'''simple docstring'''






def    __UpperCAmelCase			(  a_:       int							):
   _UpperCAmelCase							:	str							=   int(_lowerCamelCase							)
   if n_element < 1:
      _UpperCAmelCase							:	List[str]							=   ValueError("a should be a positive number"							)
      raise my_error

   _UpperCAmelCase							:	List[Any]							=   [1]
   _UpperCAmelCase							:	Optional[int]							=   (0, 0, 0)
   _UpperCAmelCase							:	List[str]							=   1
   while index < n_element:
      while hamming_list[i] * 2 <= hamming_list[-1]:
         i += 1
      while hamming_list[j] * 3 <= hamming_list[-1]:
         j += 1
      while hamming_list[k] * 5 <= hamming_list[-1]:
         k += 1
      hamming_list.append(
          min(hamming_list[i] * 2,					hamming_list[j] * 3,					hamming_list[k] * 5							)							)
      index += 1
   return hamming_list


if __name__ == "__main__":
     __a										=					input('Enter the last number (nth term) of the Hamming Number Series: ')
     print('Formula of Hamming Number Series => 2^i * 3^j * 5^k')
     __a										=					hamming(int(n))
     print('-----------------------------------------------------')
     print(f'The list with nth numbers is: {hamming_numbers}')
     print('-----------------------------------------------------')




'''simple docstring'''




import json
import os
from functools import lru_cache
from typing import Dict, List, Optional, Tuple, Union

import regex as re

from ...tokenization_utils import AddedToken, PreTrainedTokenizer
from ...tokenization_utils_base import BatchEncoding, EncodedInput
from ...utils import PaddingStrategy, logging


UpperCamelCase__       :	List[str]    = logging.get_logger(__name__)


UpperCamelCase__       :	Tuple    = {'''vocab_file''': '''vocab.json''', '''merges_file''': '''merges.txt'''}

# See all LED models at https://huggingface.co/models?filter=LED
UpperCamelCase__       :	Tuple    = {
    '''vocab_file''': {
        '''allenai/led-base-16384''': '''https://huggingface.co/allenai/led-base-16384/resolve/main/vocab.json''',
    },
    '''merges_file''': {
        '''allenai/led-base-16384''': '''https://huggingface.co/allenai/led-base-16384/resolve/main/merges.txt''',
    },
    '''tokenizer_file''': {
        '''allenai/led-base-16384''': '''https://huggingface.co/allenai/led-base-16384/resolve/main/tokenizer.json''',
    },
}

UpperCamelCase__       :	List[Any]    = {
    '''allenai/led-base-16384''': 1_63_84,
}


@lru_cache()
# Copied from transformers.models.bart.tokenization_bart.bytes_to_unicode
def 				lowerCAmelCase_   (	):
		__SCREAMING_SNAKE_CASE       :		Tuple           =		(
		    list(range(ord("""!"""					)       ,      ord("""~"""					) + 1					)					) + list(range(ord("""¡"""					)       ,      ord("""¬"""					) + 1					)					) + list(range(ord("""®"""					)       ,      ord("""ÿ"""					) + 1					)					)
		)
		__SCREAMING_SNAKE_CASE       :		Any           =		bs[:]
		__SCREAMING_SNAKE_CASE       :		Tuple           =		0
		for b in range(2**8					):
				if b not in bs:
						bs.append(_lowerCamelCase					)
						cs.append(2**8 + n					)
						n += 1
		__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		[chr(_lowerCamelCase					) for n in cs]
		return dict(zip(_lowerCamelCase       ,      _lowerCamelCase					)					)


def 				lowerCAmelCase_   (	_lowerCamelCase:   Optional[int]					):
		__SCREAMING_SNAKE_CASE       :		Dict           =		set()
		__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		word[0]
		for char in word[1:]:
				pairs.add((prev_char, char)					)
				__SCREAMING_SNAKE_CASE       :		str           =		char
		return pairs






class 						_UpperCamelCase  (							lowerCamelCase__    ):


			'''simple docstring'''

