def       A	(    _lowercase		,  _lowercase		,  _lowercase		,  _lowercase						):
						global f  # a global dp table for knapsack
						if f[i][j] < 0:
												if j < wt[i - 1]:
																		SCREAMING_SNAKE_CASE							:    List[str]							=							mf_knapsack(i - 1		,  _lowercase		,  _lowercase		,  _lowercase						)
												else:
																		SCREAMING_SNAKE_CASE							:    List[Any]							=							max(
																		    mf_knapsack(i - 1		,  _lowercase		,  _lowercase		,  _lowercase						)		,  mf_knapsack(i - 1		,  _lowercase		,  _lowercase		,  j - wt[i - 1]						) + val[i - 1]		,  )
												SCREAMING_SNAKE_CASE							:    Optional[int]							=							val
						return f[i][j]
def       A	(    _lowercase		,  _lowercase		,  _lowercase		,  _lowercase						):
						SCREAMING_SNAKE_CASE							:    Tuple							=							[[0] * (w + 1) for _ in range(n + 1						)]

						for i in range(1		,  n + 1						):
												for w_ in range(1		,  w + 1						):
																		if wt[i - 1] <= w_:
																								SCREAMING_SNAKE_CASE							:    int							=							max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]		,  dp[i - 1][w_]						)
																		else:
																								SCREAMING_SNAKE_CASE							:    List[str]							=							dp[i - 1][w_]

						return dp[n][w_], dp
def       A	(    _lowercase		,  _lowercase		,  _lowercase						):
						if not (isinstance(_lowercase		,  (list, tuple)						) and isinstance(_lowercase		,  (list, tuple)						)):
												raise ValueError(
												    '''Both the weights and values vectors must be either lists or tuples'''						)

						SCREAMING_SNAKE_CASE							:    int							=							len(_lowercase						)
						if num_items != len(_lowercase						):
												SCREAMING_SNAKE_CASE							:    int							=							(
												    '''The number of weights must be the same as the number of values.\n'''
												    f"""But got {num_items} weights and {len(_lowercase						)} values"""
												)
												raise ValueError(_lowercase						)
						for i in range(_lowercase						):
												if not isinstance(wt[i]		,  _lowercase						):
																		SCREAMING_SNAKE_CASE							:    Tuple							=							(
																		    '''All weights must be integers but got weight of '''
																		    f"""type {type(wt[i]						)} at index {i}"""
																		)
																		raise TypeError(_lowercase						)

						SCREAMING_SNAKE_CASE				,  SCREAMING_SNAKE_CASE							:    Any							=							knapsack(_lowercase		,  _lowercase		,  _lowercase		,  _lowercase						)
						SCREAMING_SNAKE_CASE							:    set							=							set()
						_construct_solution(_lowercase		,  _lowercase		,  _lowercase		,  _lowercase		,  _lowercase						)

						return optimal_val, example_optional_set
def       A	(    _lowercase		,  _lowercase		,  _lowercase		,  _lowercase		,  _lowercase						):
						# for the current item i at a maximum weight j to be part of an optimal subset,
						# the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
						# where i - 1 means considering only the previous items at the given maximum weight
						if i > 0 and j > 0:
												if dp[i - 1][j] == dp[i][j]:
																		_construct_solution(_lowercase		,  _lowercase		,  i - 1		,  _lowercase		,  _lowercase						)
												else:
																		optimal_set.add(_lowercase						)
																		_construct_solution(_lowercase		,  _lowercase		,  i - 1		,  j - wt[i - 1]		,  _lowercase						)


if __name__ == "__main__":
					__UpperCamelCase		:       Any									=     [3, 2, 4, 4]
					__UpperCamelCase		:       Optional[int]									=     [4, 3, 2, 3]
					__UpperCamelCase		:       Tuple									=     4
					__UpperCamelCase		:       Optional[int]									=     6
					__UpperCamelCase		:       int									=     [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
					__UpperCamelCase						,			__UpperCamelCase		:       Union[str, Any]									=     knapsack(w, wt, val, n)
					print(optimal_solution)
					print(mf_knapsack(n, wt, val, w))  # switched the n and w

					# testing the dynamic programming problem with example
					# the optimal subset for the above example are items 3 and 4
					__UpperCamelCase						,			__UpperCamelCase		:       Optional[int]									=     knapsack_with_example_solution(w, wt, val)
					assert optimal_solution == 8
					assert optimal_subset == {3, 4}
					print('optimal_value = ', optimal_solution)
					print('An optimal subset corresponding to the optimal value', optimal_subset)






from ...configuration_utils import PretrainedConfig
from ...utils import logging


__UpperCamelCase		:       Any									=     logging.get_logger(__name__)

__UpperCamelCase		:       Optional[int]									=     {
    'facebook/nllb-moe-54B': 'https://huggingface.co/facebook/nllb-moe-54b/resolve/main/config.json',
}





class 					lowercase__						(   UpperCamelCase_):
						UpperCamelCase_     =		"""nllb-moe"""
						UpperCamelCase_     =		["""past_key_values"""]
						UpperCamelCase_     =		{"""num_attention_heads""": """encoder_attention_heads""", """hidden_size""": """d_model"""}


