code: 
  """simple docstring"""
  
  
  
  
  
  
  
  def 			__UpperCAmelCase		(		a_			:		int = 20				)     ->       int:
  
     try:
        _UpperCAmelCase   	=					int(a_				)
     except (TypeError, ValueError):
        raise TypeError("Parameter n must be int or castable to int."				)
     if n <= 0:
        raise ValueError("Parameter n must be greater than or equal to one."				)
     _UpperCAmelCase   	=					0
     while 1:
        i += n * (n - 1)
        _UpperCAmelCase   	=					0
        for j in range(2    ,  a_				):
           if i % j != 0:
              _UpperCAmelCase   	=					1
              break
        if nfound == 0:
           if i == 0:
              _UpperCAmelCase   	=					1
           return i
     return None
  
  
  if __name__ == "__main__":
    print(f'''{solution() = }''')
  
  
style_context: 
  """simple docstring"""
  
  
  
  
  
  
  
  import argparse
  import inspect
  import logging
  from typing import Tuple
  
  import numpy as np
  import torch
  
  from transformers import (
      AutoTokenizer,
      BloomForCausalLM,
      BloomTokenizerFast,
      CTRLLMHeadModel,
      CTRLTokenizer,
      GenerationMixin,
      GPTaLMHeadModel,
      GPTaTokenizer,
      GPTJForCausalLM,
      LlamaForCausalLM,
      LlamaTokenizer,
      OpenAIGPTLMHeadModel,
      OpenAIGPTTokenizer,
      OPTForCausalLM,
      TransfoXLLMHeadModel,
      TransfoXLTokenizer,
      XLMTokenizer,
      XLMWithLMHeadModel,
      XLNetLMHeadModel,
      XLNetTokenizer,
  )
  from transformers.modeling_outputs import CausalLMOutputWithPast
  
  
  logging.basicConfig(
      format='%(asctime)s - %(levelname)s - %(name)s - %(message)s',
      datefmt='%m/%d/%Y %H:%M:%S',
      level=logging.INFO,
  )
  SCREAMING_SNAKE_CASE_     				=   logging.getLogger(__name__)
  
  SCREAMING_SNAKE_CASE_     				=   int(10000)  # Hardcoded max length to avoid infinite loop
  
  SCREAMING_SNAKE_CASE_     				=   {
      'gpt2': (GPTaLMHeadModel, GPTaTokenizer),
      'ctrl': (CTRLLMHeadModel, CTRLTokenizer),
      'openai-gpt': (OpenAIGPTLMHeadModel, OpenAIGPTTokenizer),
      'xlnet': (XLNetLMHeadModel, XLNetTokenizer),
      'transfo-xl': (TransfoXLLMHeadModel, TransfoXLTokenizer),
      'xlm': (XLMWithLMHeadModel, XLMTokenizer),
      'gptj': (GPTJForCausalLM, AutoTokenizer),
      'bloom': (BloomForCausalLM, BloomTokenizerFast),
      'llama': (LlamaForCausalLM, LlamaTokenizer),
      'opt': (OPTForCausalLM, GPTaTokenizer),
  }
  
  # Padding text to help Transformer-XL and XLNet with short prompts as proposed by Aman Rusia
  # in https://github.com/rusiaaman/XLNet-gen#methodology
  # and https://medium.com/@amanrusia/xlnet-speaks-comparison-to-gpt-2-ea1a4e9ba39e
  SCREAMING_SNAKE_CASE_     				=   'In 1991, the remains of Russian Tsar Nicholas II and his family\n(except for Alexei and Maria) are discovered.\nThe voice of Nicholas\'s young son, Tsarevich Alexei Nikolaevich, narrates the\nremainder of the story. 1883 Western Siberia,\na young Grigori Rasputin is asked by his father and a group of men to perform magic.\nRasputin has a vision and denounces one of the men as a horse thief. Although his\nfather initially slaps him for making such an accusation, Rasputin watches as the\nman is chased outside and beaten. Twenty years later, Rasputin sees a vision of\nthe Virgin Mary, prompting him to become a priest. Rasputin quickly becomes famous,\nwith people, even a bishop, begging for his blessing. <eod> </s> <eos>'
  def 			__UpperCAmelCase		(		a_			:		List[Any]				)     ->       Optional[int]:
     np.random.seed(args.seed				)
     torch.manual_seed(args.seed				)
     if args.n_gpu > 0:
        torch.cuda.manual_seed_all(args.seed				)
  def 			__UpperCAmelCase		(		a_			:		Optional[int]    ,  a_			:		Union[str, Any]    ,  a_			:		Tuple    ,  a_			:		str				)     ->       Optional[Any]:
     if args.temperature > 0.7:
        logger.info("CTRL typically works better with lower temperatures (and lower top_k)."				)
  
