
import inspect

import jax
import jax.lax as lax
import jax.numpy as jnp

from ..utils import add_start_docstrings
from ..utils.logging import get_logger


_A  =	get_logger(__name__)


_A  =	R"\n    Args:\n        input_ids (`jnp.ndarray` of shape `(batch_size, sequence_length)`):\n            Indices of input sequence tokens in the vocabulary.\n\n            Indices can be obtained using [`PreTrainedTokenizer`]. See [`PreTrainedTokenizer.encode`] and\n            [`PreTrainedTokenizer.__call__`] for details.\n\n            [What are input IDs?](../glossary#input-ids)\n        scores (`jnp.ndarray` of shape `(batch_size, config.vocab_size)`):\n            Prediction scores of a language modeling head. These can be logits for each vocabulary when not using beam\n            search or log softmax for each vocabulary token when using beam search\n        kwargs (`Dict[str, Any]`, *optional*):\n            Additional logits processor specific kwargs.\n\n    Return:\n        `jnp.ndarray` of shape `(batch_size, config.vocab_size)`: The processed prediction scores.\n\n"





class       _lowerCAmelCase   :




				@add_start_docstrings(_UpperCamelCase	)
				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase	)							-> jnp.ndarray:
							raise NotImplementedError(
							    f"""{self.__class__} is an abstract class. Only classes inheriting this class can be called."""	)





class       _lowerCAmelCase   :




				@add_start_docstrings(_UpperCamelCase	)
				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase	)							-> jnp.ndarray:
							raise NotImplementedError(
							    f"""{self.__class__} is an abstract class. Only classes inheriting this class can be called."""	)





class       _lowerCAmelCase   (      __a			):




				@add_start_docstrings(_UpperCamelCase	)
				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase							,							**_UpperCamelCase	)							-> jnp.ndarray:
							for processor in self:
										lowerCAmelCase_         =      inspect.signature(processor.__call__	).parameters
										if len(_UpperCamelCase	) > 3:
													if not all(arg in kwargs for arg in list(function_args.keys()	)[2:]	):
																raise ValueError(
																    f"""Make sure that all the required parameters: {list(function_args.keys()	)} for """
																    f"""{processor.__class__} are passed to the logits processor."""	)
													lowerCAmelCase_         =      processor(_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase							,							**_UpperCamelCase	)
										else:
													lowerCAmelCase_         =      processor(_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)
							return scores





class       _lowerCAmelCase   (      __a			):




				def __init__(   self							,							_UpperCamelCase	)							-> Union[str, Any]:
							if not isinstance(_UpperCamelCase							,							_UpperCamelCase	) or not (temperature > 0):
										raise ValueError(f"""`temperature` has to be a strictly positive float, but is {temperature}"""	)

							lowerCAmelCase_         =      temperature




				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)							-> jnp.ndarray:
							lowerCAmelCase_         =      scores / self.temperature
							return scores





class       _lowerCAmelCase   (      __a			):




				def __init__(   self							,							_UpperCamelCase							,							_UpperCamelCase = -float("Inf"	)							,							_UpperCamelCase = 1	)							-> Any:
							if not isinstance(_UpperCamelCase							,							_UpperCamelCase	) or (top_p < 0 or top_p > 1.0):
										raise ValueError(f"""`top_p` has to be a float > 0 and < 1, but is {top_p}"""	)
							if not isinstance(_UpperCamelCase							,							_UpperCamelCase	) or (min_tokens_to_keep < 1):
										raise ValueError(f"""`min_tokens_to_keep` has to be a positive integer, but is {min_tokens_to_keep}"""	)

							lowerCAmelCase_         =      top_p
							lowerCAmelCase_         =      filter_value
							lowerCAmelCase_         =      min_tokens_to_keep




				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)							-> jnp.ndarray:
							lowerCAmelCase_      ,    lowerCAmelCase_         =      lax.top_k(_UpperCamelCase							,							scores.shape[-1]	)

							lowerCAmelCase_         =      jnp.full_like(_UpperCamelCase							,							self.filter_value	)
							lowerCAmelCase_         =      jax.nn.softmax(_UpperCamelCase							,							axis=-1	).cumsum(axis=-1	)
							lowerCAmelCase_         =      cumulative_probs < self.top_p

