
'''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


lowerCAmelCase					:    Optional[Any]           = get_logger(__name__)


lowerCAmelCase					:    List[str]           = 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 			SCREAMING_SNAKE_CASE__      :







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







											'''simple docstring'''






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


class 			SCREAMING_SNAKE_CASE__      :







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







											'''simple docstring'''






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


class 			SCREAMING_SNAKE_CASE__      (     snake_case_):







				@add_start_docstrings(A_     )
				def __call__(       self						,				A_						,				A_						,				A_						,				**A_     )->		jnp.ndarray:







											'''simple docstring'''






											for processor in self:
																		UpperCamelCase   			=     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.'''     )
																									UpperCamelCase   			=     processor(A_						,				A_						,				A_						,				**A_     )
																		else:
																									UpperCamelCase   			=     processor(A_						,				A_						,				A_     )
											return scores


class 			SCREAMING_SNAKE_CASE__      (     snake_case_):







				def __init__(       self						,				A_     )->		int:







											'''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}'''     )

											UpperCamelCase   			=     temperature







				def __call__(       self						,				A_						,				A_						,				A_     )->		jnp.ndarray:







											'''simple docstring'''






											UpperCamelCase   			=     scores / self.temperature
											return scores


class 			SCREAMING_SNAKE_CASE__      (     snake_case_):







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







											'''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}'''     )

											UpperCamelCase   			=     top_p
											UpperCamelCase   			=     filter_value
											UpperCamelCase   			=     min_tokens_to_keep







				def __call__(       self						,				A_						,				A_						,				A_     )->		jnp.ndarray:







											'''simple docstring'''






											UpperCamelCase			,	UpperCamelCase   			=     lax.top_k(A_						,				scores.shape[-1]     )

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

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

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

											UpperCamelCase   			=     jnp.where(A_						,				A_						,				A_     )
											UpperCamelCase   			=     jax.lax.sort_key_val(A_						,				A_     )[-1]

											return next_scores


class 			SCREAMING_SNAKE_CASE__      (     snake_case_):







				def __init__(       self						,				A_						,				A_ = -float('Inf'     )						,				A_ = 1     )->		Dict:







											'''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}'''     )

											UpperCamelCase   			=     max(A_						,				A_     )
											UpperCamelCase   			=     filter_value







				def __call__(       self						,				A_						,				A_						,				A_     )->		jnp.ndarray:







											'''simple docstring'''






											UpperCamelCase			,	UpperCamelCase   			=     scores.shape
											UpperCamelCase   			=     jnp.full(batch_size * vocab_size						,				self.filter_value     )

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

											UpperCamelCase   			=     next_scores_flat.at[topk_indices_flat].set(A_     )
											UpperCamelCase   			=     next_scores_flat.reshape(A_						,				A_     )
											return next_scores


class 			SCREAMING_SNAKE_CASE__      (     snake_case_):







				def __init__(       self						,				A_     )->		Any:







											'''simple docstring'''






											UpperCamelCase   			=     bos_token_id







				def __call__(       self						,				A_						,				A_						,				A_     )->		jnp.ndarray:







											'''simple docstring'''






											UpperCamelCase   			=     jnp.full(scores.shape						,				-float('inf'     )     )

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

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

											return scores


class 			SCREAMING_SNAKE_CASE__      (     snake_case_):







				def __init__(       self						,				A_						,				A_     )->		Dict:







											'''simple docstring'''






											UpperCamelCase   			=     max_length
											UpperCamelCase   			=     eos_token_id







				def __call__(       self						,				A_						,				A_						,				A_     )->		jnp.ndarray:







											'''simple docstring'''






											UpperCamelCase   			=     jnp.full(scores.shape						,				-float('inf'     )     )

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

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

											return scores


class 			SCREAMING_SNAKE_CASE__      (     snake_case_):







				def __init__(       self						,				A_						,				A_     )->		Tuple:







											'''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}'''     )

											UpperCamelCase   			=     min_length
											UpperCamelCase   			=     eos_token_id







				def __call__(       self						,				A_						,				A_						,				A_     )->		jnp.ndarray:







											'''simple docstring'''






											UpperCamelCase   			=     1 - jnp.clip(cur_len - self.min_length						,				0						,				1     )

											UpperCamelCase   			=     jnp.where(A_						,				scores.at[:, self.eos_token_id].set(-float('inf'     )     )						,				A_     )

											return scores


class 			SCREAMING_SNAKE_CASE__      (     snake_case_):







				def __init__(       self						,				A_						,				A_     )->		int:







											'''simple docstring'''






											UpperCamelCase   			=     list(A_     )
											UpperCamelCase   			=     begin_index







				def __call__(       self						,				A_						,				A_						,				A_     )->		Optional[Any]:







											'''simple docstring'''






											UpperCamelCase   			=     1 - jnp.bool_(cur_len - self.begin_index     )

											UpperCamelCase   			=     jnp.where(A_						,				scores.at[:, self.begin_suppress_tokens].set(-float('inf'     )     )						,				A_     )

											return scores


class 			SCREAMING_SNAKE_CASE__      (     snake_case_):







				def __init__(       self						,				A_     )->		int:







											'''simple docstring'''






											UpperCamelCase   			=     list(A_     )







				def __call__(       self						,				A_						,				A_						,				A_     )->		jnp.ndarray:







											'''simple docstring'''






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

											return scores


class 			SCREAMING_SNAKE_CASE__      (     snake_case_):







				def __init__(       self						,				A_     )->		Optional[int]:







											'''simple docstring'''






											UpperCamelCase   			=     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.
											UpperCamelCase   			=     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:
																									UpperCamelCase   			=     force_token_array.at[index].set(A_     )
											UpperCamelCase   			=     jnp.intaa(A_     )







				def __call__(       self						,				A_						,				A_						,				A_     )->		jnp.ndarray:







											'''simple docstring'''






											def _force_token(A_     ):
																		UpperCamelCase   			=     scores.shape[0]
																		UpperCamelCase   			=     self.force_token_array[generation_idx]

																		UpperCamelCase   			=     jnp.ones_like(A_						,				dtype=scores.dtype     ) * -float('inf'     )
																		UpperCamelCase   			=     jnp.zeros((batch_size, 1)						,				dtype=scores.dtype     )
																		UpperCamelCase   			=     lax.dynamic_update_slice(A_						,				A_						,				(0, current_token)     )
																		return new_scores

											UpperCamelCase   			=     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 			SCREAMING_SNAKE_CASE__      (     snake_case_):







				def __init__(       self						,				A_						,				A_						,				A_     )->		int:







											'''simple docstring'''






											UpperCamelCase   			=     generate_config.eos_token_id
											UpperCamelCase   			=     generate_config.no_timestamps_token_id
											UpperCamelCase   			=     generate_config.no_timestamps_token_id + 1

											UpperCamelCase   			=     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'     ):
																		UpperCamelCase   			=     generate_config.max_initial_timestamp_index
											else:
																		UpperCamelCase   			=     model_config.vocab_size
											if self.max_initial_timestamp_index is None:
																		UpperCamelCase   			=     model_config.vocab_size







				def __call__(       self						,				A_						,				A_						,				A_     )->		int:







											'''simple docstring'''






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

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

																		UpperCamelCase   			=     jnp.where((cur_len - self.begin_index) < 2						,				A_						,				A_     )
																		UpperCamelCase   			=     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_						,				)

											UpperCamelCase   			=     jax.vmap(A_     )(A_						,				A_     )

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

											UpperCamelCase   			=     self.timestamp_begin + self.max_initial_timestamp_index

											UpperCamelCase   			=     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
											UpperCamelCase   			=     jax.nn.log_softmax(A_						,				axis=-1     )

											def handle_cumulative_probs(A_						,				A_     ):
																		UpperCamelCase   			=     jax.nn.logsumexp(logprobs_k[self.timestamp_begin :]						,				axis=-1     )
																		UpperCamelCase   			=     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_						,				)

											UpperCamelCase   			=     jax.vmap(A_     )(A_						,				A_     )

											return scores






from math import sqrt






def   lowerCamelCase__							(							__lowerCAmelCase    :    int							):




			"""simple docstring"""


			lowerCAmelCase_         =      0
			for i in range(1       ,				int(sqrt(__lowerCAmelCase							) + 1							)							):
						if n % i == 0 and i != sqrt(__lowerCAmelCase							):
									total += i + n // i
						elif i == sqrt(__lowerCAmelCase							):
									total += i
			return total - n






def   lowerCamelCase__							(							__lowerCAmelCase    :    int = 10000							):




			"""simple docstring"""


			lowerCAmelCase_         =      sum(
			    i
			    for i in range(1       ,				__lowerCAmelCase							)
			    if sum_of_divisors(sum_of_divisors(__lowerCAmelCase							)							) == i and sum_of_divisors(__lowerCAmelCase							) != i							)
			return total


if __name__ == "__main__":
			print(solution(int(str(input()).strip())))



