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


SCREAMING_SNAKE_CASE__		:					Optional[Any]						=					get_logger(__name__)


SCREAMING_SNAKE_CASE__		:					List[Any]						=					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       snake_case					:




  @add_start_docstrings(a_				)
  def __call__(      self     :	Optional[int]     , a_     :	jnp.ndarray     , a_     :	jnp.ndarray				)->       jnp.ndarray:




       """simple docstring"""
       raise NotImplementedError(
           F'''{self.__class__} is an abstract class. Only classes inheriting this class can be called.'''				)




class       snake_case					:




  @add_start_docstrings(a_				)
  def __call__(      self     :	Any     , a_     :	jnp.ndarray     , a_     :	jnp.ndarray				)->       jnp.ndarray:




       """simple docstring"""
       raise NotImplementedError(
           F'''{self.__class__} is an abstract class. Only classes inheriting this class can be called.'''				)




class       snake_case					(      UpperCamelCase_						):




  @add_start_docstrings(a_				)
  def __call__(      self     :	Optional[Any]     , a_     :	jnp.ndarray     , a_     :	jnp.ndarray     , a_     :	int     , **a_     :	Union[str, Any]				)->       jnp.ndarray:




       """simple docstring"""
       for processor in self:
            SCREAMING_SNAKE_CASE__				:				List[str]			=		inspect.signature(processor.__call__				).parameters
            if len(a_				) > 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.'''				)
                 SCREAMING_SNAKE_CASE__				:				int			=		processor(a_     , a_     , a_     , **a_				)
            else:
                 SCREAMING_SNAKE_CASE__				:				int			=		processor(a_     , a_     , a_				)
       return scores




class       snake_case					(      UpperCamelCase_						):




  def __init__(      self     :	Optional[Any]     , a_     :	float				)->       str:




       """simple docstring"""
       if not isinstance(a_     , a_				) or not (temperature > 0):
            raise ValueError(F'''`temperature` has to be a strictly positive float, but is {temperature}'''				)

       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		temperature




  def __call__(      self     :	Any     , a_     :	jnp.ndarray     , a_     :	jnp.ndarray     , a_     :	int				)->       jnp.ndarray:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		scores / self.temperature
       return scores




class       snake_case					(      UpperCamelCase_						):




  def __init__(      self     :	Optional[Any]     , a_     :	float     , a_     :	float = -float('Inf'				)     , a_     :	int = 1				)->       Tuple:




       """simple docstring"""
       if not isinstance(a_     , a_				) 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(a_     , a_				) 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}'''				)

       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		top_p
       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		filter_value
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		min_tokens_to_keep




  def __call__(      self     :	Any     , a_     :	jnp.ndarray     , a_     :	jnp.ndarray     , a_     :	int				)->       jnp.ndarray:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		lax.top_k(a_     , scores.shape[-1]				)

       SCREAMING_SNAKE_CASE__				:				List[str]			=		jnp.full_like(a_     , self.filter_value				)
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		jax.nn.softmax(a_     , axis=-1				).cumsum(axis=-1				)
       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		cumulative_probs < self.top_p

       # include the token that is higher than top_p as well
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		jnp.roll(a_     , 1				)
       score_mask |= score_mask.at[:, 0].set(a_				)

       # min tokens to keep
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		score_mask.at[:, : self.min_tokens_to_keep].set(a_				)

       SCREAMING_SNAKE_CASE__				:				Tuple			=		jnp.where(a_     , a_     , a_				)
       SCREAMING_SNAKE_CASE__				:				Any			=		jax.lax.sort_key_val(a_     , a_				)[-1]

       return next_scores




class       snake_case					(      UpperCamelCase_						):




  def __init__(      self     :	Union[str, Any]     , a_     :	int     , a_     :	float = -float('Inf'				)     , a_     :	int = 1				)->       Optional[Any]:




       """simple docstring"""
       if not isinstance(a_     , a_				) or top_k <= 0:
            raise ValueError(F'''`top_k` has to be a strictly positive integer, but is {top_k}'''				)

       SCREAMING_SNAKE_CASE__				:				str			=		max(a_     , a_				)
       SCREAMING_SNAKE_CASE__				:				Dict			=		filter_value




  def __call__(      self     :	Dict     , a_     :	jnp.ndarray     , a_     :	jnp.ndarray     , a_     :	int				)->       jnp.ndarray:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Dict			=		scores.shape
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		jnp.full(batch_size * vocab_size     , self.filter_value				)

