




"""simple docstring"""

import math
import time

from transformers import Trainer, is_torch_tpu_available
from transformers.trainer_utils import PredictionOutput, speed_metrics


if is_torch_tpu_available(check_device=False):
		import torch_xla.core.xla_model as xm
		import torch_xla.debug.metrics as met

class        lowercase      (    __UpperCAmelCase):







				def __init__(							self   :					List[str]      ,     *_lowerCamelCase   :					Union[str, Any]      ,     _lowerCamelCase   :					int=None      ,     _lowerCamelCase   :					int=None      ,     **_lowerCamelCase   :					List[Any]       ):



					"""simple docstring"""

					super().__init__(*_lowerCamelCase      ,     **_lowerCamelCase       )
					A_  :				str	   =		eval_examples
					A_  :				str	   =		post_process_function







				def 					a_  (							self   :					Any      ,     _lowerCamelCase   :					Dict=None      ,     _lowerCamelCase   :					Any=None      ,     _lowerCamelCase   :					int=None      ,     _lowerCamelCase   :					str = "eval"       ):



					"""simple docstring"""

					A_  :				Any	   =		self.eval_dataset if eval_dataset is None else eval_dataset
					A_  :				Tuple	   =		self.get_eval_dataloader(_lowerCamelCase       )
					A_  :				Any	   =		self.eval_examples if eval_examples is None else eval_examples

					# Temporarily disable metric computation, we will do it in the loop here.
					A_  :				Optional[Any]	   =		self.compute_metrics
					A_  :				Optional[int]	   =		None
					A_  :				Dict	   =		self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
					A_  :				str	   =		time.time()
					try:
						A_  :				List[str]	   =		eval_loop(
						    _lowerCamelCase      ,     description='''Evaluation'''      ,     prediction_loss_only=True if compute_metrics is None else None      ,     ignore_keys=_lowerCamelCase      ,     metric_key_prefix=_lowerCamelCase      ,     )
					finally:
						A_  :				Optional[Any]	   =		compute_metrics
					A_  :				int	   =		self.args.eval_batch_size * self.args.world_size
					if F"""{metric_key_prefix}_jit_compilation_time""" in output.metrics:
						start_time += output.metrics[F"""{metric_key_prefix}_jit_compilation_time"""]
					output.metrics.update(
					    speed_metrics(
					        _lowerCamelCase      ,     _lowerCamelCase      ,     num_samples=output.num_samples      ,     num_steps=math.ceil(output.num_samples / total_batch_size       )      ,     )       )
					if self.post_process_function is not None and self.compute_metrics is not None and self.args.should_save:
						# Only the main node write the results by default
						A_  :				Union[str, Any]	   =		self.post_process_function(_lowerCamelCase      ,     _lowerCamelCase      ,     output.predictions       )
						A_  :				int	   =		self.compute_metrics(_lowerCamelCase       )

						# Prefix all keys with metric_key_prefix + '_'
						for key in list(metrics.keys()       ):
							if not key.startswith(F"""{metric_key_prefix}_"""       ):
								A_  :				List[Any]	   =		metrics.pop(_lowerCamelCase       )
						metrics.update(output.metrics       )
					else:
						A_  :				Tuple	   =		output.metrics

					if self.args.should_log:
						# Only the main node log the results by default
						self.log(_lowerCamelCase       )

					if self.args.tpu_metrics_debug or self.args.debug:
						# tpu-comment: Logging debug metrics for PyTorch/XLA (compile, execute times, ops, etc.)
						xm.master_print(met.metrics_report()       )

					A_  :				Tuple	   =		self.callback_handler.on_evaluate(self.args      ,     self.state      ,     self.control      ,     _lowerCamelCase       )
					return metrics







				def 					a_  (							self   :					List[str]      ,     _lowerCamelCase   :					Dict      ,     _lowerCamelCase   :					Optional[int]      ,     _lowerCamelCase   :					List[str]=None      ,     _lowerCamelCase   :					str = "test"       ):



					"""simple docstring"""

					A_  :				Union[str, Any]	   =		self.get_test_dataloader(_lowerCamelCase       )

					# Temporarily disable metric computation, we will do it in the loop here.
					A_  :				Optional[int]	   =		self.compute_metrics
					A_  :				List[Any]	   =		None
					A_  :				Optional[int]	   =		self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
					A_  :				int	   =		time.time()
					try:
						A_  :				Optional[Any]	   =		eval_loop(
						    _lowerCamelCase      ,     description='''Prediction'''      ,     prediction_loss_only=True if compute_metrics is None else None      ,     ignore_keys=_lowerCamelCase      ,     metric_key_prefix=_lowerCamelCase      ,     )
					finally:
						A_  :				str	   =		compute_metrics
					A_  :				Union[str, Any]	   =		self.args.eval_batch_size * self.args.world_size
					if F"""{metric_key_prefix}_jit_compilation_time""" in output.metrics:
						start_time += output.metrics[F"""{metric_key_prefix}_jit_compilation_time"""]
					output.metrics.update(
					    speed_metrics(
					        _lowerCamelCase      ,     _lowerCamelCase      ,     num_samples=output.num_samples      ,     num_steps=math.ceil(output.num_samples / total_batch_size       )      ,     )       )

					if self.post_process_function is None or self.compute_metrics is None:
						return output

					A_  :				Optional[Any]	   =		self.post_process_function(_lowerCamelCase      ,     _lowerCamelCase      ,     output.predictions      ,     '''predict'''       )
					A_  :				Tuple	   =		self.compute_metrics(_lowerCamelCase       )

					# Prefix all keys with metric_key_prefix + '_'
					for key in list(metrics.keys()       ):
						if not key.startswith(F"""{metric_key_prefix}_"""       ):
							A_  :				List[Any]	   =		metrics.pop(_lowerCamelCase       )
					metrics.update(output.metrics       )
					return PredictionOutput(predictions=predictions.predictions      ,     label_ids=predictions.label_ids      ,     metrics=_lowerCamelCase       )











"""simple docstring"""

import random

from .binary_exp_mod import bin_exp_mod

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase=1000	):




	"""simple docstring"""






	if n < 2:
		return False

	if n % 2 == 0:
		return n == 2

	# this means n is odd
	A_  :				List[Any]	   =		n - 1
	A_  :				Dict	   =		0
	while d % 2 == 0:
		d /= 2
		exp += 1

	# n - 1=d*(2**exp)
	A_  :				Optional[Any]	   =		0
	while count < prec:
		A_  :				Optional[int]	   =		random.randint(2  ,      n - 1	)
		A_  :				Any	   =		bin_exp_mod(_UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase	)
		if b != 1:
			A_  :				Dict	   =		True
			for _ in range(_UpperCAmelCase	):
				if b == n - 1:
					A_  :				Optional[int]	   =		False
					break
				A_  :				Any	   =		b * b
				b %= n
			if flag:
				return False
			count += 1
	return True


if __name__ == "__main__":
		_lowerCamelCase  :			List[str]        =       abs(int(input('Enter bound : ').strip()))
		print('Here\'s the list of primes:')
		print(', '.join(str(i) for i in range(n + 1) if is_prime_big(i)))





