






'''simple docstring'''



from typing import List, Optional

from tokenizers import ByteLevelBPETokenizer

from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import logging
from .tokenization_blenderbot_small import BlenderbotSmallTokenizer


lowerCamelCase	 =       logging.get_logger(__name__)

lowerCamelCase	 =       {
    """vocab_file""": """vocab.json""",
    """merges_file""": """merges.txt""",
    """tokenizer_config_file""": """tokenizer_config.json""",
}

lowerCamelCase	 =       {
    """vocab_file""": {
        """facebook/blenderbot_small-90M""": """https://huggingface.co/facebook/blenderbot_small-90M/resolve/main/vocab.json"""
    },
    """merges_file""": {
        """facebook/blenderbot_small-90M""": """https://huggingface.co/facebook/blenderbot_small-90M/resolve/main/merges.txt"""
    },
    """tokenizer_config_file""": {
        """facebook/blenderbot_small-90M""": (
            """https://huggingface.co/facebook/blenderbot_small-90M/resolve/main/tokenizer_config.json"""
        )
    },
}

lowerCamelCase	 =       {
    """facebook/blenderbot_small-90M""": 512,
}





class _UpperCamelCase		(     lowercase_		):





				'''simple docstring'''





				lowerCAmelCase__					    =    VOCAB_FILES_NAMES
				lowerCAmelCase__					    =    PRETRAINED_VOCAB_FILES_MAP
				lowerCAmelCase__					    =    PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
				lowerCAmelCase__					    =    BlenderbotSmallTokenizer

				def __init__(							self  :  Dict  ,       _lowerCAmelCase  :  str=None  ,       _lowerCAmelCase  :  Dict=None  ,       _lowerCAmelCase  :  Optional[int]="<|endoftext|>"  ,       _lowerCAmelCase  :  Union[str, Any]="<|endoftext|>"  ,       _lowerCAmelCase  :  Optional[Any]="<|endoftext|>"  ,       _lowerCAmelCase  :  Optional[Any]=False  ,       _lowerCAmelCase  :  List[str]=True  ,       **_lowerCAmelCase  :  Tuple  ,       ):







											'''simple docstring'''

											super().__init__(
											    ByteLevelBPETokenizer(
											        vocab=_lowerCAmelCase  ,       merges=_lowerCAmelCase  ,       add_prefix_space=_lowerCAmelCase  ,       trim_offsets=_lowerCAmelCase  ,       )  ,       bos_token=_lowerCAmelCase  ,       eos_token=_lowerCAmelCase  ,       unk_token=_lowerCAmelCase  ,       **_lowerCAmelCase  ,       )
											__lowercase       	=add_prefix_space

				def 				__lowerCamelCase     (							self  :  int  ,       _lowerCAmelCase  :  Dict  ,       _lowerCAmelCase  :  Optional[int]=None):







											'''simple docstring'''

											__lowercase       	=[self.bos_token_id] + token_ids_a + [self.eos_token_id]
											if token_ids_a is None:
																		return output

											return output + [self.eos_token_id] + token_ids_a + [self.eos_token_id]

				def 				__lowerCamelCase     (							self  :  List[str]  ,       _lowerCAmelCase  :  Tuple  ,       _lowerCAmelCase  :  Optional[Any] = None):







											'''simple docstring'''

											__lowercase       	=[self.sep_token_id]
											__lowercase       	=[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]








'''simple docstring'''



from decimal import Decimal, getcontext
from math import ceil, factorial



def   _A       (   _lowerCAmelCase					):



							"""simple docstring"""



							if not isinstance(_lowerCAmelCase  ,   _lowerCAmelCase					):
														raise TypeError('Undefined for non-integers'					)
							elif precision < 1:
														raise ValueError('Undefined for non-natural numbers'					)

							__lowercase       	=precision
							__lowercase       	=ceil(precision / 14					)
							__lowercase       	=426_880 * Decimal(10_005					).sqrt()
							__lowercase       	=1
							__lowercase       	=13_591_409
							__lowercase       	=Decimal(_lowerCAmelCase					)
							for k in range(1  ,   _lowerCAmelCase					):
														__lowercase       	=factorial(6 * k					) // (factorial(3 * k					) * factorial(_lowerCAmelCase					) ** 3)
														linear_term += 545_140_134
														exponential_term *= -262_537_412_640_768_000
														partial_sum += Decimal(multinomial_term * linear_term					) / exponential_term
							return str(constant_term / partial_sum					)[:-1]


if __name__ == "__main__":
		lowerCamelCase	 =       50
		print(f"The first {n} digits of pi is: {pi(n)}")