							# include the token that is higher than top_p as well
							lowerCAmelCase_         =      jnp.roll(_UpperCamelCase							,							1	)
							score_mask |= score_mask.at[:, 0].set(_UpperCamelCase	)

							# min tokens to keep
							lowerCAmelCase_         =      score_mask.at[:, : self.min_tokens_to_keep].set(_UpperCamelCase	)

							lowerCAmelCase_         =      jnp.where(_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)
							lowerCAmelCase_         =      jax.lax.sort_key_val(_UpperCamelCase							,							_UpperCamelCase	)[-1]

							return next_scores





class       _lowerCAmelCase   (      __a			):




				def __init__(   self							,							_UpperCamelCase							,							_UpperCamelCase = -float("Inf"	)							,							_UpperCamelCase = 1	)							-> str:
							if not isinstance(_UpperCamelCase							,							_UpperCamelCase	) or top_k <= 0:
										raise ValueError(f"""`top_k` has to be a strictly positive integer, but is {top_k}"""	)

							lowerCAmelCase_         =      max(_UpperCamelCase							,							_UpperCamelCase	)
							lowerCAmelCase_         =      filter_value




				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)							-> jnp.ndarray:
							lowerCAmelCase_      ,    lowerCAmelCase_         =      scores.shape
							lowerCAmelCase_         =      jnp.full(batch_size * vocab_size							,							self.filter_value	)

							lowerCAmelCase_         =      min(self.top_k							,							scores.shape[-1]	)  # Safety check
							lowerCAmelCase_      ,    lowerCAmelCase_         =      lax.top_k(_UpperCamelCase							,							_UpperCamelCase	)
							lowerCAmelCase_         =      jnp.broadcast_to((jnp.arange(_UpperCamelCase	) * vocab_size)[:, None]							,							(batch_size, topk)	).flatten()
							lowerCAmelCase_         =      topk_scores.flatten()
							lowerCAmelCase_         =      topk_indices.flatten() + shift

							lowerCAmelCase_         =      next_scores_flat.at[topk_indices_flat].set(_UpperCamelCase	)
							lowerCAmelCase_         =      next_scores_flat.reshape(_UpperCamelCase							,							_UpperCamelCase	)
							return next_scores





class       _lowerCAmelCase   (      __a			):




				def __init__(   self							,							_UpperCamelCase	)							-> int:
							lowerCAmelCase_         =      bos_token_id




				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)							-> jnp.ndarray:
							lowerCAmelCase_         =      jnp.full(scores.shape							,							-float("inf"	)	)

							lowerCAmelCase_         =      1 - jnp.bool_(cur_len - 1	)

							lowerCAmelCase_         =      jnp.where(_UpperCamelCase							,							new_scores.at[:, self.bos_token_id].set(0	)							,							_UpperCamelCase	)

							return scores





class       _lowerCAmelCase   (      __a			):




				def __init__(   self							,							_UpperCamelCase							,							_UpperCamelCase	)							-> List[Any]:
							lowerCAmelCase_         =      max_length
							lowerCAmelCase_         =      eos_token_id




				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)							-> jnp.ndarray:
							lowerCAmelCase_         =      jnp.full(scores.shape							,							-float("inf"	)	)

							lowerCAmelCase_         =      1 - jnp.bool_(cur_len - self.max_length + 1	)

							lowerCAmelCase_         =      jnp.where(_UpperCamelCase							,							new_scores.at[:, self.eos_token_id].set(0	)							,							_UpperCamelCase	)

							return scores





class       _lowerCAmelCase   (      __a			):




				def __init__(   self							,							_UpperCamelCase							,							_UpperCamelCase	)							-> List[Any]:
							if not isinstance(_UpperCamelCase							,							_UpperCamelCase	) or min_length < 0:
										raise ValueError(f"""`min_length` has to be a positive integer, but is {min_length}"""	)

							if not isinstance(_UpperCamelCase							,							_UpperCamelCase	) or eos_token_id < 0:
										raise ValueError(f"""`eos_token_id` has to be a positive integer, but is {eos_token_id}"""	)

							lowerCAmelCase_         =      min_length
							lowerCAmelCase_         =      eos_token_id




