


'''simple docstring'''
import math







def       a_				(	UpperCamelCase_ ):
							A_			    =		math.loga(math.sqrt(4 * positive_integer + 1 ) / 2 + 1 / 2 )

							return exponent == int(UpperCamelCase_ )







def       a_				(	UpperCamelCase_ = 1 / 1_2_3_4_5 ):
							A_			    =		0
							A_			    =		0

							A_			    =		3
							while True:
														A_			    =		(integer**2 - 1) / 4
														# if candidate is an integer, then there is a partition for k
														if partition_candidate == int(UpperCamelCase_ ):
																					A_			    =		int(UpperCamelCase_ )
																					total_partitions += 1
																					if check_partition_perfect(UpperCamelCase_ ):
																												perfect_partitions += 1
														if perfect_partitions > 0:
																					if perfect_partitions / total_partitions < max_proportion:
																												return int(UpperCamelCase_ )
														integer += 1


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









'''simple docstring'''
import functools
import operator

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


__SCREAMING_SNAKE_CASE					:				Dict									=		logging.get_logger(__name__)

__SCREAMING_SNAKE_CASE					:				int									=		{
    '''facebook/wav2vec2-base-960h''': '''https://huggingface.co/facebook/wav2vec2-base-960h/resolve/main/config.json''',
    # See all Wav2Vec2 models at https://huggingface.co/models?filter=wav2vec2
}






class 					__lowerCAmelCase   (   lowercase						):

						"""simple docstring"""






						_UpperCAmelCase		:       Dict   						="wav2vec2"






						def __init__(  self							:      str ,  lowerCAmelCase							:      Dict=32 ,  lowerCAmelCase							:      List[Any]=7_68 ,  lowerCAmelCase							:      List[str]=12 ,  lowerCAmelCase							:      List[str]=12 ,  lowerCAmelCase							:      List[Any]=30_72 ,  lowerCAmelCase							:      Optional[Any]="gelu" ,  lowerCAmelCase							:      Optional[int]=0.1 ,  lowerCAmelCase							:      Optional[int]=0.1 ,  lowerCAmelCase							:      List[Any]=0.1 ,  lowerCAmelCase							:      Dict=0.0 ,  lowerCAmelCase							:      Union[str, Any]=0.0 ,  lowerCAmelCase							:      str=0.1 ,  lowerCAmelCase							:      List[str]=0.1 ,  lowerCAmelCase							:      Dict=0.0_2 ,  lowerCAmelCase							:      List[str]=1e-5 ,  lowerCAmelCase							:      Optional[Any]="group" ,  lowerCAmelCase							:      List[Any]="gelu" ,  lowerCAmelCase							:      int=(5_12, 5_12, 5_12, 5_12, 5_12, 5_12, 5_12) ,  lowerCAmelCase							:      Union[str, Any]=(5, 2, 2, 2, 2, 2, 2) ,  lowerCAmelCase							:      Any=(10, 3, 3, 3, 3, 2, 2) ,  lowerCAmelCase							:      str=False ,  lowerCAmelCase							:      Tuple=1_28 ,  lowerCAmelCase							:      Union[str, Any]=16 ,  lowerCAmelCase							:      List[str]=False ,  lowerCAmelCase							:      Union[str, Any]=True ,  lowerCAmelCase							:      Any=0.0_5 ,  lowerCAmelCase							:      Any=10 ,  lowerCAmelCase							:      Dict=2 ,  lowerCAmelCase							:      List[Any]=0.0 ,  lowerCAmelCase							:      int=10 ,  lowerCAmelCase							:      List[str]=0 ,  lowerCAmelCase							:      Tuple=3_20 ,  lowerCAmelCase							:      List[str]=2 ,  lowerCAmelCase							:      int=0.1 ,  lowerCAmelCase							:      List[Any]=1_00 ,  lowerCAmelCase							:      List[str]=2_56 ,  lowerCAmelCase							:      int=2_56 ,  lowerCAmelCase							:      Optional[Any]=0.1 ,  lowerCAmelCase							:      str="sum" ,  lowerCAmelCase							:      List[Any]=False ,  lowerCAmelCase							:      List[str]=False ,  lowerCAmelCase							:      Tuple=2_56 ,  lowerCAmelCase							:      str=(5_12, 5_12, 5_12, 5_12, 15_00) ,  lowerCAmelCase							:      List[str]=(5, 3, 3, 1, 1) ,  lowerCAmelCase							:      Tuple=(1, 2, 3, 1, 1) ,  lowerCAmelCase							:      Optional[Any]=5_12 ,  lowerCAmelCase							:      Any=0 ,  lowerCAmelCase							:      str=1 ,  lowerCAmelCase							:      Any=2 ,  lowerCAmelCase							:      Any=False ,  lowerCAmelCase							:      List[Any]=3 ,  lowerCAmelCase							:      Any=2 ,  lowerCAmelCase							:      List[str]=3 ,  lowerCAmelCase							:      int=None ,  lowerCAmelCase							:      Optional[int]=None ,  **lowerCAmelCase							:      Union[str, Any] ,  ):
													super().__init__(**lowerCAmelCase ,  pad_token_id=lowerCAmelCase ,  bos_token_id=lowerCAmelCase ,  eos_token_id=lowerCAmelCase	)
													A_			    =		hidden_size
													A_			    =		feat_extract_norm
													A_			    =		feat_extract_activation
													A_			    =		list(lowerCAmelCase	)
													A_			    =		list(lowerCAmelCase	)
													A_			    =		list(lowerCAmelCase	)
													A_			    =		conv_bias
													A_			    =		num_conv_pos_embeddings
													A_			    =		num_conv_pos_embedding_groups
													A_			    =		len(self.conv_dim	)
													A_			    =		num_hidden_layers
													A_			    =		intermediate_size
													A_			    =		hidden_act
													A_			    =		num_attention_heads
													A_			    =		hidden_dropout
													A_			    =		attention_dropout
													A_			    =		activation_dropout
													A_			    =		feat_proj_dropout
													A_			    =		final_dropout
													A_			    =		layerdrop
													A_			    =		layer_norm_eps
													A_			    =		initializer_range
													A_			    =		vocab_size
													A_			    =		do_stable_layer_norm
													A_			    =		use_weighted_layer_sum

