




from __future__ import annotations

from math import ceil, floor, sqrt







def 			_a   (		SCREAMING_SNAKE_CASE_							:       int = 2_00_00_00  ):
					__lowerCAmelCase            = [0]
					__lowerCAmelCase            = 42

					for idx in range(1   ,   ceil(sqrt(target * 2  ) * 1.1  )  ):
										triangle_numbers.append(triangle_numbers[-1] + idx  )

					# we want this to be as close as possible to target
					__lowerCAmelCase            = 0
					# the area corresponding to the grid that gives the product closest to target
					__lowerCAmelCase            = 0
					# an estimate of b, using the quadratic formula
					__lowerCAmelCase            = 42
					# the largest integer less than b_estimate
					__lowerCAmelCase            = 42
					# the largest integer less than b_estimate
					__lowerCAmelCase            = 42
					# the triangle number corresponding to b_floor
					__lowerCAmelCase            = 42
					# the triangle number corresponding to b_ceil
					__lowerCAmelCase            = 42

					for idx_a, triangle_a in enumerate(triangle_numbers[1:]   ,   1  ):
										__lowerCAmelCase            = (-1 + sqrt(1 + 8 * target / triangle_a  )) / 2
										__lowerCAmelCase            = floor(SCREAMING_SNAKE_CASE_  )
										__lowerCAmelCase            = ceil(SCREAMING_SNAKE_CASE_  )
										__lowerCAmelCase            = triangle_numbers[b_floor]
										__lowerCAmelCase            = triangle_numbers[b_ceil]

										if abs(target - triangle_b_first_guess * triangle_a  ) < abs(
										    target - best_product  ):
															__lowerCAmelCase            = triangle_b_first_guess * triangle_a
															__lowerCAmelCase            = idx_a * b_floor

										if abs(target - triangle_b_second_guess * triangle_a  ) < abs(
										    target - best_product  ):
															__lowerCAmelCase            = triangle_b_second_guess * triangle_a
															__lowerCAmelCase            = idx_a * b_ceil

					return area


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










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


UpperCamelCase__					    =    logging.get_logger(__name__)

UpperCamelCase__					    =    {
    """facebook/nllb-moe-54B""": """https://huggingface.co/facebook/nllb-moe-54b/resolve/main/config.json""",
}
class     a__					(      snake_case__   ):
						_a							:					Tuple      =					"""nllb-moe"""
						_a							:					Dict      =					["""past_key_values"""]
						_a							:					Optional[int]      =					{"""num_attention_heads""": """encoder_attention_heads""", """hidden_size""": """d_model"""}






						def __init__(     self	,    _A=1_2_8_1_1_2	,    _A=1_0_2_4	,    _A=1_2	,    _A=4_0_9_6	,    _A=1_6	,    _A=1_2	,    _A=4_0_9_6	,    _A=1_6	,    _A=0.05	,    _A=0.05	,    _A=True	,    _A=True	,    _A="relu"	,    _A=1_0_2_4	,    _A=0.1	,    _A=0.1	,    _A=0.0	,    _A=0.02	,    _A=2	,    _A=True	,    _A=False	,    _A="float32"	,    _A=False	,    _A=1_2_8	,    _A=6_4	,    _A=4	,    _A=4	,    _A=0.0_01	,    _A=0.0_01	,    _A="all"	,    _A=False	,    _A=False	,    _A=1.0	,    _A=0.2	,    _A=1	,    _A=0	,    _A=2	,    _A=False	,    **_A	,    ):




											"""simple docstring"""



											__lowerCAmelCase            = vocab_size
											__lowerCAmelCase            = max_position_embeddings
											__lowerCAmelCase            = d_model
											__lowerCAmelCase            = encoder_ffn_dim
											__lowerCAmelCase            = encoder_layers
											__lowerCAmelCase            = encoder_attention_heads
											__lowerCAmelCase            = decoder_ffn_dim
											__lowerCAmelCase            = decoder_layers
											__lowerCAmelCase            = decoder_attention_heads
											__lowerCAmelCase            = dropout
											__lowerCAmelCase            = attention_dropout
											__lowerCAmelCase            = activation_dropout
											__lowerCAmelCase            = activation_function
											__lowerCAmelCase            = init_std
											__lowerCAmelCase            = encoder_layerdrop
											__lowerCAmelCase            = decoder_layerdrop
											__lowerCAmelCase            = use_cache
											__lowerCAmelCase            = encoder_layers
											__lowerCAmelCase            = scale_embedding  # scale factor will be sqrt(d_model) if True
											__lowerCAmelCase            = router_z_loss_coef
											__lowerCAmelCase            = router_aux_loss_coef
											__lowerCAmelCase            = decoder_sparse_step
											__lowerCAmelCase            = encoder_sparse_step
											__lowerCAmelCase            = num_experts
											__lowerCAmelCase            = expert_capacity
											__lowerCAmelCase            = 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}"""    )
											__lowerCAmelCase            = router_dtype

											__lowerCAmelCase            = router_ignore_padding_tokens
											__lowerCAmelCase            = batch_prioritized_routing
											__lowerCAmelCase            = second_expert_policy
											__lowerCAmelCase            = normalize_router_prob_before_dropping
											__lowerCAmelCase            = moe_eval_capacity_token_fraction
											__lowerCAmelCase            = moe_token_dropout
											__lowerCAmelCase            = output_router_logits
											super().__init__(
											    pad_token_id=_A	,    bos_token_id=_A	,    eos_token_id=_A	,    is_encoder_decoder=_A	,    decoder_start_token_id=_A	,    **_A	,    )