				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)							-> jnp.ndarray:
							# create boolean flag to decide if min length penalty should be applied
							lowerCAmelCase_         =      1 - jnp.clip(cur_len - self.min_length							,							0							,							1	)

							lowerCAmelCase_         =      jnp.where(_UpperCamelCase							,							scores.at[:, self.eos_token_id].set(-float("inf"	)	)							,							_UpperCamelCase	)

							return scores





class       _lowerCAmelCase   (      __a			):




				def __init__(   self							,							_UpperCamelCase							,							_UpperCamelCase	)							-> Optional[Any]:
							lowerCAmelCase_         =      list(_UpperCamelCase	)
							lowerCAmelCase_         =      begin_index




				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)							-> Dict:
							lowerCAmelCase_         =      1 - jnp.bool_(cur_len - self.begin_index	)

							lowerCAmelCase_         =      jnp.where(_UpperCamelCase							,							scores.at[:, self.begin_suppress_tokens].set(-float("inf"	)	)							,							_UpperCamelCase	)

							return scores





class       _lowerCAmelCase   (      __a			):




				def __init__(   self							,							_UpperCamelCase	)							-> Dict:
							lowerCAmelCase_         =      list(_UpperCamelCase	)




				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)							-> jnp.ndarray:
							lowerCAmelCase_         =      scores.at[..., self.suppress_tokens].set(-float("inf"	)	)

							return scores





class       _lowerCAmelCase   (      __a			):




				def __init__(   self							,							_UpperCamelCase	)							-> Optional[int]:
							lowerCAmelCase_         =      dict(_UpperCamelCase	)
							# Converts the dictionary of format {index: token} containing the tokens to be forced to an array, where the
							# index of the array corresponds to the index of the token to be forced, for XLA compatibility.
							# Indexes without forced tokens will have a negative value.
							lowerCAmelCase_         =      jnp.ones((max(force_token_map.keys()	) + 1)							,							dtype=jnp.intaa	) * -1
							for index, token in force_token_map.items():
										if token is not None:
													lowerCAmelCase_         =      force_token_array.at[index].set(_UpperCamelCase	)
							lowerCAmelCase_         =      jnp.intaa(_UpperCamelCase	)




				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)							-> jnp.ndarray:
							def _force_token(_UpperCamelCase	):
										lowerCAmelCase_         =      scores.shape[0]
										lowerCAmelCase_         =      self.force_token_array[generation_idx]

										lowerCAmelCase_         =      jnp.ones_like(_UpperCamelCase							,							dtype=scores.dtype	) * -float("inf"	)
										lowerCAmelCase_         =      jnp.zeros((batch_size, 1)							,							dtype=scores.dtype	)
										lowerCAmelCase_         =      lax.dynamic_update_slice(_UpperCamelCase							,							_UpperCamelCase							,							(0, current_token)	)
										return new_scores

							lowerCAmelCase_         =      lax.cond(
							    cur_len >= self.force_token_array.shape[0]							,							lambda: scores							,							lambda: lax.cond(
							        self.force_token_array[cur_len] >= 0							,							lambda: _force_token(_UpperCamelCase	)							,							lambda: scores							,							)							,							)
							return scores





class       _lowerCAmelCase   (      __a			):




				def __init__(   self							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)							-> List[Any]:
							lowerCAmelCase_         =      generate_config.eos_token_id
							lowerCAmelCase_         =      generate_config.no_timestamps_token_id
							lowerCAmelCase_         =      generate_config.no_timestamps_token_id + 1

							lowerCAmelCase_         =      decoder_input_length + 1

							if generate_config.is_multilingual:
										# room for language token and task token
										self.begin_index += 2
							if hasattr(_UpperCamelCase							,							"max_initial_timestamp_index"	):
										lowerCAmelCase_         =      generate_config.max_initial_timestamp_index
							else:
										lowerCAmelCase_         =      model_config.vocab_size
							if self.max_initial_timestamp_index is None:
										lowerCAmelCase_         =      model_config.vocab_size




				def __call__(   self							,							_UpperCamelCase							,							_UpperCamelCase							,							_UpperCamelCase	)							-> Any:
							# suppress <|notimestamps|> which is handled by without_timestamps
							lowerCAmelCase_         =      scores.at[:, self.no_timestamps_token_id].set(-float("inf"	)	)

