






"""simple docstring"""





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


UpperCamelCase_	:				Dict										= get_logger(__name__)


UpperCamelCase_	:				Dict										= r"""
    Args:
        input_ids (`jnp.ndarray` of shape `(batch_size, sequence_length)`):
            Indices of input sequence tokens in the vocabulary.

            Indices can be obtained using [`PreTrainedTokenizer`]. See [`PreTrainedTokenizer.encode`] and
            [`PreTrainedTokenizer.__call__`] for details.

            [What are input IDs?](../glossary#input-ids)
        scores (`jnp.ndarray` of shape `(batch_size, config.vocab_size)`):
            Prediction scores of a language modeling head. These can be logits for each vocabulary when not using beam
            search or log softmax for each vocabulary token when using beam search
        kwargs (`Dict[str, Any]`, *optional*):
            Additional logits processor specific kwargs.

    Return:
        `jnp.ndarray` of shape `(batch_size, config.vocab_size)`: The processed prediction scores.

"""


class      _lowercase :


      @add_start_docstrings(a						)
      def __call__(    self				:	List[str]							,   a				:	jnp.ndarray							,   a				:	jnp.ndarray						):





            """simple docstring"""







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



class      _lowercase :


      @add_start_docstrings(a						)
      def __call__(    self				:	List[str]							,   a				:	jnp.ndarray							,   a				:	jnp.ndarray						):





            """simple docstring"""







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



class      _lowercase (     lowerCAmelCase						):


      @add_start_docstrings(a						)
      def __call__(    self				:	List[str]							,   a				:	jnp.ndarray							,   a				:	jnp.ndarray							,   a				:	int							,   **a				:	Dict						):





            """simple docstring"""







            for processor in self:
                  __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.'''						)
                        __snake_case      :    List[str]  			=processor(a							,   a							,   a							,   **a						)
                  else:
                        __snake_case      :    int  			=processor(a							,   a							,   a						)
            return scores



class      _lowercase (     lowerCAmelCase						):


      def __init__(    self				:	Union[str, Any]							,   a				:	float						):





            """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}'''						)

            __snake_case      :    str  			=temperature







      def __call__(    self				:	List[str]							,   a				:	jnp.ndarray							,   a				:	jnp.ndarray							,   a				:	int						):





            """simple docstring"""







            __snake_case      :    List[Any]  			=scores / self.temperature
            return scores



class      _lowercase (     lowerCAmelCase						):


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





            """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}'''						)

            __snake_case      :    int  			=top_p
            __snake_case      :    int  			=filter_value
            __snake_case      :    int  			=min_tokens_to_keep







      def __call__(    self				:	Any							,   a				:	jnp.ndarray							,   a				:	jnp.ndarray							,   a				:	int						):





            """simple docstring"""







            __snake_case			,				__snake_case      :    str  			=lax.top_k(a							,   scores.shape[-1]						)

            __snake_case      :    Dict  			=jnp.full_like(a							,   self.filter_value						)
            __snake_case      :    List[str]  			=jax.nn.softmax(a							,   axis=-1						).cumsum(axis=-1						)
            __snake_case      :    str  			=cumulative_probs < self.top_p

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

            # min tokens to keep
            __snake_case      :    List[Any]  			=score_mask.at[:, : self.min_tokens_to_keep].set(a						)

            __snake_case      :    List[Any]  			=jnp.where(a							,   a							,   a						)
            __snake_case      :    List[str]  			=jax.lax.sort_key_val(a							,   a						)[-1]

            return next_scores



class      _lowercase (     lowerCAmelCase						):


      def __init__(    self				:	Tuple							,   a				:	int							,   a				:	float = -float('''Inf'''						)							,   a				:	int = 1						):





            """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}'''						)

            __snake_case      :    List[Any]  			=max(a							,   a						)
            __snake_case      :    Any  			=filter_value







      def __call__(    self				:	Dict							,   a				:	jnp.ndarray							,   a				:	jnp.ndarray							,   a				:	int						):





