






from collections import defaultdict
from math import ceil, sqrt




def 					lowercase__				(					__snake_case   :							int = 1_000_000					,	__snake_case   :							int = 10  ):


					'''simple docstring'''


					UpperCAmelCase_   :				defaultdict						=						defaultdict(__snake_case  )

					for outer_width in range(3					,	(t_limit // 4) + 2  ):
										if outer_width * outer_width > t_limit:
															UpperCAmelCase_   :				Union[str, Any]						=						max(
															    ceil(sqrt(outer_width * outer_width - t_limit  )  )					,	1  )
										else:
															UpperCAmelCase_   :				int						=						1

										hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

										for hole_width in range(__snake_case					,	outer_width - 1					,	2  ):
															count[outer_width * outer_width - hole_width * hole_width] += 1

					return sum(1 for n in count.values() if 1 <= n <= 10  )


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














import os
from shutil import copyfile
from typing import Any, Dict, List, Optional, Tuple

import sentencepiece as spm

from ...tokenization_utils import AddedToken, BatchEncoding, PreTrainedTokenizer
from ...utils import logging


__UpperCAmelCase     							=						logging.get_logger(__name__)

__UpperCAmelCase     							=						'▁'

__UpperCAmelCase     							=						{'vocab_file': 'sentencepiece.bpe.model'}

__UpperCAmelCase     							=						{
    'vocab_file': {
        'facebook/mbart-large-en-ro': (
            'https://huggingface.co/facebook/mbart-large-en-ro/resolve/main/sentencepiece.bpe.model'
        ),
        'facebook/mbart-large-cc25': (
            'https://huggingface.co/facebook/mbart-large-cc25/resolve/main/sentencepiece.bpe.model'
        ),
    }
}

__UpperCAmelCase     							=						{
    'facebook/mbart-large-en-ro': 1024,
    'facebook/mbart-large-cc25': 1024,
}

# fmt: off
__UpperCAmelCase     							=						['ar_AR', 'cs_CZ', 'de_DE', 'en_XX', 'es_XX', 'et_EE', 'fi_FI', 'fr_XX', 'gu_IN', 'hi_IN', 'it_IT', 'ja_XX', 'kk_KZ', 'ko_KR', 'lt_LT', 'lv_LV', 'my_MM', 'ne_NP', 'nl_XX', 'ro_RO', 'ru_RU', 'si_LK', 'tr_TR', 'vi_VN', 'zh_CN']



class   lowerCamelCase				(_snake_case      ):







		'''simple docstring'''



		_snake_case   :   List[Any]							=  VOCAB_FILES_NAMES
		_snake_case   :   Union[str, Any]							=  PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
		_snake_case   :   Tuple							=  PRETRAINED_VOCAB_FILES_MAP
		_snake_case   :   Any							=  ['''input_ids''', '''attention_mask''']

		_snake_case   :   List[int]							=  []
		_snake_case   :   List[int]							=  []



		def __init__(							self    ,		_UpperCamelCase    ,		_UpperCamelCase="<s>"    ,		_UpperCamelCase="</s>"    ,		_UpperCamelCase="</s>"    ,		_UpperCamelCase="<s>"    ,		_UpperCamelCase="<unk>"    ,		_UpperCamelCase="<pad>"    ,		_UpperCamelCase="<mask>"    ,		_UpperCamelCase=None    ,		_UpperCamelCase=None    ,		_UpperCamelCase=None    ,		_UpperCamelCase = None    ,		_UpperCamelCase=None    ,		**_UpperCamelCase    ,		)     ->							List[str]:
							# Mask token behave like a normal word, i.e. include the space before it
							UpperCAmelCase_   :				List[Any]						=						AddedToken(_UpperCamelCase    ,		lstrip=_UpperCamelCase    ,		rstrip=_UpperCamelCase       ) if isinstance(_UpperCamelCase    ,		_UpperCamelCase       ) else mask_token

							UpperCAmelCase_   :				Optional[int]						=						{} if sp_model_kwargs is None else sp_model_kwargs

							super().__init__(
							    bos_token=_UpperCamelCase    ,		eos_token=_UpperCamelCase    ,		unk_token=_UpperCamelCase    ,		sep_token=_UpperCamelCase    ,		cls_token=_UpperCamelCase    ,		pad_token=_UpperCamelCase    ,		mask_token=_UpperCamelCase    ,		tokenizer_file=_UpperCamelCase    ,		src_lang=_UpperCamelCase    ,		tgt_lang=_UpperCamelCase    ,		additional_special_tokens=_UpperCamelCase    ,		sp_model_kwargs=self.sp_model_kwargs    ,		**_UpperCamelCase    ,		)

