


def 	__lowerCamelCase						(							lowerCamelCase__		:						int      ):





			'''simple docstring'''




			if isinstance(lowerCamelCase__  ,							lowerCamelCase__      ):
						raise TypeError("""'float' object cannot be interpreted as an integer"""      )
			if isinstance(lowerCamelCase__  ,							lowerCamelCase__      ):
						raise TypeError("""'str' object cannot be interpreted as an integer"""      )

			if num == 0:
						return "0b0"

			lowerCamelCase    		=  False

			if num < 0:
						lowerCamelCase    		=  True
						lowerCamelCase    		=  -num

			lowerCamelCase    		=  []
			while num > 0:
						binary.insert(0  ,							num % 2      )
						num >>= 1

			if negative:
						return "-0b" + "".join(str(lowerCamelCase__      ) for e in binary      )

			return "0b" + "".join(str(lowerCamelCase__      ) for e in binary      )


if __name__ == "__main__":
		import doctest

		doctest.testmod()





def 	__lowerCamelCase						(							lowerCamelCase__		:						int      ):





			'''simple docstring'''




			lowerCamelCase    		=  (1 + 24 * n) ** 0.5
			return ((1 + root) / 6) % 1 == 0






def 	__lowerCamelCase						(							lowerCamelCase__		:						int = 5000      ):





			'''simple docstring'''




			lowerCamelCase    		=  [(i * (3 * i - 1)) // 2 for i in range(1  ,							lowerCamelCase__      )]
			for i, pentagonal_i in enumerate(lowerCamelCase__      ):
						for j in range(lowerCamelCase__  ,							len(lowerCamelCase__      )      ):
									lowerCamelCase    		=  pentagonal_nums[j]
									lowerCamelCase    		=  pentagonal_i + pentagonal_j
									lowerCamelCase    		=  pentagonal_j - pentagonal_i
									if is_pentagonal(lowerCamelCase__      ) and is_pentagonal(lowerCamelCase__      ):
												return b

			return -1


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