			_A      :		Union[str, Any]			    =		VOCAB_FILES_NAMES
			_A      :		Any			    =		PRETRAINED_VOCAB_FILES_MAP
			_A      :		Any			    =		PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
			_A      :		Optional[Any]			    =		['''input_ids''', '''attention_mask''']

			def __init__(							self     : Tuple							,     lowerCAmelCase__     : List[str]							,     lowerCAmelCase__     : Optional[Any]							,     lowerCAmelCase__     : Union[str, Any]="replace"							,     lowerCAmelCase__     : Dict="<s>"							,     lowerCAmelCase__     : List[str]="</s>"							,     lowerCAmelCase__     : Tuple="</s>"							,     lowerCAmelCase__     : Tuple="<s>"							,     lowerCAmelCase__     : Union[str, Any]="<unk>"							,     lowerCAmelCase__     : Union[str, Any]="<pad>"							,     lowerCAmelCase__     : int="<mask>"							,     lowerCAmelCase__     : str=False							,     **lowerCAmelCase__     : int							,     ):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		AddedToken(lowerCAmelCase__							,     lstrip=lowerCAmelCase__							,     rstrip=lowerCAmelCase__						) if isinstance(lowerCAmelCase__							,     lowerCAmelCase__						) else bos_token
					__SCREAMING_SNAKE_CASE       :		List[str]           =		AddedToken(lowerCAmelCase__							,     lstrip=lowerCAmelCase__							,     rstrip=lowerCAmelCase__						) if isinstance(lowerCAmelCase__							,     lowerCAmelCase__						) else eos_token
					__SCREAMING_SNAKE_CASE       :		List[str]           =		AddedToken(lowerCAmelCase__							,     lstrip=lowerCAmelCase__							,     rstrip=lowerCAmelCase__						) if isinstance(lowerCAmelCase__							,     lowerCAmelCase__						) else sep_token
					__SCREAMING_SNAKE_CASE       :		Dict           =		AddedToken(lowerCAmelCase__							,     lstrip=lowerCAmelCase__							,     rstrip=lowerCAmelCase__						) if isinstance(lowerCAmelCase__							,     lowerCAmelCase__						) else cls_token
					__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		AddedToken(lowerCAmelCase__							,     lstrip=lowerCAmelCase__							,     rstrip=lowerCAmelCase__						) if isinstance(lowerCAmelCase__							,     lowerCAmelCase__						) else unk_token
					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		AddedToken(lowerCAmelCase__							,     lstrip=lowerCAmelCase__							,     rstrip=lowerCAmelCase__						) if isinstance(lowerCAmelCase__							,     lowerCAmelCase__						) else pad_token

					# Mask token behave like a normal word, i.e. include the space before it
					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		AddedToken(lowerCAmelCase__							,     lstrip=lowerCAmelCase__							,     rstrip=lowerCAmelCase__						) if isinstance(lowerCAmelCase__							,     lowerCAmelCase__						) else mask_token

					super().__init__(
					    errors=lowerCAmelCase__							,     bos_token=lowerCAmelCase__							,     eos_token=lowerCAmelCase__							,     unk_token=lowerCAmelCase__							,     sep_token=lowerCAmelCase__							,     cls_token=lowerCAmelCase__							,     pad_token=lowerCAmelCase__							,     mask_token=lowerCAmelCase__							,     add_prefix_space=lowerCAmelCase__							,     **lowerCAmelCase__							,     )

					with open(lowerCAmelCase__							,     encoding="""utf-8"""						) as vocab_handle:
							__SCREAMING_SNAKE_CASE       :		str           =		json.load(lowerCAmelCase__						)
					__SCREAMING_SNAKE_CASE       :		List[str]           =		{v: k for k, v in self.encoder.items()}
					__SCREAMING_SNAKE_CASE       :		Dict           =		errors  # how to handle errors in decoding
					__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		bytes_to_unicode()
					__SCREAMING_SNAKE_CASE       :		Tuple           =		{v: k for k, v in self.byte_encoder.items()}
					with open(lowerCAmelCase__							,     encoding="""utf-8"""						) as merges_handle:
							__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		merges_handle.read().split("""\n"""						)[1:-1]
					__SCREAMING_SNAKE_CASE       :		int           =		[tuple(merge.split()						) for merge in bpe_merges]
					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		dict(zip(lowerCAmelCase__							,     range(len(lowerCAmelCase__						)						)						)						)
					__SCREAMING_SNAKE_CASE       :		int           =		{}
					__SCREAMING_SNAKE_CASE       :		Any           =		add_prefix_space

					# Should have added re.IGNORECASE so BPE merges can happen for capitalized versions of contractions
					__SCREAMING_SNAKE_CASE       :		str           =		re.compile(r"""'s|'t|'re|'ve|'m|'ll|'d| ?\p{L}+| ?\p{N}+| ?[^\s\p{L}\p{N}]+|\s+(?!\S)|\s+"""						)

			@property
			# Copied from transformers.models.bart.tokenization_bart.BartTokenizer.vocab_size
			def UpperCamelCase__					(							self     : Union[str, Any]						):





					"""simple docstring"""






					return len(self.encoder						)

			def UpperCamelCase__					(							self     : Any						):