													if (
													    (len(self.conv_stride	) != self.num_feat_extract_layers)
													    or (len(self.conv_kernel	) != self.num_feat_extract_layers)
													    or (len(self.conv_dim	) != self.num_feat_extract_layers)
													):
																				raise ValueError(
																				    "Configuration for convolutional layers is incorrect. It is required that `len(config.conv_dim)` =="
																				    " `len(config.conv_stride)` == `len(config.conv_kernel)`, but is `len(config.conv_dim) ="
																				    F" {len(self.conv_dim	)}`, `len(config.conv_stride) = {len(self.conv_stride	)}`,"
																				    F" `len(config.conv_kernel) = {len(self.conv_kernel	)}`."	)

													# fine-tuning config parameters for SpecAugment: https://arxiv.org/abs/1904.08779
													A_			    =		apply_spec_augment
													A_			    =		mask_time_prob
													A_			    =		mask_time_length
													A_			    =		mask_time_min_masks
													A_			    =		mask_feature_prob
													A_			    =		mask_feature_length
													A_			    =		mask_feature_min_masks

													# parameters for pretraining with codevector quantized representations
													A_			    =		num_codevectors_per_group
													A_			    =		num_codevector_groups
													A_			    =		contrastive_logits_temperature
													A_			    =		feat_quantizer_dropout
													A_			    =		num_negatives
													A_			    =		codevector_dim
													A_			    =		proj_codevector_dim
													A_			    =		diversity_loss_weight

													# ctc loss
													A_			    =		ctc_loss_reduction
													A_			    =		ctc_zero_infinity

													# adapter
													A_			    =		add_adapter
													A_			    =		adapter_kernel_size
													A_			    =		adapter_stride
													A_			    =		num_adapter_layers
													A_			    =		output_hidden_size or hidden_size
													A_			    =		adapter_attn_dim

													# SequenceClassification-specific parameter. Feel free to ignore for other classes.
													A_			    =		classifier_proj_size

													# XVector-specific parameters. Feel free to ignore for other classes.
													A_			    =		list(lowerCAmelCase	)
													A_			    =		list(lowerCAmelCase	)
													A_			    =		list(lowerCAmelCase	)
													A_			    =		xvector_output_dim






						@property
						def 				_UpperCAmelCase       (  self							:      Tuple	):
													return functools.reduce(operator.mul ,  self.conv_stride ,  1	)





