
def      lowerCamelCase__       (       __lowerCAmelCase						:						Any=28123       ):




			"""simple docstring"""


			lowerCAmelCase_      			=			[1] * (limit + 1)

			for i in range(2					,							int(limit**0.5       ) + 1       ):
						sum_divs[i * i] += i
						for k in range(i + 1					,							limit // i + 1       ):
									sum_divs[k * i] += k + i

			lowerCAmelCase_      			=			set()
			lowerCAmelCase_      			=			0

			for n in range(1					,							limit + 1       ):
						if sum_divs[n] > n:
									abundants.add(__lowerCAmelCase       )

						if not any((n - a in abundants) for a in abundants       ):
									res += n

			return res


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





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  )       ->   Tuple:
							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  )       ->   Union[str, 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  )       ->   List[Any]:
							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  )       ->   Any:
							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[str]:
							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  )       ->   Optional[int]:
							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  )       ->   int:
							lowerCAmelCase_      			=			list(_UpperCamelCase  )
							lowerCAmelCase_      			=			begin_index




				def __call__(      self       ,       _UpperCamelCase       ,       _UpperCamelCase       ,       _UpperCamelCase  )       ->   int:
							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  )       ->   Optional[Any]:
							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  )       ->   List[Any]:
							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  )       ->   Tuple:
							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  )       ->   Optional[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