						def __init__(       self	:				List[str]    ,		UpperCamelCase__	:				List[str]=12_8112    ,		UpperCamelCase__	:				str=1024    ,		UpperCamelCase__	:				Optional[int]=12    ,		UpperCamelCase__	:				Union[str, Any]=4096    ,		UpperCamelCase__	:				Optional[Any]=16    ,		UpperCamelCase__	:				Optional[Any]=12    ,		UpperCamelCase__	:				str=4096    ,		UpperCamelCase__	:				Dict=16    ,		UpperCamelCase__	:				Any=0.05    ,		UpperCamelCase__	:				Any=0.05    ,		UpperCamelCase__	:				Optional[Any]=True    ,		UpperCamelCase__	:				Optional[Any]=True    ,		UpperCamelCase__	:				List[Any]="relu"    ,		UpperCamelCase__	:				Union[str, Any]=1024    ,		UpperCamelCase__	:				Optional[int]=0.1    ,		UpperCamelCase__	:				Any=0.1    ,		UpperCamelCase__	:				Optional[Any]=0.0    ,		UpperCamelCase__	:				str=0.02    ,		UpperCamelCase__	:				Tuple=2    ,		UpperCamelCase__	:				List[str]=True    ,		UpperCamelCase__	:				Dict=False    ,		UpperCamelCase__	:				Any="float32"    ,		UpperCamelCase__	:				List[Any]=False    ,		UpperCamelCase__	:				Tuple=128    ,		UpperCamelCase__	:				Tuple=64    ,		UpperCamelCase__	:				List[str]=4    ,		UpperCamelCase__	:				Union[str, Any]=4    ,		UpperCamelCase__	:				Dict=0.001    ,		UpperCamelCase__	:				Optional[Any]=0.001    ,		UpperCamelCase__	:				Optional[Any]="all"    ,		UpperCamelCase__	:				Tuple=False    ,		UpperCamelCase__	:				List[Any]=False    ,		UpperCamelCase__	:				List[Any]=1.0    ,		UpperCamelCase__	:				str=0.2    ,		UpperCamelCase__	:				List[Any]=1    ,		UpperCamelCase__	:				List[Any]=0    ,		UpperCamelCase__	:				Optional[int]=2    ,		UpperCamelCase__	:				Tuple=False    ,		**UpperCamelCase__	:				Union[str, Any]    ,		):





												'''simple docstring'''





												SCREAMING_SNAKE_CASE							:    List[str]							=							vocab_size
												SCREAMING_SNAKE_CASE							:    Dict							=							max_position_embeddings
												SCREAMING_SNAKE_CASE							:    int							=							d_model
												SCREAMING_SNAKE_CASE							:    Any							=							encoder_ffn_dim
												SCREAMING_SNAKE_CASE							:    List[Any]							=							encoder_layers
												SCREAMING_SNAKE_CASE							:    Union[str, Any]							=							encoder_attention_heads
												SCREAMING_SNAKE_CASE							:    List[str]							=							decoder_ffn_dim
												SCREAMING_SNAKE_CASE							:    Dict							=							decoder_layers
												SCREAMING_SNAKE_CASE							:    List[Any]							=							decoder_attention_heads
												SCREAMING_SNAKE_CASE							:    List[str]							=							dropout
												SCREAMING_SNAKE_CASE							:    Any							=							attention_dropout
												SCREAMING_SNAKE_CASE							:    Union[str, Any]							=							activation_dropout
												SCREAMING_SNAKE_CASE							:    List[Any]							=							activation_function
												SCREAMING_SNAKE_CASE							:    Union[str, Any]							=							init_std
												SCREAMING_SNAKE_CASE							:    int							=							encoder_layerdrop
												SCREAMING_SNAKE_CASE							:    List[Any]							=							decoder_layerdrop
												SCREAMING_SNAKE_CASE							:    Any							=							use_cache
												SCREAMING_SNAKE_CASE							:    str							=							encoder_layers
												SCREAMING_SNAKE_CASE							:    List[Any]							=							scale_embedding  # scale factor will be sqrt(d_model) if True
												SCREAMING_SNAKE_CASE							:    List[str]							=							router_z_loss_coef
												SCREAMING_SNAKE_CASE							:    List[str]							=							router_aux_loss_coef
												SCREAMING_SNAKE_CASE							:    int							=							decoder_sparse_step
												SCREAMING_SNAKE_CASE							:    Optional[int]							=							encoder_sparse_step
												SCREAMING_SNAKE_CASE							:    List[str]							=							num_experts
												SCREAMING_SNAKE_CASE							:    int							=							expert_capacity
												SCREAMING_SNAKE_CASE							:    Any							=							router_bias
												if router_dtype not in ["float32", "float16", "bfloat16"]:
																		raise ValueError(f"""`router_dtype` must be one of 'float32', 'float16' or 'bfloat16', got {router_dtype}"""						)
												SCREAMING_SNAKE_CASE							:    str							=							router_dtype

												SCREAMING_SNAKE_CASE							:    List[Any]							=							router_ignore_padding_tokens
												SCREAMING_SNAKE_CASE							:    int							=							batch_prioritized_routing
												SCREAMING_SNAKE_CASE							:    str							=							second_expert_policy
												SCREAMING_SNAKE_CASE							:    Optional[Any]							=							normalize_router_prob_before_dropping
												SCREAMING_SNAKE_CASE							:    Optional[Any]							=							moe_eval_capacity_token_fraction
												SCREAMING_SNAKE_CASE							:    Optional[int]							=							moe_token_dropout
												SCREAMING_SNAKE_CASE							:    Optional[int]							=							output_router_logits
												super().__init__(
												    pad_token_id=UpperCamelCase__    ,		bos_token_id=UpperCamelCase__    ,		eos_token_id=UpperCamelCase__    ,		is_encoder_decoder=UpperCamelCase__    ,		decoder_start_token_id=UpperCamelCase__    ,		**UpperCamelCase__    ,		)