					"""simple docstring"""






					return dict(self.encoder							,     **self.added_tokens_encoder						)

			def UpperCamelCase__					(							self     : Dict							,     lowerCAmelCase__     : Any						):





					"""simple docstring"""






					if token in self.cache:
							return self.cache[token]
					__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		tuple(lowerCAmelCase__						)
					__SCREAMING_SNAKE_CASE       :		Dict           =		get_pairs(lowerCAmelCase__						)

					if not pairs:
							return token

					while True:
							__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		min(lowerCAmelCase__							,     key=lambda lowerCAmelCase__						: self.bpe_ranks.get(lowerCAmelCase__							,     float("""inf"""						)						)						)
							if bigram not in self.bpe_ranks:
									break
							__SCREAMING_SNAKE_CASE       ,						__SCREAMING_SNAKE_CASE       :		Dict           =		bigram
							__SCREAMING_SNAKE_CASE       :		List[Any]           =		[]
							__SCREAMING_SNAKE_CASE       :		Optional[int]           =		0
							while i < len(lowerCAmelCase__						):
									try:
											__SCREAMING_SNAKE_CASE       :		Dict           =		word.index(lowerCAmelCase__							,     lowerCAmelCase__						)
									except ValueError:
											new_word.extend(word[i:]						)
											break
									else:
											new_word.extend(word[i:j]						)
											__SCREAMING_SNAKE_CASE       :		Dict           =		j

									if word[i] == first and i < len(lowerCAmelCase__						) - 1 and word[i + 1] == second:
											new_word.append(first + second						)
											i += 2
									else:
											new_word.append(word[i]						)
											i += 1
							__SCREAMING_SNAKE_CASE       :		Tuple           =		tuple(lowerCAmelCase__						)
							__SCREAMING_SNAKE_CASE       :		Any           =		new_word
							if len(lowerCAmelCase__						) == 1:
									break
							else:
									__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		get_pairs(lowerCAmelCase__						)
					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		""" """.join(lowerCAmelCase__						)
					__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		word
					return word

			def UpperCamelCase__					(							self     : Optional[Any]							,     lowerCAmelCase__     : Dict						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		[]
					for token in re.findall(self.pat							,     lowerCAmelCase__						):
							__SCREAMING_SNAKE_CASE       :		Any           =		"""""".join(
							    self.byte_encoder[b] for b in token.encode("""utf-8"""						)						)  # Maps all our bytes to unicode strings, avoiding control tokens of the BPE (spaces in our case)
							bpe_tokens.extend(bpe_token for bpe_token in self.bpe(lowerCAmelCase__						).split(""" """						)						)
					return bpe_tokens

			def UpperCamelCase__					(							self     : List[str]							,     lowerCAmelCase__     : List[str]						):





					"""simple docstring"""






					return self.encoder.get(lowerCAmelCase__							,     self.encoder.get(self.unk_token						)						)

			def UpperCamelCase__					(							self     : int							,     lowerCAmelCase__     : Optional[int]						):





					"""simple docstring"""






					return self.decoder.get(lowerCAmelCase__						)

			def UpperCamelCase__					(							self     : Optional[Any]							,     lowerCAmelCase__     : List[Any]						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		str           =		"""""".join(lowerCAmelCase__						)
					__SCREAMING_SNAKE_CASE       :		Optional[Any]           =		bytearray([self.byte_decoder[c] for c in text]						).decode("""utf-8"""							,     errors=self.errors						)
					return text

			def UpperCamelCase__					(							self     : List[str]							,     lowerCAmelCase__     : str							,     lowerCAmelCase__     : Optional[str] = None						):





					"""simple docstring"""






					if not os.path.isdir(lowerCAmelCase__						):
							logger.error(F"Vocabulary path ({save_directory}) should be a directory"						)
							return
					__SCREAMING_SNAKE_CASE       :		int           =		os.path.join(
					    lowerCAmelCase__							,     (filename_prefix + """-""" if filename_prefix else """""") + VOCAB_FILES_NAMES["""vocab_file"""]						)
					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		os.path.join(
					    lowerCAmelCase__							,     (filename_prefix + """-""" if filename_prefix else """""") + VOCAB_FILES_NAMES["""merges_file"""]						)

					with open(lowerCAmelCase__							,     """w"""							,     encoding="""utf-8"""						) as f:
							f.write(json.dumps(self.encoder							,     indent=2							,     sort_keys=lowerCAmelCase__							,     ensure_ascii=lowerCAmelCase__						) + """\n"""						)

