





import math
import time
from typing import Dict, List, Optional

from torch.utils.data import Dataset

from transformers import SeqaSeqTrainer, 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       __A     (						a    ):


				def __init__(		self   , *UpperCAmelCase_   , UpperCAmelCase_=None   , UpperCAmelCase_=None   , **UpperCAmelCase_							):
								super().__init__(*UpperCAmelCase_   , **UpperCAmelCase_							)
								lowerCamelCase	 =eval_examples
								lowerCamelCase	 =post_process_function


				def _snake_case       (		self   , UpperCAmelCase_ = None   , UpperCAmelCase_=None   , UpperCAmelCase_ = None   , UpperCAmelCase_ = "eval"   , **UpperCAmelCase_   , ):
								lowerCamelCase	 =gen_kwargs.copy()
								lowerCamelCase	 =(
								    gen_kwargs["""max_length"""] if gen_kwargs.get("""max_length"""							) is not None else self.args.generation_max_length
								)
								lowerCamelCase	 =(
								    gen_kwargs["""num_beams"""] if gen_kwargs.get("""num_beams"""							) is not None else self.args.generation_num_beams
								)
								lowerCamelCase	 =gen_kwargs

								lowerCamelCase	 =self.eval_dataset if eval_dataset is None else eval_dataset
								lowerCamelCase	 =self.get_eval_dataloader(UpperCAmelCase_							)
								lowerCamelCase	 =self.eval_examples if eval_examples is None else eval_examples

								# Temporarily disable metric computation, we will do it in the loop here.
								lowerCamelCase	 =self.compute_metrics
								lowerCamelCase	 =None
								lowerCamelCase	 =time.time()
								lowerCamelCase	 =self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
								try:
												lowerCamelCase	 =eval_loop(
												    UpperCAmelCase_   , description="""Evaluation"""   , prediction_loss_only=True if compute_metrics is None else None   , ignore_keys=UpperCAmelCase_   , metric_key_prefix=UpperCAmelCase_   , )
								finally:
												lowerCamelCase	 =compute_metrics
								lowerCamelCase	 =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(
								        UpperCAmelCase_   , UpperCAmelCase_   , 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
												lowerCamelCase	 =self.post_process_function(UpperCAmelCase_   , UpperCAmelCase_   , UpperCAmelCase_							)
												lowerCamelCase	 =self.compute_metrics(UpperCAmelCase_							)

												# Prefix all keys with metric_key_prefix + '_'
												for key in list(metrics.keys()							):
																if not key.startswith(f"""{metric_key_prefix}_"""							):
																				lowerCamelCase	 =metrics.pop(UpperCAmelCase_							)

												metrics.update(output.metrics							)
								else:
												lowerCamelCase	 =output.metrics

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

								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()							)

								lowerCamelCase	 =self.callback_handler.on_evaluate(self.args   , self.state   , self.control   , UpperCAmelCase_							)
								return metrics


				def _snake_case       (		self   , UpperCAmelCase_   , UpperCAmelCase_   , UpperCAmelCase_=None   , UpperCAmelCase_ = "test"   , **UpperCAmelCase_							):
								lowerCamelCase	 =gen_kwargs.copy()

								lowerCamelCase	 =self.get_test_dataloader(UpperCAmelCase_							)

								# Temporarily disable metric computation, we will do it in the loop here.
								lowerCamelCase	 =self.compute_metrics
								lowerCamelCase	 =None
								lowerCamelCase	 =time.time()
								lowerCamelCase	 =self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
								try:
												lowerCamelCase	 =eval_loop(
												    UpperCAmelCase_   , description="""Prediction"""   , prediction_loss_only=True if compute_metrics is None else None   , ignore_keys=UpperCAmelCase_   , metric_key_prefix=UpperCAmelCase_   , )
								finally:
												lowerCamelCase	 =compute_metrics

								lowerCamelCase	 =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(
								        UpperCAmelCase_   , UpperCAmelCase_   , 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

								lowerCamelCase	 =self.post_process_function(UpperCAmelCase_   , UpperCAmelCase_   , UpperCAmelCase_   , """predict"""							)
								lowerCamelCase	 =self.compute_metrics(UpperCAmelCase_							)

								# Prefix all keys with metric_key_prefix + '_'
								for key in list(metrics.keys()							):
												if not key.startswith(f"""{metric_key_prefix}_"""							):
																lowerCamelCase	 =metrics.pop(UpperCAmelCase_							)
								metrics.update(output.metrics							)
								return PredictionOutput(predictions=predictions.predictions   , label_ids=predictions.label_ids   , metrics=UpperCAmelCase_							)












def      _lowercase					(						_UpperCAmelCase			,      _UpperCAmelCase				)						->  List[str]:
				lowerCamelCase	 =[0 for i in range(r + 1				)]
				# nc0 = 1
				lowerCamelCase	 =1
				for i in range(1			,      n + 1				):
								# to compute current row from previous row.
								lowerCamelCase	 =min(_UpperCAmelCase			,      _UpperCAmelCase				)
								while j > 0:
												c[j] += c[j - 1]
												j -= 1
				return c[r]




print(binomial_coefficient(n=10, r=5))





