




from math import factorial

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				List[str]:
       return factorial(lowercase_					) / (factorial(lowercase_					) * factorial(n - r					))

def   A   (   )			->				Dict:
       lowerCamelCase     :   Optional[Any]    				=      0

       for i in range(1				,101					):
              for j in range(1				,i + 1					):
                     if combinations(lowercase_				,lowercase_					) > 1e6:
                            total += 1
       return total


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











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


SCREAMING_SNAKE_CASE__ :   List[Any]						=     logging.get_logger(__name__)




class 	UpperCamelCase__			(lowerCAmelCase__  ):

    '''simple docstring'''



    lowerCamelCase_   :			PyTorchBenchmarkArguments
    lowerCamelCase_   :			PretrainedConfig
    lowerCamelCase_   :			str			  =   "PyTorch"







    @property
    def 					_lowercase  (					self  )  ->   Optional[int]:
           return torch.__version__







    def 					_lowercase  (					self  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )  ->   float:
           lowerCamelCase     :   List[Any]    				=      self._prepare_inference_func(UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )
           return self._measure_speed(_inference  )







    def 					_lowercase  (					self  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )  ->   [Memory, Optional[MemorySummary]]:
           lowerCamelCase     :   List[Any]    				=      self._prepare_inference_func(UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )
           return self._measure_memory(_inference  )







    def 					_lowercase  (					self  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )  ->   float:
           lowerCamelCase     :   Dict    				=      self._prepare_train_func(UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )
           return self._measure_speed(_train  )







    def 					_lowercase  (					self  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )  ->   [Memory, Optional[MemorySummary]]:
           lowerCamelCase     :   Optional[Any]    				=      self._prepare_train_func(UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )
           return self._measure_memory(_train  )







    def 					_lowercase  (					self  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )  ->   Callable[[], None]:
           lowerCamelCase     :   Optional[Any]    				=      self.config_dict[model_name]

           if self.args.torchscript:
                  lowerCamelCase     :   Optional[Any]    				=      True

           lowerCamelCase     :   Dict    				=      (
               hasattr(UpperCamelCase__  ,						"architectures"  )
               and isinstance(config.architectures  ,						UpperCamelCase__  )
               and len(config.architectures  ) > 0
           )
           if not self.args.only_pretrain_model and has_model_class_in_config:
                  try:
                         lowerCamelCase     :   Optional[Any]    				=      config.architectures[0]
                         lowerCamelCase     :   Optional[int]    				=      __import__("transformers"  ,						fromlist=[model_class]  )
                         lowerCamelCase     :   Optional[int]    				=      getattr(UpperCamelCase__  ,						UpperCamelCase__  )
                         lowerCamelCase     :   List[str]    				=      model_cls(UpperCamelCase__  )
                  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:
                  lowerCamelCase     :   Tuple    				=      MODEL_MAPPING[config.__class__](UpperCamelCase__  )

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

           # encoder-decoder has vocab size saved differently
           lowerCamelCase     :   str    				=      config.vocab_size if hasattr(UpperCamelCase__  ,						"vocab_size"  ) else config.encoder.vocab_size
           lowerCamelCase     :   int    				=      torch.randint(UpperCamelCase__  ,						(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():
                         lowerCamelCase     :   Optional[int]    				=      torch.jit.trace(UpperCamelCase__  ,						UpperCamelCase__  )
           else:
                  lowerCamelCase     :   Dict    				=      model

           def encoder_decoder_forward():
                  with torch.no_grad():
                         lowerCamelCase     :   Dict    				=      inference_model(UpperCamelCase__  ,						decoder_input_ids=UpperCamelCase__  )
                  return outputs

           def encoder_forward():
                  with torch.no_grad():
                         lowerCamelCase     :   Union[str, Any]    				=      inference_model(UpperCamelCase__  )
                  return outputs

           lowerCamelCase     :   Dict    				=      encoder_decoder_forward if config.is_encoder_decoder else encoder_forward
           return _forward







