

from __future__ import annotations





def  _snake_case		(snake_case_					:     int  )							->		int | None:
  for r in range(1    ,       snake_case_  ):
    __UpperCAmelCase	:  List[str]		=     []
    for x in range(n - 1  ):
      __UpperCAmelCase	:  Union[str, Any]		=     pow(snake_case_    ,       snake_case_    ,       snake_case_  )
      if val in li:
        break
      li.append(snake_case_  )
    else:
      return r
  return None


if __name__ == "__main__":
      _SCREAMING_SNAKE_CASE							 =			int(input('''Enter a prime number q: '''))
      _SCREAMING_SNAKE_CASE							 =			find_primitive(q)
      if a is None:
            print(F'''Cannot find the primitive for the value: {a!r}''')
      else:
            _SCREAMING_SNAKE_CASE							 =			int(input('''Enter private key of A: '''))
            _SCREAMING_SNAKE_CASE							 =			pow(a, a_private, q)
            _SCREAMING_SNAKE_CASE							 =			int(input('''Enter private key of B: '''))
            _SCREAMING_SNAKE_CASE							 =			pow(a, b_private, q)

            _SCREAMING_SNAKE_CASE							 =			pow(b_public, a_private, q)
            _SCREAMING_SNAKE_CASE							 =			pow(a_public, b_private, q)

            print('''The key value generated by A is: ''', a_secret)
            print('''The key value generated by B is: ''', b_secret)








"""simple docstring"""






import timeit
from typing import Callable, Optional

from ..configuration_utils import PretrainedConfig
from ..models.auto.modeling_auto import MODEL_MAPPING, MODEL_WITH_LM_HEAD_MAPPING
from ..utils import is_pyanvml_available, is_torch_available, logging
from .benchmark_utils import (
    Benchmark,
    Memory,
    MemorySummary,
    measure_peak_memory_cpu,
    start_memory_tracing,
    stop_memory_tracing,
)


if is_torch_available():
							import torch

							from .benchmark_args import PyTorchBenchmarkArguments


if is_pyanvml_available():
							import pyanvml.pyanvml as nvml


__lowerCAmelCase				      =   logging.get_logger(__name__)
class 	_lowerCAmelCase    (      __snake_case       ):
							__lowerCAmelCase					:    PyTorchBenchmarkArguments
							__lowerCAmelCase					:    PretrainedConfig
							__lowerCAmelCase					:    str     =  "PyTorch"

							@property
							def 					_lowerCAmelCase  ( self       :    Dict    )   ->    Dict:

									"""simple docstring"""
									return torch.__version__

							def 					_lowerCAmelCase  ( self       :    List[Any] ,		a       :    str ,		a       :    int ,		a       :    int    )   ->    float:

									"""simple docstring"""
									lowercase										=							self._prepare_inference_func(a ,		a ,		a    )
									return self._measure_speed(_inference    )

							def 					_lowerCAmelCase  ( self       :    str ,		a       :    str ,		a       :    int ,		a       :    int    )   ->    [Memory, Optional[MemorySummary]]:

									"""simple docstring"""
									lowercase										=							self._prepare_inference_func(a ,		a ,		a    )
									return self._measure_memory(_inference    )

							def 					_lowerCAmelCase  ( self       :    Union[str, Any] ,		a       :    str ,		a       :    int ,		a       :    int    )   ->    float:

									"""simple docstring"""
									lowercase										=							self._prepare_train_func(a ,		a ,		a    )
									return self._measure_speed(_train    )

							def 					_lowerCAmelCase  ( self       :    int ,		a       :    str ,		a       :    int ,		a       :    int    )   ->    [Memory, Optional[MemorySummary]]:

									"""simple docstring"""
									lowercase										=							self._prepare_train_func(a ,		a ,		a    )
									return self._measure_memory(_train    )

							def 					_lowerCAmelCase  ( self       :    List[Any] ,		a       :    str ,		a       :    int ,		a       :    int    )   ->    Callable[[], None]:

									"""simple docstring"""
									lowercase										=							self.config_dict[model_name]

									if self.args.torchscript:
											lowercase										=							True

									lowercase										=							(
									    hasattr(a ,		'''architectures'''    )
									    and isinstance(config.architectures ,		a    )
									    and len(config.architectures    ) > 0
									)
									if not self.args.only_pretrain_model and has_model_class_in_config:
											try:
													lowercase										=							config.architectures[0]
													lowercase										=							__import__('''transformers''' ,		fromlist=[model_class]    )
													lowercase										=							getattr(a ,		a    )
													lowercase										=							model_cls(a    )
											except ImportError:
													raise ImportError(
													    f"""{model_class} does not exist. If you just want to test the pretrained model, you might want to"""
													    ''' set `--only_pretrain_model` or `args.only_pretrain_model=True`.'''    )
									else:
											lowercase										=							MODEL_MAPPING[config.__class__](a    )

									model.eval()
									model.to(self.args.device    )

									# encoder-decoder has vocab size saved differently
									lowercase										=							config.vocab_size if hasattr(a ,		'''vocab_size'''    ) else config.encoder.vocab_size
									lowercase										=							torch.randint(a ,		(batch_size, sequence_length) ,		dtype=torch.long ,		device=self.args.device    )

									if self.args.fpaa:
											logger.info('''Running training in Mixed Precision...'''    )
											if not self.args.is_gpu:
													raise ValueError('''Mixed precision is possible only for GPU.'''    )
											# amp seems to have memory leaks so that memory usage
											# is measured using .half() for now https://github.com/NVIDIA/apex/issues/439
											model.half()

									if self.args.torchscript:
											with torch.no_grad():
													lowercase										=							torch.jit.trace(a ,		a    )
									else:
											lowercase										=							model

									def encoder_decoder_forward():
											with torch.no_grad():
													lowercase										=							inference_model(a ,		decoder_input_ids=a    )
											return outputs

									def encoder_forward():
											with torch.no_grad():
													lowercase										=							inference_model(a    )
											return outputs

									lowercase										=							encoder_decoder_forward if config.is_encoder_decoder else encoder_forward
									return _forward

							def 					_lowerCAmelCase  ( self       :    int ,		a       :    str ,		a       :    int ,		a       :    int    )   ->    Callable[[], None]:

