelCase					:  Tuple         =    value
          _UpperCAmelCase					:  Node | None         =    None
          _UpperCAmelCase					:  Node | None         =    None







def __A  (    lowerCAmelCase_ ,       lowerCAmelCase_       ):
     if treea is None:
          return treea
     if treea is None:
          return treea

     _UpperCAmelCase					:  Optional[Any]         =    treea.value + treea.value
     _UpperCAmelCase					:  Any         =    merge_two_binary_trees(treea.left ,       treea.left       )
     _UpperCAmelCase					:  Optional[Any]         =    merge_two_binary_trees(treea.right ,       treea.right       )
     return treea







def __A  (    lowerCAmelCase_       ):
     if root:
          print(root.value       )
          print_preorder(root.left       )
          print_preorder(root.right       )


if __name__ == "__main__":
   lowerCAmelCase_			:			Union[str, Any]			   =     Node(1)
   lowerCAmelCase_			:			Union[str, Any]			   =     Node(2)
   lowerCAmelCase_			:			Tuple			   =     Node(3)
   lowerCAmelCase_			:			Any			   =     Node(4)

   lowerCAmelCase_			:			List[str]			   =     Node(2)
   lowerCAmelCase_			:			str			   =     Node(4)
   lowerCAmelCase_			:			Dict			   =     Node(6)
   lowerCAmelCase_			:			List[Any]			   =     Node(9)
   lowerCAmelCase_			:			Tuple			   =     Node(5)

   print('''Tree1 is: ''')
   print_preorder(treea)
   print('''Tree2 is: ''')
   print_preorder(treea)
   lowerCAmelCase_			:			Dict			   =     merge_two_binary_trees(treea, treea)
   print('''Merged Tree is: ''')
   print_preorder(merged_tree)




'''simple docstring'''

from __future__ import annotations







def __A  (    lowerCAmelCase_       ):
     _UpperCAmelCase					:  Optional[int]         =    {1}
     _UpperCAmelCase					:  Union[str, Any]         =    [1]
     for _ in range(2 ,       depth + 1       ):
          _UpperCAmelCase					:  Dict         =    [*previous_coefficients, 0]
          _UpperCAmelCase					:  int         =    [0, *previous_coefficients]
          _UpperCAmelCase					:  List[Any]         =    []
          for x, y in zip(lowerCAmelCase_ ,       lowerCAmelCase_       ):
               coefficients.add(x + y       )
               previous_coefficients.append(x + y       )
     return coefficients







def __A  (    lowerCAmelCase_       ):
     _UpperCAmelCase					:  Dict         =    set()
     for number in unique_coefficients:
          _UpperCAmelCase					:  Tuple         =    2
          _UpperCAmelCase					:  List[str]         =    number
          while divisor**2 <= copy_number:
               _UpperCAmelCase					:  Tuple         =    0
               while copy_number % divisor == 0:
                    copy_number //= divisor
                    multiplicity += 1
               if multiplicity >= 2:
                    non_squarefrees.add(lowerCAmelCase_       )
                    break
               divisor += 1

     return unique_coefficients.difference(lowerCAmelCase_       )







def __A  (    lowerCAmelCase_ = 51       ):
     _UpperCAmelCase					:  List[str]         =    get_pascal_triangle_unique_coefficients(lowerCAmelCase_       )
     _UpperCAmelCase					:  Optional[Any]         =    get_squarefrees(lowerCAmelCase_       )
     return sum(lowerCAmelCase_       )


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


