


"""simple docstring"""






from math import sqrt





def 				A_       ( snake_case__ = 1_00_00_00		)					->  int:
			_UpperCamelCase					:int					     =	0
			_UpperCamelCase					:int					     =	0
			_UpperCamelCase					:int

			while num_cuboids <= limit:
						max_cuboid_size += 1
						for sum_shortest_sides in range(2       ,					2 * max_cuboid_size + 1		):
									if sqrt(sum_shortest_sides**2 + max_cuboid_size**2		).is_integer():
												num_cuboids += (
												    min(snake_case__       ,					sum_shortest_sides // 2		)
												    - max(1       ,					sum_shortest_sides - max_cuboid_size		)
												    + 1
												)

			return max_cuboid_size


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





"""simple docstring"""






def 				A_       ( snake_case__       ,					snake_case__ = " "		)					->  list:
			_UpperCamelCase					:List[str]					     =	[]

			_UpperCamelCase					:int					     =	0
			for index, char in enumerate(snake_case__		):
						if char == separator:
									split_words.append(string[last_index:index]		)
									_UpperCamelCase					:Dict					     =	index + 1
						elif index + 1 == len(snake_case__		):
									split_words.append(string[last_index : index + 1]		)
			return split_words


if __name__ == "__main__":
					from doctest import testmod

					testmod()

