


import logging
import os
from dataclasses import dataclass
from enum import Enum
from typing import List, Optional, Union

from filelock import FileLock

from transformers import PreTrainedTokenizer, is_tf_available, is_torch_available


snake_case							: int      =   logging.getLogger(__name__)







@dataclass
class  snake_case_     :
					UpperCAmelCase__      :					str
					UpperCAmelCase__      :					List[str]
					UpperCAmelCase__      :					Optional[List[str]]







@dataclass
class  snake_case_     :
					UpperCAmelCase__      :					List[int]
					UpperCAmelCase__      :					List[int]
					UpperCAmelCase__      :					Optional[List[int]]					   =    None
					UpperCAmelCase__      :					Optional[List[int]]					   =    None







class  snake_case_     (lowerCamelCase_   ):
					UpperCAmelCase__      :					List[Any]					   =    '''train'''
					UpperCAmelCase__      :					str					   =    '''dev'''
					UpperCAmelCase__      :					Union[str, Any]					   =    '''test'''







class  snake_case_     :
					@staticmethod
					def 				lowerCamelCase__(   __snake_case     :List[str]    ,__snake_case     :Union[Split, str]   )      ->					List[InputExample]:
												raise NotImplementedError
					@staticmethod
					def 				lowerCamelCase__(   __snake_case     :str   )      ->					List[str]:
												raise NotImplementedError



					@staticmethod
					def 				lowerCamelCase__(   __snake_case     :List[InputExample]    ,__snake_case     :List[str]    ,__snake_case     :int    ,__snake_case     :PreTrainedTokenizer    ,__snake_case     :List[Any]=False    ,__snake_case     :str="[CLS]"    ,__snake_case     :List[str]=1    ,__snake_case     :str="[SEP]"    ,__snake_case     :Optional[int]=False    ,__snake_case     :List[str]=False    ,__snake_case     :List[Any]=0    ,__snake_case     :Optional[int]=0    ,__snake_case     :int=-1_00    ,__snake_case     :str=0    ,__snake_case     :Union[str, Any]=True    ,)      ->					List[InputFeatures]:
												a__    =  {label: i for i, label in enumerate(__snake_case   )}

												a__    =  []
												for ex_index, example in enumerate(__snake_case   ):
																			if ex_index % 1_00_00 == 0:
																										logger.info('Writing example %d of %d'    ,__snake_case    ,len(__snake_case   )   )

																			a__    =  []
																			a__    =  []
																			for word, label in zip(example.words    ,example.labels   ):
																										a__    =  tokenizer.tokenize(__snake_case   )

																										# bert-base-multilingual-cased sometimes output "nothing ([]) when calling tokenize with just a space.
																										if len(__snake_case   ) > 0:
																																	tokens.extend(__snake_case   )
																																	# Use the real label id for the first token of the word, and padding ids for the remaining tokens
																																	label_ids.extend([label_map[label]] + [pad_token_label_id] * (len(__snake_case   ) - 1)   )

            # Account for [CLS] and [SEP] with "- 2" and with "- 3" for RoBERTa.
																			a__    =  tokenizer.num_special_tokens_to_add()
																			if len(__snake_case   ) > max_seq_length - special_tokens_count:
																										a__    =  tokens[: (max_seq_length - special_tokens_count)]
																										a__    =  label_ids[: (max_seq_length - special_tokens_count)]

																			# The convention in BERT is:
																			# (a) For sequence pairs:
																			#  tokens:   [CLS] is this jack ##son ##ville ? [SEP] no it is not . [SEP]
																			#  type_ids:   0   0  0    0    0     0       0   0   1  1  1  1   1   1
																			# (b) For single sequences:
																			#  tokens:   [CLS] the dog is hairy . [SEP]
																			#  type_ids:   0   0   0   0  0     0   0
																			#
																			# Where "type_ids" are used to indicate whether this is the first
																			# sequence or the second sequence. The embedding vectors for `type=0` and
																			# `type=1` were learned during pre-training and are added to the wordpiece
																			# embedding vector (and position vector). This is not *strictly* necessary
																			# since the [SEP] token unambiguously separates the sequences, but it makes
																			# it easier for the model to learn the concept of sequences.
																			#
																			# For classification tasks, the first vector (corresponding to [CLS]) is
																			# used as the "sentence vector". Note that this only makes sense because
																			# the entire model is fine-tuned.
																			tokens += [sep_token]
																			label_ids += [pad_token_label_id]
																			if sep_token_extra:
																										# roberta uses an extra separator b/w pairs of sentences
																										tokens += [sep_token]
																										label_ids += [pad_token_label_id]
																			a__    =  [sequence_a_segment_id] * len(__snake_case   )

																			if cls_token_at_end:
																										tokens += [cls_token]
																										label_ids += [pad_token_label_id]
																										segment_ids += [cls_token_segment_id]
																			else:
																										a__    =  [cls_token] + tokens
																										a__    =  [pad_token_label_id] + label_ids
																										a__    =  [cls_token_segment_id] + segment_ids

																			a__    =  tokenizer.convert_tokens_to_ids(__snake_case   )