     _UpperCAmelCase   	=					tokenizer.encode(a_    ,  add_special_tokens=a_				)
     if not any(encoded_prompt[0] == x for x in tokenizer.control_codes.values()				):
        logger.info("WARNING! You are not starting your generation from a control code so you won't get good results"				)
     return prompt_text
  def 			__UpperCAmelCase		(		a_			:		Any    ,  a_			:		Tuple    ,  a_			:		Dict    ,  a_			:		List[Any]				)     ->       str:
     # kwargs = {"language": None, "mask_token_id": None}
  
     # Set the language
     _UpperCAmelCase   	=					hasattr(model.config    ,  "use_lang_emb"				) and model.config.use_lang_emb
     if hasattr(model.config    ,  "lang2id"				) and use_lang_emb:
        _UpperCAmelCase   	=					model.config.langaid.keys()
        if args.xlm_language in available_languages:
           _UpperCAmelCase   	=					args.xlm_language
        else:
           _UpperCAmelCase   	=					None
           while language not in available_languages:
              _UpperCAmelCase   	=					input("Using XLM. Select language in " + str(list(a_				)				) + " >>> "				)
  
        _UpperCAmelCase   	=					model.config.langaid[language]
        # kwargs["language"] = tokenizer.lang2id[language]
  
     # TODO fix mask_token_id setup when configurations will be synchronized between models and tokenizers
     # XLM masked-language modeling (MLM) models need masked token
     # is_xlm_mlm = "mlm" in args.model_name_or_path
     # if is_xlm_mlm:
     #     kwargs["mask_token_id"] = tokenizer.mask_token_id
  
     return prompt_text
  def 			__UpperCAmelCase		(		a_			:		str    ,  a_			:		Union[str, Any]    ,  a_			:		Any    ,  a_			:		int				)     ->       List[Any]:
     _UpperCAmelCase   	=					args.prefix if args.prefix else args.padding_text if args.padding_text else PREFIX
     _UpperCAmelCase   	=					prefix + prompt_text
     return prompt_text
  def 			__UpperCAmelCase		(		a_			:		Optional[Any]    ,  a_			:		Dict    ,  a_			:		Union[str, Any]    ,  a_			:		Union[str, Any]				)     ->       Dict:
     _UpperCAmelCase   	=					args.prefix if args.prefix else args.padding_text if args.padding_text else PREFIX
     _UpperCAmelCase   	=					prefix + prompt_text
     return prompt_text
  
  
  SCREAMING_SNAKE_CASE_     				=   {
      'ctrl': prepare_ctrl_input,
      'xlm': prepare_xlm_input,
      'xlnet': prepare_xlnet_input,
      'transfo-xl': prepare_transfoxl_input,
  }
  def 			__UpperCAmelCase		(		a_			:		Union[str, Any]    ,  a_			:		Tuple				)     ->       str:
     if length < 0 and max_sequence_length > 0:
        _UpperCAmelCase   	=					max_sequence_length
     elif 0 < max_sequence_length < length:
        _UpperCAmelCase   	=					max_sequence_length  # No generation bigger than model size
     elif length < 0:
        _UpperCAmelCase   	=					MAX_LENGTH  # avoid infinite loop
     return length
  def 			__UpperCAmelCase		(		a_			:		List[str]				)     ->       Optional[int]:
     _UpperCAmelCase   	=					None
     if hasattr(a_    ,  "hidden_size"				):
        _UpperCAmelCase   	=					model_config.hidden_size
     elif hasattr(a_    ,  "n_embed"				):
        _UpperCAmelCase   	=					model_config.n_embed
     elif hasattr(a_    ,  "n_embd"				):
        _UpperCAmelCase   	=					model_config.n_embd
  
     _UpperCAmelCase   	=					None
     if hasattr(a_    ,  "num_attention_heads"				):
        _UpperCAmelCase   	=					model_config.num_attention_heads
     elif hasattr(a_    ,  "n_head"				):
        _UpperCAmelCase   	=					model_config.n_head
  
     if embedding_size is None or num_head is None or num_head == 0:
        raise ValueError("Check the model config"				)
  
