





from math import ceil, sqrt





def     _UpperCamelCase     (a__   :int = 100_0000       ):






							"""simple docstring"""





							UpperCamelCase__				     =			0

							for outer_width in range(3   ,			(limit // 4) + 2       ):
														if outer_width**2 > limit:
																					UpperCamelCase__				     =			max(ceil(sqrt(outer_width**2 - limit       )       )   ,			1       )
														else:
																					UpperCamelCase__				     =			1
														if (outer_width - hole_width_lower_bound) % 2:
																					hole_width_lower_bound += 1

														answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

							return answer


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











import math

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


UpperCamelCase__											= logging.get_logger(__name__)

UpperCamelCase__											= {
    "facebook/data2vec-base-960h": "https://huggingface.co/facebook/data2vec-audio-base-960h/resolve/main/config.json",
    # See all Data2VecAudio models at https://huggingface.co/models?filter=data2vec-audio
}

class        __SCREAMING_SNAKE_CASE					(     _a       ):
							snake_case     :      Optional[Any]						     =       """data2vec-audio"""






							def __init__(						self  , __lowerCAmelCase=32  , __lowerCAmelCase=768  , __lowerCAmelCase=12  , __lowerCAmelCase=12  , __lowerCAmelCase=3072  , __lowerCAmelCase="gelu"  , __lowerCAmelCase=0.1  , __lowerCAmelCase=0.1  , __lowerCAmelCase=0.1  , __lowerCAmelCase=0.0  , __lowerCAmelCase=0.1  , __lowerCAmelCase=0.1  , __lowerCAmelCase=0.02  , __lowerCAmelCase=1E-5  , __lowerCAmelCase="gelu"  , __lowerCAmelCase=(512, 512, 512, 512, 512, 512, 512)  , __lowerCAmelCase=(5, 2, 2, 2, 2, 2, 2)  , __lowerCAmelCase=(10, 3, 3, 3, 3, 2, 2)  , __lowerCAmelCase=False  , __lowerCAmelCase=16  , __lowerCAmelCase=19  , __lowerCAmelCase=5  , __lowerCAmelCase=0.05  , __lowerCAmelCase=10  , __lowerCAmelCase=2  , __lowerCAmelCase=0.0  , __lowerCAmelCase=10  , __lowerCAmelCase=0  , __lowerCAmelCase="sum"  , __lowerCAmelCase=False  , __lowerCAmelCase=False  , __lowerCAmelCase=256  , __lowerCAmelCase=(512, 512, 512, 512, 1500)  , __lowerCAmelCase=(5, 3, 3, 1, 1)  , __lowerCAmelCase=(1, 2, 3, 1, 1)  , __lowerCAmelCase=512  , __lowerCAmelCase=0  , __lowerCAmelCase=1  , __lowerCAmelCase=2  , __lowerCAmelCase=False  , __lowerCAmelCase=3  , __lowerCAmelCase=2  , __lowerCAmelCase=3  , __lowerCAmelCase=None  , **__lowerCAmelCase  , ):
														super().__init__(**__lowerCAmelCase  , pad_token_id=__lowerCAmelCase  , bos_token_id=__lowerCAmelCase  , eos_token_id=__lowerCAmelCase  )
														UpperCamelCase__				     =			hidden_size
														UpperCamelCase__				     =			feat_extract_activation
														UpperCamelCase__				     =			list(__lowerCAmelCase  )
														UpperCamelCase__				     =			list(__lowerCAmelCase  )
														UpperCamelCase__				     =			list(__lowerCAmelCase  )
														UpperCamelCase__				     =			conv_bias
														UpperCamelCase__				     =			num_conv_pos_embeddings
														UpperCamelCase__				     =			num_conv_pos_embedding_groups
														UpperCamelCase__				     =			conv_pos_kernel_size
														UpperCamelCase__				     =			len(self.conv_dim  )
														UpperCamelCase__				     =			num_hidden_layers
														UpperCamelCase__				     =			intermediate_size
														UpperCamelCase__				     =			hidden_act
														UpperCamelCase__				     =			num_attention_heads
														UpperCamelCase__				     =			hidden_dropout
														UpperCamelCase__				     =			attention_dropout
														UpperCamelCase__				     =			activation_dropout
														UpperCamelCase__				     =			feat_proj_dropout
														UpperCamelCase__				     =			final_dropout
														UpperCamelCase__				     =			layerdrop
														UpperCamelCase__				     =			layer_norm_eps
														UpperCamelCase__				     =			initializer_range
														UpperCamelCase__				     =			vocab_size
														UpperCamelCase__				     =			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
														UpperCamelCase__				     =			mask_time_prob
														UpperCamelCase__				     =			mask_time_length
														UpperCamelCase__				     =			mask_time_min_masks
														UpperCamelCase__				     =			mask_feature_prob
														UpperCamelCase__				     =			mask_feature_length
														UpperCamelCase__				     =			mask_feature_min_masks

														# ctc loss
														UpperCamelCase__				     =			ctc_loss_reduction
														UpperCamelCase__				     =			ctc_zero_infinity

														# adapter
														UpperCamelCase__				     =			add_adapter
														UpperCamelCase__				     =			adapter_kernel_size
														UpperCamelCase__				     =			adapter_stride
														UpperCamelCase__				     =			num_adapter_layers
														UpperCamelCase__				     =			output_hidden_size or hidden_size

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

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







							@property
							def 				_lowerCamelCase		(						self  ):
														return math.prod(self.conv_stride  )




