




'''simple docstring'''






from __future__ import annotations






def 		UpperCamelCase__     (		__SCREAMING_SNAKE_CASE		)						->      set[int]:
      snake_case__					:      Any  			=						{1}
      snake_case__					:      Optional[int]  			=						[1]
      for _ in range(2							,			depth + 1		):
            snake_case__					:      str  			=						[*previous_coefficients, 0]
            snake_case__					:      Optional[int]  			=						[0, *previous_coefficients]
            snake_case__					:      List[Any]  			=						[]
            for x, y in zip(snake_case_							,			snake_case_		):
                  coefficients.add(x + y		)
                  previous_coefficients.append(x + y		)
      return coefficients






def 		UpperCamelCase__     (		__SCREAMING_SNAKE_CASE		)						->      set[int]:
      snake_case__					:      List[str]  			=						set()
      for number in unique_coefficients:
            snake_case__					:      List[str]  			=						2
            snake_case__					:      Optional[Any]  			=						number
            while divisor**2 <= copy_number:
                  snake_case__					:      str  			=						0
                  while copy_number % divisor == 0:
                        copy_number //= divisor
                        multiplicity += 1
                  if multiplicity >= 2:
                        non_squarefrees.add(snake_case_		)
                        break
                  divisor += 1

      return unique_coefficients.difference(snake_case_		)






def 		UpperCamelCase__     (		__SCREAMING_SNAKE_CASE = 51		)						->      int:
      snake_case__					:      Tuple  			=						get_pascal_triangle_unique_coefficients(snake_case_		)
      snake_case__					:      Optional[Any]  			=						get_squarefrees(snake_case_		)
      return sum(snake_case_		)


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






'''simple docstring'''






class 					lowercase_			:





     def __init__(    self    :				Any ):
           snake_case__					:      List[str]  			=						[0]
           snake_case__					:      Optional[Any]  			=						0





     def  _lowerCAmelCase			(    self    :				List[str]    ,       __lowerCamelCase    :				int ):
           snake_case__					:      Optional[int]  			=						self.__heap[i]
           while i // 2 > 0:
                 if self.__heap[i] > self.__heap[i // 2]:
                       snake_case__					:      Union[str, Any]  			=						self.__heap[i // 2]
                       snake_case__					:      Union[str, Any]  			=						temporary
                 i //= 2





     def  _lowerCAmelCase			(    self    :				int    ,       __lowerCamelCase    :				int ):
           self.__heap.append(__lowerCamelCase )
           self.__size += 1
           self.__swap_up(self.__size )





     def  _lowerCAmelCase			(    self    :				Dict    ,       __lowerCamelCase    :				int ):
           while self.__size >= 2 * i:
                 if 2 * i + 1 > self.__size:
                       snake_case__					:      List[str]  			=						2 * i
                 else:
                       if self.__heap[2 * i] > self.__heap[2 * i + 1]:
                             snake_case__					:      Any  			=						2 * i
                       else:
                             snake_case__					:      Tuple  			=						2 * i + 1
                 snake_case__					:      int  			=						self.__heap[i]
                 if self.__heap[i] < self.__heap[bigger_child]:
                       snake_case__					:      Tuple  			=						self.__heap[bigger_child]
                       snake_case__					:      int  			=						temporary
                 snake_case__					:      int  			=						bigger_child





     def  _lowerCAmelCase			(    self    :				Union[str, Any] ):
           snake_case__					:      Any  			=						self.__heap[1]
           snake_case__					:      List[str]  			=						self.__heap[self.__size]
           self.__size -= 1
           self.__heap.pop()
           self.__swap_down(1 )
           return max_value





     @property
     def  _lowerCAmelCase			(    self    :				Union[str, Any] ):
           return self.__heap[1:]





     def __len__(    self    :				int ):
           return self.__size


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      # create an instance of BinaryHeap
      A_ 			=		BinaryHeap()
      binary_heap.insert(6)
      binary_heap.insert(10)
      binary_heap.insert(15)
      binary_heap.insert(12)
      # pop root(max-values because it is max heap)
      print(binary_heap.pop())  # 15
      print(binary_heap.pop())  # 12
      # get the list and size after operations
      print(binary_heap.get_list)
      print(len(binary_heap))