																			# The mask has 1 for real tokens and 0 for padding tokens. Only real
																			# tokens are attended to.
																			a__    =  [1 if mask_padding_with_zero else 0] * len(__snake_case   )

																			# Zero-pad up to the sequence length.
																			a__    =  max_seq_length - len(__snake_case   )
																			if pad_on_left:
																										a__    =  ([pad_token] * padding_length) + input_ids
																										a__    =  ([0 if mask_padding_with_zero else 1] * padding_length) + input_mask
																										a__    =  ([pad_token_segment_id] * padding_length) + segment_ids
																										a__    =  ([pad_token_label_id] * padding_length) + label_ids
																			else:
																										input_ids += [pad_token] * padding_length
																										input_mask += [0 if mask_padding_with_zero else 1] * padding_length
																										segment_ids += [pad_token_segment_id] * padding_length
																										label_ids += [pad_token_label_id] * padding_length

																			assert len(__snake_case   ) == max_seq_length
																			assert len(__snake_case   ) == max_seq_length
																			assert len(__snake_case   ) == max_seq_length
																			assert len(__snake_case   ) == max_seq_length

																			if ex_index < 5:
																										logger.info('*** Example ***'   )
																										logger.info('guid: %s'    ,example.guid   )
																										logger.info('tokens: %s'    ,' '.join([str(__snake_case   ) for x in tokens]   )   )
																										logger.info('input_ids: %s'    ,' '.join([str(__snake_case   ) for x in input_ids]   )   )
																										logger.info('input_mask: %s'    ,' '.join([str(__snake_case   ) for x in input_mask]   )   )
																										logger.info('segment_ids: %s'    ,' '.join([str(__snake_case   ) for x in segment_ids]   )   )
																										logger.info('label_ids: %s'    ,' '.join([str(__snake_case   ) for x in label_ids]   )   )

																			if "token_type_ids" not in tokenizer.model_input_names:
																										a__    =  None

																			features.append(
																			    InputFeatures(
																			        input_ids=__snake_case    ,attention_mask=__snake_case    ,token_type_ids=__snake_case    ,label_ids=__snake_case   )   )
												return features


if is_torch_available():
						import torch
						from torch import nn
						from torch.utils.data import Dataset







						class  snake_case_     (lowerCamelCase_   ):
											UpperCAmelCase__      :					List[InputFeatures]
											UpperCAmelCase__      :					int					   =    nn.CrossEntropyLoss().ignore_index
											def __init__(   self     :Union[str, Any]    ,__snake_case     :TokenClassificationTask    ,__snake_case     :str    ,__snake_case     :PreTrainedTokenizer    ,__snake_case     :List[str]    ,__snake_case     :str    ,__snake_case     :Optional[int] = None    ,__snake_case     :Tuple=False    ,__snake_case     :Split = Split.train    ,)      ->					List[Any]:
																		# Load data features from cache or dataset file
																		a__    =  os.path.join(
																		    __snake_case    ,'cached_{}_{}_{}'.format(mode.value    ,tokenizer.__class__.__name__    ,str(__snake_case   )   )    ,)

