"""simple docstring"""





from random import randint, random





def 				a_     (      _lowerCAmelCase  : int   , _lowerCAmelCase  : int   , _lowerCAmelCase  : int   , _lowerCAmelCase  : bool = False   , _lowerCAmelCase  : bool = False   , _lowerCAmelCase  : int = 5   , ):





       '''simple docstring'''

       lowercase__			:		str       =	[[-1] * number_of_cells]  # Create a highway without any car
       lowercase__			:		Union[str, Any]       =	0
       lowercase__			:		List[Any]       =	max(_lowerCAmelCase   , 0     )
       while i < number_of_cells:
              lowercase__			:		Tuple       =	(
                  randint(0   , _lowerCAmelCase     ) if random_speed else initial_speed
              )  # Place the cars
              i += (
                  randint(1   , max_speed * 2     ) if random_frequency else frequency
              )  # Arbitrary number, may need tuning
       return highway





def 				a_     (      _lowerCAmelCase  : list   , _lowerCAmelCase  : int     ):





       '''simple docstring'''

       lowercase__			:		Tuple       =	0
       lowercase__			:		List[Any]       =	highway_now[car_index + 1 :]
       for cell in range(len(_lowerCAmelCase     )     ):  # May need a better name for this
              if cells[cell] != -1:  # If the cell is not empty then
                     return distance  # we have the distance we wanted
              distance += 1
       # Here if the car is near the end of the highway
       return distance + get_distance(_lowerCAmelCase   , -1     )





def 				a_     (      _lowerCAmelCase  : list   , _lowerCAmelCase  : float   , _lowerCAmelCase  : int     ):





       '''simple docstring'''

       lowercase__			:		List[Any]       =	len(_lowerCAmelCase     )
       # Beforce calculations, the highway is empty
       lowercase__			:		Any       =	[-1] * number_of_cells

       for car_index in range(_lowerCAmelCase     ):
              if highway_now[car_index] != -1:
                     # Add 1 to the current speed of the car and cap the speed
                     lowercase__			:		Dict       =	min(highway_now[car_index] + 1   , _lowerCAmelCase     )
                     # Number of empty cell before the next car
                     lowercase__			:		Any       =	get_distance(_lowerCAmelCase   , _lowerCAmelCase     ) - 1
                     # We can't have the car causing an accident
                     lowercase__			:		Any       =	min(next_highway[car_index]   , _lowerCAmelCase     )
                     if random() < probability:
                            # Randomly, a driver will slow down
                            lowercase__			:		Tuple       =	max(next_highway[car_index] - 1   , 0     )
       return next_highway





def 				a_     (      _lowerCAmelCase  : list   , _lowerCAmelCase  : int   , _lowerCAmelCase  : float   , _lowerCAmelCase  : int     ):





       '''simple docstring'''

       lowercase__			:		Any       =	len(highway[0]     )

       for i in range(_lowerCAmelCase     ):
              lowercase__			:		List[Any]       =	update(highway[i]   , _lowerCAmelCase   , _lowerCAmelCase     )
              lowercase__			:		Union[str, Any]       =	[-1] * number_of_cells

              for car_index in range(_lowerCAmelCase     ):
                     lowercase__			:		Any       =	next_speeds_calculated[car_index]
                     if speed != -1:
                            # Change the position based on the speed (with % to create the loop)
                            lowercase__			:		Optional[int]       =	(car_index + speed) % number_of_cells
                            # Commit the change of position
                            lowercase__			:		Any       =	speed
              highway.append(_lowerCAmelCase     )

       return highway


if __name__ == "__main__":
       import doctest

       doctest.testmod()


'''simple docstring'''




from math import sqrt






def 				snake_case__							(			_A:					int = 1000000 )    ->	int:

		'''simple docstring'''


		lowerCAmelCase   					=  0
		lowerCAmelCase   					=  0
		lowerCAmelCase   					=  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(_A      ,   sum_shortest_sides // 2 )
								    - max(1      ,   sum_shortest_sides - max_cuboid_size )
								    + 1
								)

		return max_cuboid_size


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




