






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 							_lowerCAmelCase(			UpperCAmelCase_   ):





       """simple docstring"""







       def __init__(   self    ,     *_lowerCamelCase    ,     _lowerCamelCase=None    ,     _lowerCamelCase=None    ,     **_lowerCamelCase				):
         super().__init__(*_lowercase    ,     **_lowercase				)
         UpperCamelCase_:   List[Any]        =							eval_examples
         UpperCamelCase_:   Union[str, Any]        =							post_process_function





       def      _a       (   self    ,     _lowerCamelCase=None    ,     _lowerCamelCase=None    ,     _lowerCamelCase=None    ,     _lowerCamelCase = "eval"				):
         UpperCamelCase_:   Tuple        =							self.eval_dataset if eval_dataset is None else eval_dataset
         UpperCamelCase_:   Any        =							self.get_eval_dataloader(_lowercase				)
         UpperCamelCase_:   List[Any]        =							self.eval_examples if eval_examples is None else eval_examples

         # Temporarily disable metric computation, we will do it in the loop here.
         UpperCamelCase_:   Dict        =							self.compute_metrics
         UpperCamelCase_:   str        =							None
         UpperCamelCase_:   int        =							self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
         UpperCamelCase_:   List[str]        =							time.time()
         try:
           UpperCamelCase_:   int        =							eval_loop(
               _lowercase    ,     description='Evaluation'    ,     prediction_loss_only=True if compute_metrics is None else None    ,     ignore_keys=_lowercase    ,     metric_key_prefix=_lowercase    ,     )
         finally:
           UpperCamelCase_:   Dict        =							compute_metrics
         UpperCamelCase_:   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(
                 _lowercase    ,     _lowercase    ,     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
           UpperCamelCase_:   str        =							self.post_process_function(_lowercase    ,     _lowercase    ,     output.predictions				)
           UpperCamelCase_:   Any        =							self.compute_metrics(_lowercase				)

           # Prefix all keys with metric_key_prefix + '_'
           for key in list(metrics.keys()				):
             if not key.startswith(f'''{metric_key_prefix}_'''				):
               UpperCamelCase_:   List[Any]        =							metrics.pop(_lowercase				)
           metrics.update(output.metrics				)
         else:
           UpperCamelCase_:   Dict        =							output.metrics

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

         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()				)

         UpperCamelCase_:   Optional[int]        =							self.callback_handler.on_evaluate(self.args    ,     self.state    ,     self.control    ,     _lowercase				)
         return metrics





       def      _a       (   self    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase=None    ,     _lowerCamelCase = "test"				):
         UpperCamelCase_:   str        =							self.get_test_dataloader(_lowercase				)

         # Temporarily disable metric computation, we will do it in the loop here.
         UpperCamelCase_:   Dict        =							self.compute_metrics
         UpperCamelCase_:   List[str]        =							None
         UpperCamelCase_:   List[Any]        =							self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
         UpperCamelCase_:   Union[str, Any]        =							time.time()
         try:
           UpperCamelCase_:   Union[str, Any]        =							eval_loop(
               _lowercase    ,     description='Prediction'    ,     prediction_loss_only=True if compute_metrics is None else None    ,     ignore_keys=_lowercase    ,     metric_key_prefix=_lowercase    ,     )
         finally:
           UpperCamelCase_:   Tuple        =							compute_metrics
         UpperCamelCase_:   Dict        =							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(
                 _lowercase    ,     _lowercase    ,     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

         UpperCamelCase_:   str        =							self.post_process_function(_lowercase    ,     _lowercase    ,     output.predictions    ,     'predict'				)
         UpperCamelCase_:   Any        =							self.compute_metrics(_lowercase				)

         # Prefix all keys with metric_key_prefix + '_'
         for key in list(metrics.keys()				):
           if not key.startswith(f'''{metric_key_prefix}_'''				):
             UpperCamelCase_:   Union[str, Any]        =							metrics.pop(_lowercase				)
         metrics.update(output.metrics				)
         return PredictionOutput(predictions=predictions.predictions    ,     label_ids=predictions.label_ids    ,     metrics=_lowercase				)


def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_ = 1_0_0_0_0_0_0			)->						int:



    """simple docstring"""






    UpperCamelCase_			  =						[i - 1 for i in range(limit + 1			)]

    for i in range(2			,						limit + 1			):
        if phi[i] == i - 1:
            for j in range(2 * i			,						limit + 1			,						SCREAMING_SNAKE_CASE_			):
                phi[j] -= phi[j] // i

    return sum(phi[2 : limit + 1]			)


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