    def 					_lowercase  (					self  ,						UpperCamelCase__  ,						UpperCamelCase__  ,						UpperCamelCase__  )  ->   Callable[[], None]:
           lowerCamelCase     :   Optional[int]    				=      self.config_dict[model_name]

           lowerCamelCase     :   List[Any]    				=      (
               hasattr(UpperCamelCase__  ,						"architectures"  )
               and isinstance(config.architectures  ,						UpperCamelCase__  )
               and len(config.architectures  ) > 0
           )
           if not self.args.only_pretrain_model and has_model_class_in_config:
                  try:
                         lowerCamelCase     :   Union[str, Any]    				=      config.architectures[0]
                         lowerCamelCase     :   int    				=      __import__("transformers"  ,						fromlist=[model_class]  )
                         lowerCamelCase     :   Tuple    				=      getattr(UpperCamelCase__  ,						UpperCamelCase__  )
                         lowerCamelCase     :   Tuple    				=      model_cls(UpperCamelCase__  )
                  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:
                  lowerCamelCase     :   List[str]    				=      MODEL_WITH_LM_HEAD_MAPPING[config.__class__](UpperCamelCase__  )

           if self.args.torchscript:
                  raise NotImplementedError("Training for torchscript is currently not implemented"  )
           else:
                  lowerCamelCase     :   Dict    				=      model

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

           # encoder-decoder has vocab size saved differently
           lowerCamelCase     :   Union[str, Any]    				=      config.vocab_size if hasattr(UpperCamelCase__  ,						"vocab_size"  ) else config.encoder.vocab_size
           lowerCamelCase     :   List[str]    				=      torch.randint(UpperCamelCase__  ,						(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():
                  lowerCamelCase     :   Tuple    				=      train_model(UpperCamelCase__  ,						labels=UpperCamelCase__  )[0]
                  loss.backward()
                  return loss

           def compute_loss_and_backprob_encoder_decoder():
                  lowerCamelCase     :   Optional[int]    				=      train_model(UpperCamelCase__  ,						decoder_input_ids=UpperCamelCase__  ,						labels=UpperCamelCase__  )[0]
                  loss.backward()
                  return loss

           lowerCamelCase     :   Union[str, Any]    				=      (
               compute_loss_and_backprob_encoder_decoder
               if config.is_encoder_decoder
               else compute_loss_and_backprob_encoder
           )
           return _train







    def 					_lowercase  (					self  ,						UpperCamelCase__  )  ->   float:
           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(
                             UpperCamelCase__  ,						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
                  lowerCamelCase     :   List[str]    				=      timeit.repeat(
                      UpperCamelCase__  ,						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(UpperCamelCase__  ) / 10.0
           except RuntimeError as e:
                  self.print_fn(F'''Doesn\'t fit on GPU. {e}'''  )
                  return "N/A"







    def 					_lowercase  (					self  ,						UpperCamelCase__  )  ->   [Memory, MemorySummary]:
           try:
                  if self.args.trace_memory_line_by_line:
                         lowerCamelCase     :   str    				=      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."  )
                                lowerCamelCase     :   Optional[Any]    				=      "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()
                                lowerCamelCase     :   int    				=      nvml.nvmlDeviceGetHandleByIndex(self.args.device_idx  )
                                lowerCamelCase     :   Dict    				=      nvml.nvmlDeviceGetMemoryInfo(UpperCamelCase__  )
                                lowerCamelCase     :   int    				=      meminfo.used
                                lowerCamelCase     :   Dict    				=      Memory(UpperCamelCase__  )
                                # shutdown nvml
                                nvml.nvmlShutdown()
                  else:
                         # cpu
                         lowerCamelCase     :   Union[str, Any]    				=      measure_peak_memory_cpu(UpperCamelCase__  )
                         lowerCamelCase     :   int    				=      Memory(UpperCamelCase__  ) if isinstance(UpperCamelCase__  ,						UpperCamelCase__  ) else memory_bytes

                  if self.args.trace_memory_line_by_line:
                         lowerCamelCase     :   List[str]    				=      stop_memory_tracing(UpperCamelCase__  )
                  else:
                         lowerCamelCase     :   int    				=      None

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






