




'''simple docstring'''
def 							snake_case_    (  a__						:      Optional[Any]     ):



    """simple docstring"""




    return n * (2 * n - 1)
def 							snake_case_    (  a__						:      Dict     ):



    """simple docstring"""




    __lowercase     							=		(1 + 24 * n) ** 0.5
    return ((1 + root) / 6) % 1 == 0
def 							snake_case_    (  a__						:      str = 1_44     ):



    """simple docstring"""




    __lowercase     							=		start
    __lowercase     							=		hexagonal_num(A__     )
    while not is_pentagonal(A__     ):
        n += 1
        __lowercase     							=		hexagonal_num(A__     )
    return num


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





def 					UpperCamelCase__		(							A__ = 400_0000       )  ->   int:

				if n <= 1:
								return 0
				snake_case__   :      Optional[Any]   				= 0
				snake_case__   :      Optional[int]   				= 2
				snake_case__   :      str   				= 0
				while 4 * b + a <= n:
								snake_case__				,    snake_case__   :      Optional[Any]   				= b, 4 * b + a
								count += a
				return count + b


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