									"""simple docstring"""
									lowercase										=							self.config_dict[model_name]

									lowercase										=							(
									    hasattr(a ,		'''architectures'''    )
									    and isinstance(config.architectures ,		a    )
									    and len(config.architectures    ) > 0
									)
									if not self.args.only_pretrain_model and has_model_class_in_config:
											try:
													lowercase										=							config.architectures[0]
													lowercase										=							__import__('''transformers''' ,		fromlist=[model_class]    )
													lowercase										=							getattr(a ,		a    )
													lowercase										=							model_cls(a    )
											except ImportError:
													raise ImportError(
													    f"""{model_class} does not exist. If you just want to test the pretrained model, you might want to"""
													    ''' set `--only_pretrain_model` or `args.only_pretrain_model=True`.'''    )
									else:
											lowercase										=							MODEL_WITH_LM_HEAD_MAPPING[config.__class__](a    )

									if self.args.torchscript:
											raise NotImplementedError('''Training for torchscript is currently not implemented'''    )
									else:
											lowercase										=							model

									model.train()
									model.to(self.args.device    )

									# encoder-decoder has vocab size saved differently
									lowercase										=							config.vocab_size if hasattr(a ,		'''vocab_size'''    ) else config.encoder.vocab_size
									lowercase										=							torch.randint(a ,		(batch_size, sequence_length) ,		dtype=torch.long ,		device=self.args.device    )

									if self.args.fpaa:
											logger.info('''Running training in Mixed Precision...'''    )
											if not self.args.is_gpu:
													raise ValueError('''Mixed precision is possible only for GPU.'''    )

											# amp seems to have memory leaks so that memory usage
											# is measured using .half() for now https://github.com/NVIDIA/apex/issues/439
											model.half()

									def compute_loss_and_backprob_encoder():
											lowercase										=							train_model(a ,		labels=a    )[0]
											loss.backward()
											return loss

									def compute_loss_and_backprob_encoder_decoder():
											lowercase										=							train_model(a ,		decoder_input_ids=a ,		labels=a    )[0]
											loss.backward()
											return loss

									lowercase										=							(
									    compute_loss_and_backprob_encoder_decoder
									    if config.is_encoder_decoder
									    else compute_loss_and_backprob_encoder
									)
									return _train

							def 					_lowerCAmelCase  ( self       :    int ,		a       :    Optional[Any]    )   ->    float:

									"""simple docstring"""
									try:
											if self.args.is_tpu or self.args.torchscript:
													# run additional 10 times to stabilize compilation for tpu and torchscript
													logger.info('''Do inference on TPU or torchscript. Running model 5 times to stabilize compilation'''    )
													timeit.repeat(
													    a ,		repeat=1 ,		number=5 ,		)

											# as written in https://docs.python.org/2/library/timeit.html#timeit.Timer.repeat, min should be taken rather than the average
											lowercase										=							timeit.repeat(
											    a ,		repeat=self.args.repeat ,		number=10 ,		)

											if self.args.is_tpu and self.args.torch_xla_tpu_print_metrics:
													import torch_xla.debug.metrics as met

													self.print_fn(met.metrics_report()    )

											return min(a    ) / 10.0
									except RuntimeError as e:
											self.print_fn(f"""Doesn't fit on GPU. {e}"""    )
											return "N/A"

							def 					_lowerCAmelCase  ( self       :    str ,		a       :    Callable[[], None]    )   ->    [Memory, MemorySummary]:

									"""simple docstring"""
									try:
											if self.args.trace_memory_line_by_line:
													lowercase										=							start_memory_tracing('''transformers'''    )

											if self.args.is_tpu:
													# tpu
													raise NotImplementedError(
													    '''Memory Benchmarking is currently not implemented for TPU. Please disable memory benchmarking with'''
													    ''' `--no-memory` or `args.memory=False`'''    )
											elif self.args.is_gpu:
													if not is_pyanvml_available():
															logger.warning(
															    '''py3nvml not installed, we won\'t log GPU memory usage. '''
															    '''Install py3nvml (pip install py3nvml) to log information about GPU.'''    )
															lowercase										=							'''N/A'''
													else:
															logger.info(
															    '''Measuring total GPU usage on GPU device. Make sure to not have additional processes running'''
															    ''' on the same GPU.'''    )
															# init nvml
															nvml.nvmlInit()
															func()
															lowercase										=							nvml.nvmlDeviceGetHandleByIndex(self.args.device_idx    )
															lowercase										=							nvml.nvmlDeviceGetMemoryInfo(a    )
															lowercase										=							meminfo.used
															lowercase										=							Memory(a    )
															# shutdown nvml
															nvml.nvmlShutdown()
											else:
													# cpu
													lowercase										=							measure_peak_memory_cpu(a    )
													lowercase										=							Memory(a    ) if isinstance(a ,		a    ) else memory_bytes

											if self.args.trace_memory_line_by_line:
													lowercase										=							stop_memory_tracing(a    )
											else:
													lowercase										=							None

											return memory, summary
									except RuntimeError as e:
											self.print_fn(f"""Doesn't fit on GPU. {e}"""    )
											return "N/A", None