					__SCREAMING_SNAKE_CASE       :		Tuple           =		0
					with open(lowerCAmelCase__							,     """w"""							,     encoding="""utf-8"""						) as writer:
							writer.write("""#version: 0.2\n"""						)
							for bpe_tokens, token_index in sorted(self.bpe_ranks.items()							,     key=lambda lowerCAmelCase__						: kv[1]						):
									if index != token_index:
											logger.warning(
											    F"Saving vocabulary to {merge_file}: BPE merge indices are not consecutive."
											    """ Please check that the tokenizer is not corrupted!"""						)
											__SCREAMING_SNAKE_CASE       :		List[Any]           =		token_index
									writer.write(""" """.join(lowerCAmelCase__						) + """\n"""						)
									index += 1

					return vocab_file, merge_file

			def UpperCamelCase__					(							self     : str							,     lowerCAmelCase__     : List[int]							,     lowerCAmelCase__     : Optional[List[int]] = None						):





					"""simple docstring"""






					if token_ids_a is None:
							return [self.cls_token_id] + token_ids_a + [self.sep_token_id]
					__SCREAMING_SNAKE_CASE       :		List[Any]           =		[self.cls_token_id]
					__SCREAMING_SNAKE_CASE       :		str           =		[self.sep_token_id]
					return cls + token_ids_a + sep + sep + token_ids_a + sep

			def UpperCamelCase__					(							self     : Any							,     lowerCAmelCase__     : List[int]							,     lowerCAmelCase__     : Optional[List[int]] = None							,     lowerCAmelCase__     : bool = False						):





					"""simple docstring"""






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

					if token_ids_a is None:
							return [1] + ([0] * len(lowerCAmelCase__						)) + [1]
					return [1] + ([0] * len(lowerCAmelCase__						)) + [1, 1] + ([0] * len(lowerCAmelCase__						)) + [1]

			def UpperCamelCase__					(							self     : Any							,     lowerCAmelCase__     : List[int]							,     lowerCAmelCase__     : Optional[List[int]] = None						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		int           =		[self.sep_token_id]
					__SCREAMING_SNAKE_CASE       :		List[Any]           =		[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     : Optional[Any]							,     lowerCAmelCase__     : int							,     lowerCAmelCase__     : List[Any]=False							,     **lowerCAmelCase__     : Tuple						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		kwargs.pop("""add_prefix_space"""							,     self.add_prefix_space						)
					if (is_split_into_words or add_prefix_space) and (len(lowerCAmelCase__						) > 0 and not text[0].isspace()):
							__SCREAMING_SNAKE_CASE       :		int           =		""" """ + text
					return (text, kwargs)



			def UpperCamelCase__					(							self     : Optional[Any]							,     lowerCAmelCase__     : Union[Dict[str, EncodedInput], BatchEncoding]							,     lowerCAmelCase__     : Optional[int] = None							,     lowerCAmelCase__     : PaddingStrategy = PaddingStrategy.DO_NOT_PAD							,     lowerCAmelCase__     : Optional[int] = None							,     lowerCAmelCase__     : Optional[bool] = None							,     ):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		str           =		super()._pad(
					    encoded_inputs=lowerCAmelCase__							,     max_length=lowerCAmelCase__							,     padding_strategy=lowerCAmelCase__							,     pad_to_multiple_of=lowerCAmelCase__							,     return_attention_mask=lowerCAmelCase__							,     )

					# Load from model defaults
					if return_attention_mask is None:
							__SCREAMING_SNAKE_CASE       :		Tuple           =		"""attention_mask""" in self.model_input_names

					if return_attention_mask and "global_attention_mask" in encoded_inputs:
							__SCREAMING_SNAKE_CASE       :		str           =		encoded_inputs[self.model_input_names[0]]
							# `global_attention_mask` need to have the same length as other (sequential) inputs.
							__SCREAMING_SNAKE_CASE       :		str           =		len(encoded_inputs["""global_attention_mask"""]						) != len(lowerCAmelCase__						)

							if needs_to_be_padded:
									__SCREAMING_SNAKE_CASE       :		Dict           =		len(lowerCAmelCase__						) - len(encoded_inputs["""global_attention_mask"""]						)

									if self.padding_side == "right":
											# Use `-1` since `0` in `global_attention_mask` means `local attention` instead of `not to attend`
											__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		(
											    encoded_inputs["""global_attention_mask"""] + [-1] * difference
											)
									elif self.padding_side == "left":
											__SCREAMING_SNAKE_CASE       :		Dict           =		[-1] * difference + encoded_inputs[
											    """global_attention_mask"""
											]
									else:
											raise ValueError("""Invalid padding strategy:""" + str(self.padding_side						)						)

					return encoded_inputs