



def   _UpperCamelCase				(						lowerCAmelCase_   )						->list[int]:

   if length <= 0 or not isinstance(lowerCAmelCase_  ,						lowerCAmelCase_   ):
      raise ValueError("""Length must be a positive integer."""   )
   return [n * (2 * n - 1) for n in range(lowerCAmelCase_   )]


if __name__ == "__main__":
 print(hexagonal_numbers(length=5))
 print(hexagonal_numbers(length=10))







from math import sqrt
def   _UpperCamelCase				(						lowerCAmelCase_ = 1_0_0_0_0_0_0   )						->int:
   UpperCAmelCase							=     0
   UpperCAmelCase							=     0
   UpperCAmelCase							=     42

   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(lowerCAmelCase_  ,						sum_shortest_sides // 2   )
                - max(1  ,						sum_shortest_sides - max_cuboid_size   )
                + 1
            )

   return max_cuboid_size


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



