



'''simple docstring'''






def       lowerCamelCase__       (						_A = 1000				):
  a						:					List[Any]        =     -1
  a						:					Union[str, Any]        =     0
  for a in range(1 ,			n // 3				):
    # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
    a						:					str        =     (n * n - 2 * a * n) // (2 * n - 2 * a)
    a						:					Any        =     n - a - b
    if c * c == (a * a + b * b):
      a						:					Union[str, Any]        =     a * b * c
      if candidate >= product:
        a						:					List[Any]        =     candidate
  return product


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



'''simple docstring'''


import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ..auto import CONFIG_MAPPING


lowerCamelCase__					=   logging.get_logger(__name__)

lowerCamelCase__					=   {
    'ut/deta': 'https://huggingface.co/ut/deta/resolve/main/config.json',
}






class 		lowerCAmelCase__	(	UpperCAmelCase__		):
			lowerCAmelCase       :		Any				      =   "deta"
			lowerCAmelCase       :		Union[str, Any]				      =   {
			    "hidden_size": "d_model",
			    "num_attention_heads": "encoder_attention_heads",
			}




			def __init__(						self     :   Optional[Any]		,     lowerCamelCase__     :   str=None		,     lowerCamelCase__     :   str=9_00		,     lowerCamelCase__     :   Any=20_48		,     lowerCamelCase__     :   Optional[int]=6		,     lowerCamelCase__     :   str=20_48		,     lowerCamelCase__     :   Dict=8		,     lowerCamelCase__     :   Any=6		,     lowerCamelCase__     :   Union[str, Any]=10_24		,     lowerCamelCase__     :   Optional[int]=8		,     lowerCamelCase__     :   List[Any]=0.0		,     lowerCamelCase__     :   Tuple=True		,     lowerCamelCase__     :   int="relu"		,     lowerCamelCase__     :   str=2_56		,     lowerCamelCase__     :   Dict=0.1		,     lowerCamelCase__     :   Dict=0.0		,     lowerCamelCase__     :   Dict=0.0		,     lowerCamelCase__     :   Optional[int]=0.0_2		,     lowerCamelCase__     :   List[Any]=1.0		,     lowerCamelCase__     :   Optional[int]=True		,     lowerCamelCase__     :   Any=False		,     lowerCamelCase__     :   Any="sine"		,     lowerCamelCase__     :   str=5		,     lowerCamelCase__     :   Optional[int]=4		,     lowerCamelCase__     :   int=4		,     lowerCamelCase__     :   Optional[Any]=True		,     lowerCamelCase__     :   Dict=3_00		,     lowerCamelCase__     :   int=True		,     lowerCamelCase__     :   Dict=True		,     lowerCamelCase__     :   Union[str, Any]=1		,     lowerCamelCase__     :   Any=5		,     lowerCamelCase__     :   List[Any]=2		,     lowerCamelCase__     :   Union[str, Any]=1		,     lowerCamelCase__     :   str=1		,     lowerCamelCase__     :   Union[str, Any]=5		,     lowerCamelCase__     :   str=2		,     lowerCamelCase__     :   Optional[Any]=0.1		,     lowerCamelCase__     :   Union[str, Any]=0.2_5		,     **lowerCamelCase__     :   Optional[Any]		,     )      ->List[str]:



					'''simple docstring'''







					if backbone_config is None:
							logger.info("`backbone_config` is `None`. Initializing the config with the default `ResNet` backbone."       )
							_UpperCAmelCase						:				int	    =					CONFIG_MAPPING["resnet"](out_features=["stage2", "stage3", "stage4"]       )
					else:
							if isinstance(lowerCamelCase__		,     lowerCamelCase__       ):
									_UpperCAmelCase						:				Any	    =					backbone_config.pop("model_type"       )
									_UpperCAmelCase						:				Optional[int]	    =					CONFIG_MAPPING[backbone_model_type]
									_UpperCAmelCase						:				List[str]	    =					config_class.from_dict(lowerCamelCase__       )

					_UpperCAmelCase						:				Optional[Any]	    =					backbone_config
					_UpperCAmelCase						:				Optional[int]	    =					num_queries
					_UpperCAmelCase						:				Union[str, Any]	    =					max_position_embeddings
					_UpperCAmelCase						:				Union[str, Any]	    =					d_model
					_UpperCAmelCase						:				str	    =					encoder_ffn_dim
					_UpperCAmelCase						:				Optional[int]	    =					encoder_layers
					_UpperCAmelCase						:				int	    =					encoder_attention_heads
					_UpperCAmelCase						:				Union[str, Any]	    =					decoder_ffn_dim
					_UpperCAmelCase						:				Tuple	    =					decoder_layers
					_UpperCAmelCase						:				Union[str, Any]	    =					decoder_attention_heads
					_UpperCAmelCase						:				Any	    =					dropout
					_UpperCAmelCase						:				List[str]	    =					attention_dropout
					_UpperCAmelCase						:				Union[str, Any]	    =					activation_dropout
					_UpperCAmelCase						:				Optional[int]	    =					activation_function
					_UpperCAmelCase						:				str	    =					init_std
					_UpperCAmelCase						:				Tuple	    =					init_xavier_std
					_UpperCAmelCase						:				Optional[Any]	    =					encoder_layerdrop
					_UpperCAmelCase						:				int	    =					auxiliary_loss
					_UpperCAmelCase						:				Union[str, Any]	    =					position_embedding_type
					# deformable attributes
					_UpperCAmelCase						:				List[Any]	    =					num_feature_levels
					_UpperCAmelCase						:				List[Any]	    =					encoder_n_points
					_UpperCAmelCase						:				Tuple	    =					decoder_n_points
					_UpperCAmelCase						:				Optional[int]	    =					two_stage
					_UpperCAmelCase						:				Dict	    =					two_stage_num_proposals
					_UpperCAmelCase						:				int	    =					with_box_refine
					_UpperCAmelCase						:				str	    =					assign_first_stage
					if two_stage is True and with_box_refine is False:
							raise ValueError("If two_stage is True, with_box_refine must be True."       )
					# Hungarian matcher
					_UpperCAmelCase						:				Optional[int]	    =					class_cost
					_UpperCAmelCase						:				Dict	    =					bbox_cost
					_UpperCAmelCase						:				int	    =					giou_cost
					# Loss coefficients
					_UpperCAmelCase						:				int	    =					mask_loss_coefficient
					_UpperCAmelCase						:				List[Any]	    =					dice_loss_coefficient
					_UpperCAmelCase						:				Dict	    =					bbox_loss_coefficient
					_UpperCAmelCase						:				int	    =					giou_loss_coefficient
					_UpperCAmelCase						:				Optional[Any]	    =					eos_coefficient
					_UpperCAmelCase						:				int	    =					focal_alpha
					super().__init__(is_encoder_decoder=lowerCamelCase__		,     **lowerCamelCase__       )




			@property
			def 							lowerCAmelCase__			(						self     :   int       )      ->int:



					'''simple docstring'''







					return self.encoder_attention_heads




			@property
			def 							lowerCAmelCase__			(						self     :   List[Any]       )      ->int:



					'''simple docstring'''







					return self.d_model






			def 							lowerCAmelCase__			(						self     :   Union[str, Any]       )      ->int:



					'''simple docstring'''







					_UpperCAmelCase						:				Optional[int]	    =					copy.deepcopy(self.__dict__       )
					_UpperCAmelCase						:				Tuple	    =					self.backbone_config.to_dict()
					_UpperCAmelCase						:				List[Any]	    =					self.__class__.model_type
					return output