							def handle_pairs(_UpperCamelCase							,							_UpperCamelCase	):
										lowerCAmelCase_         =      jnp.where((cur_len - self.begin_index) >= 1							,							_UpperCamelCase							,							_UpperCamelCase	)
										lowerCAmelCase_         =      jnp.where(
										    input_ids_k[cur_len - 1] >= self.timestamp_begin							,							True and last_was_timestamp							,							_UpperCamelCase							,							)

										lowerCAmelCase_         =      jnp.where((cur_len - self.begin_index) < 2							,							_UpperCamelCase							,							_UpperCamelCase	)
										lowerCAmelCase_         =      jnp.where(
										    input_ids_k[cur_len - 2] >= self.timestamp_begin							,							_UpperCamelCase							,							_UpperCamelCase							,							)

										return jnp.where(
										    _UpperCamelCase							,							jnp.where(
										        penultimate_was_timestamp > 0							,							scores_k.at[self.timestamp_begin :].set(-float("inf"	)	)							,							scores_k.at[: self.eos_token_id].set(-float("inf"	)	)							,							)							,							_UpperCamelCase							,							)

							lowerCAmelCase_         =      jax.vmap(_UpperCamelCase	)(_UpperCamelCase							,							_UpperCamelCase	)

							lowerCAmelCase_         =      jnp.where(cur_len == self.begin_index							,							_UpperCamelCase							,							_UpperCamelCase	)
							lowerCAmelCase_         =      jnp.where(
							    self.max_initial_timestamp_index is not None							,							True and apply_max_initial_timestamp							,							_UpperCamelCase							,							)

							lowerCAmelCase_         =      self.timestamp_begin + self.max_initial_timestamp_index

							lowerCAmelCase_         =      jnp.where(
							    _UpperCamelCase							,							scores.at[:, last_allowed + 1 :].set(-float("inf"	)	)							,							_UpperCamelCase							,							)

							# if sum of probability over timestamps is above any other token, sample timestamp
							lowerCAmelCase_         =      jax.nn.log_softmax(_UpperCamelCase							,							axis=-1	)

							def handle_cumulative_probs(_UpperCamelCase							,							_UpperCamelCase	):
										lowerCAmelCase_         =      jax.nn.logsumexp(logprobs_k[self.timestamp_begin :]							,							axis=-1	)
										lowerCAmelCase_         =      jnp.max(logprobs_k[: self.timestamp_begin]	)
										return jnp.where(
										    timestamp_logprob > max_text_token_logprob							,							scores_k.at[: self.timestamp_begin].set(-float("inf"	)	)							,							_UpperCamelCase							,							)

							lowerCAmelCase_         =      jax.vmap(_UpperCamelCase	)(_UpperCamelCase							,							_UpperCamelCase	)

							return scores





from functools import reduce

_A  =	(
    "73167176531330624919225119674426574742355349194934"
    "96983520312774506326239578318016984801869478851843"
    "85861560789112949495459501737958331952853208805511"
    "12540698747158523863050715693290963295227443043557"
    "66896648950445244523161731856403098711121722383113"
    "62229893423380308135336276614282806444486645238749"
    "30358907296290491560440772390713810515859307960866"
    "70172427121883998797908792274921901699720888093776"
    "65727333001053367881220235421809751254540594752243"
    "52584907711670556013604839586446706324415722155397"
    "53697817977846174064955149290862569321978468622482"
    "83972241375657056057490261407972968652414535100474"
    "82166370484403199890008895243450658541227588666881"
    "16427171479924442928230863465674813919123162824586"
    "17866458359124566529476545682848912883142607690042"
    "24219022671055626321111109370544217506941658960408"
    "07198403850962455444362981230987879927244284909188"
    "84580156166097919133875499200524063689912560717606"
    "05886116467109405077541002256983155200055935729725"
    "71636269561882670428252483600823257530420752963450"
)






def   lowerCamelCase__							(							__lowerCAmelCase    :    str = N							):




			"""simple docstring"""


			return max(
			    # mypy cannot properly interpret reduce
			    int(reduce(lambda __lowerCAmelCase       ,				__lowerCAmelCase							: str(int(__lowerCAmelCase							) * int(__lowerCAmelCase							)							)       ,				n[i : i + 13]							)							)
			    for i in range(len(__lowerCAmelCase							) - 12							)							)


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