            """simple docstring"""







            __snake_case			,				__snake_case      :    int  			=scores.shape
            __snake_case      :    List[Any]  			=jnp.full(batch_size * vocab_size							,   self.filter_value						)

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

            __snake_case      :    int  			=next_scores_flat.at[topk_indices_flat].set(a						)
            __snake_case      :    str  			=next_scores_flat.reshape(a							,   a						)
            return next_scores



class      _lowercase (     lowerCAmelCase						):


      def __init__(    self				:	str							,   a				:	int						):





            """simple docstring"""







            __snake_case      :    Optional[int]  			=bos_token_id







      def __call__(    self				:	Optional[Any]							,   a				:	jnp.ndarray							,   a				:	jnp.ndarray							,   a				:	int						):





            """simple docstring"""







            __snake_case      :    Tuple  			=jnp.full(scores.shape							,   -float('''inf'''						)						)

            __snake_case      :    Dict  			=1 - jnp.bool_(cur_len - 1						)

            __snake_case      :    Dict  			=jnp.where(a							,   new_scores.at[:, self.bos_token_id].set(0						)							,   a						)

            return scores



class      _lowercase (     lowerCAmelCase						):


      def __init__(    self				:	Optional[int]							,   a				:	int							,   a				:	int						):





            """simple docstring"""







            __snake_case      :    List[Any]  			=max_length
            __snake_case      :    Optional[int]  			=eos_token_id







      def __call__(    self				:	Any							,   a				:	jnp.ndarray							,   a				:	jnp.ndarray							,   a				:	int						):





            """simple docstring"""







            __snake_case      :    Dict  			=jnp.full(scores.shape							,   -float('''inf'''						)						)

            __snake_case      :    Optional[Any]  			=1 - jnp.bool_(cur_len - self.max_length + 1						)

            __snake_case      :    Any  			=jnp.where(a							,   new_scores.at[:, self.eos_token_id].set(0						)							,   a						)

            return scores



class      _lowercase (     lowerCAmelCase						):


      def __init__(    self				:	Any							,   a				:	int							,   a				:	int						):





            """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}'''						)

            __snake_case      :    Union[str, Any]  			=min_length
            __snake_case      :    Dict  			=eos_token_id







      def __call__(    self				:	int							,   a				:	jnp.ndarray							,   a				:	jnp.ndarray							,   a				:	int						):





            """simple docstring"""







            __snake_case      :    List[Any]  			=1 - jnp.clip(cur_len - self.min_length							,   0							,   1						)

            __snake_case      :    int  			=jnp.where(a							,   scores.at[:, self.eos_token_id].set(-float('''inf'''						)						)							,   a						)

            return scores



class      _lowercase (     lowerCAmelCase						):


      def __init__(    self				:	List[Any]							,   a				:	Tuple							,   a				:	int						):





            """simple docstring"""







            __snake_case      :    Union[str, Any]  			=list(a						)
            __snake_case      :    Optional[Any]  			=begin_index







      def __call__(    self				:	Any							,   a				:	Optional[Any]							,   a				:	Tuple							,   a				:	int						):





            """simple docstring"""







            __snake_case      :    Dict  			=1 - jnp.bool_(cur_len - self.begin_index						)

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

            return scores



class      _lowercase (     lowerCAmelCase						):


      def __init__(    self				:	Optional[int]							,   a				:	list						):





            """simple docstring"""







            __snake_case      :    List[Any]  			=list(a						)







      def __call__(    self				:	Optional[int]							,   a				:	jnp.ndarray							,   a				:	jnp.ndarray							,   a				:	int						):





            """simple docstring"""







            __snake_case      :    Any  			=scores.at[..., self.suppress_tokens].set(-float('''inf'''						)						)

            return scores



class      _lowercase (     lowerCAmelCase						):


      def __init__(    self				:	int							,   a				:	str						):