							UpperCAmelCase_   :				Any						=						spm.SentencePieceProcessor(**self.sp_model_kwargs       )
							self.sp_model.Load(str(_UpperCamelCase       )       )
							UpperCAmelCase_   :				int						=						vocab_file

							# Original fairseq vocab and spm vocab must be "aligned":
							# Vocab    |    0    |    1    |   2    |    3    |  4  |  5  |  6  |   7   |   8   |  9
							# -------- | ------- | ------- | ------ | ------- | --- | --- | --- | ----- | ----- | ----
							# fairseq  | '<s>'   | '<pad>' | '</s>' | '<unk>' | ',' | '.' | '▁' | 's'   | '▁de' | '-'
							# spm      | '<unk>' | '<s>'   | '</s>' | ','     | '.' | '▁' | 's' | '▁de' | '-'   | '▁a'

							# Mimic fairseq token-to-id alignment for the first 4 token
							UpperCAmelCase_   :				List[str]						=						{'<s>': 0, '<pad>': 1, '</s>': 2, '<unk>': 3}

							# The first "real" token "," has position 4 in the original fairseq vocab and position 3 in the spm vocab
							UpperCAmelCase_   :				str						=						1

							UpperCAmelCase_   :				Optional[int]						=						len(self.sp_model       )
							UpperCAmelCase_   :				str						=						{
							    code: self.sp_model_size + i + self.fairseq_offset for i, code in enumerate(_UpperCamelCase       )
							}
							UpperCAmelCase_   :				int						=						{v: k for k, v in self.lang_code_to_id.items()}
							UpperCAmelCase_   :				List[Any]						=						len(self.sp_model       ) + len(self.lang_code_to_id       ) + self.fairseq_offset

							self.fairseq_tokens_to_ids.update(self.lang_code_to_id       )
							UpperCAmelCase_   :				Tuple						=						{v: k for k, v in self.fairseq_tokens_to_ids.items()}
							UpperCAmelCase_   :				int						=						list(self.lang_code_to_id.keys()       )

							if additional_special_tokens is not None:
												# Only add those special tokens if they are not already there.
												self._additional_special_tokens.extend(
												    [t for t in additional_special_tokens if t not in self._additional_special_tokens]       )

							UpperCAmelCase_   :				Any						=						src_lang if src_lang is not None else 'en_XX'
							UpperCAmelCase_   :				Any						=						self.lang_code_to_id[self._src_lang]
							UpperCAmelCase_   :				Dict						=						tgt_lang
							self.set_src_lang_special_tokens(self._src_lang       )



		def __getstate__(							self       )     ->							Dict:
							UpperCAmelCase_   :				Optional[int]						=						self.__dict__.copy()
							UpperCAmelCase_   :				str						=						None
							UpperCAmelCase_   :				str						=						self.sp_model.serialized_model_proto()
							return state



		def __setstate__(							self    ,		_UpperCamelCase       )     ->							Dict:
							UpperCAmelCase_   :				Union[str, Any]						=						d

							# for backward compatibility
							if not hasattr(self    ,		'sp_model_kwargs'       ):
												UpperCAmelCase_   :				Any						=						{}

							UpperCAmelCase_   :				Any						=						spm.SentencePieceProcessor(**self.sp_model_kwargs       )
							self.sp_model.LoadFromSerializedProto(self.sp_model_proto       )



		@property
		def  __UpperCAmelCase      (							self       )     ->							Tuple:
							return len(self.sp_model       ) + len(self.lang_code_to_id       ) + self.fairseq_offset + 1  # Plus 1 for the mask token



		@property
		def  __UpperCAmelCase      (							self       )     ->							str:
							return self._src_lang



		@src_lang.setter
		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase       )     ->							None:
							UpperCAmelCase_   :				Tuple						=						new_src_lang
							self.set_src_lang_special_tokens(self._src_lang       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase = None    ,		_UpperCamelCase = False       )     ->							List[int]:

							if already_has_special_tokens:
												return super().get_special_tokens_mask(
												    token_ids_a=_UpperCamelCase    ,		token_ids_a=_UpperCamelCase    ,		already_has_special_tokens=_UpperCamelCase       )

							UpperCAmelCase_   :				Tuple						=						[1] * len(self.prefix_tokens       )
							UpperCAmelCase_   :				Dict						=						[1] * len(self.suffix_tokens       )
							if token_ids_a is None:
												return prefix_ones + ([0] * len(_UpperCamelCase       )) + suffix_ones
							return prefix_ones + ([0] * len(_UpperCamelCase       )) + ([0] * len(_UpperCamelCase       )) + suffix_ones



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase = None       )     ->							List[int]:
							if token_ids_a is None:
												return self.prefix_tokens + token_ids_a + self.suffix_tokens
							# We don't expect to process pairs, but leave the pair logic for API consistency
							return self.prefix_tokens + token_ids_a + token_ids_a + self.suffix_tokens