     _UpperCAmelCase   	=					int(embedding_size / num_head				)
     if hasattr(a_    ,  "n_layer"				):
        _UpperCAmelCase   	=					model_config.n_layer
     elif hasattr(a_    ,  "num_hidden_layers"				):
        _UpperCAmelCase   	=					model_config.num_hidden_layers
     else:
        raise ValueError("Number of hidden layers couldn't be determined from the model config"				)
  
     return num_layer, num_head, num_embedding_size_per_head
  def 			__UpperCAmelCase		(		a_			:		Union[str, Any]    ,  a_			:		List[Any]    ,  a_			:		Optional[Any]				)     ->       int:
     _UpperCAmelCase	,							_UpperCAmelCase	,							_UpperCAmelCase   	=					sparse_model_config(model.config				)
     if model.config.model_type == "bloom":
        _UpperCAmelCase   	=					tuple(
            (
                torch.empty(int(num_attention_heads * batch_size				)    ,  a_    ,  a_				)
                .to(model.dtype				)
                .to(model.device				),
                torch.empty(int(num_attention_heads * batch_size				)    ,  a_    ,  a_				)
                .to(model.dtype				)
                .to(model.device				),
            )
            for _ in range(a_				)				)
     else:
        _UpperCAmelCase   	=					tuple(
            (
                torch.empty(a_    ,  a_    ,  a_    ,  a_				)
                .to(model.dtype				)
                .to(model.device				),
                torch.empty(a_    ,  a_    ,  a_    ,  a_				)
                .to(model.dtype				)
                .to(model.device				),
            )
            for _ in range(a_				)				)
     return past_key_values
  def 			__UpperCAmelCase		(		a_			:		List[Any]    ,  a_			:		Union[str, Any]    ,  a_			:		Optional[Any]				)     ->       List[Any]:
     _UpperCAmelCase   	=					len(a_				)
     _UpperCAmelCase   	=					tokenizer.batch_encode_plus(a_    ,  return_tensors="pt"				)
     _UpperCAmelCase   	=					dummy_input.to(model.device				)
     if model.config.use_cache:
        _UpperCAmelCase   	=					generate_past_key_values(a_    ,  a_    ,  1				)
     _UpperCAmelCase   	=					torch.cat(
         [
             torch.zeros(dummy_input["attention_mask"].shape[0]    ,  1				)
             .to(dummy_input["attention_mask"].dtype				)
             .to(model.device				),
             dummy_input["attention_mask"],
         ]    ,  -1    ,  )
     return dummy_input
  
  
  
  
  
  
  class     __a			(					lowerCAmelCase_			):
         _lowerCamelCase							:							str       =			('_optimized', '_default')
  
  
  
  
  
  
  
         def __init__(					self							,lowerCamelCase_							,lowerCamelCase_		):
  
  
  
            '''simple docstring'''
  
            _UpperCAmelCase   	=					optimized
            _UpperCAmelCase   	=					default
  
  
  
  
  
  
  
         def __call__(					self							,*lowerCamelCase_							,**lowerCamelCase_		):
  
  
  
            '''simple docstring'''
  
            if kwargs["past_key_values"] is None and self._default.config.use_cache:
               _UpperCAmelCase   	=					generate_past_key_values(self._default							,kwargs["input_ids"].shape[0]							,0		)
            kwargs.pop("position_ids"							,lowerCamelCase_		)
            for k in list(kwargs.keys()		):
               if kwargs[k] is None or isinstance(kwargs[k]							,lowerCamelCase_		):
                  kwargs.pop(lowerCamelCase_		)
            _UpperCAmelCase   	=					self._optimized(**lowerCamelCase_		)
            _UpperCAmelCase   	=					outputs[0]
            _UpperCAmelCase   	=					outputs[1]
            _UpperCAmelCase   	=					CausalLMOutputWithPast(
                loss=lowerCamelCase_							,logits=lowerCamelCase_							,past_key_values=lowerCamelCase_							,hidden_states=lowerCamelCase_							,attentions=lowerCamelCase_							,)
            return fixed_output
  
  
  
  
  
  
  
         def __getattr__(					self							,lowerCamelCase_		):
  
  
  
            '''simple docstring'''
  
            return getattr(self._default							,lowerCamelCase_		)
  