            """simple docstring"""







            __snake_case      :    Union[str, 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.
            __snake_case      :    Optional[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:
                        __snake_case      :    int  			=force_token_array.at[index].set(a						)
            __snake_case      :    Dict  			=jnp.intaa(a						)







      def __call__(    self				:	str							,   a				:	jnp.ndarray							,   a				:	jnp.ndarray							,   a				:	int						):





            """simple docstring"""







            def _force_token(a				:	int						):
                  __snake_case      :    str  			=scores.shape[0]
                  __snake_case      :    Dict  			=self.force_token_array[generation_idx]

                  __snake_case      :    Tuple  			=jnp.ones_like(a							,   dtype=scores.dtype						) * -float('''inf'''						)
                  __snake_case      :    Dict  			=jnp.zeros((batch_size, 1)							,   dtype=scores.dtype						)
                  __snake_case      :    int  			=lax.dynamic_update_slice(a							,   a							,   (0, current_token)						)
                  return new_scores

            __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      _lowercase (     lowerCAmelCase						):


      def __init__(    self				:	Dict							,   a				:	Any							,   a				:	int							,   a				:	Tuple						):





            """simple docstring"""







            __snake_case      :    Optional[Any]  			=generate_config.eos_token_id
            __snake_case      :    List[Any]  			=generate_config.no_timestamps_token_id
            __snake_case      :    Dict  			=generate_config.no_timestamps_token_id + 1

            __snake_case      :    str  			=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'''						):
                  __snake_case      :    Optional[int]  			=generate_config.max_initial_timestamp_index
            else:
                  __snake_case      :    str  			=model_config.vocab_size
            if self.max_initial_timestamp_index is None:
                  __snake_case      :    Union[str, Any]  			=model_config.vocab_size







      def __call__(    self				:	Union[str, Any]							,   a				:	List[Any]							,   a				:	Optional[int]							,   a				:	str						):





            """simple docstring"""







            __snake_case      :    Tuple  			=scores.at[:, self.no_timestamps_token_id].set(-float('''inf'''						)						)

            def handle_pairs(a				:	str							,   a				:	Optional[int]						):
                  __snake_case      :    str  			=jnp.where((cur_len - self.begin_index) >= 1							,   a							,   a						)
                  __snake_case      :    List[str]  			=jnp.where(
                      input_ids_k[cur_len - 1] >= self.timestamp_begin							,   True and last_was_timestamp							,   a							,   )

                  __snake_case      :    List[str]  			=jnp.where((cur_len - self.begin_index) < 2							,   a							,   a						)
                  __snake_case      :    Any  			=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							,   )

            __snake_case      :    List[str]  			=jax.vmap(a						)(a							,   a						)

            __snake_case      :    Optional[Any]  			=jnp.where(cur_len == self.begin_index							,   a							,   a						)
            __snake_case      :    str  			=jnp.where(
                self.max_initial_timestamp_index is not None							,   True and apply_max_initial_timestamp							,   a							,   )

            __snake_case      :    Union[str, Any]  			=self.timestamp_begin + self.max_initial_timestamp_index

            __snake_case      :    Union[str, Any]  			=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
            __snake_case      :    Tuple  			=jax.nn.log_softmax(a							,   axis=-1						)

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

            __snake_case      :    str  			=jax.vmap(a						)(a							,   a						)

            return scores










"""simple docstring"""





def     __lowercase					(    a :				int       ,		a :				int )					->					int:
      return x if y == 0 else greatest_common_divisor(a       ,		x % y )



def     __lowercase					(    a :				int       ,		a :				int )					->					int:
      return (x * y) // greatest_common_divisor(a       ,		a )



def     __lowercase					(    a :				int = 20 )					->					int:
      __snake_case      :    Optional[Any]  			=1
      for i in range(1       ,		n + 1 ):
            __snake_case      :    Optional[int]  			=lcm(a       ,		a )
      return g


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