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase = None       )     ->							List[int]:
							UpperCAmelCase_   :				int						=						[self.sep_token_id]
							UpperCAmelCase_   :				Optional[int]						=						[self.cls_token_id]

							if token_ids_a is None:
												return len(cls + token_ids_a + sep       ) * [0]
							return len(cls + token_ids_a + sep + sep + token_ids_a + sep       ) * [0]



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		**_UpperCamelCase       )     ->							int:
							if src_lang is None or tgt_lang is None:
												raise ValueError('Translation requires a `src_lang` and a `tgt_lang` for this model'       )
							UpperCAmelCase_   :				Optional[int]						=						src_lang
							UpperCAmelCase_   :				Dict						=						self(_UpperCamelCase    ,		add_special_tokens=_UpperCamelCase    ,		return_tensors=_UpperCamelCase    ,		**_UpperCamelCase       )
							UpperCAmelCase_   :				int						=						self.convert_tokens_to_ids(_UpperCamelCase       )
							UpperCAmelCase_   :				Any						=						tgt_lang_id
							return inputs



		def  __UpperCAmelCase      (							self       )     ->							str:
							UpperCAmelCase_   :				str						=						{self.convert_ids_to_tokens(_UpperCamelCase       ): i for i in range(self.vocab_size       )}
							vocab.update(self.added_tokens_encoder       )
							return vocab



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase       )     ->							List[str]:
							return self.sp_model.encode(_UpperCamelCase    ,		out_type=_UpperCamelCase       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase       )     ->							Tuple:
							if token in self.fairseq_tokens_to_ids:
												return self.fairseq_tokens_to_ids[token]
							UpperCAmelCase_   :				Dict						=						self.sp_model.PieceToId(_UpperCamelCase       )

							# Need to return unknown token if the SP model returned 0
							return spm_id + self.fairseq_offset if spm_id else self.unk_token_id



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase       )     ->							str:
							if index in self.fairseq_ids_to_tokens:
												return self.fairseq_ids_to_tokens[index]
							return self.sp_model.IdToPiece(index - self.fairseq_offset       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase       )     ->							Optional[int]:
							UpperCAmelCase_   :				Optional[int]						=						''.join(_UpperCamelCase       ).replace(_UpperCamelCase    ,		' '       ).strip()
							return out_string



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase = None       )     ->							Tuple[str]:
							if not os.path.isdir(_UpperCamelCase       ):
												logger.error(f"Vocabulary path ({save_directory}) should be a directory"       )
												return
							UpperCAmelCase_   :				List[Any]						=						os.path.join(
							    _UpperCamelCase    ,		(filename_prefix + '-' if filename_prefix else '') + VOCAB_FILES_NAMES['vocab_file']       )

							if os.path.abspath(self.vocab_file       ) != os.path.abspath(_UpperCamelCase       ) and os.path.isfile(self.vocab_file       ):
												copyfile(self.vocab_file    ,		_UpperCamelCase       )
							elif not os.path.isfile(self.vocab_file       ):
												with open(_UpperCamelCase    ,		'wb'       ) as fi:
																	UpperCAmelCase_   :				Optional[Any]						=						self.sp_model.serialized_model_proto()
																	fi.write(_UpperCamelCase       )

							return (out_vocab_file,)



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase = "en_XX"    ,		_UpperCamelCase = None    ,		_UpperCamelCase = "ro_RO"    ,		**_UpperCamelCase    ,		)     ->							BatchEncoding:
							UpperCAmelCase_   :				Union[str, Any]						=						src_lang
							UpperCAmelCase_   :				Dict						=						tgt_lang
							return super().prepare_seqaseq_batch(_UpperCamelCase    ,		_UpperCamelCase    ,		**_UpperCamelCase       )



		def  __UpperCAmelCase      (							self       )     ->							Union[str, Any]:
							return self.set_src_lang_special_tokens(self.src_lang       )



		def  __UpperCAmelCase      (							self       )     ->							Optional[Any]:
							return self.set_tgt_lang_special_tokens(self.tgt_lang       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase       )     ->							None:
							UpperCAmelCase_   :				Any						=						self.lang_code_to_id[src_lang]
							UpperCAmelCase_   :				Optional[Any]						=						[]
							UpperCAmelCase_   :				str						=						[self.eos_token_id, self.cur_lang_code]



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase       )     ->							None:
							UpperCAmelCase_   :				Any						=						self.lang_code_to_id[lang]
							UpperCAmelCase_   :				Dict						=						[]
							UpperCAmelCase_   :				int						=						[self.eos_token_id, self.cur_lang_code]