  
  
  
  
  
  
         def    _snake_case			(					self							,lowerCamelCase_							,lowerCamelCase_=None							,lowerCamelCase_=None							,lowerCamelCase_=None							,**lowerCamelCase_		):
  
  
  
            '''simple docstring'''
  
            return self._default.prepare_inputs_for_generation(
                lowerCamelCase_							,past_key_values=lowerCamelCase_							,inputs_embeds=lowerCamelCase_							,use_cache=lowerCamelCase_							,**lowerCamelCase_		)
  
  
  
  
  
  
  
         def    _snake_case			(					self							,lowerCamelCase_							,lowerCamelCase_		):
  
  
  
            '''simple docstring'''
  
            return self._default._reorder_cache(lowerCamelCase_							,lowerCamelCase_		)
  
  
  
  def 			__UpperCAmelCase		(		)     ->       List[str]:
     _UpperCAmelCase   	=					argparse.ArgumentParser()
     parser.add_argument(
         "--model_type"    ,  default=a_    ,  type=a_    ,  required=a_    ,  help="Model type selected in the list: " + ", ".join(MODEL_CLASSES.keys()				)    ,  )
     parser.add_argument(
         "--model_name_or_path"    ,  default=a_    ,  type=a_    ,  required=a_    ,  help="Path to pre-trained model or shortcut name selected in the list: " + ", ".join(MODEL_CLASSES.keys()				)    ,  )
  
     parser.add_argument("--prompt"    ,  type=a_    ,  default=""				)
     parser.add_argument("--length"    ,  type=a_    ,  default=20				)
     parser.add_argument("--stop_token"    ,  type=a_    ,  default=a_    ,  help="Token at which text generation is stopped"				)
  
     parser.add_argument(
         "--temperature"    ,  type=a_    ,  default=1.0    ,  help="temperature of 1.0 has no effect, lower tend toward greedy sampling"    ,  )
     parser.add_argument(
         "--repetition_penalty"    ,  type=a_    ,  default=1.0    ,  help="primarily useful for CTRL model; in that case, use 1.2"				)
     parser.add_argument("--k"    ,  type=a_    ,  default=0				)
     parser.add_argument("--p"    ,  type=a_    ,  default=0.9				)
  
     parser.add_argument("--prefix"    ,  type=a_    ,  default=""    ,  help="Text added prior to input."				)
     parser.add_argument("--padding_text"    ,  type=a_    ,  default=""    ,  help="Deprecated, the use of `--prefix` is preferred."				)
     parser.add_argument("--xlm_language"    ,  type=a_    ,  default=""    ,  help="Optional language when used with the XLM model."				)
  
     parser.add_argument("--seed"    ,  type=a_    ,  default=42    ,  help="random seed for initialization"				)
     parser.add_argument("--no_cuda"    ,  action="store_true"    ,  help="Avoid using CUDA when available"				)
     parser.add_argument("--num_return_sequences"    ,  type=a_    ,  default=1    ,  help="The number of samples to generate."				)
     parser.add_argument(
         "--fp16"    ,  action="store_true"    ,  help="Whether to use 16-bit (mixed) precision (through NVIDIA apex) instead of 32-bit"    ,  )
     parser.add_argument("--jit"    ,  action="store_true"    ,  help="Whether or not to use jit trace to accelerate inference"				)
     _UpperCAmelCase   	=					parser.parse_args()
  
     _UpperCAmelCase   	=					torch.device("cuda" if torch.cuda.is_available() and not args.no_cuda else "cpu"				)
     _UpperCAmelCase   	=					0 if args.no_cuda else torch.cuda.device_count()
  
     logger.warning(F'''device: {args.device}, n_gpu: {args.n_gpu}, 16-bits training: {args.fpaa}'''				)
  
     set_seed(a_				)
  
     # Initialize the model and tokenizer
     try:
        _UpperCAmelCase   	=					args.model_type.lower()
        _UpperCAmelCase	,							_UpperCAmelCase   	=					MODEL_CLASSES[args.model_type]
     except KeyError:
        raise KeyError("the model {} you specified is not supported. You are welcome to add it and open a PR :)"				)
  
