code: 
  
  
  
  
  
  
  from __future__ import annotations
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int ):
      UpperCamelCase :int										=     {1}
      UpperCamelCase :Optional[int]										=     [1]
      for _ in range(2  ,						depth + 1 ):
          UpperCamelCase :Union[str, Any]										=     [*previous_coefficients, 0]
          UpperCamelCase :List[str]										=     [0, *previous_coefficients]
          UpperCamelCase :List[str]										=     []
          for x, y in zip(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ ):
              coefficients.add(x + y )
              previous_coefficients.append(x + y )
      return coefficients
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			set[int] ):
      UpperCamelCase :Union[str, Any]										=     set()
      for number in unique_coefficients:
          UpperCamelCase :Optional[int]										=     2
          UpperCamelCase :List[Any]										=     number
          while divisor**2 <= copy_number:
              UpperCamelCase :List[Any]										=     0
              while copy_number % divisor == 0:
                  copy_number //= divisor
                  multiplicity += 1
              if multiplicity >= 2:
                  non_squarefrees.add(SCREAMING_SNAKE_CASE__ )
                  break
              divisor += 1
  
      return unique_coefficients.difference(SCREAMING_SNAKE_CASE__ )
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int = 51 ):
      UpperCamelCase :Any										=     get_pascal_triangle_unique_coefficients(SCREAMING_SNAKE_CASE__ )
      UpperCamelCase :str										=     get_squarefrees(SCREAMING_SNAKE_CASE__ )
      return sum(SCREAMING_SNAKE_CASE__ )
  
  
  if __name__ == "__main__":
   print(f'''{solution() = }''')
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  from __future__ import annotations
  
  
  
  
  
  
  
  class     UpperCAmelCase_		:
  
  
  
        """simple docstring"""
        def __init__(       self					,       SCREAMING_SNAKE_CASE_				)       ->   None:
            UpperCamelCase :Tuple										=     value
            UpperCamelCase :Node | None										=     None
            UpperCamelCase :Node | None										=     None
  
  
  
  
  
  
  
  class     UpperCAmelCase_		:
  
  
  
        """simple docstring"""
        UpperCamelCase_       :      int
        def __init__(       self				)       ->   None:
            UpperCamelCase :List[Any]										=     0
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_					,       SCREAMING_SNAKE_CASE_				)       ->   None:
            if node is None:
                return
  
            if path_sum == self.target:
                self.paths += 1
  
            if node.left:
                self.depth_first_search(node.left					,       path_sum + node.left.value				)
            if node.right:
                self.depth_first_search(node.right					,       path_sum + node.right.value				)
  
  
  
  
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_					,       SCREAMING_SNAKE_CASE_ = None				)       ->   int:
            if node is None:
                return 0
            if target is not None:
                UpperCamelCase :Tuple										=     target
  
            self.depth_first_search(SCREAMING_SNAKE_CASE_					,       node.value				)
            self.path_sum(node.left				)
            self.path_sum(node.right				)
  
            return self.paths
  
  
  if __name__ == "__main__":
   import doctest
  
   doctest.testmod()
  
  
  
  
  
  