       SCREAMING_SNAKE_CASE__				:				List[Any]			=		min(self.top_k     , scores.shape[-1]				)  # Safety check
       SCREAMING_SNAKE_CASE__				:				Dict			=		lax.top_k(a_     , a_				)
       SCREAMING_SNAKE_CASE__				:				Any			=		jnp.broadcast_to((jnp.arange(a_				) * vocab_size)[:, None]     , (batch_size, topk)				).flatten()
       SCREAMING_SNAKE_CASE__				:				Any			=		topk_scores.flatten()
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		topk_indices.flatten() + shift

       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		next_scores_flat.at[topk_indices_flat].set(a_				)
       SCREAMING_SNAKE_CASE__				:				str			=		next_scores_flat.reshape(a_     , a_				)
       return next_scores




class       snake_case					(      UpperCamelCase_						):




  def __init__(      self     :	str     , a_     :	int				)->       int:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Any			=		bos_token_id




  def __call__(      self     :	Optional[int]     , a_     :	jnp.ndarray     , a_     :	jnp.ndarray     , a_     :	int				)->       jnp.ndarray:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Any			=		jnp.full(scores.shape     , -float('inf'				)				)

       SCREAMING_SNAKE_CASE__				:				int			=		1 - jnp.bool_(cur_len - 1				)

       SCREAMING_SNAKE_CASE__				:				Any			=		jnp.where(a_     , new_scores.at[:, self.bos_token_id].set(0				)     , a_				)

       return scores




class       snake_case					(      UpperCamelCase_						):




  def __init__(      self     :	Any     , a_     :	int     , a_     :	int				)->       Any:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[str]			=		max_length
       SCREAMING_SNAKE_CASE__				:				Dict			=		eos_token_id




  def __call__(      self     :	Tuple     , a_     :	jnp.ndarray     , a_     :	jnp.ndarray     , a_     :	int				)->       jnp.ndarray:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		jnp.full(scores.shape     , -float('inf'				)				)

       SCREAMING_SNAKE_CASE__				:				List[str]			=		1 - jnp.bool_(cur_len - self.max_length + 1				)

       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		jnp.where(a_     , new_scores.at[:, self.eos_token_id].set(0				)     , a_				)

       return scores




class       snake_case					(      UpperCamelCase_						):




  def __init__(      self     :	Optional[Any]     , a_     :	int     , a_     :	int				)->       Dict:




       """simple docstring"""
       if not isinstance(a_     , a_				) or min_length < 0:
            raise ValueError(F'''`min_length` has to be a positive integer, but is {min_length}'''				)

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

       SCREAMING_SNAKE_CASE__				:				Dict			=		min_length
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		eos_token_id




  def __call__(      self     :	Any     , a_     :	jnp.ndarray     , a_     :	jnp.ndarray     , a_     :	int				)->       jnp.ndarray:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		1 - jnp.clip(cur_len - self.min_length     , 0     , 1				)

       SCREAMING_SNAKE_CASE__				:				Dict			=		jnp.where(a_     , scores.at[:, self.eos_token_id].set(-float('inf'				)				)     , a_				)

       return scores




class       snake_case					(      UpperCamelCase_						):




  def __init__(      self     :	Tuple     , a_     :	List[str]     , a_     :	Optional[int]				)->       Dict:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		list(a_				)
       SCREAMING_SNAKE_CASE__				:				int			=		begin_index




  def __call__(      self     :	List[Any]     , a_     :	Dict     , a_     :	Optional[Any]     , a_     :	int				)->       Optional[int]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Dict			=		1 - jnp.bool_(cur_len - self.begin_index				)

       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		jnp.where(a_     , scores.at[:, self.begin_suppress_tokens].set(-float('inf'				)				)     , a_				)

       return scores




class       snake_case					(      UpperCamelCase_						):




  def __init__(      self     :	List[Any]     , a_     :	list				)->       List[Any]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[Any]			=		list(a_				)




  def __call__(      self     :	List[Any]     , a_     :	jnp.ndarray     , a_     :	jnp.ndarray     , a_     :	int				)->       jnp.ndarray:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[str]			=		scores.at[..., self.suppress_tokens].set(-float('inf'				)				)

       return scores




class       snake_case					(      UpperCamelCase_						):




  def __init__(      self     :	List[Any]     , a_     :	Union[str, Any]				)->       Optional[int]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Any			=		dict(a_				)
       # 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.
       SCREAMING_SNAKE_CASE__				:				int			=		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:
                 SCREAMING_SNAKE_CASE__				:				List[Any]			=		force_token_array.at[index].set(a_				)
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		jnp.intaa(a_				)




  def __call__(      self     :	str     , a_     :	jnp.ndarray     , a_     :	jnp.ndarray     , a_     :	int				)->       jnp.ndarray:




       """simple docstring"""
       def _force_token(a_     :	Any				):
            SCREAMING_SNAKE_CASE__				:				List[str]			=		scores.shape[0]
            SCREAMING_SNAKE_CASE__				:				str			=		self.force_token_array[generation_idx]

            SCREAMING_SNAKE_CASE__				:				Tuple			=		jnp.ones_like(a_     , dtype=scores.dtype				) * -float('inf'				)
            SCREAMING_SNAKE_CASE__				:				List[str]			=		jnp.zeros((batch_size, 1)     , dtype=scores.dtype				)
            SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		lax.dynamic_update_slice(a_     , a_     , (0, current_token)				)
            return new_scores

       SCREAMING_SNAKE_CASE__				:				Any			=		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(a_				)     , lambda: scores     , )     , )
       return scores




class       snake_case					(      UpperCamelCase_						):




  def __init__(      self     :	int     , a_     :	Dict     , a_     :	Optional[int]     , a_     :	List[Any]				)->       Dict:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		generate_config.eos_token_id
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		generate_config.no_timestamps_token_id
       SCREAMING_SNAKE_CASE__				:				Optional[int]			=		generate_config.no_timestamps_token_id + 1

       SCREAMING_SNAKE_CASE__				:				int			=		decoder_input_length + 1

       if generate_config.is_multilingual:
            # room for language token and task token
            self.begin_index += 2
       if hasattr(a_     , 'max_initial_timestamp_index'				):
            SCREAMING_SNAKE_CASE__				:				str			=		generate_config.max_initial_timestamp_index
       else:
            SCREAMING_SNAKE_CASE__				:				List[Any]			=		model_config.vocab_size
       if self.max_initial_timestamp_index is None:
            SCREAMING_SNAKE_CASE__				:				str			=		model_config.vocab_size




  def __call__(      self     :	Union[str, Any]     , a_     :	List[str]     , a_     :	List[Any]     , a_     :	List[Any]				)->       Union[str, Any]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Tuple			=		scores.at[:, self.no_timestamps_token_id].set(-float('inf'				)				)

       def handle_pairs(a_     :	int     , a_     :	Union[str, Any]				):
            SCREAMING_SNAKE_CASE__				:				List[str]			=		jnp.where((cur_len - self.begin_index) >= 1     , a_     , a_				)
            SCREAMING_SNAKE_CASE__				:				str			=		jnp.where(
                input_ids_k[cur_len - 1] >= self.timestamp_begin     , True and last_was_timestamp     , a_     , )

            SCREAMING_SNAKE_CASE__				:				List[Any]			=		jnp.where((cur_len - self.begin_index) < 2     , a_     , a_				)
            SCREAMING_SNAKE_CASE__				:				int			=		jnp.where(
                input_ids_k[cur_len - 2] >= self.timestamp_begin     , a_     , a_     , )

            return jnp.where(
                a_     , 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'				)				)     , )     , a_     , )

       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		jax.vmap(a_				)(a_     , a_				)

       SCREAMING_SNAKE_CASE__				:				int			=		jnp.where(cur_len == self.begin_index     , a_     , a_				)
       SCREAMING_SNAKE_CASE__				:				List[Any]			=		jnp.where(
           self.max_initial_timestamp_index is not None     , True and apply_max_initial_timestamp     , a_     , )

       SCREAMING_SNAKE_CASE__				:				str			=		self.timestamp_begin + self.max_initial_timestamp_index

       SCREAMING_SNAKE_CASE__				:				List[str]			=		jnp.where(
           a_     , scores.at[:, last_allowed + 1 :].set(-float('inf'				)				)     , a_     , )

       # if sum of probability over timestamps is above any other token, sample timestamp
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		jax.nn.log_softmax(a_     , axis=-1				)

       def handle_cumulative_probs(a_     :	str     , a_     :	Any				):
            SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		jax.nn.logsumexp(logprobs_k[self.timestamp_begin :]     , axis=-1				)
            SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		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'				)				)     , a_     , )

       SCREAMING_SNAKE_CASE__				:				List[str]			=		jax.vmap(a_				)(a_     , a_				)

       return scores




def     _a				(      lowercase__  :			int = 1_00_00_00 ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__				:				str			=		[i - 1 for i in range(limit + 1 )]

     for i in range(2     ,  limit + 1 ):
          if phi[i] == i - 1:
               for j in range(2 * i     ,  limit + 1     ,  lowercase__ ):
                    phi[j] -= phi[j] // i

     return sum(phi[2 : limit + 1] )


if __name__ == "__main__":
      print(solution())