																		# Make sure only the first process in distributed training processes the dataset,
																		# and the others will use the cache.
																		a__    =  cached_features_file + '.lock'
																		with FileLock(__snake_case   ):
																									if os.path.exists(__snake_case   ) and not overwrite_cache:
																																logger.info(F'Loading features from cached file {cached_features_file}'   )
																																a__    =  torch.load(__snake_case   )
																									else:
																																logger.info(F'Creating features from dataset file at {data_dir}'   )
																																a__    =  token_classification_task.read_examples_from_file(__snake_case    ,__snake_case   )
																																# TODO clean up all this to leverage built-in features of tokenizers
																																a__    =  token_classification_task.convert_examples_to_features(
																																    __snake_case    ,__snake_case    ,__snake_case    ,__snake_case    ,cls_token_at_end=bool(model_type in ['xlnet']   )    ,cls_token=tokenizer.cls_token    ,cls_token_segment_id=2 if model_type in ['xlnet'] else 0    ,sep_token=tokenizer.sep_token    ,sep_token_extra=__snake_case    ,pad_on_left=bool(tokenizer.padding_side == 'left'   )    ,pad_token=tokenizer.pad_token_id    ,pad_token_segment_id=tokenizer.pad_token_type_id    ,pad_token_label_id=self.pad_token_label_id    ,)
																																logger.info(F'Saving features into cached file {cached_features_file}'   )
																																torch.save(self.features    ,__snake_case   )
											def __len__(   self     :List[Any]   )      ->					str:
																		return len(self.features   )



											def __getitem__(   self     :Tuple    ,__snake_case     :Any   )      ->					InputFeatures:
																		return self.features[i]


if is_tf_available():
						import tensorflow as tf







						class  snake_case_     :
											UpperCAmelCase__      :					List[InputFeatures]
											UpperCAmelCase__      :					int					   =    -1_0_0
											def __init__(   self     :Optional[Any]    ,__snake_case     :TokenClassificationTask    ,__snake_case     :str    ,__snake_case     :PreTrainedTokenizer    ,__snake_case     :List[str]    ,__snake_case     :str    ,__snake_case     :Optional[int] = None    ,__snake_case     :Optional[int]=False    ,__snake_case     :Split = Split.train    ,)      ->					List[str]:
																		a__    =  token_classification_task.read_examples_from_file(__snake_case    ,__snake_case   )
																		# TODO clean up all this to leverage built-in features of tokenizers
																		a__    =  token_classification_task.convert_examples_to_features(
																		    __snake_case    ,__snake_case    ,__snake_case    ,__snake_case    ,cls_token_at_end=bool(model_type in ['xlnet']   )    ,cls_token=tokenizer.cls_token    ,cls_token_segment_id=2 if model_type in ['xlnet'] else 0    ,sep_token=tokenizer.sep_token    ,sep_token_extra=__snake_case    ,pad_on_left=bool(tokenizer.padding_side == 'left'   )    ,pad_token=tokenizer.pad_token_id    ,pad_token_segment_id=tokenizer.pad_token_type_id    ,pad_token_label_id=self.pad_token_label_id    ,)

																		def gen():
																									for ex in self.features:
																																if ex.token_type_ids is None:
																																							yield (
																																							    {"input_ids": ex.input_ids, "attention_mask": ex.attention_mask},
																																							    ex.label_ids,
																																							)
																																else:
																																							yield (
																																							    {
																																							        "input_ids": ex.input_ids,
																																							        "attention_mask": ex.attention_mask,
																																							        "token_type_ids": ex.token_type_ids,
																																							    },
																																							    ex.label_ids,
																																							)

																		if "token_type_ids" not in tokenizer.model_input_names:
																									a__    =  tf.data.Dataset.from_generator(
																									    __snake_case    ,({'input_ids': tf.intaa, 'attention_mask': tf.intaa}, tf.intaa)    ,(
																									        {'input_ids': tf.TensorShape([None]   ), 'attention_mask': tf.TensorShape([None]   )},
																									        tf.TensorShape([None]   ),
																									    )    ,)
																		else:
																									a__    =  tf.data.Dataset.from_generator(
																									    __snake_case    ,({'input_ids': tf.intaa, 'attention_mask': tf.intaa, 'token_type_ids': tf.intaa}, tf.intaa)    ,(
																									        {
																									            'input_ids': tf.TensorShape([None]   ),
																									            'attention_mask': tf.TensorShape([None]   ),
																									            'token_type_ids': tf.TensorShape([None]   ),
																									        },
																									        tf.TensorShape([None]   ),
																									    )    ,)
											def 				lowerCamelCase__(   self     :int   )      ->					Union[str, Any]:
																		a__    =  self.dataset.apply(tf.data.experimental.assert_cardinality(len(self.features   )   )   )

																		return self.dataset
											def __len__(   self     :Optional[int]   )      ->					Tuple:
																		return len(self.features   )



											def __getitem__(   self     :Union[str, Any]    ,__snake_case     :int   )      ->					InputFeatures:
																		return self.features[i]








from math import ceil, sqrt






def 							__lowercase     (				__lowerCAmelCase							:       int = 1_0_0_0_0_0_0     ):
							a__    =  0

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