     _UpperCAmelCase   	=					tokenizer_class.from_pretrained(args.model_name_or_path				)
     if tokenizer.pad_token is None:
        _UpperCAmelCase   	=					tokenizer.eos_token
     _UpperCAmelCase   	=					model_class.from_pretrained(args.model_name_or_path				)
     model.to(args.device				)
  
     if args.fpaa:
        model.half()
     _UpperCAmelCase   	=					getattr(model.config    ,  "max_position_embeddings"    ,  0				)
     _UpperCAmelCase   	=					adjust_length_to_model(args.length    ,  max_sequence_length=a_				)
     logger.info(a_				)
  
     _UpperCAmelCase   	=					args.prompt if args.prompt else input("Model prompt >>> "				)
  
     # Different models need different input formatting and/or extra arguments
     _UpperCAmelCase   	=					args.model_type in PREPROCESSING_FUNCTIONS.keys()
     if requires_preprocessing:
        _UpperCAmelCase   	=					PREPROCESSING_FUNCTIONS.get(args.model_type				)
        _UpperCAmelCase   	=					prepare_input(a_    ,  a_    ,  a_    ,  a_				)
  
        if model.__class__.__name__ in ["TransfoXLLMHeadModel"]:
           _UpperCAmelCase   	=					{"add_space_before_punct_symbol": True}
        else:
           _UpperCAmelCase   	=					{}
  
        _UpperCAmelCase   	=					tokenizer.encode(
            a_    ,  add_special_tokens=a_    ,  return_tensors="pt"    ,  **a_				)
     else:
        _UpperCAmelCase   	=					args.prefix if args.prefix else args.padding_text
        _UpperCAmelCase   	=					tokenizer.encode(prefix + prompt_text    ,  add_special_tokens=a_    ,  return_tensors="pt"				)
     _UpperCAmelCase   	=					encoded_prompt.to(args.device				)
  
     if encoded_prompt.size()[-1] == 0:
        _UpperCAmelCase   	=					None
     else:
        _UpperCAmelCase   	=					encoded_prompt
  
     if args.jit:
        _UpperCAmelCase   	=					["enable jit"]
        _UpperCAmelCase   	=					prepare_jit_inputs(a_    ,  a_    ,  a_				)
        torch._C._jit_set_texpr_fuser_enabled(a_				)
        _UpperCAmelCase   	=					False
        if hasattr(a_    ,  "forward"				):
           _UpperCAmelCase   	=					inspect.signature(model.forward				)
        else:
           _UpperCAmelCase   	=					inspect.signature(model.__call__				)
        _UpperCAmelCase   	=					tuple(jit_inputs[key] for key in sig.parameters if jit_inputs.get(a_    ,  a_				) is not None				)
        _UpperCAmelCase   	=					torch.jit.trace(a_    ,  a_    ,  strict=a_				)
        _UpperCAmelCase   	=					torch.jit.freeze(traced_model.eval()				)
        traced_model(*a_				)
        traced_model(*a_				)
  
        _UpperCAmelCase   	=					_ModelFallbackWrapper(a_    ,  a_				)
  
     _UpperCAmelCase   	=					model.generate(
         input_ids=a_    ,  max_length=args.length + len(encoded_prompt[0]				)    ,  temperature=args.temperature    ,  top_k=args.k    ,  top_p=args.p    ,  repetition_penalty=args.repetition_penalty    ,  do_sample=a_    ,  num_return_sequences=args.num_return_sequences    ,  )
  
     # Remove the batch dimension when returning multiple sequences
     if len(output_sequences.shape				) > 2:
        output_sequences.squeeze_()
  
     _UpperCAmelCase   	=					[]
  
     for generated_sequence_idx, generated_sequence in enumerate(a_				):
        print(F'''=== GENERATED SEQUENCE {generated_sequence_idx + 1} ==='''				)
        _UpperCAmelCase   	=					generated_sequence.tolist()
  
        # Decode text
        _UpperCAmelCase   	=					tokenizer.decode(a_    ,  clean_up_tokenization_spaces=a_				)
  
        # Remove all text after the stop token
        _UpperCAmelCase   	=					text[: text.find(args.stop_token				) if args.stop_token else None]
  
        # Add the prompt at the beginning of the sequence. Remove the excess text that was used for pre-processing
        _UpperCAmelCase   	=					(
            prompt_text + text[len(tokenizer.decode(encoded_prompt[0]    ,  clean_up_tokenization_spaces=a_				)				) :]
        )
  
        generated_sequences.append(a_				)
        print(a_				)
  
     return generated_sequences
  
  
  if __name__ == "__main__":
    main()
  
  