




"""simple docstring"""







from __future__ import annotations

class 				snake_case_			:







   """simple docstring"""




   def __init__(		self       ,					lowerCamelCase_)				->   None:
       UpperCamelCase              =	data
       UpperCamelCase              =	None
       UpperCamelCase              =	None





def      __snake_case (				_lowercase    ):  # In Order traversal of the tree


    """simple docstring"""







    if tree:
        display(tree.left    )
        print(tree.data    )
        display(tree.right    )





def      __snake_case (				_lowercase    ):


    """simple docstring"""







    return 1 + max(depth_of_tree(tree.left    )			,depth_of_tree(tree.right    )    ) if tree else 0





def      __snake_case (				_lowercase    ):


    """simple docstring"""







    if not tree:
        return True
    if tree.left and tree.right:
        return is_full_binary_tree(tree.left    ) and is_full_binary_tree(tree.right    )
    else:
        return not tree.left and not tree.right





def      __snake_case (				):  # Main function for testing.


    """simple docstring"""







    UpperCamelCase              =	Node(1    )
    UpperCamelCase              =	Node(2    )
    UpperCamelCase              =	Node(3    )
    UpperCamelCase              =	Node(4    )
    UpperCamelCase              =	Node(5    )
    UpperCamelCase              =	Node(6    )
    UpperCamelCase              =	Node(7    )
    UpperCamelCase              =	Node(8    )
    UpperCamelCase              =	Node(9    )

    print(is_full_binary_tree(_lowercase    )    )
    print(depth_of_tree(_lowercase    )    )
    print('''Tree is: '''    )
    display(_lowercase    )


if __name__ == "__main__":
  main()




from __future__ import annotations

from math import ceil, floor, sqrt





def 		a__      (		_UpperCamelCase      :			int = 2_00_00_00				):
   __lowerCamelCase    				=     [0]
   __lowerCamelCase    				=     42

   for idx in range(1			,ceil(sqrt(target * 2				) * 1.1				)				):
      triangle_numbers.append(triangle_numbers[-1] + idx				)

   # we want this to be as close as possible to target
   __lowerCamelCase    				=     0
   # the area corresponding to the grid that gives the product closest to target
   __lowerCamelCase    				=     0
   # an estimate of b, using the quadratic formula
   __lowerCamelCase    				=     42
   # the largest integer less than b_estimate
   __lowerCamelCase    				=     42
   # the largest integer less than b_estimate
   __lowerCamelCase    				=     42
   # the triangle number corresponding to b_floor
   __lowerCamelCase    				=     42
   # the triangle number corresponding to b_ceil
   __lowerCamelCase    				=     42

   for idx_a, triangle_a in enumerate(triangle_numbers[1:]			,1				):
      __lowerCamelCase    				=     (-1 + sqrt(1 + 8 * target / triangle_a				)) / 2
      __lowerCamelCase    				=     floor(_UpperCamelCase				)
      __lowerCamelCase    				=     ceil(_UpperCamelCase				)
      __lowerCamelCase    				=     triangle_numbers[b_floor]
      __lowerCamelCase    				=     triangle_numbers[b_ceil]

      if abs(target - triangle_b_first_guess * triangle_a				) < abs(
          target - best_product				):
         __lowerCamelCase    				=     triangle_b_first_guess * triangle_a
         __lowerCamelCase    				=     idx_a * b_floor

      if abs(target - triangle_b_second_guess * triangle_a				) < abs(
          target - best_product				):
         __lowerCamelCase    				=     triangle_b_second_guess * triangle_a
         __lowerCamelCase    				=     idx_a * b_ceil

   return area


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






